Berichte des Meteorologischen Institutes
der Universität Freiburg
Nr. 8
Mahmoud El-Nouby Adam Haggagy
A Sodar-based Investigation of the
Atmospheric Boundary Layer
Freiburg, September 2003
b
ISSN 1435-618X
Alle Rechte, insbesondere die Rechte der Vervielfältigung und Verbreitung sowie der
Übersetzung vorbehalten.
Eigenverlag des Meteorologischen Instituts der Albert-Ludwigs-Universität Freiburg
Druck:
Druckerei der Albert-Ludwigs-Universität Freiburg
Herausgeber:
Prof. Dr. Helmut Mayer und PD Dr. Andreas Matzarakis
Meteorologisches Institut der Universität Freiburg
Werderring 10, D-79085 Freiburg
Tel.: 0049/761/203-3590; Fax: 0049/761/203-3586
e-mail: [email protected]
Dokumentation:
Ber. Meteor. Inst. Univ. Freiburg Nr. 8, 2003, 259 S.
Dissertation an der Fakultät für Forst- und Umweltwissenschaften der Albert-LudwigsUniversität Freiburg
ACKNOWLEDGEMENTS
First of all, I wish to express my gratitude to God for guiding me and giving me strength
in my efforts to acquaint more knowledge.
In what follows, I would like to express my gratitude to all those who contributed to my
Ph.D. thesis:
My deepest appreciation gave to Prof. Dr. Helmut Mayer, Head of the Meteorological
Institute, University of Freiburg, Germany, for suggesting the problem, supervising me
and providing all the necessary supports throughout the course of this work. I am extremely grateful to him for his kindness and encouragement, which kept me going during the study period.
I wish to express my deep gratitude to the Mission Department - Ministry of Higher
Education and Scientific Research (Egypt) for providing the scholarship that covered
my living expenses during the study period. I would also like to thank the German Federal Ministry of Education and Research for funding the Atmospheric Research Programme AFO2000, in the framework of which my study (VERTIKO-ALUF1) was conducted.
My cordial thanks to my colleagues at the Meteorological Institute, who assisted me to
solve many problems during the analysis of data for my study. They also created a
good atmosphere for my daily works. In particular, Dirk Schindler, who assisted me with
software-related problems during the analysis of my data.
I wish to express my gratitude to the secretarial and technical staffs of the Meteorological Institute for creating a friendly and stimulating atmosphere, which made my stay in
Freiburg very enjoyable and worthwhile.
Thanks to my friend Dr. Moses Iziomon (presently in Canada), who assisted me a lot
during his stay in Freiburg to start my work. I appreciate his efforts at checking my thesis manuscript.
I am most grateful to Prof. em. Dr. Abdelazeem M. Abdelmegeed, Department of Physics, Faculty of Science, Qena - South Valley University (Egypt), and Prof. Dr. Sayed M.
El-Shazly, Professor of Atmospheric Physics and vice Dean for post graduate studies
II
and researches, Faculty of Science, Qena - South Valley University (Egypt), for their
moral support.
Furthermore, I'm grateful to everybody who gave me a hand during this study.
Finally, special thanks to my dear wife for her love, encouragement and support as well
as her patience to be separated from her extended family during our stay in Germany.
This work is dedicated to those who loved me. First and foremost, to the memory of my
mother, who gave so much and asked for so little.
Mahmoud Haggagy
Freiburg, Germany
10 May 2003
III
TABLE OF CONTENTS
Acknowledgements
I
Table of contents
III
Summary
X
Zusammenfassung
XVII
1
Introduction
1
2
Literature review
5
2.1
Acoustic remote sensing
5
2.2
Sodar studies of atmospheric stability
6
2.3
Turbulence of the atmospheric boundary layer
8
3
Objectives and applications of the present study
11
3.1
Necessity of the present study
12
3.2
Objectives of the present study
13
3.3
Application of the present work
14
4
Theoretical concepts
16
4.1
Atmospheric boundary layer
16
4.1.1
Wind and flow
17
4.1.2
Turbulence
18
4.1.2.1
Turbulence kinetic energy
19
4.1.2.2
Turbulence intensity
22
IV
4.1.2.3
Free and forced convection
23
4.1.3
Depth and structure of the atmospheric boundary layer
25
4.1.3.1
Mixed layer
26
4.1.3.2
Residual layer
28
4.1.3.3
Stable boundary layer
28
4.1.4
Atmospheric stability
29
4.1.5
Micrometeorological variables
30
4.1.5.1
Friction velocity
30
4.1.5.2
Monin-Obukhov length
31
4.1.5.3
Convective velocity scale
32
4.1.5.4
Roughness length
32
4.2
Sound propagation in the atmosphere
33
4.3
Theory of the sodar measurement
38
4.3.1
Physical principle of the method
38
4.3.2
Sodar system configurations
41
5
Measurements, data processing and experimental sites
43
5.1
Measurements
43
5.1.1
Principles of sodar measurement
43
5.1.1.1
Beam pattern
43
5.1.1.2
Backscatter
44
5.1.1.3
Doppler shift
44
5.1.1.4
Height determination
45
5.1.1.5
Signal analysis
46
5.1.1.6
Limitation of sodar operation
47
V
5.1.2
Accuracy of sodar measurements
47
5.1.3
Instrumentation: Description of the FAS64
49
5.1.4
Description of the software: FASrun program
53
5.2
Data processing
54
5.3
Experimental sites
57
6
Results
59
6.1
Hartheim: Scots pine forest
60
6.1.1
Global solar radiation, wind direction, and wind speed variation
60
6.1.1.1
Global solar radiation
60
6.1.1.2
Wind direction
61
6.1.1.3
Horizontal wind speed
61
6.1.1.4
Vertical wind speed component
61
6.1.2
Atmospheric stability classification
61
6.1.3
Variance of horizontal and vertical wind speed
68
6.1.4
Turbulence kinetic energy
68
6.1.5
Turbulence intensity
69
6.1.5.1
Variation of turbulence intensity with wind directions under
neutral conditions
69
6.1.5.2
Turbulence intensity under different stratifications
69
6.1.6
Relationship between normalized standard deviations
of velocity components and z/L
69
6.2
Bremgarten: Grassland
80
6.2.1
Global solar radiation, wind direction, and wind speed variation
80
6.2.1.1
Global solar radiation
80
6.2.1.2
Wind direction speed
80
VI
6.2.1.3
Horizontal wind speed
80
6.2.1.4
Vertical wind speed component
81
6.2.2
Atmospheric stability classification
81
6.2.3
Variance of horizontal and vertical wind speed
81
6.2.4
Turbulence kinetic energy
82
6.2.5
Turbulence intensity
88
6.2.5.1
Variation of turbulence intensity with wind directions
under neutral conditions
88
6.2.5.2
Turbulence intensity under different stratifications
88
6.2.6
Relationship between normalized standard deviations
of velocity components and z/L
89
6.3
Blankenhornsberg: Vineyard
100
6.3.1
Global solar radiation, wind direction, and wind speed variation
100
6.3.1.1
Global solar radiation
100
6.3.1.2
Wind direction
100
6.3.1.3
Horizontal wind speed
100
6.3.1.4
Vertical wind speed component
101
6.3.2
Atmospheric stability classification
101
6.3.3
Variance of horizontal and vertical wind speed
101
6.3.4
Turbulence kinetic energy
108
6.3.5
Turbulence intensity
108
6.3.5.1
Variation of turbulence intensity with wind directions
under neutral conditions
108
6.3.5.2
Turbulence intensity under different stratifications
109
6.3.5.3
Relationship between normalized standard deviations
of velocity components and z/L
109
VII
6.4
Oberbärenburg: Norway spruce forest
120
6.4.1
Global solar radiation, wind direction, and wind speed variation
120
6.4.1.1
Global solar radiation
120
6.4.1.2
Wind direction
120
6.4.1.3
Horizontal wind speed
120
6.4.1.4
Vertical wind speed component
120
6.4.2
Atmospheric stability classification
121
6.4.3
Variance of horizontal and vertical wind speed
126
6.4.4
Turbulence kinetic energy
126
6.4.5
Turbulence intensity
127
6.4.5.1
Variation of turbulence intensity with wind directions
under neutral conditions
127
6.4.5.2
Turbulence intensity under different stratifications
127
6.4.6
Relationship between normalized standard deviations
of velocity components and z/L
127
6.5
Melpitz: Grassland
139
6.5.1
Global solar radiation, wind direction, and wind speed variation
139
6.5.1.1
Global solar radiation
139
6.5.1.2
Wind direction
139
6.5.1.3
Horizontal wind speed
139
6.5.1.4
Vertical wind speed component
140
6.5.2
Atmospheric stability classification
146
6.5.3
Variance of horizontal and vertical wind speed
146
6.5.4
Turbulence kinetic energy
147
6.5.5
Turbulence intensity
147
VIII
6.5.5.1
Variation of turbulence intensity with wind directions
under neutral conditions
147
6.5.5.2
Turbulence intensity under different stratifications
148
6.6
Freiburg: Urban area
158
6.6.1
Global solar radiation, wind direction, and wind speed variation
158
6.6.1.1
Global solar radiation
158
6.6.1.2
Wind direction
158
6.6.1.3
Horizontal wind speed
158
6.6.1.4
Vertical wind speed component
159
6.6.2
Variance of horizontal and vertical wind speed
159
6.6.3
Turbulence kinetic energy
160
7
General discussion
171
7.1
Global solar radiation, wind direction, and wind speed variation
171
7.1.1
Global solar radiation
171
7.1.2
Wind direction
172
7.1.3
Wind speed components
173
7.2
Atmospheric stability classification
174
7.3
Variance of horizontal and vertical wind speed
174
7.4
Turbulence kinetic energy
176
7.5
Turbulence intensity components
178
7.5.1
Variation of turbulence intensity components with
wind directions under neutral conditions
179
7.5.2
Turbulence intensity under different stratifications
181
7.6
Relationship between normalized standard deviations of
velocity components and z/L under unstable conditions
183
IX
7.6.1
Horizontal component
183
7.6.2
Vertical component
185
7.7
Profile of normalized variance of vertical wind speed component
185
8
Conclusions
202
References
207
List of abbreviations and symbols
219
List of captions for figures
223
List of captions for tables
231
Curriculum vitae
X
SUMMARY
On one hand, environmental studies need information and forecasts on the state,
trends and impacts of air pollutant concentrations on different scales. On the other
hand, air pollution control needs information on parameters of the atmospheric boundary layer (ABL), with reference to accumulation, dispersion and transport of air pollutants. Turbulence is one of the important transport processes, and is also used sometimes to define the ABL. The ABL is the layer where interactions take place between
the earth’s surface (which captures most of the incoming solar energy and redistributes
it in different forms) and the large scale atmospheric flow (which is driven by this energy). This transfer of energy is partly accomplished by turbulent eddies which are produced by two different mechanisms, namely wind shear and buoyancy.
The investigation presented here deals with the experimental determination of main
atmospheric variables affecting the ABL structure over different land use types in Germany by use of a FAS64 sodar (sonic detecting and ranging) from the Scintec Company (Tübingen, Germany). The investigation has been carried out at the Meteorological Institute, University of Freiburg, Germany, and performed as project ALUF1 within
the scope of the AFO2000 network VERTIKO (Vertical Transports of Energy and Trace
Gases at Anchor Stations and their Spatial/Temporal Extrapolation under Complex
Natural Conditions). Forest, urban and agricultural areas are land use types which are
typical of the small-scale heterogeneity in many parts of Germany. Among all types of
surfaces, the aerodynamic roughness of an urban area is almost constant. Forests and
urban areas are associated with comparatively high values of aerodynamic roughness.
Aerodynamic surface roughness of forests shows a long-term dependence on growth
dynamics. In contrast to that, aerodynamic surface roughness of agricultural areas is
smaller and has an annual pattern, which depends on plant growth.
The experimental sites of this investigation are located at Hartheim (47° 56` N, 07° 36`
E, 201 m a.s.l.), Bremgarten (47° 54` N, 07° 37` E, 200 m a.s.l.), Blankenhornsberg
(48° 03` N, 07° 36` E, 285 m a.s.l.), Oberbärenburg (50° 47` N, 13° 43` E, 735 m a.s.l.),
Melpitz (51° 31` N, 12° 55` E, 86 m a.s.l.) and Freiburg (48° 56` N, 07° 50` E, 272 m
a.s.l.). These sites represent different land use types: grassland (Bremgarten and
Melpitz), vineyard (Blankenhornsberg), forest (Hartheim and Oberbärenburg), and urban area (Freiburg).
XI
The data from the FAS64 sodar, such as wind speed components, wind direction and
turbulence parameters (particularly standard deviation of the vertical wind speed), are
30-min mean values. They were measured at each site within the same range of height
(20-500 m a.g.l.), but at different times. The measurement extends in Hartheim from 30
March, 2000 to 25 April, 2000, in Bremgarten from 10 July, 2001 to 26 July, 2001, in
Blankenhornsberg from 01 August, 2001 to 22 August, 2001, in Oberbärenburg from 29
August, 2001 to 24 September, 2001, in Melpitz from 26 September, 2001 to 12 October, 2001, and in Freiburg from 16 November, 2001 to 19 November, 2001. Due to the
acoustic noise produced by the sodar and acting as disturbance for people, the measurement campaign in Freiburg has to be broken off after a short period.
Global solar radiation was necessary to interpret the results of the sodar measurements. For Hartheim, Bremgarten and Blankenhornsberg it was taken over from the
forest-meteorological site Hartheim that is operated by the Meteorological Institute,
University of Freiburg. However, it is located 3.5 km and 9 km far from Bremgarten and
Blankenhornsberg, respectively. In addition, global solar radiation data for Oberbärenburg and Melpitz were provided by the weather stations at Rotherdbach (1 km from
Oberbärenburg) and Melpitz, respectively. For Freiburg, global radiation was taken
over from the urban climate experimental site, which is run by the Meteorological Institute, University of Freiburg, on a high-rise building (approximately 51 m a.g.l.) in the
northern downtown of Freiburg. Moreover, the German Weather Service (DWD) provided some data on fog, precipitation and cloud fraction.
Besides directly monitoring meteorological variables such as wind speed components,
wind direction, and the standard deviations of the wind direction and wind speed components, the application of a number of methods and algorithms enabled the estimation
of features of the atmospheric turbulence such as Pasquill-Gifford (P-G) stability
classes, Monin-Obukhov length, and friction velocity, which are all crucial for both
straightforward meteorological applications and as inputs to atmospheric pollutant dispersion models. In particular, a typical sodar-related method has been used to classify
atmospheric stability over the sites of the study through the periods of the measurements. Such a stability classification is the first step for applying a number of traditional
algorithms aiming at estimating the main atmospheric parameters that typically de-
XII
scribe the ABL structure (e.g. Monin-Obukhov length, friction velocity and mixing
height) in dependence on land use, weather as well as time of day and year.
This investigation focuses on the study of turbulence characteristics within the ABL
over different land use types: grassland, vineyard, forest and urban area. Thereby, the
main purpose of this study is to analyze the influences of thermal and roughness
changes on the properties of turbulence within the ABL over these land use types. To
fulfill the objectives of this investigation, the following points were taken into account:
∗∗
An overall measure of the intensity of turbulence is the turbulent kinetic energy
per unit mass (TKE). It is usually produced at the scale of the ABL depth. The
quantity σ3w/z (σw: standard deviation of the vertical wind speed at a height z) is
connected to the production terms of convective and mechanical origin of TKE.
Hence the behavior of this quantity was studied to explain the influence of thermal and roughness changes on the characteristics of the TKE. In addition, the
mean kinetic energy per unit mass (MKE) has a considerable role on the values
of TKE. Therefore, it was considered in this study. Moreover, daily midday-hour(11:00-14:00 CET) and midnight-hour- (23:00-02:00 CET) averages of σ3w/z,
MKE, and TKE at different levels were calculated for two cloudless and two
cloudy days at each of the sites.
∗∗
The components Iu, Iv and Iw of the turbulence intensity depend on measuring
height, surface roughness and atmospheric stability. Therefore, they were included in this investigation.
∗∗
For the sites Hartheim, Bremgarten, Blankenhornsberg and Oberbärenburg,
mean values of the normalized (by the friction velocity u∗) standard deviations of
the wind speed components, σi/u∗ (i=u,v,w), in the surface layer were discussed
as a function of the stability parameter (z/L) under unstable conditions. In contrast to σw, the determination of σu and σv from sodar measurements is extremely problematic due to the measuring method. The manufacturer (Scintec
Company) of the FAS64 sodar, however, states, that half-hourly mean values of
σu and σv are utilizable for further calculations even if their accuracy is lower
than for σw. Mean values of σu/u∗, σv/u∗ and σw/u∗ in the range of -z/L from 0.86 to
XIII
3.66 in the surface layer over the land use types under investigation are compared with analogous values from previous studies at flat and complex terrain.
∗∗
The variation of the normalized (by the square of the convective velocity w∗2)
variance of the vertical wind speed component, σ2w/w∗2, with the normalized (by
the mixing height zi) height z/zi was discussed for the grassland site Bremgarten.
In order to explain the influence of thermal and roughness changes on the characteristics of TKE and turbulence intensity components, background information on the behavior of global radiation, wind direction and its standard deviation, horizontal and vertical wind speed components, and the variance of horizontal and vertical wind speed
components was provided for each site during the measurement campaigns.
The results of this investigation can be summarized as follows:
∗∗
Using only sodar data, the atmospheric stability (according to P-G stability classification) was determined at four levels a.g.l. at Hartheim (50-80, 80-110, 140170, and 200-230 m), Bremgarten (40-60, 60-100, 100-180, and 180-260 m),
Blankenhornsberg (40-60, 80-120, 120-160, and 160-240 m), Oberbärenburg
(50-80, 80-110, 140-170, and 200-230 m), and Melpitz (50-80, 80-110, 140-170,
and 200-230 m). In order to optimize the sodar measurements, its setup varied
between the measurement campaigns. Therefore, the graduation of layers is
slightly different between the sites. Land use-specific values of the frequency
distribution of the P-G stability classes A to F within the range, approximately,
from 40 to 260 m a.g.l. were A (1%, 5%, 5%, 1%, 1%), B (3%, 15%, 19%, 6%,
3%), C (21%, 22%, 26%, 34%, 21%), D (72%, 41%, 33%, 55%, 72%), E (2%,
7%, 5%, 1%, 2%), and F (1%, 10%, 10%, 2%, 1%) for Scots pine forest (Hartheim), grassland (Bremgarten), vineyard (Blankenhornsberg), Norway spruce
forest (Oberbärenburg), and grassland (Melpitz), respectively. Considering the
period of the year for every site, these results seem to be reliable.
∗∗
Case studies showed that half-hourly mean values of σ3w/z under various stability conditions (neutral, stable and unstable) decreased with height. This was due
to the increasing of the mechanical and buoyancy turbulence production in the
surface layer. In addition, the analysis of daily mean values of σ3w/z at different
levels within the surface layer on cloudless and cloudy conditions revealed lower
XIV
values at the upper level than at the lower level: 44% (cloudless) and 64%
(cloudy) at Hartheim (80-110 m compared to 20-50 m a.g.l.), 60% (cloudless)
and 64% (cloudy) at Bremgarten (60-100 m compared to 20-30 m a.g.l.), 76%
(cloudless) and 65% (cloudy) at Blankenhornsberg (80-120 m compared to 2030 m a.g.l.), 33% (cloudless) and 64% (cloudy) at Oberbärenburg (80-110 m
compared to 20-50 m a.g.l.), 48% (cloudless) and 51% (cloudy) at Melpitz (80110 m compared to 20-50 m a.g.l.), as well as 61% (cloudless) and 45%
(cloudy) at Freiburg (60-80 m compared to 20-30 m a.g.l.).
∗∗
The values of σ3w/z during cloudless conditions throughout the night were lower
even in the presence of wind shear. This reflected the effect of the global radiation on σ3w/z in the daytime, especially when the wind speed is relatively low. In
addition, this effect could be obviously seen by comparing the average values of
σ3w/z at the midday (11:00-14:00 CET) and midnight hours (23:00-02:00 CET)
during cloudless conditions. The decrease of the mean values of σ3w/z for three
levels within the range approximately from 20 to 110 m a.g.l. in the midnight
hours (23:00-02:00 CET) were 93%, 72%, 56%, 84%, 85% and 62% at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg, Melpitz and Freiburg, respectively. At cloudy conditions, the effect of the mechanical turbulence on the
values of σ3w/z became apparent, especially when the values of the horizontal
wind speed were relatively high (for example in Bremgarten). The midnight
hours (23:00-02:00 CET) average of σ3w/z was greater than those for the midday
hours (11:00-14:00 CET). The increases of the midnight hours (23:00-02:00
CET) average of σ3w/z were 3% at the level of 20-30 m and 6% at the level of
40-60 m a.g.l.. However the average values of the horizontal wind speed at the
level of 20-30 m and 40-60 m a.g.l. were 1.4 and 2.7 m/s for the midnight hours
(23:00-02:00 CET) and 0.2 and 0.3 m/s for the midday hours (11:00-14:00 CET).
∗∗
Under neutral conditions, the variations of the aerodynamic roughness over the
study areas for various fetch conditions due to various wind directions affect the
turbulence intensity components (Iu, Iv, Iw). This behavior appeared qualitatively
by the study of the variation of the Iu, Iv and Iw with the angular sectors at
Bremgarten, Blankenhornsberg, Oberbärenburg and Melpitz. At Hartheim and
Freiburg, there were not enough data to carry out this study. The results show,
XV
for example, at Bremgarten a small fluctuation in the values of Iu, Iv and Iw from
one angular sector to another. This behaviour was expected, because the surrounding of the sodar at this site was not completely symmetric.
∗∗
It is known that the turbulence intensity components (Iu, Iv, Iw) show a dependence on P-G stability classes and increase with increasing instability. This behavior was illustrated qualitatively by the investigation of the variation of the Iu, Iv
and Iw with the P-G stability classes for the sites Hartheim, Bremgarten,
Blankenhornsberg, Oberbärenburg and Melpitz. At Freiburg, there were not
enough data to perform this study. To reduce the effect of the change of the
roughness, this relationship was investigated for angular sectors of 30°. As a result the horizontal turbulence intensities increased faster with increasing instability contrary to the vertical turbulence intensity.
∗∗
The turbulence intensity components (Iu, Iv, Iw) decreased with the increase of
the observation height. This dependence could be determined analyzing the
characteristics of Iu, Iv and Iw for various fetch conditions arising under various
wind directions at different level and under neutral conditions. At the Scots pine
forest site Hartheim, the values of Iu, Iv and Iw for the angular sector of 180-210°
at the level of 200-230 m a.g.l. were lower than those at the level of 50-80 m
a.g.l. (21%, 51% and 47% respectively). At the grassland site Bremgarten, the
values of Iu, Iv and Iw for some angular sectors at the level of 180-260 m a.g.l.
were lower than those at the level of 40-60 m a.g.l. (64%, 63% and 82% for 180210° and 30%, 37% and 72% for 210-240° respectively). At the vineyard site
Blankenhornsberg, the values of Iv and Iw at the levels of 160–240 m a.g.l. were
lower than those for 40-60 m a.g.l. (15% and 72% for 150-180° and 35% and
75% for 180-210° respectively), while the values of Iu at the levels of 160–240 m
a.g.l. were higher than those for 40-60 m a.g.l. (57% and 21% for the angular
sectors 150-180° and 180-210° respectively). This may be due to the difference
between the number of observations in both levels and the inhomogeneous terrain. At the grassland site Melpitz, the values of Iu, Iv and Iw at the level of 200230 m a.g.l. were lower than those for 50-80 m a.g.l. (47%, 46% and 50% for
180-210° and 30%, 38% and 44% for 210-240° respectively). At the Norway
spruce site Oberbärenburg, the mean value of Iu, Iv and Iw calculated for some
XVI
angular sectors (210-330°) at the level of 200-230 m a.g.l. were lower than those
values at the levels of 50-80 m a.g.l. (61%, 50% and 85% respectively).
∗∗
Under unstable conditions, the mean values of σu/u∗, σv/u∗ and σw/u∗ were functions of (z/L)1/3. σu/u∗ and σv/u∗ were strongly affected by the change in the surface roughness. For -z/L within the range 0.86 to 3.66, the mean values of σu/u∗
and σv/u∗ over the grassland site were approximately in the same magnitude as
over the vineyard site, but they were lower (34% and 52% respectively) than
those observed over the forest sites. The change of surface roughness between
the investigated land use types did not apparently influence the properties of σw
/u∗.
∗∗
The profile of the normalized (by the square of the convective velocity w2∗) variance of the vertical wind speed component, σ2w/w∗2 under free convective conditions over grassland (Bremgarten) increased with height and reached maximum
values (≈ 0.46) within the mixed layer at z = 0.32 zi. After it these values decreased with height and were very small.
XVII
ZUSAMMENFASSUNG
Untersuchung der atmosphärischen Grenzschicht mit einem Sodar
Umweltstudien erfordern Daten über Konzentrationen von Luftverunreinigungen in der
atmosphärischen Grenzschicht (ABL), ihre Niveaus, Trends und Auswirkungen, wobei
die Skalenebenen räumlich und zeitlich variieren. In der Kausalkette der Luftverunreinigungen wird ihre Ausbreitung und Verdünnung in der ABL wesentlich von meteorologischen Parametern beeinflusst. Der turbulente Luftmassenaustausch stellt dabei einen
bedeutenden Transportprozess dar. Ursache für den turbulenten Luftmassenaustausch
in der ABL sind zwei verschiedene Prozesse, die dynamisch bedingte Turbulenz und
die thermisch bedingte Turbulenz.
Zur Definition der ABL werden oft Eigenschaften der Turbulenz herangezogen. Die atmosphärische Grenzschicht, die im Mittel die untersten 1000 m der Atmosphäre umfasst, bildet die Schicht, in der Wechselwirkungen zwischen der Erdoberfläche - in ihrer
Funktion als Umsetzungsfläche für Strahlung, Wärme, Wasser, Stoffe und Impuls - und
der übergeordneten Strömung in der Atmosphäre stattfinden.
In der vorliegenden experimentellen Untersuchung werden bedeutende meteorologische Parameter zur Kennzeichnung der ABL über verschiedenen Landnutzungen an
ausgewählten Standorten in Deutschland bestimmt. Für die in diesem Zusammenhang
notwendigen Messungen wurde ein FAS64 Sodar (sonic detecting and ranging) der
Firma Scintec (Tübingen) eingesetzt. Diese Untersuchung wurde am Meteorologischen
Institut der Universität Freiburg als Teilprojekt ALUF1 im Rahmen des AFO2000 Verbundprojektes VERTIKO durchgeführt.
Wälder, Stadtflächen und landwirtschaftlich genutzte Flächen stellen Landnutzungsformen dar, die für die kleinteilige Heterogenität in vielen Teilen Deutschlands typisch
sind. Wälder und Stadtflächen weisen eine große aerodynamische Oberflächenrauhigkeit auf. Während sie bei Stadtflächen fast konstant ist, zeigt sie bei Wäldern eine langfristige Abhängigkeit von ihrer Wuchsdynamik. Im Gegensatz dazu nimmt die aerodynamische Oberflächenrauhigkeit von landwirtschaftlich genutzten Flächen kleinere
Werte an und ist zusätzlich durch eine Jahresvariabilität gekennzeichnet, die vom
Pflanzenwachstum abhängt.
XVIII
Die Standorte für die Sodarmessungen waren in Hartheim (47° 56` N, 07° 36` E, 201 m
ü. NN), Bremgarten (47° 54` N, 07° 37` E, 200 m ü. NN), Blankenhornsberg (48° 03` N,
07° 36` E, 285 m ü. NN), Oberbärenburg (50° 47` N, 13° 43` E, 735 m ü. NN), Melpitz
(51° 31` N, 12° 55` E, 86 m ü. NN) und Freiburg (48° 56` N, 07° 50` E, 272 m ü. NN).
Die Standorte repräsentieren die Landnutzungeformen Grasland (Bremgarten und
Melpitz), Weingarten (Blankenhornsberg), Wald (Hartheim und Oberbärenburg) und
Stadt (Freiburg).
Die Sodarmessungen lieferten im Höhenbereich zwischen 20 und 500 m ü. Grund 30Minuten-Mittelwerte der drei Komponenten des Windvektors sowie von Windrichtung
und Turbulenzparametern, insbesondere der Standardabweichung der vertikalen
Windvektorkomponente. Da nur ein Sodarsystem zur Verfügung stand, konnten die
Sodarmessungen an den einzelnen Standorten nicht parallel, sondern nur in sequentieller Abfolge durchgeführt werden. Sie fanden zu folgenden Terminen statt:
** Hartheim, Landnutzung Waldkiefern (Pinus sylvestris): 30. Mai bis 25. April 2000;
** Bremgarten, Landnutzung Grasland: 10. bis 26. Juli 2001,
** Blankenhornsberg, Landnutzung Weingarten: 1. bis 22. August 2001,
** Oberbärenburg, Landnutzung Fichten (Picea abies): 29. August bis 24. September
2001,
** Melpitz, Landnutzung Grasland: 26. September bis 12. Oktober 2001,
** Freiburg, Landnutzung Stadt: 16. bis 19. November 2001.
Wegen der Schallemissionen des Sodars und der damit verbundenen Lärmbelästigung
für Menschen mussten die Sodarmessungen in Freiburg schon nach relativ kurzer Zeit
abgebrochen werden.
Zur Interpretation der Ergebnisse aus den Sodarmessungen waren Globalstrahlungswerte erforderlich. Für die Standorte Hartheim, Bremgarten and Blankenhornsberg
wurden sie von der Forstmeteorologischen Messstelle Hartheim des Meteorologischen
Instituts der Universität Freiburg übernommen. Dabei musste allerdings beachtet werden, dass sich diese Messstelle 3.5 km von Bremgarten und 9 km von Blankenhornsberg entfernt befindet. Globalstrahlungswerte für den Standort Oberbärenburg konnten
von der 1 km entfernten Station Rotherdbach übernommen werden. Am Standort Melpitz wurde die parallel zu den Sodarmessungen erfasste Globalstrahlung vom Institut
für Troposphärenforschung bereit gestellt. Für den Standort Freiburg konnten Werte
XIX
der Globalstrahlung von der Meteorologischen Stadtstation verwendet werden, die das
Meteorologische Institut der Universität Freiburg auf dem Dach des Chemiehochhauses (51 m ü. Grund) betreibt. Zusätzlich wurden vom Deutschen Wetterdienst Daten
über Nebel, Niederschlag und Himmelsbedeckung zur Verfügung gestellt.
Die direkt über Sodarmessungen bestimmten meteorologischen Variablen bilden die
Grundlage für die Anwendung von verschiedenen Methoden, über die sich Kennzeichen der atmosphärischen Turbulenz in ihrer landnutzungsspezifischen Ausprägung
ableiten lassen. Dazu zählen u.a. die Pasquill-Gifford (P-G) Stabilitätsklassen, MoninObukhov Länge und Schubspannungsgeschwindigkeit. Sie sind wichtig für direkte meteorologische Anwendungen, bilden aber auch Eingangsgrößen für atmosphärische
Ausbreitungsmodelle. In dieser Untersuchung wurde eine spezielle Methode angewendet, die auf Sodardaten beruht und damit eine Klassifizierung der thermischen Schichtung in der ABL während der Sodarmessungen an den einzelnen Standorten ermöglicht. Solch eine Stabilitätsklassifizierung ist notwendig, um traditionelle Algorithmen zur
Bestimmung von Parametern (u.a. Monin-Obukhov Länge, Schubspannungsgeschwindigkeit oder Mischungsschichthöhe) anwenden zu können, die die Struktur der ABL in
ihrer vielfältigen Abhängigkeit (u.a. Landnutzung, Wetterlage, Tages- und Jahreszeit)
beschreiben.
Diese Untersuchung hat als Zielsetzung die Charakterisierung der Kenngrößen der
Turbulenz in der atmosphärischen Grenzschicht, wobei der Schwerpunkt auf den thermisch- und oberflächenrauhigkeitsbedingten Auswirkungen der ausgewählten Landnutzungen Grasland, Weingarten, Wald und Stadt liegt. Zur Erreichung dieser Zielsetzung wurde folgende Fakten berücksichtigt:
∗∗
Ein allgemeines Maß für die Intensität der Turbulenz in der ABL stellt die turbulente kinetische Energie pro Masseneinheit (TKE) dar. Die Größe σ3w/z (σw:
Standardabweichung der vertikalen Windgeschwindigkeit in der Höhe z) bezieht
sich auf die Produktionsterme von TKE konvektiven und mechanischen Ursprungs. Daher wurde diese Größe analysiert, um die Einflüsse thermischer und
rauhigkeitsbedingter Änderungen auf TKE zu erklären. Die mittlere kinetische
Energie pro Masseneinheit (MKE) weist Zusammenhänge mit TKE auf und wurde deshalb in diese Untersuchung aufgenommen. Zur Berücksichtigung der
Auswirkungen von Tageszeit und Wetterbedingungen wurden Mittelwerte von
XX
σ3w/z, MKE und TKE zur Mittagszeit (11:00-14:00 Uhr MEZ) und um Mitternacht
(23:00-02:00 Uhr MEZ) in verschiedenen Höhenschichten berechnet, und zwar
je Messkampagne für zwei wolkenlose Tage und zwei bedeckte Tage.
**
Die Komponenten Iu, Iv und Iw der Turbulenzintensität hängen von aerodynamischer Oberflächenrauhigkeit, thermischer Schichtung und Bezugsniveau ab und
wurden daher in diese Untersuchung einbezogen.
**
Mittelwerte der mit der Schubspannungsgeschwindigkeit u∗ normierten Standardabweichungen der Windgeschwindigkeitskomponenten σi/u∗ (i= u,v,w) in der
Surface Layer werden bei instabilen Bedingungen in Abhängigkeit vom Stabilitätsparameter z/L an den Standorten Hartheim, Bremgarten, Blankenhornsberg
und Oberbärenburg diskutiert. Dabei wird auch auf die im Gegensatz zu σw bestehende Problematik der Bestimmung von σu und σv aus Sodarmessungen eingegangen. Beim Scintec Sodar FAS64 gibt der Hersteller an, dass Halbstundenmittelwerte von σu und σv für weitere Analysen verwendbar sind, auch wenn
ihre Genauigkeit messtechnisch bedingt deutlich unter derjenigen von σw liegt.
Hier erzielte Mittelwerte von σu/u∗, σv/u∗ und σw/u∗ im Bereich von –z/L zwischen
0.86 und 3.66 werden vergleichend diskutiert und Ergebnissen aus anderen Untersuchungen gegenübergestellt.
**
Für den Grasland-Standort Bremgarten wurde die Variation der mit der quadrierten konvektiven Geschwindigkeit w∗2 normierten Varianz der vertikalen Windgeschwindigkeit σ2w/w∗2 in Abhängigkeit von der mit der Mischungsschichthöhe zi
normierten Höhe z/zi diskutiert.
Als Grundlage für die Analyse der direkten und indirekten Ergebnisse aus den einzelnen Sodarmesskampagnen wurden für jeden Standort die Wetterbedingungen im
Messzeitraum anhand von Daten für Globalstrahlung, Windrichtung einschließlich
Standardabweichung sowie horizontale und vertikale Windgeschwindigkeit einschließlich ihrer Standardabweichungen beschrieben.
Die Ergebnisse dieser Untersuchung lassen sich wie folgt zusammenfassen:
**
Die thermische Schichtung in der ABL nach den P-G Stabilitätsklassen wurde
allein aus Sodardaten abgeleitet und für jeweils vier Höhenschichten bestimmt:
XXI
Hartheim (50-80, 80-110, 140-170 und 200-230 m ü. Grund), Bremgarten (4060, 60-100, 100-180 and 180-260 m ü. Grund), Blankenhornsberg (40-60, 80120, 120-160 und 160-240 m ü. Grund), Oberbärenburg (50-80, 80-110, 140170 und 200-230 m ü. Grund) und Melpitz (50-80, 80-110, 140-170 and 200-230
m ü. Grund). Da das Sodar-Setup aus Optimierungsgründen bei den Messkampagnen nicht immer identisch war, gibt es zwischen den einzelnen Standorten
Unterschiede in der Schichteneinteilung. Die standortsspezifischen Häufigkeiten
der P-G Stabilitätsklassen A bis F in der Schicht zwischen ca. 40 und 260 m ü.
Grund betrugen an den Standorten Hartheim (Waldkiefer), Bremgarten (Grasland), Blankenhornsberg (Weingarten), Oberbärenburg (Fichte) und Melpitz
(Grasland): A (1%, 5%, 5%, 1%, 1%), B (3%, 15%, 19%, 6%, 3%), C (21%,
22%, 26%, 34%, 21%), D (72%, 41%, 33%, 55%, 72%), E (2%, 7%, 5%, 1%,
2%) und F (1%, 10%, 10%, 2%, 1%).
∗∗
In Fallbeispielen wurde gezeigt, dass Halbstundenmittelwerte von σ3w/z bei unterschiedlicher atmosphärischer Schichtung (neutral, stabil und labil) mit ansteigender Höhe abnahmen, was durch die Produktion von mechanischer und
thermischer Turbulenz in der Surface Layer bedingt war. Bei wolkenlosen und
bedeckten Bedingungen erbrachte die Analyse der Tagesmittel von σ3w/z in verschiedenen Höhenschichten innerhalb der Surface Layer niedrigere Werte im
oberen Bereich dieser Schicht: 44% (wolkenlos) und 64% (bedeckt) in Hartheim
(80-110 m bezogen auf to 20-50 m ü. Grund), 60% (wolkenlos) und 64% (bedeckt) in Bremgarten (60-100 m bezogen auf 20-30 m ü. Grund), 76% (wolkenlos) und 65% (bedeckt) in Blankenhornsberg (80-120 m bezogen auf 20-30 m ü.
Grund), 33% (wolkenlos) und 64% (bedeckt) in Oberbärenburg (80-110 m bezogen auf 20-50 m ü. Grund), 48% (wolkenlos) und 51% (bedeckt) in Melpitz (80110 m bezogen auf 20-50 m ü. Grund) sowie 61% (wolkenlos) und 45% (bedeckt) in Freiburg (60-80 m bezogen auf 20-30 m ü. Grund).
∗∗
Während wolkenloser Bedingungen war σ3w/z in der Nacht, auch bei vorhandener Windscherung, kleiner als tagsüber, was die Wirkung der Globalstrahlung
aufzeigt, insbesondere wenn die Windgeschwindigkeit klein ist. Die Tag- und
Nachtunterschiede von σ3w/z ließen sich systematischer bei der Analyse von
Mittagsmittelwerten (11:00-14:00 Uhr MEZ) und Mitternachtsmittelwerten (23:00-
XXII
02:00 Uhr MEZ) an Strahlungstagen erkennen. Bezogen auf Mittelwerte über
drei Schichten zwischen ca. 20 und 110 m ü. Grund betrugen die Mitternachtsmittelwerte von σ3w/z, bezogen auf die Mittagsmittelwerte, in Hartheim 93%,
Bremgarten 72%, Blankenhornsberg 56%, Oberbärenburg 84%, Melpitz 85%
und Freiburg 62%. Bei bedecktem Himmel erhöhte sich der Effekt der mechanischen Turbulenz auf σ3w/z, und zwar insbesondere bei großer horizontaler
Windgeschwindigkeit. So war dann z.B. in Bremgarten der Mitternachtsmittelwert von σ3w/z größer als der Mittagsmittelwert; die relative Erhöhung des Mitternachtsmittelwertes von σ3w/z betrug 3% in der Schicht 20-30 m und 6 % in der
Schicht 40-60 m ü. Grund. Die Mitternachtsmittelwerte der horizontalen Windgeschwindigkeit beliefen sich auf 1.4 m/s in der Schicht 20-30 m und 2.7 m/s in der
Schicht 40-60 m ü. Grund. Die analogen Mittagsmittelwerte erreichten nur 0.2
m/s in der Schicht 20-30 m und 0.3 m/s in der Schicht 40-60 m ü. Grund.
∗∗
Die Komponenten (Iu, Iv, Iw) der Turbulenzintensität wurden von der aerodynamischen Oberflächenrauhigkeit im Luv des Sodars beeinflusst. Diese Abhängigkeit
ließ sich qualitativ über die Variation von Iu, Iv und Iw bei differierenden Windrichtungssektoren (jeweils 30°) für die Landnutzungen an den Standorten Bremgarten, Blankenhornsberg, Oberbärenburg und Melpitz bestätigen. In Bremgarten
zeigte sich z.B. nur eine geringe sektorspezifische Variabilität der Werte für Iu, Iv
und Iw, weil an diesem ebenem Grasland-Standort relativ gute horizontal homogene Bedingungen vorhanden sind.
∗∗
Die Abhängigkeit der Komponenten (Iu, Iv, Iw) der Turbulenzintensität von der
atmosphärischen Schichtung, die in dieser Untersuchung über die P-G Stabilitätsklassen repräsentiert wurde, konnte für die Landnutzungen an den Standorten Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg und Melpitz
nachgewiesen werden, wobei sich die bekannte Zunahme von Iu, Iv und Iw mit
ansteigender Instabilität widerspiegelte. Sie war bei Iu und Iv starker als bei Iw
ausgeprägt.
∗∗
Für neutrale Schichtung und verschiedene standortsspezifische Anströmungsbedingungen konnte gezeigt werden, dass die Komponenten (Iu, Iv, Iw) der Turbulenzintensität mit ansteigender Höhe über Grund abnahmen. Am Kiefernwald-
XXIII
Standort Hartheim waren im Richtungssektor 180-210° die Werte von Iu, Iv und Iw
in der Schicht 200-230 m ü. Grund um 21%, 51% bzw. 47% kleiner als in der
Schicht 50-80 m ü. Grund. Für den Grasland-Standort Bremgarten wurde der
zusätzliche Einfluss der Anströmungsbedingungen auf Iu, Iv und Iw aufgezeigt. So
ergaben sich Werte für Iu, Iv und Iw in der Schicht 180-260 m ü. Grund, die richtungsspezifisch variabel unter denjenigen für die Schicht 40-60 m ü. Grund lagen (64%, 63% und 82% im Sektor 180-210° sowie 30%, 37% and 72% im Sektor 210-240°). Am Weingarten-Standort Blankenhornsberg waren die Werte für Iv
und Iw in der Schicht 160–240 m ü. Grund niedriger als in der Schicht 40-60 m ü.
Grund (15% und 72% im Sektor 150-180° sowie 35% und 75% im Sektor 180210°). Dagegen erreichte Iu an diesem Standort in der Schicht 160–240 m ü.
Grund höhere Werte als in der Schicht 40-60 m ü. Grund (57% im Sektor 150180° und 21% im Sektor 180-210°). Gründe dafür waren ein unterschiedlich großes Datenkollektiv in den beiden Schichten und das inhomogene Gelände an
diesem Standort. Am Grasland-Standort Melpitz waren die Werte für Iu, Iv und Iw
in der Schicht 200-230 m ü. Grund kleiner als in der Schicht 50-80 m ü. Grund
(47%, 46% and 50% im Sektor 180-210° sowie 30%, 38% and 44% im Sektor
210-240°). Für den Fichtenwald-Standort Oberbärenburg ergaben sich über
mehrere Sektoren (210-330°) Mittelwerte von Iu, Iv und Iw , die in der Schicht 200230 m ü. Grund ebenfalls unter den Vergleichswerten in der Schicht 50-80 m ü.
Grund lagen (61%, 50% and 85%).
∗∗
Für instabile Bedingungen ließen sich die Mittelwerte von σu/u∗, σv/u∗ und σw/u∗
als Funktionen von (z/L)1/3 darstellen. Dabei zeigte sich der ausgeprägte Einfluss der Oberflächenrauhigkeit auf σu/u∗ und σv/u∗. Im Bereich von –z/L zwischen 0.86 und 3.66 erreichten die Mittelwerte von σu/u∗ und σv/u∗ an den Grasland-Standorten in etwa die gleiche Größenordnung wie am WeingartenStandort, waren aber niedriger (34% und 52%) als an den Wald-Standorten. Bei
den Eigenschaften von σw /u∗ konnte für die untersuchten Landnutzungen keine
Abhängigkeit von der Oberflächenrauhigkeit festgestellt werden.
∗∗
Bei freier Konvektion stieg am Grasland-Standort Bremgarten die mit dem
Quadrat der konvektiven Geschwindigkeit (w2∗) normierte Varianz der vertikalen
Windgeschwindigkeit (σ2w/w∗2) mit der Höhe an, erreichte maximale Werte (um
XXIV
0.46) in der Mischungsschicht bei der relativen Höhe z/zi = 0.32 und nahm anschließend mit der Höhe auf sehr kleine Werte ab.
1
1
INTRODUCTION
Sunrise-sunset-sunrise, the daily cycle of radiative heating causes a daily cycle of sensible and latent heat fluxes between the earth and the air. These fluxes cannot directly
reach the whole atmosphere, but they are confined by the troposphere to a shallow
layer near the ground. This layer is called the atmospheric boundary layer, ABL (Stull,
2000). It is defined as the part of the troposphere that is directly influenced by the presence of earth’s surface and responds to surface forcings with a timescale of about an
hour or less. These forcings include the fractional drag, evaporation and transpiration,
heat transfer, pollutant emission, and terrain induced flow modification (Stull, 1988).
Within this layer most of the human activities takes place. Processes of the boundary
layer are of extreme importance both for the large-scale atmospheric dynamics and for
a large number of meteorological applications such as agriculture, air pollution studies,
urban planning, etc (McBean et al., 1979).
The ABL thickness is quite variable in time and space, ranging from hundreds of meters to a few kilometers (Stull, 1988). Indirectly, the whole troposphere can change in
response to surface characteristics, but this response is relatively slow outside of the
ABL. Hence, the definition of the ABL includes a statement about one-hour time scales.
This does not imply that the boundary reaches an equilibrium in that time, but that alterations have at least begun. The study of the ABL involves the study of micro-scale
processes. However, phenomena in ABL are with space scales smaller than about 3
km and with time scales shorter than about 1 hour (Stull, 1988).
As mentioned before, the importance of ABL studies is founded on two main reasons. It
is the pathway for fluxes of momentum, heat and water vapor to reach the free atmosphere and give it the energy responsible for large-scale circulation. Moreover, it is the
place where most of human activities (with their consequences) take place. The information on the “open” structure of ABL is of great importance since it may have an impact on future weather prediction methods. In addition, the knowledge of the “close”
structure associated with the stable case should assist in predicting the strength and
the duration of air pollution events (Brown, 1987).
Sensors used for ABL measurements fall into two broad categories:
2
**
in situ sensors that can be mounted at the ground, on masts or towers as well as
tethered balloons, free balloons, or aircrafts;
**
remote sensors, ground-based or aircraft-mounted, that infer atmospheric properties through their effects on acoustic, microwave and optical signals propagating through the air.
In situ sensors are the traditional instruments of choice for surface and lower boundary
layer studies, being the only ones capable of the accuracy and resolution needed for
quantitative work. Remote sensors have the advantage of increased range and spatial
scanning capability, but the constraints on minimum range and spatial resolution limit
their usefulness for surface layer measurements. Used in combination, however, the
two types of sensors provide a more complete description of the flow field being studied
than either of the two can provide separately. New remote sensors with shorter minimum ranges and finer range resolutions are now becoming available for boundary layer
applications (Kaimal and Finnigan, 1994).
In addition to observing the ABL, another important area of research involves the numerical simulation of boundary-layer structure and behaviour. This allows experimentation under carefully controlled conditions and thus offers an advantage over real-word
field experiments where no such control is possible. The effects of radiation, atmospheric composition, clouds, orography, the earth’s rotation, surface friction, gravity
waves and turbulence are taken into account in order to derive realistic fields for wind,
temperature, humidity and pressure (Garratt, 1992).
The increasing knowledge about atmospheric turbulence has made it possible to physically model important aspects of ABL. Consequently, many numerical models have already been developed for a wide range of applications with different degrees of sophistication. The demands on the models vary as well as the formulation, or parameterization,
of basic physical processes. Numerical models of the ABL are today capable of simulating, or coping with, a number of different aspects of atmospheric motions. Very sophisticated models are used in testing new hypotheses about the ABL structure. Others try to
deal with air pollution dispersion and diffusion, for prediction, local weather forecasting,
etc (McBean et al., 1979).
3
In this study one of the remote sensing methods was used. Therefore, a brief description of the general characteristics of these sensors, especially the ground-based remote sensing, is given. In the ABL, considered as a three-dimensional fluid, remote
sensing means measuring the characteristics of some region in the fluid with instrumentation that does not have a sensing element in or surrounding the volume of interest. Remote sensing of ABL variables can be done actively or passively (Schwiesow,
1986).
Active measurements involve transmitting acoustic or electromagnetic radiation to the
region of interest and measuring the portion of the radiation that is returned from the
region to the instrument (for example; sodar, radar, lidar). However, Tyndall (1874) in
England investigated acoustic scattering in the atmosphere before the turn of the century but Gilman et al. (1946) started the modern era of sodar. Radar returns from the
ionosphere were obtained by Appleton and Barnett (1925), but the development of
shorter-wavelength radars with steerable antennas during World War II made ABL
measurements practical (for more details see Marshall et al., 1947; Wexler, 1947 and
Hardy et al., 1966). Lidar at first used large, modulated searchlights separated from the
receiver location and scanned in elevation angle to intersect a vertically pointing receiver beam at various altitudes up to 60 km (Elterman, 1951). Fiocco and Smullin
(1963) demonstrated a lidar based on a ruby laser and since then many different types
of lasers have been used for lidar (Schwiesow, 1986).
Passive measurements involve receiving and analyzing radiation naturally emitted from
the atmosphere. Visual observations and infrared radiometry are examples of passive
remote-sensing technique. For more details about the applications of sodar, radar and
Lidar as well as the passive microwave radiometry and other passive techniques, see
Schwiesow (1986) and Chadwick and Gossard (1986).
There is no doubt that the sodar is of great significance in the ABL investigations. Although by itself it may not be able to give a complete description of ABL, it measures
the wind profile, one of the most important mean quantities characterizing the ABL.
Moreover this quantity is particularly useful to monitor the vertical diffusion and the
transport processes that are of paramount importance to the study and the modeling of
pollution (Mastrantonio et al., 1994, 1996). The knowledge of the diffusion mechanism
and of the circulation pattern in these cases is very important since severe pollution
4
episode may be associated to these circulations. Moreover, they may have harmful
effects since recirculation of pollutants is made more dangerous by chemical changes,
as in the case of breezes (Lalas et al., 1983), or by converging the pollutants in the
center of urban areas, as it may happen with the toroidal heat island circulation (Bennett and Saab, 1982). As a consequence, the knowledge of the local circulation and of
the associated dispersion mechanisms is a first step toward a possibility to forecast
conditions in which severe pollution episodes may be expected. The sodar may reveal
its usefulness also in the characterization of urban ABL (Melas et al., 1998).
Beside wind, temperature and depth of the ABL, the most important parameters in the
ABL are the surface heat flux and the surface momentum flux, which are required to
define the parameter z/L (needed to estimate the atmospheric stability). Furthermore,
some statistics turbulent parameters such as the standard deviations of wind speed are
used to assess dispersions of plumes (Melas et al., 1998).
In conclusion, although with some limitations due to an incomplete coverage of the full
ABL extension sometimes and to the acoustic pollution, the acoustic remote sensing
represent a powerful, relatively cheap technique for ABL investigations (Melas et al.,
1998) and it is a new “eye” looking from a different point of view into the atmosphere
(Graber, 1993).
The data for this study were provided from measurement campaigns based on a Flat
Array Sodar (FAS64) operated by the Meteorology Institute, University of Freiburg, over
different sites in Germany. The campaigns were performed as project ALUF1 within the
framework of the AFO2000 research network VERTIKO (Vertical Transports of Energy
and Trace Gases at Anchor Stations and their Spatial/Temporal Extrapolation under
Complex Natural Conditions).
5
2
LITERATURE REVIEW
2.1
Acoustic remote sensing
An English physicist Tyndall (1874) was apparently the first who observed sound scattering from turbulence when studying the propagation of acoustic signals through the
sea fog to determine the potentialities of acoustic beacons. On the cloudless day of 27
October 1873, he observed echo-signals from a height of 200 m. His contemporaries,
in particular, Rayleigh (1877) did not accept his hypothesis and considered refraction to
be responsible for this effect (Kalistratova, 1997).
A theoretical problem of sound scattering by turbulence was first formulated and generally solved by Obukhov in 1941, who applied the theory of locally isotropic turbulence
that he had developed together with Kolmogorov at that time. During the following two
decades the fundamental theory of sound wave scattering was independently developed in Russia by Obukhov (1943), Blokhintsev (1946a, 1946b), Tatarskii (1959, 1967),
Monin (1962), and in the USA by Pekeris (1947), Kraichnan (1953), Lighthill (1953),
Batchelor (1957).
The first time the term “sodar” acronym of sonic detection and ranging, appears in the
literature is in a paper by Gilman et al. (1946). In this paper, to study the radar signal
fading in particular atmospheric conditions an “acoustic radar” was realized that allowed them to correlate large acoustic echoes to the presence of thermal inversion and
radar signal fading. In this system the acoustic echo intensity was displayed by means
of an oscilloscope. By analyzing the same problem McAllister (1968) and McAllister et
al. (1969a, 1969b) carried out the prototype of the modern sodars: the key novelty of
the McAllister system is the facsimile recording of echo intensity that allows to have a
picture of the thermal structure of the ABL as well as the sonars trace of the sea bottom
on ships. Ever since, with the technology progress and the capability to measure in
real-time the wind profile and other quantities of geophysical interest, acoustic remote
sensing technique has increased in popularity also due to the relatively inexpensive
cost and its capability to continuously monitor the first 500-1000 m of the atmosphere
(Melas et al., 1998).
The theoretical and experimental papers of the 1960’s contained everything necessary
for performing acoustic sounding as a way of probing the lower troposphere. The deci-
6
sive step in this direction was made in 1969 by Little (1969) who generalized the experience gained by Russian, American and Australian researchers and analyzed systematically the potentialities of the new method. These works have been analyzed in
the perfect review by Brown and Hall (1978) and in the papers by Neff and Coulter
(1986), Singal (1988, 1990), Weill and Lehmann (1990) and Kallistratova (1994).
Kallistratova (1997), Kleppe (1997) and Melas et al. (1998) have described a brief history of acoustic sensing and its developments. Singal (1997) is just one of numerous
investigators, who showed the acoustic remote sensing applications. Moreover, Coulter
(1998) has explained the place of acoustic sensing in a high technology environment.
The development of basic physical concepts of influence of turbulent inhomogeneities
on acoustic wave propagation and scattering in the atmosphere was surveyed briefly
by Kallistratova (2000). However, the main theoretical and experimental results obtained per the last decades were summarized and the analysis of fundamental problems, requiring solution for practical applications of sound waves in the atmospheric
researches, was given.
Singal (2000) has introduced shortly a notice about the developments of the acoustic
sensing and the history of the International Society for Acoustic Remote Sensing (ISARS). However, for 20 years the biennial symposiums organized by the ISARS have
been held in different countries of the world. The role of ISRS symposiums in development of acoustic sounding of the atmosphere has been outlined by Kallistratova (2002).
2.2
Sodar studies of atmospheric stability
Pasquill (1962) divided the ABL into six categories of stability from A to F which can be
classified on the basis of data of surface wind speed, wind direction, daytime insulation,
nighttime sky conditions and temperature lapse rate etc. Singal et al. (1983, 1984, 1985
and 1990) developed an approach based on sodar echo patterns to classify Pasquill
stability categories. Using standard deviation of horizontal wind direction fluctuations to
represent the various stability categories, Singal et al. (1985) have worked out a
scheme to determine Pasquill stability categories based on different types of signatures
traced on sodar records under varying atmospheric conditions (Singal et al., 1994).
7
Singal (1993), has done a brief description of the remote sensing technique and a review of the work done during the last two decades to determine the various air quality
related to meteorological parameters. However, amongst the early works, Beran et al.
(1972) were the first to demonstrate the potential of the acoustic sounding device for
making continuous meso-scale measurements in critical air pollution situations. Subsequently, Tombach et al. (1973) showed relevance of the acoustic sounding technique to
obtain information on atmospheric stability. In this paper, he referred to the works done
to determine Pasquill stability category based on sodar data during this period.
Singal et al. (1997) explained the role of sodar in studying the characteristics of hazardous situations in air pollution and communication. This work also outlined the importance of atmospheric stability for air quality studies, as well as the role of sodar in determining the stability categories. Singal et al. (1997), has referred to the numerous
techniques which categorized Pasquill stability on the basis of meteorological measurements made close to the ground and by sodar.
Marzorati and Anfossi (1993) determined Pasquil stability categories from sodar data,
using a method proposed by Thomas (1986). However, in this paper, Thomas compared the standard deviations of the vertical wind angle [vertical angle = arctg(σw/vh);
where σw is the standard deviation of the vertical component of the wind speed and vh
is the horizontal wind speed] obtained by sodar, to the same values obtained by a vector vane. Capanni et al. (1999) as well as Capanni and Gualtieri (1999) used also the
same methods to do a classifying of the atmospheric stability. The results that they obtained, if one considers the period of the year, were reliable.
In the present study a method proposed by Thomas (1988) was used to determine the
Pasquill stability categories. Thomas (1988) used the standard deviation of the horizontal wind direction to determine the Pasquill stability categories. He found the correlation
between the values of the standard deviation of wind direction at the tower and by the
sodar increases with the wind speed and height of measurement.
Although, Thomas (1988) used the standard deviation of the wind direction obtained by
sodar to carry out the Pasquill stability classification. Best et al. (1986) found that the
use of the standard deviation of the wind direction for stability determination could be
misleading in all but very flat and uniform terrain. They preferred to use the turbulence
8
parameter, σw/vh, at Stanwell (Australia). Gland (1980) also considered using turbulence intensity parameter, σw/vh, for the stability classification. He, however, found
(Gland, 1981) that it was leading to unrealistic results in cases of weak wind associated
with strong atmospheric stability (Singal et al., 1997).
2.3
Turbulence of the atmospheric boundary layer
Beginning with the pioneering work of Osborne Reynolds (1876), meteorologists first
become interested in turbulence in 1915 (Taylor). They have reviewed the developments of the study of the turbulence and the important literatures. Panofsky and Dutton
(1984) and Garratt (1992) surveyed the history of atmospheric turbulence and ABL
studies. Here the recent important results through this time are summarized.
In the 1950s and into 1960s major advances took place in the ability to interpret observations in the understanding of the role of buoyancy in modifying the wind profile and in
modifying flux-gradient relations in general. This involved the surface-layer similarity
theory of Monin and Obukhov (1954) and ABL similarity theory of Kazanski and Monin
(1960, 1961). Many of the observations are associated with the major field experiments
of 1950s to 1970s. From the late 1960s to the present day, major advances in the
knowledge of ABL structure have taken place through the use of numerical modeling to
simulate the ABL, and the application of higher-order closure theory for representing
the effects of turbulence more realistically (Garratt, 1992).
Since the 1960s the rapid development of atmospheric instrumentation and computers
has made it possible to examine the characteristics of atmospheric turbulence in more
detail. The turbulence characteristics over a homogeneous surface are well understood
(Haugen, 1973; Panofsky and Dutton, 1984). Moreover, several models have been developed by Panofsky and Townsed (1964), Peterson (1969), Peterson et al. (1976) and
Højstrup (1981) to describe the development of wind profiles and surface stress profiles. However the study of turbulence parameters over complex surfaces (with varying
topography and roughness) helps in dealing with problems of wind energy conversion
system, pollutant transfer, etc (AL-Jiboori et al., 2001).
Zhang et al. (2001), have shown briefly the nature of the relationship between the normalized (by the friction velocity, u∗) standard deviation of the wind velocity component,
9
σu,v,w/u∗ and the stability parameter z/L (L: Monin-Obukhov length) under unstable conditions. However, under unstable conditions, the normalized standard deviations of
horizontal velocity, σu,v/u∗ follow the similarity hypotheses (Roth, 1993):
σ u ,v
u*
= 2.5(1 − 1.6 L)
1
3
(2.1)
Experimental data from the homogeneous surface layer of the horizontal wind component are usually less supportive of the Monin-Obukhov similarity prediction and it is often argued and also observed that u and v scales can be better fitted with mixed-layer
variables. It is often unclear whether z or zi is the better scaling variable (Roth, 1993).
Panofsky and Dotton (1984) showed that σu,v/u∗ scale with zi/L rather than with z/L and
suggested that (under unstable conditions):
σ u ,v
u*
1
z
= (12 − 0.5 i ) 3
L
(2.2)
Also, the analysis from large-eddy simulations shows that the horizontal wind components scale with zi, and not with z (Khanna and Brasseur, 1998). Although, the values
of zi affect σu,v/u∗ in unstable conditions, the values of σu,v/u∗ are almost constant and
not influenced by zi in near neutral conditions. The relationship between the normalized
standard deviations of horizontal velocity σu,v/u∗ and stability z/L may involve the surface roughness as well.
The relationship between the normalized standard deviations of vertical velocity σw/u∗
and stability z/L shows a similar form over homogeneous surfaces (under unstable
conditions), as given in (Panofsky et al., 1977):
σw
1
z
= 1.3(1 − 3 ) 3
u*
L
(2.3)
The result over a suburban surface condition from Roth (1993) is similar to this equation but the empirical constants are slightly different:
σw
1
z
= 1.2(1 − 2.5 ) 3
u*
L
(2.4)
10
Meanwhile, Roth (1993) quoted other reports to prove this equation and pointed out
that the relationship between the normalized standard deviations of vertical velocity
σw/u∗ and stability z/L varies with observation site. Roth (1993) and Yersel and Goble
(1986) showed that the normalized standard deviations decrease with an increase of
the roughness length z0 and that the influence of roughness on horizontal components
of wind deviations is larger than that on the vertical component.
In the last years, few articles have appeared comparing behavior of the turbulence parameters over different land use types (e.g. Zhang et al., 2001; AL-Jiboori et al., 2001).
However, Zhang et al. (2001) have surveyed the developments of the relationship between σu/u∗, σv/u∗ and σw/u∗, and the stability parameter z/L under the unstable conditions. Furthermore, they have done a comprehensive study of this relationship under
unstable conditions over a desert, grassland, suburban and urban sites. The turbulence
data was measured at the four sites with the same instrumentation (sonic anemometerthermometer), but the observational periods and measurements heights are different.
This study indicated that under unstable conditions, the normalized standard deviation
of the wind velocity components (σu/u∗, σv/u∗ and σw/u∗) are functions of (z/L)1/3.
In addition, AL-Jiboori et al. (2001) have studied the characteristics of the atmospheric
turbulence over flat and complex terrain for various fetch conditions arising under various wind directions, and different atmospheric stability. In this study a sonic anemometer-thermometer was used. However, they compared the results with those reported by
Miyake et al. (1970), Kaimal et al. (1972), Bradley (1980), Panofsky et al. (1977) and
Xu et al. (1993). These studies indicated that, in unstable conditions, the normalized
standard deviation of the wind velocity components (σu/u∗, σv/u∗ and σw/u∗) were functions of (z/L)1/3. The study of AL-Jiboori et al. (2001) referred to the strong dependence
of the characteristics of turbulence on the upwind change of roughness of the surface.
Moreover the values of σu/u∗ and σv/u∗ were strongly affected by the change in the surface roughness, while that for vertical velocity (σw/u∗) was almost not influenced.
11
3
OBJECTIVES AND APPLICATIONS OF THE PRESENT STUDY
The turbulence characteristics in the surface layer over flat, homogeneous surface and
under various atmospheric stratifications are well understood (Kaimal et al., 1972; Roth
and Oke, 1993). Since the 1960s several models were developed to describe the modification of wind profiles and surface stress profiles downstream a change in surface
roughness from a smooth to a rough surface (Panofsky and Townsend, 1964; Peterson, 1969; Peterson et al., 1976; Højstrup, 1981). The study of turbulence parameters
over complex surfaces (heterogeneous topography and roughness) has special features in dealing with problems of wind energy conversion system, pollutant transfer, etc
(AL-Jiboori et al., 2001).
Until now there are few studies comparing the behavior of turbulence parameters over
different land use types (e.g. AL-Jiboori et al., 2001 ; Zhang et al., 2001). Both studies
used a three-dimensional sonic anemometer-thermometer instrument (Kaijo-Denki Dat300, path 0.2 m). In the first study, AL-Jiboori et al. (2001), the instrument was installed
on mast of height 4.9 m above the ground on August 16, 1992. The observation duration for each run was half an hour. The experimental site is located in a Gobi Desert
(west China) and surrounded by different topography. Under south to northwest wind
direction, conditions can be considered as being locally flat terrain, while for the other
wind directions it should be regarded as complex. In the second one, Zhang et al.
(2001), the instruments were installed in the same way at the four experimental sites
(desert, grassland, suburban and urban) but the observational periods and the measurement height were different. The measurement heights at the four sites were 4.9,
3.45, 75.0 and 47.0 m a.g.l. for the periods Aug.6-17.1992, Aug. 13-19, 1993, Sept.214, 1994 and May 13-27,1993 respectively.
In this study a Scintec FAS64 sodar was used to investigate turbulence characteristics
in the ABL over different land use types. However, with some limitations due to incomplete coverage of the full ABL extension and sometimes to the acoustic pollution, the
acoustic remote sensing represents a powerful, relatively cheap technique for ABL investigations (Melas et al., 1998).
Hence a need for these studies was given to enrich the knowledge of the characteristics of the turbulence over the study areas and to detect and quantify the impact of for-
12
ested, urban, and agricultural land use type on the structure of ABL. Forests and urban
areas are associated with comparatively high values of aerodynamic roughness.
Among all types of surfaces, aerodynamic roughness of urban is almost constant.
Aerodynamic surface roughness of forests shows a short-term dependence on growth
dynamics. In contrast to that, aerodynamic surface roughness of agricultural areas is
smaller and has an annual pattern which depends on plant growth.
In addition air pollution control needs the information on parameters of the ABL, with
impact on accumulation, dispersion and transport of pollutants (Pekour et al., 1993).
3.1
Necessity of the present study
During a weak advection, the nature of convection and turbulence is controlled by wind
speed, incoming solar radiation (insulation), cloud shading and time of day or night.
Pasquill and Gifford suggested a practical way to estimate the nature of convection,
based on these forcings (Stull, 2000). Hence a better knowledge about these parameters is significant in order to understand the nature of the turbulence in the ABL. In addition, in this study a particular attention will be given to the variance of the horizontal
wind speed σ2h and the variance of the vertical wind speed component σ2w, because
the velocity variances represent the turbulent kinetic energy per unit mass (TKE) and a
measure of the intensity of turbulence (Stull, 2000).
However the stability classification of the atmosphere is the first step to applying a
number of traditional algorithms aiming at estimating the main atmospheric parameters
which typically describe the ABL structure such as Monin-Obukhov length, friction velocity and the ABL height (Capanni and Gualtieri, 1999). A method, starting from sodar
data only, is applied to determine the P-G stability classes. However many authors
used the sodar to determine the atmospheric stability. Section (2.2) explained a literature review about the use of sodar to determine P-G stability classes. This method is
the one proposed by Thomas (1988). He used σdd to determine the P-G stability
classes. Section (5.3) explains the algorithms necessary for calculating the parameters
which are used in this study such as Monin-Obukhov length (L), friction velocity (u∗),
convective velocity (w∗), turbulent kinetic energy per unit mass (TKE), mean kinetic energy per unit mass (MKE), production of turbulent kinetic energy of convective and me-
13
chanical origin (σ3w/z) and turbulence intensity components for longitudinal, lateral and
vertical wind speed components (Iu, Iv, Iw respectively).
3.2
Objectives of the present study
This work focuses on the study of characteristics of turbulence of the ABL over the different land use types grassland, vineyard, forest and urban area. But the main purpose
of this study is to analyze the influence of thermal and roughness changes on properties of turbulence within the ABL over these land use types. The following investigations are necessary to fulfill the objectives of this work:
∗∗
determination of characteristics of vertical profiles and diurnal courses (at different heights a.g.l.) of σ3w/z, MKE and TKE under various sky conditions within the
areas of investigation,
∗∗
performing a comparative study between the mid-day hours and midnight hours
averages of σ3w/z, MKE, and TKE on cloudless and cloudy days within the areas
of investigation,
∗∗
determination of characteristics of the turbulence intensity components over the
study areas during the study periods as experienced for various fetch conditions
arising under various wind directions and different atmospheric stability at different levels,
∗∗
analysis of mean values of the normalized standard deviations of the wind speed
components, σi/u∗ (i=u,v,w), as functions of the stability parameter (z/L) under
unstable conditions in the surface layer,
∗∗
comparison of the mean values of σu/u∗, σv/u∗ and σw/u∗ in the range of -z/L from
0.86 to 3.66 in the surface layer over different land use types with some previous
studies at flat and complex terrain,
∗∗
analysis of vertical profiles of the normalized values σ2w/w∗2.
14
3.3
Application of the present work
The ABL plays an important role in many fields such as air pollution, dispersal of pollutants, agricultural meteorology, hydrology, aeronautical meteorology, mesoscale meteorology, weather forecasting and climate (Garratt, 1992). The investigation of the atmospheric processes affecting transport and removal of pollutants in the ABL is generally performed with models. The quality of the models is strongly influenced by their
meteorological input. Therefore, the meteorological input has to comprise the meteorological factors that have a direct effect on the dispersion of a pollutant that is emitted
into the atmosphere. Here some of these factors are summarized (Melas et al, 1998):
wind (determines where the pollutant goes and how fast), atmospheric turbulence (determines turbulent dispersion) and air temperature (affects the rise of a buoyant plume).
A few of the problems are summarized for which the knowledge of characteristics of
turbulence within the ABL is important (Garratt, 1992):
∗∗
The control and management of air quality is closely associated with the transport and dispersal of atmospheric pollutants. In this field, the research on the
atmospheric turbulent is very important.
∗∗
Urban meteorology is associated with low-level urban environment and air pollution including air pollution episodes, photochemical smog and accidental releases of dangerous gases. The dispersal of smog and low-level pollutant depends strongly on meteorological conditions.
∗∗
Agricultural meteorological and hydrology are concerned with processes such as
dry deposition of natural gases and pollutants to crops, evaporation, dewfall and
frost formation. The last three are intimately associated with the state of the
ABL, with the intensity of turbulence and with the energy balance at the surface.
∗∗
The wind shears in the lower part of ABL can be dangerous for landing and
taken-off of heavy aircrafts. So information on wind conditions and also turbulence in the ABL are of great importance to air traffic safety (Kallistratova, 1997).
∗∗
Numerical weather predication (NWP) and climate simulation based on dynamical models of the atmosphere depend on the realistic representation of the
Earth’s surface and the major physical processes occurring in the atmosphere. It
15
has been said that no general circulation model is conceptually complete without
the inclusion of ABL effects (Stewart, 1979), and that no predication model can
succeed without a sufficiently accurate inclusion of the influence of the boundary.
∗∗
In the last years, the need to develop new sources of energy has largely increased
in order to solve a part of the energy demand problem. The wind is one of the energy sources which reduce the environmental pollution and the costs associated.
In addition, it represents one of the most promising renewable source of energy.
For these applications, not only a good and accurate knowledge of the wind data
are required but also the investigation of the turbulence intensity is necessary for
the design of these systems (Axel and Klug, 1995; van Dam and Werkhoven,
1999).
16
4
THEORETICAL CONCEPTS
4.1
Atmospheric boundary layer
The troposphere extends from the ground up to an average altitude of 11km, but often
only the lowest couple of kilometers are directly modified by the underlying surface.
The earth’s surface is a boundary on the domain of the atmosphere (Ahrens, 1994).
Transport processes at this boundary modify the lowest 100 to 3000 m of the atmosphere, creating what is called the ABL Fig. 4.1. The remainder of the air in the troposphere is loosely called the free atmosphere (Stull, 1988).
It responds to surface forcings with a timescale of about an hour or less. These forcings
include the frictional drag, evaporation and transpiration, heat transfer, pollutant emission, and terrain induced flow modification.
Fig. 4.1:
Location of the ABL (Stull, 2000)
The diurnal variation of temperature near the ground is one of the key characteristics of
the ABL over land. The diurnal variation is not caused by direct forcing of solar radiation on the ABL. Little solar radiation is absorbed in the ABL; most is transmitted to the
ground where typical absorptivities on the order of 90% result in absorption of much of
the solar energy. It is the ground that warms and cools in response to the radiation,
which in turn forces changes in the ABL via transport processes. The role of the ABL
on the human life is put into perspective when the characteristics of the ABL and free
atmosphere are compared. Its processes influence the human life directly and indirectly
via its influence on the rest of the weather (Stull, 1988).
17
4.1.1
Wind and flow
Air flow, or wind, can be divided into three broad categories: mean wind, turbulence,
and waves (Fig. 4.2). Each can exist separately, or in the presence of any of the others.
Each can exist in the ABL, where transport of quantities such as moisture, heat, momentum, and pollutants is dominated in the horizontal by the mean wind, and in the
vertical by turbulence (Stull, 1988).
Fig. 4.2:
Idealization of (a) mean wind alone, (b) waves alone, and (c) turbulence
alone. In reality waves or turbulence are often superimposed on a mean
wind. u is the component of wind in the x-direction (after Stull, 1988)
Mean wind is responsible for very rapid horizontal transport, or advection. Horizontal
winds of the order of 2 to 10 m/s are common in the ABL. Friction causes the mean
wind speed to be slowest near the ground. Vertical mean winds are much smaller, usually on the order of millimeters to centimeters per second.
Waves, which are frequently observed in the night time ABL, transport little heat, humidity, and other scalars such as pollutants. They are, however, effective at transporting momentum and energy. These waves can be generated locally by mean wind
shears, such as thunderstorm or an explosion.
The relatively high frequency of occurrence of turbulence near the ground is one of the
characteristics that make the ABL different from the rest of the atmosphere. Outside the
ABL, turbulence is primarily found in convective clouds, and near the jet stream where
strong wind shears can create clear air turbulent.
18
There is an easy way to isolate the large-scale variations from the turbulent ones. By
averaging wind speed measurements over a period of 30 minutes to one hour, the
positive and negative deviations of the turbulent velocities about the mean can be
eliminated or “averaged out”. Knowing the mean velocity, u, for any time period, it can
be subtracted from the actual instantaneous velocity, u`, to give just the turbulent part
(u`-u). The term u`-u can be illustrated as the gust that is superimposed on the mean
wind. It represents the part of flow that varies with periods shorter than about one hour.
The mean, u, represents the part that varies with a period longer than about one hour
(Stull, 1988).
4.1.2
Turbulence
Turbulence may be regarded as a complex assembly of locally organized but unsteady
velocity patterns which interact strongly with each other as they move with the flow.
Thus turbulence is a random, three-dimensional state of motion which is characterized
by high degree of chaotic velocity. Unstable and stable flows tend to remain in the
same state unless there is an imbalance between the paired destabilizing and stabilizing force acting on the flow. If the net effect of destabilizing factor is more than the net
effect of stabilizing factor, then turbulence will occur. It is governed mainly by the nonlinear terms of the equation of motion with strong interaction between motion on different spatial and temporal scales. Only statistical average correlated in time and space
describe turbulence. Turbulence structure is considered to be made up of eddies of
various sizes which interact with each other and with the mean flow. The eddy interaction cascades the energy to smaller and smaller eddy sizes until the energy is essentially lost by the action of viscosity. Thus turbulence is dissipative and diffusive in character to a high enough degree which cannot be accounted for by the molecular diffusivities and the mean strain rate. The diameter of eddies whose influence is predominant under any conditions roughly defines the scale of turbulence. There are two major
types of turbulence in the ABL; mechanical due to the instability of the vertical wind
shear and thermal due to the buoyancy forces in the atmosphere. The combination of
wind and temperature stratification, therefore, plays an important role in characterizing
the stability of the atmosphere and the generation and nature of turbulence (Singal et
al., 1997).
19
In the atmosphere, the flow near the ground is almost always turbulent up to a height 1
km or more in the daytime over land, to 100 m or so over land at night, and to a few
hundred meters over the ocean. At larger heights, turbulence occurs in the cumulus
clouds and in layers with strong changes in average wind speed or direction (Panofsky
and Dutton, 1984).
Here the three reasons can be formally listed why atmospheric scientists and engineers
are concerned with the properties of turbulence; turbulence imposes forces on buildings, bridges, towers, airplanes, and other structures; turbulence mixes air with different
properties and creates fluxes of important physical quantities, and turbulence creates
spatial and temporal variations of refractive index and thus leads to scattering of electromagnetic and acoustic radiation (Panofsky and Dutton, 1984).
4.1.2.1
Turbulence kinetic energy
Generally, the usual definition of kinetic energy (KE) is KE=0.5 m M2 (kg m2/s2), where
m is mass (kg) and M is the magnitude of wind (m/s). When dealing with a fluid such as
air it is more convenient to talk about kinetic energy per unit mass, which is just 0.5M2
(Stull, 1988).
It is enticing to partition the kinetic energy of the flow into a portion associated with the
mean wind, and a portion associated with turbulence. By taking the advantage of the
mean and turbulent parts of velocity, as reported in section (4.1.1), the equations of the
mean kinetic energy per unit mass (MKE, m2/s2) and the turbulence kinetic energy per
unit mass (TKE, m2/s2) can be immediately written. Moreover, the energy that is mechanically produced as turbulence is lost from the mean flow, and vice versa (Stull,
1988).
(
MKE =
1 2
u + v 2 + w2
2
TKE =
1 2
σ u + σ v2 + σ w2
2
(
)
(4.1)
)
(4.2)
where σ2u , σ2v and σ2w (m2/s2) are the variances of the wind velocity components in
the east (u), north (v) and vertical (w) directions (m/s) respectively.
20
TKE is one of the most important variables in micrometeorology, because it is a measure of the intensity of turbulence. It is directly related to the momentum, heat and moisture transport through the ABL (Stull, 1988).
The tendency of TKE to increase or decrease is given by the following TKE budget
equation (Stull, 2000):
∆TKE
= A + S + B + Tr − ε
∆t
(4.3)
where
A:
advection of TKE by the mean wind (m2/s3),
S:
shear generation (m2/s3),
B:
buoyant production or consumption (m2/s3),
Tr:
transport by turbulent motions and pressure (m2/s3),
ε:
viscous dissipation rate (m2/s3).
The individual terms in the TKE budget equation describe physical processes that generate turbulence. The relative balance of these processes determines the ability of the
flow to maintain turbulence or become turbulent, and indicates flow stability (Stull,
1988)
Mean wind blows TKE from one location to another. The advection term is given by:
A = −u
∆TKE
∆TKE
∆TKE
−v
−w
∆x
∆y
∆z
(4.4)
Thus, turbulence can increase (or decrease) at any location if the wind is blowing in
higher (or lower) values of TKE from somewhere else.
Wind shear generates turbulence near the ground according to:
S = u*2
∆M
∆z
In the surface layer, where u* is the friction velocity (m/s), and
(1/s). To good approximation:
(4.5)
∆M
is the wind shear
∆z
21
S ≈ aM 3
(4.6)
where a ≅ 2∗10-5 m-1 for wind speed measured at standard height of z =10 m above the
ground. Greater wind speeds at near the ground cause greater wind shear, and generate more turbulence.
Buoyancy can either increase or decrease turbulence. When thermals are rising from a
warm surface, they generate TKE. Conversely, when the ground is cold and the ABL is
statically stable, buoyancy opposes vertical motion and consumes TKE. The rate of
buoyant production or consumption of TKE is:
B=
g
H0
Tv
(4.7)
where
g:
acceleration due to gravity (m/s2),
H 0:
kinematic surface heat flux (positive when the ground is warmer than the air)
(K.m/s). Over land, H0 and B are usually positive during the daytime, and negative at night.
Tv:
absolute virtual air temperature near the ground (K).
Turbulence can advect or transport itself. For example, if turbulence is produced by
shear near the ground (in the surface layer), then turbulence motions will tend to move
the excess TKE from the surface layer to location higher in the ABL. Pressure fluctuations can have a similar effect, because turbulent pressure forces can generate turbulence motions. These terms are here grouped with the turbulent transport term, Tr.
Molecular viscosity dissipates turbulent motions into heat. The amount of heating is
small, but the amount of damping of TKE is large. The dissipation is always a loss:
3
TKE 2
ε≈
Lε
(4.8)
where Lε is a dissipation length scale (m).
The ratio of buoyancy to shear terms of TKE equation is called the flux Richardson
number, Rf, which is approximately equal to the gradient or bulk Richardson number:
22
Rf =
− B − ( g / Tv ) H 0 − ( g / Tv ) H 0
≈
≈
∆M
S
aM 3
u
∆z
4.1.2.2
(4.9)
Turbulence intensity
Generally, the standard deviation can be interpreted as a measure of magnitude of the
spread or dispersion of the original data from its mean. For this reason, it is used as a
measure of the intensity of turbulence. Near the ground, the turbulence intensity might
be expected to increase as the mean wind speed, M, increases. For this reason a dimensionless measure of the turbulence intensity, I, is often defined as (Stull, 1988):
I=
σM
(4.10)
M
where σM is the standard deviation and M the average of M (m/s). For mechanically
generated turbulence, one might expect σM to be a simple function of M.
The wind profile in general can be given by (Yersel and Goble, 1986):
M ( z) =
u*
z
z
[ln − ψ ( )]
k
z0
L
(4.11)
where k is von Kármán constant and ψ is some function of z/L.
The turbulence intensities may then be expressed as:
I=
kσ M
z
z
u*[ln − ψ ( )]
z0
L
(4.12)
In line with section 4.1.2.1, the standard deviations of the wind speed components, σi
(i=u,v,w), are intimately related to the turbulent kinetic energy, it is to be anticipated that
the intensity of turbulence should be related to the processes generating this energy.
Richardson (1920) shows these to be mainly shearing stresses and buoyancy forces.
The shearing stresses are to a large degree functions of surface roughness, which may
be taking as dependent on wind direction (Brook, 1972).
From equation (4.12), the nature of turbulence intensity depends on the height of observation, the surface roughness and the atmospheric stability (Roth, 1993). But at
23
near-neutral condition as z/L → 0, the turbulence intensity components are function of z
and z0 (Yersel and Goble, 1986).
The turbulence intensity components are defined as the ratio of the standard deviations
of the respective wind component to the mean wind speed, namely, the turbulence intensity components for the along-wind (Iu), crosswind (Iv) and the vertical (Iw) wind
components are given by (Roth, 1993);
Iu =
σu
M
4.1.2.3
,
Iv =
σv
M
and I w =
σw
M
(4.13)
Free and forced convection
The nature of turbulence, and therefore the nature of pollutant dispersion, changes with
the relative magnitudes of terms in the TKE budget. Two terms of interest are the shear
S and buoyancy B terms (Stull, 2000).
When B < S / 3 , the atmosphere is said to be in a state of forced convection (Fig. 4.3).
These conditions are typical of windy overcast days, and are associated with near neutral static stability. Turbulence is nearly isotropic. Smoke plumes disperse at nearly
equal rates in the vertical and lateral, which is called coning. The sign of B is not important here- only the magnitude.
When B is positive and B > 3S , the atmosphere is said to be in a state of free convection. Thermals are typical in this situation, and the ABL is statically unstable. These
conditions often happen in the daytime over land, and during periods of cold-air advection over warmer surfaces. Turbulence is anisotropic, with more energy in the vertical,
and smoke plumes loop up and down in a pattern called looping.
When B is negative and B > S , static stability is so strong that turbulence cannot exist. During these conditions, there is virtually no dispersion while the smoke blows
downwind. Buoyancy waves (gravity waves) are possible, and appear as waves in the
smoke plumes. For values of B ≅ S , breaking Kelvin-Helmholtz waves can occur,
which cause some dispersion.
24
When B is negative but B < S , weak turbulence is possible. These conditions can
occur at night. This is sometimes called stably stratified turbulence (SST). Vertical dispersion is much weaker than lateral, causing an anisotropic condition where smoke
spreads more horizontally than vertically, in a process called fanning.
Fig. 4.3 shows the relationship between different types of convection and the terms of
TKE equation. While the ratio of B to S determines the nature of convection, the sum
S+B determines the intensity of turbulence. A Pasquill-Gifford turbulence type (Fig. 4.3)
can also be defined from the relative magnitudes of S and B. They use the letters “A”
through “F” to denote different turbulence types, as sketched in Fig. 4.3. “A” denotes
free convection in statically unstable conditions. “D” is forced convection in statically
neutral conditions. Type “F” is for statically stable turbulence. Type “G” was added later
to indicate meandering, wavy plumes in otherwise-nonturbulent flow.
Fig. 4.3:
Rate of generation of TKE by buoyancy (abscissa) and shear (ordinate).
Shape and rates of plume dispersion (dark spots or waves). Dashed lines
separate sectors of different Pasquill-Gifford turbulence type. Isopleths of
TKE intensity (dark diagonal lines). Rf is flux Richardson number. SST is
stably stratified turbulence (after Stull, 2000)
25
4.1.3
Depth and structure of the atmospheric boundary layer
The depth of ABL depends on many factors including surface character, time of day,
atmospheric stability (e.g. the type of air mass), and insulation of the surface. In low
pressure regions the upward motions carry boundary-layer air away from the ground to
large altitudes throughout the troposphere. It is difficult to define a boundary-layer top
for these situations. Cloud base is often used as an arbitrary cut-off for the ABL studies
in these cases. Thus the region studies by ABL meteorologists may actually be thinner
in low-pressure regions than in high-pressure ones. But over land surfaces in highpressure regions the ABL has a well-defined structure that evolves with the diurnal cycle. The three major components of this structure are the mixed layer, the residual
layer, and the stable ABL. When clouds are present in the mixed layer, it is further subdivided into a cloud layer and subcloud layer Fig. 4.4 (Stull, 1988).
The surface layer is the region at the bottom of the ABL where turbulent fluxes and
stress vary by less than 10% of their magnitude. Thus, the bottom 10% of the ABL is
called the surface layer, regardless of whether it is part of a mixed layer or stable ABL.
Finally, a thin layer called a micrometer or interfacial layer has been identified in the
lowest centimeters of air, where molecular transport dominates over turbulence transport. For more details about the structure of the ABL, see Stull (1988).
The thickness of the ABL can be characterised in a number of ways. First, the depth of
the ABL can be defined by h, the thickness of the turbulent region next to the ground.
This is also called the depth of the mixed layer or the mixing depth, since atmospheric
properties are well mixed within it (Panofsky and Dutton, 1984).
Another height used to describe the thickness of the ABL in the daytime or at night over
heated surfaces is the height zi of the lowest inversion. Roughly, h and zi are the same
at the daytime. Actually, however, h tends to be 10% or so larger than zi, because the
lowest part of the inversion is still turbulent, partly because of the overshooting from
below and partly because there is often strong wind shear in the inversion (Panofsky
and Dutton, 1984).
At night, an inversion often extends to the ground, because the ground cools rapidly by
emitting infrared radiation (IR). When the wind is strong, mechanical turbulence is created and heat is lost to the ground by turbulent mixing through the ABL. However, on
26
clear nights with weak winds, only the bottom of the ABL is turbulent. The upper part
cools by divergence of flux of infrared radiation (IR). Under such conditions, the mixing
depth h (the turbulent region) and the ABL depth zi (the top of the cooled region) may
be very different from each other (note that zi is now the top of the ground-based inversion) (Panofsky and Dutton, 1984). For more details about the mixing depth and its
definitions see Beyrich (1996, 1997a), Seibert et al. (1996, 1998, 2000) and Gryning et
al. (1997).
Fig. 4.4:
The ABL in high pressure regions over land consists of three major parts:
a very turbulent mixed layer, a less-turbulent residual layer containing
former mixed layer air, and a nocturnal stable boundary layer of sporadic
turbulence (after Stull, 1988)
4.1.3.1
Mixed layer
The convective atmosphere constitutes the daytime unstable ABL. It consists of thermal plumes i.e. updrafts surrounded by large downdrafts. They grow in the morning
with the solar heating of the surface of the earth, become maximum up to a height of 12 km around midday and decrease in the afternoon (Singal et al., 1997).
27
After Driedonks and Tennekes (1984), three layers can be identified within the convective boundary layer as shown in Fig. 4.4 (Stull, 1988):
∗∗
the surface layer in the bottom 5 to 10%,
∗∗
the mixed layer (ML) composing the middle 35 to 80%,
∗∗
the entrainment zone in the top 10 to 60%.
In the unstable surface layer there are small-scale structures such as buoyant vertical
plumes, convergence lines, sheets of rising air, and dust devils. Higher in the mixed
layer, larger-diameter thermals, horizontal roll vortices, and mesoscale cellular convection patterns are observed. In the entrainment zone at the top of the mixed layer, these
are intermittent turbulence, overshooting thermals, Kelvin-Helmholtz waves, internal
gravity waves, and sometimes clouds. Often the whole convective ABL is called the
mixed layer. The mixed layer is so named because intense vertical mixing tends to
leave conserved variables such as potential temperature and humidity nearly constant
with height. Sometimes the mixed layer is called the well-mixed layer (Stull, 1988).
Mixing can be generated mechanically by shears, or convectively by buoyancy. Buoyantly generated MLs tends to be more uniformly mixed than ones driven mechanically,
because anisotropy in convection favors vertical motions, while shear anisotropy favours horizontal motions. Shears near the ground are usually more important for generating mixing than shears across the top of the ML, for atmospheric situations. Shears
at the ML top, however, can cause a separate layer to form. A mixed layer dominated
by buoyant turbulence generation is called a convective boundary layer (CBL) or convective mixed layer (Stull, 1988).
During the early morning the mixed layer is shallow, starting with a depth on the order
of tens of meters for calm situations to the depth of a couple of hundred meters for
windier situations. By the late morning, for many cases, the cool nocturnal air warms to
a temperature near that of the residual layer, and the top of the ML moves up to the
residual layer base. When the thermals reach the capping inversion at the top of the
residual layer, they meet resistance to vertical motion again and the ML growth rate
rabidly decrease (Stull, 1988). At the sunset, the generation rate of the convective turbulence decrease to the point where turbulence cannot be maintained against dissipation (Nieuwstadt and Brost, 1986). In the absence of the mechanical forcings, turbu-
28
lence in the ML decays completely, causing us to reclassify that layer as a residual
layer. Temperature fluctuations decay the fastest, while turbulence kinetic energy decays more slowly. During this decay process the last few weak thermals may still be
rising in the upper part of the ML and can still cause entrainment, while the surface
layer has already become stably stratified (Stull and Driedonks, 1987).
4.1.3.2
Residual layer
About a half hour before sunset the thermals cease to form (in the absence of cold air
advection), allowing turbulence to decay in the formerly well-mixed layer. The resulting
layer of air is sometimes called residual layer because its initial mean state variables
and concentration variables are the same those of the recently decayed mixed layer.
Non-passive pollutants may react with other constituents during the night to create
compounds that were not originally emitted from the ground. Sometimes gaseous
chemicals may react to form aerosols or particulates which can precipitate out. The
Residual layer (RL) often exists for a while in the mornings being entrained into the ML.
During this time solar radiation may trigger photochemical reactions among the constituents in the RL. Variables such as virtual potential temperature usually decrease
slowly during the night because of radiation divergence (Stull, 1988).
The RL does not have direct contact with the ground. During the night, the nocturnal
stable layer gradually increases in thickness by modifying the bottom of the RL. Thus,
the remainder of the RL is not affected by turbulent transport of surface-related properties and hence does not really fall within the definition of ABL (Stull, 1988).
4.1.3.3
Stable boundary layer
As the night progresses, the bottom portion of the residual layer is transformed by its
contact with the ground into a stable boundary layer. The ABL can become stably
stratified whenever the surface is colder than the air. This stable boundary layer (SBL)
often forms at night over land, where it is known as a nocturnal boundary layer (NBL). It
also forms by advection of warmer air over a cooler surface. This layer is characterized
by statically stable air with weaker, sporadic turbulence. Although the wind at ground
level frequently becomes lighter or calm at night, the winds aloft may accelerate to su-
29
pergeostrophic speeds in a phenomenon that is called the low-level jet or nocturnal jet.
The statically stable air tends to suppress turbulence, while the developing nocturnal jet
enhances wind shears that tend to generate turbulence. As a result, turbulence sometimes occurs in relatively short bursts that can cause mixing throughout the SBL. During the nonturbulent periods, the flow becomes essentially decoupled from the surface
(Stull, 1988).
As opposed to the daytime ML which has a clearly defined top, the SBL has a poorly
defined top that smoothly blends into the RL above. The top of the ML is defined as the
base of stable layer, while the SBL top is defined as the top of the stable layer or the
height where turbulence intensity is a small fraction of its surface value. SBLs can also
form during the day, as long as the underlying surface is colder than the air. These
situations often occur during warm-air advection over a colder surface, such as after a
warm frontal passage or near shorelines (Stull, 1988).
4.1.4
Atmospheric stability
Unstable flows become or remain turbulent. Stable flows become or remain laminar.
There are many factors that can cause laminar flow to become turbulent, and other factors that tend to stabilize flows. If the net effect of all the destabilizing factors exceeds
the net effect of the stabilizing factors, then turbulence will occur. These factors can be
interpreted as terms in the turbulence kinetic energy budget equation. To simplify the
concept of the atmospheric stability, investigators have historically paired one destabilizing factor with one stabilizing factor, and expressed these factors as a dimensionless
ratio. Some other stability parameters such as static stability are not expressed in dimensionless form (Stull, 1988).
The stability is static, if it does not depend on wind but it is a measure of capability for
buoyant convection. In this case, it is determined by the local lapse rate. Even if the air
is statically stable, wind shears may be able to generate turbulence dynamically. This is
called dynamic stability (Stull, 1988).
In the ABL the air flow is turbulent because of two different mechanisms: friction with
the surface and surface heating by the sun. The airflow follows the non-slip condition at
the surface. The result is a vertical velocity gradient (wind shear). Turbulence is gener-
30
ated and energy from the mean shear is obtained. The resulting turbulent atmospheric
flow is called a mechanically generated flow (or neutral condition). On the other hand,
at daytime, the sun warms up the earth surface and the heat is molecularly transferred
to the first few centimeters of air above the ground and then further transported by turbulence processes. A positive vertical temperature gradient develops and results in
vertical acceleration of air parcels (thermals). The resulting turbulent atmospheric flow
is called a buoyancy generated flow (or unstable condition). Rise of a thermal depends
whether the parcel of air is less dense than the surrounding. But, at nighttime, before
the sunset the soil starts to release heat by long wave radiation and becomes cooler
than the overlaying air. In this way vertical upward motions are suppressed. The resulting atmospheric flow is called stable (Melas et al., 1998).
Atmospheric stability can be characterized by several methods or parameters (Zannetti,
1990):
∗∗
empirical methods, such as the Pasquill and Turner methods,
∗∗
Monin-Obukhov length L (1/L < 0 for unstable conditions, ≅0 for neutral conditions, and > 0 for stable conditions),
∗∗
Richardson number Ri, the ratio of the rate of dissipation (or production) of turbulence by buoyancy to the rate of creation of turbulence by shear (Ri < 0 for
unstable conditions, Ri = 0 for neutral conditions, and Ri > 0 for stable conditions).
4.1.5
Micrometeorological variables
4.1.5.1
Friction velocity
Friction velocity as one of the fundamental scaling parameters of boundary-layer meteorology is not uniquely defined in the literature. A survey of several textbooks on meteorology and of some recent research articles on ABL meteorology was made by Weber
(1999) to show the different definitions of friction velocity.
Since turbulence is often generated by wind shear at the base of the ABL, the magnitude of the Reynolds’ stress (turbulent momentum flux) in the surface layer turns out to
be very important. The Reynolds’ stress ( τ , kg/ms2) is given by:
31
{
2
2
s
2
s
}
1
2
τ = − ρ (u´w´ + v´w´ )
(4.14)
where ρ is the average density of air (in kg/m3), u´, v´ and w´ are Cartesian components of instantaneous wind (in m/s) and the subscript "s" denotes a quantity measured
at the surface.
This magnitude of Reynolds’ stress is used to calculate a natural velocity scale, the
friction velocity (u∗). The friction velocity gives a measure of the vertical kinematic flux
of the horizontal momentum in the surface layer. When horizontal winds flow over
roughness elements protruding from a surface, drag slows wind speeds near the surface relative to those aloft, creating vertical wind shear. Wind shear produces eddies
that exchange momentum, energy, gases, and aerosols vertically. The greater the
height, the roughness elements protrude from a surface, and the greater the horizontal
wind speed, the greater the resulting wind shear and the mechanical turbulence. The
greater the mechanical turbulence, the greater is friction velocity, and the faster momentum, energy, and pollutants from aloft are mixed with surface air. Typical roughness elements at the surface include rocks, trees, buildings, grass, and sand. The friction velocity, can be parameterized or found from the following (Jacobson, 1999):
{
2
2
s
2
s
} = τρ
u = − ρ (u´w´ + v´w´ )
2
*
4.1.5.2
1
2
(4.15)
Monin-Obukhov length
The Monin-Obukhov length L is a parameter that characterizes the stability of the surface layer and is calculated from ground-level measurements. It is computed from
(Stull, 2000):
L=−
u*3
g
k ( )H0
Tv
where:
g:
acceleration due to gravity,
(4.16)
32
H 0:
kinematic surface heat flux (positive when the ground is warmer than the air),
Tv:
absolute virtual air temperature near the ground.
L has the unit “m” and it can refer to the atmospheric stability, 1/L < 0 for unstable conditions, ≅ 0 for neutral conditions, and > 0 for stability conditions (Zannetti, 1990).
4.1.5.3
Convective velocity scale
The strong diurnal cycle in solar heating creates a strong heat flux into the air from the
earth’s surface. The buoyancy associated with this flux fuels the thermals. A buoyancy
flux can be defined as ( g / θ v )( w′θ ′v ) . Although the surface buoyancy flux could be used
directly as scaling variable, it is usually more convenient to generate a velocity scale
instead, using the two variables being important in free convection: buoyancy flux at the
surface, and zi. Combining these yields a velocity scale known as free convection scaling velocity, w∗; also sometimes called the convective velocity scale for short (Stull,
1988):
1
3
 gz
w* =  i ( w′θ ′v ) s 

 θv
(4.17)
where θ v is the virtual potential temperature (K) and ( w′θ ′v ) is the kinematic virtual potential temperature flux in the vertical (K m/s).
Free convection and forced convection are names for states of turbulence in the ABL.
The ABL is said to be in free convection if buoyant convection dominates, and in forced
convection if mechanically generated turbulence dominates. Note that for forced convection, u∗ is likely to be a more appropriate length scaling parameter than w* (Stull,
1988):
4.1.5.4
Roughness length
Roughness parameter represents the direct effect of the surface on the wind above and
is thus a very useful concept. Normally, within the layer of air near the ground viscosity
predominates. However, as the wind speed (shearing stress) increases over a given
33
surface, i.e. departure from the ground level, or as the surface becomes increasingly
rough at a constant wind speed, the shearing stress becomes partly turbulent and
partly viscous. Soon a stage is reached at which the pure viscous stress of the surface
is outweighed by the effect of pressure forces associated with the eddying wakes from
the roughness elements i.e. at this stage the viscosity ceases to influence the wind profile and thus the shearing stress primarily defines the turbulence motions. Such an
aerodynamically rough stage where the flow is practically zero is characteristic of the
surface roughness and gives a measure of the roughness parameter z0 of the surface
(Melas et al.1998).
z0 is defined as the height at which the wind speed becomes zero. It is generally not
the same as surface height. For example z0 for a forest is always greater than z0 for
short grass. Although z0 is usually inferred from wind speed measurements at the
measurement height, Lettau (1969) suggests that it can be estimated from:
z0 = 0.5h* ( ss / sl )
(4.18)
where:
h∗
average vertical extent of roughness elements,
ss
average cross section presented to wind by each element,
sl
total ground surface area / number of elements.
From the point of view of surface layer ground based measurements, z0 is useful in
estimating the effect of the ground on the flow. Especially, large values of z0 give larger
mean eddy sizes.
4.2
Sound propagation in the atmosphere
Sound energy propagates in the atmosphere as a longitudinal pressure wave. The attenuation of the sound wave as it propagates is frequency dependent. Since the variation of attenuation with frequency is a smooth step less continuous curve, the decrease
in intensity of a plane sound wave in a small frequency interval can be expressed as an
exponential decay function (DIN-VDI, 1999):
I = I 0 exp(−αl )
(4.19)
34
Here l is the distance (m) and α the atmospheric attenuation coefficient composed of
three components (m-1);
α = αc + αm + αs
(4.20)
Here αc is the classical attenuation due to dissipation of energy resulting from the viscosity of the air, radiation and heat conduction. Under normal atmospheric conditions αc
is very much smaller than αm and αs and is dependent on the frequency f:
α c = 4.24 f 2 10 −11 m −1
(4.21)
The molecular attenuation αm decreases with decreasing temperature. The attenuation
component αs is due to scattering of sound by temperature structures and turbulence.
This component is very large with respect to the other components. However, the
sound waves propagating in a perfectly homogenous and continuous medium are not
scattered. Scattering requires an inhomogeneity of the refractive index.
The velocity of sound in the atmosphere depends on the wind velocity component, on
the temperature, and on the chemical composition of the atmosphere. Water vapor is
the constituent most likely to fluctuate. As a guide to the change in refractive index, Table 4.1 shows the relative change in wavelength per Kelvin of temperature change, per
m/s of change in wind speed, and per hPa of change in water vapor pressure (DIN-VDI,
1999).
Table 4.1: Change of wavelength of sound waves in the atmosphere as a function of changes in temperature, wind speed and water vapor content
∆λ
λ
in K-1
1800 10-6
∆λ
λ
in (m/s)-1
3000.10-6
∆λ
λ
in hPa-1
160.10-6
For the energy σ( θ ) scattered from unit volume from unit flow at angle θ , the following
can be derived:
θ 
4π

θ
θ
4π
sin 
Φ (T )
sin ) cos 2
Φ (V )(

32 π cos θ
2
γ
2
2 +
λ


σ (θ ) =
4
2
2
C0
4T
λ




5
2
(4.22)
35
where:
λ
sound wavelength at mean temperature T (m),
θ
scatter angle in relation to the incident wave (°),
Φ(V) three-dimensional spectral density of wind velocity fluctuation,
Φ(T) three-dimensional spectral density of temperature fluctuation.
The functions
λ
λ′ =
2 sin
Φ(V) and Φ(T) relate to the spatial region λ´ :
(4.23)
θ
2
Assuming a Kolmogorov turbulence spectrum, the following can be written:
−11
 CV2
CT2 
θ 3
2θ
σ (θ ) = 0.055λ cos θ  2 cos + 0.13 2  (sin )
T 
2
2
C
−1
2
(4.24)
The structure parameters CV2 and CT2 are defined as follows:


u ( x) − u ( x + r ) 
2

CV =
1


r3


2


T ( x) − T ( x + r ) 
2

CT =
1


r3


(4.25)
2
(4.26)
Here u and T are the wind speed and temperature at location x and r.
Not only random fluctuations of air temperature but also uniform temperature gradients
contribute to the scattering. This is only so in the case of a marked change in refractive
index.
The relationship between transmitted and received acoustic power Pt and Pr from scattering volume for the monostatic sodar is described by Eq. 4.27 (Neff, 1975; Hall and
Wescott, 1974):
Pr = Ptηtηrσ (π )Cτ l Ar G
exp(−2αz )
2z
(4.27)
36
where σ (π ) is the acoustic backscatter cross section per unit volume, ηt and ηr the
efficiencies of transmitter and receiver respectively, C the speed of sound, τl is the
pulse length, Ar the antenna effective aperture, G the directivity compensation factor, α
the acoustic attenuation coefficient and z being the range to scattering region. σ (π ) is
related to the turbulent state of air temperature represented by the structure constant
for air temperature C2T as follows:
1
σ (π ) = 0.0039 K 3 CT2 / T `2
(4.28)
where:
K:
is the wave number (m-1),
T`:
the air temperature of the scattering volume (K).
Fig. 4.5 shows the variation of the absorption with temperature and relative humidity
while Fig. 4 6 shows how the coefficient of molecular attenuation αm varies as a function of humidity and frequency (DIN-VDI, 1999).
Fig. 4.5:
Dependence of sound absorption on temperature and humidity (DIN-VDI,
1999)
37
Fig. 4.6:
Coefficient of molecular attenuation of sound waves as a function of humidity at various frequencies (after Little, 1969)
Beside the above mentioned, precipitation, rain, snow, or fog, has an insignificant effect
on sound levels although the presence of precipitation will obviously affect the humidity
and may also affect wind and temperature gradients. Under normal circumstances, atmospheric absorption can be neglected except where long distances or very high frequencies are involved (Ingard, 1953). For more details, a historical review of the propagation of sound in the atmosphere was presented by Delany (1977) to explain the
mechanisms associated with propagation of sound in the atmosphere, including velocity of propagation, attenuation within the medium, refraction by wind and temperature
gradients, the effect of fog and precipitation, scattering and fluctuations due to turbulence, and ground reflection effects and the influence of vegetation. In addition, measured values of the absorption of sound in air by Harris (1963) were given as function of
humidity in the frequency range between 2000 and 12500 Hz, at normal atmospheric
pressure and at a temperature of 20° C. Furthermore, an extended works by the same
author (1966) over wide temperature range (-0.5 to 25.1°C) were made at normal atmospheric pressure.
38
4.3
Theory of sodar measurement
Acoustic sensing is based on the sound wave scattering by turbulent air inhomogeneities that are always present in the atmosphere. This technique does not differ basically
from clear air radiolocation. However, the former has some specific properties (Kallistratova, 1997):
∗∗
The speed of sound is more sensitive to temperature variations than that of electromagnetic waves. For the same temperature variations the changes in the values of the refractive index for sound waves are 1000 times greater than those in
the values of the refractive index for electromagnetic waves. Therefore a crosssection of acoustic scattering from the atmospheric temperature inhomogeneities is about a million times greater than that of electromagnetic waves. As a result of this fact, sodar is simpler in design than clear air radar and its prime cost
is much lower.
∗∗
The speed of sound is responsive to changes in wind velocity. Therefore sodar
provides a more detailed information on dynamic properties of turbulence.
∗∗
The velocity of sound propagation is a million times lower than that of electromagnetic waves. Due to this fact the processing sodar information is considerably simplified, moreover, a better spatial resolution and a short dead zone can
be reached.
∗∗
Acoustic waves of both centimeter and decimeter bands used usually in sodars
are readily absorbed in the air. Therefore the altitude range for acoustic sounding is rather low and bounded to the heights of the order of 1 km.
4.3.1
Physical principle of the method
Adiabatic speed of sound C in motionless air is determined from the Laplace formula
(Kallistratova, 1997):
C=
γP
ρ
(4.29)
where P is the air pressure (hPa), ρ the air density (kg/m3), and γ =1.4 is the ratio of
39
heat capacities for constant pressure and constant volume. Using the equation for ideal
gases condition:
P
ρ
= RT
(4.30)
Eq. (4.29) can be rewritten in the form:
C=
γRT
µ
(4.31)
where T is the mean temperature (K), R the universal gas constant (JK-1.kg-1), and µ
the molecular weight of the mixture of gases that are constituents of air (g/mol). In the
real atmosphere, water vapor is always present and the values of ρ , µ and γ depend
on water vapor concentration. Fluctuations of sound speed in wet air are due to both
adiabatic changes in density when air temperature varies, and changes in density owing to turbulent fluctuations in water vapor concentration q.
In the atmosphere, the phase sound velocity Cph, that governs the process of scatterr
ing, depends also on the projection of wind velocity vector V (m/s) on the normal to the
wave front:
C ph
rr
VK
=C+ r
K
(4.32)
r
where K is the wave vector. In what follows, just a phase sound speed will be implied,
the subscript ph being omitted. Atmospheric turbulence results in random fluctuations
r
of T, q and V that are responsible for fluctuations of the sound refractive index:
n=
C0
C
(4.33)
where C0 is the mean speed of sound. The intensity of a scattered wave carries information of the intensity of turbulent fluctuations n´= n – 1.
Characteristic frequencies of turbulent fluctuations are below audio frequencies; therefore not temporal fluctuations but a spatial field of random inhomogeneities n´ is essential for audio sound scattering. Only those inhomogeneities, whose characteristic scales
40
lt are comparable with the lengths of sound waves λ , are responsible for scattering;
irregularities of considerably larger scales result in wave refraction.
Inhomogeneities of the refractive index for the atmosphere are too slight and n´ values
usually do not exceed n´ ≈ 10-2. That is why the intensity of scattering from chaotically
occurring inhomogeneities is low. Scattering is known to increase in certain directions
due to a constructive interference, when inhomogeneities are periodic and the Bragg
conditions holds (Fig. 4.7):
lt =
λ
(4.34)
2 sin Θ B
In Eq. 4.34, lt is the period (scale) of inhomogeneities (m) and
ΘB the
angle of wave
incidence (the Bragg angle) which is half the scattering angle θ . As the spatial power
spectrum of atmospheric turbulent inhomogeneities is continuous, the spectral component K= 2 π /lt satisfying (4.34) will always be found, which will determine the intensity of
scattering at the angle θ .
Fig. 4.7:
Wave scattering by periodical structure inhomogeneities (Kallistratova,
1997)
Since spectral density of the small-scale atmospheric turbulence rapidly increases with
increase in the scale lt, scattering indicatrix is extended toward small angles. Variations
in temperature and wind velocity enter in different ways in the expression for sound
speed and refractive index. It is important that in this case temperature is the scalar
value and velocity is the vector. Due to this fact, an angle dependence of scattering
41
intensity is different for temperature and velocity fluctuations. In particular, backscattering (at θ =180°) occurs only from temperature and humidity inhomegenieties. This
fact offers a possibility to determine separately the fluctuations of scalar parameters
and wind velocity from the measurement of sound scattering at different angles.
Mean wind flows that carry small-scale inhomogeneities are always present in the atmosphere. The time of transfer of such inhomogeneities by wind flows through the sodar beam is usually quite less than the characteristic time of their evolution. Therefore it
is possible to consider that the spatial, the field of scatters moves as a frozen one. In
this case, the frequency of the received scattered signal fs is shifted from the radiation
frequency f0 due to the Doppler effect. At backscattering:
fs = f0 (1-2 υ r/C)
(4.35)
where υ r is the projection of wind velocity in the direction of sounder beam. Thus, using a Doppler sodar it is possible to determine a beam component of the mean wind
velocity and using a three-component sodar it is possible to determine the whole vector
r
of wind velocity V .
4.3.2
Sodar system configurations
The principle of acoustic sounding is based on the detection of the backscattered signal
from acoustic refractive index discontinuities or disturbances in the atmosphere. Based
on the equations (4.24), two elementary configurations are possible (Melas et al., 1998;
for more details about the basic design of Doppler sodar, see Ito 1997):
Monostatic: the same antenna is used for the acoustic tone emission and for the echo
reception. There are some disadvantages to take into account when using this configuration:
∗∗
The echo intensity, having only the contribution from thermal fluctuations, is
weaker than in the bistatic configuration and vanishes when the temperature
lapse rate approaches to adiabatic. That may happen in the period following the
sunset and leads to a systematic lack of data in some parts of the day.
∗∗
The estimates of the wind values at each range gate derive from radial vertical
component measured at three different positions in space. This problem is usu-
42
ally overcome by averaging over several scans. However this can be a severe
limitation even for mean wind estimates (Neff and Coulter, 1986) in high horizontal dishomogeneity conditions such as for example over complex terrain or landwater interfaces.
Bistatic: at least two antenna are needed, one to emit the tone, the other to receive the
echo. This configuration, using bistatic scattering, rely on a more continuous signal for
Doppler wind estimate since echo is present also when the temperature lapse rate is
close to adiabatic. Moreover in this configuration the sodar is the only remote sensor
directly sensitive to the small-scale velocity field (Neff and Coulter, 1986). Several disadvantages, however, are associated with this configuration.
∗∗
Bistatic systems usually require 100 to 300 m base lines with all the related cabling.
∗∗
There are ground clutter problems because of the refraction and reflection of the
signal going through the broad beams from low objects.
The need to measure the wind components in several directions for the wind profile
retrieving leads to multi-axes (bistatic and /or monostatic) sodar systems.
In the last decade the increasing computing power of PC's and the possibility to plug in
their bus DSP (Digital Signal Processing) cards permitted the setting-up of configurations that allows for simultaneous monostatic and bistatic modes of operation (Mastrantonio et al. 1986). In this case each of the antennas radiates a different frequency, and
each is allowed to receive and process signals at three frequencies.
More recently to make systems easy to move, array antennas have been developed,
that is antennas resulting from a set of elementary microphones (typically between 25
and 220 elements) that radiate the acoustic tones simultaneously. The control of the
relative phase of each emitter permits the beam steering in the desired direction; the
alternately transmitting along three different directions, after an appropriate averaging
period, allows retrieval of the wind profile (Melas et al., 1998).
43
5
MEASUREMENTS, DATA PROCESSING AND EXPERIMENTAL SITES
5.1
Measurements
5.1.1
Principles of sodar measurement
The sodar emits short pulses of sound which are backscattered by temperature and
velocity inhomogeneities in the atmosphere. The sodar measures the return time, the
amplitude as well as the frequency distribution of echoed pulse. The time of travel is
used to evaluate the distance of the scattering volume the frequency shift to calculate
its velocity and the amplitude of the returned signal to obtain information about the
structure of the inhomogeneity.
5.1.1.1
Beam pattern
The sodar uses a single antenna system to both transmit acoustic signals upward into
the atmosphere and to measure the reflection of those signals back from small scale
turbulence caused by small scale thermal and wind velocity fluctuations in the air.
Three beam axes (not in the same plane) are required for wind measurements. Usually, there is one in the vertical beam and two tilted beams, but three tilted beams also
work. Standard measurements are made by transmitting a pulse along the first beam
path and its symmetrical (if tilted) beam path, then waiting a few seconds for all reflected energy from the atmosphere to be received back at the antenna and processed,
then transmitting on the second third beam paths in the same manner as the first. The
cycle is repeated continuously to accumulate measurements for further averaging during the automated data process. In the sodar (FAS64) of the Meteorological Institute,
University of Freiburg, which was used within this investigation, the antenna pointing
directions include one vertical beam and many tilted beams. The direction cycle can be
individually defined by the user and it can emit beams in 9 different directions which are
as following (Scintec, 2002):
∗∗
0°
vertically,
∗∗
9°
east, 22°
west
∗∗
29°
north, 22°
south
∗∗
29°
west, 22°
east
∗∗
29°
south, 22°
north
44
5.1.1.2
Backscatter
Sodar record the strength of the reflected acoustic energy, called “ backscatter” as
shown in Fig. 5.1. Backscatter strength is proportional to the thermal turbulence, so
echo intensity plots give information about the vertical distribution of the turbulence layers in the atmosphere. The resulting time history of atmospheric layer elevations and
relative strengths can be interpreted to provide estimates of mixing heights or inversions (REMTECH, 2000).
Fig. 5.1:
Backscatter is the returned radiation from the transmitted pulse (REMTECH, 2000)
5.1.1.3
Doppler shift
Sodar calculates the radial wind speed along the beam axis at each altitude layer sampled. It uses the frequency difference called the Doppler shift between the transmitted
and the reflected acoustic energy to determine the movement of air that reflects the
acoustic energy. The frequency shift from each beam path is converted into a radial
wind along that path, and the radial winds from the respective beam paths are then
combined mathematically to produce horizontal wind direction and speed at designated
45
height intervals in the vertical profile above the antenna system. The resultant horizontal wind direction and speed value for each vertical interval represents an average for
the volume measured over the specified time span. The size of the volume measured
depends on the characteristics of the beams used and on the depth of the height intervals set by the operator. The heights are assigned according to the total two-way travel
time from the antenna to the scattering volume and back to the antenna (REMTECH,
2000).
5.1.1.4
Height determination
In time, t, the sound travels a distance, Ct. If the antenna beam is vertical, the height, z,
between the transceiver and the scattering inhomogeneity is (DIN- DVI, 1999):
z=
Ct
2
(5.1)
where t is the elapsed time between transmitting and receiving. The minimum measurable height depends on the finite switchover time between transmit and receive modes.
Fig. 5.2:
Schematic showing relationship between travel time and measured height
(DIN- DVI, 1999)
For an antenna whose beam is inclined at an angle ϕ to the vertical, it is valid
z = Ct cos
ϕ
2
(5.2)
46
Fig. 5.2 shows the relationship between travel time of the sound and the target height.
The slope of the straight lines is the speed of sound C. It also illustrates that sodar
does not make point measurements, but measurements over a small volume. The radial resolution is determined by the transmission time and the receiving time.
5.1.1.5
Signal analysis
The objective of the signal analysis is to determine from the backscattered signal for
each height layer (range gate) the backscattered amplitude, the radial components of
wind velocity and if appropriate their standard deviation. For each antenna direction
typically many range gates can be set, each with a different travel time between transmit and receive, as shown in Fig. 5.2 (DIN- DVI, 1999).
The instantaneous Doppler spectra are found for each antenna direction and each
range gate. From these the Doppler parameters are calculated. The return signal amplitude is the zero-order Doppler parameter, the radial wind velocity is the first-order
Doppler parameter, and the standard deviation of the radial wind velocity the secondorder Doppler parameter, see Fig. 5.3. The three parameters are measured as means
over an interval of typically 30 min to one hour. Alternatively, first the means of the
Doppler spectra are taken and then the mean Doppler parameters calculated from
them (DIN- DVI, 1999).
Fig. 5.3:
Doppler spectrum (DIN- DVI, 1999): A, backscattered amplitude (zeroorder); L, spectral power; N, noise; N , noise level; r, radial wind speed
(first-order); σr, width of Doppler spectrum (second-order); f, frequency; f0,
transmitter frequency
47
The horizontal and vertical wind velocity and the horizontal wind direction are calculated from the first-order parameters. The standard deviations of the wind values can
be calculated from the instantaneous values of the first order parameters or from the
second-order parameter. For each antenna and each range gate, it is possible to calculate: Doppler spectrum; return signal amplitude, A; radial wind velocity; vertical wind
velocity, w; horizontal wind velocity, horizontal wind directions, standard deviations of
horizontal wind velocity and standard deviation of horizontal wind direction.
5.1.1.6
Limitation of sodar operation
The limitation to a sodar's operation stem principally from the use of acoustics as a
probing technique (Atmospheric Research Pty. Ltd., 2000):
∗∗
Range: Sound is attenuated in the atmosphere. At higher frequency, sound is
attenuated much more than lower frequencies. With increasing temperatures,
and/or lower relative humidity, the attenuation of sound increases. The height
performance of a sodar in a hot, dry, desert may only be 60% of the same instrument in a cool and damp location.
∗∗
Audible sound: The use of sound can limit its use in built-up areas.
∗∗
Background noise: The background noise where a sodar is operating can also
limit a sodar’s performance. In general sodars should not be operated in areas
where the noise level (at the frequency of operation of the sodar) is high.
∗∗
Local structures: Sodars should not be installed near structures (or vegetation)
which can produce fixed echoes.
5.1.2
Accuracy of sodar measurements
The ability of Doppler sodar to measure profiles of mean wind speed with good accuracy and reliability is well proved (Shurygin et al., 2000). Comparisons with tower instruments, tethersondes, and pilot balloons have shown that Doppler sodars offer a
reliable estimations of the mean wind speed and wind direction (e.g. Balser et al., 1976;
Caughey et al., 1976; Asimakopoulos et al., 1978; Kaimal et al., 1980; Congeduti et al.,
48
1981; Gaynor and Korrell, 1981; Thomas et al., 1983; Kaimal et al., 1984; Helmis et al.,
1985; Kallistratova et al., 1985; Tsvang et al., 1985; Finkelstein et al., 1986; Gaynor
and Kristensen, 1986; Ito et al., 1986; Santovasi, 1986; Kallistratova et al., 1987; Thomas, 1988; Chintawongvanisch et al., 1989; Ito et al., 1989; Keder et al., 1989; Gaynor
et al., 1990; Thomas and Vogt, 1990, 1993; Kurzeja, 1994; Piringer, 1994; Vogt and
Thomas, 1994; Beyrich, 1997b; Ito, 1997b; Peters et al., 1998; Reitebuch and Emeis,
1998; Seibert et al., 2000; Emeis, 2001; Görsdorf et al., 2002; Kramer and Kouznetsov,
2002). Doppler sodar configurations examined in these studies included bistatic,
monostatic and phased-array sodars, but only Ito et al. (1989); Gaynor et al. (1990) Xontech phased-array sodar; Vogt and Thomas (1994) - Remtech phased-array sodar;
Kurzeja (1994) - Xontech phased-array sodar; Piringer (1994) - Remtech phased-array
sodar - and Ito (1997b) have used phased-array sodars. The results of most studies
that have made quantitative comparisons of sodar-data against those obtained by in
situ instruments and other ground-based remote sensing methods were compiled by
Grescenti (1997). He summarized a brief descriptions of all published sodar comparison studies over the last 20 years and the statistical measures which were used in
these studies.
Some results of these investigations are: the sodar-derived wind speed and wind direction are highly correlated against reference measurements (correlation coefficient r ≈
0.92) with precision of 1.1 m/s and 21.5°, respectively. Correlations of sodar-derived
values of σw were not quite as good (r ≈ 0.81) with an average precision of 0.18 m/s.
Past studies have shown that σw accuracies vary significantly from day (convective
conditions) to night (stable conditions). Very few data values were available for σdd,
which had a poor correlation of r ≈ 0.57 and precision of 10.7°. The conclusions from
many of these studies have shown that Doppler sodars can accurately obtain the mean
wind speed and wind direction. Sodar-derived values of σw show much promise, especially in the more recent studies; however, caution is still recommended with their use
(Grescenti, 1997).
With regard to the standard deviations of the longitudinal and lateral wind speed, σu
and σv, only a poor correlation exists with other methods (Gaynor, 1992). Unfortunately, sodar-derived σu and σv values have very large uncertainties that make them
49
unacceptable for any practical use at this time. Much of the observed scatter in sodar
measurements can be attributed to a number of factors. These include, but are not limited to, instrument configuration, noise and processing techniques (Grescenti, 1997).
Gaynor (1992, 1994) examined the standard deviation of the lateral or cross-wind component σv acquired during the International Sodar Intercomparison Experiment (ISIE)
and found that the errors were in excess of 50% and many instances approached or
equal the magnitudes of the variances themselves. Corrective measures have shown
limited success. Kristensen and Gaynor (1986) developed a geometric matrix model to
correct for the observed scatter in σv. While the model was successful in obtaining better values of σv, considerable scatter still remained in those measurements.
In addition, Ito et al. (1989) explained that the phased array Doppler sodar operated
with five beams could supply enough information to evaluate the random errors without
comparison with other instruments. On the basis of the method presented for a UHF
wind profiler by Strauch et al. (1987) or for a sodar by Takehisa et al. (1991), a study of
Ito (1997b) provides the error estimation involved in a five-beam sodar used in the field
test near the tower of Meteorological Research Institute (MRI) of Japan. Ito (1997b)
compared his sodar values with those from a sonic anemometer on an adjacent tower.
One of his result was that the standard deviations of the sodar-derived horizontal wind
speed, σu and σv, are about twice as large as those measured by the sonic, even
though the mean horizontal wind speed and the standard deviation of the vertical wind
speed σw are in reasonable agreement with the sonic measurements. Moreover, error
analysis indicates that the five-beam direction system can separate the random errors
from the measured wind variances. The variance error in wind fluctuations can be canceled by correcting for these errors, and the discrepancy of the wind variances between
sodar and tower measurements becomes small. With the compensation of such measurement errors, the wind variances averaged over 60 min of horizontal components
agree with those values obtained by the sonic anemometer on the tower (Ito, 1997b).
5.1.3
Instrumentation: Description of the FAS64
A FAS64 sodar from Scintec, Tübingen, Germany, was used in this investigation. The
FAS64 is an advanced, very powerful sodar for the remote measurement of profiles of
50
three-dimensional wind speed and directions and turbulence characteristics in the
lower atmosphere. With its superior performance, flexibility and ease-of-operation, the
FAS64 do not only meet the needs of routine ABL monitoring but in particular is powerful tools for a variety of research applications. The FAS64 consists of three main subsystems; antenna subsystem, control electronics subsystem and display computer
subsystem. A block diagram of the FAS64 is shown in Fig. 5.4. Furthermore the specification of FAS64 is presented in Table 5.1.
Fig. 5.4:
The main subsystem of FAS64 (FAS64-booklet, Scintec, 2002)
51
Table 5.1:
Specifications of FAS64 (Scintec, 2002)
description
numerical
remarks
64
piezoelectric transducers
1650 – 2750 Hz
frequencies user selectable
Acoustic output power
7.5 W
description
Number of frequencies
up to 10 base frequencies
selectable
0o, ±22o, ±29o
9 beams, selectable
100
maximum, selectable
Thickness of vertical layers
10 – 250 m
selectable
lowest measurement height
20 m
beginning of lowest layer
Maximum range
500 – 1000 m
15 min averaging time
Averaging time
single pulse/ sequence to 60 min
selectable
Accuracy of horizontal wind speed
0.1 - 0.3 m/s
in multi-frequency mode
Accuracy of vertical wind speed
0.03 - 0.1 m/s
in multi-frequency mode
2 - 3o
at wind speeds above 2
m/s
Measurement range horizontal
-50 to +50 m/s
depending on mode
Measurement range vertical
-10 to +10 m/s
depending on mode
Operation temperature range
-35 to +60 oC
antenna and processing
Unit
±12 VDC, 150W peak
50 - 100 W average consumption
Number of elements
Frequency range
Emission/reception angles
Number of vertical layers
Accuracy of wind direction
Power requirements
Size
Weight
0.74 m x 0.72m x
0.2m
32 kg
antenna without enclosure
antenna without enclosure
The acoustic antenna consists of 64 pizo-electric transducers for acoustic emission and
reception. The acoustic antennas of Scintec sodars contain highly efficient transducers
in a new flat array configuration. Moreover it is an active antenna. This means that the
antenna does not only house the transducers and switches, but also contains audio
52
power drivers for emission and audio preamplifiers for reception mode. As emission
elements, highly efficient transducers are use. The same elements reconvert the received sound waves into electric signals. The acoustic antenna is connected with the
processing unit and the power supply. By the acoustic antenna, the following analogue
and digital information is received from or transmitted to the processing unit: audio signal for emission, receiver audio signal, direction mode, operation mode (emission/reception) and self-test row /column selection.
The orientation of the acoustic antenna is defined such that it is horizontally leveled and
the “North” sign is pointing to the north direction. Moreover, under normal precipitation
conditions, the acoustic antenna can be operated without additional weather protection.
In order to reduce emitted stray nose and lower instrument’s susceptibility to active and
passive environmental noise (including fixed echoes), an acoustic enclosure can be
mounted to the acoustic antenna.
Fig. 5.5:
The acoustic arranges 64 highly efficient piezoelectric transducers
(FAS64 sodar, Scintec)
53
5.1.4
Description of the software: FASrun program
The FAS64 sodar system is operated with the FASrun software. This software must be
installed on an IBM compatible PC with a Pentium or higher Processor, Windows 3x,
Windows 95, Windows 98, Windows NT operating system, a minimum of 8MB free
RAM, and a minimum of 12 MB free hard-disk space. It allows the user to set the parameters for emission and reception. It also displays the measured data. All output data
files are written in ASCII format. The actual data can be viewed during the measurement to verify the parameters with respect to consistency. The received spectra, the
wind speeds and their standard deviations, the gains and the backscatter of signal are
visualized. If the wind data are calibrated with the sensible heat flux, the program displays the values of the temperature structure function, CT, and other atmospheric parameters like the stability parameter and eddy diffusivity (an input for z0 is required to
obtain correct estimates of the eddy diffusivity).
The “received spectra” window shows the received frequency distribution normalized to
the emitted frequencies as function of the altitude. It also displays the fitted frequency
function, which used by the program for determining the wind speed.
The “wind speed” window displays for each height the three wind speed components,
the resulting horizontal wind speed and its direction and the standard deviations of the
three wind components (not the accuracy of the wind speed measurement).
In the “gain” window the actual automatically fitted gains are shown.
The “sodargram” window displays the backscatter of the emitted signal. The data
represents the absolute signal returned by the system at all frequencies used.
These values can also be viewed after the measurement. But it is not possible to display the gains and the fitted spectra.
The parameters for the emission and reception govern the frequencies and their duration in an emitted sequence, the vertical resolution and the averaging time. Setting
these parameters also controls some algorithms.
The vertical resolutions set the average ranging of the returned signal. The user sets
ranges in meters and not the time which the sound needs for this distance. The relation
between the range and the time through the velocity of sound is done by the process-
54
ing units. The program needs the temperature and air pressure at ground for this relation. The vertical resolution should correlate with the structure of the ABL, if it is known.
To achieve good results even in higher altitudes, the resolution is reduced with increasing height, so that more information is retrieved from a given average.0
The composition of the emitted frequencies can be independent for each direction. Up
to ten frequencies can be emitted in one sequence.
In this study, only the main data output files (extensions *.mnd) were used which can
be converted to other software to make other treatment of these results. For more details about the FASrun program, see the user’s manual of Flat Array Sodars, Scintec
(2002) and Pavel Schilinsky (2000).
5.2
Data processing
In this study, the FAS64 provided the following data in the range from 20 m to 500 m
a.g.l. for all investigated land use types in form of vertical layer related mean values
over 30 minutes: longitudinal (u), lateral (v) and vertical (w) wind speed; horizontal wind
speed (vh); wind direction (dd); standard deviations of all wind speed components (σi;
i=u,v,w) and standard deviations of the wind direction (σdd). Although the variances of
horizontal wind speed, σ2u and σ2v, measured by the phased-sodar may be about twice
as large as those measured at the tower (Ito, 1997b), these variables were used in this
study, because the manufacturer of the FAS64 Sodar gave a physically based declaration for the use of σu and σv. In addition, the shape of the variation of σu/u∗ and σv/u∗
with increasing instability (-z/L) in the surface layer showed the same behavior as in
other studies, which used sonic anemometer-thermometer instruments such as ALJiboori et al., 2001 (see figures 6.1.14, 6.2.15, 6.3.15 and 6.4.14).
Besides directly monitoring such meteorological variables as u, v, w, vh, dd, σi (i=u,v,w),
σdd, the application of a number of methods and algorithms enabled the estimation of
features of the atmospheric turbulence were calculated. These can be concluded as
follows:
∗∗
P-G stability classes: Such a stability classification is the first step for applying a
number of traditional algorithms aiming at estimating the main atmospheric pa-
55
rameters which typically describe the ABL structure such as Monin-Obukhov
length (L) and friction velocity (u∗) (Capanni and Gualtieri, 1999). A method,
starting from sodar data only, was applied to determine the P-G stability classes.
This method is the one proposed by Thomas (1988). He used the standard deviations of the horizontal wind speed (σdd) by measurements of a tower (at 100
m a.g.l.) and sodar (at 60, 100, 160, 200 m a.g.l.) to determine the P-G stability
classes. The class limits of the σdd-values measured at these heights by the sodar have been compiled in table 5. 2.
∗∗
Stability parameter (z/L), the Monin-Obukhov length could be calculated from the
empirical method developed by Liu et al. (1976) and Irwin (1979), as described
in Zannetti (1990), by using power law functions of z0 as:
1
= az0b
L
(5.3)
where a and b are empirical coefficients and their values have been compiled in
table 5. 3.
∗∗
Turbulent kinetic energy per unit mass, TKE, could be calculated from Eq. (4.2).
∗∗
Mean kinetic energy per unit mass, MKE, can be calculated from Eq. (4.1).
∗∗
The production of turbulent kinetic energy of convective and mechanical origin
can be represented by the σ3w/z (Weill et al., 1980) and can be calculated from
the data of sodar.
∗∗
The turbulence intensity components for longitudinal, lateral and vertical wind
speed components, Iu, Iv, Iw, could be calculated from Eq. (4.13).
∗∗
The standard deviations of the wind speed components normalized by the friction velocity, σi/u∗ (i=u,v,w), in the surface layer and under unstable conditions:
σi could be obtained from the sodar’s data. The friction velocity, u∗, under unstable conditions and in the surface layer, could be calculated from the similarity relationship (Stull, 1988):
σw
−1
z
u* =
(− ) 3
1.9 L
(5.4)
56
∗∗
The variance of the vertical component of the wind speed scaled by the square
value of the convective velocity, σ2w/w∗2, under the free convective weather. The
convective velocity was given by (Melas, 1993):
w* =
σ wm
(5.5)
0.6
where σwm is the average of σw between 100 m and the uppermost sodar level.
∗∗
The data of mixed layer, zi, are not available in this study but a rough estimate of
zi could be obtained from the σ2w profile. However, σ2w has a maximum at
zm ≈ 0.35zi. Measurements in the CBL show that zm occurs in the range 0.3zi0.6zi (Caughey, 1982). A good compromise is therefore (Melas, 1993):
zi ≈ 2.8 zm
Table 5.2:
(5.6)
Method of stability classification (class limits) (Thomas, 1988)
height
P-G stability classes
F
E
D
C
B
A
60 m
4.6°
9.1
22.6
44.0
67.6
100 m
4.3°
6.9
15.1
27.9
51.3
160 m
2.0°
4.7
14.4
30.5
52.7
200 m
2.3°
4.4
13.2
30.4
54.5
Table 5.3:
P-G stability
The values of coefficient a and b (Liu et al., 1976; Irwin, 1979)
A
B
C
D
E
F
A
-0.08750
-0.03849
-0.00807
0.0
0.00807 0.03849
B
-0.1029
-0.1714
-0.3049
0.0
-0.3049
classes
-0.1714
57
5.3
Experimental sites
The general description of the experimental sites used for this study is presented in
Table 5.4. However, these sites are chosen to represent different land use types. Furthermore Fig. 5.4 shows the study sites and the surrounding locations in south-western
and eastern Germany. The values of z0 can be obtained from many literatures such as
Stull, 2000.
Table 5.4:
Site
The general description of the study areas
Latitude
Longitude Elevation, a.s.l.
Land use type
Period
47° 6´ N
07° 36´ E
201 m
Scots pine forest
z0 = 1 m
07° 37´ E
200 m
grassland
z0 = 0.01 m
48° 03´ N
07° 36´ E
285 m
vineyard
z0 = 0.25 m
Oberbärenburg
50° 47´ N
13° 43´ E
735 m
Melpitz
51° 31´ N
12° 55´ E
86 m
Norway spruce
forest
z0 = 1 m
grassland
z0 = 0.01 m
Freiburg
48° 00´ N
07° 50´ E
272 m
30 Mar., 2000
to
25 Apr., 2000
10 July, 2001
to
26 July, 2001
01 Aug., 2001
to
22 Aug., 2001
29 Aug., 2001
to
24 Sep., 2001
26 Sep., 2001
to
12 Oct., 2001
16 Nov., 2001
to
19 Nov., 2001
Bremgarten 47° 54´ N
Blankenhornsberg
Hartheim
urban area
z0 = 1.5 m
58
Melpitz Î
Oberbärenburg Î
Blankenhornsberg
Ð
Hartheim Î
Í Freiburg
Í Bremgarten
Fig. 5.6:
Location of investigated sites in Germany
59
6
RESULTS
In this section a description of some measurements is given for the investigation sites
concerning incoming solar radiation, wind direction and its standard deviation, wind
speed components (horizontal and vertical), atmospheric stability (except for Freiburg),
variances of the horizontal and vertical wind speed, turbulent kinetic energy, and turbulence intensity. Although the variances of horizontal wind speed, σ2u and σ2v, measured
by a phased-sodar may be about twice as large as those measured by sonics at towers
(Ito, 1997b), these variables were used in this study as mentioned before.
Table 5.4 summarizes some of the information about the sites of this study. For every
site included in this study, the following results are shown:
∗∗
characteristic of the global solar radiation G received on a horizontal surface on
two cloudless and two cloudy days (except for: Melpitz with one cloudless day
and two cloudy days and Freiburg with one cloudless day and one cloudy day),
∗∗
wind roses at different levels during the period of the study,
∗∗
atmospheric stability classification at different levels,
∗∗
profiles of dd, σdd, vh, w, σ2h, σ2w, σ3w/z, MKE and TKE under various atmospheric conditions in the range 20 to 500 m a.g.l. (except for Oberbärenburg); the
weather was cloudy, rainy and foggy most times at Freiburg during the measurement campaign from 16 November, 2001 to 19 November, 2001; thus sodar
data above 100 m a.g.l. were not available,
∗∗
diurnal course of two days mean of σdd, vh, w, σ2h, σ2w, σ3w/z, MKE and TKE in
cloudless and cloudy sky conditions (except for: Melpitz with one cloudless day
and two cloudy days and Freiburg with one cloudless day and one cloudy day),
∗∗
characteristics of the turbulence intensity components (Iu, Iv, Iw) over the study
areas for various fetch conditions arising under various wind direction and different atmospheric stability at different levels,
∗∗
behavior of the relationship between the standard deviations of the velocity
components normalized by the u∗, σi/u∗ (i=u,v,w), and z/L in the surface layer
60
and under the unstable atmospheric conditions (except for Melpitz and
Freiburg).
The used data, such as wind speed components, wind direction and the turbulence
parameters are 30-min mean values and are measured by the same instrumentation
within the same range of the height (20-500 m a.g.l.) but the periods of the observations differ (see Table 5.4).
The global solar radiation measurements at Hartheim, Bremgarten and Blankenhornsberg were collected at a forest-meteorological experimental site Hartheim which is operated by the Meteorological Institute, Freiburg University (Mayer et al., 2000). However, it is 3.5 km and 9 km far from Bremgarten and Blankenhornsberg respectively.
The global solar radiation data for Oberbärenburg and Melpitz were provided by the
weather stations at Rotherdbach (one km from Oberbärenburg) and Melpitz respectively. In Freiburg, the data were collected from the urban climate station, operated by
the Meteorological Institute, University of Freiburg, at the top of a high-rise building (approximately 50 m a.g.l.) in the northern downtown of Freiburg.
6.1
Hartheim: Scots pine forest
6.1.1
Global solar radiation, wind direction, and wind speed variation
6.1.1.1
Global solar radiation
The diurnal variation of the global solar radiation G received on a horizontal surface at
Hartheim on two cloudless days (21/22 April, 2000) and two cloudy days (17/18 April,
2000) is given by Fig. 6.1.1. In which the maximum values are recorded around the
noon hours (11:00-14:00 CET) with average values >600 W/m2 in the cloudless and
approximately <300 W/m2 at the cloudy days.
6.1.1.3
Wind direction
The frequency distribution of the wind direction at different levels, 20-50 m, 230-260 m
and 470-500 m a.g.l. at Hartheim during the day and night, the daytime (6:00–18:00
CET) and the nighttime (18:00–6:00 CET) through the period from 30 March, 2000 to
25 April, 2000 is shown in Fig. 6.1.2. In addition, the profile of the wind direction, dd,
61
and the standard deviation of the wind direction, σdd, at Hartheim under various atmospheric conditions; neutral (17 April, 2000, 03:30-04:00 CET) and unstable (03 April,
2000, 12:00-12:30 CET), are given in Fig. 6.1.3 (c and f respectively). Beside the wind
rose and the profile of dd and σdd, the diurnal course of two days mean of σdd at different levels, 20-50 m, 50-80 m and 80-110 m a.g.l. over Hartheim under cloudless sky
conditions (21/22 April, 2000) and cloudy sky conditions (17/18 April, 2000) are summarized in Fig. 6.2.4.
6.1.1.3
Horizontal wind speed
The profile of the horizontal wind speed at Hartheim under various atmospheric conditions such as neutral (17 April, 2000, 03:30-04:00 CET) and unstable (03 April, 2000,
12:00-12:30 CET) are given in Fig. 6.2.3 (a). The diurnal course of two days mean of
vh at different levels, 20-50 m, 50-80 m, and 80-110 m a.g.l. in Hartheim under cloudless sky conditions (21/22 April, 2000) and cloudy sky conditions (17/18 April, 2000)
are illustrated in Fig. 6.2.5.
6.1.1.4
Vertical wind speed component
Beside the data of the horizontal wind speed, profiles and diurnal variations of the vertical wind speed component w are presented. Fig. 6.2.3 (b) reflects the behavior of the
profile of w at Hartheim under various atmospheric stability [such as neutral (17 April,
2000, 03:30-04:00 CET) and unstable (03 April, 2000, 12:00-12:30 CET)]. Fig. 6.1.6
shows the different between the two days mean values of w at different levels, 20-50
m, 50-80 m, and 80-110 m a.g.l. on cloudless days (21/22 April, 2000) and cloudy days
(17/18 April, 2000).
6.1.2
Atmospheric stability classification
Section (2.1) explained a literature review about the use of sodar to determine P-G stability classes. Here, the method proposed by Thomas (1988) was applied. He used σdd
to determine the P-G stability classes. The results obtained utilizing 30-min mean values of the standard deviation of the wind direction σdd, and measured at the levels 50-
62
80 m, 80-110 m, 140-170 m and 200-230 m a.g.l. by sodar at Hartheim through the
period from 30 March, 2000 to 25 April, 2000, are shown in Fig. 6.1.7. However, during
the study period, the percentage frequency distribution of P-G stability classes at different heights a.g.l. can be noticed. For example, in the period of this study and at the
level 50-80 m a.g.l., the stability conditions were unstable for 30% of the time, they
were slightly unstable for 22% of the time, they were neutral for 19% of the time and
they were stable for only 29% of the time.
800
21 April, 2000
22 April, 2000
17 April, 2000
18 April, 2000
2
G (W/m )
600
400
200
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.1.1:
Diurnal variation of the global solar radiation G at Hartheim on two cloudless days (21/22 April, 2000) and two cloudy days (17/18 April, 2000)
63
day and night
6:00 - 18:00 CET
18:00 - 6:00 CET
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
0%
(W) 270 °
90 ° (E)
240 °
120 °
210 °
(a) 20 - 50 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
(W) 270 °
0%
90 ° (E)
240 °
120 °
210 °
(b) 230 - 260 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
0%
(W) 270 °
90 ° (E)
-10%
240 °
120 °
210 °
(c) 470 - 500 m
150 °
180 ° (S)
Fig. 6.1.2:
Frequency distribution of wind direction at (a) 20-50 m, (b) 230-260 m
and (c) 470-500 m a.g.l. at Hartheim during the day and night, the daytime (6:00–18:00 CET) and the nighttime (18:00–6:00 CET), during the
period of the study (30 March, 2000 to 25 April, 2000)
64
neutral
unstable
500
z (m)
400
(a)
300
(c)
(b)
200
100
0
0
-0.5
5
10
vh (m/s)
0.5
0
360
w (m/s)
dd ( ° )
500
z (m)
400
(d)
(e)
(f)
300
200
100
0
0
3
σ
2
h
6
2
9
0
2
0.5
σ
(m /s )
2
1
2
0
40
2
σdd ( ° )
(m /s )
w
80
500
z (m)
400
(g)
300
(i)
(h)
200
100
0
0
5
10
2
2
TKE (m /s )
Fig. 6.1.3:
0
25
50
2
75
2
MKE (m /s )
0.00
0.01
3
2
0.02
3
σ w /z (m /s )
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE and σ3w/z at Hartheim under
various atmospheric conditions; neutral (17 April, 2000, 03:30-04:00 CET)
and unstable (03 April, 2000, 12:00-12:30 CET)
65
100
20 - 50 m
50 - 80 m
80 - 110 m
σdd (°)
80
60
(a)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
100
20 - 50 m
50 - 80 m
80 - 110 m
σdd (°)
80
60
(b)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.1.4:
Diurnal variation of two days mean of the standard deviation of the wind
direction, σdd at Hartheim (a) cloudless sky conditions (21/22 April, 2000)
(b) cloudy sky conditions (17/18 April, 2000)
66
10
20 - 50 m
50 - 80 m
vh (m/s)
8
80 - 110 m
6
(a)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
10
20 - 50 m
50 - 80 m
80 - 110 m
vh (m/s)
8
6
(b)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.1.5:
Diurnal variation of two days mean of the horizontal wind speed, vh at
Hartheim (a) cloudless sky conditions (21/22 April, 2000) (b) cloudy sky
conditions (17/18 April, 2000)
67
0.9
20 - 50 m
50 - 80 m
80 - 110 m
0.6
w (m/s)
0.3
(a)
0.0
-0.3
-0.6
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.9
20 - 50 m
50 - 80 m
w (m/s)
0.6
80 - 110 m
0.3
(b)
0.0
-0.3
-0.6
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.1.6:
Diurnal variation of two days mean of the vertical wind speed component,
w at Hartheim (a) cloudless sky conditions (21/22 April, 2000) (b) cloudy
sky conditions (17/18 April, 2000)
68
50%
50 - 80 m
80 - 110 m
40%
140 - 170 m
frequency (% )
200 - 230 m
30%
20%
10%
0%
A
B
C
D
E
F
P-G stability classes
Fig. 6.1.7:
Frequency distribution of P-G stability classes at different levels a.g.l. in
Hartheim for the study period (30 March, 2000 to 25 April, 2000)
6.1.3
Variance of horizontal and vertical wind speed
The profiles of the variance of the horizontal wind speed, σ2h, and the vertical wind
speed component σ2w, at Hartheim under various atmospheric stability; neutral (17
April, 2000, 03:30-04:00 CET) and unstable (03 April, 2000, 12:00-12:30 CET), are
given in Fig. 6.1.3 (d and e respectively). Furthermore the diurnal course of the two
days mean of the σ2h and σ2w at different levels in Hartheim under cloudless sky conditions (21/22 April, 2000) and cloudy sky conditions (17/18 April, 2000) are presented in
Fig. 6.1.8 and Fig. 6.1.9.
6.1.4
Turbulence kinetic energy
In the present section, the profiles of the σ3w/z, MKE and TKE at Hartheim under various atmospheric conditions such as neutral (17 April, 2000, 03:30-04:00 CET) and unstable (03 April, 2000, 12:00-12:30 CET) were shown. Fig. 6.1.3 (g-i) illustrate the profiles of these parameters. In order to illustrate the influence of clouds on σ3w/z, MKE
and TKE the behavior of these parameters at different levels, 20-50 m, 50-80 m, and
69
80-110 m a.g.l. over Hartheim in the case of cloudless sky conditions (21/22 April,
2000) and cloudy sky conditions (17 April, 2000 and 18 April 2000) were studied. Fig.
6.1.10-Fig. 6.1.12 present a comparative study between the diurnal course of two days
mean of σ3w/z, MKE and TKE in the cloudless and cloudy sky conditions.
6.1.5
Turbulence intensity
6.1.5.1
Variation of turbulence intensity with wind directions under neutral
conditions
During neutral conditions, the variation of turbulence intensity components, Iu, Iv and Iw,
with the angular sectors can be investigated to illustrate the effect of the roughness in
the values of the turbulent intensity components. Table 6.1.1 shows the mean, standard deviations and the number of the observation of the turbulence intensity components, Iu, Iv and Iw, at different levels, 50-80 m, 80-110 m, 140-170 m, and 200-230 m
a.g.l. under neutral conditions, grouped by wind direction, during the period of this
study (30 March, 2000 to 25 April, 2000).
6.1.5.2
Turbulence intensity under different stratifications
The turbulence intensity components, Iu, Iv and Iw, can be analyzed according to P-G
stability classes for the angular sector 180-210° at different levels. This angular sector
has been chosen for this study since the major wind directions are approximately observed to be between 180° and 210°. Table 6.1.2 summarizes the mean, standard deviations and the number of observations of the turbulence intensity components, Iu, Iv
and Iw, at different levels, 50-80 m, 80-110 m, 140-170 m, and 200-230 m a.g.l. in Hartheim during the period from 30 March, 2000 to 25 April, 2000. These data were
grouped according to P-G stability classes for the angular sector 210-240° and the
mean values are schown in Fig. 6.1.13.
6.1.6
Relationship between normalized standard deviations of velocity
components and z/L
The mean values of the standard deviations of the velocity components were normalized by u∗, σi/u∗  (i=u,v,w), and the dependence of the normalized values on the stability
70
parameter (-z/L) under the unstable stratified would be explained. Fig. 6.1.14 shows the
behavior of σu/u∗, σv/u∗ and σw/u∗ as a function of -z/L under the unstable conditions
(0.28 <-z/L<8.31) at Hartheim during the period from 30 March, 2000 to 25 April, 2000.
This data was collected in the surface layer (less than 110 m a.g.l.).
The shape of the variation of σu/u∗, σv/u∗ and σw/u∗ with increasing instability (-z/L) have
the same variation of the following general function (after Al-Jiboori et al., 2001):
σi
1
z
= a i (1 + bi ) 3
u*
L
(6.1)
where ai and bi are empirical constants. In this study they were found to be 2.95, 2.99
and 1.1, and 2.2, 2.7 and 4 for u, v and w components respectively.
71
Table 6.1.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels
grouped by direction. Under each component are given the mean, standard deviation and number of observations in each group at Hartheim for
the study period (30 March, 2000 to 25 April, 2000)
height
a.g.l.
50 - 80 m
(a)
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
wind direction sector
0-30°
30-60°
60-90°
0.41
0.15
10
0.32
0.09
15
0.32
0.11
26
0.32
0.11
20
0.55
0.12
7
0.40
0.14
15
0.37
0.16
21
0.68
0.18
3
°
°
°
90-120°
0.68
0.11
4
0.42
2
height
(b)
0-30
50 - 80 m
0.72
0.30
10
0.50
0.17
15
0.37
0.19
26
0.37
0.20
20
0.65
0.13
7
0.39
0.14
15
0.35
0.11
21
30-60
°
°
60-90
°
90-120
(c)
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
0.36
0.12
92
0.33
0.10
77
0.28
0.09
84
0.28
0.10
64
0.69
0.21
3
0.38
0.10
4
0.33
0.09
24
0.31
0.13
51
0.37
0.09
6
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.57
0.04
4
0.09
2
0.50
0.08
3
height
a.g.l.
50 - 80 m
0.31
0.08
19
0.25
0.08
11
0.35
0.12
11
0.47
0.18
5
330-360°
0.41
0.07
7
0.38
0.07
4
0.27
0.06
5
0.30
0.06
2
wind direction sector
a.g.l.
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.52
0.17
19
0.35
0.19
11
0.45
0.14
11
0.44
0.18
5
0.57
0.25
92
0.42
0.21
77
0.29
0.16
84
0.28
0.14
64
0.61
0.09
3
0.42
0.13
4
0.34
0.14
24
0.30
0.12
51
330-360°
0.61
0.09
7
0.61
0.24
4
0.39
0.18
5
0.38
0.12
6
wind direction sector
0-30
0.17
0.07
10
0.11
0.03
15
0.07
0.02
26
0.07
0.02
20
30-60
°
60-90
°
90-120
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.11
0.02
4
0.11
0.01
7
0.05
0.02
15
0.06
0.02
21
0.04
2
0.07
0.05
3
0.10
0.02
19
0.09
0.05
11
0.06
0.03
11
0.09
0.03
5
0.12
0.05
92
0.10
0.03
77
0.06
0.04
84
0.06
0.03
64
0.13
0.05
3
0.09
0.02
4
0.06
0.01
24
0.07
0.05
51
330-360°
0.15
0.10
7
0.10
0.01
4
0.07
0.02
5
0.06
0.04
6
Av. = average, std. = standard deviations, no. = number of observations
72
Table 6.1.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different levels
grouped by P-G stability classes in one angular sector (180-210°). Under
each component are given the mean, standard deviation and number of
the observation in each group at Hartheim for the study period (30 March,
2000 to 25 April, 2000)
height
a.g.l.
50 - 80 m
80 - 110 m
(a)
P-G stability classes
av.
std.
no.
av.
std.
no.
Α
5.55
0.85
7
3.83
2.60
6
D
0.36
0.12
109
0.33
0.10
104
E
0.74
0.21
30
0.52
0.08
2
F
2.28
1.52
12
2.18
2.17
26
2.84
1.40
0.46
0.29
0.55
1.59
std.
no.
200 - 230 m av.
std.
no.
0.53
2
4.17
0.53
16
1.15
0.46
14
0.15
40
0.45
0.13
29
0.08
115
0.29
0.11
71
0.06
5
0.55
0.13
4
1.96
21
2.59
1.34
7
a.g.l.
50 - 80 m
1
P-G stability classes
Α
4.80
Β
2.67
C
1.20
D
0.58
E
1.36
F
3.19
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
1.04
7
4.28
1.77
6
3.72
1.04
32
1.33
0.41
42
1.49
0.30
59
0.56
0.16
45
0.48
0.25
109
0.41
0.20
104
0.29
0.27
30
0.78
0.22
2
0.81
1.43
12
2.71
2.17
26
1.79
std.
0.57
0.74
0.13
0.15
0.16
1.03
no.
200 - 230 m av.
std.
no.
2
4.17
16
1.10
0.37
14
40
0.43
0.17
29
115
0.28
0.13
71
5
0.72
0.09
4
20
3.21
2.01
7
E
0.24
0.08
30
0.11
0.01
2
0.10
0.04
5
0.11
0.02
4
F
1.88
2.25
16
0.69
0.94
27
0.31
0.48
21
0.47
0.47
7
av.
1
height
a.g.l.
50 - 80 m
(c)
C
0.69
0.35
59
0.41
0.11
45
140 - 170 m av.
height
(b)
Β
2.18
0.85
32
0.95
0.43
42
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
P-G stability classes
Α
1.84
0.85
8
1.34
0.52
6
0.63
0.35
2
5.20
1
Β
1.06
0.77
32
0.38
0.33
42
0.25
0.23
16
0.25
0.16
14
C
0.32
0.30
59
0.15
0.06
45
0.10
0.03
40
0.09
0.05
29
D
0.12
0.05
109
0.10
0.03
104
0.06
0.04
115
0.06
0.03
71
73
15
20 - 50 m
50 - 80 m
80 - 110 m
(m2/s2)
6
σ
2
9
h
12
(a)
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
15
20 - 50 m
50 - 80 m
σ
2
h
(m2/s2)
12
80 - 110 m
9
(b)
6
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.1.8:
Diurnal variation of two days mean of the variance of the horizontal wind
speed, σ2h, at Hartheim (a) cloudless sky conditions (21/22 April, 2000) (b)
cloudy sky conditions (17/18 April, 2000)
74
2.0
2
2
(m /s )
1.5
20 - 50 m
50 - 80 m
80 - 110 m
1.0
σ
2
w
(a)
0.5
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
2.0
20 - 50 m
50 - 80 m
80 - 110 m
(b)
1.0
σ
2
w
(m2/s2)
1.5
0.5
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.1.9:
Diurnal variation of two days mean of the variance of vertical wind speed
component, σ2w, at Hartheim (a) cloudless sky conditions (21/22 April,
2000) (b) cloudy sky conditions (17/18 April, 2000)
75
0.03
20 - 50 m
50 - 80 m
80 - 110 m
2
3
σ w/z (m /s )
0.02
3
(a)
0.01
0.00
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.03
20 - 50 m
50 - 80 m
3
2 3
σ w/z (m /s )
80 - 110 m
0.02
(b)
0.01
0.00
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.1.10: Diurnal variation of two days mean of the quantity, σ3w/z, at Hartheim (a)
cloudless sky conditions (21/22 April, 2000) (b) cloudy sky conditions
(17/18 April, 2000)
76
40
20 - 50 m
50 - 80 m
MKE (m 2/s2)
30
80 - 110 m
20
(a)
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
40
20 - 50 m
50 - 80 m
80 - 110 m
MKE (m 2/s2)
30
20
(b)
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.1.11: Diurnal variation of two days mean of the mean kinetic energy per unit
mass, MKE, at Hartheim (a) cloudless sky conditions (21/22 April, 2000)
(b) cloudy sky conditions (17/18 April, 2000)
77
15
20 - 50 m
50 - 80 m
TKE (m2/s2)
12
80 - 110 m
9
(a)
6
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
15
20 - 50 m
12
50 - 80 m
TKE (m2/s2)
80 - 110 m
9
(b)
6
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.1.12: Diurnal variation of two days mean of the turbulence kinetic energy per
unit mass, TKE, at Hartheim (a) cloudless sky conditions (21/22 April,
2000) (b) cloudy sky conditions (17/18 April, 2000)
78
1.5
50 - 80 m
140 - 170 m
80 - 110 m
200 - 230 m
1.0
Iu
(a)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
1.5
1.0
Iv
(b)
0.5
50 - 80 m
80 - 110 m
140 - 170 m
200 - 230 m
0.0
A
B
C
D
P-G stability classes
E
F
1.5
80 - 110 m
140 - 170 m
200 - 230 m
Iw
1.0
50 - 80 m
(c)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
Fig. 6.1.13: Variation of the mean values of the turbulence intensity components, Iu, Iv
and Iw, with the P-G stability classes in the angular sector 210-240° at different levels over Hartheim for the study period (30 March, 2000 to 25
April, 2000)
79
10
8
σu/u∗
6
(a)
4
data
general function
2
0
0
1
2
3
4
5
6
7
8
9
- (z/L)
10
σv/u∗
8
6
(b)
4
data
2
general function
0
0
1
2
3
4
5
6
7
8
9
- (z/L)
10
data
general function
σw/u∗
8
6
(c)
4
2
0
0
1
2
3
4
5
6
7
8
9
- (z/L)
Fig. 6.1.14: Mean of the standard deviation of wind speed components, σu, σv and σw,
normalized by u* as a function of -z/L at Hartheim for the study period (30
March, 2000 to 25 April, 2000); including general function according to AlJiboori et al. (2001)
80
6.2
Bremgarten: Grassland
6.2.1
Global solar radiation, wind direction, and wind speed variation
6.2.1.1
Global solar radiation
The characteristics of the global solar radiation G received on a horizontal surface at
Hartheim (approximately 3.5 km far from Bremgarten) on two cloudless days (22/23
July, 2001) and two cloudy days (14/15 July, 2001) are presented in Fig. 6.2.1. The
highest G was recorded around the noon hours (11:00-13:00 CET) with average values
greater than 800 W/m2 in the cloudless days and lower than 210 W/m2 in the cloudy
ones.
6.2.1.2
Wind direction
A general note about the frequency distribution of the wind direction is presented for
different levels (20-30 m, 180-260 m and 320-500 m a.g.l.) in Bremgarten during the
day and night, the daytime (6:00–18:00 CET), and nighttime (18:00–6:00 CET) through
the period from 10 July, 2001 to 26 July, 2001. Fig. 6.2.2 illustrates the wind rose at
these levels.
The profiles of the wind direction, dd, and the standard deviation of the wind direction,
σdd, at Bremgarten under various atmospheric stratification such as neutral (14 July,
2001, 22:30-23:00 CET), stable (16 July, 2001, 23:00-23:30 CET) and unstable (22
July, 2001, 11:30-12:00 CET) are presented in Fig. 6.2.3 (c and f respectively). Furthermore the diurnal course of two days mean of σdd at different levels, 20-30 m, 40-60
m, and 60-100 m a.g.l. over Bremgarten are summarized in Fig. 6.2.4, to show the
various characteristics on cloudless (22/23 July, 2001) and cloudy days (14/15 July,
2001)
6.2.1.3
Horizontal wind speed
The profile of the horizontal wind speed vh at Bremgarten under various atmospheric
conditions such as neutral (14 July, 2001, 22:30-23:00 CET), stable (16 July, 2001,
23:00-23:30 CET) and unstable (22 July, 2001, 11:30-12:00 CET) is given by Fig. 6.2.3
(a). Moreover, the diurnal course of two mean days of vh at different levels, 20-30 m,
81
40-60 m, and 60-100 m a.g.l. in Bremgarten on cloudless days (22/23 July, 2001) and
cloudy days (14/15 July, 2001) is illustrated in Fig. 6.2.5.
6.2.1.4
Vertical wind speed component
The effect of the atmospheric stability on the profile of the vertical component of the
wind speed, w, at Bremgarten under various atmospheric conditions such as neutral
(14 July, 2001,22:30-23:00 CET), stable (16 July, 2001, 23:00-23:30 CET) and unstable (22 July, 2001, 11:30-12:00 CET) is given by Fig. 6.2.6 (b). In addition, the difference between the diurnal variation of the two days mean values of w at various levels,
20-30 m, 40-60 m, and 60-100 m a.g.l. at Bremgarten on cloudless days (22/23 July,
2001) and cloudy days (14/15 July, 2001) is presented in Fig. 6.2.6.
6.2.2
Atmospheric stability classification
Similar to section 6.1.2, the P-G stability classes were determined according to Thomas
(1988). The results that obtained utilizing 30-min mean values of the standard deviation
of the wind direction, σdd, measured at the levels 40-60 m, 60-100 m, 100-180 m and
180-260 m a.g.l. by sodar are shown in Fig. 6.2.7.
However, during the study period (10 July, 2001 to 26 July, 2001) the percentage frequency distribution of P-G stability classes at different heights a.g.l. could be noticed.
For example, in the period of this study and at the level 40-60 m a.g.l. the stability conditions were unstable for 16% of the time, they were slightly unstable for 18% of the
time, they were neutral for 48% of the time and they were stable for only 18% of the
time.
6.2.2
Variance of horizontal and vertical wind speed
The profiles of the variance of the horizontal wind speed, σ2h, and the vertical wind
speed component, σ2w, at Bremgarten under various atmospheric conditions such as
neutral (14 July, 2001,22:30-23:00 CET), stable (16 July, 2001, 23:00-23:30 CET) and
unstable (22 July, 2001, 11:30-12:00 CET) are given in Fig. 6.2.3 (d and e respec-
82
tively). Moreover the diurnal course of the two days mean of σ2h and σ2w, at different
levels, 20-30 m, 40-60 m, and 60-100 m a.g.l. over Bremgarten in cloudless sky conditions (22/23 July, 2001) and cloudy sky conditions (14/15 July, 2001), are presented in
Fig. 6.1.8 and Fig. 6.1.9 respectively.
6.2.4
Turbulence kinetic energy
In line with section 6.1.4 the behavior of the profiles of σ3w/z, MKE and TKE at
Bremgarten under various atmospheric conditions such as neutral (14 July, 2001,
22:30-23:00 CET), stable (16 July, 2001, 23:00-23:30 CET) and unstable (22 July,
2001, 11:30-12:00 CET) are presented in Fig. 6.2.3 (g-i). In order to illustrate the influence of the clouds on the variation of σ3w/z, MKE and TKE, the behavior of these parameters in the case of cloudless sky and cloudy sky conditions were studied. Fig.
6.1.10 - Fig. 6.1.12, respectively illustrate these variations at different levels, 20-30 m,
40-60 m, and 60-100 m a.g.l. in Bremgarten under cloudless sky conditions (22/23 July,
2001) and cloudy sky conditions (14/15 July, 2001).
1000
14 July, 2001
800
15 July, 2001
22 July, 2001
2
G (W/m )
23 July, 2001
600
400
200
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.2.1:
Diurnal variation of the global solar radiation G at Hartheim on two cloudless days (22/23 July, 2001) and two cloudy days (14/15 July, 2001)
83
day and night
6:00 - 18:00 CET
18:00 - 6:00 CET
360 ° (N)
20%
330 °
300 °
30 °
60 °
10%
(W) 270 °
0%
90 ° (E)
240 °
120 °
210 °
(a) 20 - 30 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
(W) 270 °
0%
90 ° (E)
240 °
120 °
210 °
180 - 260 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
(W) 270 °
0%
90 ° (E)
240 °
120 °
210 °
380 - 500 m
150 °
180 ° (S)
Fig. 6.2.2:
Frequency distribution of wind direction at (a) 20-30 m a.g.l. (b) 180-260
m a.g.l. and (c) 380-500 m a.g.l. during day and night, daytime (6:00–
18:00 CET) and nighttime (18:00–6:00 CET) at Bremgarten through the
period of the study (10 July, 2001 to 26 July, 2001)
84
neutral
unstable
stable
500
z (m)
400
(a)
300
(c)
(b)
200
100
0
0
5
10
vh (m/s)
15
-0.1
0.4
0.9
1.4
0
w (m/s)
360
dd ( ° )
500
z (m)
400
(d)
(e)
(f)
300
200
100
0
0
3
σ
2
h
6
2
9
0
2
1
σ
(m /s )
2
w
2
2
0
2
45
90
σdd ( ° )
(m /s )
500
z (m)
400
(g)
300
(i)
(h)
200
100
0
0
3
6
2
9
2
TKE (m /s )
Fig. 6.2.3:
0
30
60
2
2
MKE (m /s )
0.00
0.04
0.08
σ3w /z (m 2/s3)
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE, and σ3w/z under various atmospheric conditions; neutral (14-07-2001, 12:30-13:00 CET), stable (16
July, 2001,23:00-23:300) and unstable (22 July, 2001,11:30:12:00C CET)
85
100
80
σdd (°)
60
(a)
40
20 - 30 m
20
40 - 60 m
60 - 100 m
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
100
20 - 30 m
40 - 60 m
60 - 100 m
σdd (°)
80
60
(b)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.2.4:
Diurnal variation of two days mean of the standard deviation of the wind
direction, σdd, at Bremgarten (a) cloudless sky conditions (22/23 July,
2001) and (b) cloudy sky conditions (14/15 July, 2001)
86
10
20 - 30 m
40 - 60 m
vh (m/s)
8
60 - 100 m
6
(a)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
10
20 - 30 m
40 - 60 m
60 - 100 m
vh (m/s)
8
6
(b)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.2.5:
Diurnal variation of two days mean of the horizontal wind speed, vh, at
Bremgarten (a) cloudless sky conditions (22/23 July, 2001) and (b) cloudy
sky conditions (14/15 July, 2001)
87
0.9
20 - 30 m
40 - 60 m
60 - 100 m
0.6
w (m/s)
0.3
(a)
0.0
-0.3
-0.6
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.9
20 - 30 m
40 - 60 m
w (m/s)
0.6
60 - 100 m
0.3
(b)
0.0
-0.3
-0.6
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.2.6:
Diurnal variation of two days mean of the vertical wind speed component,
w, at Bremgarten (a) cloudless sky conditions (22/23 July, 2001) and (b)
cloudy sky conditions (14/15 July, 2001)
88
50%
40 - 60 m
60 - 100 m
40%
100 - 180 m
frequency (% )
180 - 260 m
30%
20%
10%
0%
A
B
C
D
E
F
P-G stability classes
Fig. 6.2.7:
Frequency distribution of P-G stability classes at different heights a.g.l. in
Bremgarten for the study period (10 July, 2001 to 26 July, 2001)
6.2.5
Turbulence intensity
6.2.5.1
Variation of turbulence intensity with wind directions under neutral
conditions
Similar to the results of section 6.1.5.1, during the neutral conditions, the variation of
the turbulence intensity components, Iu, Iv and Iw, with the angular sectors was studied
at Bremgarten during the investigation period (10 July, 2001 to 26 July, 2001) to illustrate the effect of the roughness in its values. Table 6.2.1 gives the mean, standard
deviations and the observation number of the turbulence intensity components, Iu, Iv
and Iw, at different levels, 40-60 m, 60-100 m, 100-180 m, and 180-260 m a.g.l.
grouped by wind direction. The mean values are summarized in Fig. 6.2.13.
6.2.5.2
Turbulence intensity under different stratifications
The turbulence intensity components, Iu, Iv and Iw, can be analyzed according to P-G
stability classes at one angular sector, 180-210°, at different levels. The angular sector
180-210° has been chosen for this study because the major wind directions are ob-
89
served to be between 180° and 210°. Table 6.2.2 summarizes the mean and standard
deviations of the turbulence intensity components, Iu, Iv and Iw, at different levels, 40-60
m, 60-100 m, 100-180 m, and 180-260 m a.g.l. in Bremgarten grouped according to PG stability classes for the angular sector 180-210°. The mean values are summarized
in Fig. 6.2.14.
6.2.6
Relationship between normalized standard deviations of velocity
components and z/L
The mean values of the standard deviations of the velocity components normalized by
u∗, σi/u∗ (i=u,v,w), and the dependence of the normalized values on the stability parameter (-z/L) under the unstable stratified will be explained.
Fig. 6.1.15 shows the behavior of σu/u∗, σv/u∗ and σw/u∗ as a function of -z/L under the
unstable conditions (0.82<-z/L <11.24) at Bremgarten during the period from 10 July,
2001 to 26 July, 7-2001. This data was collected in the surface layer (less than 100 m
a.g.l.).
The shape of the variation of σu/u∗, σv/u∗ and σw/u∗ with the increasing of the instability
(-z/L) have the same variation of the Eq. (6.1), but the empirical constants ai and bi at
this site are found to be 1.7, 1.7 and 1.2, and 1.6, 1.5 and 4 for u, v and w components
respectively.
90
Table 6.2.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels
grouped by direction. Under each component are given the mean, standard deviation and number of observation in each group at Bremgarten
during the study period (10 July, 2001 to 26 July, 2001)
height
a.g.l.
40 - 60 m
(a)
av.
std.
no.
60 - 100 m av.
std.
no.
100 - 180 m av.
std.
no.
180 - 260 m av.
std.
no.
wind direction sector
°
0-30
°
30-60
°
60-90
90-120
0.37
0.10
12
0.43
0.15
16
0.39
0.14
3
0.54
0.40
8
0.34
0.13
9
0.43
0.16
3
0.43
0.11
3
0.41
0.13
6
0.34
0.12
16
0.34
0.09
8
0.34
0.14
5
0.36
0.14
5
°
height
a.g.l.
40 - 60 m
(b)
av.
std.
no.
60 - 100 m av.
std.
no.
100 - 180 m av.
std.
no.
180 - 260 m av.
std.
no.
(c)
av.
std.
no.
60 - 100 m av.
std.
no.
100 - 180 m av.
std.
no.
180 - 260 m av.
std.
no.
°
°
°
°
°
300-330
°
330-360
°
300-330
°
330-360
°
300-330
°
330-360
150-180
180-210
210-240
240-270
270-300
0.33
0.13
17
0.14
0.02
4
0.32
0.11
126
0.22
0.09
80
0.26
0.06
74
0.24
0.05
32
0.34
0.14
35
0.25
0.15
25
0.33
0.23
41
0.29
0.16
51
0.36
0.09
10
0.28
0.11
3
0.26
0.06
5
0.42
0.15
9
0.44
0.13
3
0.23
0.11
2
°
0.46
0.10
5
wind direction sector
0-30
°
30-60
°
60-90
°
90-120
°
0.38
0.09
12
0.31
0.07
3
0.38
0.17
3
0.49
0.09
6
0.38
0.11
16
0.34
0.11
8
0.30
0.03
5
0.37
0.15
5
0.49
0.37
16
0.40
0.15
3
0.43
0.15
8
0.38
0.14
9
°
0-30
°
30-60
°
60-90
90-120
0.24
0.06
12
0.25
0.08
16
0.21
0.02
3
0.14
0.04
8
0.08
0.04
9
0.34
0.04
3
0.24
0.02
3
0.14
0.03
6
0.17
0.08
2
0.27
0.10
16
0.19
0.03
8
height
a.g.l.
40 - 60 m
°
120-150
°
120-150
°
°
°
°
150-180
180-210
210-240
240-270
270-300
0.39
0.11
17
0.22
0.05
4
0.31
0.12
125
0.25
0.14
80
0.27
0.10
74
0.24
0.04
32
0.36
0.21
35
0.28
0.11
25
0.32
0.16
40
0.30
0.11
51
0.40
0.08
10
0.25
0.12
3
0.24
0.06
5
0.42
0.12
9
0.38
0.09
3
°
0.42
0.12
5
wind direction sector
0.11
0.02
5
0.08
0.05
5
°
°
120-150
°
°
°
°
150-180
180-210
210-240
240-270
270-300
0.21
0.04
17
0.14
0.01
4
0.20
0.07
126
0.16
0.03
80
0.09
0.02
74
0.08
0.03
32
0.19
0.06
35
0.18
0.04
25
0.11
0.04
41
0.08
0.02
51
0.23
0.05
10
0.20
0.04
3
0.16
0.06
5
0.16
0.14
9
0.15
0.04
3
0.12
0.07
5
°
91
Table 6.2.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different levels
grouped by P-G stability classes in one angular sector (180-210°). Under
each component are given the mean, standard deviation and number of
the observation in each group during the study period (10 July, 2001 to 26
July, 2001)
height
a.g.l.
40 - 60 m
60 - 100 m
(a)
100 - 180 m
180 - 260 m
P-G stability classes
Α
av.
std.
no.
av.
std.
no.
av.
std.
no.
av.
std.
no.
4.19
1.63
5
3.06
0.34
4
height
a.g.l.
40 - 60 m
60 - 100 m
(b)
100 - 180 m
180 - 260 m
60 - 100 m
(c)
100 - 180 m
180 - 260 m
C
0.70
0.34
9
0.38
0.14
18
0.39
0.11
31
0.40
0.14
53
D
0.34
0.14
37
0.27
0.15
38
0.31
0.19
73
0.28
0.14
91
E
0.63
0.41
8
0.46
0.24
6
0.78
0.03
2
F
2.11
0.15
2
0.92
0.56
10
2.05
1.41
10
2.95
2.76
4
P-G stability classes
av.
Β
2.74
C
0.82
D
0.36
E
0.66
F
2.06
std.
no.
av.
std.
no.
av.
std.
no.
av.
std.
no.
1.05
9
1.11
0.49
9
1.35
0.59
3
1.35
0.43
4
0.31
9
0.45
0.14
18
0.45
0.15
31
0.40
0.13
53
0.20
37
0.34
0.17
38
0.31
0.13
72
0.28
0.10
91
0.50
8
0.70
0.41
6
0.80
0.02
2
0.36
2
1.07
0.24
10
2.22
1.20
10
5.07
5.77
4
D
0.19
0.05
37
0.18
0.04
38
0.10
0.04
73
0.08
0.03
91
E
0.37
0.18
8
0.29
0.11
6
0.17
0.06
2
F
0.79
0.30
2
0.45
0.30
10
0.46
0.32
10
2.40
3.93
4
Α
3.32
1.36
5
2.89
0.86
4
height
a.g.l.
40 - 60 m
Β
2.14
1.03
9
1.35
0.51
10
1.61
0.26
3
1.29
0.67
4
P-G stability classes
Α
av.
std.
no.
av.
std.
no.
av.
std.
no.
av.
std.
no.
2.99
1.42
5
0.82
0.28
4
Β
2.04
1.60
9
0.60
0.43
10
0.58
0.04
3
0.53
0.25
4
C
0.49
0.38
9
0.23
0.13
18
0.17
0.06
31
0.13
0.05
53
92
12
20 - 30 m
40 - 60 m
60 - 100 m
(a)
6
σ
2
h
(m2/s2)
9
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
12
20 - 30 m
40 - 60 m
60 - 100 m
6
(b)
σ
2
h
(m2/s2)
9
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.2.8:
Diurnal variation two days mean of the variance of the horizontal wind
speed, σ2h, at Bremgarten (a) cloudless sky conditions (22/23 July, 2001)
and (b) cloudy sky conditions (14/15 July, 2001)
93
3.0
20 - 30 m
2.5
40 - 60 m
60 - 100 m
2
2
(m /s )
2.0
1.5
σ
2
w
(a)
1.0
0.5
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
3.0
20 - 30 m
2.5
40 - 60 m
60 - 100 m
(b)
1.5
σ
2
w
(m2/s2)
2.0
1.0
0.5
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.2.9:
Diurnal variation of two days mean of the variance of vertical wind speed
component, σ2w, (a) cloudless sky conditions (22/23 July, 2001) and (b)
cloudy sky conditions (14/15 July, 2001)
94
0.12
20 - 30 m
40 - 60 m
60 - 100 m
2
3
σ w/z (m /s )
0.09
(a)
3
0.06
0.03
0.00
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.12
20 - 30 m
40 - 60 m
60 - 100 m
3
2 3
σ w/z (m /s )
0.09
0.06
(b)
0.03
0.00
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.2.10: Diurnal variation of two days mean of the quantity, σ3w/z, (a) cloudless sky
conditions (22/23 July, 2001) and (b) cloudy sky conditions (14/15 July,
2001)
95
50
20 - 30 m
40
40 - 60 m
MKE (m 2/s2)
60 - 100 m
30
(a)
20
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
50
20 - 30 m
40 - 60 m
MKE (m2/s2)
40
60 - 100 m
30
(b)
20
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.2.11: Diurnal variation of two days mean of the mean kinetic energy per unit
mass, MKE, (a) cloudless sky conditions (22/23 July, 2001) and (b)
cloudy sky conditions. (14/15 July, 2001)
96
12
20 - 30 m
40 - 60 m
60 - 100 m
TKE (m2/s2)
9
6
(a)
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
12
20 - 30 m
40 - 60 m
60 - 100 m
TKE (m2/s2)
9
6
(b)
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.2.12: Diurnal variation of two days mean of the turbulence kinetic energy per
unit mass, TKE, (a) cloudless sky conditions (22/23 July, 2001) and (b)
cloudy sky conditions (14/15 July, 2001)
97
1.0
40 - 60 m
100 - 180 m
0.8
60 - 100 m
180 - 260 m
0.6
Iu
(a)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
1.0
40 - 60 m
100 - 180 m
0.8
60 - 100 m
180 - 260 m
0.6
Iv
(b)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
1.0
0.8
40 - 60 m
60 - 100 m
100 - 180 m
180 - 260 m
Iw
0.6
(c)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
Fig. 6.2.13: Variation of the mean values of the turbulence intensity components, (a)
Iu, (b) Iv and (c) Iw, with the angular sectors under the neutral stratified at
different levels. in Bremgarten during the study period (10 July, 2001 to
26 July, 2001)
98
1.5
40 - 60 m
100 - 180 m
60 - 100 m
180 - 260 m
1.0
Iu
(a)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
1.5
1.0
40 - 60 m
60 - 100 m
100 - 180 m
180 - 260 m
Iv
(b)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
1.5
60 - 100 m
100 - 180 m
180 - 260 m
Iw
1.0
40 - 60 m
(c)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
Fig. 6.2.14: Variation of the mean values of the turbulence intensity components (a)
Iu, (b) Iv and (c) Iw, with the P-G stability classes in the angular sector 210240° at different levels in Bremgarten during the study (10 July, 2001 to
26 July, 2001)
99
10
data
general function
8
σu/u∗
6
(a)
4
2
0
0
2
4
6
- (z/L)
8
10
12
10
data
8
σv/u∗
general function
6
(b)
4
2
0
0
2
4
6
- (z/L)
8
10
12
10
data
general function
σw/u∗
8
6
(c)
4
2
0
0
2
4
6
- (z/L)
8
10
12
Fig. 6.2.15: Mean of the standard deviation of wind speed components, σu, σv and σw,
normalized by u* as a function of -z/L at Bremgarten during the period
from 10 July, 2001 to 26 July, 2001, including the general function according to Al-Jiboori et al. (2001)
100
6.3
Blankenhornsberg: Vineyard
6.3.1
Global solar radiation, wind direction, and wind speed variation
6.3.1.1
Global solar radiation
The diurnal variation of the global solar radiation G received on a horizontal surface at
Hartheim (approximately 9 km far from Blankenhornsberg) on two cloudless days
(12/15 August, 2001) and two cloudy days (03/17 August, 2001) is presented in Fig.
6.3.1. The maximum values were recorded around noon hours (11:00-13:00 CET) with
average values greater than 800 W/m2 in the cloudless sky conditions. But in the
cloudy conditions there was a high fluctuation in these values.
6.3.1.2
Wind direction
Here, the patterns of the wind roses at different levels (20-30 m, 180-260 m and 320500 m a.g.l.) are presented for Blankenhornsberg during the day and night, daytime
(6:00–18:00 CET), and nighttime (18:00–6:00 CET) during the period from 01 August,
2001 to 22 August, 2001 (Fig. 6.3.2).
The behavior of the profile of the wind direction, dd, and the standard deviation of the
wind direction, σdd, at Blankenhornsberg under various atmospheric conditions such as
neutral (04 August, 2001, 02:30-03:00 CET) and unstable (12 August, 2001, 13:3014:00 CET) is illustrated in Fig. 6.3.3 (c and f respectively). Furthermore, the diurnal
course variation of the two days mean of σdd at different levels, 20-30 m, 40-60 m, and
80-120 m a.g.l. in Blankenhornsberg under cloudless sky conditions (12/15 August,
2001) and cloudy sky conditions (03/17 August, 2001) are summarized in Fig. 6.3.4 to
show the various behavior on the cloudy and cloudless days.
6.3.1.3
Horizontal wind speed
The profile of the horizontal wind speed under various atmospheric stratification such
as neutral (04 August, 2001, 02:30-03:00 CET) and unstable (12 August, 2001, 13:3014:00 CET) at Blankenhornsberg are given in Fig. 6.3.3 (a).
101
In additions, the two-day mean of the diurnal course of vh is illustrated in Fig. 6.3.5 at
different levels, 20-30 m, 40-60 m, and 80-120 m a.g.l. in Blankenhornsberg on cloudless days (12/15 August, 2001) and cloudy days (03/17 August, 2001).
6.3.1.5
Vertical wind speed component
The values of the vertical wind speed component, w, was affected by the atmospheric
stability. Fig. 6.3.3 (b) reflects its behavior under various atmospheric conditions such
as neutral (04 August, 2001, 02:30-03:00 CET) and unstable (12 August, 2001, 13:3014:00 CET) at Blankenhornsberg.
Furthermore the difference between the two days mean values of w at different levels,
20-30 m, 40-60 m, and 80-120 m a.g.l. in Blankenhornsberg on cloudless days (12/15
August, 2001) and cloudy days (03/17 August, 2001) are presented in Fig. 6.3.6.
6.3.2
Atmospheric stability classification
Similar to section 6.1.2.and 6.2.2, Fig. 6.3.7 illustrates the P-G stability classes at different levels at Blankenhornsberg during the period from 01 August, 2001 to 22 August,
2001. The results that obtained utilizing 30-min mean values of the standard deviation
of the wind direction, σdd, and measured by sodar at the levels 40-60 m, 80-120 m,
120-160 m and 160-240 m a.g.l. are shown in Fig. 6.3.7.
During the study period (01 August, 2001 to 22 August, 2001) the percentage frequency distribution of P-G stability classes at different heights a.g.l. could be noticed.
For example in the period of this study and at the level 40-60 m a.g.l., the stability conditions were unstable for 32% of the time, they were slightly unstable for 23% of the
time, they were neutral for 25% of the time and they were stable for only 20% of the
time.
6.4.3
Variance of horizontal and vertical wind speed
The profiles of the variance of the horizontal wind speed, σ2h, and the vertical wind
speed component, σ2w, at Blankenhornsberg under various atmospheric conditions
102
such as neutral (04 August, 2001, 02:30-03:00 CET) and unstable (12 August, 2001,
13:30-14:00 CET) are given in Fig. 6.1.3 (d and e respectively). Moreover the diurnal
course of the two days mean of the σ2h and the σ2w, at different levels, 20-30 m, 40-60
m, and 80-120m, in Blankenhornsberg under cloudless sky conditions (12/15 August,
2001) and cloudy sky conditions (03/17 August, 2001) are presented in Fig. 6.1.8. and
Fig. 6.1.9 respectively.
1000
12 August, 2001
800
15 August, 2001
17 August, 2001
2
G (W/m )
03 August, 2001
600
400
200
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.3.1:
Diurnal variation of the global solar radiation G at Hartheim on two cloudless days (12/15 August, 2001) and two cloudy days (03/17 August,
2001)
103
day and night
6:00 - 18:00 CET
18:00 - 6:00 CET
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
0%
(W) 270 °
90 ° (E)
240 °
120 °
210 °
(a) 20 - 30 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
(W) 270 °
0%
90 ° (E)
240 °
120 °
210 °
160 - 240 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
(W) 270 °
0%
90 ° (E)
240 °
120 °
210 °
400 - 500 m
150 °
180 ° (S)
Fig. 6.3.2:
Frequency distribution of wind direction at (a) 20-30 m, (b) 160-240 m and
(c) 400-500 m a.g.l. at Blankenhornsberg during the day and night, daytime (6:00–18:00 CET), and nighttime (18:00–6:00 CET) through the
study period (01 August, 2001 to 22 August, 2001)
104
neutral
unstable
500
z (m)
400
(c)
(b)
(a)
300
200
100
0
0
vh
5
(m/s)
10
-1
3
0
w (m/s)
360
dd ( ° )
500
z (m)
400
(e)
(d)
(f)
300
200
100
0
0
8
16
0
σ2h (m2/s2)
1
2
0
σ2w (m2/s2)
40
80
σdd ( ° )
500
z (m)
400
(g)
300
(i)
(h)
200
100
0
0
10
20
2
2
TKE (m /s )
Fig. 6.3.3:
0
25
50
2
2
MKE (m /s )
0.00
0.03
0.06
σ3w/z (m2/s3)
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE, and σ3w/z at Blankenhornsberg under various atmospheric conditions; neutral (04 August, 2001,
02:30-03:00 CET) and unstable (12 August, 2001, 13:30-14:00 CET)
105
100
80
σdd (°)
60
(a)
40
20
20 - 30 m
40 - 60 m
80 - 120 m
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
100
20 - 30 m
40 - 60 m
80 - 120 m
σdd (°)
80
60
(b)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.3.4:
Diurnal variation of two days mean of the standard deviation of the wind
direction, σdd, at Blankenhornsberg (a) cloudless sky conditions (12/15
August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
106
10
20 - 30 m
40 - 60 m
vh (m/s)
8
80 - 120 m
6
(a)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
10
20 - 30 m
40 - 60 m
80 - 120 m
vh (m/s)
8
6
(b)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.3.5:
Diurnal variation of two days mean of the horizontal wind speed, vh, at
Blankenhornsberg (a) cloudless sky conditions (12/15 August, 2001) (b)
cloudy sky conditions (03/17 August, 2001)
107
2.0
20 - 30 m
40 - 60 m
1.5
80 - 120 m
w (m/s)
1.0
(a)
0.5
0.0
-0.5
-1.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
2.0
20 - 30 m
1.5
40 - 60 m
80 - 120 m
w (m/s)
1.0
0.5
(b)
0.0
-0.5
-1.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.3.6:
Diurnal variation of two days mean of the vertical wind speed component,
w, at Blankenhornsberg (a) cloudless sky conditions (12/15 August, 2001)
(b) cloudy sky conditions (03/17 August, 2001)
108
50%
40 - 60 m
80 - 120 m
40%
120 - 160 m
frequency (% )
160 - 240m
30%
20%
10%
0%
A
B
C
D
E
F
P-G stability classes
Fig. 6.3.7:
Frequency distribution of P-G stability classes at different levels a.g.l. at
Blankenhornsberg for the study period (01 August, 2001 to 22 August,
2001)
6.3.4
Turbulence kinetic energy
In line with section 6.1.4 and 6.2.4, the profile of σ3w/z, MKE and TKE at Blankenhornsberg under various atmospheric conditions such as neutral (04 August, 2001, 02:3003:00 CET) and unstable (12 August, 2001, 13:30-14:00 CET) are presented in Fig.
6.3.3 (g-i). Furthermore a comparative study between the diurnal course of two days
mean of σ3w/z, MKE and TKE at different levels, 20-30 m, 40-60 m, and 80-120m a.g.l.
in Blankenhornsberg under cloudless sky conditions (12/15 August, 2001) and cloudy
sky conditions (03/17 August, 2001) are given in Fig. 6.3.10-Fig. 6.3.12.
6.3.5
Turbulence intensity
6.3.5.1
Variation of turbulence intensity with wind directions under neutral
conditions
In line with the results of sections 6.1.5.1 and 6.2.5.1, the effect of the roughness in the
nature of turbulence intensity components, Iu, Iv and Iw, might be shown by the study of
109
the turbulence intensity for different angular sectors under the neutral conditions at
Blankenhornsberg during the period of the study (from 01-08-01 to 22-08-01). Table
6.3.1 gives the mean, standard deviations and the observation number of the turbulence intensity components, Iu, Iv and Iw, at different levels, 40-60 m, 80-120 m, 120160 m, 160-240 m a.g.l. under the neutral conditions grouped by wind direction. But the
mean values were summarized in Fig. 6.3.13.
6.3.5.2
Turbulence intensity under different stratifications
The turbulence intensity components, Iu, Iv and Iw, could be analyzed according to P-G
stability classes for the angular sectors 210-240° at different levels. The angular sector
210-240° has been chosen for this study because of the major wind directions were
approximately observed to be between 210° and 240°. Table 6.3.2 summarizes the
mean and standard deviations of the turbulence intensity components, Iu, Iv and Iw, at
different levels, 40-60 m, 80-120 m, 120-160 m and 160-240 m a.g.l. which are
grouped according to P-G stability classes for the angular sector 210-240°. The mean
values are summarized in Fig. 6.3.14.
6.3.5.3
Relationship between the normalized standard deviations of velocity
components and z/L
The dependence of the mean of normalized values (by u*) of the standard deviations of
the velocity components, σi/u∗ (i=u,v,w) on the stability parameter (-z/L) under the unstable stratified within the surface layer (less than 80 m a.g.l.) were illustrated in this
section. Fig. 6.3.1.16 shows the behavior of σu/u∗, σv/u∗ and σw/u∗ as a function of z/L
under the unstable conditions (0.31 < -z/L < 7.06) at Blankenhornsberg. The shape of
the variation of σu/u∗, σv/u∗ and σw/u∗ with the increasing of the instability (-z/L) have the
same variation of the Eq. (6.1) but the empirical constants ai and bi at this site were
found to be 1.8, 1.8 and 1.2, and 1.8, 1.8 and 4 for u, v and w components respectively.
110
Table 6.3.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels
grouped by direction. Under each component are given the mean, standard deviation and number of observation in each group at Blankenhornsberg through the period from 01 August, 2001 to 22 August, 2001
height
a.g.l.
40 - 60 m
(a)
av.
std.
no.
80 - 120 m av.
std.
no.
120 - 160 m av.
std.
no.
160 - 240 m av.
std.
no.
wind direction sector
°
°
°
0-30
30-60
0.31
0.08
15
0.41
0.16
9
0.40
0.09
11
0.30
0.07
4
0.71
0.07
2
0.34
0.16
9
0.38
0.12
13
0.41
0.15
14
0.53
0.09
5
0.57
0.17
5
0.57
0.10
8
°
0-30
°
30-60
°
0.62
0.23
15
0.54
0.24
9
0.45
0.12
11
0.50
0.24
4
0.46
0.23
2
0.38
0.16
9
0.41
0.12
13
0.50
0.17
14
0.59
0.12
5
0.62
0.19
5
0.49
0.19
8
°
0-30
°
30-60
°
0.36
0.11
15
0.22
0.05
9
0.12
0.07
11
0.14
0.09
4
0.33
0.06
2
0.16
0.05
9
0.10
0.05
13
0.09
0.04
14
60-90
°
90-120
0.40
0.15
23
0.44
0.15
22
0.35
0.11
12
0.42
0.21
10
0.44
0.18
11
0.48
0.31
5
height
a.g.l.
40 - 60 m
(b)
av.
std.
no.
80 - 120 m av.
std.
no.
120 - 160 m av.
std.
no.
160 - 240 m av.
std.
no.
(c)
av.
std.
no.
80 - 120 m av.
std.
no.
120 - 160 m av.
std.
no.
160 - 240 m av.
std.
no.
0.28
0.10
45
0.52
0.12
15
0.47
0.11
13
0.44
0.10
7
0.26
0.07
55
0.32
0.11
85
0.32
0.11
82
0.32
0.10
38
0.31
0.11
84
0.30
0.11
113
0.31
0.11
103
0.44
0.11
13
0.37
0.12
19
0.40
0.16
40
0.50
0.08
4
0.39
0.01
3
0.38
0.10
7
0.40
0.04
2
0.34
0.08
5
0.31
0.10
4
330-360°
0.24
0.06
4
0.36
0.09
11
0.31
0.04
6
0.29
0.10
5
wind direction sector
60-90
°
90-120
0.43
0.19
23
0.44
0.16
22
0.33
0.09
12
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.44
0.27
10
0.37
0.12
11
0.48
0.20
5
height
a.g.l.
40 - 60 m
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.55
0.31
45
0.51
0.15
15
0.46
0.13
13
0.46
0.17
7
0.63
0.35
55
0.33
0.16
85
0.32
0.12
82
0.41
0.19
38
0.34
0.14
84
0.32
0.12
113
0.41
0.19
103
0.51
0.15
13
0.40
0.13
19
0.46
0.18
40
0.78
0.41
4
0.45
0.18
3
0.43
0.15
7
0.24
0.04
2
0.38
0.10
5
0.48
0.13
4
330-360°
0.65
0.28
4
0.34
0.10
11
0.32
0.01
6
0.45
0.13
5
wind direction sector
60-90
0.23
0.02
5
0.15
0.16
5
0.12
0.04
8
°
90-120
0.16
0.05
23
0.12
0.16
22
0.10
0.06
12
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.16
0.04
10
0.11
0.09
11
0.09
0.08
5
0.33
0.09
45
0.20
0.04
15
0.08
0.05
13
0.09
0.04
7
0.30
0.08
55
0.15
0.03
85
0.09
0.03
82
0.07
0.04
38
0.15
0.08
84
0.09
0.06
113
0.08
0.03
103
0.14
0.06
13
0.09
0.02
19
0.13
0.16
40
0.21
0.09
4
0.11
0.02
3
0.11
0.09
7
0.22
0.02
2
0.11
0.04
5
0.12
0.04
4
330-360°
0.28
0.08
4
0.17
0.05
11
0.09
0.01
6
0.09
0.02
5
111
Table 6.3.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different levels
grouped by P-G stability classes in one angular sector (210-240°). Under
each component are given the mean, standard deviation and number of
the observation in each group at Blankenhornsberg for the study period
(01 August, 2001 to 22 August, 2001)
height
a.g.l.
40 - 60 m
(a)
av.
std.
no.
80 - 120 m av.
std.
no.
120 - 160 m av.
std.
no.
160 - 240 m av.
std.
no.
height
a.g.l.
40 - 60 m
(b)
av.
std.
no.
80 - 120 m av.
std.
no.
120 - 160 m av.
std.
no.
160 - 240 m av.
std.
no.
P-G stability classes
Α
10.57
8.14
6
2.86
1.18
5
2.98
0.99
4
Β
2.44
1.28
10
0.98
0.39
29
1.12
0.29
11
1.13
0.50
13
Α
11.28
7.45
6
3.05
0.42
5
3.55
1.82
3
Β
3.36
1.41
10
1.04
0.34
29
1.21
0.48
11
1.34
0.42
13
height
a.g.l.
40 - 60 m
(c)
av.
std.
no.
80 - 120 m av.
std.
no.
120 - 160 m av.
std.
no.
160 - 240 m av.
std.
no.
C
0.88
0.23
14
0.45
0.12
61
0.43
0.13
73
0.40
0.13
99
D
E
F
0.30
0.10
90
0.30
0.11
121
0.31
0.11
106
0.51
0.34
3
0.78
0.02
2
0.67
0.05
2
2.10
0.71
6
3.52
4.21
3
2.62
2.14
4
E
F
0.87
0.80
3
0.75
0.03
2
1.17
0.02
2
2.49
0.60
6
4.17
4.70
3
2.55
2.30
4
D
E
F
0.15
0.06
169
0.09
0.05
195
0.08
0.04
141
0.24
0.10
7
0.18
0.07
4
0.09
0.07
7
0.59
0.40
19
0.33
0.47
14
0.20
0.30
14
P-G stability classes
C
D
0.92
0.30
14
0.47
0.33
0.15
0.14
61
90
0.46
0.32
0.13
0.12
73
121
0.49
0.40
0.15
0.19
99
106
P-G stability classes
Α
10.05
7.61
13
1.73
0.89
6
0.93
0.54
5
Β
2.48
1.50
24
0.37
0.16
40
0.40
0.15
20
0.38
0.19
23
C
0.54
0.28
45
0.20
0.08
93
0.16
0.08
106
0.14
0.08
121
112
10
20 - 30 m
40 - 60 m
80 - 120 m
(m2/s2)
4
σ
2
6
h
8
(a)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
10
20 - 30 m
σ
2
h
(m2/s2)
8
40 - 60 m
80 - 120 m
6
(b)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.3.8:
Diurnal variation of two days mean of the variance of vertical wind speed
component, σ2h, at Blankenhornsberg (a) cloudless sky conditions (12/15
August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
113
3.0
20 - 30 m
2.5
40 - 60 m
80 - 120 m
2
2
(m /s )
2.0
1.5
σ
2
w
(a)
1.0
0.5
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
3.0
20 - 30 m
2.5
40 - 60 m
80 - 120 m
(b)
1.5
σ
2
w
(m2/s2)
2.0
1.0
0.5
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.3.9:
Diurnal variation of two days mean of the variance of the horizontal wind
speed, σ2w, at Blankenhornsberg (a) cloudless sky conditions (12/15 August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
114
0.20
20 - 30 m
40 - 60 m
80 - 120 m
2
3
σ w/z (m /s )
0.15
(a)
3
0.10
0.05
0.00
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.20
20 - 30 m
40 - 60 m
80 - 120 m
3
2 3
σ w/z (m /s )
0.15
0.10
(b)
0.05
0.00
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.3.10: Diurnal variation of two days mean of the quantity, σ3w/z, at Blankenhornsberg (a) cloudless sky conditions (12/15 August, 2001) (b) cloudy
sky conditions (03/17 August, 2001)
115
50
20 - 30 m
40
40 - 60 m
MKE (m 2/s2)
80 - 120 m
30
(a)
20
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
50
20 - 30 m
40 - 60 m
MKE (m 2/s2)
40
80 - 120 m
30
(b)
20
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.3.11: Diurnal variation of two days mean of the mean kinetic energy per unit
mass, MKE, at Blankenhornsberg (a) cloudless sky conditions (12/15 August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
116
12
20 - 30 m
40 - 60 m
80 - 120 m
TKE (m2/s2)
9
6
(a)
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
12
20 - 30 m
40 - 60 m
80 - 120 m
TKE (m2/s2)
9
6
(b)
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.3.12: Diurnal variation of two days mean of the turbulence kinetic energy per
unit mass, TKE, at Blankenhornsberg (a) cloudless sky conditions (12/15
August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
117
1.0
40 - 60 m
120 - 160 m
0.8
80 - 120 m
160 - 240 m
0.6
Iu
(a)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
1.0
0.8
0.6
Iv
(b)
0.4
0.2
0.0
40 - 60 m
120 - 160 m
0-30°
80 - 120 m
160 - 240 m
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
1.0
40 - 60 m
120 - 160 m
0.8
80 - 120 m
160 - 240 m
Iw
0.6
(c)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
Fig. 6.3.13: Variation of the mean values of the turbulence intensity components, Iu, Iv
and Iw, with the wind direction under the neutral stratified at different levels in Blankenhornsberg through the period of the study (01 August, 2001
to 22 August, 2001)
118
1.5
40 - 60 m
120 - 160 m
80 - 120 m
160 - 240 m
1.0
Iu
(a)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
1.5
1.0
Iv
(b)
0.5
40 - 60 m
80 - 120 m
120 - 160 m
160 - 240 m
A
B
0.0
C
D
P-G stability classes
E
F
1.5
80 - 120 m
120 - 160 m
160 - 240 m
Iw
1.0
40 - 60 m
(c)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
Fig. 6.3.14: Variation of the mean values of the turbulence intensity components, Iu, Iv
and Iw, with the P-G stability classes in the angular sector 210-240° at different levels at Blankenhornsberg through the period of the study (01 August, 2001 to 22 August, 2001)
119
10
data
general function
8
σu/u∗
6
(a)
4
2
0
0
1
2
3
4
- (z/L)
5
6
7
8
10
data
σv/u∗
8
general function
6
(b)
4
2
0
0
1
2
3
4
- (z/L)
5
6
7
8
10
data
general function
σw/u∗
8
6
(c)
4
2
0
0
1
2
3
4
- (z/L)
5
6
7
8
Fig. 6.3.15: Mean of standard deviation of wind speed components σu, σv and σW,
normalized by u* as a function of –z/L at Blankenhornsberg through the
period of the study (01 August, 2001 to 22 August, 2001) , including general function according to Al-Jiboori et al. (2001)
120
6.4
Oberbärenburg: Norway Spruce forest
6.4.1
Global solar radiation, wind direction, and wind speed variation
6.4.1.1
Global solar radiation
The diurnal variation of the global solar radiation G received on a horizontal surface at
Rotherdbach (one km from Oberbärenburg) on two cloudless days (30 August, 2001
and 23 September, 2001) and two cloudy days (31 August, 2001 and 01 September,
2001) is presented in Fig. 6.4.1. The maximum values were recorded around the noon
hours with average values greater than 600 W/m2 on the cloudless days and approximately lower than 200 W/m2 on the cloudy days.
6.4.1.2
Wind direction
A preliminary analysis of wind rose at different heights, 20-50 m, 230-260 m and 470500 m a.g.l. at Oberbärenburg during the day and night, daytime (6:00-8:00 CET) and
the nighttime (18:00-6:00 CET), through the period from 29 August, 2001 to 24 September, 2001, are presented in Fig. 6.4.2. The diurnal course of two days mean of σdd
at different levels 20-50 m, 50-80 m, 80-110 m a.g.l. at Oberbärenburg in cloudless sky
conditions (30 August, 2001 and 23 September, 2001) and cloudy sky conditions (31
August, 2001 and 01 September, 2001), are shown in Fig. 6.4.3.
6.4.1.3
Horizontal wind speed
The two days mean of the diurnal variation of vh is illustrated in Fig. 6.4.4 at different
levels, 20-50 m, 50-80 m, and 80-110 m a.g.l. in Oberbärenburg on cloudless days (30
August, 2001 and 23 September, 2001) and cloudy days (31 August, 2001 and 01 September, 2001).
6.4.1.4
Vertical wind speed component
Besides the data of the horizontal wind speed, diurnal variation of the vertical wind
speed component, w, at Oberbärenburg is shown. Fig. 6.4.5 presents the different between the two days mean values of w on cloudless days (30 August, 2001 and 23 Sep-
121
tember, 2001) and cloudy days (31 August, 2001 and 01 September, 2001) at different
levels, 20-50 m, 50-80 m, and 80-110 m a.g.l.
6.4.2
Atmospheric stability classification
As indicated in section 6.1.2, 6.2.2 and 6.3.2, the P-G stability classes were determined
from the sodar according to the method by Thomas (1988) for Oberbärenburg during
the period from 29 August, 2001 to 24 September, 2001. The results that obtained utilizing 30-min mean values of the standard deviation of the wind direction, σdd, and
measured at the levels 50-80 m, 80-110 m, 140-170 m and 200-230 m a.g.l. are shown
in Fig. 6.4.6. However, during the study period, the percentage frequency distribution of
P-G stability classes at different heights a.g.l. was noticed. For example in the period of
this study (29 August, 2001 to 24 September, 2001) and at the level 50-80 m a.g.l., the
stability conditions were unstable for 9% of the time, they were slightly unstable for
40% of the time, they were neutral for 40% of the time and they were stable for only
11% of the time.
800
31 August, 2001
01 September, 2001
23 September, 2001
30 August, 2001
2
G (W/m )
600
400
200
0
00:00
Fig. 6.4.1:
04:00
08:00
12:00
time (CET)
16:00
20:00
00:00
Diurnal variation of the global solar radiation G at Rotherdbach on two
cloudless days (30 August, 2001 and 23 September, 2001) and two
cloudy days (31 August, 2001 and 01 September, 2001)
360 ° (N)
40%
330 °
122
day and night
6:00 - 18:00 CET
18:00 - 6:00 CET
30 °
30%
300 °
60 °
20%
10%
(W) 270 °
90 ° (E)
0%
240 °
120 °
210 °
(a) 20 - 50 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
(W) 270 °
90 ° (E)
0%
240 °
120 °
210 °
(b) 230 - 260 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
0%
-10%
(W) 270 °
90 ° (E)
240 °
120 °
210 °
(c) 470 - 500 m
150 °
180 ° (S)
Fig. 6.4.2:
Frequency distribution of wind direction at (a) 20-50 m, (b) 230-260 m
a.g.l and (c) 470-500 m a.g.l. during the day and night, daytime (6:00–
18:00 CET) and the nighttime (18:00–6:00 CET) at Oberbärenburg
through the period of the study (29 August, 2001 to 24 September,
2001)
123
100
20 - 50 m
50 - 80 m
80 - 110 m
σdd (°)
80
60
(a)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
100
20 - 50 m
50 - 80 m
80 - 110 m
σdd (°)
80
60
(b)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.4.3:
Diurnal variation of two days mean of the standard deviation of the wind
direction, σdd, at Oberbärenburg (a) cloudless sky conditions (30 August,
2001 and 23 September, 2001) (b) cloudy sky conditions (31 August,
2001 and 01 September, 2001)
124
10
20 - 50 m
50 - 80 m
80 - 110 m
vh (m/s)
8
6
(a)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
10
20 - 50 m
50 - 80 m
vh (m/s)
8
80 - 110 m
6
(b)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.4.4:
Diurnal variation of two days mean of the horizontal wind speed, vh, at
Oberbärenburg (a) cloudless sky conditions (30 August, 2001 and 23
September, 2001) (b) cloudy sky conditions (31 August, 2001 and 01
September, 2001)
125
0.9
20 - 50 m
50 - 80 m
80 - 110 m
0.6
w (m/s)
0.3
(a)
0.0
-0.3
-0.6
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.9
20 - 50 m
50 - 80 m
w (m/s)
0.6
80 - 110 m
0.3
(b)
0.0
-0.3
-0.6
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.4.5:
Diurnal variation of two days mean of the vertical wind speed component,
w, at Oberbärenburg (a) cloudless sky conditions (30 August, 2001 and
23 September, 2001) (b) cloudy sky conditions (31 August, 2001 and 01
September, 2001)
126
80%
50 - 80 m
80 - 110 m
140 - 170 m
frequency (% )
60%
200 - 230 m
40%
20%
0%
A
B
C
D
E
F
P-G stability classes
Fig. 6.4.6
Frequency distribution of P-G stability classes at different levels a.g.l. at
Oberbärenburg for the study period (29 August, 2001 to 24 September,
2001)
6.4.3
Variance of horizontal and vertical wind speed
The diurnal course of two days mean of σ2h and σ2w, at Oberbärenburg on two cloudless days (30 August, 2001 and 23 September, 2001) and two cloudy days (31 August,
2001 and 01 September, 2001), are presented in Fig. 6.4.7. and Fig. 6.4.8 respectively.
6.4.4
Turbulence kinetic energy
In order to illustrate the influence of the clouds on the σ3w/z, MKE and TKE, the behavior of these parameters at Oberbärenburg in the case of cloudless sky conditions (30
August, 2001 and 23 September, 2001) and cloudy sky conditions (31 August, 2001
and 01 September, 2001) was studied. Thus a comparative study between two days
mean of σ3w/z, MKE and TKE in the cloudless and cloudy sky conditions are given in
Fig. 6.4.9-Fig. 6.4.11.
127
6.4.5
Turbulence intensity
6.4.5.1
Variation of turbulence intensity with wind directions under neutral
conditions
As indicated in sections 6.1.5.1, 6.2.5.1 and 6.3.5.1, the variations of the turbulence
intensity components, Iu, Iv and Iw, with the angular sectors were investigated under the
neutral conditions to illustrate the effect of the roughness in their values. Table 6.4.1
illustrates the mean, standard deviations and the observation number of the turbulence
intensity components, Iu, Iv and Iw, at different levels, 50-80 m, 80-110 m, 140-170 m,
200-230 m a.g.l. under the neutral conditions, grouped by the wind direction at Oberbärenburg through the period of the study (from 29 August, 2001 to 24 September,
2001). The mean values are summarized in Fig. 6.4.12.
6.4.5.3
Turbulence intensity under different stratifications
The turbulence intensity components, Iu, Iv and Iw, could be analyzed according to P-G
stability classes at the angular sector 180-210° at different levels. The angular sector
180-210° has been chosen for this study because of the major wind directions were
approximately observed to be between 180° and 210° at these levels. Table 6.4.2 summarizes the mean, standard deviations and the number of the observations of the turbulence intensity components, Iu, Iv and Iw, at different levels, 50-80 m, 80-110 m, 140170 m, 200-230 m a.g.l. in Oberbärenburg during the period from 29 August, 2001 to
24 September, 2001. These data are grouped according to P-G stability classes for the
angular sector 180-210° and the mean values are illustrated in Fig. 6.4.13.
6.4.6
Relationship between normalized standard deviations of velocity
components and z/L
The dependence of the mean of the standard deviations of the velocity components
normalized by u∗, σi/u∗ (i=u,v,w), on the stability parameter (-z/L) under the unstable
conditions would be studied. Fig. 6.4.14 shows the behavior of σu/u∗, σv/u∗ and σw/u∗ as
a function of -z/L (0.28 < -z/L <8.31) under the unstable conditions at Oberbärenburg
128
during the period. from 29 August, 2001 to 24 September, 2001. However, this data
was collected within the surface layer (less than 110 m a.g.l.).
The shape of the variation of σu/u∗, σv/u∗ and σw/u∗ with the increasing of the instability
(-z/L) have the same variation of the Eq. (6.1), but the empirical constants ai and bi at
this site were found to be 2.6, 2.5 and 1.25, and 1.8, 3.5 and 4.1 for u, v and w components respectively.
129
Table 6.4.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels
grouped by direction. Under each component are given the mean, standard deviation and number of observation in each group at Oberbärenburg through the period from 29 August, 2001 to 24 September, 2001
height
a.g.l.
50 - 80 m
(a)
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
wind direction sector
0-30°
30-60°
60-90°
0.33
0.05
4
0.26
0.04
4
90-120°
0.42
0.22
7
0.33
0.13
6
0.48
0.13
16
0.32
0.11
15
0.20
0.06
12
0.19
0.07
6
height
a.g.l.
50 - 80 m
(b)
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
(c)
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
0.55
0.24
9
0.34
0.10
4
0.42
0.09
30
0.35
0.09
22
0.28
0.08
7
0.16
0.04
10
0.44
0.14
42
0.29
0.07
37
0.21
0.04
47
0.19
0.04
38
0.59
0.26
49
0.37
0.14
47
0.22
0.05
57
0.20
0.04
43
0.55
0.27
34
0.39
0.18
31
0.24
0.06
43
0.22
0.05
27
0.72
0.28
27
0.42
0.13
22
0.25
0.06
23
0.20
0.05
21
330-360°
0.41
0.06
7
0.28
0.03
11
0.21
0.08
4
0.30
0.09
4
wind direction sector
0-30°
30-60°
60-90°
0.47
0.07
4
0.55
0.23
4
90-120°
0.36
0.12
7
0.29
0.06
6
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.53
0.19
16
0.38
0.16
15
0.23
0.06
12
0.17
0.05
6
0.33
1
height
a.g.l.
50 - 80 m
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.58
0.23
9
0.35
0.04
4
0.52
0.25
30
0.42
0.26
22
0.25
0.04
7
0.22
0.06
10
0.40
0.09
42
0.30
0.17
37
0.20
0.03
47
0.19
0.05
38
0.43
0.12
49
0.33
0.10
47
0.23
0.06
57
0.19
0.04
43
0.37
0.12
34
0.31
0.08
31
0.23
0.06
43
0.21
0.05
27
0.61
0.21
27
0.39
0.16
22
0.26
0.05
23
0.20
0.04
21
330-360°
0.55
0.23
7
0.28
0.04
11
0.17
0.03
4
0.36
0.15
4
wind direction sector
°
0-30
0.12
0.03
4
0.10
0.04
4
°
30-60
°
60-90
°
90-120
0.09
0.02
7
0.08
0.01
6
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.19
0.09
16
0.15
0.11
15
0.05
0.03
12
0.04
0.03
6
0.23
0.03
9
0.16
0.06
4
0.04
1
0.18
0.16
30
0.13
0.13
22
0.05
0.07
7
0.03
0.04
10
0.13
0.04
42
0.09
0.02
37
0.03
0.02
47
0.02
0.02
38
0.16
0.06
49
0.11
0.03
47
0.03
0.02
57
0.02
0.02
43
0.14
0.06
34
0.12
0.05
31
0.02
0.02
43
0.03
0.04
27
0.20
0.08
27
0.12
0.03
22
0.04
0.02
23
0.03
0.04
21
330-360°
0.12
0.02
7
0.08
0.01
11
0.03
0.03
4
0.01
0.01
4
130
Table 6.4.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different levels
grouped by P-G stability classes in one angular sector (180-210°). Under
each component are given the mean, standard deviation and number of
the observation in each group at Oberbärenburg through the period of the
study (29 August, 2001 to 24 September, 2001)
height
a.g.l.
50 - 80 m
(a)
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
P-G stability classes
Α
7.17
2.84
8
4.00
1
1.55
1
4.64
1
height
a.g.l.
50 - 80 m
(b)
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
(c)
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
C
0.46
0.22
33
0.51
0.13
34
0.44
0.11
34
0.40
0.11
25
D
0.26
0.07
76
0.32
0.11
85
0.32
0.11
82
0.32
0.10
38
E
0.46
0.17
17
0.59
0.16
4
0.64
0.09
2
0.70
0.16
5
F
1.45
2.40
7
1.17
0.73
13
1.56
1.02
11
1.81
1.46
11
E
1.18
0.43
17
0.69
0.23
4
0.65
0.23
2
0.84
0.04
5
F
4.32
5.18
7
1.69
1.52
13
1.82
1.21
11
3.34
4.47
11
E
0.58
0.22
17
0.29
0.12
4
0.16
0.11
2
0.08
0.07
5
F
1.70
3.04
7
0.57
0.42
13
0.24
0.32
11
0.18
0.34
11
P-G stability classes
Α
8.57
3.12
8
2.32
1
2.89
1
4.87
1
height
a.g.l.
50 - 80 m
Β
2.12
0.90
14
0.99
0.34
13
1.09
0.35
9
1.13
0.43
10
Β
2.95
0.83
14
0.93
0.57
13
1.24
0.25
9
1.29
0.36
10
C
1.00
0.35
33
0.49
0.16
34
0.42
0.11
34
0.47
0.17
25
D
0.60
0.31
76
0.33
0.16
85
0.32
0.12
82
0.41
0.19
38
P-G stability classes
Α
7.38
3.13
8
1.98
1
0.83
1
1.51
1
Β
2.30
1.20
14
0.39
0.20
13
0.41
0.17
9
0.35
0.16
10
C
0.53
0.28
33
0.21
0.06
34
0.16
0.09
34
0.13
0.06
25
D
0.30
0.07
76
0.15
0.03
85
0.09
0.03
82
0.07
0.04
38
131
15
20 - 50 m
50 - 80 m
80 - 110 m
(m2/s2)
6
σ
2
9
h
12
(a)
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
15
20 - 50 m
50 - 80 m
80 - 110 m
σ
2
h
(m2/s2)
12
9
(b)
6
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.4.7:
Diurnal variation of two days mean of the variance of the horizontal wind
speed, σ2h, at Oberbärenburg (a) cloudless sky conditions (30 August,
2001 and 23 September, 2001) (b) cloudy sky conditions (31 August,
2001 and 01 September, 2001)
132
2.0
20 - 50 m
50 - 80 m
80 - 110 m
2
2
(m /s )
1.5
1.0
σ
2
w
(a)
0.5
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
2.0
20 - 50 m
50 - 80 m
80 - 110 m
(b)
1.0
σ
2
w
(m2/s2)
1.5
0.5
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.4.8: Diurnal variation of two days mean of the variance of vertical wind speed
component, σ2w, at Oberbärenburg (a) cloudless sky conditions (30 August,
2001 and 23 September, 2001) (b) cloudy sky conditions (31 August, 2001
and 01 September, 2001)
133
0.05
20 - 50 m
50 - 80 m
80 - 110 m
0.03
3
2
3
σ w/z (m /s )
0.04
(a)
0.02
0.01
0.00
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.05
20 - 50 m
50 - 80 m
3
2 3
σ w/z (m /s )
0.04
80 - 110 m
0.03
(b)
0.02
0.01
0.00
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.4.9:
Diurnal variation of two days mean of the quantity, σ3w/z, at Oberbärenburg (a) cloudless sky conditions (30 August, 2001 and 23 September,
2001) (b) cloudy sky conditions (31 August, 2001 and 01 September,
2001)
134
40
20 - 50 m
50 - 80 m
MKE (m 2/s2)
30
80 - 110 m
20
(a)
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
40
20 - 50 m
50 - 80 m
80 - 110 m
MKE (m2/s2)
30
20
(b)
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.4.10: Diurnal variation of two days mean of the mean kinetic energy per unit
mass, MKE, at Oberbärenburg (a) cloudless sky conditions (30 August,
2001 and 23 September, 2001) (b) cloudy sky conditions (31 August,
2001 and 01 September, 2001)
135
15
20 - 50 m
50 - 80 m
TKE (m2/s2)
12
80 - 110 m
9
(a)
6
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
15
20 - 50 m
50 - 80 m
TKE (m2/s2)
12
80 - 110 m
9
(b)
6
3
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.4.11: Diurnal variation of two days mean of the turbulence kinetic energy per
unit mass, TKE, at Oberbärenburg (a) cloudless sky conditions (30 August, 2001 and 23 September, 2001) (b) cloudy sky conditions (29-082001 and 01-09-2001)
136
1.0
50 - 80 m
140 - 170 m
0.8
80 - 110 m
200 - 230 m
0.6
Iu
(a)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
1.0
50 - 80 m
140 - 170 m
0.8
80 - 110 m
200 - 230 m
0.6
Iv
(b)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
1.0
50 - 80 m
140 - 170 m
0.8
80 - 110 m
200 - 230 m
Iw
0.6
(c)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
Fig. 6.4.12: Variation of the mean values of the turbulence intensity components, Iu, Iv
and Iw, with the wind direction under the neutral stratified at different levels at Oberbärenburg for the study period (29-08-01 to 24-09-01)
137
1.5
50 - 80 m
140 - 170 m
80 - 110 m
200 - 230 m
1.0
Iu
(a)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
1.5
1.0
Iv
(b)
0.5
50 - 80 m
80 - 110 m
140 - 170 m
200 - 230 m
0.0
A
B
C
D
P-G stability classes
E
F
1.5
80 - 110 m
140 - 170 m
200 - 230 m
Iw
1.0
50 - 80 m
(c)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
Fig. 6.4.13: Variation of the mean values of the turbulence intensity components, Iu, Iv
and Iw, with the P-G stability classes in the angular sector 210-240° at different levels at Oberbärenburg through the period of the study (29 August, 2001 to 24 September, 2001)
138
10
8
σu/u∗
6
(a)
4
data
general function
2
0
0
1
2
3
4
5
6
7
8
9
- (z/L)
10
σv/u∗
8
6
(b)
4
data
2
general function
0
0
1
2
3
4
5
6
7
8
9
- (z/L)
10
data
general function
σw/u∗
8
6
(c)
4
2
0
0
1
2
3
4
- (z/L)
5
6
7
8
9
Fig. 6.4.14: Mean standard deviation of wind speed components σu, σv and σw, normalized by u* as a function of -z/L at Oberbärenburg through the period of
the study (29 August, 2001 to 24 September, 2001), including general
function according to Al-Jiboori et al. (2001)
139
6.5
Melpitz: grassland
6.5.1
Global solar radiation, wind direction, and wind speed variation
6.5.1.1
Global solar radiation
The diurnal variation of the global solar radiation G received on a horizontal surface at
Melpitz on a cloudless day (06 October, 2001) and two cloudy days (30 September,
2001 and 01 October, 2001) is presented in Fig. 6.5.1. The maximum values were recorded around the noon hours (11:00-13:00 CET) with average values greater than 500
W/m2 in the cloudless. But in the cloudy conditions, there was a fluctuation in these
values from 50 to 200 W/m2.
6.5.1.2
Wind direction
The wind rose at different heights, 20-50 m, 230-260 m and 470-500 m a.g.l. in Melpitz
during the day and night, daytime (6:00–18:00 CET), and nighttime (18:00–6:00 CET)
through the period from 26 September, 2001 to 12 October, 2001, is presented in Fig.
6.4.2.
Beside the wind rose, the profiles of the wind direction, dd, and the standard deviation
of the wind direction, σdd, at various atmospheric conditions such as neutral (03 October, 2001, 03:30-04:00 CET) and unstable (06 October, 2001, 13:00-13:30 CET) are
presented in Fig. 6.5.3 (d and f respectively). Furthermore the diurnal course variation
of σdd at different levels (20-50 m, 50-80 m, and 80-110 m a.g.l.) in cloudless sky conditions (06 October, 2001) and two days mean in cloudy sky conditions (30 September,
2001 and 01 October, 2001) in Melpitz are summarized in Fig. 6.4.4.
6.5.1.3
Horizontal wind speed
The profile of the horizontal wind speed at Melpitz under various atmospheric stratification such as neutral (03 October, 2001, 03:30-04:00 CET) and unstable (06 October,
2001, 13:00-13:30 CET) are given in Fig. 6.5.3 (a). In addition, the diurnal course variation of vh at a different levels 20-50 m, 50-80 m, 80-110 m a.g.l. in cloudless sky conditions (06 October, 2001) and two days mean in cloudy sky conditions (30 September,
2001 and 01 October, 2001) are presented in Fig. 6.5.5.
140
6.5.1.5
Vertical wind speed component
The values of the vertical wind speed component, w, was affected by the atmospheric
stability. Fig. 6.5.3 (b) reflects its behavior at Melpitz under various atmospheric conditions such as the neutral (03 October, 2001, 03:30-04:00 CET) and unstable (06 October, 2001, 13:00-13:30 CET). In addition, the diurnal course of w in Melpitz under
cloudless sky (06 October, 2001) and two days mean under cloudy sky (30 September,
2001 and 01 October, 2001) at a different levels 20-50 m, 50-80 m, 80-110 m a.g.l. are
presented in Fig. 6.5.6.
600
30 September, 2001
01 October, 2001
06 October, 2001
2
G (W/m )
400
200
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.5.1:
Diurnal variation of the global solar radiation G at Melpitz on a cloudless
day (06 October, 2001) and two cloudy days (30 September, 2001 and 01
October, 2001)
360 ° (N)
30%
330 °
141
day and night
6:00 - 18:00 CET
18:00 - 6:00 CET
30 °
20%
300 °
60 °
10%
(W) 270 °
90 ° (E)
0%
240 °
120 °
210 °
(a) 20 - 50 m
150 °
180 ° (S)
360 ° (N)
40%
330 °
30 °
30%
300 °
60 °
20%
10%
0%
(W) 270 °
90 ° (E)
240 °
120 °
210 °
(b) 230 - 260 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
0%
-10%
(W) 270 °
90 ° (E)
240 °
120 °
210 °
(c) 470 - 500 m
150 °
180 ° (S)
Fig. 6.5.2:
Frequency distribution of wind direction at (a) 20-50 m, (b) 230-260 m and
m, (c) 470-500 m a.g.l. during the day and night, daytime (6:00–18:00
CET) and the nighttime (18:00–6:00 CET) at Melpitz through the period of
the study (26 September, 2001 to 12 October, 2001)
142
neutral
unstable
stable
500
z (m)
400
(a)
300
(c)
(b)
200
100
0
0
5
10
vh (m/s)
15
-0.5
0
0.5
1
0
360
w (m/s)
dd ( ° )
500
z (m)
400
(d)
(e)
(f)
300
200
100
0
0
4
σ
2
h
8
2
0
2
0.5
σ
(m /s )
2
w
1
2
0
20
2
40
σdd ( ° )
(m /s )
500
z (m)
400
(g)
300
(i)
(h)
200
100
0
0
5
10
2
2
TKE (m /s )
Fig. 6.5.3:
0
25
50
75 100
2
2
MKE (m /s )
0.000
0.003
0.006
σ3w /z (m 2/s3)
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE, and σ3w/z at Melpitz under
various atmospheric conditions; neutral (03 October, 2001, 03:30-04:00)
and unstable (06 October, 2001, 13:00-13:30)
143
100
20 - 50 m
50 - 80 m
80 - 110 m
σdd (°)
80
60
(a)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
100
20 - 50 m
50 - 80 m
80 - 110 m
σdd (°)
80
60
(b)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.5.4:
Diurnal variation of the standard deviation of the wind direction, σdd, at
Melpitz (a) one cloudless day (06 October, 2001) and (b) two days mean
in cloudy sky (30 September, 2001 and 01 October, 2001)
144
10
20 - 50 m
50 - 80 m
vh (m/s)
8
80 - 110 m
6
(a)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
10
vh (m/s)
8
20 - 50 m
50 - 80 m
80 - 110 m
6
(b)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.5.5:
Diurnal variation of the horizontal wind speed, vh, at Melpitz (a) one cloudless day (06 October, 2001) and (b) two days mean in cloudy sky (30
September, 2001 and 01 October, 2001)
145
0.9
20 - 50 m
50 - 80 m
80 - 110 m
0.6
w (m/s)
0.3
(a)
0.0
-0.3
-0.6
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.9
20 - 50 m
50 - 80 m
w (m/s)
0.6
80 - 110 m
0.3
(b)
0.0
-0.3
-0.6
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.5.6:
Diurnal variation of the vertical wind speed component, w, at Melpitz (a)
one cloudless day (06 October, 2001) and (b) two days mean in cloudy
sky (30 September, 2001 and 01 October, 2001)
146
80%
50 - 80 m
80 - 110 m
140 - 170 m
frequency (% )
60%
200 - 230 m
40%
20%
0%
A
B
C
D
E
F
P-G stability classes
Fig. 6.5.7:
Frequency distribution of P-G stability classes at different levels a.g.l. at
Melpitz for the study period (26 September, 2001 to 12 October, 2001)
6.5.2
Atmospheric stability classification
Similar to 6.1.2, 6.2.2, 6.3.2 and 6.4.2, P-G stability classes were determined by sodar
measurements at Melpitz during the period of study (26 September, 2001 to 12 October, 2001). The results obtained from 30-min mean values of the standard deviation of
the wind direction, σdd, and measured at the levels 50-80 m, 80-110 m, 120-160 m and
160-240 m a.g.l. are shown in Fig. 6.5.7. During the study period the percentage frequency distribution of P-G stability classes at different heights a.g.l. was noticed. For
example in the period of this study (26 September, 2001 to 12 October, 2001) and at
the level 50-80 m a.g.l. the stability conditions were unstable for 5% of the time, they
were slightly unstable for 13% of the time, they were neutral for 77% of the time and
they were stable for only 5% of the time.
6.5.3
Variance of horizontal and vertical wind speed
The profiles of the variance of the horizontal wind speed, σ2h, and the variance of the
vertical wind speed component, σ2w, at Melpitz under different atmospheric conditions
147
such as the neutral (03 October, 2001, 03:30-04:00 CET) and unstable (06 October,
2001, 13:00-13:30 CET) are given in Fig. 6.5.3 (d and e respectively).
In addition, the diurnal course variation of σh and σw at different levels (20-50 m, 50-80
m, and 80-110 m a.g.l.) in cloudless sky conditions (06 October, 2001) and two days
mean in cloudy sky conditions (30 September, 2001 and 01 October, 2001) are presented in Fig. 6.5.8. and Fig. 6.5.9 respectively.
6.5.4
Turbulence kinetic energy
The behavior of the profiles of σ3w/z, MKE and TKE at Melpitz under various atmospheric conditions such as neutral (03 October, 2001, 03:30-04:00 CET) and unstable
(06 October, 2001, 13:00-13:30 CET) is presented in Fig. 6.5.3 (g-i).
Moreover a comparative study between the values of σ3w/z, MKE and TKE at different
levels, 20-50 m, 50-80 m, 80-110 m a.g.l in Melpitz for cloudless (06 October, 2001)
and a two days means in cloudy sky conditions (30 September, 2001 and 01 October,
2001) are given in Fig. 6.5.10 - Fig. 6.5.12.
6.5.5
Turbulence intensity
6.5.5.1
Variation of turbulence intensity with wind directions under neutral
conditions
In line with the sections 6.1.5.1, 6.2.5.1, 6.3.5.1 and 6.4.5.1, the effect of the roughness
in the nature of the turbulence intensity components, Iu, Iv and Iw, might be shown by
the study of the intensity components, Iu, Iv and Iw, at different angular sectors under
the neutral conditions over Melpitz during the period of the study (26 September, 2001
to 12 October, 2001).
Table 6.5.1 gives the mean, standard deviations and the observation number of the
turbulence intensity components, Iu, Iv and Iw, at different levels (50-80 m, 80-110 m,
120-160 m, and 160-240 m a.g.l.) under the neutral conditions, grouped by wind direction. But the mean values are summarized in Fig. 6.5.13.
148
6.5.5.2
Turbulence intensity under different stratifications
The turbulence intensity components, Iu, Iv and Iw, could be analyzed according to P-G
stability classes for the angular sectors 210-240° at different levels. The angular sector
210-240° has been chosen for this study because of the major wind directions were
approximately observed to be between 210 and 240°. Table 6.5.2 summarizes the
mean and standard deviations of the turbulence intensity components Iu, Iv and Iw at
different levels (50-80 m, 80-110 m, 120-160 m, 160-240 m a.g.l.) grouped according to
P-G stability classes for the angular sector 210-240°. The mean values are illustrated in
Fig. 6.5.14.
149
Table 6.5.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels
grouped by direction. Under each component are given the mean, standard deviation and number of observation in each group at Melpitz
through the period from 26 September, 2001 to 12 October, 2001
height
a.g.l.
50 - 80 m
(a)
30-60
°
60-90
°
90-120
0.82
0.94
8
0.29
0.08
21
0.25
0.04
3
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.29
0.06
18
0.25
0.07
29
0.33
0.13
12
0.54
0.14
8
0.34
0.12
50
0.22
0.06
31
0.21
0.12
17
0.40
0.25
31
0.28
0.08
132
0.24
0.11
109
0.21
0.06
96
0.32
0.15
49
0.26
0.07
175
0.21
0.04
197
0.23
0.11
155
0.67
0.46
19
0.28
0.07
64
0.22
0.05
105
0.21
0.11
106
0.87
0.44
8
0.28
0.07
8
0.30
0.10
15
0.48
0.43
8
330-360°
1.16
0.43
3
0.29
0.09
3
0.27
0.15
5
0.24
0.05
5
wind direction sector
0-30°
30-60°
60-90°
av.
std.
no.
80 - 110 m av. 0.16
std.
no. 1
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
height
a.g.l.
50 - 80 m
(c)
0-30
°
av.
std.
no.
80 - 110 m av.
std.
no.
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
height
a.g.l.
50 - 80 m
(b)
wind direction sector
°
90-120°
0.94
1.32
8
0.31
0.13
21
0.30
0.12
3
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.32
0.09
18
0.24
0.05
29
0.22
0.07
12
0.51
0.23
8
0.36
0.07
50
0.23
0.06
31
0.32
0.18
17
0.41
0.26
31
0.29
0.07
132
0.23
0.06
109
0.22
0.07
96
0.33
0.15
49
0.28
0.08
175
0.21
0.04
197
0.20
0.05
155
0.72
0.47
19
0.29
0.10
64
0.23
0.07
105
0.21
0.05
106
0.74
0.28
8
0.30
0.06
8
0.31
0.12
15
0.26
0.12
8
330-360°
1.31
0.55
3
0.39
0.05
3
0.23
0.08
5
0.24
0.03
5
wind direction sector
°
0-30
av.
std.
no.
80 - 110 m av. 0.04
std.
no. 1
140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
°
30-60
°
60-90
°
90-120
0.16
0.13
8
0.08
0.01
21
0.05
0.01
3
120-150° 150-180° 180-210° 210-240° 240-270° 270-300° 300-330°
0.08
0.01
18
0.06
0.04
29
0.05
0.02
12
0.10
0.02
8
0.09
0.03
50
0.06
0.03
31
0.08
0.10
17
0.11
0.06
31
0.08
0.02
132
0.06
0.02
109
0.05
0.03
96
0.10
0.03
49
0.08
0.02
175
0.06
0.02
197
0.06
0.02
155
0.16
0.12
19
0.09
0.02
64
0.06
0.04
105
0.06
0.03
106
0.15
0.07
8
0.10
0.04
8
0.08
0.03
15
0.07
0.03
8
0.19
0.07
3
0.09
0.01
3
0.06
0.01
5
0.11
0.09
5
330-360°
150
Table 6.5.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different levels
grouped by P-G stability classes in one angular sector (210-240°). Under
each component are given the mean, standard deviation and number of
the observation in each group at Melpitz through the period from 26 September, 2001 to 12 October, 2001
height
a.g.l.
50 - 80 m
av.
std.
no.
80 - 110 m av.
std.
no.
(a) 140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
height
a.g.l.
50 - 80 m
av.
std.
no.
80 - 110 m av.
std.
no.
(b) 140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
height
a.g.l.
50 - 80 m
av.
std.
no.
80 - 110 m av.
std.
no.
(c) 140 - 170 m av.
std.
no.
200 - 230 m av.
std.
no.
Α
8.82
5.92
13
3.05
1.15
6
2.69
1.07
5
4.64
1
Α
10.01
5.45
13
2.93
0.48
6
3.39
1.52
4
4.87
1
Α
10.05
7.61
13
1.73
0.89
6
0.93
0.54
5
1.51
1
Β
2.25
1.06
24
0.96
0.36
40
1.11
0.31
20
1.13
0.46
23
P-G stability classes
C
D
0.59
0.26
0.30
0.07
45
76
0.47
0.31
0.13
0.11
93
169
0.44
0.31
0.13
0.11
106
195
0.40
0.31
0.13
0.11
121
141
E
0.46
0.17
17
0.56
0.23
7
0.71
0.10
4
0.69
0.13
7
F
1.45
2.40
7
1.47
0.83
19
1.98
2.05
14
1.77
1.34
14
P-G stability classes
C
D
Β
3.12
0.97
0.60
1.10
0.33
0.31
24
45
76
1.02
0.48
0.34
0.42
0.15
0.15
40
93
169
1.22
0.44
0.32
0.38
0.13
0.12
20
106
195
1.32
0.48
0.41
0.39
0.16
0.19
23
121
141
E
1.18
0.43
17
0.77
0.50
7
0.70
0.15
4
0.93
0.17
7
F
4.32
5.18
7
1.94
1.34
19
2.32
2.35
14
2.93
4.02
14
P-G stability classes
C
D
Β
2.48
0.54
0.30
1.50
0.28
0.07
24
45
76
0.37
0.20
0.15
0.16
0.08
0.06
40
93
169
0.40
0.16
0.09
0.15
0.08
0.05
20
106
195
0.38
0.14
0.08
0.19
0.08
0.04
23
121
141
E
0.58
0.22
17
0.24
0.10
7
0.18
0.07
4
0.09
0.07
7
F
1.70
3.04
7
0.59
0.40
19
0.33
0.47
14
0.20
0.30
14
151
10
20 - 50 m
50 - 80 m
80 - 110 m
(m2/s2)
4
σ
2
6
h
8
(a)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
10
20 - 50 m
50 - 80 m
σ
2
h
(m2/s2)
8
80 - 110 m
6
(b)
4
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.5.8:
Diurnal variation of the variance of the horizontal wind speed, σ2h, at
Melpitz (a) one cloudless day (06 October, 2001) and (b) two days mean
in cloudy sky (30 September, 2001 and 01 October, 2001)
152
1.0
20 - 50 m
50 - 80 m
80 - 110 m
0.6
σ
2
w
2
2
(m /s )
0.8
(a)
0.4
0.2
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
1.0
20 - 50 m
50 - 80 m
σ
2
w
(m2/s2)
0.8
80 - 110 m
0.6
(b)
0.4
0.2
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.5.9:
Diurnal variation of the variance of the vertical wind speed, σ2w, at Melpitz
(a) one cloudless day (06 October, 2001) and (b) two days mean in
cloudy sky (30 September, 2001 and 01 October, 2001)
153
0.01
20 - 50 m
50 - 80 m
80 - 110 m
2
3
σ w/z (m /s )
0.01
(a)
3
0.01
0.00
0.00
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.012
20 - 50 m
50 - 80 m
80 - 110 m
3
2 3
σ w/z (m /s )
0.009
(b)
0.006
0.003
0.000
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.5.10: Diurnal variation of the quantity, σ3w/z, at Melpitz (a) one cloudless day
(06 October, 2001) and (b) two days mean in cloudy sky (30 September,
2001 and 01 October, 2001)
154
50
20 - 50 m
40
50 - 80 m
MKE (m 2/s2)
80 - 110 m
30
(a)
20
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
50
20 - 50 m
50 - 80 m
80 - 110 m
MKE (m 2/s2)
40
30
(b)
20
10
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.5.11: Diurnal variation of the mean kinetic energy per unit mass, MKE, at
Melpitz (a) one cloudless day (06 October, 2001) and (b) two days mean
in cloudy sky (30 September, 2001 and 01 October, 2001)
155
8
20 - 50 m
50 - 80 m
80 - 110 m
TKE (m2/s2)
6
4
(a)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
8
20 - 50 m
50 - 80 m
80 - 110 m
TKE (m2/s2)
6
4
(b)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.5.12: Diurnal variation of the turbulence kinetic energy per unit mass, TKE, at
Melpitz (a) one cloudless day (06 October, 2001) and (b) two days mean
in cloudy sky (30 September, 2001 and 01 October, 2001)
156
1.0
0.8
0.6
50 - 80 m
80 - 110 m
140 - 170 m
200 - 230 m
Iu
(a)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
1.0
0.8
(b)
Iv
0.6
50 - 80 m
80 - 110 m
140 - 170 m
200 - 230 m
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
1.0
0.8
50 - 80 m
80 - 110 m
140 - 170 m
200 - 230 m
Iw
0.6
(c)
0.4
0.2
0.0
0-30°
60-90°
120-150°
180-210°
240-270°
300-330°
angular sectors (°)
Fig. 6.5.13: Variation of the mean values of the turbulence intensity components, Iu, Iv
and Iw, with the wind direction under the neutral stratified at different levels at Melpitz through the period of the study (26 September, 2001 to 12
October, 2001)
157
1.5
50 - 80 m
140 - 170 m
1.0
80 - 110 m
200 - 230 m
Iu
(a)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
1.5
1.0
Iv
(b)
0.5
0.0
50 - 80 m
80 - 110 m
140 - 170 m
200 - 230 m
A
B
C
D
P-G stability classes
E
F
1.5
80 - 110 m
140 - 170 m
200 - 230 m
Iw
1.0
50 - 80 m
(c)
0.5
0.0
A
B
C
D
P-G stability classes
E
F
Fig. 6.5.14: Variation of the mean values of the turbulence intensity components, Iu, Iv
and Iw, with the P-G stability classes in the angular sector 210-240° at different levels at Melpitz through the period of the study (26 September,
2001 to 12 October, 2001)
158
6.6
Freiburg: Urban area
6.6.1
Global solar radiation, wind direction, and wind speed variation
6.6.1.1
Global solar radiation
The behavior of the diurnal variation of the global solar radiation G received on a horizontal surface on a cloudless day (17 November, 2001) and a cloudy day (18 November, 2001) at Freiburg is presented in Fig. 6.6.1. This Figure refers to the different between the values of the global solar radiation in these days.
6.6.1.2
Wind direction
The frequency distribution of the wind direction for different levels, 20-30 m, 40-60 m
and 60-80 m a.g.l. at Freiburg during the day and night, daytime (6:00–18:00 CET), and
nighttime (18:00 – 6:00 CET), through the period from 16 November, 2001 to 19 November, 2001, is shown in Fig. 6.6.2.
In addition, the profiles of the wind direction, dd, and the standard deviation of the wind
direction, σdd, at Freiburg under various atmospheric conditions such as stable (18 November, 2001, 04:30-05:00 CET) and unstable (17 November, 2001, 12:00-12:30 CET)
in the range from 20 to 100 m a.g.l. are given in Fig. 6.6.3 (c and f respectively). Furthermore, the diurnal course variation of σdd at a different levels 20-30 m, 40-60 m, 6080 m a.g.l. in cloudless sky conditions (17 November, 2001) and cloudy sky conditions
(18 November, 2001) is presented in Fig. 6.6.4.
6.6.1.4
Horizontal wind speed
The profile of the horizontal wind speed at Freiburg under various atmospheric conditions - stable (18 November, 2001, 04:30-05:00 CET) and unstable (17 November,
2001, 12:00-12:30 CET) - from 20 to 100 m a.g.l. is given in Fig. 6.6.3 (a).
In addition, the diurnal variation of vh at different levels, 20-30 m, 40-60 m, and 60-80 m
a.g.l. on cloudless day (17 November, 2001) and cloudy day (18 November, 2001) is
shown in Fig. 6.6.5.
159
6.6.1.4
Vertical wind speed component
Besides the data of the horizontal wind speed, profiles and diurnal variations of the vertical wind speed component, w, at Freiburg are presented. Fig. 6.6.3 (b) reflects its behavior under various atmospheric conditions [such as stable (18 November, 2001,
04:30-05:00 CET) and unstable (17 November, 2001, 12:00-12:30 CET)]. Furthermore,
Fig. 6.6.6 shows the different between the values of w on cloudless day (17 November,
2001) and cloudy day (18 November, 2001) at different levels, 20-30 m, 40-60 m, and
60-80 m a.g.l.
400
17 November, 2001
18 November, 2001
G (W/m2)
300
200
100
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.6.1:
Diurnal variation of the global solar radiation G at Freiburg on cloudless
day (17 November, 2001) and cloudy day (18 November, 2001)
6.6.2
Variance of horizontal and vertical wind speed
The profiles of the variance of the horizontal wind speed, σ2h, and the vertical wind
speed component, σ2w, from 20 to 100 m a.g.l. at Freiburg under various atmospheric
conditions such as stable (18 November, 2001, 04:30-05:00 CET) and unstable (17
November, 2001, 12:00-12:30 CET) are given in Fig. 6.6.3 (d and e respectively).
160
Moreover, the diurnal courses of σ2h and σ2w, at different levels, 20-30 m, 40-60 m, and
60-80 m a.g.l. in Freiburg under cloudless sky conditions (17 November, 2001) and
cloudy sky conditions (18 November, 2001) are presented in Fig. 6.6.7 and Fig. 6.6.8
respectively.
6.6.3
Turbulence kinetic energy
In line with section 6.1.4, 6.2.4, 6.3.4, 6.4.4 and 6.5.4, profiles of the σ3w/z, MKE and
TKE at Freiburg are shown under various atmospheric conditions such as stable (18
November, 2001, 04:30-05:00 CET) and unstable (17 November, 2001, 12:00-12:30
CET). Moreover the diurnal courses of the σ3w/z, MKE and TKE at different levels, 2030 m, 40-60 m, 60-80 m a.g.l. under cloudless (17 November, 2001) and cloudy (18
November, 2001) sky conditions at Freiburg are shown in Fig. 6.6.9-Fig. 6.6.11.
161
day and night
6:00 - 18:00 CET
18:00 - 6:00 CET
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
(W) 270 °
90 ° (E)
0%
240 °
120 °
210 °
(a) 20 - 30 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
(W) 270 °
90 ° (E)
0%
240 °
120 °
210 °
40 - 60 m
150 °
180 ° (S)
360 ° (N)
30%
330 °
30 °
20%
300 °
60 °
10%
(W) 270 °
90 ° (E)
0%
240 °
120 °
210 °
60 - 80 m
150 °
180 ° (S)
Fig. 6.6.2:
Frequency distribution of wind direction at (a) 20-30 m, (b) 40-60 m, (c)
60-80 m a.g.l. during the day and night, daytime (6:00–18:00 CET) and
nighttime (18:00–6:00 CET) at Freiburg through the period of the study
(16 November, 2001 to 19 November)
162
unstable
stable
100
z (m)
80
(a)
60
(c)
(b)
40
20
0
0
2
-0.25
vh (m/s)
0.5
0
w (m/s)
360
dd ( ° )
100
z (m)
80
(d)
(e)
(f)
60
40
20
0
0
3
0
σ2h (m /s )
2
0.5
0
σ2w (m /s )
2
2
2
60
σdd ( ° )
100
z (m)
80
(g)
60
(i)
(h)
40
20
0
0
3
2
2
TKE (m /s )
Fig. 6.6.3:
0
2
2
2
MKE (m /s )
0.00
0.01
3
σ w/z
2
3
(m /s )
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE, and σ3w/z at Freiburg under
various atmospheric conditions; stable (18 November, 2001, 04:30-05:00
CET) and unstable (17 November, 2001, 12:00-12:30 CET)
163
100
20 - 30 m
40 - 60 m
60 - 80 m
σdd (°)
80
60
(a)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
100
20 - 30 m
40 - 60 m
60 - 80 m
σdd (°)
80
60
(b)
40
20
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.6.4:
Diurnal variation of the standard deviation of the wind direction, σdd, at
Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy sky
conditions (18 November, 2001)
164
6
20 - 30 m
40 - 60 m
60 - 80 m
vh (m/s)
4
(a)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
6
20 - 30 m
40 - 60 m
60 - 80 m
vh (m/s)
4
(b)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.6.5
Diurnal variation of the horizontal wind speed, vh, at Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy sky conditions (18
November, 2001)
165
0.6
20 - 30 m
40 - 60 m
60 - 80 m
w (m/s)
0.3
(a)
0.0
-0.3
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.6
20 - 30 m
40 - 60 m
60 - 80 m
w (m/s)
0.3
(b)
0.0
-0.3
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.6.6:
Diurnal variation of the vertical wind speed component, w at Freiburg (a)
cloudless sky conditions (17 November, 2001) (b) cloudy sky conditions
(18 November, 2001)
166
6
20 - 30 m
40 - 60 m
60 - 80 m
(m2/s2)
4
σ
2
h
(a)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
6
20 - 30 m
40 - 60 m
60 - 80 m
(m2/s2)
4
σ
2
h
(b)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.6.7:
Diurnal variation of the variance of the horizontal wind speed, σ2h, at
Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy sky
conditions (18 November, 2001)
167
0.5
20 - 30 m
40 - 60 m
60 - 80 m
0.3
σ
2
w
2
2
(m /s )
0.4
(a)
0.2
0.1
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.5
20 - 30 m
40 - 60 m
σ
2
w
(m2/s2)
0.4
60 - 80 m
0.3
(b)
0.2
0.1
0.0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.6.8:
Diurnal variation of the variance of vertical wind speed component, σ2w, at
Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy sky
conditions (18 November, 2001)
168
0.012
20 - 30 m
40 - 60 m
60 - 80 m
2
3
σ w/z (m /s )
0.009
(a)
3
0.006
0.003
0.000
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
0.012
20 - 30 m
40 - 60 m
3
2 3
σ w/z (m /s )
0.009
60 - 80 m
(b)
0.006
0.003
0.000
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.6.9:
Diurnal variation of the quantity, σ3w/z, at Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy sky conditions (18 November,
2001)
169
20
20 - 30 m
40 - 60 m
60 - 80 m
MKE (m 2/s2)
15
10
(a)
5
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
20
20 - 30 m
40 - 60 m
60 - 80 m
MKE (m 2/s2)
15
10
(b)
5
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.6.10: Diurnal variation of the mean kinetic energy per unit mass, MKE, at
Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy sky
conditions (18 November, 2001)
170
6
20 - 30 m
40 - 60 m
60 - 80 m
TKE (m2/s2)
4
(a)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
6
20 - 30 m
40 - 60 m
60 - 80 m
TKE (m2/s2)
4
(b)
2
0
00:00
04:00
08:00
12:00
16:00
20:00
00:00
time (CET)
Fig. 6.6.11: Diurnal variation of the turbulence kinetic energy per unit mass, TKE, at
Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy sky
conditions (18 November, 2001)
171
7
GENERAL DISCUSSION
7.1
Global solar radiation, wind direction, and wind speed variation
To explain the influence of thermal and roughness changes on the characteristics of
the turbulent parameters such as turbulent kinetic energy per unit mass (TKE), turbulence intensity components (Iu, Iv, Iw) and the mean values of the normalized (by the
friction velocity) standard deviations of the velocity components, σi/u∗ (i=u,v,w) over the
sites of this study, the characteristics of the incoming solar radiation, wind direction and
its standard deviation, horizontal and vertical wind speed components, and the variances of horizontal and vertical wind speed components are briefly discussed for all
study sites through the periods of the measurements. The importance of these measurements for this study is due to their effects in the turbulence of the atmosphere. During weak advection, the nature of convection and turbulence are controlled by the wind
speed, incoming solar radiation (insulation) cloud shading and time of day and night
(Stull, 2000).
7.1.1
Global solar radiation
Within the ABL, there are significant daily variations of temperature, winds, static stability, and turbulence. These variations are driven by the diurnal cycle of solar heating
during day and IR cooling at night (Stull, 2000). The knowledge of the variability of G
gives an insight the effect of thermal in the behavior of the turbulence parameters in the
cloudless and cloudy sky conditions. Sections 6.1.1.1, 6.2.1.1, 6.3.1.1, 6.4.1.1, 6.5.1.1
and 6.6.1.1 summarize the results of the global solar radiation on the days in which the
turbulence parameters are investigated over Hartheim, Bremgarten, Blankenhornsberg,
Oberbärenburg, Melpitz and Freiburg respectively. These results reflect the effect of
clouds in the quantity of the incoming solar radiation. The difference between the midday hours (11:00-14:00 CET) average of G on two cloudless and cloudy days (except
for Melpitz: one cloudless day, and Freiburg: one cloudless and one cloudy day) were,
respectively, 67%, 82%, 66%, 86%, 78% and 73% at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg, Melpitz and Freiburg.
In addition, a high difference of the midday hours (11:00-14:00 CET) average of G on
cloudless and cloudy days were noticed from one site to another. These values were
172
701, 857, 817, 690, 495, and 381 (cloudless days), and 230, 156, 280, 94, 110 and 102
W/m2 (cloudy days) at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg,
Melpitz and Freiburg respectively. This is due to the seasonal effect of the incoming
solar radiation, as the measurements were gathered in a different periods of the year
(Table 5.4). The high difference in G from the cloudless days to the cloudy ones, as
well from one site to another, were important to show the effect of the incoming solar
radiation on some turbulence parameters (such as σw and σ3w/z) which are affected by
the thermal variation.
7.1.2
Wind direction
As reported in Stull (2000) the wind shear is one process of the production of the turbulence of the boundary layer and it is associated with the change of wind speed or wind
direction with the height. Moreover the values of σdd were used to determine the P-G
stability classes, according to Thomas (1988). Profiles of σdd under different atmospheric conditions and the diurnal course of σdd during cloudless and cloudy sky conditions are presented in the sections 6.1.1.2, 6.2.1.2, 6.3.1.2, 6.4.1.2, 6.5.1.2, and
6.6.1.2. As well these sections included the wind rose at different levels during the period of the study at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg, Melpitz
and Freiburg respectively. From these results, it can be concluded:
∗∗
The pattern of the wind rose varies for the different levels at the whole site of this
study but this change varies from one sites to another.
∗∗
There are high values of σdd at the low levels than those values of the high levels
at the whole sites of this study (see Figures 6.1.4, 6.2.4, 6.3.4, 6.4.3, 6.5.4 and
6.6.4). But these differences between the low and the high levels vary from one
site to another in both cases of cloudless and cloudy sky conditions.
In addition, the daily, midday hours (11:00-14:00 CET) and midnight hours (23:0002:00 CET) averages of σdd at different levels were calculated on two cloudless and
cloudy days (except for Melpitz and Freiburg: there were no many cloudless days) over
the sites of this study. Tables 7.1 - 7.6 summarize these averages and the standard
deviations at the sites of this study.
173
7.1.3
Wind speed components
Each local has a unique landscape that creates or modifies the wind. The change of
wind speed or wind direction with height leads to the wind shear which is one process
of the production of the turbulence of the atmospheric boundary layer. Furthermore, the
study of the MKE relates to the values of the wind speed components. Thus, profiles of
the horizontal and vertical wind speed under different atmospheric conditions as well as
the diurnal course at different levels in cloudless and cloudy sky conditions over all the
sites of this investigation are shown. Sections 6.1.1.3 , 6.2.1.3, 6.3.1.3, 6.4.1.3, 6.5.1.3
and 6.6.1.3 summarize the results of vh at Hartheim, Bremgarten, Blankenhornsberg,
Oberbärenburg, Melpitz and Freiburg respectively. Moreover, sections 6.1.1.4 , 6.2.1.4,
6.3.1.4, 6.4.1.4, 6.5.1.4 and 6.6.1.4 summarize the results of w at the same site respectively. From these results it can be concluded:
∗∗
The values of w under unstable conditions were greater than those under the
neutral conditions which were greater than those under stable conditions (see
Fig. 6.1.3(b), 6.2.3(b), 6.3.3(b), 6.5.3(b), and 6.1.3(b)). This is an expected behavior, however, the high instability causes a strong upward and downward motion of the air.
∗∗
There is a vibration of the values of w in cloudless and cloudy conditions. In the
first case (cloudless sky conditions), the values of w fluctuate through the most
time of the day and night with a high fluctuation values in the daytime. This is
due to the effect of the incoming solar radiation.
∗∗
At the two cases (cloudless and cloudy conditions), there is a difference of the
values of w from level to level. This is a result of the effect of the warming and
cooling of the earth’s surface in the upward and downward motion of the air.
In addition to the above remarks, the daily, midday hours (11:00-14:00 CET) and midnight hours (23:00-02:00 CET) averages of vh and w at different levels were calculated
on two cloudless and cloudy days (except for Melpitz and Freiburg: there is no many
cloudless days) over the sites of this study. Tables 7.1-Table 7.6 summarize these averages and the standard deviations at Hartheim, Bremgarten, Blankenhornsberg,
Oberbärenburg, Melpitz and Freiburg respectively. Moreover a comparison study be-
174
tween the midday-hours and midnight-hours-averages of vh and w on cloudless and
cloudy days are presented in Fig. 7.1-Fig. 7.6.
7.2
Atmospheric stability classification
The stability classification of the atmosphere is the first step for applying a number of
traditional algorithms aiming at estimating the main atmospheric parameters which
typically describe the boundary layer structure such as: Monin-Obukhov length, friction
velocity and the boundary layer height (Capanni and Gualtieri, 1999). The atmospheric
stability according to P-G stability classification was determined at four levels a.g.l, at
Hartheim (50-80, 80-110, 140-170, and 200-230 m), Bremgarten (40-60, 60-100, 100180, and 180-260 m), Blankenhornsberg (40-60, 80-120, 120-160, and 160-240 m),
Oberbärenburg (50-80, 80-110, 140-170, and 200-230 m), and Melpitz (50-80, 80-110,
140-170, and 200-230 m) for the study period. The mean value of the percentage frequency distribution for each class within the range, approximately, from 40 to 260 m
a.g.l, were respectively: A (1%, 5%, 5%, 1%, 1%), B (3%, 15%, 19%, 6%, 3%), C (21%,
22%, 26%, 34%, 21%), D (72%, 41%, 33%, 55%, 72%), E (2%, 7%, 5%, 1%, 2%), and
F (1%, 10%, 10%, 2%, 1%) at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg, and Melpitz. If one considers the period of the year for every site, these results
seem reliable.
7.3
Variance of horizontal and vertical wind speed
Turbulence is a quasi-random phenomenon that can be described by statistics. Velocity
variances represent TKE and a measure of the intensity of turbulence (Stull, 2000). As
σ2u , σ2v and σ2w are intimately related to the turbulent kinetic energy, it is to be antici-
pated that the intensity of turbulence should be related to the processes generating this
energy. Richardson (1920) showed these to be mainly shearing stresses and buoyancy
forces. Hence a particular attention will be given to the variance of the horizontal wind
speed, σ2h, and the variance of the vertical wind speed component, σ2w, in order to understand the nature of TKE and the turbulence intensity components.
175
The profiles of σ2h and σ2w under different atmospheric conditions, as well as, the diurnal course at different levels in cloudless and cloudy sky conditions over all the sites of
this study, are presented in sections 6.1.3, 6.2.3, 6.3.3, 6.4.3, 6.5.3 and 6.6.2 at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg, Melpitz and Freiburg respectively. From these results the following facts can be summarized:
∗∗
The fluctuations of the profile of σ2h and σ2w in the lower part are relatively higher
than those of the above part through the range of the FAS64 (20-500 m a.g.l.)
under the whole stability conditions (especially neutral and unstable conditions).
The nature of this fluctuation varies from one sites to the other ones. This may
be due to the increase of the mechanically and buoyancy production which occurs intensively in the surface layer,
∗∗
The general feature of the diurnal variation of both σ2h and σ2w under the two
cases have various variability from level to level and from hour to hour with
some peaks at different time,
∗∗
The effect of the solar radiation in the σ2w is obviously at the day-time, especially, during interval from 11:00 to 13:00 CET under the cloudless sky conditions,
∗∗
Sometime there is a high fluctuation in the values of σ2w under the cloudy sky
conditions (such as at the interval from 04:00 to 12:00 CET, Fig. 6.1.8), this may
be due to the downward and upward motion of the atmosphere through this interval as it illustrated in the variation of w, see Fig. 6.1.6.
Beside the above notice, the daily, midday hours (11:00-14:00 CET) and midnight
hours (23:00-02:00 CET) averages of σ2h and σ2w at different levels were calculated on
two cloudless and cloudy days (except for Melpitz and Freiburg: there is no many
cloudless days) over the sites of this study. Tables 7.1 - 7.6 summarize these averages
and the standard deviations at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg, Melpitz and Freiburg respectively. Moreover a comparison between the midday
hours and midnight hours averages of σ2h and σ2w on cloudless and cloudy days are
presented in Fig. 7.1 - Fig. 7.6.
176
7.4
Turbulence kinetic energy
In line with section (4.1.2.1), the value of TKE depends on: advection by the mean
wind, shear generation, buoyancy production, transport by turbulent motions and pressure, and viscous dissipation rate. This means, the nature of the changes of TKE varies
with the relative change of the magnitudes of these terms. But two terms of interest are
the shear and buoyancy terms (Stull, 2000). Moreover σ2w is connected to the production terms of convective and mechanical origin (σ3w/z), appearing in the equation of turbulent energy balance (Weill et al., 1980). Hence a particular attention will be given to
this quantity (σ3w/z) in this work.
To explain the influence of thermal and roughness changes on the properties of TKE
turbulence of the atmospheric boundary layer over the sites of this study, the profiles of
σ3w/z, MKE and TKE under different atmospheric stability conditions as well as the di-
urnal course at different levels in cloudless and cloudy sky conditions over the whole
sites of this study, were presented in sections 6.1.4, 6.2.4, 6.3.4, 6.4.4, 6.5.4 and 6.6.3
at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg, Melpitz and Freiburg respectively. The following features can be summarized from these results:
∗∗
At the whole site of this study, the vertical profiles of σ3w/z show that, the values
at the surface layer are higher than those at the rest range under the neutral and
unstable conditions. As well under the neutral and unstable atmospheric conditions, the values of σ3w/z are greater than those under the stable conditions, see
Fig. 6.1.3 (i), 6.2.3 (i), 6.3.3 (i), 6.5.3 (i) and 6.6.3 (i). Moreover, the variation of
σ3w/z is similar to the change of σ2w and depends on the buoyancy and the me-
chanical turbulence which occur intensively at the surface layer (Weill et al.,
1980).
∗∗
During cloudless conditions throughout the night, the values of the quantity σ3w/z
are low, even in the presence of wind shear. The effect of the incoming solar radiation is obvious in the day-time. But in the case of cloudy conditions, there are
some high peaks in the first level which correspond to the high values of σ2w
(see Fig. 6.1.10, 6.2.10, 6.3.10, 6.4.9, 6.5.10, and 6.6.9).
∗∗
However, the quantity σ3w/z is conducted by the mechanical and buoyancy turbulence production which occurs intensively in the surface layer. Hence the high
177
values of σ3w/z can be noticed at the low levels in the case of cloudless and
cloudy conditions.
∗∗
At the whole sites of this study, the values of MKE depend on the values of the
horizontal and vertical wind speed components and it has the same shape of the
variation of horizontal wind speed. This is obvious by the comparison of the
change of the profile and diurnal course of MKE and vh. Moreover the values of
MKE have a noticeable influence on TKE, as reported in Stull (1988), in which
the energy that is mechanically produced as turbulence is lost from the mean
flow and vice versa.
∗∗
As a result of the change of σ3w/z and MKE, the values of TKE vary too but this
change is not identical with these parameters. This is due to the fact that the
values of TKE do not depend on σ3w/z and MKE only but also on other parameters, see section 4.1.2.1. This change conduct with the behavior of σ2h and σ2w,
in which the effect of the σ2h is obvious because its values are relatively greater
than σ2w.
Beside the above remarks, the daily, midday hours (11:00-14:00 CET) and midnight
hours (23:00-02:00 CET) average of σ3w/z, MKE, and TKE at different levels are calculated on two cloudless and cloudy days (except for Melpitz and Freiburg: there were not
many cloudless days) over the sites of this study. Tables 7.1 - Table 7.6 summarize
these averages and the standard deviations at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg, Melpitz and Freiburg respectively. Moreover a comparative study
between the midday-hours and midnight-hours-averages of σ3w/z, MKE, and TKE on
cloudless and cloudy days is presented in Fig. 7.1 - Fig. 7.6. The following conclusions
can be drawn from the figures:
∗∗
The effect of the incoming solar radiation on σ3w/z is obviously by the comparison of the difference between its average values at the midday hours (11:0014:00 CET) and midnight hours (23:00-02:00 CET) on cloudless and cloudy
days. However the difference between the average values of the quantity σ3w/z
of the midday hours (11:00-14:00 CET) and midnight hours (23:00-02:00 CET)
for the whole levels in the sites of the study on the cloudless days are greater
than those on the cloudy days. Sometimes on cloudy days, these average val-
178
ues at midnight hours (23:00-02:00 CET) are equal to those at midday hours
(11:00-14:00 CET). For example in Bremgarten, for the whole levels under
cloudy conditions the average values at the midday and midnight hours are the
same, because the average of the wind speeds at the midday hours are smaller
than those at the midnight hours and the average global solar radiation is small
(~ 150 W/m2). This possibly suggests that, in the presence of developed convection, as at (11:00–14:00 CET), especially when the wind shear is less intense
(the horizontal wind speed is <1 m/s), the mechanical production term contributing to σ3w/z is negligible with respect to the buoyancy term (Greenhut et al.
1989). But the effect of the mechanical term on σ3w/z at the midnight hours and
under the cloudy days can be seen, especially in the low levels, when the values
of the horizontal wind speed are relatively high in this time.
∗∗
The midday hours (11:00-14:00 CET) and midnight hours (23:00-02:00 CET)
averages of MKE depend on the values of the horizontal and vertical wind speed
components and it has the same shape of the variation of the horizontal wind
speed. However, the values of the horizontal wind speed are greater than the
values of the vertical wind speed.
∗∗
The values of TKE do not depend on σ3w/z and MKE only but also on some
other parameters (see section 4.1.2.1). The variation of the midday hours
(11:00-14:00 CET) and midnight hours (23:00-02:00 CET) averages of TKE vary
and this variations are not identical with the variations of σ3w/z and MKE. But the
change of TKE is related to the behavior of σ2h and σ2w, in which the effect of the
σ2h is obvious because its values are relatively greater than σ2w. One can see
this behavior by the comparison of the values of TKE with the values of σ3w/z,
MKE, σ2h and σ2w in Fig. 7.1 - Fig. 7.6.
7.5
Turbulence intensity components
The turbulence intensity components, Iu, Iv and Iw, are the important variables for diffusion modeling and depend on the height of observation, the surface roughness and the
stability (Roth, 1993). Characteristics of the turbulence intensity components, Iu, Iv and
Iw, are shown over the study areas and investigation periods for various fetch condi-
179
tions arising under various wind directions, and different atmospheric stability at different levels.
7.5.2
Variation of turbulence intensity components with wind directions
under neutral conditions
In line with section 4.1.2.2, during the neutral conditions, the variation of the turbulence
intensity components, Iu, Iv and Iw, with the angular sectors are explained to illustrate
the effect of the roughness in the values of the turbulent intensity components. Table
6.1.1, 6.2.1, 6.3.1, 6.4.1 and 6.5.1 show the mean, standard deviations and the observation number of the turbulence intensity components, Iu , Iv and Iw, at different levels
under the neutral conditions, grouped by wind direction in Hartheim, Bremgarten,
Blankenhornsberg, Oberbärenburg and Melpitz respectively. In addition, the mean values are summarized in Fig. 6.2.13, 6.3.13, 6.4.12, and 6.5.13 in Bremgarten, Blankenhornsberg, Oberbärenburg and Melpitz respectively (this analysis could not be done for
Freiburg because the period of study was very short, 16 November, 2001 to 19 November, 2001). These tables and figures summarize the following:
∗∗
Generally the most frequent wind direction in the wind rose at the different levels
in the range of sodar for every site in this study are not the same for the whole
angular sectors and sometime there are no data in a number of angular sectors.
Consequently, the variation of the turbulence intensity components at the whole
angular sectors could not be analyzed. Also, these values could not be compared together, but this comparison could be made for the angular sectors for
which a considerable number of observations are available. For example, at
Hartheim (Table 6.1.1) results of the turbulence intensity components, Iu, Iv and
Iw, could not be compared at all angular sectors. But for the angular sector 180210°, the number of observation was suitable (92, 77, 84, and 28 at the heights
50-80 m, 80-110 m, 140-170 m and 200-230 m respectively). Thus, the dependence of the turbulence intensity components on the height of observation could
be analyzed. It shows a decrease with increasing height. The decrease of the
values of Iu, Iv and Iw were 21%, 51% and 47% respectively between the level
50-80 m and 200-230 m a.g.l..
180
∗∗
At Bremgarten, there is a small fluctuation in the values of Iu , Iv and Iw from one
angular sector to another as illustrated in Fig. 6.2.13. This behavior is expected,
as the surrounding of the sodar in this site is not completely symmetric. This
may be due to the presence of some trees with an average height 11 m (125 m
far from the site of sodar in the north-east direction), houses with an average
height 12 m (500 m far from the site of the sodar in the north-east and southeast) and a big group of trees in the west direction with an average height 10 m
(1800 m far from the site of the sodar). Beside the non-symmetric of the surrounding of the sodar, the high difference in the number of observations for the
wind direction sectors can play a considerable role in this variation. Furthermore,
the values of Iu, Iv and Iw decrease with the altitude (see Table 6.2.1 and Fig.
6.2.13). The decrease of the values of Iu, Iv and Iw from the level of 40-60 m to
180-260 m a.g.l. was calculated for the angular sectors which have a considerable number of observation such as 180-210° and 210-240°. The decrease of
the values of Iu, Iv and Iw were 64%, 63% and 82% for 180-210° and 30%, 37%
and 72% respectively for 210-240°. But some discrepancies in the results (such
as in the angular sectors 240-270° and 270-300°) may be due to the difference
between the number of the observations.
∗∗
At Blankenhornsberg and Melpitz, generally there is a very small fluctuation in
the values of Iu, Iv and Iw as it is illustrated in Fig. 6.3.13 and Fig. 6.5.14. This
fluctuation in the data is due to the non-symmetry of the surrounding and the
high difference of the number of the observations between the wind direction
sectors. Moreover the values of Iu, Iv and Iw decrease with the altitude (see Table
6.3.1 and 6.5.1). At Blankenhornsberg, the decrease of the values of Iu, Iv and Iw
from the level 40-60 m to 160-240 m a.g.l. was calculated for the angular sectors
(which have a considerable number of observation such as 150-180° and 180210°). The decrease of the values of Iv and Iw were 15% and 72% for 150-180°
and 35% and 75% respectively for 180-210°. There is a discrepancy in the values of Iu (its value increase 57% and 21% for the angular sectors 150-180° and
180-210° respectively). This may be due to the difference of the number of observations between the level 40-60 m a.g.l. (45 and 55) and the level 160-240 m
a.g.l. (7 and 38). At Melpitz, the values of Iu, Iv and Iw decrease with the increase
181
of the height for the angular sectors (which have a considerable number of observation such as 180-210° and 210-240°). The decrease of the values of Iu, Iv
and Iw were 47%, 46% and 50% respectively for 180-210°, and 30%, 38% and
44% respectively for 210-240°.
∗∗
At Oberbärenburg (Fig. 6.1.12), there is a variation of the values of the turbulence intensity component Iu, Iv and Iw with angular sector. This may be due to
the variation of the nature of the surface from sector to sector. Moreover, this
variation is high at the level 50-80 m a.g.l. and decrease with the increase of the
height a.g.l.. The mean value of the decrease of the values of Iu, Iv and Iw from
the level 50-80 m to 200-230 m a.g.l. was calculated for some angular sectors
(210-330°). The mean decrease of the values of Iu, Iv and Iw were 61%, 50% and
85% for this angular sector. This is an expected behavior. However, the nature
of turbulence intensity depends on the height of observation, the surface roughness (Roth, 1993).
From the previous remarks, the effect of the roughness index in the turbulence intensity
can be obviously seen when the surrounding of the sodar is not symmetric, as explained in the study of Brook (1972), which indicated the variation of the turbulence intensity components for various wind sector at different level in a complex terrain. Moreover, it can be seen that the intensity of turbulence is significantly different from the altitude above the ground level. This type of studies needs a large number of observations
to provide more reliable results.
7.5.2
Turbulence intensity under different stratifications
In order to study the effect of the height of observation and stability on turbulence intensity components, Iu, Iv and Iw, their values according to P-G stability classes were
analyzed at one angular sector at different levels for each site. This study was done at
one angular sector to reduce the change of z0. This led to its value approximately fixed
and only the effect of the stability on the turbulence intensity components could be investigated. Sections 6.1.5.2, 6.2.5.2, 6.3.5.2, 6.4.5.2 and 6.5.5.2 summarize the results
of this study at Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg and Melpitz
182
respectively (however at Freiburg there were not enough data to do this study). These
results led to the following:
∗∗
At all the sites of the study a high difference between the number of observations from class to class was observed, especially for A, E, F and sometimes for
B. Thus, these data were neglected in the discussion, because they are not representative data. Regardless of the number of observation at the stable conditions (E and F), the values of the turbulence intensity components are less reliable than for the neutral (D) and unstable (A, B and C) case. This behavior has
been observed by Smith and Abbott (1961), as well, McBean (1971) found a
less reliable data for σi/u*(i=u,v,w) under the stable than the unstable conditions.
Panofsky and Dutton (1984) explained that for a strong stability the quantities
σi/u∗ (i=u,v,w), σu/vh and σv/vh increase and become extremely variable. They
show that, the large standard deviations are produced by low-frequency fluctuations, not associated with turbulence.
∗∗
At all the sites of the study the nature of the relationship between turbulence intensity components, Iu, Iv and Iw, and the atmospheric stability was investigated
in the range from the class B (unstable) to class D (neutral). The values of the
turbulence intensity components, Iu, Iv and Iw, increase with the increase of the
instability from the neutral conditions (D) to the unstable (B). The values of the
turbulence intensity components Iu, Iv and Iw vary from level to level but they
have the same shape of variation. The relationship between turbulence intensity
components, Iu, Iv and Iw, and the atmospheric stability reflects high values of the
horizontal components of the turbulence intensity with respect to the vertical
component.
Similar to these results are those of Clarke et al. (1982), who also observed that values
increased with the increase of instability (for -1.6 < z/L < 0.8) and they reported higher
turbulence intensities for the horizontal components. Roth (1993) obtained similar results. On the other hand, Ramsdell (1975) (for -2.5 < z/L > 0.17; 1 < z < 50 m in an urban residential area), Högström et al. (1982) and Rotach (1991) could not observe any
relationship.
183
7.6
Relationship between normalized standard deviations of velocity
components and z/L under unstable conditions
In the present study, the mean values of the normalized standard deviations of the velocity components, σi/u∗ (i=u,v,w) as functions of the stability parameter (z/L) under the
unstable conditions over Hartheim (Scots pine forest), Bremgarten (grassland),
Blankenhornsberg (vineyard) and Oberbärenburg (Norway spruce forest), are summarized in Fig. 7.7 and compared to the results of other studies, which used sonic anemometer-thermometer instrument, over complex and flat terrain. The relationship between the mean values of the σi/u∗ (i=u,v,w) and z/L showed the same behavior over all
the sites and was in good agreement with the general function given by AL-Jiboori et al.
(2001).
σi
u*
1
= ai (1 + bi
z 3
)
L
7.8
where i = u, v, w as well as ai and bi are empirical constants. Table 7.7 summarizes the
values of ai and bi for this study and shows values of ai and bi as applied in this study
for different sites. Fig. 7.7 (a and b) and Table 7.7 show the increase of the mean values of σu/u∗ and σv/u∗ with increasing -z/L. The values of the empirical constant au,v and
bu,v at grassland and vineyard were smaller than those given by AL-Jiboori et al.
(2001). The values of au,v and bu,v at Scots pine forest, Norway spruce forest were
higher than those of AL-Jiboori et al. (2001). The mean values of σw/u∗ at the all sites
showed an increase with increasing instability (Fig. 7.7 c). Changes of aw and bw were
very small.
7.6.1
Horizontal components
The results of Scots pine forest (Hartheim), grassland (Bremgarten), vineyard
(Blankenhornsberg) and Norway spruce forest (Oberbärenburg) show the behavior that
the variation of the values of σu/u∗ and σv/u∗ increases with the increasing -z/L and has
the same trends described by Eq. (7.8) and Fig. (7.7). Previous studies such as ALJiboori et al., 2001 found the dependence of σu/u∗ and σv/u∗ on the stability parameter
z/L under unstable condition. Moreover, Monin and Obukhov (1954) hypothesized that
184
any dimensionless characteristic of the turbulence can depend only upon u∗, z, g/Tv,
H0, i.e. upon z/L (Garratt, 1992). The model proposed by Højstrup (1982), obtained by
integration of a model spectrum of horizontal variance, acknowledges a dependence of
σu/u∗ and σv/u∗ on both zi/L and z/L (Zhang et al., 2001).
In addition, Garratt (1992) pointed out that the relationships between σu/u∗ and σv/u∗
and -z/L show no height-dependence throughout the surface layer, even under very
unstable conditions, i.e. Monin-Obukhov scaling does not apply under these conditions,
and the mixed layer height zi becomes the relevant scaling height. But the mixing
height data, zi, are not available in the present study, thus the present results are unable to discriminate as to whether the horizontal components scale better with zi/L
rather than z/L as suggested by Panofsky et al. (1977) and Wyngaard and Cotè (1974).
To illustrate the effect of surface roughness on σu/u∗ and σv/u∗, the behavior of the relationship between these parameters and -z/L was compared for the different four sites
(Scots pine forest, grassland, vineyard and Norway spruce forest) as well as the data of
AL-Jiboori et al., 2001 for flat and complex terrain (Fig. 7.7, a and b). Furthermore, the
variation of the mean values of σu/u∗ and σv/u∗ in the same range of -z/L (0.86 to 3.86)
at the four sites and compares the results to the data of AL-Jiboori et al., 2001 for flat
and complex terrain will be discussed (Table 7.8).
Under unstable conditions, it is of interest to show that the data points of σu/u∗ and σv/u∗
were separated for different values of Scots pine forest, grassland, vineyard and Norway spruce forest. The lower values are from grassland and vineyard, while the higher
values upper points are from Scots pine forest and Norway spruce forest. This is in
good agreement with the result of AL-Jiboori et al., 2001. On the other hand, other
studies such as Zhang et al., 2001 compared the values of σu/u∗ and σv/u∗ over rough
surface (suburban and urban area) and a smooth surface (desert an grassland site).
The result gives a reduction for the rough site compared to the smooth surface condition for a given z/L. Garratt (1992) pointed out that the relationship between σu,v /u∗ and
-z/L shows no height-dependence throughout the surface layer, even in highly unstable
conditions, so Monin-Obukhov scaling does not apply, and the mixed layer height zi
becomes the relevant scaling height. These results revealed a dependence on the observational height. Zhang et al. (2001) have interpreted this behavior as follows: during
185
the course of a day the variation in zi may be small compared to the corresponding
variation in L and the measurements over various surface conditions were taken at different heights, so an apparent variation of σu/u∗ and σv/u∗ with height will results. But
the data were gathered with approximately a small difference in the height range, moreover the data of Al-Jiboori et al. 2001 were gathered at the same height (4.9 m a.g.l.).
Table 7.8 display the variation of the mean values of σu/u∗ and σv/u∗ in the same range
of -z/L (0.86 to 3.86) at the four sites and compares the results to the data of AL-Jiboori
et al., 2001 for flat and complex terrain. σu/u∗ and σv/u∗ differ from site to site and increase with increasing of the roughness length z0. The difference between the values
of σu/u∗ and σv/u∗ over flat terrain are smaller than those over complex terrain.
7.6.1
Vertical component
The vertical component σw/u∗ also showed an increase with increasing instability (Fig.
7.7c) which is in an agreement with results over flat (Al-Jiboori et al., 2001; Panofsky et
al., 1977; Xu et al., 1993; Zhang et al., 2001), and complex terrain (Al-Jiboori et al.,
2001; Founda et al., 1997; Zhang et al., 2001). The change of the surface roughness
does not seem to influence the properties of σw/u∗ (Fig. 7.7, c and Table 7.8). This
might be due to the fact that vertical velocity fluctuations are produced by small eddies
which rapidly adjust to changing surface properties (Panofsky and Dutton, 1984).
7.7
Profile of normalized variance of vertical wind speed component
Argentini et al. (1999) discussed the behavior of the normalized variances σ2w/w∗2 as a
function of the normalized height z/zi. They did this work in Milan (Italy) in the center
part of Po Valley, a densely populated and industrialized flat area of approximately 400
x 200 km2 surrounded on three sides by mountain but on the eastern part, the Po Valley is open to the Adriatic sea. They obtained a scatter data corresponding to the scaling:
σ w2
2
z
z
= c( ) 3 (1 − 0.8 ) 2
2
w*
zi
zi
7.9
186
with c = 1.8, 1.4, and 1. They found that, most of their experimental data are in the region delimited by the curves obtained with c = 1.8 and c = 1, while the curve with c =
1.4 is the best fit to these data.
In the present study, the variance of the vertical component of the wind speed, σ2w,
scaled by the square value of the convective velocity w∗2 and the profile of the normalized variance of the vertical wind speed component, σ2w/w∗2 under the free convective
conditions at Bremgarten, is presented in Fig. 7.9 (there is no available data about zi at
the other sites). The general behavior of the experimental data seems as a scatter diagram for of σ2w/w∗2, (full dots), but these values increases with the height to reach the
maximum values within the mixed layer. After it, these values decrease with the height
and reach very small values. Similar to Argentini et al. (1999), a scatter plot corresponding to Eq. (7.9) was obtained.
But most of the experimental data are in the region delimited by the curves 1and 2 (see
Fig. 7.9) obtained with c = 1 and 2.6. Moreover the maximum values of the normalized
vertical velocity variances is 0.67 (between z = 0.29zi and z = 0.36 zi). While the curve
with c = 1.7 (Stull, 1988) and 1.8 (Lenschow and Wyngaard, 1980) are suitable to
agree with the experimental data of this study. The maximum values in the case of c =
1.7 and 1.8 are 0.44 and 0.47at z = 0.32zi respectively.
The behavior of the data of this investigation is similar to most data in the literatures.
From the study of Hibber and Sawford (1994) in which they carried out a comparison
between their study and those of others in literatures, it can be concluded, that the
most others works give a scatter data in the same characters. Moreover in the surface
layer, the experimental data agree with the data of Wyngaard et al. (1971), given by the
formula:
σ w2
2
z
= 1.9( ) 3
2
w*
zi
7.10
2
h
(m 2 /s 2 )
TKE
(m 2 /s 2 )
MKE
(m 2 /s 3 )
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
(°)
σ 3 w /z
c lo u d le s s
c lo u d y
c lo u d le s s
σdd
(m 2 /s 2 )
σ
c lo u d y
c lo u d le s s
σ 2w
(m 2 /s 2 )
c lo u d y
m /s
c lo u d le s s
c lo u d y
m /s
w
c lo u d le s s
c o n d itio n
sky
vh
p a ra m e te r
Table 7.1:
2 .8 8
2 .8 4
1 .5 6
0 .1 8
0 .0 0 7 1
0 .0 0 4 8
4 8 .1 4
6 4 .4 3
2 .7 0
2 .7 0
0 .3 5
0 .2 7
0 .0 0
0 .0 1
1 .3 0
0 .4 6
av.
0 .9 2
1 .1 4
1 .3 7
0 .2 2
0 .0 0 6 0
0 .0 0 5 7
1 0 .6 7
9 .7 4
0 .8 6
1 .1 8
0 .1 9
0 .2 0
0 .0 7
0 .0 8
0 .6 4
0 .3 0
s td .
d a ily a v e ra g e
3 .8 4
1 .5 9
1 .4 5
0 .0 5
0 .0 1 1 9
0 .0 1 6 1
5 2 .2 7
6 5 .9 9
3 .5 8
1 .2 6
0 .5 1
0 .6 6
0 .0 1
0 .0 9
1 .2 6
0 .2 4
av.
1 .1 2
0 .9 8
0 .9 4
0 .0 4
0 .0 0 6 3
0 .0 0 7 4
3 .7 0
6 .5 6
1 .1 0
1 .0 9
0 .1 6
0 .2 4
0 .1 1
0 .1 5
0 .4 2
0 .0 7
s td .
m id d a y h o u rs
2 0 -5 0 m
2 .4 1
2 .3 9
0 .8 1
0 .1 3
0 .0 0 2 4
0 .0 0 2 0
4 3 .7 9
6 2 .5 5
2 .3 2
2 .3 0
0 .1 9
0 .1 7
-0 .0 3
-0 .0 2
1 .1 5
0 .4 6
av.
0 .4 6
0 .3 6
0 .5 2
0 .1 1
0 .0 0 1 3
0 .0 0 0 5
7 .2 2
6 .7 0
0 .4 6
0 .3 7
0 .0 6
0 .0 3
0 .0 4
0 .0 3
0 .4 2
0 .1 9
s td .
m id n ig h t h o u rs
3 .8 1
4 .6 2
5 .3 4
2 .5 0
0 .0 0 3 5
0 .0 0 3 2
3 8 .6 1
4 6 .7 3
3 .6 5
4 .4 7
0 .3 3
0 .3 0
-0 .0 5
0 .0 2
2 .5 4
1 .6 4
av.
2 .2 7
2 .4 0
4 .7 9
3 .1 1
0 .0 0 2 8
0 .0 0 4 7
1 4 .6 1
1 1 .2 7
2 .2 1
2 .3 5
0 .1 9
0 .2 6
0 .1 1
0 .1 3
1 .5 6
0 .9 4
s td .
d a ily a v e ra g e
4 .6 2
6 .5 3
2 .9 4
1 .2 8
0 .0 0 7 7
0 .0 1 1 3
4 0 .9 7
5 0 .3 0
4 .3 3
6 .1 4
0 .6 1
0 .7 7
0 .0 7
0 .1 7
2 .0 0
1 .3 9
av.
1 .2 6
1 .9 7
1 .8 3
0 .7 3
0 .0 0 2 1
0 .0 0 8 0
8 .3 7
9 .3 1
1 .1 9
2 .0 6
0 .1 1
0 .3 5
0 .2 4
0 .2 4
0 .7 1
0 .5 2
s td .
m id d a y h o u rs
5 0 -8 0 m
2 .7 9
1 .9 5
6 .2 3
0 .7 6
0 .0 0 1 0
0 .0 0 0 7
3 1 .8 8
5 1 .7 9
2 .7 2
1 .8 9
0 .1 5
0 .1 2
-0 .0 6
0 .0 2
3 .0 2
0 .9 1
av.
0 .5 9
0 .7 7
1 .8 6
0 .8 0
0 .0 0 0 4
0 .0 0 0 2
1 0 .8 4
7 .8 1
0 .5 9
0 .7 7
0 .0 4
0 .0 2
0 .0 2
0 .0 4
0 .6 4
0 .5 3
s td .
m id n ig h t h o u rs
3 .8 6
4 .1 5
9 .6 7
4 .6 2
0 .0 0 2 6
0 .0 0 2 7
3 5 .1 3
4 1 .1 6
3 .6 9
3 .9 9
0 .3 5
0 .3 3
-0 .0 4
0 .0 5
3 .4 2
2 .2 3
av.
2 .3 4
2 .8 1
8 .2 9
4 .8 0
0 .0 0 2 1
0 .0 0 4 1
1 4 .8 7
1 1 .5 5
2 .2 7
2 .7 2
0 .2 1
0 .3 2
0 .1 6
0 .1 8
2 .0 3
1 .1 8
s td .
d a ily a v e ra g e
5 .7 8
7 .8 7
4 .1 7
2 .3 3
0 .0 0 5 4
0 .0 0 9 5
3 9 .5 3
4 5 .2 3
5 .4 7
7 .4 2
0 .6 3
0 .9 0
0 .1 9
0 .1 9
2 .3 9
1 .8 4
av.
1 .6 0
3 .9 2
2 .2 9
1 .8 1
0 .0 0 2 0
0 .0 0 6 1
8 .6 1
1 3 .4 6
1 .5 3
3 .9 2
0 .1 6
0 .3 6
0 .2 8
0 .2 8
0 .8 7
0 .8 0
s td .
m id d a y h o u rs
8 0 -1 1 0 m
2 .8 9
2 .0 2
9 .9 9
1 .9 2
0 .0 0 0 8
0 .0 0 0 3
2 9 .4 8
4 4 .7 0
2 .8 1
1 .9 8
0 .1 7
0 .0 8
-0 .0 4
0 .0 0
3 .7 8
1 .3 9
av.
1 .1 1
0 .5 1
2 .1 1
2 .6 7
0 .0 0 0 4
0 .0 0 0 2
1 0 .2 9
8 .0 5
1 .1 0
0 .5 1
0 .0 5
0 .0 3
0 .0 4
0 .0 4
0 .6 8
0 .8 0
s td .
m id n ig h t h o u rs
Daily, midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z,
MKE, and TKE at different levels in Hartheim on two cloudless days (21-04-2000 and 22-04-200) and two cloudy
days (17-04-200 and 18-04-2000)
187
Table 7.2:
sky
188
4 0 -6 0 m
6 0 -1 0 0 m
Daily, midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z,
MKE, and TKE at different levels in Bremgarten on two cloudless days (22/23 July, 2001) and two cloudy days
(14/15 July, 2001)
2 0 -3 0 m
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
0 .6 7
0 .5 6
0 .0 1
0 .0 2
4 .3 1
0 .9 3
av.
2 .0 8
0 .4 4
0 .3 9
0 .2 2
0 .2 1
0 .8 9
1 .1 3
s td .
3 .3 5
0 .8 2
0 .6 7
0 .9 9
-0 .1 9
0 .2 3
4 .3 1
0 .1 7
av.
5 .5 1
1 .5 6
0 .2 8
0 .5 4
0 .2 1
0 .2 8
0 .1 6
1 .4 1
0 .0 7
s td .
1 5 .2 4
3 9 .4 8
2 .4 4
2 .4 1
0 .7 5
0 .3 2
0 .0 8
-0 .0 6
5 .0 4
1 .4 2
av.
0 .0 0 5 1
4 .0 0
1 7 .1 4
0 .6 4
1 .0 4
0 .1 8
0 .1 8
0 .1 2
0 .0 7
0 .7 6
0 .7 7
s td .
0 .0 2 0 0
0 .0 1 3 9
1 5 .1 9
3 9 .3 3
2 .4 6
2 .1 0
0 .9 6
0 .7 4
0 .0 3
0 .1 0
5 .1 0
1 .7 4
av.
4 .0 4
0 .0 0 7 8
0 .0 0 8 8
4 .0 1
1 6 .6 5
1 .0 8
1 .5 2
0 .2 3
0 .3 2
0 .1 3
0 .2 2
1 .0 0
1 .5 1
s td .
1 3 .8 7
0 .2 1
0 .0 2 1 0
0 .0 2 4 3
1 3 .9 1
5 8 .8 2
2 .3 2
0 .9 1
1 .0 1
1 .1 2
0 .0 0
0 .4 6
5 .1 5
0 .3 4
av.
0 .3 0
4 .7 6
0 .0 9
0 .0 0 8 6
0 .0 0 8 5
1 .7 9
3 .9 0
1 .0 2
0 .2 9
0 .2 4
0 .2 6
0 .1 6
0 .1 6
0 .9 3
0 .0 9
s td .
2 .6 3
2 .0 3
1 8 .6 3
3 .8 6
0 .0 2 2 3
0 .0 0 9 0
1 4 .3 9
2 0 .3 6
2 .1 2
1 .7 8
1 .0 3
0 .5 7
0 .1 2
0 .0 5
5 .7 7
2 .7 4
av.
0 .6 3
1 .5 5
4 .5 9
1 .3 9
0 .0 0 7 2
0 .0 0 4 5
5 .2 2
1 0 .5 7
0 .6 6
1 .5 8
0 .2 0
0 .1 7
0 .0 9
0 .1 7
1 .0 1
0 .5 3
s td .
3 .2 8
2 .6 7
1 8 .8 3
2 .8 8
0 .0 1 0 1
0 .0 0 8 4
1 5 .2 5
4 0 .5 6
2 .8 5
2 .3 1
0 .8 3
0 .7 2
0 .0 4
0 .1 3
5 .7 4
1 .7 2
av.
2 .2 1
1 .5 3
9 .7 0
4 .6 0
0 .0 0 3 3
0 .0 0 7 7
7 .0 8
1 7 .8 1
2 .2 3
1 .5 3
0 .1 8
0 .3 9
0 .1 0
0 .3 3
1 .6 2
1 .5 2
s td .
2 .7 3
2 .0 5
1 9 .4 1
0 .3 8
0 .0 1 0 9
0 .0 1 3 4
1 3 .7 9
5 6 .2 5
2 .3 0
1 .5 4
0 .8 9
1 .0 3
0 .0 2
0 .5 0
5 .8 8
0 .5 3
av.
1 .5 3
0 .5 7
1 1 .4 6
0 .2 0
0 .0 0 2 1
0 .0 0 3 9
6 .8 1
8 .0 0
1 .5 2
0 .5 8
0 .1 2
0 .1 9
0 .0 8
0 .3 0
2 .0 6
0 .2 1
s td .
1 .9 4
2 .0 9
2 6 .7 5
2 .1 2
0 .0 1 0 7
0 .0 0 3 8
1 0 .6 4
3 5 .9 6
1 .5 0
1 .8 6
0 .8 8
0 .4 5
0 .1 7
-0 .1 0
6 .9 5
1 .7 6
av.
0 .3 4
0 .7 2
5 .9 3
1 .8 4
0 .0 0 2 2
0 .0 0 0 6
4 .2 5
2 1 .6 8
0 .3 9
0 .7 0
0 .1 5
0 .0 5
0 .0 8
0 .0 6
1 .1 5
1 .0 4
s td .
p a ra m e te r
c lo u d y
2 .0 8
2 .2 0
7 0 .7 5
6 .2 6
0 .0 0 8 0
0 .0 0 8 3
2 .7 8
5 .3 9
1 .4 7
1 .0 9
m id n ig h t h o u rs
c lo u d le s s
3 .5 0
1 9 .7 9
1 9 .5 8
0 .0 1 2 7
0 .0 2 7 7
1 .1 9
1 4 .1 7
1 .5 0
2 .8 3
m id d a y h o u rs
c lo u d y
5 6 .0 6
5 .7 9
0 .0 4 0 6
0 .0 3 1 3
1 .2 3
3 .3 4
2 .5 1
1 .0 7
d a ily a v e ra g e
c lo u d le s s
1 9 .3 1
0 .0 1 8 2
0 .0 2 6 9
0 .0 6
1 3 .7 7
0 .9 9
2 .9 5
m id n ig h t h o u rs
c lo u d y
0 .0 2 0 8
0 .0 2 6 0
0 .0 6
6 .2 4
2 .6 0
0 .5 7
m id d a y h o u rs
vh
c lo u d le s s
0 .0 2 7 8
2 .0 0
1 0 .2 8
0 .3 2
2 .8 2
d a ily a v e ra g e
m /s
c lo u d y
1 .1 1
4 .3 5
1 .3 1
1 .3 7
m id n ig h t h o u rs
m /s
c lo u d le s s
1 0 .2 1
1 .9 8
3 .6 7
m id d a y h o u rs
σ 2w
c lo u d y
2 .4 0
2 .0 7
c o n d itio n d a ily a v e ra g e
σdd
c lo u d le s s
3 .8 4
TKE
(m 2 /s 2 )
M KE
(m 2 /s 3 )
σ 3 w /z
(m 2 /s 2 )
σ 2h
(m 2 /s 2 )
w
(°)
c lo u d y
(m 2 /s 2 )
2
(m 2 /s 2 )
TKE
(m 2 /s 2 )
M KE
(m 2 /s 3 )
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
(°)
σ 3 w /z
c lo u d le s s
c lo u d y
c lo u d le s s
σdd
(m /s )
2
σ 2h
c lo u d y
c lo u d le s s
σ 2w
(m 2 /s 2 )
c lo u d y
m /s
c lo u d le s s
c lo u d y
m /s
w
c lo u d le s s
c o n d itio n
sky
4 .1 5
2 .1 2
1 .6 9
0 .3 1
0 .0 3 6
0 .0 3 1
5 0 .9 4
6 5 .1 7
3 .5 3
1 .7 3
0 .8 4
0 .7 7
0 .0 9
0 .0 5
1 .2 3
0 .3 4
av.
2 .3 3
1 .0 1
2 .6 8
0 .2 7
0 .0 3 0
0 .0 1 9
1 5 .8 4
1 1 .2 1
2 .0 4
1 .1 7
0 .4 9
0 .3 7
0 .5 2
0 .5 8
1 .0 8
0 .2 5
s td .
d a ily a v e ra g e
6 .2 6
1 .5 7
3 .1 9
0 .3 3
0 .0 4 0
0 .0 4 3
5 1 .7 1
6 7 .4 4
4 .7 8
1 .0 6
0 .9 3
1 .0 1
0 .5 8
0 .4 2
1 .6 6
0 .2 4
av.
3 .5 2
0 .2 4
5 .3 2
0 .2 8
0 .0 2 2
0 .0 1 3
2 0 .3 0
6 .1 9
2 .6 5
0 .1 8
0 .3 9
0 .2 1
0 .4 7
0 .2 6
1 .8 1
0 .0 8
s td .
m id d a y h o u rs
2 0 -3 0 m
2 .3 6
2 .6 2
0 .4 9
0 .3 0
0 .0 3 0
0 .0 1 9
5 0 .3 7
6 3 .0 9
1 .8 9
2 .3 5
0 .7 9
0 .5 4
-0 .0 9
-0 .3 2
0 .7 7
0 .4 3
av.
0 .7 6
1 .1 3
0 .5 6
0 .2 6
0 .0 0 9
0 .0 1 1
1 4 .9 5
1 3 .7 7
0 .7 7
1 .2 8
0 .1 9
0 .2 7
0 .4 1
0 .2 9
0 .5 4
0 .2 9
s td .
m id n ig h t h o u rs
5 .5 5
3 .1 6
6 .0 6
1 .1 1
0 .0 3 6
0 .0 1 9
2 6 .2 5
5 5 .2 9
2 .9 9
2 .6 8
1 .3 8
0 .9 3
0 .0 2
0 .0 9
3 .0 5
0 .9 7
av.
1 1 .1 3
2 .1 3
4 .7 4
1 .9 3
0 .0 2 0
0 .0 0 9
1 2 .3 8
1 5 .1 7
1 .7 8
2 .1 5
0 .5 4
0 .3 0
0 .2 4
0 .4 2
1 .4 3
0 .9 9
s td .
d a ily a v e ra g e
4 .0 8
2 .7 9
4 .8 4
1 .1 0
0 .0 4 8
0 .0 2 4
3 1 .2 1
5 8 .7 6
3 .1 8
2 .5 4
1 .7 5
1 .1 1
0 .2 2
0 .3 8
2 .6 8
0 .8 2
av.
1 .2 6
0 .5 8
3 .0 5
0 .1 2
0 .0 2 0
0 .0 1 0
9 .9 2
9 .3 3
1 .2 2
0 .5 9
0 .4 6
0 .2 8
0 .3 0
0 .2 0
1 .2 1
0 .1 8
s td .
m id d a y h o u rs
4 0 -6 0 m
3 .1 8
3 .8 3
7 .5 7
1 .1 2
0 .0 2 6
0 .0 1 4
2 1 .3 7
4 9 .3 4
2 .4 6
2 .9 6
1 .1 5
0 .7 5
-0 .1 2
-0 .2 1
3 .4 0
1 .2 1
av.
1 .9 9
2 .7 8
8 .5 2
1 .2 2
0 .0 1 0
0 .0 0 4
4 .9 2
1 4 .6 8
1 .8 0
2 .0 0
0 .3 2
0 .1 8
0 .1 4
0 .2 0
2 .1 2
0 .8 5
s td .
m id n ig h t h o u rs
4 .7 5
4 .5 6
1 6 .0 0
5 .0 9
0 .0 1 2
0 .0 0 7
2 5 .9 7
3 6 .3 7
4 .1 6
4 .1 8
1 .0 4
0 .7 2
0 .0 5
0 .1 7
4 .7 6
2 .6 4
av.
2 .0 1
1 .8 7
1 1 .9 4
3 .5 3
0 .0 1 0
0 .0 0 6
1 4 .3 9
9 .7 9
1 .7 5
1 .8 0
0 .5 3
0 .4 4
0 .3 0
0 .3 2
2 .1 8
0 .8 8
s td .
d a ily a v e ra g e
5 .9 6
5 .3 4
1 4 .6 6
5 .5 0
0 .0 1 9
0 .0 1 1
2 2 .9 3
3 7 .1 0
4 .7 5
4 .8 1
1 .4 8
1 .0 1
0 .2 5
0 .3 5
4 .8 7
2 .7 1
av.
2 .3 3
1 .6 9
3 .9 3
1 .1 8
0 .0 0 6
0 .0 0 6
5 .0 8
7 .2 8
1 .2 8
1 .9 5
0 .3 2
0 .3 5
0 .4 6
0 .3 0
0 .5 7
0 .4 2
s td .
m id d a y h o u rs
8 0 -1 2 0 m
3 .3 1
3 .7 8
1 6 .7 2
4 .5 9
0 .0 0 7
0 .0 0 4
2 6 .8 5
3 5 .5 1
2 .9 8
3 .5 8
0 .7 2
0 .4 2
0 .1 2
-0 .0 1
4 .5 8
2 .5 5
av.
0 .8 4
1 .7 0
1 7 .5 6
2 .6 7
0 .0 0 3
0 .0 0 2
1 2 .8 8
1 1 .4 7
0 .9 1
1 .6 5
0 .1 7
0 .1 9
0 .2 1
0 .2 2
2 .9 7
0 .8 3
s td .
m id n ig h t h o u rs
Daily, midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z,
MKE, and TKE at different levels in Blankenhornsberg on two cloudless days (12-08-2001 and 15-08-2001) and
two cloudy days (03-08-2001 and 17-08-2001)
vh
p a ra m e te r
Table 7.3:
189
Table 7.4:
sky
190
5 0 -8 0 m
8 0 -1 1 0 m
Daily, midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z,
MKE, and TKE at different levels in Oberbärenburg on two cloudless days (30 August, 2001 and 23 September,
2001) and two cloudy days (31 August, 2001 and 01 September, 2001)
2 0 -5 0 m
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
0 .4 8
0 .4 6
0 .0 4
0 .0 1
0 .3 3
0 .8 1
a v.
0 .9 5
0 .2 6
0 .3 2
0 .1 2
0 .1 5
0 .4 0
0 .4 6
s td .
0 .7 9
3 .0 1
0 .5 6
0 .9 1
0 .1 7
-0 .0 9
0 .1 1
1 .3 9
av.
3 .7 1
0 .5 8
0 .8 8
0 .2 3
0 .2 2
0 .0 6
0 .1 8
0 .0 5
0 .2 3
s td .
6 5 .2 8
4 9 .1 5
3 .8 2
2 .8 8
0 .3 1
0 .2 4
-0 .0 4
-0 .0 1
0 .4 6
0 .9 7
av.
0 .0 0 1 6
8 .7 6
1 2 .8 4
2 .1 3
0 .7 3
0 .3 0
0 .0 6
0 .1 2
0 .0 9
0 .2 4
0 .4 7
s td .
0 .0 0 7 1
0 .0 0 8 6
3 8 .3 8
2 9 .2 8
3 .9 5
6 .4 0
0 .5 1
0 .6 2
-0 .0 9
-0 .0 6
2 .6 9
3 .8 3
av .
4 .6 6
0 .0 0 5 1
0 .0 0 6 6
2 2 .1 3
1 4 .1 8
3 .0 3
3 .3 9
0 .2 5
0 .3 3
0 .2 4
0 .1 5
2 .1 0
1 .4 6
std .
4 .3 6
1 1 .8 5
0 .0 0 7 8
0 .0 1 8 0
2 9 .7 3
2 5 .1 7
4 .3 2
9 .0 0
0 .5 3
1 .0 9
0 .1 1
-0 .1 3
2 .7 3
4 .7 3
a v.
2 .6 1
2 .7 5
4 .0 5
0 .0 0 6 8
0 .0 0 4 7
1 2 .1 9
3 .8 9
3 .3 2
2 .5 5
0 .3 1
0 .1 9
0 .1 3
0 .1 7
0 .9 4
0 .9 0
std .
2 .4 0
3 .3 4
4 .7 5
1 1 .7 0
0 .0 0 6 3
0 .0 0 3 7
3 5 .1 8
1 8 .2 5
2 .3 5
3 .2 1
0 .4 7
0 .3 6
-0 .3 3
-0 .0 7
2 .6 0
4 .7 0
av.
0 .7 1
0 .5 2
4 .0 2
0 .3 8
0 .0 0 1 5
0 .0 0 2 9
2 5 .4 5
0 .8 3
0 .6 9
0 .5 2
0 .0 8
0 .1 9
0 .1 8
0 .0 5
1 .7 9
0 .1 1
s td .
3 .3 6
5 .6 6
8 .8 3
1 6 .6 9
0 .0 0 4 2
0 .0 0 7 2
2 6 .6 6
2 0 .0 0
3 .2 6
5 .3 1
0 .4 7
0 .7 0
-0 .1 4
-0 .0 4
3 .7 2
5 .4 7
av.
2 .5 2
2 .4 1
8 .4 8
8 .1 3
0 .0 0 3 2
0 .0 0 6 4
1 6 .9 9
7 .4 0
2 .4 6
2 .2 7
0 .2 4
0 .4 1
0 .2 3
0 .1 6
2 .3 1
1 .6 0
s td .
3 .2 9
7 .5 0
1 0 .1 1
1 5 .3 7
0 .0 0 3 8
0 .0 1 9 0
1 9 .4 0
2 1 .6 1
3 .1 5
6 .9 0
0 .4 5
1 .4 3
0 .0 3
-0 .0 2
4 .2 4
5 .3 2
av .
1 .4 1
2 .2 3
6 .7 3
7 .1 3
0 .0 0 2 5
0 .0 0 5 7
4 .0 4
4 .0 2
1 .3 6
2 .2 0
0 .2 1
0 .3 0
0 .0 9
0 .2 3
1 .1 9
1 .2 8
s td .
2 .5 1
3 .1 0
7 .4 7
2 4 .8 1
0 .0 0 3 6
0 .0 0 2 4
2 8 .0 9
1 2 .1 5
2 .4 4
2 .9 5
0 .4 2
0 .3 6
-0 .3 3
-0 .1 0
3 .4 2
7 .0 2
a v.
1 .9 9
0 .5 1
5 .6 7
3 .8 3
0 .0 0 1 5
0 .0 0 1 3
2 4 .9 1
1 .0 9
2 .0 0
0 .5 0
0 .0 9
0 .1 4
0 .2 1
0 .1 1
1 .9 4
0 .5 6
std .
p a ra m e te r
c lo u d y
2 .6 9
2 .5 1
4 1 .9 0
3 .7 2
0 .0 0 3 6
0 .0 1 0 4
8 .7 1
6 .4 9
9 .5 2
3 .3 9
m id n ig h t h o u rs
c lo u d le s s
2 .4 2
1 1 .6 5
7 5 .0 3
0 .0 0 9 2
0 .0 0 7 3
0 .4 6
5 .2 7
3 .5 2
4 .4 5
m id d a y h o u rs
c lo u d y
5 4 .1 9
9 .3 0
0 .0 2 5 8
0 .0 0 7 9
0 .6 2
0 .0 8
6 .6 8
3 .1 0
d aily av e ra g e
c lo u d le s s
7 3 .2 6
0 .0 1 0 8
0 .0 1 3 6
0 .3 8
0 .1 5
0 .7 4
4 .0 8
m id n ig h t h o u rs
c lo u d y
0 .0 1 0 8
0 .0 0 9 0
1 .1 9
0 .0 1
3 .0 0
1 .9 9
m id d a y h o u rs
c lo u d le s s
0 .0 1 1 5
0 .5 2
0 .0 3
0 .8 1
3 .9 8
d a ily a ve rag e
c lo u d y
0 .5 5
0 .5 3
3 .4 7
0 .5 5
m id n ig h t h o u rs
vh
c lo u d le s s
0 .2 3
0 .9 5
1 .0 7
m id d a y h o u rs
m /s
c lo u d y
2 .9 2
2 .4 3
c o n d itio n d a ily a v e ra g e
σdd
c lo u d le s s
2 .6 7
3
2
2
w
h
w /z
TKE
(m 2 /s 2 )
M KE
(m 2 /s 3 )
σ
(m 2 /s 2 )
σ
(m 2 /s 2 )
σ
m /s
w
(°)
c lo u d y
(m 2 /s 2 )
2
w
2
h
w /z
(m 2 /s 2 )
TKE
(m 2 /s 2 )
M KE
(m 2 /s 3 )
3
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
(°)
σ
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
c lo u d y
σdd
(m 2 /s 2 )
σ
(m 2 /s 2 )
σ
m /s
c lo u d le s s
c lo u d y
m /s
w
c lo u d le s s
3 .3 3
2 .8 7
1 1 .7 9
1 .2 3
0 .0 0 5 6
0 .0 0 2 2
1 9 .7 1
4 6 .8 2
3 .1 8
2 .7 9
0 .3 0
0 .1 6
-0 .0 8
0 .1 0
4 .4 5
1 .3 2
av.
0 .8 2
0 .9 0
5 .3 4
1 .1 9
0 .0 0 2 8
0 .0 0 2 3
3 .7 9
1 9 .5 7
0 .7 8
0 .8 7
0 .1 0
0 .1 1
0 .0 7
0 .1 5
1 .0 1
0 .8 4
s td .
c o n d itio n d a ily a v e ra g e
sky
4 .0 8
3 .8 1
1 6 .6 8
2 .0 1
0 .0 0 7 9
0 .0 0 6 6
1 9 .5 8
3 6 .4 0
3 .8 9
3 .6 2
0 .3 9
0 .3 7
-0 .0 3
0 .3 4
5 .2 1
1 .8 8
av.
0 .5 5
0 .5 9
3 .8 9
1 .2 1
0 .0 0 2 4
0 .0 0 2 4
3 .5 6
6 .9 0
0 .5 5
0 .5 8
0 .0 8
0 .0 9
0 .0 6
0 .2 5
0 .6 3
0 .6 0
std .
m id d a y h o u rs
2 0 -5 0 m
2 .6 1
2 .8 2
8 .4 7
1 .2 5
0 .0 0 3 1
0 .0 0 1 0
1 8 .7 4
4 5 .7 7
2 .5 0
2 .7 7
0 .2 2
0 .1 0
-0 .0 2
0 .0 2
4 .0 1
1 .3 6
av.
0 .3 1
0 .4 0
2 .2 5
1 .0 7
0 .0 0 0 8
0 .0 0 0 4
2 .8 3
1 9 .7 7
0 .3 0
0 .4 1
0 .0 4
0 .0 3
0 .0 4
0 .0 5
0 .5 8
0 .8 6
std .
m id n ig h t h o u rs
3 .5 2
2 .6 4
1 8 .0 6
5 .5 6
0 .0 0 3 6
0 .0 0 1 4
1 6 .4 9
2 6 .2 1
3 .3 5
2 .5 5
0 .3 4
0 .1 8
-0 .1 4
0 .1 1
5 .5 9
3 .0 1
av.
0 .6 8
1 .0 2
5 .5 0
4 .6 0
0 .0 0 1 8
0 .0 0 1 4
2 .8 7
1 3 .9 4
0 .6 4
0 .9 9
0 .1 1
0 .1 2
0 .1 0
0 .2 1
0 .9 1
1 .4 3
std .
d a ily a v e ra g e
3 .9 8
3 .4 1
2 4 .6 3
3 .0 8
0 .0 0 4 9
0 .0 0 3 8
1 5 .0 2
3 5 .0 5
3 .7 5
3 .2 1
0 .4 2
0 .3 8
-0 .1 1
0 .4 4
6 .4 7
2 .1 3
av.
0 .7 4
0 .9 9
6 .7 9
3 .1 6
0 .0 0 0 8
0 .0 0 1 6
2 .6 6
1 2 .6 7
0 .7 3
1 .0 1
0 .0 6
0 .1 1
0 .1 1
0 .2 9
1 .0 6
1 .2 6
std .
m id d a y h o u rs
5 0 -8 0 m
2 .7 9
2 .0 4
1 5 .8 5
6 .4 8
0 .0 0 1 7
0 .0 0 0 6
1 4 .5 7
1 8 .4 3
2 .6 8
1 .9 9
0 .2 3
0 .1 1
-0 .0 4
0 .0 3
5 .5 4
3 .5 3
av.
0 .3 9
0 .4 2
2 .8 9
2 .9 9
0 .0 0 0 5
0 .0 0 0 5
1 .5 1
1 .8 0
0 .3 8
0 .3 9
0 .0 5
0 .0 6
0 .0 8
0 .0 9
0 .5 9
0 .7 5
s td .
m id n ig h t h o u rs
3 .7 9
2 .6 3
2 4 .8 6
8 .0 2
0 .0 0 2 8
0 .0 0 1 1
1 4 .5 5
2 1 .9 5
3 .6 0
2 .5 3
0 .3 7
0 .2 0
-0 .1 8
0 .0 9
6 .6 0
3 .6 8
av.
1 .0 3
0 .8 5
7 .3 3
6 .0 8
0 .0 0 1 3
0 .0 0 1 3
2 .3 7
1 0 .3 5
0 .9 8
0 .8 1
0 .1 2
0 .1 5
0 .1 0
0 .1 7
1 .0 7
1 .5 9
s td .
d aily a v e ra g e
4 .5 2
3 .4 1
3 3 .5 2
3 .7 1
0 .0 0 4 2
0 .0 0 3 3
1 4 .1 1
3 4 .0 1
4 .2 6
3 .1 9
0 .5 1
0 .4 5
-0 .2 0
0 .3 6
7 .5 4
2 .3 2
av.
1 .6 1
1 .0 8
9 .4 2
4 .1 6
0 .0 0 1 7
0 .0 0 1 2
2 .8 6
1 5 .1 8
1 .5 5
1 .0 7
0 .1 5
0 .1 1
0 .1 2
0 .1 5
1 .4 8
1 .5 1
s td .
m id d a y h o u rs
8 0 -1 1 0 m
2 .7 5
2 .0 3
2 2 .3 1
1 0 .4 6
0 .0 0 1 6
0 .0 0 0 5
1 2 .3 7
1 5 .2 0
2 .6 1
1 .9 7
0 .2 7
0 .1 3
-0 .0 9
0 .0 3
6 .5 9
4 .5 0
av.
0 .3 4
0 .2 3
3 .1 6
4 .2 4
0 .0 0 0 5
0 .0 0 0 4
1 .3 7
2 .1 9
0 .3 4
0 .2 1
0 .0 5
0 .0 6
0 .0 5
0 .1 1
0 .5 3
0 .8 8
s td .
m id n ig h t h o u rs
Daily, midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z,
MKE, and TKE at different levels in Melpitz on a cloudless day (06 October, 2001) and two cloudy days (30 September, 2001 and 01 October, 2001)
vh
p a ra m e te r
Table 7.5:
191
Table 7.6:
sky
192
4 0 -6 0 m
6 0 -8 0 m
Daily, midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z,
MKE, and TKE at different levels in Freiburg on a cloudless day (17 November, 2001) and a cloudy day (18 November, 2001)
2 0 -3 0 m
c lo u d y
c lo u d le s s
c lo u d y
c lo u d le s s
0 .1 2
0 .0 1
-0 .0 3
0 .2 1
0 .6 8
av.
0 .0 8
0 .1 1
0 .0 7
0 .1 1
0 .1 6
0 .3 6
s td .
1 .5 2
0 .1 9
0 .3 0
0 .0 8
0 .0 6
0 .1 8
0 .9 9
a v.
0 .1 8
0 .2 7
0 .0 4
0 .0 7
0 .0 8
0 .1 0
0 .0 9
0 .2 8
s td .
5 0 .4 4
1 .3 5
1 .4 3
0 .0 5
0 .0 6
-0 .0 3
-0 .0 9
0 .4 0
0 .6 3
a v.
3 .4 9
7 .0 7
0 .2 7
0 .2 7
0 .0 3
0 .0 2
0 .0 2
0 .0 7
0 .1 1
0 .2 2
s td .
0 .0 0 1 4
5 0 .3 8
3 1 .6 3
1 .4 9
2 .2 2
0 .1 4
0 .1 5
0 .0 5
-0 .0 5
1 .0 5
2 .5 1
av .
0 .0 0 0 8
0 .0 0 1 5
1 8 .5 8
1 7 .0 2
0 .5 8
0 .7 6
0 .0 7
0 .1 1
0 .1 2
0 .0 9
1 .3 0
1 .3 4
s td .
1 .4 9
0 .0 0 2 2
0 .0 0 3 4
5 2 .5 4
3 4 .6 6
1 .3 4
2 .4 0
0 .2 2
0 .2 9
0 .1 6
0 .0 3
0 .6 0
1 .6 6
av.
0 .2 6
0 .8 1
0 .0 0 0 9
0 .0 0 2 3
1 1 .1 0
6 .0 8
0 .2 6
0 .3 8
0 .0 6
0 .1 4
0 .1 2
0 .0 9
0 .3 6
0 .5 2
std .
2 .2 9
1 .7 3
6 .9 6
0 .0 0 0 8
0 .0 0 1 8
3 8 .9 3
1 8 .9 9
1 .5 4
2 .2 0
0 .1 1
0 .1 9
-0 .0 2
-0 .1 4
1 .4 9
3 .6 2
av.
0 .4 6
0 .6 1
2 .2 5
4 .2 0
0 .0 0 0 5
0 .0 0 1 5
1 8 .2 3
3 .0 7
0 .4 9
0 .6 0
0 .0 5
0 .1 1
0 .0 7
0 .1 3
1 .2 8
1 .0 1
std .
1 .8 9
2 .3 5
1 .6 6
4 .0 1
0 .0 0 1 0
0 .0 0 0 8
4 6 .8 5
3 1 .2 7
1 .8 0
2 .2 8
0 .1 6
0 .1 4
0 .0 8
-0 .0 3
1 .2 7
2 .5 1
av.
0 .7 9
0 .7 1
3 .2 5
3 .6 1
0 .0 0 0 8
0 .0 0 0 7
1 8 .4 9
1 7 .0 0
0 .7 8
0 .6 9
0 .0 8
0 .0 9
0 .1 5
0 .1 1
1 .3 1
1 .3 2
s td .
2 .1 0
2 .9 0
0 .3 2
1 .9 2
0 .0 0 1 9
0 .0 0 1 7
5 1 .7 5
3 3 .6 7
1 .9 7
2 .7 9
0 .2 6
0 .2 3
0 .1 9
0 .0 6
0 .7 0
1 .8 7
av.
0 .5 0
0 .6 9
0 .2 5
1 .1 0
0 .0 0 1 0
0 .0 0 1 1
9 .0 5
6 .6 7
0 .5 1
0 .6 6
0 .1 0
0 .1 0
0 .1 3
0 .1 3
0 .3 2
0 .6 1
s td .
1 .9 5
2 .2 9
1 .7 1
6 .3 3
0 .0 0 0 5
0 .0 0 0 9
3 7 .3 9
2 0 .2 3
1 .9 0
2 .2 2
0 .1 0
0 .1 5
-0 .0 1
-0 .1 0
1 .5 9
3 .4 1
a v.
0 .5 5
0 .4 3
1 .8 1
4 .4 2
0 .0 0 0 3
0 .0 0 0 6
1 6 .7 5
3 .7 8
0 .5 7
0 .4 2
0 .0 4
0 .0 7
0 .0 9
0 .0 6
1 .0 9
1 .0 9
s td .
p a ra m e te r
c lo u d le s s
0 .1 2
0 .5 8
0 .6 9
5 .3 6
5 8 .6 6
0 .0 0 0 3
0 .0 0 1 2
3 .5 6
0 .2 5
0 .4 0
1 .5 9
m id n ig h t h o u rs
c lo u d y
1 .5 0
0 .4 2
4 0 .5 1
8 .4 8
0 .0 0 0 6
0 .0 0 0 4
4 .0 1
3 .1 9
2 .5 5
0 .2 5
m id d a y h o u rs
c lo u d le s s
0 .9 2
1 1 .0 0
6 7 .9 9
0 .0 0 2 3
0 .0 0 0 5
0 .1 3
1 .3 8
0 .7 8
1 .4 6
d aily a v era g e
c lo u d y
5 0 .9 5
1 0 .7 6
0 .0 0 6 6
0 .0 0 1 0
0 .2 2
0 .0 5
2 .3 0
0 .5 8
m id n ig h t h o u rs
c lo u d le s s
6 8 .5 7
0 .0 0 2 7
0 .0 0 3 4
0 .2 8
0 .0 9
0 .2 6
1 .5 6
m id d a y h o u rs
c lo u d y
0 .0 0 2 2
0 .0 0 1 7
0 .5 3
0 .0 1
1 .4 6
0 .2 6
d a ily a ve ra g e
c lo u d le s s
0 .0 0 1 8
0 .2 7
0 .0 3
0 .2 7
1 .3 8
m id n ig h t h o u rs
c lo u d y
0 .3 0
0 .0 4
1 .6 7
0 .1 7
m id d a y h o u rs
vh
c lo u d le s s
0 .0 4
0 .5 8
0 .7 9
d aily a v erag e
m /s
c lo u d y
1 .5 6
0 .3 9
c o n d itio n
σ dd
c lo u d le s s
0 .9 7
3
2
w
2
h
w /z
TKE
(m 2 /s 2 )
M KE
(m 2 /s 3 )
σ
(m 2 /s 2 )
σ
(m 2 /s 2 )
σ
m /s
w
(°)
c lo u d y
(m 2 /s 2 )
193
Table 7.7:
Comparison between the value of ai and bi in the present study and some
previous studies
site
u
v
W
stability
au
bu
av
bv
aw
bw
Scots pine forest
2.95
2.20
2.99
2.70
1.10
4.00
0.28<-z/L<8.31
Grassland
1.70
1.60
1.70
1.50
1.20
4.00
0.82<-z/L<11.24
Vineyard
1.80
1.80
1.80
1.80
1.20
4.00
0.31<-z/L<7.06
Norway spruce forest
2.60
1.80
2.50
3.50
1.25
4.10
0.28<-z/L<8.31
Al-Jiboori et al. (2001), complex and flat terrain
2.55
1.71
2.62
2.26
1.20
4.05
unstable
Xu et al. (1993), flat terrain
2.35
1.40
-
-
1.40
2.00
unstable
Panofsky et al. (1977), flat
terrain
-
-
-
-
1.30
3.00
unstable
Table 7.8:
Comparison of the mean values of the standard deviation of the wind
speed components normalized by friction velocity under the atmospheric
unstable conditions in the surface layer at sites of the present study with
other studies at flat and complex terrain
σu/u∗
σv/u∗
σw/u∗
stability
Scots pine forest
5.54±0.64
5.95±0.70
2.46±0.31
0.86<-z/L<3.66
Grassland
2.75±0.34
2.70±0.33
2.49±0.37
0.86<-z/L<3.66
Vineyard
3.04±0.40
3.04±0.40
2.54±0.38
0.86<-z/L<3.66
Norway spruce forest
4.54±0.60
5.27±0.77
2.76±0.41
0.86<-z/L<3.66
Al-Jiboori et al. (2001), flat 4.31±0.54
and complex terrain
4.77±0.64
2.58±0.38
0.86<-z/L<3.66
Site
Al-Jiboori et al. (2001), flat
terrain(I)
3.57
3.19
1.66
unstable
Al-Jiboori et al. (2001), complex terrain (Oasis to flat II)
5.90
6.70
3.00
unstable
Al-Jiboori et al. (2001), complex terrain (Oasis to flat III)
3.19
3.14
1.32
unstable
Panofsky et al. (1977), flat
terrain
-
-
2.56±0.36
0.86<-z/L<3.66
2.46±0.32
0.86<-z/L<3.66
Xu et al. (1993)
Zhang et al. (2001), grassland
2.29
2.12
1.18
near-neutral
Bradley (1980), complex terrain
3.67
4.13
2.73
unstable
194
m id n ig h t h o u rs
12
0
0.05
0.04
0.03
0.02
0.01
0.00
2.0
1.5
1.0
0.5
0.0
10
8
5
3
0
2
2
h
2
w (m/s)
0 .6
0 .4
0 .2
0 .0
-0 .2
-0 .4
vh (m/s)
σ
σdd (°)
80
60
40
20
0
8
6
4
2
0
9 00
2
G (W/m )
m id d ay h o u rs
24
(m /s )
σ
2
w
2
2
(m /s )
3
2
3
σ w/z (m /s )
2
2
2
2
MKE (m /s ) TKE (m /s )
12
9
6
3
0
36
6 00
3 00
0
fo re st (S c ots
pine)
grasslan d
(B r.)
vin eya rd
fore st
(N orw a y
sp ruc e )
gras sla nd
(M e.)
urban area
la nd use typ es
Fig. 7.1:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET)
average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudless conditions at levels from 20-50 m a.g.l. [forest and grassland (Me.)] and 20-30
m a.g.l. [grassland (Br.), vineyard and urban area], (Table 7.1 to 7.6)
195
m id n ig h t h o u rs
12
0
0.05
0.04
0.03
0.02
0.01
0.00
2.0
1.5
1.0
0.5
0.0
2
2
w
2
σ
2
2
(m /s )
h
2
σ
σdd (°)
w (m/s)
0 .6
0 .4
0 .2
0 .0
-0.2
-0.4
vh (m/s)
10
8
5
3
0
80
60
40
20
0
8
6
4
2
0
90 0
2
G (W/m )
m id d ay h o u rs
24
(m /s )
3
2
3
σ w/z (m /s )
2
2
2
2
MKE (m /s ) TKE (m /s )
12
9
6
3
0
36
60 0
30 0
0
fore s t (S co ts
pin e)
grassland
(B r.)
vine yard
fo re st
(N orw ay
spruce)
gras sla nd
(M e.)
urban area
la nd u se types
Fig. 7.2:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET)
average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudy conditions at levels from 20-50 m a.g.l. [forest and grassland (Me.)] and 20-30
m a.g.l. [grassland (Br.), vineyard and urban area], (Table 7.1 to 7.6)
196
2
2
2
2
MKE (m /s ) TKE (m /s )
12
9
6
3
0
36
m id n ig h t h o u rs
24
12
0
2.0
1.5
1.0
0.5
0.0
σ
2
h
2
2
(m /s )
σ
2
w
2
2
(m /s )
3
2
3
σ w/z (m /s )
0.05
0.04
0.03
0.02
0.01
0.00
10
8
5
3
0
w (m/s)
vh (m/s)
σdd (°)
80
60
40
20
0
0.6
0.4
0.2
0.0
-0.2
-0.4
8
6
4
2
0
90 0
2
G (W/m )
m id d ay h o u rs
60 0
30 0
0
fo rest
(S co ts p in e)
g rasslan d
(B r.)
v in eyard
fo rest
(N o rw ay
sp ru ce)
g rasslan d
(M e.)
u rb an area
la nd u se types
Fig. 7.3:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET)
average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudless conditions at levels from 50-80 m a.g.l. [forest and grassland (Me.)] and 40-60
m a.g.l [grassland (Br.), vineyard and urban area], (Table 7.1 to 7.6)
197
m id n ig h t h o u rs
12
0
0.05
0.04
0.03
0.02
0.01
0.00
2.0
1.5
1.0
0.5
0.0
10
8
5
3
0
2
2
h
2
w (m/s)
0 .6
0 .4
0 .2
0 .0
-0.2
-0.4
vh (m/s)
σ
σdd (°)
80
60
40
20
0
8
6
4
2
0
90 0
2
G (W/m )
m id d ay h o u rs
24
(m /s )
σ
2
w
2
2
(m /s )
3
2
3
σ w/z (m /s )
2
2
2
2
MKE (m /s ) TKE (m /s )
12
9
6
3
0
36
60 0
30 0
0
fore s t (S co ts
pin e)
grassland
(B r.)
vine yard
fo re st
(N orw ay
spruce)
gras sla nd
(M e.)
urban area
la nd u se types
Fig. 7.4:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET)
average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudy conditions at levels from 50-80 m a.g.l [forest and grassland (Me.)] and 40-60
m a.g.l [grassland (Br.), vineyard and urban area], (Table 7.1 to 7.6)
198
m id n ig h t h o u rs
12
0
0 .0 5
0 .0 4
0 .0 3
0 .0 2
0 .0 1
0 .0 0
2 .0
1 .5
1 .0
0 .5
0 .0
2
2
w
2
σ
σdd (°)
w (m/s)
0 .6
0 .4
0 .2
0 .0
-0 .2
-0 .4
vh (m/s)
σ
2
h
2
2
(m /s )
10
8
5
3
0
80
60
40
20
0
8
6
4
2
0
900
2
G (W/m )
m id d a y h o u rs
24
(m /s )
3
2
3
σ w/z (m /s )
2
2
2
2
MKE (m /s ) TKE (m /s )
12
9
6
3
0
36
600
300
0
fo re s t (S c o ts
p in e )
g ra s s la n d
vin e ya rd
fo re s t
(N o rw a y
s p ru c e )
g ra s s la n d
u rb a n a re a
la n d u s e typ e s
Fig. 7.5:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET)
average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudless conditions at levels from 80 to 110 m a.g.l. [forest and grassland (Me.)], 60-100
m a.g.l. [grassland (Br.)], 80-120 m a.g.l. [vineyard] and 60-80 m a.g.l.
[urban area], (Table 7.1 to 7.6)
199
m id n ig h t h o u rs
12
0
0 .0 5
0 .0 4
0 .0 3
0 .0 2
0 .0 1
0 .0 0
2 .0
1 .5
1 .0
0 .5
0 .0
2
2
w
2
σ
σdd (°)
w (m/s)
0 .6
0 .4
0 .2
0 .0
-0 .2
-0 .4
vh (m/s)
σ
2
h
2
2
(m /s )
10
8
5
3
0
80
60
40
20
0
8
6
4
2
0
900
2
G (W/m )
m id d a y h o u rs
24
(m /s )
3
2
3
σ w/z (m /s )
2
2
2
2
MKE (m /s ) TKE (m /s )
12
9
6
3
0
36
600
300
0
fo re s t (S c o ts
p in e )
g ra s s la n d
(B r.)
vin e ya rd
fo re s t
(N o rw a y
s p ru c e )
g ra s s la n d
(M e .)
u rb a n a re a
la n d u s e typ e s
Fig. 7.6:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00 CET)
average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudy conditions at levels from 80 to 110 m a.g.l. [forest and grassland (Me.)], 60-100
m a.g.l. [grassland (Br.)], 80-120 m a.g.l. [vineyard] and 60-80 m a.g.l.
[urban area], (Table 7.1 to 7.6)
200
10
forest (Scots pine)
vineyard
Al-Jiboori et al. (2001)
σu/u∗
8
grassland
forest (Norway spruce)
6
(a)
4
2
0
0
1
2
3
4
5
6
7
8
- (z/L)
10
σv/u∗
8
6
(b)
4
2
forest (Scots pine)
vineyard
Al-Jiboori et al. (2001)
0
0
1
2
grassland
forest (Norway spruce)
3
4
5
6
7
8
- (z/L)
10
σw/u∗
8
forest (Scots pine)
grassland
vineyard
Panofsky et al. (1977)
forest (Norway spruce)
Al-Jiboori et al.(2001)
Xu et al. (1993)
6
(c)
4
2
0
0
1
2
3
4
5
6
7
8
- (z/L)
Fig. 7.7:
Mean values of the dimensionless of standard deviations of velocity components σi/u∗ (i=u,v,w) as a function of -z/L under free convective conditions in the surface layer
201
7
6
σi/u∗ (i=u,v,w)
5
4
3
2
σu/u∗
σv/u∗
σw/u∗
1
0
forest (Scots
pine)
Fig. 7.8:
grassland
vineyard
forest (Norway
spruce)
Site
Al-Jiboori et al.
(2001)
The mean values of σi/u∗ (i=u,v,w) (from table 7.2) over different land use
types, and the data of AL-Jiboori et al. (2001) (complex and flat terrain)
1.0
0.9
data
0.8
Lenschow et al. (1980)
0.7
1, see text
Wyngaard et al. (1971)
2, see text
z/zi
0.6
Stull, 1988
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
σ2w/w∗2
Fig. 7.9:
Normalized vertical velocity variance, σw/w∗ as a function of the normalized height, z/zi at Bremgarten under the free convection conditions
202
8
CONCLUSIONS
The Scintec FAS64 sodar was used to study the influence of thermal and roughness
changes on the characteristics of the turbulent parameters such as turbulent kinetic
energy per unit mass (TKE), turbulence intensity components (Iu, Iv, Iw), and the mean
values of the normalized (by the friction velocity) standard deviations of the velocity
components, σi/u∗ (i=u,v,w) over different land use types such as grassland, forest
vineyard and urban sites. To explain the influence of thermal and roughness changes
on the characteristics of these parameters, the characteristics of incoming solar radiation (G), wind direction (dd) and its standard deviation (σdd), horizontal and vertical wind
speed components (vh and w respectively), and the variances of horizontal and vertical
wind speed components (σ2h and σ2w) are briefly discussed for the whole study sites
through the periods of the measurements. The importance of these measurements for
this study are due to their effects in the turbulence of the atmosphere. As reported in
Stull (2000), during weak advection, the nature of convection and turbulence are controlled by the wind speed, incoming solar radiation (insulation) cloud shading and time
of day and night.
Besides directly monitoring such meteorological variables as vh, w, dd, σdd, σh and σw,
the application of a number of methods and algorithms enabled the estimation of features of the atmospheric turbulence such as Pasquill-Gifford (P-G) stability classes,
Monin-Obukhov length (L), friction velocity (u∗), and convective velocity scale (w∗). In
particular, a typical sodar-related method has been used to classify atmospheric stability over the sites of the study through the periods of the measurements (except for
Freiburg). The variable used σdd was used to determine the P-G stability classes according to Thomas (1988). Such a stability classification is the first step for applying a
number of traditional algorithms aiming at estimating the main atmospheric parameters
which typically describe the ABL structure such as L, u∗ and zi. For every site of the
study the following results were obtained:
∗∗
characteristic of the global solar radiation G received on a horizontal surface on
two cloudless and two cloudy days (except for Melpitz: one cloudless day and
two cloudy days, and Freiburg: one cloudless day and one cloudy day),
∗∗
wind roses at different levels during the period of the study,
203
∗∗
atmospheric stability classification at different levels,
∗∗
profiles of dd, σdd, vh, w, σ2h, σ2w, σ3w/z, MKE and TKE under various atmospheric conditions (stable, neutral and unstable) in the range from 20 to 500 m
a.g.l. (except for Oberbärenburg, there was not enough result). But at Freiburg
the weather was cloudy, rainy and foggy most of the time during the measurement campaign from 16 November, 2001 to 19 November, 2001. Thus, no sodar
data are available in the range above 100 m a.g.l.,
∗∗
diurnal course of two days mean of σdd, vh, w, σ2h, σ2w, σ3w/z, MKE and TKE in
cloudless and cloudy sky conditions (except for: Melpitz; with one cloudless day
and two cloudy days and Freiburg; with one cloudless day and one cloudy day),
∗∗
characteristics of the turbulence intensity components (Iu, Iv, Iw) over the study
areas for various fetch conditions arising under various wind direction and different atmospheric stability at different levels (except for Freiburg: there was not
enough result),
∗∗
behavior of the relationship between the standard deviations of the velocity
components normalized by the u∗, σi/u∗ (i=u,v,w) and z/L in the surface layer
under the unstable atmospheric conditions (except for Melpitz and Freiburg),
∗∗
variation of the normalized (by the square value of the convective velocity, w∗2)
variance of the vertical wind speed component, σ2w,/w∗2, with the normalized (by
the mixing height) height, z/zi.
This study yielded the following results:
∗∗
By using sodar data only, the atmospheric stability according to P-G stability
classification was quantified at different levels at Hartheim, Bremgarten,
Blankenhornsberg, Oberbärenburg, and Melpitz through the periods of the studies. If one considers the period of the year for every site these results seem reliable.
∗∗
The profile of σ3w/z under the various stability conditions (neutral, stable and unstable) showed a decline with the height a.g.l.. This is due to the increasing of
the mechanical and buoyancy turbulence production which is intensively present
in the surface layer.
204
∗∗
The values of the quantity σ3w/z, at the cloudless conditions, throughout the
night, were low even in the presence of wind shear. This reflects the effect of the
incoming solar radiation of σ3w/z which appears in the daytime, especially when
the value of the wind speed is relatively small. As well this effect could be obviously seen in the comparison of the difference between the average values of
σ3w/z at the midday hours (11:00-14:00 CET) and midnight hours (23:00-02:00
CET) on cloudless conditions. But on the cloudy conditions, the role of the mechanical turbulence increases, especially when the value of the horizontal wind
speed is relatively high.
∗∗
Under neutral conditions, the variations of the roughness over the study areas
for various fetch conditions arising for various wind directions have impact on the
turbulence intensity components (Iu, Iv, Iw). This behavior appeared qualitatively
by the study of the variation of the Iu, Iv and Iw with the angular sectors at
Bremgarten, Blankenhornsberg, Oberbärenburg and Melpitz. But at Hartheim
and Freiburg there is no enough data to do this study.
∗∗
The turbulence intensity components (Iu, Iv, Iw) showed dependence on P-G stability classes and increase with increasing of instability. This behavior was illustrated qualitatively by the study of the variation of the Iu, Iv and Iw with the P-G
stability classes over Hartheim, Bremgarten, Blankenhornsberg, Oberbärenburg
and Melpitz. But at Freiburg there is no enough data to do this study. To reduce
the effect of the change of the roughness, this relationship has been investigated
at small angular sector (30°). The turbulence intensities for horizontal components increased faster with increasing instability incomparable with vertical component.
∗∗
The turbulence intensity components (Iu, Iv, Iw) decreased with the increasing of
the height of the observation. This dependence was determined by the study of
the characteristics of Iu, Iv and Iw for various fetch conditions arising under various wind directions, and different atmospheric stability at different level.
∗∗
Under unstable conditions, the mean values σu/u∗, σv/u∗ and σw/u∗ are functions
of (z/L)1/3. σu/u∗ and σv/u∗ are strongly affected by the change in the surface
roughness. In the range of -z/L (0.86 to 3.66), σu/u∗ and σv/u∗ over the grassland
205
site were approximately in the same magnitude as over the vineyard site, but
they were smaller (34% and 52% respectively) than those observed over forest.
But the change of surface roughness does not seem to influence the properties
of σw/u∗.
∗∗
The profile of the normalized (by the square value of the convective velocity w2∗)
variance of the vertical wind speed component, σ2w/w∗2 under the free convective conditions over grassland (Bremgarten) increases with the height to reach
the maximum equal to 0.46 within the mixed layer at z = 0.32 zi. After that these
values decrease with the height to reach a very small values. The behavior of
this results is similar to most data in the literatures (For example: Argentini et al.,
1999; Hibber and Sawford, 1994; Lenschow and Wyngaard, 1980).
All these above conclusions indicate that this study has given a quantitatively variation
of the effect of the thermal and roughness change in some turbulence parameters such
as σu/u∗, σv/u∗ and σw/u∗ in the surface layer over grassland, vineyard and forest under
unstable conditions. In addition, a qualitatively variation of the effect of the thermal and
roughness change in the intensity components (Iu, Iv, Iw) in the surface layer and the
lower part of the mixed layer over grassland, vineyard and forest under the all stability
conditions (neutral, stable and unstable). Furthermore, It determined the height at
which σw is maximum (0.32 zi) under the free convective conditions over grassland
(Bremgarten). This study can be resumed to investigate quantitatively the following:
∗∗
the relationship between the turbulence intensity components Iu, Iv and Iw and z0
under the neutral stability conditions,
∗∗
the relationship between the turbulence intensity components Iu, Iv and Iw and
z/L at different z/z0 over flat and complex terrain,
∗∗
the dependence of σu/u∗, σv/u∗ and σw/u∗ on the thermal and roughness change
under neutral and near-neutral stability conditions,
∗∗
some terms in the turbulence kinetic energy (TKE) budget such as dissipation
rate, buoyancy production, shear production and vertical transport of the TKE
over flat and complex terrain,
206
∗∗
the characteristics of normalized (by variance / covariance) spectra / cospectra
of the wind speed components and some turbulence parameters.
207
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219
LIST OF ABBREVIATIONS AND SYMBOLS
-Abbreviation
ABL
atmospheric boundary layer
a.g.l.
above ground level
a.s.l.
above see level
Av.
average
Br.
Bremgarten (47° 54` N, 07° 37` E, 200 m a.s.l.)
Bl.
Blankenhornsberg (48° 03` N, 07° 36` E, 285 m a.s.l.)
CBL
convective boundary layer
CET
central Europe time
DIN-VDI
German institutes for standardization-association of German engineers
(Deutsche Institute für Normung e.V. – Verein Deutscher Ingenieure)
DWD
German weather serves (Deutsche Wetter Dienst)
FAS
flat array sodar
Fr.
Freiburg (48° 56` N, 07° 50` E, 272 m a.s.l.)
Ha.
Hartheim (47° 56` N, 07° 36` E, 201 m a.s.l.)
IR
Infrared radiation
ISARS
international symposium of acoustic remote sensing
KE
kinetic energy
Me.
Melpitz (51° 31` N, 12° 55` E, 86 m a.s.l.)
MKE
mean kinetic energy per unit mass
ML
mixed Layer
no.
number of observations
Ob.
Oberbärenburg (50° 47` N, 13° 43` E, 735 m a.s.l.)
P-G
Pasquill and Gifford
RL
residual Layer
SBL
stable boundary layer
Sodar
sonic detecting and ranging
SST
stably-stratified turbulence
std
standard deviations
TKE
turbulence kinetic energy per unit mass
220
-Symbols
a,b,c
empirical coefficient
dd
wind direction
(°)
f
frequency
(Hz)
f0
transmitter frequency
(Hz)
fs
frequency of the received scattered signal
(Hz)
g
acceleration due to gravity
(m/s2)
h
the thickness of the turbulent region next to the ground
(mixing depth)
(m)
h*
average vertical extent of roughness elements
(m)
Iu, Iv, Iw
turbulence intensity components for longitudinal,
lateral and vertical wind speed components
k
von Kármán constant
l
distance
(m)
lt
period (scale) of inhomogeneities
(m)
n
sound refractive index
r
radial wind speed (first-order)
(m/s)
q
water vapor concentration
(kg/m3)
ss
average cross section presented to wind by each roughness
element
(m2)
sl
total ground surface area/number of roughness elements
(m2)
u,v,w
mean wind velocity components in; east-west,
north-south and vertical direction
(m/s)
u`,v`,w`
Cartesian components of instantaneous wind velocity
(m/s)
u∗
friction wind velocity
(m/s)
vh
mean horizontal wind velocity
(m/s)
w∗
convective wind velocity scale
(m/s)
z
height above the ground level
(m)
z0
aerodynamic roughness length
(m)
zi
height of lowest inversion (mixing height)
(m)
A
backscattered amplitude (zero-order)
(W)
A
advection of TKE by the mean wind
(m2/s3)
B
buoyant production or consumption of TKE
(m2/s3)
221
C
speed of sound
(m/s)
C0
mean speed of sound
(m/s)
Cph
phase sound velocity
(m/s)
CT2
temperature structure parameter
(k2m2/3)
CV2
velocity structure parameter
G
global solar radiation
(W/m2)
H0
kinematic surface heat flux
(K.m/s)
K
r
K
wave number
(1/m)
wave vector
L
Monin-Obukhov length
(m)
L
spectral power of the backscatter signal
(W)
Lε
dissipation length scale of TKE
(m)
M
magnitude of wind (wind speed)
(m/s)
N
noise
(dB)
N
noise level
(dB)
Ri
Richardson number
R
universal gas constant
Rf
flux Richardson number
P
air pressure
(hPa)
Pt
transmitted acoustic power
(W)
Pr
received acoustic power
(W)
S
shear generation of TKE
(m2/s3)
Tv
absolute virtual air temperature near the ground
(K)
Tr
transport by turbulent motions and pressure term of TKE
(m2/s3)
T`
r
V
air temperature of the scattering volume
(K)
α
acoustic attenuation coefficient
(1/m)
αc
classical attenuation due to dissipation of energy due to
the viscosity of the air
(1/m)
αm
molecular attenuation coefficient
(1/m)
αs
scattering coefficient of sound by turbulence
(1/m)
γ
ratio of heat capacities for constant pressure and
constant volume (1.4)
(m4/3/s2)
(J/K.kg)
projection of wind velocity vector on the normal to the wave front
222
ε
viscous dissipation rate of TKE
ηt
efficiency of transmitter of the acoustic wave
ηr
efficiency of receiver of the acoustic wave
θ
scatter angle in relation to the incident wave
(°)
ΘB
angle of wave incidence (Bragg angle) which is half the
scattering angle θ
(°)
θv
virtual potential temperature
(K)
λ
sound wavelength at mean temperature T
(m)
µ
molecular weight of the mixture of gases that are
constituents of air
(g/mol)
(m2/s3)
υr
projection of wind velocity in the direction of sounder beam
ρ
air density
(kg/m3)
ρ
average density of air
(kg/m3)
σdd
standard deviation of the wind direction
(°)
σi
standard deviation of the wind speed components (i=u,v,w)
(m/s)
variance of the wind speed components (i=u,v,w)
(m2/s2)
σ2 h
variance of the horizontal wind speed
(m2/s2)
σr
width of Doppler spectrum (second-order)
σwm
average of σw between 100 m and the uppermost sodar level
(m/s)
τl
pulse length
(m)
τ
magnitude of the Reynolds’ stress (turbulent momentum flux)
in the surface layer
σ
2
i
∆M
∆z
wind shear
z
L
stability parameter
σ w3
z
(kg/ms2)
(1/s)
represent of the quantity of convective and mechanical
production origin of TKE
(m2/s3)
223
LIST OF CAPTIONS FOR FIGURES
Figure
Caption
Page
Fig. 4.1:
Location of the atmospheric boundary layer
16
Fig. 4.2:
Idealization of (a) mean wind alone, (b) waves alone, and (c) turbulence alone
17
Fig. 4.3:
Rate of generation of TKE by buoyancy, shear. As well as shape and
rates of plume dispersion, separate sectors of different PasquillGifford turbulence type
24
Fig. 4.4:
The boundary layer in high pressure regions over land consists of
three major parts
26
Fig. 4.5:
Dependence of sound absorption on temperature and humidity
36
Fig. 4 6:
Coefficient of molecular attenuation of sound waves as a function of
humidity at various frequencies
37
Fig. 4.7:
Wave scattering by periodical structure inhomogeneities
40
Fig. 5.1:
Backscatter is the returned radiation from the transmitted pulse
44
Fig. 5.2:
Schematic showing relationship between travel time and measured
height
45
Fig. 5.3:
Doppler spectrum
46
Fig. 5.4:
The main subsystem of FAS64
50
Fig. 5.5:
The acoustic arranges 64 highly efficient piezoelectric transducers
52
Fig. 5.6:
Location of investigated sites in Germany
58
Fig. 6.1.1:
Diurnal variation of the global solar radiation G at Hartheim on two
cloudless days (21/22 April, 2000) and two cloudy days (17/18 April,
2000)
62
Fig. 6.1.2:
Frequency distribution of wind direction at (a) 20-50 m, (b) 230-260 m
and (c) 470-500 m a.g.l. at Hartheim during the day and night, the
daytime (6:00–18:00 CET) and the nighttime (18:00–6:00 CET), during the period of the study (30 March, 2000 to 25 April, 2000)
63
Fig. 6.1.3:
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE and σ3w/z at Hartheim under various atmospheric conditions; neutral (17 April, 2000, 03:3004:00 CET) and unstable (03 April, 2000, 12:00-12:30 CET)
64
Fig. 6.1.4:
Diurnal variation of two days mean of the standard deviation of the
wind direction, σdd at Hartheim (a) cloudless sky conditions (21/22
April, 2000) (b) cloudy sky conditions (17/18 April, 2000)
65
Fig. 6.1.5:
Diurnal variation of two days mean of the horizontal wind speed, vh at
Hartheim (a) cloudless sky conditions (21/22 April, 2000) (b) cloudy
sky conditions (17/18 April, 2000)
66
224
Fig. 6.1.6:
Diurnal variation of two days mean of the vertical wind speed component, w at Hartheim (a) cloudless sky conditions (21/22 April, 2000) (b)
cloudy sky conditions (17/18 April, 2000)
67
Fig. 6.1.7:
Frequency distribution of P-G stability classes at different levels a.g.l.
in Hartheim for the study period (30 March, 2000 to 25 April, 2000)
68
Fig. 6.1.8:
Diurnal variation of two days mean of the variance of the horizontal
wind speed, σ2h, at Hartheim (a) cloudless sky conditions (21/22 April,
2000) (b) cloudy sky conditions (17/18 April, 2000)
73
Fig. 6.1.9:
Diurnal variation of two days mean of the variance of vertical wind
speed component, σ2w, at Hartheim (a) cloudless sky conditions
(21/22 April, 2000) (b) cloudy sky conditions (17/18 April, 2000)
74
Fig. 6.1.10: Diurnal variation of two days mean of the quantity, σ3w/z, at Hartheim
(a) cloudless sky conditions (21/22 April, 2000) (b) cloudy sky conditions (17/18 April, 2000)
75
Fig. 6.1.11: Diurnal variation of two days mean of the mean kinetic energy per unit
mass, MKE, at Hartheim (a) cloudless sky conditions (21/22 April,
2000) (b) cloudy sky conditions (17/18 April, 2000)
76
Fig. 6.1.12: Diurnal variation of two days mean of the turbulence kinetic energy
per unit mass, TKE, at Hartheim (a) cloudless sky conditions (21/22
April, 2000) (b) cloudy sky conditions (17/18 April, 2000)
77
Fig. 6.1.13: Variation of the mean values of the turbulence intensity components,
Iu, Iv and Iw, with the P-G stability classes in the angular sector 210240° at different levels over Hartheim for the study period (30 March,
2000 to 25 April, 2000)
78
Fig. 6.1.14: Mean of the standard deviation of wind speed components, σu, σv and
σw, normalized by u* as a function of –z/L at Hartheim for the study period (30 March, 2000 to 25 April, 2000); including general function according to Al-Jiboori et al. (2001)
79
Fig. 6.2.1:
Diurnal variation of the global solar radiation G at Hartheim on two
cloudless days (22/23 July, 2001) and two cloudy days (14/15 July,
2001)
82
Fig. 6.2.2:
Frequency distribution of wind direction at (a) 20-30 m a.g.l. (b) 180260 m a.g.l. and (c) 380-500 m a.g.l. during day and night, daytime
(6:00–18:00 CET) and nighttime (18:00–6:00 CET) at Bremgarten
through the period of the study (10 July, 2001 to 26 July, 2001)
83
Fig. 6.2.3:
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE, and σ3w/z under various
atmospheric conditions; neutral (14-07-2001, 12:30-13:00 CET), stable (16 July, 2001,23:00-23:300) and unstable (22 July,
2001,11:30:12:00C CET)
84
Fig. 6.2.4:
Diurnal variation of two days mean of the standard deviation of the
wind direction, σdd, at Bremgarten (a) cloudless sky conditions (22/23
July, 2001) and (b) cloudy sky conditions (14/15 July, 2001)
85
Fig. 6.2.5:
Diurnal variation of two days mean of the horizontal wind speed, vh, at
86
225
Bremgarten (a) cloudless sky conditions (22/23 July, 2001) and (b)
cloudy sky conditions (14/15 July, 2001)
Fig. 6.2.6:
Diurnal variation of two days mean of the vertical wind speed component, w, at Bremgarten (a) cloudless sky conditions (22/23 July, 2001)
and (b) cloudy sky conditions (14/15 July, 2001)
87
Fig. 6.2.7:
Frequency distribution of P-G stability classes at different heights a.g.l.
in Bremgarten for the study period (10 July, 2001 to 26 July, 2001)
88
Fig. 6.2.8:
Diurnal variation two days mean of the variance of the horizontal wind
speed, σ2h, at Bremgarten (a) cloudless sky conditions (22/23 July,
2001) and (b) cloudy sky conditions (14/15 July, 2001)
92
Fig. 6.2.9:
Diurnal variation of two days mean of the variance of vertical wind
speed component, σ2w, (a) cloudless sky conditions (22/23 July, 2001)
and (b) cloudy sky conditions (14/15 July, 2001)
93
Fig. 6.2.10: Diurnal variation of two days mean of the quantity, σ3w/z, (a) cloudless
sky conditions (22/23 July, 2001) and (b) cloudy sky conditions (14/15
July, 2001)
94
Fig. 6.2.11: Diurnal variation of two days mean of the mean kinetic energy per unit
mass, MKE, (a) cloudless sky conditions (22/23 July, 2001) and (b)
cloudy sky conditions. (14/15 July, 2001)
95
Fig. 6.2.12: Diurnal variation of two days mean of the turbulence kinetic energy
per unit mass, TKE, (a) cloudless sky conditions (22/23 July, 2001)
and (b) cloudy sky conditions (14/15 July, 2001)
96
Fig. 6.2.13: Variation of the mean values of the turbulence intensity components,
(a) Iu, (b) Iv and (c) Iw, with the angular sectors under the neutral stratified at different levels. in Bremgarten during the study period (10 July,
2001 to 26 July, 2001)
97
Fig. 6.2.14: Variation of the mean values of the turbulence intensity components
(a) Iu, (b) Iv and (c) Iw, with the P-G stability classes in the angular sector 210-240° at different levels in Bremgarten during the study (10
July, 2001 to 26 July, 2001)
98
Fig. 6.2.15: Mean of the standard deviation of wind speed components, σu, σv and
σw, normalized by u* as a function of -z/L at Bremgarten during the period from 10 July, 2001 to 26 July, 2001, including the general function
according to Al-Jiboori et al. (2001)
99
Fig. 6.3.1:
Diurnal variation of the global solar radiation G at Hartheim on two
cloudless days (12/15 August, 2001) and two cloudy days (03/17 August, 2001)
102
Fig. 6.3.2:
Frequency distribution of wind direction at (a) 20-30 m, (b) 160-240 m
and (c) 400-500 m a.g.l. at Blankenhornsberg during the day and
night, daytime (6:00–18:00 CET), and nighttime (18:00–6:00 CET)
through the study period (01 August, 2001 to 22 August, 2001)
103
Fig. 6.3.3:
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE, and σ3w/z at Blankenhornsberg under various atmospheric conditions; neutral (04 August,
104
226
2001, 02:30-03:00 CET) and unstable (12 August, 2001, 13:30-14:00
CET)
Fig. 6.3.4:
Diurnal variation of two days mean of the standard deviation of the
wind direction, σdd, at Blankenhornsberg (a) cloudless sky conditions
(12/15 August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
105
Fig. 6.3.5:
Diurnal variation of two days mean of the horizontal wind speed, vh, at
Blankenhornsberg (a) cloudless sky conditions (12/15 August, 2001)
(b) cloudy sky conditions (03/17 August, 2001)
106
Fig. 6.3.6:
Diurnal variation of two days mean of the vertical wind speed component, w, at Blankenhornsberg (a) cloudless sky conditions (12/15 August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
107
Fig. 6.3.7:
Frequency distribution of P-G stability classes at different levels a.g.l.
at Blankenhornsberg for the study period (01 August, 2001 to 22 August, 2001)
108
Fig. 6.3.8:
Diurnal variation of two days mean of the variance of vertical wind
speed component, σ2h, at Blankenhornsberg (a) cloudless sky conditions (12/15 August, 2001) (b) cloudy sky conditions (03/17 August,
2001)
112
Fig. 6.3.9:
Diurnal variation of two days mean of the variance of the horizontal
wind speed, σ2w, at Blankenhornsberg (a) cloudless sky conditions
(12/15 August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
113
Fig. 6.3.10: Diurnal variation of two days mean of the quantity, σ3w/z, at Blankenhornsberg (a) cloudless sky conditions (12/15 August, 2001) (b)
cloudy sky conditions (03/17 August, 2001)
114
Fig. 6.3.11: Diurnal variation of two days mean of the mean kinetic energy per unit
mass, MKE, at Blankenhornsberg (a) cloudless sky conditions (12/15
August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
115
Fig. 6.3.12: Diurnal variation of two days mean of the turbulence kinetic energy
per unit mass, TKE, at Blankenhornsberg (a) cloudless sky conditions
(12/15 August, 2001) (b) cloudy sky conditions (03/17 August, 2001)
116
Fig. 6.3.13: Variation of the mean values of the turbulence intensity components,
Iu, Iv and Iw, with the wind direction under the neutral stratified at different levels in Blankenhornsberg through the period of the study (01
August, 2001 to 22 August, 2001)
117
Fig. 6.3.14: Variation of the mean values of the turbulence intensity components,
Iu, Iv and Iw, with the P-G stability classes in the angular sector 210240° at different levels at Blankenhornsberg through the period of the
study (01 August, 2001 to 22 August, 2001)
118
Fig. 6.3.15: Mean of standard deviation of wind speed components σu, σv and σW,
normalized by u* as a function of –z/L at Blankenhornsberg through
the period of the study (01 August, 2001 to 22 August, 2001), including general function according to Al-Jiboori et al. (2001)
119
Fig. 6.4.1:
121
Diurnal variation of the global solar radiation G at Rotherdbach on two
227
cloudless days (30 August, 2001 and 23 September, 2001) and two
cloudy days (31 August, 2001 and 01 September, 2001)
Fig. 6.4.2:
Frequency distribution of wind direction at (a) 20-50 m, (b) 230-260 m
a.g.l. and (c) 470-500 m a.g.l. during the day and night, daytime
(6:00–18:00 CET) and the nighttime (18:00–6:00 CET) at Oberbärenburg through the period of the study (29 August, 2001 to 24 September, 2001)
122
Fig. 6.4.3:
Diurnal variation of two days mean of the standard deviation of the
wind direction, σdd, at Oberbärenburg (a) cloudless sky conditions (30
August, 2001 and 23 September, 2001) (b) cloudy sky conditions (31
August, 2001 and 01 September, 2001)
123
Fig. 6.4.4:
Diurnal variation of two days mean of the horizontal wind speed, vh, at
Oberbärenburg (a) cloudless sky conditions (30 August, 2001 and 23
September, 2001) (b) cloudy sky conditions (31 August, 2001 and 01
September, 2001)
124
Fig. 6.4.5:
Diurnal variation of two days mean of the vertical wind speed component, w, at Oberbärenburg (a) cloudless sky conditions (30 August,
2001 and 23 September, 2001) (b) cloudy sky conditions (31 August,
2001 and 01 September, 2001)
125
Fig. 6.4.6
Frequency distribution of P-G stability classes at different levels a.g.l.
at Oberbärenburg for the study period (29 August, 2001 to 24 September, 2001)
126
Fig. 6.4.7:
Diurnal variation of two days mean of the variance of the horizontal
wind speed, σ2h, at Oberbärenburg (a) cloudless sky conditions (30
August, 2001 and 23 September, 2001) (b) cloudy sky conditions (31
August, 2001 and 01 September, 2001)
131
Fig. 6.4.8:
Diurnal variation of two days mean of the variance of vertical wind
speed component, σ2w, at Oberbärenburg (a) cloudless sky conditions
(30 August, 2001 and 23 September, 2001) (b) cloudy sky conditions
(31 August, 2001 and 01 September, 2001)
132
Fig. 6.4.9:
Diurnal variation of two days mean of the quantity, σ3w/z, at Oberbärenburg (a) cloudless sky conditions (30 August, 2001 and 23 September, 2001) (b) cloudy sky conditions (31 August, 2001 and 01 September, 2001)
133
Fig. 6.4.10: Diurnal variation of two days mean of the mean kinetic energy per unit
mass, MKE, at Oberbärenburg (a) cloudless sky conditions (30 August, 2001 and 23 September, 2001) (b) cloudy sky conditions (31
August, 2001 and 01 September, 2001)
134
Fig. 6.4.11: Diurnal variation of two days mean of the turbulence kinetic energy
per unit mass, TKE, at Oberbärenburg (a) cloudless sky conditions (30
August, 2001 and 23 September, 2001) (b) cloudy sky conditions (2908-2001 and 01-09-2001)
135
Fig. 6.4.12: Variation of the mean values of the turbulence intensity components,
Iu, Iv and Iw, with the wind direction under the neutral stratified at dif-
136
228
ferent levels at Oberbärenburg for the study period (29-08-01 to 2409-01)
Fig. 6.4.13: Variation of the mean values of the turbulence intensity components,
Iu, Iv and Iw, with the P-G stability classes in the angular sector 210240° at different levels at Oberbärenburg through the period of the
study (29 August, 2001 to 24 September, 2001)
137
Fig. 6.4.14: Mean standard deviation of wind speed components σu, σv and σw,
normalized by u* as a function of -z/L at Oberbärenburg through the
period of the study (29 August, 2001 to 24 September, 2001), including general function according to Al-Jiboori et al. (2001)
138
Fig. 6.5.1:
Diurnal variation of the global solar radiation G at Melpitz on a cloudless day (06 October, 2001) and two cloudy days (30 September,
2001 and 01 October, 2001)
140
Fig. 6.5.2:
Frequency distribution of wind direction at (a) 20-50 m, (b) 230-260 m
and m, (c) 470-500 m a.g.l. during the day and night, daytime (6:00–
18:00 CET) and the nighttime (18:00–6:00 CET) at Melpitz through the
period of the study (26 September, 2001 to 12 October, 2001)
141
Fig. 6.5.3:
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE, and σ3w/z at Melpitz under
various atmospheric conditions; neutral (03 October, 2001, 03:3004:00) and unstable (06 October, 2001, 13:00-13:30).
142
Fig. 6.5.4:
Diurnal variation of the standard deviation of the wind direction, σdd, at
Melpitz (a) one cloudless day (06 October, 2001) and (b) two days
mean in cloudy sky (30 September, 2001 and 01 October, 2001)
143
Fig. 6.5.5:
Diurnal variation of the horizontal wind speed, vh, at Melpitz (a) one
cloudless day (06 October, 2001) and (b) two days mean in cloudy sky
(30 September, 2001 and 01 October, 2001)
144
Fig. 6.5.6:
Diurnal variation of the vertical wind speed component, w, at Melpitz
(a) one cloudless day (06 October, 2001) and (b) two days mean in
cloudy sky (30 September, 2001 and 01 October, 2001)
145
Fig. 6.5.7:
Frequency distribution of P-G stability classes at different levels a.g.l.
at Melpitz for the study period (26 September, 2001 to 12 October,
2001)
146
Fig. 6.5.8:
Diurnal variation of the variance of the horizontal wind speed, σ2h, at
Melpitz (a) one cloudless day (06 October, 2001) and (b) two days
mean in cloudy sky (30 September, 2001 and 01 October, 2001)
151
Fig. 6.5.9:
Diurnal variation of the variance of the vertical wind speed, σ2w, at
Melpitz (a) one cloudless day (06 October, 2001) and (b) two days
mean in cloudy sky (30 September, 2001 and 01 October, 2001)
152
Fig. 6.5.10: Diurnal variation of the quantity, σ3w/z, at Melpitz (a) one cloudless day
(06 October, 2001) and (b) two days mean in cloudy sky (30 September, 2001 and 01 October, 2001)
153
Fig. 6.5.11: Diurnal variation of the mean kinetic energy per unit mass, MKE, at
Melpitz (a) one cloudless day (06 October, 2001) and (b) two days
154
229
mean in cloudy sky (30 September, 2001 and 01 October, 2001)
Fig. 6.5.12: Diurnal variation of the turbulence kinetic energy per unit mass, TKE,
at Melpitz (a) one cloudless day (06 October, 2001) and (b) two days
mean in cloudy sky (30 September, 2001 and 01 October, 2001)
155
Fig. 6.5.13: Variation of the mean values of the turbulence intensity components,
Iu, Iv and Iw, with the wind direction under the neutral stratified at different levels at Melpitz through the period of the study (26 September,
2001 to 12 October, 2001)
156
Fig. 6.5.14: Variation of the mean values of the turbulence intensity components,
Iu, Iv and Iw, with the P-G stability classes in the angular sector 210240° at different levels at Melpitz through the period of the study (26
September, 2001 to 12 October, 2001)
157
Fig. 6.6.1:
Diurnal variation of the global solar radiation G at Freiburg on cloudless day (17 November, 2001) and cloudy day (18 November, 2001)
159
Fig. 6.6.2:
Frequency distribution of wind direction at (a) 20-30 m, (b) 40-60 m,
(c) 60-80 m a.g.l. during the day and night, daytime (6:00–18:00 CET)
and nighttime (18:00–6:00 CET) at Freiburg through the period of the
study (16 November, 2001 to 19 November)
161
Fig. 6.6.3:
Profile of vh, w, dd, σ2h, σ2w, σdd, TKE, MKE, and σ3w/z at Freiburg under various atmospheric conditions; stable (18 November, 2001,
04:30-05:00 CET) and unstable (17 November, 2001, 12:00-12:30
CET)
162
Fig. 6.6.4:
Diurnal variation of the standard deviation of the wind direction, σdd, at
Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy
sky conditions (18 November, 2001)
163
Fig. 6.6.5
Diurnal variation of the horizontal wind speed, vh, at Freiburg (a)
cloudless sky conditions (17 November, 2001) (b) cloudy sky conditions (18 November, 2001)
164
Fig. 6.6.6:
Diurnal variation of the vertical wind speed component, w at Freiburg
(a) cloudless sky conditions (17 November, 2001) (b) cloudy sky conditions (18 November, 2001)
165
Fig. 6.6.7:
Diurnal variation of the variance of the horizontal wind speed, σ2h, at
Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy
sky conditions (18 November, 2001)
166
Fig. 6.6.8:
Diurnal variation of the variance of vertical wind speed component,
σ2w, at Freiburg (a) cloudless sky conditions (17 November, 2001) (b)
cloudy sky conditions (18 November, 2001)
167
Fig. 6.6.9:
Diurnal variation of the quantity, σ3w/z, at Freiburg (a) cloudless sky
conditions (17 November, 2001) (b) cloudy sky conditions (18 November, 2001)
168
Fig. 6.6.10: Diurnal variation of the mean kinetic energy per unit mass, MKE, at
Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy
169
230
sky conditions (18 November, 2001)
Fig. 6.6.11: Diurnal course of the turbulence kinetic energy per unit mass, TKE, at
Freiburg (a) cloudless sky conditions (17 November, 2001) (b) cloudy
sky conditions (18 November, 2001)
170
Fig. 7.1:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00
CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudless conditions at levels from 20-50 m a.g.l. [forest and grassland
(Me.)] and 20-30 m a.g.l. [grassland (Br.), vineyard and urban area],
(Table 7.1 to 7.6)
194
Fig. 7.2:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00
CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudy
conditions at levels from 20-50 m a.g.l. [forest and grassland (Me.)]
and 20-30 m a.g.l. [grassland (Br.), vineyard and urban area], (Table
7.1 to 7.6)
195
Fig. 7.3:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00
CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudless conditions at levels from 50-80 m a.g.l. [forest and grassland
(Me.)] and 40-60 m a.g.l [grassland (Br.), vineyard and urban area],
(Table 7.1 to 7.6)
196
Fig. 7.4:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00
CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudy
conditions at levels from 50-80 m a.g.l [forest and grassland (Me.)]
and 40-60 m a.g.l [grassland (Br.), vineyard and urban area], (Table
7.1 to 7.6)
197
Fig. 7.5:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00
CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudless conditions at levels from 80 to 110 m a.g.l. [forest and grassland
(Me.)], 60-100 m a.g.l. [grassland (Br.)], 80-120 m a.g.l. [vineyard] and
60-80 m a.g.l. [urban area], (Table 7.1 to 7.6)
198
Fig. 7.6:
Midday hours (11:00-14:00 CET) and midnight hours (23:00-2:00
CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE, and TKE for a cloudy
conditions at levels from 80 to 110 m a.g.l. [forest and grassland
(Me.)], 60-100 m a.g.l. [grassland (Br.)], 80-120 m a.g.l. [vineyard] and
60-80 m a.g.l. [urban area], (Table 7.1 to 7.6)
199
Fig. 7.7:
Mean values of the dimensionless of standard deviations of velocity
components σi/u∗ (i=u,v,w) as a function of –z/L under free convective
conditions in the surface layer
200
Fig. 7.8:
The mean values of σi/u∗ (i=u,v,w) (from table 7.2) over different land
use types, and the data of AL-Jiboori et al. (2001) (complex and flat
terrain)
201
Fig. 7.9:
Normalized vertical velocity variance, σw/w∗ as a function of the normalized height, z/zi at Bremgarten under the free convection conditions
201
231
LIST OF CAPTIONS FOR TABLES
Table
Caption
Page
Table 4.1:
Change of wavelength of sound waves in the atmosphere as a
function of changes in temperature, wind speed and water vapor
content.
34
Table 5.1:
Specifications of FAS64
51
Table 5.2:
Method of stability classification (class limits)
56
Table 5.3:
The values of coefficient a and b (Liu et al., 1976 and Irwin,
1979)
56
Table 5.4:
The general description of the study areas.
57
Table 6.1.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels grouped by direction. Under each component are
given the mean, standard deviation and number of observations
in each group at Hartheim for the study period (30 March, 2000
to 25 April, 2000)
71
Table 6.1.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different levels grouped by P-G stability classes in one angular sector
(180-210°). Under each component are given the mean, standard deviation and number of the observation in each group at
Hartheim for the study period (30 March, 2000 to 25 April, 2000)
72
Table 6.2.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels grouped by direction. Under each component are
given the mean, standard deviation and number of observation
in each group at Bremgarten during the study period (10 July,
2001 to 26 July, 2001)
90
Table 6.2.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different
levels grouped by P-G stability classes in one angular sector
(180-210°). Under each component are given the mean, standard deviation and number of the observation in each group during the study period (10 July, 2001 to 26 July, 2001)
91
Table 6.3.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels grouped by direction. Under each component are
given the mean, standard deviation and number of observation
in each group at Blankenhornsberg through the period from 01
August, 2001 to 22 August, 2001
110
Table 6.3.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different
levels grouped by P-G stability classes in one angular sector
(210-240°).Under each component are given the mean, standard deviation and number of the observation in each group at
Blankenhornsberg for the study period (01 August, 2001 to 22
111
232
August, 2001)
Table 6.4.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels grouped by direction. Under each component are
given the mean, standard deviation and number of observation
in each group at Oberbärenburg through the period from 29 August, 2001 to 24 September, 2001
129
Table 6.4.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different levels grouped by P-G stability classes in one angular sector
(180-210°). Under each component are given the mean, standard deviation and number of the observation in each group at
Oberbärenburg through the period of the study (29 August, 2001
to 24 September, 2001)
130
Table 6.5.1: Turbulence intensity components (a) Iu, (b) Iv and (c) Iw at different levels grouped by direction. Under each component are
given the mean, standard deviation and number of observation
in each group at Melpitz through the period from 26 September,
2001 to 12 October, 2001
149
Table 6.5.2: Turbulence intensity component (a) Iu, (b) Iv and (c) Iw at different levels grouped by P-G stability classes in one angular sector
(210-240°). Under each component are given the mean, standard deviation and number of the observation in each group at
Melpitz through the period from 26 September, 2001 to 12 October, 2001
150
Table 7.1:
Daily, midday hours (11:00-14:00 CET) and midnight hours
(23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE,
and TKE at different levels in Hartheim on two cloudless days
(21-04-2000 and 22-04-200) and two cloudy days (17-04-200
and 18-04-2000)
187
Table 7.2:
Daily, midday hours (11:00-14:00 CET) and midnight hours
(23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE,
and TKE at different levels in Bremgarten on two cloudless days
(22/23 July, 2001) and two cloudy days (14/15 July, 2001)
188
Table 7.3:
Daily, midday hours (11:00-14:00 CET) and midnight hours
(23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE,
and TKE at different levels in Blankenhornsberg on two cloudless days (12-08-2001 and 15-08-2001) and two cloudy days
(03-08-2001 and 17-08-2001)
189
Table 7.4:
Daily, midday hours (11:00-14:00 CET) and midnight hours
(23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE,
and TKE at different levels in Oberbärenburg on two cloudless
days (30 August, 2001 and 23 September, 2001) and two cloudy
days (31 August, 2001 and 01 September, 2001)
190
Table 7.5:
Daily, midday hours (11:00-14:00 CET) and midnight hours
(23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE,
191
233
and TKE at different levels in Melpitz on a cloudless day (06 October, 2001) and two cloudy days (30 September, 2001 and 01
October, 2001)
Table 7.6:
Daily, midday hours (11:00-14:00 CET) and midnight hours
(23:00-2:00 CET) average of vh, w, σ2w, σ2h, σdd, σ3w/z, MKE,
and TKE at different levels in Freiburg on a cloudless day (17
November, 2001) and a cloudy day (18 November, 2001)
192
Table 7.7:
Comparison between the value of ai and bi in the present study
and some previous studies
193
Table 7.8:
Comparison of the mean values of the standard deviation of the
wind speed components normalized by friction velocity under the
atmospheric unstable conditions in the surface layer at sites of
the present study with other studies at flat and complex terrain
193
234
235
Berichte des Meteorologischen Institutes der Universität Freiburg
Nr. 1:
Fritsch, J.: Energiebilanz und Verdunstung eines bewaldeten Hanges. Juni
1998.
Nr.2:
Gwehenberger, J.: Schadenpotential über den Ausbreitungspfad Atmosphäre
bei Unfällen mit Tankfahrzeugen zum Transport von Benzin, Diesel, Heizöl oder Flüssiggas. August 1998.
Nr. 3:
Thiel, S.: Einfluß von Bewölkung auf die UV-Strahlung an der Erdoberfläche
und ihre ökologische Bedeutung. August 1999.
Nr. 4:
Iziomon, M.G.: Characteristic variability, vertical profile and modelling of surface radiation budget in the southern Upper Rhine valley region. Juli 2000.
Nr. 5:
Mayer, H. (Hrsg.): Festschrift „Prof. Dr. Albrecht Kessler zum 70. Geburtstag“.
Oktober 2000.
Nr. 6:
Matzarakis, A.: Die thermische Komponente des Stadtklimas. Juli 2001.
Nr. 7:
Kirchgäßner, A.: Phänoklimatologie von Buchenwäldern im Südwesten der
Schwäbischen Alb. Dezember 2001
Nr. 8:
Haggagy, M.: A sodar-based investigation of the atmospheric boundary layer.
September 2003
236