Theor. Appl. Climatol. 45, 113-126 (1992)
Theoretical
and Ap.plied
Climatology
© Springer-Verlag 1992
Printed in Austria
551.55:551.588.2
Institut fiir Meteorologie und Klimaforschung Kernforschungszentrum Karlsruhe/Universitfit Karlsruhe, Bundesrepublik
Deutschland
Counter-Current and Channelling Effect Under Stable Stratification
in the Area of Karlsruhe
N. Kalthoff and B. Vogel
With 19 Figures
Received March 21, 1991
Summary
The topic of this study is the investigation of channelling of
the airflow and the so-called counter-current within the area
of Karlsruhe. These phenomena of a strong turning of the
wind direction with respect to the height generally develop
under conditions of stable stratification and are of great
importance in air pollution modelling.
First a case study of a channelling event with data from the
200m high IMK-tower is analysed in detail. During this
channelling event a deviation angle, i.e. a difference of the
wind direction between the upper (200 m) and lower levels
(40m) of about 100 ° exists.
In the second part, the data collected at the IMK-tower
over a period of 16 years are used to evaluate from the climatological point of view the frequency of channelling events in
conjunction with the meteorological conditions. Concerning
the deviation angle it can be found that there is an increase
of the mean deviation angle at the transition from unstable
stratification to stable stratification, but only a slight dependence on the degree of stable stratification. In contrast a
considerable dependence on the wind speed is found, i.e. there
is a decrease of the deviation angle with increasing wind
speed. The mean deviation angle for a gradient Richardson
number Ri < 0 is about 10°, while for Ri > 0 this value increases up to 50 °.
Finally, numerical simulations are carried out with the
meso-scale model KAMM. The simulated deviation angles
are in good agreement with the observations. Especially from
these simulations the dependence of the deviation angle on
the wind speed can be explained.
1. lntro,~uction
Valleys of every size modify the wind system which
appears under homogeneous conditions. Even
broad and flat valleys like the upper Rhine valley,
which is located in the southwestern part of the
Federal Republic of Germany, have remarkable
effects on the prevailing wind conditions. This was
clearly shown by Dammann (1960), who referred
to the observations made during three years (19361938) in the Rhine-Main area between Mannheim
and Frankfurt. He found that for stable stratification northern winds occur close to the ground,
while there was geostrophic wind from southeast
(the axis of the valley points from south to north
in this area). Other climatological investigations
of the wind field or the channelling effect in the
upper Rhine valley were performed by Peppler
(1930), Malsch (1953), Ahrens (1970), Diem (1971)
and Dorn (1977) for the area of Karlsruhe.
In 1979 the MESOKLIP-experiment (Fiedler
and Prenosil, 1980) was carried out in the Rhine
valley south of Mannheim where again the strong
influence of the valley was found even under
neutral conditions.
Later on Wippermann and Grol3 (1981) were
able to reproduce the observed wind rose of
Mannheim with a two-dimensional version of a
non-hydrostatic meso-scale model. They investigated the strong modification of the flow field
caused by the Rhine valley and called these effects
channelling and counter-current.
Fiedler (1983) gave an explanation of both effects
from observed data. He assumed that the airflow
in the upper Rhine valley follows the pressure
114
N. Kalthoff and B. Vogel
gradient along the valley's axis and is decoupled
from the airflow in the free atmosphere under
conditions of low turbulence, i.e. stable stratification. Wippermann (1984), referred to as Wi84
in the following text, gave a theoretical explanation
of channelling and counter-current using a linearised model for neutral conditions. Vogel et al.
(1986) were able to simulate reasonably well the
daily variation of channelling as observed during
MESOKLIP. Vogel (1987) carried out numerical
studies to estimate the influence of parameters like
the width and the depth of the valley, the Coriolis
force, the wind speed and direction and the thermal
stratification.
It is clear that both channelling and counterc u r r e n t - in our case study there is a windshift
of more than 100 ° in the lowest 200m of the
atmosphere - play an important role if one thinks
of the behaviour of accidental releases, and therefore they are of great interest, as mentioned by
Fiedler (1987). Especially as in most valleys in
industrialised countries a number of powerplants
and industrial facilities are sited along the Rhine.
In this paper we study the flow conditions in
the area of Karlsruhe where the axis of the Rhine
valley turns from southwest-northeast in the
southern part to s o u t h - n o r t h in the northern part
(see Fig. 1). The cut of the Kraichgau, which separates the southern part of the Odenwald from
200 •
150.
?
:33
i00
50 ¸
o
so
loo
1so
x
20o
25o
(km)
Fig. 1. Map of the upper Rhine valley. Heights below 300 m
MSL are shaded
the northern part of the Schwarzwald, modifies
the airflow in the Rhine valley as we will see later.
We will refer to the observations made at the
meteorological tower of the 'Institut fiir Meteorologie und Klimaforschung' (IMK) at the Karlsruhe
Nuclear Research Center (KfK) as well as to
numerical simulations with the non-hydrostatic
meso-scale model K A M M (Adrian and Fiedler,
1991).
For this study, we are only interested in flow
conditions with easterly geostrophic winds, i.e. a
high pressure system in the north with clear sky
conditions, because these wind directions are
normaly accompanied by strong channelling events.
The clear sky conditions are necessary for the
evolution of a stably stratified boundary layer.
For westerly winds, however, the contrary is
valid. Generally they are accompanied by frontal
passages. Thus the atmosphere is nearly neutrally
startified and the decoupling of the different layers
is prevented.
2. Definition of Channelling
and Counter-Current
If there is no spatial variation of the topography
i.e. under homogeneous conditions one would expect values of the cross isobar angle c~o between
ten and fourty degrees depending on the thermal
stratification. Small values would occur under unstable conditions, the largest values would occur
under extremely stable stratification. If we find
cross isobar angles greater than these values inside
of a valley and if we can be sure that they are not
caused by thermal circulation systems like slope
or valley winds we speak of channelling.
In order to explain the mechanism that leads to
channelling a valley directed from south to north
as illustrated in Fig. 2 is assumed. Our coordinate
system is oriented in that way, that the ordinate
is parallel to the valley's axis pointing from south
to north and the abscissa is perpendicular to the
valley's axis. The dashed lines are marking the
bounds of the valley. We specify a large scale
pressure field with high pressure in the north and
low pressure in the south and isobars (solid lines)
perpendicular to the valley. This results in a geostrophic wind vg blowing from east to west. Under
conditions of stable stratification or small turbulence the upper and the lower layers of the
atmosphere are decoupled. Since the air caused by
Counter-Current and Channelling EffectUnder Stable Stratification in the Area of Karlsruhe
<:]'"
I
i
i
Pl
"v9 Po
',
i
P-I
i
P-~
\v~'
vl
u
L
P-2 P-1 Po
Fig. 2. Schematicillustration of channelling(left)and countercurrent (right). v 0 is the geostrophic wind speed, % is the
surface wind speed (adopted from Fiedler (1983))
this decoupling is trapped inside of the valley the
airflow close to the ground is driven by the pressure
gradient component along the valley's axis. This
leads to surface winds v s nearly parallel to the
valley and therefore to cross isobar angles much
larger than under homogeneous conditions.
A special case of the channelling effect, which
leads to the largest cross isobar angles, is the socalled counter-current. This case is also illustrated
in Fig. 2. The solid lines indicate the large scale
pressure distribution (p. > p. 1)- This pressure field
would cause a geostrophic wind blowing from
southeast. So the geostrophic wind has a s o u t h north component v 0 greater than zero. Again
under stable stratification followed by a decoupling
of the upper and the lower layers the wind inside
of the valley is driven by the pressure gradient
along the valley i.e. surface winds blowing from
north to south.
Similar conditions are also valid for westerly
geostrophic winds, except that surface winds inside
of the valley are from the south.
In order to come to a quantitative description
of channelling and counter-current we will use the
definitions of Wi84 in a modified form. Wi84
takes into account the direction of the geostrophic
wind /3g and the directions of the surface wind
inside /3/ and outside /3o the valley. The surface
wind outside the valley is assumed to be identical
with the wind under homogeneous conditions.
Wi84 states that channelling exists if the crossisobar angle inside the valley exceeds the crossisobar angle outside, i.e. (/3o -/3i) > (/3o -/3o). If in
addition the v-components of the geostrophic and
the surface wind inside the valley have a different
sign he calls it counter-current.
As we only refer to the observations made at
the IMK-tower, at 40 m (about 10 m above the top
of the trees) and 200 m above ground, we have to
adapt Wi84's definitions to our local conditions.
115
Therefore we have to take into account the orientation of the valley's axis in the area of Karlsruhe
which deviates by 30 ° from north (see Fig. 1).
We introduce the deviation angle c~ as the difference between the wind direction 132oo 200m
above ground and the wind direction/34o 4 0 m
above ground.
As mentioned above, we concentrate our interest
on cases where the synoptic situation produces an
easterly flow in the free atmosphere. We call it
channelling, if the conditions 60 ° </?2oo < 150°
and e > 30 ° are fulfilled. Additionally, the maximum
N
~
/
/
~0 °
~200
#
/
CHANNELLIN5
COUNTER-CURRENT
Fig. 3. Illustration of the admissible angles of the upper/~zoo
and the lower/~40 airflow and the deviation angle 7 for the
definition of channelling (a) and counter-current (b)
116
N. Kalthoff and B. Vogel
wind direction offi40 is limited to 300 °. These two
boundary conditions guarantee that the flow in
the lower layer has always a negative v-component
(3000 < fi40 ~<360° v 0 ° < f14o ~< 120°)• Channelling is illustrated in Fig. 3a. The broad shaded area
indicates the admissible direction of the upper
flow, while the narrow shaded area indicates the
admissible angle of the surface flow for one upper
flow direction ~200"
The counter-current is defined by a stricter
limitation than channelling. The counter-current
is not only characterised by the fact that the lower
airflow has a negative v-component, but also that
the v-component changes it sign between the upper
and the lower layers. Since the airflow of the upper
layer is restricted to have a positive v-component,
we speak of counter-current, if the conditions
120° </~200 < 150° and c~> 30 ° are fulfilled. Again
the flow in the lower layer is limited to 300 °. The
definition of the counter-current is illustrated in
Fig. 3b.
As we require a deviation angle greater than 30 °
within the lowest 200m, while Wi84 requires a
cross-isobar angle greater than 25 ° within the entire
boundary layer, a channelling or a counter-current
event as we defined it would also be one in Wi84's
definition.
It must be pointed out here, that our definition
restricts the detection of channelled air masses to
a maximum height of 200 m above ground. Thus
channelling which appears under unstable stratification, where the height of the channelled air
is adapted to the extension of the mixed layer,
as observed by Fiedler (1983) under westerly
winds in the Rhine valley, is out of scope of this
definition.
3. Site and Instrumentation
of the IMK-Tower
The meteorological 200m-tower of the IMK is
located in the eastern part of the Rhine valley,
about 10 km north of Karlsruhe (49 ° 5' N, 8 ° 26' E)
and l l 0 m above MSL (Fig. 1). Here the Rhine
valley is about 30 km in width. At a distance of
10km eastwards of the tower the hills of the
Kraichgau rise, with a mean height of about 250 m
above NN. Thus, the top of the tower generally
surpasses the Kraichgau by about 60 m. This hilly
country marks a cutting of 50 km width between
the hills of the Odenwald (400 m-700 m) in the
north and those of the Schwarzwald (700 m-1000 m)
in the south, both much higher eastern bounds of
the Rhine valley.
The tower is equipped with a multitude of
meteorological instruments. The height and detection rates of the various instruments are summarised in Table 1. The meteorological parameters
below 20 m altitude are measured separately over
a meadow near the tower, while from 20 m altitude
upwards the data are measured at the tower. To
avoid the shadowing, anemometers are mounted
on two sides, namely on the western and eastern
sides of the tower. Data of the luff-sided anemometers are selected for the calculation of the wind
speed. From all the collected data ten-minute means
are calculated. These 10-minute means are used
for this study.
4. A Case Study of Strong Channelling
In the night from January 19th to January 20th,
1989 a development of strong channelling was
observed in the Karlsruhe area.
Table 1. Meteorological Instrumentation of the IMK-Tower
Meteorological parameter
Instrument
Measuring height in meters
Wind speed
cup anemometer
Wind direction
Wind vector
Temperature
wind vane
vector vane
PT-resistancethermometer
Humidity
Shortwave radiation
Total radiation
Soil heat flux
Pressure
Precipitation
dew point hygrometer
Kipp and Zonen pyranometer
Schulze pyrradiometer
heat flux plates
pressure transducer
rain gauge
2, 20, 30, 40, 50, 60, 80, 100,
130,160,200
40,60,80,100,160,200
40,100,160
2,10,30,60,100,130,
160,200
2,10,30,100,200
2
2
-0.05
2
1
Scanning rate in seconds
4
4
1
4
4
4
4
4
600
600
117
Counter-Current and Channelling Effect Under Stable Stratification in the Area of Karlsruhe
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-4
5m/s
'
/
FE~5ERG
50
100
150
Z
U LM
I
I
7CETI
200
250
x (km)
Fig. 4. Observed surface isobars from 19 January, 1989 16 CET to 20 January, 1989 07 CET. The arrows mark the surface
wind direction and wind speed. The arrow at the station Feldberg gives the wind direction, the number the wind speed in ms- L
The shaded area marks the heights below 300 m MSL (Top left: 16 CET, bottom right: 7 CET; time step: 3h)
118
N. Kalthoff and B. Vogel
4.1 The Synoptic Situation
7,0[
The synoptic situation during the two days from
January 19th, 1989 to January 20th, 1989 is dominated by a high pressure system, which extends
from Central Europe to the Balkan Peninsula on
the first day, and is centered over the Balkan on
the second day. The meteorological surface parameters of wind speed, wind direction and surface
pressure during the period for the area of interest
are shown in Fig. 4. According to the synoptic
situation high pressure is in the northeast and low
pressure in the southwest. This situation is encountered eventually during the transition from
the first to the second day (Fig. 4, 01 CET). In the
late afternoon of the first day the wind blows from
the east. This changes at 22 CET in the northern
part of the Rhine valley. Northerly winds arise,
following the orientation of the valley. These conditions already change at 07 CET when again
easterly winds appear in the northwest, while in
the southeast southern winds arise. Of special
interest for this study is the time, when the wind
direction in the upper Rhine valley changes from
east to north at about 20 CET. This period will
be analysed now in more detail.
5.6-L
E
4.2-.~
2.8- ~
-
16,00
120'0 1
90.0c
~..
~1/~1I~\t"
/ "" \ ~ /' *'
~" -~\ ~ ~ / \
~
j~,
/
°°,°-k;
_
30,00.0
16,00
20,00
24,O0
CET
4.00
8.00
Fig. 5. Time series of the wind directions at 40 m (solid) and
200m (dashed) above ground from 19 January, 1989 16 CET
to 20 January, 1989 08 CET
"~
\1
~J'~^
"~"
L,/
"~/
v
I
20,00
I
--
~" ~l
I
CET
I
24.00
4,00
v
8,00
Fig. 6. Same as Fig. 5, but for the wind speeds at 40 m (solid)
and 200 m (dashed) above ground
4..0
2,8-
\~' \
(.9
o
1,6-
®
o.4-
\
-0,8-
16,00
In Figs. 5 to 7 the time series of the wind direction,
wind speed and the potential temperature at different levels are shown from 19 January, 1989 16
CET until 20 January, 1989 08 CET. It can be seen
that at the beginning of that time interval the wind
blew from east at both heights. At that time the
/I '~11
°.°
-2.O
4.2 Some Meteorological Parameters
at the IMK-Tower
,-,
I
20,00
I
CET
24..00
I
4.00
8.00
Fig. 7. Same as Fig. 5, but for the potential temperatures at
2 m (solid) and 200 m (dashed) above ground
surface layer is neutrally stratified (see Fig. 7).
While the wind direction at 200 m remains nearly
constant throughout the whole period, as also
observed for the wind direction outside the valley,
the wind direction at 40 m changes to the north at
20CET. Between 22 and 23 CET the largest
difference appears between the upper and lower
wind direction. The deviation angle ~ exceeds 90 °.
The turning of the wind in the lowest layer starts
with the development of a stably stratified nocturnal boundary layer (Fig. 7). It is accompanied by
a reduction of turbulence, indicated by the standard
deviation of the vertical wind direction a s at 100 m
height (Fig. 8). This causes a decoupling of the
different layers and hence leads to the flow along
tlae pressure gradient, guided by the direction of
the Rhine valley. The evolution of the stable stratification is accompanied by a slight decrease of the
Counter-Current and Channelling Effect Under Stable Stratification in the Area of Karlsruhe
wind speed (Fig. 6). Later-on, at about 02 CET,
when the surface layer becomes less stable again,
due to development of a fog layer, the wind direction at 40 m altitude shows a remarkable turn to
northeast.
In Fig. 9 the vertical profiles of the potential
temperature 0, the specific humidity q, the wind
speed v, and the wind direction ~ are shown for
three different times. From these profiles the continuous turning of the wind direction from northern
winds at 40 m to easterly winds at 200 m can be
seen. The profile of the wind speed reveals a secondary wind maximum (nocturnal low-level jet) at
100 m, just below the top of the surface inversion
(see 22 CET).
In the course of the night, starting at 22 CET,
a nearly neutrally stratified sub-layer develops
within the surface inversion. Finally, at about 02
CET, when the surface layer is nearly neutrally
stratified, the wind direction at 40m altitude reveals a turn to the northeast. The temperature
profile indicates a fog layer which is confirmed by
the time series of the net radiation of the earth
surface (Fig. 8). The net radiation rises sharply
between 22 CET and 23 CET and thereafter becomes almost zero. This sub-layer can be well
detected from the temperature and humidity profiles
at 22:50 CET (Fig. 9b). It finally reaches a height
of 100m at 24 CET (Fig. 9c). Especially at that
time, the top of the layer is indicated by a sharp
increase in temperature, humidity and wind speed.
When the top of this neutrally stratified sub-layer and hence the layer of maximum vertical wind
shear - reaches the height of 100 m, the turbulence
increases again (see % in Fig. 8).
0.0
1,3 v ( r n / s )
I
I
1,3,0
200.0
2 7 ( ,O
120.0..-" J
///'"
.' ""
40.0.
,'
o.o
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-O
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16,00
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~ -- ~ _ _
--11,2
, \ ,
;I~" h,l
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':'l
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.C
-21.,8
16.7
0.0
I
t
7,0
24.00
CET
4.00
)
80.0
~ ' t
4-0.0
I
q(g/kg)18.3
1.~ v(~/s)
I
I
* 0 . 3 ~(deg)
~(K)
272.0
o.o
20J
3.3
I
73.~'
5.0
I
I
107.0
275
27B,0
0
/
--
-200.0
/
,f
160,0-
i,,~
160,0
120.0H(m)
-120.0
-
80.O-
80.0
40.0-
H'~';"/
1~
40.0
I
0.0
0,0
1B.7 q ( g / k g ) t a . 3
15,0
20,0
Fig. 9b. Wind direction (dashed), wind speed (dash-dotted),
potential temperature (dotted), and specific humidity (solid)
as a function of height at the IMK-tower, 22:50 CET
1.7 v (r"n / ~ I
',
272,0
3.5
I
4-3.0 # ( d e ( J )
I
H<m) .
5.0
I
]
73.0
103.0
( ~ ( K ) 27~.0
27E.0
.ij ,i
., . o
,;:
80.O.
/
/
80.0
.
/
40'(>-/'-. I . i "
I
' l
i t i i,/.J.
269.0
200.0
-32.4-
I
/
Fig. 9a. Wind direction (dashed), wind speed (dashed-dotted),
potential temperature (dotted), and specific humidity (solid)
as a function of height at the IMK-tower, 22 CET
.-
/.'.u
-120,0
"'
I
15,0
..-o-
-0.6
%'%
~
160 .0
,"
, ". -,.",
/ I , ' "
t
26g.0
./I
•
/
-
13.0
4-,8-
°
-200.0
r' i"~.-
F--
10.0
114-,0
I
/.-~
80.0-
----I
I
80.3
)
,6o.o-
H(m)
4.0
I
G(K)
.7
27
0.0
6.0
2.7
I
4-6.7 0 ( d e g
119
',
¢0.0
-4-3.0
B .00
Fig. 8. Same as Fig. 5, but for the net radiation in Wm 2
(dashed), and for the standard deviation of the vertical wind
direction in degrees (solid)
0.0 i
15.0
I
I "
16.7 q ( g / k g ) 1 8 . 3
=
0.0
20.0
Fig. 9c. Wind direction (dashed), wind speed (dash-dotted),
potential temperature (dotted), and specific humidity (solid)
as a function of height at the IMK-tower, 24 CET
120
N. Kalthoff and B. Vogel
5. Statistical Analysis of the 16-Year
IMK-Tower Data
As mentioned above, a counter-current may be
of importance for air pollution modelling when
meteorological data are not available for different
heights. Concerning this problem, the following
questions arise:
First, how often do easterly winds appear in the
upper Rhine valley? Second, how frequently are
those cases accompanied by a counter-current or
by channelling? And finally, under which circumstances does a counter-current or channelling effect
occur?
The first question can be answered by the wind
statistics calculated from the data of the I M K tower for a period of 16 years (1973-1988). The
14-
u~12~I0-
~'~ D-
56-
20-
0
30
60
90
120 150 160 210 240 270 300 330 360
wind direction
IF1 0.6-1.011--11.1-1.5 I D 1.6-2.0 I [ ] 2.1-4.0 I [ ] 4.1-8.0 IFFl > 8.0 I m/s
Fig. 10a. Frequency distribution of the wind direction at
40 m height for different intervals of wind speed
14-
u 12-
g
-
~10O
6o
o 4-
0
0
30
SO
90
120 150 150 210 240 270 300 330 360
wind direction
Irto.8-1.ol[--i1.1-1.51[]1.B-2.olD2.1-4.ol[]4.1-B,olr:Fl
>B.o I m / s
Fig. 10b. Frequency distribution of the wind direction at
200 m height for different intervals of wind speed
results are shown in Figs. 10a, b for 40 m and 200 m
heights, respectively. The frequency distribution
reveals a major m a x i m u m at SW and two secondary maxima at N and ENE. Summing up the
easterly winds (60 ° </~200 < 150°) yields about 23%
of all cases. There is a secondary m a x i m u m at 80 °
and 200 m altitude and at 60 ° at 40 m altitude. The
local minima at 20 ° at 40 m height and at 40 ° at
200 m height, can be explained by the shadowing
effect of the Odenwald for N N E winds and the
preferred flow through the Kraichgau (H6schele
and Kalb, 1988).
Concerning the second question, we have
analysed the 16-year data set considering the
aforementioned definitions for channelling and
counter-current. Summing up all the cases in which
channelling occurs under eastward flow (60°<
/~200 < 150°) leads to 31%. 96% of these cases occur
when the atmosphere is stably stratified. Summing
up all the cases in which counter-current occurs
under southeastern flow (120 ° </?a0o < 150°) yields
55%, 98% of them developing under conditions of
stable stratification. So it can be stated that channelling or counter-current events are often observed
phenomena in the Rhine valley under easterly flow
conditions. In Tables 2 and 3 additional statistical
information is given for channelling and countercurrent, respectively. There are some general facts
which characterise both phenomena. It can be
seen that both are accompanied by greater temperature differences than in the absence of channelling, even if the standard deviation is very high.
Additionally they appear when the wind speed is
low. Finally, one recognizes that the mean deviation
angle for counter-current is by about 10 ° higher
than for the channelling events. In order to examine
the prerequisite of channelling events we now
look more closely at the dependence of c~ on the
meteorological conditions. In Fig. 11 the percentage frequency distribution of associated deviation
angle and difference of the potential temperatures
between 200 m and 30 m height are shown. The
mean deviation angle ~ is added, too. Generally,
it can be stated that there is a strong scattering of
with respect to the temperature difference. Nevertheless, ~ increases with an increase in the temperature difference during transition from unstable
to stable stratification. At about AO = 1 K, the
mean deviation angle is greater than 30 °, the lower
boundary for channelling. However, a further increase in AO does not result in a remarkable increase
Counter-Current and Channelling Effect Under Stable Stratification in the Area of Karlsruhe
121
Table 2. Statistical Analysis of the I6-Year Data Set for the Channelling Events
Channelling
Mean
Standard deviation
Minimum
Maximum
No channelling
AO
~
I<~o
Iw12oo
AO
~
Iw14o
Iv12oo
2.88
1.84
-2.15
11.00
51.41
22.55
30.00
207.00
2.27
0.81
0.60
7.20
5.49
2.44
0.60
16.30
0.93
1.55
- 3 .3 5
9.71
14.26
7.90
0.00
29.00
3.42
1.31
0.60
10.50
6.73
2.76
0.60
15.80
AO is the difference of the potential temperature between 200 m and 30 m, e is the deviation angle, Iv [40 and [v 12ooare the wind
speeds at 40m and 200 m heights, respectively.
Table 3. Statistical Analysis of the I6-Year Data Set for the Counter-Current
Counter-current
Mean
Standard deviation
Minimum
Maximum
No counter-current
A0
.
Iw14o
1%oo
A0
.
Ivl4o
1%oo
3.76
1.95
-0.93
10.31
60.70
28.82
30.00
207.00
2.15
0.87
0.60
7.10
5.24
2.57
0.60
16.30
2.30
2.07
- 3 .3 5
9.71
16.45
8.21
0.00
29.00
2.72
0.99
0.60
7.80
5.45
2.94
0.60
14.60
For notations see Table 2.
210 ° -
210"
0.01
180 o_
....
180"-
150"-
150 ° 120 ° -
0,1
120 ° or.
90" -
90 ° _
60 ° -
60 ° -
30°-
30 ° -
0°
-2.0
t
I
I
I
I
B
0.0
2.0
4.0
6.0
8.0
10.0
0 °-
120
zxe in deg.
Fig. 11. Percentage frequency distribution of associated
deviation angle and difference of the potential temperature
at 200m and 30 m heights. The solid line indicates the mean
deviation angle
in 4. Only a few channelling cases can be found
during unstable stratification (AO < 0°).
In Fig. 12 the percentage frequency distribution
of deviation angle and the gradient Richardson
number Ri is shown. It is seen that for negative
Ri-numbers, i.e. higher turbulence, o7adopts a value
of about 10 °. The deviation angle remains nearly
constant until Ri becomes zero. Then g increases
-3.0
1.0
I
I
1
I
I
-2.0
-1.0
00
1,0
2.0
3.0
Ri
Fig. 12. Percentage frequency distribution of associated
deviation angle and gradient Richardson number. The solid
line indicates the mean deviation angle Y.
sharply until Ri reaches unity. For greater values
of Ri again the mean deviation angle reaches a
constant value of about 50 ° .
Therefore we study the stable cases in more
detail. An interesting behaviour can be seen in
Fig. 13 where the percentage frequency distribution of the associated deviation angle and wind
speed 4 0 m above ground is shown. Two things
should be pointe d out: the first is the exponential
122
N.
Kalthoff and B. Vogel
decrease ofc~ with increasing wind speed; it approaches about 10 ° for the highest wind speed. Moreover a second characteristic feature is the existence
of a 'forbidden area', i.e. there is an upper limit for
the deviation angle at every wind speed: e.g. c~
never reaches a value of 90 ° when the wind speed
210 °
t80 ° 0.1
150 ° -
O~ 120°90 °
60 °-
3 0 °0•
I
i.
0.0
/.I.0
2 0
~
r
60
10.0
&0
Ivl~.oin m/s
F i g . 13. Percentage frequency distribution of associated
deviation angle and wind speed at 4 0 m height. The solid line
indicates the mean deviation angle ~ (stable stratification)
210 °
180 °-
150 °-
120 ° Q:::
90 ° -
60 ° -
exceeds 5 m/s. A similar behaviour exhibits ~ as a
function of the wind speed at 200 m as shown in
Fig. 14.
Finally, channelling and counter-current are
summarised in Fig. 15. The percentage frequency
distribution of associated wind direction at 40 m
and at 200 m above ground is shown. The diagonal
lines indicate isolines of the deviation angle. The
areas of channelling and counter-current are indicated with c~= 30 ° as the lower boundary. The
thick solid line connects the maximum frequencies
of the wind direction at 200 m. It can be seen that
the wind direction from 60 ° at the upper layer
turns into the mean wind direction from 40 ° at the
lower layer, i.e. winds nearly parallel to the valley's
axis. However, the mean deviation angle is less
than 30 ° and thus the curve lies below the indicated
channelling area. When the upper air flow lies
between 120 ° and 150 °, the greatest mean deviation
angles occur. The dashed curve connects the maxim u m frequencies for wind speeds between 0.5 and
1.5 m s - t at 40 m height, the dash-dotted line connects the m a x i m u m frequencies for wind speeds
between 6.0 and 8.0 ms x at 40 m height. As can
be seen, the mean deviation angle for low wind
speeds always exceeds the line of e -- 30 ° and thus
for all wind directions channelling and countercurrents appear, while at high wind speeds no
channelling or counter-currents can be found. This
figure again illustrates the strong dependence of
the deviation angle on the wind speed for the area
of Karlsruhe.
30 °-
6. Numerical Simulations
0°
0.0
I
I
I
2.0
.C.0
6.0
I
I
I
I
8.0
10.0
12.0
1/.,..0
16.0
Ivl2ooinm/s
14. Same as F i g . 13, but for the wind speed a t 2 0 0 m
height
Fig.
Up to now we have used the measurements performed at one place to demonstrate the channelling effect caused by the Rhine valley in the Karlsruhe
area. We have found that the deviation angle
300 °
[
330 °-
- ::~ : i : .) " :- - - ' ~ : "
0 o - ~- ~
' ~ ~
VALLEYS AXES
~
C
'
~.5~:
\
'
~
.
::
:2'
-
;,:
:..:';
'~- :- " : "
.... : : ~--.:
r~-~ •
"
:~.'
o~ =180"
c~ =150"
I COUNTER-CURRENT[::
oc
.30 °~
=120"
6 0 °-
- o~ = 9 0 "
90 ° -
o~= 60"
120 ° -
o~= 30"
150 °
oc=
I
60 ~
I
90 °
120 °
[32oo
150 °
0°
F i g . 15. Percentage frequency distribution of associated wind direction at 40m altitude and wind
direction at 2 0 0 m height (stable stratification). For
more detail see text
Counter-Current and Channelling Effect Under Stable Stratificationin the Area of Kar]si~uhe
decreases with increasing wind speed (see Fig. 11)
in situations of easterly flow in the free atmosphere.
An explanation of this behaviour can be expected
from the spatial variation of the wind field.
We will use a numerical model to obtain this
information. Therefore, we proceed in the following way: first, by comparing the simulations with
the measurements, we will see whether our model
works. Second, if the agreement between observation and model simulation is satisfactory, we
will use the simulated three-dimensional wind field
over Baden-Wtirttemberg to find out whether the
behaviour of channelling in the area of interest is
quite normal or whether it is influenced by a local
particularity.
6.1 The Meso-Scale Model K A M M
Regarding its extension in the vertical and horizontal directions the channelling effect belongs to
the meso-scale 7. Therefore the numerical simulations have to be made with a non-hydrostatic
simulation model (see Wippermann, 1980). We
use the meso-scale model K A M M (in German:
Karlsruher Atmosph~irisches Mesoskaliges Modell),
which was developed at the University of Karlsruhe.
For a description of the model the reader is referred
to Adrian and Fiedler (1991).
The equations of motion and the first law of
thermodynamics are integrated numerically. In
addition, the continuity equation for shallow convection, V" v = 0, is applied to determine the mesoscale pressure deviation. The turbulent fluxes of
momentum and heat are parameterized using fluxgradient relations and Blackadar's (1962) mixing
length hypothesis. The equations are transformed
into a terrain following coordinate system to take
into account the orography.
The airflow is driven by a basic state, which is
assumed to be geostrophic and hydrostatic. In our
application we use a constant geostrophic wind in
all spatial directions, though it is possible to determine the basic state from the operational numerical weather analysis of the German Weather Service
with a method developed by Adrian (1987).
At the inflow boundaries the two-dimensional
model equations are solved; at the outflow boundaries
a so-called radiation scheme developed by Oflansky
(1976) is used.
A damping layer is introduced at the upper
boundary of the model to avoid the reflection of
internal gravity waves.
123
At the lower boundary, which is defined by the
height of the roughness length, all components of
the wind vector are zero. The temperature at the
lower boundary is determined from the surface
temperature by use of an interface condition given
by Zititinkevich (1970). In this model study, the
surface temperature is an input parameter and has
to be fixed.
6.2 Input Parameters and Results Obtained
with the Model
As mentioned above, we are especially interested
in cases where large changes of the wind directions
with height occur. On the one hand, these cases
are very important with respect to airborne releases
and, on the other hand, they are a good test to
find out whether the model is able to simulate the
wind field in such complex situations.
A problem arises from the fact that observations
are available only up to 200m height. Since we
use the geostrophic wind as input parameter, we
do not know a priori which wind direction we will
simulate 200m above ground. It is practically
impossible to carry out numerical simulations for
every wind direction which may occur and for
different wind speeds. From Fig. 15 we know that
we have to expect the largest wind shift for wind
directions close to 150 ° at 200 m above ground.
For these reasons, we proceeded as follows. We
kept constant the geostrophic wind direction flo
(fig = 150 °) and varied the geostrophic wind speed.
We made several simulations with geostrophic
wind speeds between 2 and 16ms -1 in steps of
2ms -1.
The thermal stratification of the basic state is
given by ~?O/Oz = 15 K kin- 1 below 500m above
ground and c?O/Oz=3.5Kkm -1 above 500m
above ground. The dependence of the surface temperature on height is derived from the temperature
of the basic state, i.e. from the temperature in the
free atmosphere.
Since we are interested in situations with stable
thermal stratification, it is justified to limit ourselves to stationary conditions. For a given geostrophic wind and a thermal stratification of the
basic state we apply the model until the changes
of the meteorological variables with respect to
time are negligible.
"We use for our simulations the topography shown
in Fig. 1. The horizontal grid size is 5 km in both
directions, the vertical grid size varies from 20 m
124
N. K a l t h o f f a n d B. V o g e l
close to the ground up to 500 m at the top of the
model area. The roughness length was determined
from land use data by averaging.
Figure 16 shows the simulated surface wind field
for a geostrophic wind speed of 2 m s - 1. The surface
winds are modified by the orography, especially in
the Rhine valley. In addition, the airflow is channelled by the the cut of the Kraichgau between the
Odenwald and the Schwarzwald.
In the area of the I M K - t o w e r we simulate a/~40
of 54 °, i.e. a cross isobar angle c~o of 96 °. The
simulated/72oo is 116 ° and ~ is 62 °. In this way we
obtain 2/3 of the total wind shift below 200m
above ground. The modelled surface wind field at
that time is in good agreement with the data observed in the case study at 23 CET (see Chapter 4).
Additionally, the chosen direction of the geostrophic wind and the wind direction within the free
atmosphere at 23 CET, measured with the radiosonde at Stuttgart, are nearly identical.
Figure 17 shows the surface wind field which
was simulated with a geostrophic wind speed of
8ms 1. In that case, the simulated /~0 is 103 °.
Consequently the cross-isobar angle is 48 °, and
since fi2oo = 141°, the deviation angle is 38 °.
Comparing the results of both simulations one
can see that in the case of higher wind speeds in
the free atmosphere the channelling effect of the
Kraichgau extends far into the Rhine valley in the
area of Karlsruhe. Only at the slope of the Pfiilzer
Wald one can still find a channelling effect caused
by the Rhine valley which covered the whole area
at low wind speed. In the area of Freistett, where
: ~k..'~.,--~.4tl
. / .}.,- :-
~'~]'k
, . . O - - b " Y r - ~ "~, \,'%
,... o ,.,~., ..d .,, ,.. ~ ~ ..< ~ ~
,oo- ~ ~,,~!;-",--+'
,.t,-,--' - ~"7~)~
..
;
'~ " ' " ""_':~-<,~2
o ...-..~ > . ' ~ : . 4 ~ ? , ~ i ' . -... :. ,-... ~..~.. ,-..; .~:. ::~ ,'.
0
50
IDD
150
~
250
Fig. 16. S i m u l a t e d s u r f a c e w i n d field• ]vo[ = 2 m s - 1
~oo
15o
i
J
,
,-
..~,
r.
\~X..h:,
.
.
o.
,~:~
"-,~ - - " 7 . .
- ~ - •~'~, ~ "- - -.='k~-~@
.,- 2,-<(~% ~ ~ \ ~ x " t . . . ~ 2 .. <;%~.....~-
50-
•, .-:':~ '~ t .~N"..,>~ ' ~ % % .~':2;i'i..-... ~ ..; v : , , ~ ..
0
5e
IDO
150
~DO
Fig. 17. S i m u l a t e d s u r f a c e w i n d field.
~0
Iv.I =
8 m s -1
70 ..............................................................
?0
.....................
.... :.........
:.........
i
i. . . . . . . . .
:
I
~204
......
0
~i;Ts;~;tib;
......
i
1
2
4
i. . . . . . . . .
i .........
8
wind speed in r n / s
i .........
t0
12
14
Fig. 18. S i m u l a t e d a n d o b s e r v e d v a l u e s of ~ v e r s u s w i n d
s p e e d 200 m a b o v e g r o u n d
the orography is approximately two-dimensional,
i.e. it does not change much along the valley's axis,
the behaviour of the airflow is quite different.
There the wind direction close to the ground is
independent of the geostrophic wind speed.
One should weigh in this context the consequences of an accidental release of airborne material
in the area of Karlsruhe, especially under low
wind-speed conditions, and of the application of
a simple diffusion model with the wind direction
measured at a single height and a single point as
input parameters.
In Fig. 18 the observed values of c~ and the
simulated deviation angles are plotted versus the
wind speed 200 m above ground. As we fixed flo =
150 °, the simulated wind direction for this height
varies between 116 ° and 141 °. We take the same
Counter-Current and Channelling Effect Under Stable Stratification in the Area of Karlsruhe
sector to determine the values of~ for the 16 years
period of observation. The difference of the simulated and the averaged observed values is less than
ten degrees.
Since the results of the model are in good agreement with the observations made at the IMKtower, we can use the model results to explain the
behaviour of the channelling effect in the area of
Karlsruhe. Thus we find that in this area there is
a superposition of two channelling effects: one
caused by the Kraichgau, another caused by the
Rhine valley. The penetration of the channelling
effect of the Kraichgau into the Rhine valley depends on the wind speed, i.e. the channelling effect
of the Kraichgau extends far into the Rhine valley
at higher wind speeds under easterly flow-conditions
and with stable stratification. To demonstrate the
unusual behaviour of channelling in the area of
Karlsruhe, we compare the results of simulation
for the IMK-tower with those applicable to
Freistett.
Figure 19 shows the simulated cross-isobar angle
% for different geostrophic wind speeds. The crossisobar angle shows a strong dependence on the
geostrophic wind speed for the area of Karlsruhe,
whereas at Freistett, with the exception o f ]v0l =
16 m s - t , % is almost independent of the geostrophic wind speed. This difference in the behaviour
of channelling between the two areas is again
confirmed by measurements. The wind rose at
Freistett (Fiedler et al., 1984) shows a much more
restricted distribution of the wind direction along
the direction of the valley's axis.
125
7. Summary
Using the 16-year time series at the IMK-tower
located north of Karlsruhe we have found that
channelling of the airflow under easterly flow conditions is a frequent phenomenon. It occurs in 30
percent of all cases with easterly winds.
To get channelling below 200 m above ground
two major requirements have to be met: The atmosphere has to be stably stratified (only 4% of channelling events appear under unstable conditions) and
the wind speed has to be low. 66% of the channelling
appear when the mean wind speed at 40 m is less
than 3 ms- ~. In cases of stable thermal stratification,
or gradient Richardson numbers greater than zero,
the deviation of the wind direction 200 and 40 m
above ground may exceed 100 °.
The results of the statistical analysis show impressively that the deviation angle strongly depends
upon the wind speed, i.e. the deviation angle decreases with increasing wind speed.
This behaviour was simulated with the numerical model K A M M and a good agreement exists
between observation and simulation. Thus this
investigation also served to verify the model.
With the results of the numerical simulations
we have been able to explain the local particularity
of the area of Karlsruhe and have found that it is
caused by the cut of the Kraichgau. The channelling
effect of this cut superimposes with the channelling
effect of the Rhine valley.
Acknowledgements
We thank G. Adrian for making available the KAMM-model
for our calculations and S. Hehlgans who carried out some
of the statistical calculations.
120 .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References
[
100-
-o 8 0 .E
..... ~
.~.~
:= ~,-:-
.~
..
....... . . . . . . :. . . . . . . i. . . . . . . . . . . . . . . . . . . . . . . . . . . . . i \
60o
40-
o
.....
I.,
K .......
i ~ Fre(stett r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
o
20-
i
¢
10
12
geosfrophie wind speed in m / s
14
16
Fig. 19. Simulated cross isobar angle :% versus geostrophic
wind speed
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Authors' address: N. Kalthoff and B. Vogel, Institut ffir
Meteorologie und Klimaforschung, Kernforschungszentrum
Karlsruhe, Universit/it Karlsruhe, Postfach 3640, D-W-7500
Karlsruhe 1, Federal Republik of Germany.