PARAMETERS OF VERTICAL PROFILES OF TEMPERATURE, HUMIDITY AND
REFRACTIVE INDEX OF AIR IN THE LOWEST TROPOSPHERE
Martin Grabner (1), Vaclav Kvicera (1), Pavel Pechac (2), Otakar Jicha (2)
(1)
Czech Metrology Institute, Hvozdanska 3, 148 01 Praha 4, Czech Republic,
Email: [email protected], [email protected]
(2)
Czech Technical University in Prague, Technicka 2, 166 27 Praha 6, Czech Republic,
Email: [email protected], [email protected]
ABSTRACT
Vertical profiles of temperature and relative humidity of
air are measured on the 150 meter tall mast at 19 heights
with average separation less than 8 meters and with
sampling rate 1 minute. Vertical profiles of atmospheric
refractivity are obtained and occurrence of ducting
layers is analysed using nonlinear regression. Ground
based and elevated ducting layers are observed.
Temporal evolution of ducting layers is described by
means of typical examples. Long term empirical
statistics of layer parameters are provided and
interrelations between different parameters of vertical
profiles are pointed out.
1. INTRODUCTION
Spatial distribution of the refractive index of air has an
influence on the propagation of electromagnetic (EM)
waves in atmosphere. Due to prevailing stratification of
atmosphere, the vertical profiles of the refractive index
in the lowest troposphere are particularly important for
assessment of terrestrial radio propagation paths. The
refractive index is known to be related to temperature,
pressure and relative humidity of air. Their vertical
profiles are measured regularly by radiosondes but
typically only four times a day. In order to investigate
the time evolution of the atmospheric layers with small
vertical extent occurring in the first 100 meters above
the ground, a measurement with better time and spatial
resolution is needed.
In the paper, the specific results are reported of the
measurement of vertical profiles of temperature, and
relative humidity of air carried out in Podebrady, Czech
Republic (50 km east from Prague) on the tower of a
former radio transmitter. The quantities are measured
continuously by Vaisala HUMICAP sensors located in
19 different heights up to 150 meters above the ground
level with an average separation less than 8 meters. The
vertical profiles of temperature and relative humidity
are sampled every minute. Near ground temperature
inversions are observed together with decreasing
humidity with height. The refractive index of air is
calculated using standard relations recommended by
International Telecommunication Union. The obtained
vertical profiles of refractivity are analysed by means of
nonlinear regression to extract the parameters of the
ducting layers with a nonstandard value of the vertical
gradient of the refractive index. Ground based and
elevated ducting layers are observed. Temporal
evolution of ducting layers is described by means of
typical examples. Long term empirical statistics of layer
parameters are provided and interrelations between
different parameters of vertical profiles are pointed out.
2. MEASUREMENT SETUP
The vertical profiles of air temperature and relative
humidity are continuously measured on the 150 m-high
lattice mast located in Podebrady, Czech Republic. The
GPS coordinates of the measurement site are
50°08´19.68´´N, 15°08´40.54´´E. Nineteen meteorological Vaisala HMP45D sensors (accuracy ±0.2 °C,
±2% rel. hum.), for measuring temperature and
humidity are placed nearly equidistantly on the mast,
between 5.11 m and 147.71 m above the ground.
Atmospheric pressure is measured using Vaisala
PTB100A pressure sensor (accuracy ±0.2 hPa) that is
located at the bottom of the mast at a height of 1.4 m
above the ground. In further processing, the standard
pressure lapse rate obtained from a hydrostatic equation
is assumed which is a good approximation near the
ground for different atmospheric conditions with an
exception of storms with strong vertical movements [1].
Data readings are collected once a minute. More on the
experiment can be found in [2], [3]. Fig. 1 shows the
Podebrady mast.
Figure 1. Podebrady mast of the former radio
transmitter, height 150 m
higher altitudes, e.g. dN at about 5:40 in the example.
3. ATMOSPHERIC REFRACTIVITY
The atmospheric refractivity N as a function of height
above the ground is obtained from the atmospheric
pressure P (hPa), temperature t (°C), T (K) and relative
humidity of air H (%) using the relations recommended
by ITU-R [4]:
 bt 
N=
77.6 
e
Ha  t +c 
e
 P + 4810 ; e =
T 
T
100
(1)
where a = 6.1121, b = 17.502, c = 240.97. Note that N is
defined as N = 106(n-1) where n is the refractive index
of air. The modified refractivity is calculated as
M = N + 157h where h (km) is the height. The following
modified Webster duct model was introduced in [5]:
N (h ) = N 0 + G N h +
2.96(h − h0 )
dN
tanh
2
dh
(2)
where the model parameters are: an effective nearground refractivity N0 (N-unit), an ambient gradient GN
(N-unit/km), a duct depth dN (N-unit), a duct height h0
(m) and a duct width dh (m). Figure 2 shows the
meaning of the parameters. A “tanh” function is used in
(2) instead of “arctan” in the Webster model. The model
for modified refractivity M differs from (2) only in the
value of the gradient: GM = GN + 157 (N-unit/km).
Figure 2. Duct model parameter definition with the
values of parameters: N0 = 300 N-units, GN = -40 Nunits/km, dN = -20 N-units, h0 = 80 m, dh = 40 m
Figure 3 shows the example of nonlinear regression
results. Time evolution of vertical profile of modified
refractivity during the presence of the elevated ducting
layer is depicted together with fitted model (2). Table 1
lists the fitted parameters. It is seen that during one hour
the layer height h0 was increasing steadily (cca 2 m/min)
and after reaching maximum depth the layer
disappeared at about 5:55. It is demonstrated that the
model (2) is able to describe the behavior of the
atmospheric layers in the lowest troposphere sufficiently
well. However since the maximum height of our
measurement is limited (below 150 m), some of fitted
parameters may be distorted due to lack of data from
Figure 3. Duct model fitted to vertical profiles of
modified refractivity, 19 July 2011, 5:00 – 5:55, time
resolution 5 minutes
Table 1. Modified refractivity duct model parameters,
19 July 2011
time
5:00
5:05
5:10
5:15
5:20
5:25
5:30
5:35
5:40
5:45
5:50
5:55
N0 (-)
328.1
327.8
328.4
326.6
327.4
325.1
323.5
321.0
319.9
328.4
332.0
329.6
GM (km-1)
61.5
57.5
49.9
69.9
63.6
84.2
94.2
97.7
84.6
100.0
93.7
112.9
dN (-)
-7.2
-5.9
-4.9
-6.6
-6.8
-8.7
-11.1
-16.7
-21.5
-3.3
0.9
-1.2
h0 (m)
67.2
73.2
85.0
103.3
117.7
125.4
135.5
143.6
150.0
140.3
94.6
137.1
dh (m)
45.4
34.8
35.6
51.0
46.4
42.6
46.8
54.3
56.9
25.4
38.7
19.4
The ducting layer was mainly caused by relative
humidity variation with height, see Fig. 4. On the other
hand, Fig. 5 shows that temperature did not change with
height significantly in contrast with the standard
atmosphere where the temperature decreases at the
average rate of about 6 °C/km near the ground.
Figure 4. Vertical profiles of relative humidity19 July
2011, 5:00 – 5:55, time resolution 5 minutes
Figure 7. Cumulative distribution of duct depth
Figure 5. Vertical profiles of temperature,19 July 2011,
5:00 – 5:55, time resolution 5 minutes
4. MODEL PARAMETER STATISTICS
From the vertical profiles measured in between May
2010 and September 2011, the statistics of the model
parameters (2) were obtained. Figures 5-9 show the
empirical cumulative distributions of model parameters.
From Fig. 6, the median gradient GM is about 110 km-1.
From Fig. 7, the median duct depth is zero as no layers
appear during standard atmospheric conditions. Layers
with the absolute value of duct depth larger than 100 Nunits occur for about 1 % of time. From Fig. 8, the duct
height is almost uniformly distributed with median
around 75 m that is half of the measurement range.
Figure 8. Cumulative distribution of duct height
Figure 9. Cumulative distribution of duct width
Figure 5. Cumulative distribution of effective near
ground refractivity
Figure 10 shows joint probability density of duct depth
dN and ambient gradient GM. It is revealed that larger
gradients occurred often together with larger absolute
values of duct depth, see area A in Fig. 10. However
one can also see that larger duct depths can be often
observed together with standard values of ambient
gradient, see area B in Fig. 10.
5. TIME EVOLUTION EXAMPLE
Figure 6. Cumulative distribution of ambient gradient
Some observed elevated layers had been persistent for
several hours during night, see Fig. 11-13. Temperature
inversion seen in Fig. 12 is compensated by the effect of
decreasing humidity seen in Fig. 13 causing ducting
layer at the height of about 110 m.
B
A
00 hr
Figure 10. Logarithm of joint probability density of duct
depth and ambient gradient
23 hr
00 hr
02 hr
01 hr
03 hr
Figure 13. Relative humidity evolution, 2011/06/10
6. CONCLUSIONS
01 hr
High-resolution measurements of vertical profiles in the
lowest troposphere such as one presented here are very
important for understanding dynamics of ducting layers
that influence EM wave propagation. Therefore further
measurements at different locations are appreciated.
02 hr
7. ACKNOWLEDGEMENTS
This research was supported by the Czech Science
Foundation under Project No. P102/10/1901.
03 hr
04 hr
8. REFERENCES
1. Rezacova, D., Novak, P., Kaspar, M. & Setvak, M.
(2007). Physics of clouds and precipitation,
Academia, Czechia, pp47–48 (in Czech).
Figure 11. Evolution of elevated ducting layer, from
2011/06/09 23:00 to 2011/06/10 4:55
00 hr
01 hr
2. Grabner, M. & Kvicera, V. (2009). One-year statistics
of atmospheric refractivity in the lowest
troposphere. In Proc. 6th. IASTED Conf.
Antennas, Radar and Propagation, paper 649-025,
Banff, Canada.
3. Valtr, P., Pechac, P., Kvicera, V. & Grabner, M.
(2011). Estimation of the Refractivity Structure of
the Lower Troposphere from Measurements on a
Terrestrial Multiple-Receiver Radio Link. IEEE
Trans. Antennas Propag. 59(5), 1707–1715.
4. Rec. ITU-R P.453-9, The radio refractive index: its
formula and refractivity data, ITU, Geneva,
September 2009.
02 hr
03 hr
Figure 12. Temperature evolution, 2011/06/10
5. Grabner, M., Kvicera, V., Pechac, P. & Jicha, O.
(2011). Single and Joint Statistics of Ducting
Layer Parameters Determined from Vertical
Profiles of Atmospheric Refractivity. In Proc.
General Assembly and Scientific Symposium,
2011 XXXth URSI, Istanbul, Turkey.