The document analyzes water vapor weighting functions using radiosonde data from locations between 58°N and 45°S latitude for July and August. It calculates water vapor absorption coefficients and weighting functions at different frequencies and heights. The results show that weighting functions bend more sharply above 2-3 km, indicating better vertical resolution for retrieving atmospheric parameters above this height. Among the frequencies analyzed, 23.834 GHz provided the best vertical resolution above 2-3 km based on the bending of its weighting function curves.

1. S Mondal et al. Int. Journal of Engineering Research and Applications
ISSN : 2248-9622, Vol. 3, Issue 6, Nov-Dec 2013, pp.1709-1714
RESEARCH ARTICLE
www.ijera.com
OPEN ACCESS
Analysis of Water Vapor Weighting Function in the range 58
degree North through 45 degree South over the Globe
S Mondal1, N. Sk2,P.K Karmakar3
1
Asst. Prof.,Dumkal Institute of Engineering & Technology,P.O-Basantapur,Murshidabad-742406,India,
PG student,Dumkal Institute of Engineering & Technology, P.O-Basantapur,Murshidabad-742406, India,
3
Asst. Prof., Institute of Radiophysics and Electronics, University of Calcutta, Kolkata- 700 009,India,
2
Abstract
The radiosonde data available from the British Atmospheric Data Centre (BADC) for the latitudinal occupancy
of 58 degree north through 45 degrees south were analyzed to observe the variation of water vapour absorption
and water vapour Weighting Function to select the best frequency for retrieval of atmospheric variables such as
water vapor density. It is seen that the vertical resolution of the retrieval of atmospheric parameter water vapour
density will be better above a height of 2-3 km. It is also clear from these figures (figure 7 through 13) that the
weighting function at 23.834 GHz, the curves are bending more above the height of 2-3 km comparison the to
the weighting function calculated at 22.234 GHz,23.034 GHz, 25 GHz and 30 GHz.
I.
INTRODUCTION
It is well known that the microwave and
millimeter waves get attenuated while it propagates
through the atmosphere. This attenuation largely
depends on the prevailing meteorological condition
of the atmosphere. The atmosphere is composed of
several
layers,
namely,
the
troposphere,
stratosphere, mesosphere, and thermosphere, in
order of altitude. The tropopause is the thin layer
that divides the troposphere and stratosphere. It
occurs at about 8 km in the polar region and 16 km
in the equatorial region. The temperature of the
troposphere decreases by about 0.6 degree
centigrade with every 100 m increase in altitude.
The temperature in the polar region is low yearround and high near the equator. This temperature
difference produces atmospheric circulation. The
majority of the meteorological phenomena happen
to be due to fluctuation of vapor and temperature as
well. Convection is the phenomenon where the air at
low altitude ascends when it is heated and becomes
lighter, and air surrounding it descends
to occupy the vacant space. Convection gives rise
to ascending currents that from cloud and rain.
In this paper the author have tried to find out the
water vapour absorption co-efficient and water
vapor weighting function at the five frequencies
22.234 GHz, 23.034 GHz, 23.834 GHz, 25.00 GHz
and 30.00 GHz for the various location of northern
and southern latitude.
II.
through 45 degrees south. We took three places
from the northern latitude region and three from the
southern latitude region. Dumdum, India (22.65 o N);
Chongging, China (29o N) and Aldan, Russia (58 o
N) are from the northern latitude whereas Lima
Calla ,Peru(12 o S); Porto Alegre, Brazil (29 o S) and
Commodore ,Argentina (45 o S)are belongs to the
southern latitude. We took the radiosonde data of
these places for the two months which are July and
August. One interesting point may be mentioned
here is that in the month of July and august, there is
a rainy season over the places of northern latitude
but winter season over the places of southern
latitude (Karmakar et al. 2011). All these data are
taken for the year 2005. These radiosonde data are
consisting of vertical profiles of height, z;
temperature, t (z), in degree centigrade; pressure, p
(z), in milibar; and dew point temperature, td (z), in
degree centigrade.
From the available data we computed the water
vapor pressure, e (z) in bar using the relation
(Moran and Rosen 1981):
𝑒 𝑧 = 6.105 exp⁡
{25.22 1 −
− 5.31𝐿𝑜𝑔 𝑒
(1)
water vapor pressure, e (z) and water vapor density,
ρv (z) in gm/m3 are related by the ideal gas law as
𝜌 𝑣 𝑧 = 217
ANALYSIS OF RADIOSONDE
DATA
𝑒(𝑧)
𝑇(𝑧)
(2)
here 𝑇 𝑧 = 273 + 𝑡 𝑧 and 𝑇 𝑑 𝑧 = 273 + 𝑡 𝑑 (𝑧)
are the ambient temperature and dew point
temperature in Kelvin at a vertical height of z.
We have used the radiosonde data available
from the British Atmospheric data Center (BADC)
for the latitudinal occupancy of 58 degree north
www.ijera.com
273
𝑇𝑑 𝑧
1
1709 | P a g e
𝑇𝑑 𝑧
273
}

2. S Mondal et al. Int. Journal of Engineering Research and Applications
ISSN : 2248-9622, Vol. 3, Issue 6, Nov-Dec 2013, pp.1709-1714
ABSORPTION CO-EFFICIENT(IN dB/KM)
We calculated this 𝜌 𝑣 𝑧 for each location for the
month July and august and these value is used in the
analysis of weighting function of each location for
this two months.
WEIGHTING FUNCTION
ANALYSIS
III.
The water vapour weighting function gives
an estimate of the sensitivity of a particular channel
to changes of the atmospheric variable water vapor
density and thus indicates the ability to retrieve this
particular parameter from passive observations.
The water vapor absorption co-efficient at
frequencies below 100 GHz is given by (Ulaby et al
1986 )
𝐾 𝐻2 𝑂 𝛾 𝑓, 𝑧 =
2𝑓 2 𝜌 𝑣 (
300 3
𝑇
1
)
2 𝛾1
𝑒𝑥𝑝 −644 𝑇 ×
𝑇
+ 1.2 × 10−6 ]
×[
2
494.4−𝑓 2 2 +4𝑓 2 𝛾1
300
0.3
0.0
0
20
40
FREQUENCY(IN GHz)
300 0.626
𝑇
1+
0.018 𝜌 𝑣 𝑇
𝑃
Fig. 1. Variation of water vapour Absorption co-efficient with
frequency for Dumdum, India during July-August
𝐺𝐻 (4)
ABSORPTION CO-EFFICIENT(IN dB/KM)
𝑃
1013
AT 0.004 KM
AT 0.6525 KM
AT 1.3795 KM
AT 3.0145 KM
AT 5.7450 KM
AT 7.4850 KM
AT 9.6300 KM
0.6
(3)
Where f is the frequency,z if the height , 𝜌 𝑣 is the
water vapor density, T is the temperature, 𝛾1 is the
line-width parameter and is given by
𝛾1 = 2.85
www.ijera.com
Here p is the pressure.
There is another formula for calculating the water
vapor absorption for frequency above 100 GHz, but
we have not used that formula because we are
interested for analysis of weighting function at
22.234 GHz, 23.034 GHz, 23.834 GHz, 25.00 GHz,
and 30.00 GHz, which are less than 100 GHz.
Now the following figures shows the variation of
water vapor absorption coefficient with frequency (1
GHz-40 GHz) for the location of northern and
southern latitude, for the month July and august.
AT 0.3510 KM
AT 0.6480 KM
AT 1.4050 KM
AT 3.0850 KM
AT 5.8800 KM
AT 7.6300 KM
AT 9.8000 KM
0.4
0.2
0.0
0
20
40
FREQUENCY(IN GHz)
Fig. 2. Variation of water vapour Absorption co-efficient with
frequency for Chongging,China during July-August
www.ijera.com
1
1710 | P a g e

3. AT 0.6790 KM
AT 0.7075 KM
AT 1.4165 KM
AT 3.0110 KM
AT 5.6550 KM
AT 7.3300 KM
AT 9.3700 KM
0.3
ABSORPTION CO-EFFICIENT(IN dB/KM)
ABSORPTION CO-EFFICIENT(IN dB/KM)
S Mondal et al. Int. Journal of Engineering Research and Applications
ISSN : 2248-9622, Vol. 3, Issue 6, Nov-Dec 2013, pp.1709-1714
0.2
0.1
0.0
0
20
AT 0.0030 KM
AT 0.1545 KM
AT 0.8295 KM
AT 1.5540 KM
AT 3.1820 KM
AT 5.8700 KM
AT 7.5550 KM
0.3
0.2
0.1
0.0
40
0
FREQUENCY(IN GHz)
0.3
ABSORPTION CO-EFFICIENT(IN dB/KM)
ABSORPTION CO-EFFICIENT(IN dB/KM)
40
Fig. 5. Variation of water vapour Absorption co-efficient with
frequencyfor Porto Alegre, Brazil during July-August
AT 0.012 KM
AT 0.157 KM
AT 0.815 KM
AT 1.538 KM
AT 3.387 KM
AT 5.920 KM
AT 7.620 KM
0.2
0.1
0.0
AT 0.0580 KM
AT 0.0990 KM
AT 0.7250 KM
AT 1.3960 KM
AT 2.9250 KM
AT 5.4600 KM
AT 7.0400 KM
0.14
0.07
0.00
0
20
20
FREQUENCY(IN GHz)
Fig. 3. Variation of water vapour Absorption co-efficient with
frequencyfor Aldan, Russia during July-August
0
www.ijera.com
40
20
40
FREQUENCY(IN GHz)
FREQUENCY(IN GHz)
Fig. 6. Variation of water vapour Absorption co-efficient with
frequencyfor Commodore, Argentina during July-August
Fig. 4. Variation of water vapour Absorption co-efficient with
frequencyfor Lima Callo, Peru during July-August
It is clear from all the figure that in each figure,
there are several curves that corresponds to several
height and in each curves there is a peak of the
absorption at 22.234 GHz i.e. at 22.234 GHz there is
maximum water vapor absorption occurs for all the
location of northern and southern latitude. So 22.234
GHz is the water vapor absorption spectra in our
present study and it satisfies with the theoretical
www.ijera.com
1
1711 | P a g e

4. S Mondal et al. Int. Journal of Engineering Research and Applications
ISSN : 2248-9622, Vol. 3, Issue 6, Nov-Dec 2013, pp.1709-1714
value because theoretically 22.235 GHz
considered as the water vapor absorption line.
is
10
The weighting Function for water vapor 𝑊𝜌 𝛾, 𝑧 for
the atmosphere extending between 0 to z km, is
given by (Ulaby et al)
𝑇 𝑧
𝜌𝑣 𝑧
9
8
7
𝑒𝑥𝑝(𝜏 𝑣 (0, 𝑧))
(8)
Hight(in km)
𝑊𝜌 𝛾, 𝑧 = 𝐾 𝐻2 𝑂 𝛾 𝑓, 𝑧
www.ijera.com
The figure 7 through 12 shows the height verses
weighting function curve due to the presence of
water vapor for the different places of northern and
southern latitude. In each figure there are five curves
for five selected frequency viz. 22.235 GHz, 23.034
GHz, 23.834 GHz, 25.00 GHz and 30.00 GHz.
6
5
4
3
22.234GHz
23.034GHz
23.834GHz
25.00 GHz
30.00 GHz
2
1
10
0
9
0
1
2
3
4
Weighting Function
5
6
7
8
Fig. 8. Variation of Water Wapour Weighting function with
Height for Chongging, China during July-August
6
10
5
9
4
8
3
22.234GHz
23.034GHz
23.834GHz
25.00 GHz
30.00 GHz
2
1
0
0.5
1
1.5
2
2.5
Weighting Function
3
7
Hight(in km)
Hight(in km)
7
3.5
6
5
4
3
Fig. 7. Variation of Water Wapour Weighting function with
Height for Dumdum, India during July-August.
22.234GHz
23.034GHz
23.834GHz
25.00 GHz
30.00 GHz
2
1
0
0
2
4
6
8
Weighting Function
10
12
14
Fig. 9. Variation of Water Wapour Weighting function with
Height forAldan, Russia during July-August.
www.ijera.com
1
1712 | P a g e

5. S Mondal et al. Int. Journal of Engineering Research and Applications
ISSN : 2248-9622, Vol. 3, Issue 6, Nov-Dec 2013, pp.1709-1714
7
6
6
5
5
Hight(in km)
8
7
Hight(in km)
8
4
22.234GHz
23.034GHz
23.834GHz
25.00 GHz
30.00 GHz
2
1
0
0.5
1
1.5
2
2.5
Weighting Function
3
3.5
1
0
4
6
5
4
3
22.234GHz
23.034GHz
23.834GHz
25.00 GHz
30.00 GHz
1
2
3
4
5
6
7
Weighting Function
8
9
10
Fig. 11. Variation of Water Wapour Weighting function with
Height for Porto Alegre, Brazil during July-August
www.ijera.com
2
3
4
5
6
7
Weighting Function
8
9
10
11
IV.
CONCLUSION
It is also clear from the figure 7 through 12
that, at the places of northern and southern latitude,
the curves are steeper from the surface to a height of
2-3 km and the curves are bending in nature from a
height of 3 km to the top of the height at each
location of northern and southern latitude during
July-August. This indicates that, from the surface to
a height of 2-3 km, the sensitivity of the variation of
atmospheric parameter (temperature, water vapor
density etc.) is not so significant but from the height
of 2-3 km to the top of the height, the sensitivity of
the variation of atmospheric parameter is more
significant. So it can be concluded that the vertical
resolution of the retrieval of atmospheric parameter
will be better above a height of 2-3 km. It is also
clear from these figures (figure 7 through 13) that
the weighting function at 23.834 GHz, the curves
are bending more above the height of 2-3 km
comparison the to the weighting function calculated
at 22.234 GHz,23.034 GHz, 25 GHz and 30 GHz.
So it can also be concluded that the vertical
resolution for the retrieval of atmospheric variables
will be better at frequency 22.834 GHz.
7
1
1
Fig. 12. Variation of Water Wapour Weighting function with
Height for Commodore, China during July-August
8
2
22.234GHz
23.034GHz
23.834GHz
25.00 GHz
30.00 GHz
2
Fig. 10. Variation of Water Wapour Weighting function with
Height for Lima callo, Peru during July-August
0
4
3
3
Hight(in km
www.ijera.com
REFERENCES
[1]
1
V. Mattioli, E. R. Westwater, D. Cimini, A.
J. Gasiewski, M. Klein, and V. Y. Leuski,,
“Microwave
and
millimeter-wave
radiometric and radiosonde observations in
an arctic environment,” J. Atmos.
1713 | P a g e

6. S Mondal et al. Int. Journal of Engineering Research and Applications
ISSN : 2248-9622, Vol. 3, Issue 6, Nov-Dec 2013, pp.1709-1714
Ocean.Technol ,Vol. 25, No. 10, pp. 1768–
1777,2008.
[2]
P. K. Karmakar, M. Maiti, Alan James P.
Calheiros, Carlos Frederico Angelis, Luiz
Augusto Toledo Machado and Simone
Sievert da Costa, “Ground-based singlefrequency
microwave
radiometric
measurement
of
water
vapour,”
International Journal of Remote Sensing,
pp. 1–11, 2011.
[3]
P.K. Karmakar, M. Maiti, S. Mondal and
Carlos Frederico Angelis, “Determination
of window frequency in the millimeter
wave band in the
range of 58 degreenorth through 45 degree
south over the globe” Vol.
48, pp. 146–151,2011.
[4]
J.M. Moran and B.R. Rosen, “Estimation
of propagation delay through
troposphere and microwave radiometer
data” Radio Science, Vol. 16, pp.
235–244.
[5]
Liebe, J.Hans, “An updated model for
millimeter wave propagation in
moist air”. Radio Science, Vol. 20, pp.
1069–1089, 1985.
[6]
F.T. Ulaby, , R.K Moore. and A.K Fung,
Microwave Remote Sensing:
Active and Passive, Vol. 1: Fundamentals
and Radiometry (Norwood: Artech House),
1986.
[7]
G.M Resch, “Another look at the optimum
frequencies for a water vapour radiometer.”
TDA progress report, pp. 42–76, 1983.
[8]
F.T Ulaby, R.K. Moore and A.K Fung,
“Microwave Remote Sensing: Active and
Passive,”
vol.
1.
Addison-Wesley
Publishing Company, 1981, pp. 282–283.
[9]
P.K. Karmakar, M. Maiti , S. Sett, C.F.
Angelis
and
L.A.T.
Machado,
“Radiometric estimation of water vapor
content over Brazil” Advances in
Space
Research, Vol. 48,pp. 1506–
1514,2011.
[10] F. Solheim,
J. R. Godwin,
E.R.
Westwater, Y Han, S. J. Keihm, K.
Marsh, R. Ware, “Radiometric profiling of
temperature, water vapor and cloud liquid
water using various inversion methods”
Radio Sci. 33(2), pp. 393-404, 1998.
[11] R. Ware, F. Solheim, R. Carpenter, J.
Gueldner, J. Liljegren, T. Nehrkorn and F.
Vandenberghe,
“A
multichannel
radiometric
profiler“of
temperature,
humidity and cloud liquid.” Radio Sci.
38(4), 8079, pp. 4401-4413, 2003.
[12] E. R. Westwater, J. B. Snider and A. C.
Carlson, “Experimental Determination of
Temperature Profiles by Ground-Based
www.ijera.com
[13]
[14]
[15]
[16]
1
www.ijera.com
Microwave Radiometry”. J. Appl. Meteor.
14(4), pp. 524-539, 1975.
E.R. Westwater. Ground-based Microwave
Remote Sensing of Meteorological
Variables, in: Michael A. Janssen (Eds.),
Atmospheric
Remote
Sensing
by
Microwave Radiometry.J. Wiley & Sons,
Inc., New York, pp.145-213, 1993
ED R. Westwater, Y. Han, F.,Solheim .
“Resolution and accuracy of a multifrequency
scanning radiometer
for
temperature profiling,” in: P. Pampaloni
and S. Paloscia (Eds.), Microwave
Radiometry and Remote Sensing of the
Earth’s Surface and Atmosphere. VSP
2000, Netherland, pp. 129-135, 2000
E. R. Westwater, S. Crewell and C. Matzler
“ A Review of Surface-based Microwave
and Millimeter wave Radiometric Remote
Sensing of the Troposphere.” Radio Sci.
Bull. 310, pp. 59-80, 2004.
C. D.Rodgers, “Retrieval of Atmospheric
Temperature and Composition from
Remote
Measurement
of
Thermal
Radiation” .Rev. Geophys. 14(4), pp. 609624. 1976.
1714 | P a g e