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Microwave radiometer and its application to snow measurement

Zhang Junrong, Zhao Renyu, Guo Fenglian, Zhao Kai, and Hu Xuewei
Changchun Institute of Geography, Academia Sinica China


Abstract
The microwave radioactive property of snow is briefly summarized. From 1986 to 1989, experiments were carried out the Changchun Jingyue Tan Remote Sensing Site, using self developed microwave radiometers to study the microwave radioactive property of snow. The relation between brightness temperature and observation angle was obtained with both vertical and horizontal polarizations. The curves corresponding brightness temperature and snow depth were also drawn out for different frequency band sand physical conditions. The results demonstrate the application potential of the microwave radiometer in this area.

Principile of snow measurement using microwave radiometer
All substances at a finite temperature radiate electromagnetic energy. In the microwave region, the Rayleigh-Jeans'approximation satisfied the Plank's formula which leads to

B ( l, T) = (2KT ( q, j) / l2) [ w. m-2 . s-1r. H1z].......... (1)

where l -------- wave length (m);
K -------- Boltzman constant [1.38 X 10-23 W. S. K-1];
T [ q, j] ----------Physical temperature of black body (K),
With [ q, j] denotes the angular dependence.Radiation of real materials is less than black body. A equivalent radiometer temperature TB ( q, j) called brightness temperature is relatively lower than T( q, j)

TB = e. T..........(2)

e is called the emissivity of the substance, 0[1]

PR = K. D f.(òòò TB (q,j) . D(q,j) . D· (q,j) . dW / òòò D (q,j) . D· (q,j) . dW = K. TA . Df...........(3)

where

TA = (òòò TB (q,j) . D(q,j) . D· (q,j) . dW / òòò D (q,j) . D· (q,j) . dW

The brightness temperature is averaged by the weighting function D(q,j) which is the antenna pattern. TA=TB if the medium is isotropical or the antenna beam width is sufficiently narrow. The PR is linearly related to TB when the radiometer is calibrated. and independent of. Df We conclude from the above discussion that the power intensity which is received by the microwave radiometer is determined by. the emissivity of the material. Different material have different emissivities. The emiccivity of snow depends on the ice particle size, wetness, polarization and observation angle. Therefore, it's possible to detect the depth and the state of snow accordingly. For lossy material, the emissivity and the reflectivity is related by

e = 1 -r ...............(4)

For either smooth or rough surface, r is mainly determined by the dielectric constant of the material.

The microwave dielectric property of snow
The dielectric constant of material is complex number. The real part gives the capacity of energy storing whereas the imaginary part represents the energy dissipation. The microwave dielectric property of snow is closely related to the liquid water content in the snow density rd and the permittivity of ice, the real part of the dry snow permittivity ed', like ice, is independent of frequency and temperature. And the imaginary part ed" is approximately zero[3,4].

Studies have shown that the real of the dry snow permittivity depends only on its density rd[g. cm-3]. They are related by[3]

ed‘ = 1+1.7rd + 0.7r2 d...........(5)

The imaginary part of the dry snow permittivity is a function of frequency, temperature and density. Its property can be studied by measuring the loss tangent of the dry snow. The relation is [5]

tandd = e "d / e 'd = 1.59 X 106 X (0.52rd + 0.62 r2d ) / ( 1+1.7rd + 0.7r2d ) X ( f-1 + 1.23 X 10-14Öf)e0.36T.............6

where T is the temperature of snow (°c and f denotes frequency (Hz). From (6), the tangent loss of dry snow can be calculated at different frequencies and different temperatures.

Wet snow is a mixture of air, ice partides and a certain amount of liquid water. The real and imaginary part of wet snow is much larger compared with that of dry snow. This is due to the relatively large permittivity of water. The permittivity increases with increasing wetness of snow Wv. In 4.14 GHz frequency range, the relation is given by [6]

e ’ws = 1+2rs + bW3/2v
e ”ws= (1.0994/f) . aÖe 'ws .............7

where rs is the density of wet snow (g cm-3], f, is frequency (GHz], while the wetness Wv represents fractional volume of the liquid water in snow, a is the attenuation coefficient for certain frequency and water content[6]. b is a constant when frequency is given

b = 5.87 X 10-2-3.10 X 10-4 (f-4)2 .................(8)

In 500-1000GHz frequency range, the permittivity of wet snow is given by[5]

e ’ws = 1+1.7rd+0.7 r2d+8.7Wv+70W2 v
e ”ws = f/109 (0.9Wv + 7.5W2v) ..................9

rd is the density of snow when the liquid water of wet snow is replaced by air.

The measurement of snow radiation in microwave band
In China, snow measurements have been carried out since 1986 using self-developed airborne multifrequency microwave radiometers. The null-lalancing Dicke type radiometer and the two reference temperature radiometer. with automatic gain compensation were adopted. The data collecting, storing, displaying and processing of the system is controlled by a micro computer.

On Feburary 25, 1987, an experiment was carried out at Changchun Nanhu to measure the snow cover on the lake ice surface using 8mm microwave radiometer. Snow of different depth was piled up above the lakd ice which was 80cm thick. Fig.2 corresponds the brightness temperature to the snow depth. It shows that the brightness temperature decreases exponentially with increasing snow depth. The regression equation is given

TB(d) = 252.4 X e-0.0114d ..................(10)

The brightness temperature is 170K when the snow is piled to 40cm deep, 90K lower than the bare Lake ice. The work site photo is shown on Fig. 1.

On February 23, 1990, once again a snow measurement was conducted at Changchun Nanhu using 10cm microwave radiometer on the lake ice surface. The ice depth was 90cm with water underneath. Snow was piled up on the lake. Fig. 3 gives the relation curve between the brightness temperature increases with increasing snow depth.

On February 22, 1989 at Changchun Jingyue Tan Remote Sensing Experimental Site, 5cm microwave radiometer was used to measure the brightness temperature of different snow depth which was piled up on the cement ground. The result is shown in Fig. 4

On February 21, 1989 at Changchun Nanhu, another snow measuring experiment was carried out using 8mm microwave radiometer. Fig. 5 shown the brightness temperature of different polarization via observation angles.


Fig. 1 Work site for snow measurement


Fig. 2 The brightness temprature of snow covered lake ice via snow depth.


Fig. 3 The brightness temprature of snow covered lake ice via snow depth


Fig. 4 The brightness temprature of snow covered cement ground via
snow depth


Fig. 5 The brightness temprature of snow covered lake ice via observation
angle at different polarigation


Conclusion
Fig. 2 shows that with the increasing snow depth, the brightness temperature decreases with a slope of approximately - 2.7K/cm While in Fig.3 and Fig.4. The brightness temperature increases with increasing snow depth. The slope is approximately 0.6K/cm and 0.7K/cm separately. But the brightness temperature changes very little when the snow depth is deeper than 40cm because the snow is wet. While Fig.2 represent a dry snow case. The brightness temperature decreases when the water content increases, but increases when there is water on the snow surface [8], Whatever the case, there's a big difference between the brightness temperature of the snow covered ground and that of bare ground. Therefore, we can remote sense the snow depth and its melting level accordingly. The emissivity of snow depends on the density, the ice particle size, water content, physical-temperature, covered background, surface roughaess and other parameters. It's also a difficult problem to determine the permittivity of snow accurately. So much work remains to be done both experimentally and theoretically, which will be conclusive to the measurement of snow cover of the ground by means of aerial and space remote sensing.

References
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  4. C. Matzier et al, IEEE Journal of Oceanic Eng. Vol. OE-9, No. 5, p. 366, 1984.
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  7. Zhang Dianchen et al, Proc. of Changchun Jingyue Tan Remote Sensing, Site, 1988.
  8. M.F.M. eier, Proc. 7th symp. On Remote Sensing of ENv. P.1155- 1164, 1970.