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A MULTI-polarized and Multi-angle C-band Radar System for Soil Moisture Determination Under Bare Soil Conditions

Shakil A. Romshoo*, T. Oki** and Katumi Musiake**
*Earth Obervation Research Center, NASDA, 9-9-1, Roppongi,
Minato-ku, Tokyo, Japan 
e-mail : shakil@aab.iis.u-tokyo.ac.jp
**Musaike Lab, IIS, University of Tokyo, B Building, 4-6-1, Komaba,
Meguro-ku, Tokyo, Japan
E-MAIL : prof@hydro.iis.u-tokyo.ac.jp


Abstract
This article is an attempt to determine the soil moisture under bare soil conditions at a field scale suing a ground based C-band radar with all the three linear polarizations, i.e., HYPER SPECTRAL, HV, and VV and employing 4 angles of incidences, i.e., 150, 230, 350 and 430. The experiment was concluded 12 times during the year 1999 to monitor the soil moisture variation at a field scale at Chiba, Japan. The field was purposefully maintained bare and smooth. The Integral Equation Model (IEM), based on the theory of diffraction of surfaces, was used to predict the backscattering phenomena. The model is validated with the experiment data and a good agreement between the modeled and the observed backscattering coefficient is obtained at HH polarization while as the model does overestimate the backscattering at VV polarizations. Further, a sensitivity analysis of the model reveals that radar is sometimes more sensitive to the small changes in the roughness characteristics than the larger changes in the soil moisture. Under natural roughness conditions, the C-band radar, particularly with VV polarization and lower angles of incidence, should be the ideal system for soil moisture determination. Such a configuration has been found to be more sensitive to soil moisture as compared to roughness affects.

Introduction
Through a number of models based on experiment data have been proposed (Oh et. al., 1992, Dubois et. al., 1996) but for soil moisture retrieval, but the results are very limited. Further, these empirical models derived from the experimental data may sometimes lack the consistency and the universality. They may apply to surface conditions and the radar parameters that were looked at during the time of experiments. On the other hand, the theoretical models developed have also some validity restrictions as for the frequency and roughness ranges are concerned. Among the high frequency scattering models, the Kirchoff formulation (KF) is the most commonly used. For a ground surface whose standard deviation and correlation length are much smaller than the wavelength, the small perturbation method, SPM (Ulaby, 1982), which is a low frequency solution, can be used to estimate the backscattering contribution. Attempts have also been made to unite the KF and SPM to obtain a model applicable to a wide range of roughness scales of frequencies. More recently, Fung et. al., 1992 has developed a surface scattering model based on the surface field integral equations called the Integral Equation Model (IEM). The (IEM) reduces to the SPM when the surface is smooth and to the standard Kirchoff model when the standard deviation is much larger than the incident wavelength. In its complete version, the model describes the is much larger than the incident wavelength. In its complete version, the model describes the backscattering behavior of a random rough bare surface without any limitation on the roughness scale and frequency range.

In view of the extended validity of the IEM model and to overcome the draw of the other reported surface scattering models, we selected this model for validation of our experimental results. Besides validating the model under different surface roughness and soil moisture conditions, the simulation studies have been carried out to the thoroughly understand the influence of the different factors which influence the radar backscattering behavior.

Integral Equation Model
The integral equation model (Fung et. al., 1992), abbreviated as IEM was used in this study to predict and understand the radar backscattering coefficients as a function of both target and sensor parameters. This model has been applied to a wide range of roughness for bare soil surfaces as well as sea surfaces (Altese et. al., 1992; Chen et al., 1995). Because of complexity, it is not practical to use the complete version of the model and in the application usually, the approximate versions are usually considered (Altese, et. al., 1996). The validity condition can be expressed as ks (3, where k=2p/l, the wave number; l is the wavelength; and s is the surface rms height. The like polarized backscattering coefficient s0 can be expressed as follows:) 


Where s0pq is the radar backscattering coefficient; p, q are vertical or horizontal polarizations; kz=k cosq and kx=ksinq ; s is the surface rms height and W(n) (u,v)is the roughness spectrum of the surface related to the surface correlation function. In the above equation (4.1),


R= and R^ are the Fresnel reflections coefficients for vertical and horizontal polarizations

 

q is the angle of incidence;



Where p(x,z) is the surface correlation function, a stationary random process with zero mean and () denotes the ensemble average operator. In light of the previous research function as exponential which gives a better fit with the experimental data.

There are several models which convert the volumetric soil moisture to dielectric constant and vice versa (Dobson et. al., 1981, Hallikainein et. al., 1985). I used the model given by Hallikainein et. al., 1985 which takes into consideration the soil properties like texture and bulk density as follows:



Where Î refers to the dielectric constant, q is the volumetric soil moisture, a and b are the shape factor and the texture dependent coefficient respectively, r refers to density and the subscript s, b, and fw refer to soil solids, bulk density and free water respectively. 

Scatterometer Data and Field Measurements
A C-band Scatterometer system was used in this study and have been described in details by Musiake et. al., (1997). The Figure 1(a) shows the van-mounted Scatterometer taking measurements of the bare field. The radar system was employed at three polarizations, viz., HH, HV and VV and over four angles of incidence, i.e., 150, 230, 350 and 430. moreover, on almost every occasion of the experiment, the surface roughness and soil moisture measurements were recorded. A lazer roughness profile meter was employed to record a number of roughness measurements across and along the field axis. The Fig. 1(a) shows the lazer profiler in operation. The lazer profiler, which is driven by a stepper motor, can measure a surface profile with 1mm horizontal resolution and 2 mm vertical accuracy. The profiler is connected to the laptop computer to record the measurements in X and Y directions. The horizontal resolution of the measurements on each occasion was maintained constant as 3 mm. Though the soil moisture measurements were recorded at the depth resolution of 2 cm, 5cm and 10 cm but in view of the penetration depth of the radar signals at C-band wavelength (Wilheit, 1975), only the 2 cm measurements recorded by volumetric methods were compared with the s0 measurement.

Data Analysis and Discussion 
The following sections would discuss the experimental data, the relations between various surface characteristics and the radar backscattering coefficients s0. Also the sensitivity analysis performed would be discussed to have a thoroughly understanding of the influence of these characteristics on the radar response at different sensor configuration.

Temporal Variations of s0 The Table 1 shows the relationships, i.e. coefficient of correlation and the slope obtained between the observed surface soil moisture and the radar backscattering coefficient s0. Though, the temporal relationship are reasonable for VV polarization and for all the angles of incidence but the for other polarization, the relationships are week except at an incidence angle 430. But this is in contrast to Sano et. al., (1998) and Ulbay et al., (1979) results wherein they reported higher coefficient of correlation but compatible sensitivity of the s0 to soil moisture variations under varied roughness conditions. Geng et al., 1996 reported similar relationships as obtained in this experiment. The Figure 1(b-c) shows the temporal variation of the backscattering coefficient s0 for HH and VV polarizations and four angles of incidence employed in this experiment. The dynamic range of the backscattering coefficients s0 during the conduct of the experiment is small for HH and VV polarizations. HV has comparatively better dynamic range for all the incidence angles used here. Also plotted on the figure is the temporal variation of the soil moisture. We can see on 7th experiment that despite an increase of more than 10% in the volumetric soil moisture, the backscattering coefficient has decreased by more than 5 dB for higher angles of incidence for HH polarization and a little less for 230 incidence angle. The decrease is in response to smooth surface roughness condition observed on 7th experiment. The decrease is obviously more at higher angles of incidence than at lower angles of incidence (Ulbay et al., 1979).

Table 1 Summary of the correlation coefficient and sensitivity of s0 using C-band Scatterometer system over bare field 
Polariastion Incidence Angle
  23o 35o 45o
  rSlope r Slope r Slope
HH .74 .35 .26 .11 .28 .10
HV .67 .47 .31 .23 .30 .22
VV .76 .32 .62 .30 .67 .37
             


Comparison Between Measured and simulated Radar Data The Integral Equations model was validated on three for both VV and HH polarizations. These data are 21st May, 22nd June and 28 June. The values of the rms height have been observed as 0.34, 0.525 and 0.30 cm respectively while that of the correlation length as 14.5, 13.1, and 16 cm respectively. The simulation and observed measurements for HH polarizations are plotted in Figure 1 (d-e). We could get better agreement between the two at HH polarizations than at VV polarizations. The pattern is matching reasonably well for both the polarization with a decline in the s0 as a function of incidence angle. The exponential correlation function is assumed here. Bracaglia et al., (1995) also reported a discrepancy when comparing the theory and experimental data over bare soils. He attributed it to the inaccuracies of the available surface models. While as Hoeben et al., reported of very good agreements between the theory and the experiment for VV polarization over a range of incidence angles from 110 to 230 and frequency of 1-10 GHz but for 350 angle of incidence, the deviation were quite higher than that observed here for C-band. Altese et al. (1996) also reported a wide scatter between the IEM model simulations and the ERS-1 backscattering coefficients values for VV polarization and at an incidence angle of 230. 

Sensitivity Analysis
A sensitivity of the IEM model simulations to the surface characteristics as well the radar configurations was performed to have a better understanding of the influence of these factors on soil moisture retrieval. The following subsections would deal with each of these influences separately: 

The Figure 1 (g-h) shows the sensitivity of the s0 to soil moisture variations for different frequencies, HH polarization and two angles of incidence, i.e., 230 & 430 on 7th experiment (28 June ). The sensitivity reduces with the increase of incidence angle. For all the four frequencies tested in this analysis, a variation of soil moisture from 1% to 40% results in an increase of the backscattering coefficient values of 7 to 8 dB for HH polarization at 230 incidence angle while as at 430 angle, a similar change in soil moisture causes an increase in s0 from 5 to 6 dB depending upon the frequency. Because of the smooth nature of the surfaces, the s0 values are higher at lower angles of incidence compared to the higher ones. For VV polarization, a similar analysis results in an increase of around 8 dB for both lower (230) and higher (350) angles of incidence. For both VV and HH polarization at both lower and higher incidences angles, the sensitivity is quite high at lower values of the soil moisture and as the soil moisture increases, the sensitivity decrease. 

The sensitivity analysis of backscattering coefficient to rms height has been performed for different dates. The plots in figure 1(i-j) show the sensitivity on 21st May for HH polarization and two angles of incidence, when the soil moisture is lower (13.69%). It can be seen from the Figure that the s0 sensitivity to rm height is most strong of all the parameters tested during this sensitivity analysis. The sensitivity is very strong at lower values strong at lower values of the rms height and as the surface get rough and rougher, the sensitivity decreases markedly, especially for higher frequency signals. For L-band and above, the sensitivity is quite high even for rougher surfaces. The IEM model looses its validity for X-band frequency beyond the roughness values of 1.5 cm and that is reason of the discontinuity in the X-band simulations.

The sensitivity to the correlation length for different frequencies on 21st of May when the rms height was observed as 3.4 mm and the surface soil moisture was 16.23% for HH polarization is shown in Figure 1(K-1). Though the incidence angles do not affect the dynamic range of the change in the s0 as function of correlation length, L but the magnitude of the s0 is lower by several decibels at higher angles of incidence that the lower angles. The polarization effects are not so marked on the correlation length sensitivity. Further, the higher frequencies are more sensitivity to the changes in the correlation length at low incidence angles than the lower frequencies with X-band showing the highest, followed by C-band, then L-band and the other one. The L-band sensitivity at higher incidence angles (430) is equally higher for both the polarizations. The L-band frequency shows insensitivity to the lower values of correlation length (5 cm) for both HH and VV polarization at an incidence angle 230. The 0.45 GHz frequency shows appreciable sensitivity to radar backscatter at lower values of correlation length but demonstrates week sensitivity at higher values of the parameter. 

Conclusions
The radar backscattering coefficient s0 is sometimes more sensitive to small changes in roughness characteristics than to large change in soil moisture. As observed on 7th experiment, a decrease of rms height from 5.25 mm to 3.0 mm bring about a reduction of more than 5 dB for HH and HV polarization and a little smaller change for VV polarization, despite an increase of around 10 % in the soil moisture. The small disturbances in the field, as noticed by the uprooting of weeds, can describe the surface roughness patterns and can not be assumed as constant. 

The better validation of the IEM model at HH polarization lends further confidence to the model. The disagreements between theory and experimental data at VV polarization at higher angles of incidence may be due to the negligence of the volume scattering term in IEM model at higher angles of incidence. At higher angles, the volume scattering is expected to have an important influence at such low backscatter values.

The sensitivity analysis done for various surface characteristics have made their importance and influences on radar backscattering phenomena a lot more clear. Under smooth surface conditions, as observed in this field, the rms height has been observed to be the most sensitive parameter at lower values of the surface rms height. At higher values of rms height, for the higher frequencies, the radar backscattering coefficients s0 gets insensitive or shows low sensitivity to the rms height at lower angles of incidence. The s0 sensitivity to higher values of rms height is observed even at higher angles of incidence. The polarization effects are not so distinct. The L-band frequency and beyond are sensitive to rms height irrespective of the angle and the polarization. 

The sensitivity to correlation length is also equally strong especially at higher angles of incidence for both HH and VV polarizations. The L-band frequency is noticed to be less sensitive to the correlation length at lower angles of incidence (230). The 0.45 GHz frequency exhibits week sensitivity to correlation length after 5 cm, while as before that the sensitivity is appreciable.

The sensitivity to soil moisture is equally good for all the frequencies and both the angles tested here. But it is less than that for the surface rms height values. 

References

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