Introduction
During recent years, theoretical modeling and field experiments have established the fundamentals of active microwave remote sensing as an important tool in determining physical properties of soil. The ability to estimate soil moisture in the surface layer to an approximately 5 cm depth by microwave remote sensing has been demonstrated under a variety of the topographic and land cover conditions (Engman et al., 1995). Despite the promise, its application to hydrological and agricultural sciences has been hampered by natural variability and the complexity of the vegetation canopy and surface roughness that significantly affect the sensitivity of radar backscattering to soil moisture.

Although experiments demonstrated radar sensitivity to soil moisture variation more than two decades ago (Ulaby, 1974), an operational algorithm for mapping soil moisture distribution has not been developed because of the effects of the surface roughness and vegetation cover. The inversion of soil moisture information from radar backscatter became more rigorous after the availability of multi-polarization radar data. Several algorithms have been developed for measuring bare surface soil moisture quantitatively using either dual-polarization L-band SAR image data (Dubois et al., 1995, Ulaby et al., 1996 and Shi et al., 1997) or three-polarization SAR measurements (Oh et al., 1992). The algorithms had been applied to a series of L-band SIR-C and JPL/AIRSAR image data successfully by using VV and HH polarization (Dubois 1995 and Shi 1997). However, all those algorithms were under the surface scattering consideration. They used the weighted combinations of the different polarization signatures to minimize the effect of surface roughness so that soil moisture can be directly inferred from SAR image data. The effect of vegetation cover has not been included in current available algorithms. It is clear that vegetation cover will cause an under-estimation of soil moisture and an over-estimation of surface roughness when we apply the algorithm for bare surface soil moisture estimation to vegetation covered regions.

A polarimetric SAR backscatter measurements, by using eigenvalues and eigenvectors of the covariance matrix, can be decomposed to into three components based on the scattering types - (1) an odd number of reflections, (2) an even number reflections, and (3) a cross-polarized scattering power [Van]. It can be written as


Where l and K are eigenvalues and eigenvectors. * is a conjugate operator for a complex number and T is a transpose operator for a vector. The subscript 1, 2, and 3 represents the decomposed odd, even, and defuse components, respectively. This decomposition technique allows us to obtain the estimation of single and double reflection components of backscattering coefficients for VV and HH polarization.

In this study, we evaluate the usage of the decomposition theory in application of estimating soil moisture for vegetated surface with the temporal fully polarimetric L-band SAR meaurements. Using the decomposed scattering measurements from JPL/AIRSAR image data, we evaluated their usage to reduce the vegetation effect on estimation soil moisture under configurations of a single-frequency (L-band) and multi-pass with a same incidence.

Relations the Components in Backscattering Model and the Decomposed Scattering Components
In consideration of a more general natural vegetated surface, we construct our first-order physical based scattering model as a discontinuous vegetated backscattering model. This model can be written as


Where f_v is the fraction of vegetation cover in a given pixel. L²_nn=exp(-2k_a^ppd sec(q)) is the double pass attenuation factor. K_a is the volume extinction coefficient depending on the polarization configurations. d is the thickness of the vegetation layer and q is the radar incidence angle. The superscript or subscript pp represents polarization configuration for either VV or HH. The subscript t, v, s, and sv are for total, volume, surface, and surface-volume interaction terms. The direct volume scattering and the surface-volume interaction scattering terms in (2) can be written as



and

Where K₅^pp is the volume scattering coefficient. R is the surface reflectivity. Both varies with the polarization parameter pp.

Since both volume extinction and scattering coefficients are strongly depended on the number density, shape and size parameters, as well as orientation or structure of the vegetation canopy, in addition to canopy thickness, it would be extremely difficult to estimate the surface scattering component or soil moisture from a limited SAR measurements.

By comparison of backscattering components in (2) and the decomposed scattering components in (1), we can approximately write



Where subscript number 1 and 2 represent the single and double reflection components.

Advantage of (2) is that it represents a general case of natural surface. It can be applied to both the fully vegetated surface (continuous layered vegetation when f_v = 1) and the bare surface (when f_v = 0).

Data Analysis Under Multi-Temporal Measurements Configuration
The temporal variability of surface roughness and vegetation cover are generally at much longer time scale than that of soil moisture. Unless there is a human activity we may reasonably assume that both surface roughness and vegetation cover are same at time interval from a few days to a week. The change in SAR measurements between the repeat passes, therefore, is resulted from the change of ground dielectric properties or soil moisture. Under this configuration, using two repeat pass polarimetric SAR measurements, we can write the difference of the first components



and the ratio of the second components by (4) as



Where the number after pp in either superscript or subscript represents the first and second SAR measurements. At L-band, the surface roughness parameter RMS height is small in comparison of the incidence wavelength so that we could approximate the polarization amplitude as that in the small perturbation model -a_nn which are only depends only on the surface dielectric constant e_s and incidence angle q. Where a_pp is given by



As we noticed in (9), the polarization amplitude is exactly same as the surface reflectivity for HH polarization. Under assumption of the surface roughness do not change between two SAR measurements, we have



Furthermore, using (7), (8) and (10), we obtain



and


Therefore, we can decompose or directly estimate the volume and surface scattering components by (11) and (12) for HH polarization measurements.

The SAR data used in this study was from the Washita '92 experiment. During the experiment from June 10-18, 1992, a time series of spatially distributed hydrologic data focusing on soil moisture and evaporative fluxes were collected. At the same time, the AIRSAR sensor aboard the NASA DC-8 aircraft collected a sequence of 6 L band radar images over an agricultural test site located just outside the watershed. The Washita '92 experiment was conducted immediately following a series of heavy rainfalls that ended on June 9. Thereafter, no more rain occurred throughout the entire series of the AIRSAR flights, thus allowing observation of a drying-down sequence. From any two of 6 sequence SAR measurements, we can estimated the surface and volume backscattering components using (11) and (12). Furthermore, the relative change in dielectric property of any pair from 6 sequence SAR measurements can be estimated by (10).



Figure 1. Comparison of the normalized cross product of the decomposed even reflection components with that of reflection coefficients calculated from field measurements data.

Reference

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