Keywords: Soil moisture, Surface roughness, Numerical simulation, Polarimetry, SAR

Abstract
The goal of this study is to estimate the surface soil moisture and surface roughness using polarimetric Synthetic Aperture Radar (SAR) data. In this study, a preliminary analysis for approaching this objective was conducted based on a sensitivity analysis of surface parameters. A numerical scattering model was used, and the results were compared using only like-polarized backscattering coefficients obtained from the data of an experiment conducted simultaneously with an airborne SAR. The surface correlation function was considered in this analysis. Because the problem is site-specific, and depends upon the measurement accuracy of both the ground truth data and the SAR system including speckle noise, as well as the model uncertainty, the comparison results did not agree well with measured and inferred values of both the soil moisture and surface roughness. In particular, the moisture was underestimated and the roughness was overestimated.

Introduction
Monitoring spatial and temporal changes of soil moisture is very important to numerous environmental studies, including hydrology, meteorology, and their interactive fields. In spite of its importance, soil moisture is not generally used for weather forecasting and water resources management because it is difficult to measure on a routine basis over large areas. However, recent advances in microwave remote sensing have demonstrated the potential to measure soil moisture quantitatively on bare and short-vegetated surfaces (Engman and Chauhan, 1995). In attempting to use active microwave remote sensors to estimate this important parameter, several algorithms have been developed by using Synthetic Aperture Radar (SAR) image data. The signal returned to SAR is known as the backscattering coefficient (s ⁰_qp; where subscript p is the transmitting polarization state and q is the receiving polarization state), which is affected by not only dielectric properties that depend on the soil moisture, but also on surface roughness, correlation length and other surface characteristics. Previous studies (Wang et al., 1986) have revealed that Shuttle Imaging Radar-B (SIR-B) imagery with a single frequency and single polarization system can only describe the dependence of backscattering coefficients on these surface parameters. Tadono et al. (1999) developed an algorithm including some assumptions based on hydrological knowledge, and estimated the soil moisture distribution using two seasonal Japanese Earth Resources Satellite-1 (JERS-1) SAR images.

Radar backscatter studies became more rigorous with the availability of polarimetric radar data and more sophisticated algorithms for estimating soil moisture were presented. Oh et al. (1992) developed an empirical model to estimate the root mean square (rms) roughness height and soil moisture from the co-polarized ratio (s ⁰_hh/s ⁰_vv ; where subscripts h and v are horizontal and vertical polarizations), and the cross-polarized ratio (s ⁰_hh/s ⁰_vv) over bare soils of different roughness and moisture conditions was measured by a truck-mounted scatterometer system. Also, Dubois et al. (1995) developed a model that only requires measurements of s ⁰_hh and s ⁰_vv at frequencies from 1.5 and 11GHz to retrieve both rms roughness height and soil moisture from bare soil and applied to the L-band data acquired by both the Airborne SAR (AIRSAR) and Shuttle Imaging Radar-C (SIR-C) over a test site in Oklahoma, USA. Hajnsek et al. (1999) applied the above two empirical models to L-band data of the airborne Experimental SAR (E-SAR), and compared the performance and accuracy of estimated values. They found that the valid pixels of the E-SAR data decrease to less than 56% of the total number of pixels. Furthermore, soil moisture was underestimated and roughness was overestimated for both models because the regression fits necessary to estimate the roughness and moisture were dependent on the used data sets. Shi et al. (1997) pointed out that neither of the above empirical models considered the surface power spectrum. In addition, these empirical models developed from a limited number of observations might have site-specific problems due to nonlinear responses of backscattering to the soil moisture and surface roughness parameters. Therefore, an algorithm based on the single-scattering Integral Equation Method (IEM) was developed to estimate soil moisture and surface roughness from dual-polarized SAR measurements and subsequently applied to both L-band AIRSAR and SIR-C data. Consequently, the rms errors of comparison were found to be 3.4% for moisture and 1.9dB for roughness.

The objective of this study is to consider the preliminary examination to estimate the surface soil moisture and the roughness by using polarimetric SAR data. A numerical model was used to analyze the sensitivity of surface parameters and to estimate the moisture and roughness using data from an experiment conducted simultaneously with a multi-parameter airborne SAR that has a dual-frequency (L- and X-bands) and quadruple polarization and is called “PI-SAR” (Polarimetric and Interferometric SAR) (Wakabayashi et al., 1999).

Scattering Model And Sensitivity Analysis
The scattering model used in this study formulates scattering processes from an inhomogeneous medium composed of irregular soil particles and water. The model consists of terms for surface and volume scattering. The surface scattering from the air-soil interface (soil surface) is calculated by the single-scattering IEM model (Fung, 1994), which is valid for a wider range of surface roughness conditions than the other classical model (Ulaby et al., 1986). The IEM model is needed to evaluate the surface correlation function in the general form of
p(x)=exp[x/I)ⁿ]                (1)
where l is the correlation length of the surface roughness. The general form is an exponential function when 1 =n and becomes a Gaussian function when 2 =n . The volume scattering within the medium is calculated based on the first-order radiative transfer solution (Fung, 1994; Shi and Dozier, 1995). Furthermore, the semi-empirical model for a four-component mixture (Dobson et al., 1985) is used to convert the volumetric soil moisture ( Mv) to the dielectric constant (e_r ), assuming typical sandy soil in this study.