EMISSION AND BACKSCATTERING OF ROUGH SOIL SURFACES AT L BAND BASED ON MULTILEVEL SMCG METHOD

F. Borah¹, L. Tsang¹, T. Wang², X. Xu², S. Yueh², E. Kim³

¹Department of Electrical and Computer Engineering, University of Michigan, Ann Arbor, USA, ²NASA Jet Propulsion Lab, California Institute of Technology, Pasadena, USA , ³NASA Goddard Space Flight Center, Greenbelt, USA

The accurate characterization of microwave emission and backscattering from rough soil surfaces is essential for remote sensing applications such as soil moisture retrieval, hydrology, and snow water equivalent (SWE) retrieval. At L-band, in particular, soil surface roughness plays an important role in both soil and snow remote sensing. The L band signal can see through vegetation to retrieve soil moisture under vegetation. In the case of snow, the L band signal can see through snow and can be used to characterize the surface freeze/thaw state and soil moisture below the snowpack. It can also be used to characterize the background rough surface at snow-free conditions. This is crucial for SWE retrieval at C, X and Ku bands.

Analytical and approximate methods such as the Small Perturbation Method (SPM) or Kirchhoff Approximation (KA) often break down when the roughness parameter, kh (k is the wave number, 2π/λ , and h is the rms height of the rough surface) exceeds unity, limiting their applicability for realistic natural surfaces. Past full wave numerical rough surface scattering and emission models have been limited to small rms height such as 0.1λ and exponential correlation functions while recent airborne lidar measurements indicate land surfaces are more of the that of a fractal surface in which the roughness increases with the area of interests.

To overcome these challenges, we have significantly improved our previous method of the 3D full wave solutions of Maxwell equations. The new technique uses the Multilevel Sparse Matrix Canonical Grid (SMCG) method to simulate both emission and backscattering of rough soil surfaces at L-band. The method is shown to be accurate on comparison of the results with the FEKO commercial software. However, the multi-level SMCG method is much more efficient than FEKO requiring 100 times less in memory and CPU than FEKO. This approach enables the modeling of electrically large rough surfaces while retaining the full-wave accuracy required to capture multiple scattering effects that are crucial at L-band. We have implemented ML-SMCG to handle, up to 2 roughness and simulate an area of 128×128 rough surface. We also include the fractal model for rough surface to study the impact of roughness increase with area.

To solve for the backscattering problem in the numerical ML-SMCG method, we calculate the surface currents and then find the scattered fields. To calculate the surface currents, the electromagnetic wave interaction on the rough surface is divided into near fields and non-near fields. Near fields are calculated using an exact expression of the Green’s function. The non-near fields are further divided into multiple levels, level 1,2,3, etc. At each level the Green’s function is represented as a Taylor Series expansion over a flat canonical grid. The number of terms in the Taylor series is dictated by the level. At higher levels the EM interaction is weak, and the Green’s function can be represented by just one term. This reduces the computation time and memory and makes larger roughness and areas possible to simulate.

The emission problem is related to the backscattering problem as the power absorbed by the rough surface is directly related to the emissivity of the rough surface. Using the surface currents calculated while solving for scattered fields, we calculate the power absorbed by the rough surface. Taking the ratio of power absorbed by the rough surface to the power absorbed by a flat surface with same dielectric properties gives us the ratio of emissivity of rough surface to emissivity of flat surface. Since the emissivity of flat surface, e^flat, can be calculated analytically, we can find the emissivity of rough surface, e^rough, and the brightness temperature, T_B^rough. This allows the same SMCG framework to be used for both passive (emission) and active (backscattering) characterizations.

We compare the model with the SMAP data over South Fork, Colorado and Walnut Gulch, Arizona using fractal surfaces. Numerical experiments demonstrate that the proposed multilevel SMCG method provides stable and accurate predictions for backscattering coefficients and brightness temperature of rough soils at L-band. In regimes where approximate models deviate significantly, particularly for moderate to strong roughness, the fast ML-SMCG results remain consistent with measured data. Furthermore, the method captures polarization dependence with higher fidelity compared to conventional models.

The proposed framework offers a numerical approach to treat both active and passive microwave interactions with rough soil surfaces at L-band. The capability to accurately account for realistic soil roughness and dielectric variability can help the interpretation of L-band radiometer and radar observations, including those from SMAP, SMOS, and NISAR missions.