Tien Hao Liao

Polarimetric Simulations of SAR at L-Band Over Bare Soil Using Scattering Matrices of Random Rough Surfaces From Numerical Three-Dimensional Solutions of Maxwell Equations

We have performed simulations of random rough surface scattering using 3-D numerical solution of Maxwell equations (NMM3D) using surface size up to 32 × 32 squared wavelengths. The rough surfaces are characterized by exponential correlation functions. The simulation results of crossand copolarization backscattering coefficients were in good agreement with experimental measurements of bare soils at L-band. Because in numerical solutions of Maxwell equations the electric fields of the scattered wave are calculated for each realization, scattering matrices can be simulated by NMM3D, and such simulations are performed in this paper. For a given RMS height, correlation length, soil permittivity, and incident angle, we calculated the radar scattering matrix up to 958 independent realizations. For each realization, the components of the scattering matrix, namely, SHH, SVV, SHV, and SVH, are calculated. Using the simulated scattering matrices, we calculate the polarimetric speckle statistics (amplitude and phase difference), followed by a comparison with theoretical distributions. For fully developed speckle from the homogeneous rough surface, the results are examined and validated to ensure the simulated data quality as far as polarimetric properties are concerned. By taking ensemble averages, we calculate the coherency matrix from which the eigenvalues, entropy, anisotropy, and alpha angle in coherent target decomposition are then calculated. In particular, characterization of polarimetric descriptors for rough surface is presented. Issues of scattering symmetry characteristics are also discussed.

Active and Passive Vegetated Surface Models With Rough Surface Boundary Conditions From NMM3D

In this paper, we derive an expression of the brightness temperatures of a vegetated surface based on the tau-omega model with the rough surface boundary condition that replaces the conventional exp(-h) model by NMM3D (Numerical Simulations of 3D Maxwell equations). A purpose of the paper is that the same physical rough surface scattering model based on NMM3D and the same physical parameters of rms heights and correlation lengths can be used for both passive and active remote sensing of the same scene of vegetated surfaces. The bistatic scattering of rough surfaces are decomposed into the coherent wave and the co-polarization and the cross-polarization of the incoherent waves to quantify the contribution of each of these components. Numerical results are illustrated for a variety of roughness conditions. Comparisons are made with the exp(-h) model. Results are compared with the experimental passive measurements of PORTOS 1993 for bare soil cases. Data cubes for grassland are calculated for both active and passive signatures at L band. Comparisons are then made with the L band PALS data for the grassland of SGP99 using these data cubes.

Copolarized and Cross-Polarized Backscattering From Random Rough Soil Surfaces From L-Band to Ku-Band Using Numerical Solutions of Maxwell's Equations With Near-Field Precondition

We extend the 3-D numerical method of Maxwells equation (NMM3D) for rough soil surface scattering from L-band to C-, X-, and Ku-bands. We illustrate the results for copolarization, cross-polarization, and polarization ratio (HH/VV). Copolarized and cross-polarized backscattering coefficients from NMM3D are analyzed for frequency dependence, incident angle dependence, and soil moisture dependence. We also cross compare results from analytical and empirical models. The 16 × 16 squared wavelength (λ2) of rough surface is applied for NMM3D using 256 processors on NSF Extreme Science and Engineering Discovery Environment clusters. Polarization ratio, HH/VV, is studied to address the feature of dependence on frequency for same fields (same physical parameters for the model). HH/VV is shown useful to provide additional information to study land surface. Results from NMM3D are also validated with POLARSCAT measurement data-1. NMM3D shows good agreement with data and better performance while considering copolarization, cross-polarization, and polarization ratio (HH/VV) together. The key advancement in computation efficiency in this paper is the implementation of a physically based near-field precondition algorithm in NMM3D to accelerate parallel computation. With precondition, the computation time is faster by ten times for larger root-mean-square height.

Multiple Scattering Effects With Cyclical Correction in Active Remote Sensing of Vegetated Surface Using Vector Radiative Transfer Theory

The energy transport in a vegetated (corn) surface layer is examined by solving the vector radiative transfer equation using a numerical iterative approach. This approach allows a higher order that includes the multiple scattering effects. Multiple scattering effects are important when the optical thickness and scattering albedo of the vegetation layer are large. When both the albedo and the optical thickness exceed 0.4, higher orders contribute significantly (e.g., vertical polarization at L-band). The approach is applied to vegetated surfaces using typical crop structure for backscattering from L-band to Ku-band. For corn fields at L-band, multiple scattering effects are more important for vertical scattered wave with vertical incidence (VV). For example, when vegetation water content (VWC) is 3kg/m2, the deviation between first order and multiple scattering for corn field for VV could be 3.5 dB while 0.7 dB for horizontal scattered wave with horizontal incidence (HH). The iterative approach also allows the separation of the contribution to backscattering from each scattering order and scattering mechanism. Each scattering mechanism is associated with a unique scattering path. By examining the duality of the paths, we are able to identify the cyclical terms with existence of a reflective boundary. The cyclical correction to the backscattering accounts for backscattering enhancement effects on the copolarization by a factor of two. The approach is validated against the SMAPVEX12 L-band corn dataset over the entire crop growth and large soil moisture variations. The model prediction matches the observation with 1.93 and 1.46 dB root-mean-square error (RMSE) for VV and HH, respectively, while correlations are 0.67 and 0.88, respectively. Time-series retrieval is also applied successfully for both soil moisture and VWC with 0.06 cm3/cm3 and 0.44 kg/m2 RMSE, respectively, while correlations are 0.7 and 0.92, respectively. For large VWC, this approach corrects the underestimated backscatters in the single scattering caused by large attenuation.

Coherent Model of L-Band Radar Scattering by Soybean Plants: Model Development, Evaluation, and Retrieval

An improved coherent branching model for L-band radar remote sensing of soybean is proposed by taking into account the correlated scattering among scatterers. The novel feature of the analytical coherent model consists of conditional probability functions to eliminate the overlapping effects of branches in the former branching models. Backscattering coefficients are considered for a variety of scenarios over the full growth cycle for vegetation water content (VWC) and the complete drydown conditions for soil moisture. The results of the coherent model show that HH scattering has a significant difference up to 3 dB from that of the independent scattering when VWC is low, e.g., 0.2 kg/m2. Forward model calculations are performed for the scattering from the soybean field for the full range of three axes of root-mean-square (RMS) height of bare soil, VWC, and soil moisture using the coherent model. The soybean volume scattering including the double-bounce term is combined with the back scattering of bare soil from the numerical Maxwell solutions that incorporates RMS height, soil permittivity, and correlation length, to form the forward model lookup table for the vegetated soil. The results are compared with data from 13 soybean fields collected as part of the soil moisture active passive validation experiment 2012 (SMAPVEX12). Time-series retrieval of soil moisture is also applied to the soybean fields by inverting the forward model lookup table. During the retrieval, the VWC is optimized with physical constraints obtained from ground measurements. The retrieval performances are significantly improved using the proposed coherent model: the root-mean-squared error (RMSE) of the soil moisture retrieval is decreased from 0.09 to 0.05 cm3/cm3 and the correlation coefficient is increased from 0.66 to 0.92.

High Order Extractions of Broadband Green's Function with Low Wavenumber Extractions for Arbitrary Shaped Waveguide

In this paper we develop a higher order extraction method to accelerate the convergence in the computation of broadband Green’s function (BBGFL) for an arbitrary shaped homogeneous waveguide.The broadband Green’s function is based on modal expansions in which the modal field solutions are frequency independent. The higher order extraction is obtained by using three low wavenumbers in extraction. It gives a modal expansion of Broadband Green’s Function with 6th order convergence requiring fewer evanescent modes for convergence. Numerical results are illustrated for both lossless and lossy dielectric cases. The accuracy of results are verified with direct method of moment (MoM) and HFSS. The higher order BBGFL method is computationally efficient for broadband simulations.

Propagation and Scattering by a Layer of Randomly Distributed Dielectric Cylinders Using Monte Carlo Simulations of 3D Maxwell Equations With Applications in Microwave Interactions With Vegetation

Transmission, scattering, and absorption by a layer of dielectric cylinders are studied in the context of microwave propagation through vegetation. The electromagnetic fields are calculated by numerical solutions of 3D Maxwell equations (NMM3D) using the method of Foldy-Lax multiple scattering equations combined with the method of the body of revolution (BOR). Using the calculated transmission, we derive, the “tau”, the optical thickness, which describes the magnitude of the transmission. Two cases are considered: the short-cylinder case and the extended-cylinder case. The case of short cylinders is that the lengths of cylinders are much smaller than the layer thickness, while the case of extended cylinders is that the lengths of the cylinders are the same as or comparable to the layer thickness. Numerical results are illustrated for vertically polarized plane waves obliquely incident on the layer of cylinders. The NMM3D results for the extended-cylinder case show large differences of transmission from the results of the other approaches, such as the effective permittivity (EP), the distorted Born approximation (DBA), and the radiative transfer equation (RTE). For the case of short cylinders, the NMM3D results are in close agreement with those of EP, DBA, and RTE.

Rough Surface and Volume Scattering of Soil Surfaces, Ocean Surfaces, Snow, and Vegetation Based on Numerical Maxwell Model of 3-D Simulations

In this paper, we give an overview and an update on the recent progress of our research group in numerical model of Maxwell equations in three dimensions (NMM3D) on random rough surfaces and discrete random media and their applications in active and passive microwave remote sensing. The random rough surface models were applied to soil surfaces and ocean surfaces. The discrete random media models were applied to snow and vegetation. For rough surface scattering, we use the surface integral equations of Poggio–Miller–Chang–Harrington–Wu–Tsai that are solved by the method of moments using the Rao–Wilton–Glisson basis functions. The sparse matrix canonical grid method is used to accelerate the matrix column multiplications. In modeling the rough surfaces, we use the exponential correlation functions for soil surfaces and the Durden–Vesecky ocean spectrum for ocean surfaces. In scattering by terrestrial snow and snow on sea ice, we use the volume integral equations formulated with the dyadic half-space Greens function. The microstructure of snow is modeled by the bicontinuous media. In scattering by vegetation, we use the discrete scatterers of cylinder. The NMM3D formulation is based on the Foldy–Lax multiple scattering equations in conjunction with the body of revolution for a single scatterer. For rough surface scattering, simulations results are compared with advanced integral equation model, small slope approximation, small perturbation method, and two scale model. For volume scattering by snow, results are compared with the bicontinuous dense media radiative transfer. For scattering by vegetation, results are compared with distorted Born approximation and radiative transfer equation. Comparisons are also made with experiments.

Combined active and passive microwave remote sensing of soil moisture for vegetated surfaces at L-band

The distorted Born approximation (DBA) combined with the numerical solutions of Maxwell equations (NMM3D) has been used for the radar backscattering model for NASAs Soil Moisture Active Passive (SMAP) mission. The models for vegetated surfaces such as wheat, grass, soybean and corn have been validated with the Soil Moisture Active Passive Validation Experiment 2012 (SMAPVEX12) data. In this paper we report progress on development of a consistent model for combined active and passive microwave remote sensing of vegetated surfaces by using the same approach to obtain backscatter and emissivity. The active model DBA/NMM3D is extended to calculate bistatic scattering for each of the three scattering mechanisms: volume, double bounce and surface scattering. Then emissivity is obtained by integration of the bistatic scattering. An advantage of this combined active and passive model is that the same physical parameters of vegetation and soil surfaces are used in both the active model and the passive model. The β parameter that relates backscattering to emissivity is also derived for various vegetated surfaces.

Estimating Vegetation Water Content and Soil Surface Roughness Using Physical Models of L-Band Radar Scattering for Soil Moisture Retrieval

Soil surface roughness and above-ground vegetation water content (VWC) are estimated by inverting physical models for L-band scattering and absorption at 40° incidence angle using ground, airborne and Soil Moisture Active Passive (SMAP) radar data. The spatial resolution varies from field scale (airborne and ground) to 3 km (SMAP). The temporal resolution is defined by the length and interval of observation time windows (weeks to three months for surface roughness, and three to seven days for VWC). The validation of the roughness estimates shows an accuracy of 25% (bare surface) and 29 to 46% (croplands and pasture). The correlation degrades as vegetation becomes thicker, indicating the stronger scattering and absorption by thicker vegetation. The roughness retrievals with the SMAP data are within the physical range of 0.5 cm to 4 cm. They show larger values in croplands than in natural terrain. The VWC estimate modifies a ‘first guess’ (in situ values for the airborne experiment; and 16-daily climatology for SMAP). The VWC retrievals correctly follow the full growth of crops and the RMSE is smaller than 20% in the airborne retrievals: the correlation ranges from 0.57 to 0.91. These results demonstrate that the forward model inversion has a potential to retrieve VWC for the four major crops over the entire phase of the crop growth. The VWC retrievals from the SMAP data revised the climatology first guess more in the croplands, where the climatology is more likely to depart from the contemporaneous condition than in natural landcover. The value of this work lies in the fact that the surface roughness at the footprint scale is difficult to characterize and a global VWC product at SMAP’s spatial scale from microwave observations is rare, and that this paper presents a plausible pathway towards such products. The estimates at these temporal and spatial scales derived from microwave observations will be useful for studies of climate, agriculture, and soil moisture.