Alireza Tabatabaeenejad

Bistatic scattering from three-dimensional layered rough surfaces

An analytical method to calculate the bistatic-scattering coefficients of a three-dimensional layered dielectric structure with slightly rough interfaces is presented. The interfaces are allowed to be statistically distinct, but possibly dependent. The waves in each region are represented as a superposition of an infinite number of up- and down-going spectral components whose amplitudes are found by simultaneously matching the boundary conditions at both interfaces. A small-perturbation formulation is used up to the first order, and the scattered fields are derived. The calculation intrinsically takes into account multiple scattering processes between the boundaries. The formulation is then validated against known solutions to special cases. New results are generated for several cases of two- and three-layer media, which will be directly applicable for modeling of the signals from radar systems and subsequent estimation of a layered medium subsurface properties, such as moisture content and layer depths

P-Band Radar Retrieval of Subsurface Soil Moisture Profile as a Second-Order Polynomial: First AirMOSS Results

We propose a new model for estimating subsurface soil moisture using P-band radar data over barren, shrubland, and vegetated terrains. The unknown soil moisture profile is assumed to have a second-order polynomial form as a function of subsurface depth with three unknown coefficients that we estimate using the simulated annealing algorithm. These retrieved coefficients produce the value of soil moisture at any given depth up to a prescribed depth of validity. We use a discrete scattering model to calculate the radar backscattering coefficients of the terrain. The retrieval method is tested and developed with synthetic radar data and is validated with measured radar data and in situ soil moisture measurements. Both forward and inverse models are briefly explained. The radar data used in this paper have been collected during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission flights in September and October of 2012 over a 100 km by 25 km area in Arizona, including the Walnut Gulch Experimental Watershed. The study area and the ancillary data layers used to characterize each radar pixel are explained. The inversion results are presented, and it is shown that the RMSE between the retrieved and measured soil moisture profiles ranges from 0.060 to 0.099 m3/m3, with a Root Mean Squared Error (RMSE) of 0.075 m3/m3 over all sites and all acquisition dates. We show that the accuracy of retrievals decreases as depth increases. The profiles used in validation are from a fairy dry season in Walnut Gulch and so are the accuracy conclusions.

Inversion of Subsurface Properties of Layered Dielectric Structures With Random Slightly Rough Interfaces Using the Method of Simulated Annealing

In this paper, the model parameters of a two-layer dielectric structure with random slightly rough boundaries are retrieved from data that consist of the backscattering coefficients for multiple polarizations, angles, and frequencies. We use the small perturbation method to solve the forward problem. The inversion problem is then formulated as a least square problem and is solved using a global optimization method known as simulated annealing, which is shown to be a robust retrieval algorithm for our purpose. The algorithm performance depends on several parameters. We make recommendations on these parameters and propose a technique for exiting local minima when encountered. We test the sensitivity of the inversion scheme to measurement noise and present the noise analysis results.

Coherent Scattering of Electromagnetic Waves From Two-Layer Rough Surfaces Within the Kirchhoff Regime

We present an analytical solution for coherent scattering of electromagnetic waves from a two-layer rough surface structure with uncorrelated random rough interfaces. The Kirchhoff approximation is used to predict the coherent (specular) component of the scattered wave from a layered rough surface that is assumed to have radii of curvature much larger than the wavelength to allow the application of the method. The roughness on both boundaries is assumed small such that the coherent component of the scattered wave is dominant. The derived solution includes all orders of the scattered wave and has a simple algebraic expression that can be readily computed. We validate the solution against a numerical method and present simulation results for various cases.

Study of Validity Region of Small Perturbation Method for Two-Layer Rough Surfaces

We previously derived the bistatic scattering coefficients of a 3-D two-layer dielectric structure with slightly rough boundaries using the small perturbation method (SPM). The use of SPM raises the question about its region of validity, which pertains to the conditions on each layer roughness, slope, and permittivity for which the first-order SPM is accurate within a specified error bound. To this end, the SPM solution needs to be compared with an accurate solution that does not impose roughness restrictions. We use the method of moments to solve an integral equation to analyze electromagnetic scattering from a large ensemble of two-layer structures. Simulations are performed for 1-D rough surfaces represented by zero-mean stationary random processes, separating homogeneous dielectric layers. Observations are reported on the accuracy of the first-order SPM for TM incidence at a fixed incidence angle of 45°.

Potential of L-Band Radar for Retrieval of Canopy and Subcanopy Parameters of Boreal Forests

In this paper, we study the radar retrieval of soil moisture as well as canopy parameters in a range of boreal forests. The retrieval is formulated as an optimization problem where the difference between data and prediction of a forward scattering model is minimized. The forward model is a discrete scatterer radar model, and the optimization algorithm is a global optimization scheme known as simulated annealing. The inversion method is first applied to synthetic data assuming hypothetical allometric relationships to make the retrieval possible by reducing the number of unknown vegetation parameters. The inversion algorithm is then validated using the data acquired with the National Aeronautics and Space Administration (NASA)/Jet Propulsion Laboratory (JPL) Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) in June 2010 in central Canada boreal forests in support of the prelaunch calibration and validation activities of NASAs Soil Moisture Active and Passive (SMAP) mission. The inversion results for synthetic data show that the absolute retrieval error in soil moisture and relative retrieval error in canopy height are small, while the relative output error in trunk density could be large. The inversion results for actual field data show a great accuracy in soil moisture retrieval for Old Jack Pine and Young Jack Pine forests but show large retrieval errors for many of the radar pixels in the Old Black Spruce site. This paper shows that L-band radar is capable of retrieving surface soil moisture in forests with a high biomass where the forest structure allows soil moisture information to be carried by scattering mechanisms.

Radar Retrieval of Surface and Deep Soil Moisture and Effect of Moisture Profile on Inversion Accuracy

We study the retrieval of surface and deep moisture of bare soil from noisy radar observations using simulated annealing. Due to moisture variations with depth, we model bare soil with a stratified dielectric profile with a rough surface on top. Small perturbation method (SPM) is used as the forward model. We use the full moisture profile for radar data synthesis and study the retrieval accuracy by varying the number of layers that represent the soil profile during inversion. The effect of measurement frequency on the accuracy of deep moisture retrieval is investigated. This work is intended for assessing the effect of subsurface profile on soil moisture retrieval from radar observations of NASAs Soil Moisture Active and Passive (SMAP) mission and future lower frequency airborne or spaceborne systems that may follow SMAP.

Advancing NASA’s AirMOSS P-Band Radar Root Zone Soil Moisture Retrieval Algorithm via Incorporation of Richards’ Equation

P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar observations, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For this reason, an empirical quadratic function (second order polynomial) is currently applied in the AirMOSS inversion algorithm to retrieve the SMP. The three free parameters of the polynomial are retrieved for each AirMOSS pixel using three backscatter observations (i.e., one frequency at three polarizations of Horizontal-Horizontal, Vertical-Vertical and Horizontal-Vertical). In this paper, a more realistic, physically-based SMP model containing three free parameters is derived, based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

Backscattering of electromagnetic waves from layered rough surfaces and its application in estimating deep soil moisture

An analytical method to calculate the scattering coefficients of a three-layer 3D rough surface is introduced. The two rough interfaces are assumed to be distinct. The waves in each region are represented as a superposition of an infinite number of up- and down-going spectral wave components, whose amplitudes are found by applying the boundary conditions. A small-perturbation formulation is used in the process and the scattering coefficients are derived to the first order. The formulation is validated against known solutions for special cases of flat interfaces as well as the single rough surfaces. Results are then generated for several cases of the three-layer rough interface medium, to be used for modeling of the backscattered signals from a tower-based radar system and subsequent estimation of multilayered soil properties such as moisture content and subsurface layer height

A generalized radar scattering model for multispecies forests with multilayer subsurface soil

A generalized radar scattering model to predict backscattering for different frequencies and polarizations is crucial in the endeavor to understand the relationship between radar measurement and properties of both the vegetation and soil, and for allowing the estimation of both vegetation and soil information from radar data. In this work, we develop a combined radar scattering model of vegetation and multilayered soil structure to represent realistic soils with multiple layers of various textures, depths, and moisture contents. A multilayered soil scattering model based on first order small perturbation method (SPM) is integrated [1] to account for direct ground scattering. Furthermore, the coherent interaction between the vegetation and layered ground is included using a recently developed model based on the Kirchhoff approximation [2].