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The Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) P-band synthetic aperture radar (SAR) was flown more than 1200 h from August 2012 to September 2015, covering regions of 2500 km2 spread over nine major biomes in North America. The flights, as a part of the NASA AirMOSS Earth Venture Suborbital 1 (EVS-1) mission, collected radar data used to map root-zone soil moisture (RZSM) at 3-arcsec resolution. We previously reported the baseline retrieval algorithm and demonstrated its performance for a semiarid shrubland (Walnut Gulch, AZ, USA); we represented the RZSM profile as a continuous quadratic function and solved a radar scattering nonlinear optimization problem to obtain the unknown polynomial coefficients. In this article, we expand the retrievals to other AirMOSS sites that, in addition to the semiarid shrubland, include grassland and crops (MOISST, OK, USA), woody savanna (Tonzi Ranch, CA, USA), temperate conifer forest (Metolius, OR, USA), and boreal forest (Saskatchewan, Canada). Due to a wide range of land covers, soil types, and soil moisture regimes, we parameterize the forward model and constrain the inverse algorithm for each site separately. We present the full set of retrievals for these sites, validating the results against in situ observations. Error sources and strategies to minimize their effects are discussed. The concept of sensing depth is introduced. We find that the retrieval errors are smallest for the top 25 cm of soil with a root-mean-square error (RMSE) of less than 0.05 m3/m3. The RMSE remains around 0.06 m3/m3 even for depths reaching 45 cm, which is the typical sensing depth for the sites considered. These AirMOSS RZSM products (known as Level-2/3 RZSM, or L2/3-RZSM, products) are the first of their kind in that it is the first time RZSM has been retrieved directly from remote sensing observation.

A layer of oil on the sea surface reduces the components of ocean wave spectra corresponding to the capillary and gravity-capillary waves leading to significantly reduced radar backscatter and making slicks appear dark in synthetic aperture radar (SAR) images. The ratio of the backscatter between clean and slicked ocean surfaces is known as the ‘damping ratio,’ and has been shown to be sensitive to variations within slicks that correlate with the oil layer’s thickness and fractional water volume. Although the relative thickness relationship is well established and can be used to identify areas of ‘thicker’ oil within a slick, quantifying the thickness from SAR alone remains to be shown. There is considerable uncertainty regarding the potential capability of SAR to quantitatively determine the oil layer thickness for slicks in open water given the dependence on bulk and interfacial oil layer properties and the variation of the properties typical in this setting and for different types of oil. Here, we report the results of a study modeling radar backscatter from slicked and unslicked ocean surfaces based on electromagnetic scattering theory and accounting for oil properties and meteorological conditions. The electromagnetic scattering model is used to evaluate whether the oil thickness can be quantified with reasonable accuracy based upon SAR backscatter intensities alone, and how information about metocean conditions, oil properties and ocean temperature and salinity can be used to calibrate the model to obtain more accurate thickness estimates.The research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

We develop a methodology for modeling coherent electromagnetic scattering from rough surfaces with buried inhomogeneities in three dimensions. The inhomogeneities considered in this paper include random spherical media, random cylindrical media, and root-like cylindrical clusters. They are used to simulate rocks, ice particles, and vegetation roots buried beneath the ground surface that can be seen by the low-frequency radars in Earth remote sensing applications. The approach we develop first calculates volumetric scattering from the media using coherent approaches, including both the conventional recursive transition matrix (T-matrix) method as well as a new generalized iterative extended boundary condition method we developed for tilted finite cylinders, and then transforms the T-matrix to the scattering matrix, which is then used to form the full scattered field of layered structures with rough surface and subsurfaces. We validate the methodology by comparing with other numerical solutions for special cases, and show sensitivity results for scattering from rough surface with buried random spherical media and random cylindrical media of different densities. We also construct a basic root model and calculate the scattering cross sections from single and multiple root clusters with or without a subsurface interface underneath. With the approach developed in this paper, we are able to study the sensitivity of radar signals to subsurface scatterers. For example, our simulations show that, depending on their density and water content, buried roots could enhance the backscatter from a single rough surface by as much as 5 dB in co-pol components, and substantially more in cross-pol components. The results of this model are expected to enable more accurate geophysical retrievals of soil moisture as well as soil organic content.

Modeling of terrain topography is crucial for vegetated areas given that even small slopes impact and alter the radar wave interactions between the ground and the overlying vegetation. Current missions either exclude pixels with large topographic slopes or disregard the terrain topography entirely, potentially accumulating substantial modeling errors and therefore impacting the retrieval performance over such sloped pixels. The underlying terrain topography needs to be considered and modeled to obtain a truly general and accurate radar scattering model. In this paper, a flexible and modular model is developed: the vegetation is considered by a multilayered multispecies vegetation model capable of representing a wide range of vegetation cover types ranging from bare soil to dense forests. The ground is incorporated with the stabilized extended boundary condition method, allowing the representation of an $N$ -layered soil structure with rough interfaces. Terrain topography is characterized by a 2-D slope with two tilt angles $(\alpha, \beta)$ . Simulation results for an evergreen forest show the impact of a 2-D slope for a range of tilt angles: a 10 $^{\circ}$ tilt in the plane of incidence translates to a change of up to 15 dB in HH, 10 dB in VV, and 1.5 dB in HV for the total radar backscatter. Terrain topography is shown to be crucial for accurate forward modeling, especially over forested areas.

We present an experimental verification of the recursive T-matrix method (RTM), which is a common method for solving electromagnetic scattering from multiple scatterers. This is done using an antenna and propagation model uniquely suited for T-matrices and network analyzer measurements. In the experiments, we use a multistatic system to measure the scattering from collections of objects consisting of conducting or dielectric spheres, as well as conducting cylinders. In simulation, we calculate the scattering from the objects using the RTM and further predict the transition parameters expected between the receivers and the transmitter in the measurement setup using a propagation model. The predicted and measured values of the transmission parameters are compared, and thereby used to verify the recursive T-matrix algorithm. Good agreement observed in these results provides experimental validation of the RTM.

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 m 3 /m 3 , with a Root Mean Squared Error (RMSE) of 0.075 m 3 /m 3 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.

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.

A model of 3-D electromagnetic scattering from multiple rough surfaces within homogeneous-layered or vertically inhomogeneous media is developed in this work. This model, aimed at radar remote sensing of surface-to-depth profiles of soil moisture, computes total bistatic radar cross sections from the multilayer structure based on the scattering matrix approach, cascading the scattering matrices of individual rough interfaces and the layer propagation matrices. We have recently developed the single-surface scattering matrix obtained using the stabilized extended boundary condition method (SEBCM) providing both large validity range over the surface roughness and higher computational efficiency compared to fully numerical solutions. In the presence of a vertical dielectric profile, the aggregate scattering matrix of the profile is obtained from the model of stratified homogeneous layers. Results of this multilayer SEBCM model are validated with small perturbation method of up to third order and the method of moments. Additionally, the model is used to perform a sensitivity analysis of the scattering cross section with respect to perturbations in ground parameters such as subsurface layer separation, roughness of surface and subsurface layers, and moisture content of subsurface layers. The multilayer SEBCM model developed in this work presents a realistic and computationally feasible method for solving scattering from multilayer rough surfaces of realistic roughness, providing an accurate and efficient tool for future retrievals of soil moisture profiles.

Terrain topography is of great importance for vegetated areas given that even small slopes impact and alter the radar wave interactions between the ground and the overlying vegetation. Current missions generally exclude pixels with large topographic slopes or disregard the terrain topography entirely, potentially accumulating substantial modeling errors and therefore impacting the retrieval performance over such sloped pixels. A flexible and modular radar scattering model has been developed: it describes multispecies vegetation over an N-layered soil with rough interfaces and considers a two-dimensional slope. Simulation results show the impact of a two-dimensional slope for a range of tilt angles: a 3 degree tilt in the plane of incidence translates to a change of up to 6 dB in HH, 2 dB in VV and 1 dB in HV for the total radar backscatter. The terrain topography is shown to be crucial for accurate forward modeling, especially over forested areas.

We present an overview of the radar retrieval processing system for estimation of root zone soil moisture (RZSM) in several major North American biomes as one of the products of the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) project. The AirMOSS mission is briefly described along with the methodologies implemented to collect field data, to prepare several data layers required for retrievals, and to ultimately retrieve the soil moisture profiles. The retrieved soil moisture maps over several sites will be available when the radar data from AirMOSS flights are fully processed and calibrated, which is anticipated in early 2013.

The Airborne Observatory of Subcanopy and Subsurface (AirMOSS) is one of the five Earth Venture-1 missions selected in May 2010, and seeks to improve the estimates of the north American net ecosystem carbon exchange (NEE) through high-resolution observations of root zone soil moisture (RZSM). To obtain estimates of RZSM and assess its heterogeneities, AirMOSS will fly a P-band (430 MHz) synthetic aperture radar (SAR) over 2500 km2 areas within nine major biomes of north America. Retrieval of RZSM in the presence of substantial vegetation requires the construction of accurate radar scattering models that account for diverse vegetation conditions as well as subsurface inhomogeneities. In this paper we provide a summary of recent advances in this area, emphasizing several coherent and incoherent models of scattering from multilayered inhomogeneous rough surfaces, as well as strategies for using these forward models in retrieval algorithms.

In order to really accurately predict weather and near-term climate, it is necessary to take into consideration soil moisture in the top meter of soil: it governs moisture and energy fluxes at the land-atmosphere interface, and it plays a significant role in partitioning of the precipitation into runoff and infiltration. This 68-page report presents the observations of an experiment using remotely sensed microwave observations with a view towards incorporating the findings into the models used to estimate energy and moisture fluxes and improve root zone soil moisture estimates. Written by Tara Bongiovanni, Heather Enos, Alejandro Monsivais-Huertero, Blaire Colvin, Karthik Nagarajan, Jasmeet Judge, Pang-Wei Liu, Juan Fernandez-Diaz, Roger De Roo, Yuriy Goykhman, Xueyang Duan, Daniel Preston, Ramesh Shrestha, Clint Slatton, Mahta Moghaddam, and Anthony England, and published by the UF Department of Agricultural and Biological Engineering, August 2011. http://edis.ifas.ufl.edu/ae476

Several layered rough surface and random media scattering models recently developed are discussed, including analytical methods based on small perturbation method and the stabilized extended boundary condition method. It is also shown how some of these models are being used to retrieve subsurface properties from synthetic and experimental data. This is an overview paper on the above topics, with many of them described in more detail in other papers whose citations are provided here.

In this work, a 3D scattering model from layered arbitrarily random rough surfaces with embedded discrete random scatterers is constructed based on the scattering matrix approach. Scattering matrix of a single rough surface is found using the stabilized extended boundary condition method (SEBCM). Meanwhile, by finding the T-matrices of discrete scatterers using analytical or numerical methods, the random medium scattering solution is found based on the recursive T-matrix approach and near-to-far field transformed numerical plane wave expansion of the vector spherical harmonics. Solutions provided in this work include multiple scattering effects among the medium scatterers and between subsurfaces and sublayers. The high computational efficiency and accuracy of this method enable it to serve as a powerful tool for studying the role of vegetation roots and other sublayer inhomogeneities in retrieval of subsurface and root-zone soil moisture from radar measurements.

We present an overview of recent developments in subsurface image formation using iterative profile inversion and focusing using concepts of tomography and SAR signal processing. Electromagnetic forward and inverse scattering techniques are presented, along with the subsequent focusing techniques. Experimental and simulation results are presented.

The stabilized extended boundary condition method (SEBCM) is developed in this work based on the classical EBCM to solve 3D electromagnetic scattering from arbitrary random rough surfaces. The SEBCM gives accurate full wave solutions over large range of surface roughnesses, which are far beyond the validity range of analytical methods, and perform with much higher efficiency than numerical methods. In developing SEBCM, we explicitly impose test surfaces. We further propose a method for balancing and controlling the k-boundary. We validate the results with small slope approximation (SSA) and method of moments (MoM).

[1] A model of Venus' atmosphere permittivity profile up to 300 km is developed in this paper for X band. The model includes both the real and imaginary parts of the atmospheric permittivity, derived using data sets inferred or directly measured from past exploration missions to Venus: the real part is obtained by calculating the total polarization of the mixture of the atmospheric components including CO2, N2, H2O, SO2, H2SO4, CO, etc.; the imaginary part is derived using the superposition of the absorption of each component. The properties of the atmospheric components such as polarization and absorption are modeled with respect to frequency, temperature, and pressure. The validity of this model is verified by comparing simulation results with available measurements of Venus' atmosphere. This permittivity model is intended as a critical tool for the design of next-generation orbiting radar systems, in particular interferometric radars.

A solution to scattering from two-dimensional (2D) surfaces with arbitrary roughness based on the extended boundary condition method (EBCM) is presented. The bistatic scattering cross section (SCS) is obtained from the superposition of the upgoing Floquet modes. This method places no limitation on the roughness scale of the surface, and produces both co-pol and cross-pol components of fields and scattering cross sections. The method is validated for the small roughness regime by comparing the simulation results with an existing solution using the small perturbation method (SPM) for the co-pol components. Comparison of results shows very good agreement between these two methods in the validity domain of SPM. Further validations for rougher surfaces and for cross-pol components are currently under-way.