Full-wave simulations of the effective permittivity of firn aquifer and wet snow at L-band are reported. The Monte Carlo simulations are carried out for bicontinuous media embedded in a sphere, and the scattering cross section and absorption cross section are calculated. By averaging over realizations, the effective permittivity is extracted by comparing it with Mie solutions. The simulations are validated by using three numerical methods of 3-D solutions of Maxwell equations: finite difference frequency domain (FDFD), finite element method (FEM), and the discrete dipole approximation (DDA). Full-wave simulation results are compared with those from the classical Maxwell–Garnett and Polder–van Santen mixing formulas. The results show large differences from mixing formulas when there are large permittivity contrasts between the background medium and the scatterers, which are scenarios in aquifer and wet snow. The significance of these results is examined for the L-band microwave remote sensing of terrestrial wet snow and aquifer in polar regions.

In studying the mass balance of polar ice sheets, the fluctuation of the firn density near the surface is a major uncertainty. Temporal knowledge of firn densities are used to interpret elevation change measured by altimeters in terms of ice mass change. In this paper, we use microwave radiometer from 0.5GHz to 2Ghz and radar datasets to infer firn density fluctuations. We examine data collected from four sites in the accumulation zone of Greenland (including those that experience significant melt and refreeze events), the FA-13 site on the south east coast of Greenland where firn aquifers are present, and DOME-C in Antarctica where the firn is believed to experience minimal melt effects. The Community Firn Model is used as a reference for the four locations in Greenland. UWBRAD, SMOS, and SMAP brightness temperature data and Snow radar echograms are used in the analysis. A radiative transfer model is used to account for the effects of firn density fluctuation and refrozen layers observed in the radar echograms in the accumulation zone in Greenland. The density fluctuation is treated as a 3D variation accounting for both vertical and horizontal density changes. Results over the Greenland accumulation zone show that the dynamic range of brightness temperature is correlated with the number of peaks in the radar echograms. Forward modelling results show a consistency of the input density parameters with the Community Firn Model when a good match between modeled and measured TB is achieved, and forward modeled multi-angle results also are in good agreement with SMOS observations. SMAP data at the FA- 13 site is also shown to be interpretable using the forward model. This work provides a combined active and passive method for the remote sensing of firn densities.

The density profile of a polar ice sheet is an important parameter for the estimation of ice mass balance. Wave reflections caused by density variations are also a key uncertainty in the retrieval of ice sheet temperature profiles in Ultra-Wide band radiometry. In this paper, we examine different firn density profile models and analyze the subsurface reflections they cause using an analytical partially coherent approach. We also examine firn density profiles obtained from borehole measurements, from past UWBRAD modeling studies, from a community firn model, and from snow radar echo measurements. In previous studies, the ice sheet has been model as a 1D random medium with density variations in depth. However, horizontal density variations also exist, so that the ice sheet is a 3D random medium. Analyses using the partially coherent model show that in the presence of horizontal fluctuations, contributions from short scale variations vanish as the horizontal correlation length decreases due to the diffraction of waves.

In this paper, an Analytical Kirchhoff Solution (AKS) and Numerical Kirchhoff approach (NKA) are used to study coherent and incoherent land surface near specular scattering at L and P bands. The AKS model includes both coherent and incoherent waves, and includes the effects of topographic slopes and elevations. The land profile is modelled as a summation of three scales of surface roughness corresponding to “microwave”, “fine topography”, and “coarse topography”, where the microwave roughness and fine topography are treated as random processes while the coarse topography is deterministic. An airborne lidar survey performed over the San Luis Valley, CO is used to obtain surface roughness information for the simulation results of$\mathrm{P}$and L-band scattering. Results using the lidar surface data show that coherent reflection can dominate returns from a 5 km by 5 km area at P band, while incoherent scattering dominates L band returns in the same scenario.

Stratification in terrestrial snow is a key factor in the retrieval of snow water equivalence (SWE) due to the different snow volume fractions and particle sizes. In studying the layered structure of snow, radar tomography has been used and multiple ground based experiments are performed. The conventional back projection method has been used to construct the image based on radar measurements at different incident angles and frequencies. However, the conventional back projection method based on Born's approximation would show deformation in the final snow image. In this paper, we use the asymmetrical distorted Born's approximation to correct the deformation in the image.

A comparison of three different electromagnetic scattering models for land surface delay-Doppler maps (DDMs) obtained from global navigation satellite system reflectometry (GNSS-R) along a Cyclone Global Navigation Satellite System (CYGNSS) track in the San Luis Valley, Colorado, USA, is presented. The three models are the analytical Kirchhoff solutions (AKS), the Soil And VEgetation Reflection Simulator (SAVERS), and the improved geometrical optics with topography (IGOT). Common inputs to the three models were defined by using field samples of soil moisture and texture, soil surface roughness measurements, and a digital elevation model (DEM). The resulting peak reflectivity profiles of the models and the CYGNSS data all had a range of 10 dB along the selected track, mainly due to the influence of topography. The reflectivities obtained from all three models agreed with one another to within 2.4 dB along the full length of the track. The models also showed general agreement with the corresponding CYGNSS data, although the modeled profiles were higher than CYGNSS Science Data Record Version 3.1 by an average of 5 dB and also smoother. Additional characterization of fine-scale surface roughness is identified as an area for future work to improve model fidelity. An intercomparison of DDM structure for three selected acquisitions is also provided.

The snow water equivalent (SWE, a measurement of the amount of water contained in snow packs) is an important variable in earth systems. Microwave remote sensing provides a possible solution for estimating the SWE globally. To support radar SWE retrieval, the snow backscattering theory needs to be studied; the forward simulation model needs to be validated against natural snow observations. In this study, a one-winter experiment to observe the time series backscattering coefficient of snow-covered bare soil is reported. This is the first long time series snow-covered soil backscattering experiment that was measured by an imaging radar. The backscattering coefficient was observed at three frequencies covering the X-band and dual-Ku bands, which are of great interest to the snow remote sensing community and are used for SWE estimation in mountains. The calibration of the synthetic aperture radar (SAR) system was conducted manually and carefully to ensure high-quality radar observation data. The observations from our experiment show that in general, the time series backscattering signature of snow-covered terrain is mainly driven by soil freezing, snow grain size growth, and snow accumulation processes. The time series observations for dry snow are modeled by backscattering models with model inputs directly calculated from field measurements. Our simulation results indicate that the time series radar backscattering at three frequencies and four polarizations can be simulated with high accuracy, including the cross-polarization channels. This study provides some key understanding of the time series signature of radar backscattering from snow and provides some key implications for SWE retrieval from radar observations.

A comparison of three different electromagnetic scattering models for delay-Doppler maps (DDMs) of global navigation satellite system reflectometry (GNSS-R) from land is performed along a Cyclone Global Navigation Satellite System (CYGNSS) track over a validation site in the San Luis Valley, Colorado, USA. The peak reflectivity profiles of all three models and of the corresponding CYGNSS data are found to be in general agreement and are strongly influenced by topography. An intercomparison of DDM structure for one acquisition is also included. Efforts to refine the model results using a high resolution lidar survey are ongoing.

The Ultra-Wideband Software Defined Microwave Radiometer (UWBRAD) is a wideband radiometer operating from 0.5 to 2 GHz for remote sensing of polar ice sheet temperature profiles. Small-scale (cm to m) fluctuations in firn density in the upper portion of the ice sheet significantly impact observed brightness temperatures. Previously, a fully coherent model based on solving Maxwell’s equations for thousands of layers throughout the entire ice sheet was developed. Density profiles in the model are described as the sum of a smooth average density profile with a spatially correlated random process that represents density fluctuations. In this article, we develop a “partially coherent” implementation of the coherent model that captures the impact of variations in ice density on predicted brightness temperatures while improving computational efficiency. The partially coherent model divides the ice sheet into blocks. Within each block, the coherent model is applied to take into account coherence among the contributions of closely spaced layers. A Monte Carlo procedure is used to calculate the average block reflection and transmission parameters. Between adjacent blocks, interactions are assumed to be incoherent, and the radiative transfer theory is used to incoherently cascade block parameters. Results of the partially coherent model are in good agreement with the fully coherent model and also with Soil Moisture Ocean Salinity (SMOS) and UWBRAD brightness temperature observations.

A new technique for measurement of the resonant frequency and Q-factor of resonators is presented. In this technique, the derivative of the insertion phase with respect to frequency of resonators are measured and used for the calculation of their resonance frequency and Q-factor. A slow-rate chirp signal is passed through a resonator, and the output signal is amplified and equally divided into two signals which are delayed by different amounts. The two delayed signals are fed to a phase detector measuring their phase difference. The derivative of the insertion phase with respect to frequency of the resonator can be simply found from the phase difference between the two delayed signals. The proposed measurement technique is realized using low-cost components and utilized for measuring the resonant frequency and Q-factor of several L-band resonators. Compared with the resonators' performance measured by a vector network analyzer, the introduced approach measures the resonant frequency and Q factor by less than 0.6% and 4% error, respectively.

Recently, the Synthetic Aperture Radar(SAR) Tomography (TomoSAR) has been used in monitoring the snowpack from X-band to Ku-band. This technique provides unique access to the structure of the imaged scene, and in the case of snowpack, it enables the separation of multiple snow layers as well as the detection of and compensation for soil and vegetation layers. The addition of polarimetric capabilities brings in the ability to detect spatially varying shapes, sizes, and permittivities, to decompose the backscattered signal into volumetric and surface scattering components, and to distinguish between snow, soil, and vegetation. There are a few ground-based field experiments that demonstrate the focused image recover the layering structure of the snowpack with different densities. To better understand the measurement, this paper aims to provide physical-based forward modeling to reconstruct the TomoSAR images with realistic snow profiles. Without loss of generality, we perform the analysis on a two-layer snowpack.

In this paper, we study the scattering of land surfaces for the Global Navigation Satellite System Reflectometry (GNSS-R) land applications. Topography slopes are introduced to improve the physical patch model. The entire area within the footprint is divided into patches. Each patch is on a slope with elevation. Simulation results have shown that for small rms height, the received power to transmitted power ratio, Pr/Pt is smaller than the coherent model and the patch model with only elevation effects but greater than the incoherent model. The delay-doppler maps are also simulated based on the patch model.

The Global Navigation Satellite System Reflectometry (GNSS-R) for land applications have attracted considerable attention. Prior models include the coherent model and incoherent models. There are big differences between these two models. In this paper, we propose a patch model with NMM3D (Numerical Maxwell model of 3D simulations). The models take effects of multiple elevations of land surfaces into account. Results are compared with 1) coherent model, 2) incoherent model, and (3) numerical Kirchhoff simulator (KA simulator). Results of the patch model are consistent with those of KA simulator and have many dB difference with coherent and incoherent model.

In this study, a model investigation of a ground-based active and passive microwave experiment for snow and frozen soil is presented. The experiment is carried out from October 2017 to March 2018 in Xinjiang, China. Ground based SAR and microwave radiometers are used to measure the multiple frequency and multiple polarization backscattering coefficient and brightness temperature of snow covered soil. Microwave scattering and emission model of snow and soil are used to study the measurement results, and the microwave signature of snow and frozen soil are studied by model simulations, and this is the fundamental of snow parameter retrieval from active and passive microwave observations.