Soil surfaces often exhibit moisture stratification as a result of natural processes such as precipitation and vertical infiltration, which is however commonly neglected in traditional L-band soil scattering modeling and inversion works. Understanding how different moisture stratifications affect microwave observations is therefore of critical importance. Existing soil scattering simulation algorithms face challenges in accurately modeling layered soils, especially when large lateral soil extents and internal roughness characteristics within the medium are involved. To address these challenges, this paper introduces a generalized and accurate soil scattering modeling method based on a numerical solution to Maxwell’s equations in the volume-integral form (NMM3D-VIE). To efficiently treat large lateral domains, the soil is modeled as laterally periodic, and an effective truncation in depth is implemented through half-space Green’s functions. Within each periodic unit, inhomogeneous layered moisture are constructed to represent realistic near-surface layered soil conditions. The VIE is solved using the discrete dipole approximation, and its volumetric discretization enables the handling of arbitrary layered configurations, including internal roughness. The proposed method is first compared against the surface integral equation approach (SIE) and the advanced integral equation method (AIEM) across various single-layer soil conditions, demonstrating its accuracy and broad applicability. Furthermore, we present a novel investigation of the scattering properties of various layered soil structures to emphasize the layering effects in soil scattering observations, including the bistatic scattering coefficient in the incidence plane and in the top hemisphere, as well as the emissivity. The feasibility of equivalent single-layer strategies for representing the scattering behavior of realistic layered soils is also investigated. Additionally, the phase characteristics for single-layer and multi-layer soil structures are also investigated for the first time, with the proposed full-wave approach. This advanced model provides theoretical support and guidance for future research in complex soil scattering, layered soil approximation models, and inversion methodologies.

In microwave remote sensing of vegetated land surfaces, there are volume scattering from the vegetation and rough-surface scattering of the interface between the vegetation and the ground. However, the coupling of volume scattering and surface scattering and its impact on microwave emission have not been fully studied, particularly when multiple scattering effects are to be considered as in forested scenarios. Earlier treatment with the Kirchhoff approximation neglects the incoherent bistatic scattering components from the rough soil interface and thus overestimates the transmitted upward emission from the soil half space and underestimate the reflected upward emission from the downward-going intensity streams arising from the vegetation layer in non-specular directions. To address this issue, bistatic scattering coefficients are introduced into the boundary conditions and an interpolation-accelerated numerical iterative method is employed to solve the passive radiative transfer equation to rigorously couple the volume-surface scattering interactions at the vegetation/soil interface. In this paper, the rough-surface bistatic scattering is modeled using the advanced integral equation method (AIEM). The volume scattering model is derived from a radiative transfer based multiple scattering model that accounts for the vertical profile of the vegetation structure. The SMAPVEX12 forest dataset is utilized to validate the proposed model, encompassing L-band radiometric brightness temperature (TB) observations corresponding to extensive variations in soil moisture. Comparisons are made between the TBs simulated by the model with and without considering the incoherent bistatic scattering coefficients, under diverse vegetation water contents (VWCs) and varying soil roughness conditions. Notable features are observed in the angular pattern of the vegetated surface emission by fully accounting for the multiple scattering effects and the incoherent bistatic scattering effects of the rough soil. These features become more evident at smaller observation angles, lower VWCs, and greater soil roughness. The findings reveal that the model incorporating the bistatic scattering coefficient of rough surfaces exhibits improved agreement with the measured TBs. Furthermore, the proposed model is parameterized by matching the high-order solutions to the RT equation to the widely adopted albedo-tau formalism, i.e., the zero-order solution to the passive radiative transfer equation with a flat lower boundary. The resulting equivalent optical thickness and the equivalent scattering albedo incorporates the multiple scattering effects within the vegetation layer and they are solely associated with the geometries and the electromagnetic properties of the vegetation layer. Additionally, the effective reflectivity of the soil is proposed to characterize the scattering properties of rough surfaces and the scattering coupling between the rough surface and the vegetation layer. The new model developments will enhance the prediction and interpretation of vegetated land surface emission characteristics and thus improve the remote sensing of the vegetation and the underlying soil parameters.

Surface melting of polar ice sheets alters their energy-mass balance, leading to sea level rise and exacerbating climate feedback effects. This study examines P-to-L-band emissions signatures to variations in surface wet snow profiles at the DYE-3 site, Greenland, using a partially coherent model developed by the authors. L-band model predictions, combined with SMOS observations, are used to estimate coupled parameters such as liquid water content (LWC) and snow depth (dws). Initially, short-scale density fluctuations parameters are calibrated using both partially coherent and incoherent models against the Soil Moisture and Ocean Salinity (SMOS) satellite brightness temperatures for DYE-3 in dry seasons by minimizing root mean square error (RMSE). The partially coherent model, which showed better accuracy, is then parameterized across realistic ranges of liquid water content in snow and its depth from surface to predict average brightness temperatures (Tb). The DYE-3 melt days are identified from annual SMOS Tb data using the Leduc-Leballeur et al. (2020) algorithm, and RMSE analysis with the simulated responses indicates that multiple wet snow parameter sets are associated with single melting events. Additionally, ultra-wideband emissions from 0.5 to 2 GHz are analyzed to clarify the potential ambiguity of deriving wet snow parameters from Tb observations, revealing that wet snow profiles with higher moisture exhibit consistent frequency responses. The study also compares the frequency spectra from 0.5 to 2 GHz of the partially coherent model with an Radiative Transfer theory (RT)-based incoherent model, highlighting stronger coherent wave effects for moist-shallow (3%, 0.5 m) surface snow compared to the damp-deep (1%, 8 m) conditions. This research extends the use of the partially coherent model to examine how low frequency microwave emissions are affected by thermal and density changes at ice sheet depth during surface melting. The findings indicate that these variations in ice sheet properties distinctly influence microwave emissions signatures during surface melt events. This work develops a rigorous model to support the retrieval of ice sheet and near surface wet snow parameters using low frequency passive microwave observations.

Retrieving key climate variables such as soil moisture and snow water equivalent from remote sensing data requires representative physical models. Up to date, there is no integrated remote sensing computing platform dedicated to modeling brightness temperature, backscatters, and relevant parameters based on microwave electromagnetic scattering mechanisms for complex soil, vegetation, and snow scenarios. In this paper, the Remote Sensing Hub (RSHub), a shared cloud computing platform is introduced to close the gap. The platform integrates multiple physical scattering models into a unified framework that supports soil/vegetation/snow scenarios, offering options for radiative transfer and full wave approaches. We demonstrate the use of the RSHub to predict brightness temperatures corresponding to vegetated land surface scenarios.

The radiative transfer (RT) theory has been widely utilized for wave propagation in random media, but it faces challenges in situations involving strong forward scattering, such as in forests with electrically large trunks, due to the singularity of the scattering phase matrix. In this article, we present an effective approach to compute multiple scattering solutions to RT equations with a singular phase matrix by combining the strategy of forward scattering extraction with an efficient numerical iterative procedure through interpolation. We evaluate the effectiveness and efficiency of our technique through simulations using a layer of vertically oriented, electrically large long cylinders to represent a layer of trunks over the ground. The results demonstrate that the proposed approach increases the computational efficiency by one to two orders of magnitude in cases where forward scattering is dominant. Additionally, a parameterized model is derived by matching the higher-order RT results with the$\omega -\tau $formalism under catered conditions. An explicit physical definition of the equivalent scattering albedo and equivalent optical thickness is proposed under boundary-free conditions. The multiple scattering effects are included in the physically derived equivalent parameters of the plant layer, which are independent of ground conditions by definition. Tests verify that the applicability of the parameterized model with$\omega -\tau $form can be extended to a wider range of vegetation and ground conditions. Besides, these equivalent parameters are directly linked to the geometric structures and electromagnetic properties of the vegetation layer, allowing their values to be frequency- and angle-dependent. Compared to the single-scattering albedo and optical thickness, the effective albedo derived from the RT model exhibits relatively weak polarization and angle dependence. This is consistent with many empirically derived parameterizations while providing a physically plausible origin for these equivalent parameters. Remarkably, we find that the transmittance linked to the parameterized tau value, incorporating multiple scattering effects, is similar to that obtained through full-wave simulations that account for coherent wave interactions in the trunk layer. This work is of interest to remote-sensing practitioners both in vegetation scattering modeling and in vegetated land surface parameter retrieval.

A multiple scattering model for passive radiative transfer (RT) in vegetation that accounts for the vertical profile of the plant structure is developed, offering advancements over the commonly used single-layer uniform scattering models prevalent in the vegetated land surface microwave remote sensing. The proposed model takes into account the complexities of the canopy morphology with vertical heterogeneity, enabling the representation of overlapping vegetation species applicable to diverse plant types and growth stages. Additionally, it serves as a valuable tool for understanding the influence of the vegetation vertical structure on the microwave brightness temperatures. The model is constructed based on high-order solutions to the RT equations, obtained through a numerical iterative approach with an efficient interpolation scheme for algorithm acceleration. This methodology facilitates the accurate distinction of the contributions to the brightness temperature from each scattering order and scattering mechanism, ensuring a comprehensive consideration of multiple scattering effects within various vegetated scenarios. The model is validated using the SMAPVEX12 L-band forest dataset, encompassing a wide range of soil moisture variations. Comparisons are made between the brightness temperatures simulated by the newly developed multiple-scattering model with a continuous profile or layered profile and those obtained from a uniform single-layer model. Results demonstrate significant improvements in the multilayered or the continuously profiled model, showing improved agreement with the measured brightness temperatures. Furthermore, the proposed model is parameterized by matching the high-order solutions to the RT equation to the widely adopted reduced order albedo-tau formalism. The resulting equivalent parameters are linked to the geometries and the electromagnetic properties of the vegetation layer, while also incorporating the effects of multiple scattering. Comparative analysis of the equivalent parameters derived from the layered model and those derived from the single-layer model reveals that the vertical heterogeneity of the vegetation structure has a notable influence on the effective scattering albedo and it yields a value more consistent with the albedo as chosen in the SMAP/SMOS inversion algorithms. Meanwhile, the impact of the vegetation vertical profile on the effective optical thickness and the effective transmissivity of the vegetation layer is weak. These insights are essential for the retrieval of soil moisture and vegetation characteristics including the plant vertical structures in microwave remote sensing.

This paper presents the efficient systematic methods for modeling and analysis of spike signal sequence in crossbar arrays for neuromorphic computing chips. A novel spike signal sequence is proposed, where the ideal spike sequence with only spike time information in the original spiking neural network (SNN) algorithm is mapped onto actual spike waveform by stitching neighboring sequential spikes together with certain overlaps. We thoroughly investigate and analyze the performance of the input encoding as well as the implementation of spike timing dependent plasticity (STDP)-based SNN on memristor crossbar arrays with the proposed spike signal sequence. A detailed circuit model of a crossbar array, consisting of resistance, capacitance and inductance derived by the partial equivalent element circuit (PEEC) method, is created to simulate the training process of SNN. The proposed spike signal sequence is demonstrated that is able to achieve accurate input encoding as well as high recognition accuracy when it is used to perform the classification task on MNIST handwritten digits. The spike signal sequence is further analyzed and assessed in terms of the main factors affecting its encoding accuracy and the parasitic effects of crossbar arrays on its robustness.

The vertical distribution of soil properties is crucial in accurately representing various hydrological and ecological processes such as freeze-thaw cycles and diurnal variations. In this paper, considering the complexity of the multi-parameter features of layered soil, we evaluate the potential to retrieve the vertical distribution of the moisture and temperature of soil using multi-channel passive microwave observations. To enhance the inversion efficiency and accuracy, a novel Physics-Embedded Artificial Neural Network (P-ANN) inversion algorithm combining multi-angle (30 to 50 degree), multi-frequency (L-, C-, and X-band), and multi-polarization (horizontal and vertical polarization) passive observations is proposed. In this approach, the multi-channel physical brightness temperature simulations corresponding to the predicted soil state parameters are integrated into the loss function of a standard fully connected feed-forward neural network, enabling efficient convergence with limited sampling data in the training process. Testing results exhibit that the inversion performance of P-ANN is superior to that of conventional neural network approaches which only adopts errors in soil states in the loss function to train the network. Test also shows the proposed P-ANN approach outperforms traditional optimization algorithms in dealing with layered soil retrieval. In order to further improve the retrieval accuracy, an advanced local optimization scheme is also proposed, where the output from P-ANN is further treated as the initial value to a local optimization algorithm, achieving even closer results to the ground truths without excessive computational costs. In addition, to estimate the reliability of the model predictions, this paper also establishes, in the testing process, a statistical relationship between the soil inversion error and the error of the corresponding brightness temperatures. When the trained neural network is in operation, the error of brightness temperature is calculated through the physical model, and the reliability of retrieval soil results is then acquired by putting the calculated brightness temperature errors into the pre-established statistical relationship. The proposed concepts and approaches have demonstrated the feasibility of using P-ANN model with multidimensional observations to invert the multi-variable layered soil structures. The proposed approach holds great potential for various remote sensing applications as well as solving a wide range of inverse problem challenges.

The radiative transfer equation (RTE) has been primarily adopted over the years for wave propagation in random media, but in a strongly forward scattering environments, existing approaches to solve the RTE encounter difficulties due to the singularity in the scattering phase matrix. In this paper, we propose an effective method to solve RTE with strongly forward scattering phase matrices. For the case of vegetated land surfaces with electrically large cylindrical structures, we study the applicability of the singularity extracted RTE. The comparison of transmission coefficients between the singularity extracted RTE and full wave simulations shows that our approach is effective and efficient. Besides, this formulation also provides the physical origin for the parameterization of the widely applied W-T models.

Microwave remote sensing is effective in monitoring snow distribution over large areas. The dense media radiative transfer model provides theoretical basis for deriving snow information through its scattering to electromagnetic waves. The microwave emission model of layered snowpacks (MEMLS) and the dense media radiative transfer model with bicontinuous media approximation of snow (DMRT-Bicontinuous media) are two widely adopted models. Both models assume a random media representation of snow. In this paper, the scattering properties of both models are compared and analyzed to provide guidance in model selection. Sensitivity of the bicontinuous media - discrete dipole approximation (DDA) to its numerical parameters is also discussed to improve usability of the model.

Although ice sheet internal temperature is a first-order control on glacier dynamics, relatively few in situ borehole temperature profiles exist. The ultra-wideband software-defined microwave radiometer (UWBRAD) was designed to estimate internal ice sheet temperature (Ti) by measuring microwave brightness temperatures (Tb) from 0.5 GHz to 2 GHz. The retrieval ofTifromTbis not straightforward, however, due in part to the complicating effects of ice density fluctuations onTb. In this paper, we report a simulation study to assess the feasibility of realizing three science goals: the retrieval of a)Tiat 10 m depth to within 1 K; b) vertically-averagedTito within 1 K; and c) the verticalTiprofile to within 1 K RMSE. Two analyses along the Greenland ice divide are presented. First, we assess the ideal UWBRADTiretrieval precision via the Cramér-Rao Lower Bound (CRLB). Second, we perform a “Virtual Experiment” (VE) using synthetic UWBRAD observations. Both the CRLB and VE analyses indicate that the science goals are achievable with the caveats that ice thickness and UWBRADTbprecision impact performance. Assuming a UWBRADTbprecision of 0.5 K, and for places where ice sheet thickness is less than 3 km, all science goals can be achieved. The results of the study provide a strong indication of the potential of UWBRAD to provide valuable Greenland ice temperature profile information to the scientific community.

In this article, a unified framework of vegetation scattering using radiative transfer (RT) theory for passive and active remote sensing of vegetated land surfaces, especially those associated with moderate-to-large vegetation water contents (VWCs), e.g., forest field, is presented. The framework allows for modeling passive and active microwave signatures of the vegetated field with the same physical parameters describing the vegetation structure. RT equations are solved by a numerical iterative approach for both passive and active configurations. This approach allows including higher order scattering, which represents multiple scattering. In fields such as forests with large VWCs, associated with large scattering albedo and optical thickness, multiple scattering effects are critical. In the active iterative approach, cyclical terms are identified and backscattering enhancement is included by doubling contributions from cyclical terms. The method is applied to aspen trees in forest fields to compute the brightness temperatures and backscattering coefficients for passive and active remote sensing configurations, respectively. In the passive configuration, for forest field with VWC of 15 kg/$\text{m}^{2}$, the deviation between the zeroth-order brightness temperature, i.e., the tau–omega model results, and multiple scattering results around 40° observation angle, can be as large as 50 K for vertical polarization and 35 K for horizontal polarization. In the active configuration, the deviation between first-order results, which is identical to the distorted Born approximation, and the multiple scattering results around 40° incidence angle, is about 1.6 dB for VV and 0.7 dB for HH polarization. Multiple scattering is shown to be crucial for accurate forward modeling, especially over forested areas. The proposed approach is thus suitable for vegetation scattering with large VWCs. Furthermore, the proposed model is validated with the passive and active L-band sensor (PALS) acquired in SMAPVEX12 measurements in 2012, which demonstrates the applicability of this model.

Ice sheet subsurface temperature is important for understanding glacier dynamics, yet existing methods to obtain the temperature of the ice sheet column are limited toin situsources at present. The ultrawideband software-defined microwave radiometer (UWBRAD) has been developed to investigate the remote sensing of ice sheet internal temperatures. UWBRAD measures brightness temperature spectra from 0.5 to 2 GHz using 12 subchannels and employs a sophisticated algorithm for detection and mitigation of radio frequency interference (RFI). The instrument was deployed during a flight over northwestern Greenland in September 2017 and acquired the first wideband low-frequency brightness temperature spectra over the ice sheet and coastal regions. The results reveal strong spatial and spectral variations that correlate well with internal ice sheet temperature information. In this article, the section of the flight path ranging from the Camp Century to NEEM to NGRIP boreholes is used for subsurface temperature estimation. A “partially coherent” forward model is applied along with a Robin model for the temperature profile and a two-scale model of ice sheet density variations to describe measured brightness temperatures. Using this model, vertical temperature profiles are retrieved along the flight path using a sequential Bayesian estimator; borehole measurements at the three campsites are used to obtain Bayesian priors. The retrieved temperature profiles show reasonable behaviors and demonstrate the potential of ultrawideband microwave radiometry for remotely sensing internal ice sheet temperatures.

Retrieving snow water equivalent (SWE) from X-, Ku-, and Ka-band microwave observations suffers from low sensitivity and non-uniqueness due to a lack of understanding of snow microphysics and complex terrain covered by snowpack. This paper demonstrates a general framework to combine the power of hydrology modeling and microwave remote sensing. A column-based multi-layer snow hydrology model which includes the grain size evolution is coupled with the dense media radiative transfer (DMRT-QMS). The snow variables are then updated by an ensemble Kalman Filter (EnKF) algorithm to incorporate information from microwave observations. The proposed approach has the potential to improve the accuracy of SWE remote sensing taking advantage of multi-source data fusion in a data assimilation framework. An SWE retrieval (per 4 hours) RMSE of 25.81mm is achieved, which meets the international standard such as NASA SCLP and ESA CoReH2O and is 62.25% lower than that of open-loop hydrology model prediction. This paper also makes a sensitivity analysis of the microwave observation interval to the retrieval results, offering insights into the choice of temporal resolution in microwave remote sensing.

This article presents a novel circuit modeling method for online training and testing process of the neuromorphic chip crossbar array based on the resistive random access memory (RRAM). A modified RRAM compact model is developed to realize the fast and accurate update of multiple conductance levels. Two training mechanisms with and without write-verify scheme are modeled and investigated for classifying MNIST handwritten digits and both achieve a good recognition accuracy of more than 96%. The parasitic model of the unit cell of interconnects is constructed by the domain decomposition method (DDM) and the partial equivalent element circuit (PEEC) method, which is suitable to build up a crossbar array of any size. The impact of parasitic effects of interconnects on the recognition accuracy with and without write-verify scheme is analyzed and compared. The weights trained with write-verify scheme show better robustness to parasitic noises but training with write-verify scheme spends a longer time processing the same amount of data.

The effects of sea surface temperature (SST) on ocean radar backscattering are investigated under both the neutral and nonneutral atmospheric conditions for the applications of wind retrieval. The impact factors are parameterized as functions of SST. The SST effects on the variations in ocean scattering and wind retrieval are evaluated using an analytic model which combines the KHCC03 spectrum and the second-order small slope approximation (SSA-II) model. Under the neutral condition, we present the following new insights at three commonly used bands: 1) the seawater permittivity accounts for a dominant effect of SST at the L-band. The SST effects induce a wind underestimation of 0.3 m/s over cold seawater and a wind overestimation of 0.24 m/s over warm seawater at the L-band and a wind speed of 8 m/s. The seawater viscosity plays a significant role in the SST effects on ocean scattering at the C- and Ku-bands, while its variation induced by SST has insignificant effects on L-band scattering; 2) for the C-band, the SST-induced wind retrieval error can be neglected at a medium wind speed due to the neutralization of the effects of various factors on surface roughness. Yet, the SST effects are not negligible at low and high wind speeds; and 3) both the dielectric and dynamic factors play significant roles in the SST effects on ocean scattering at the Ku-band. Under the nonneutral condition, the simulation results show that the air–sea interaction governs the SST effects on ocean scattering and wind velocity variations. Other than the air–sea interaction, the wind retrieval errors induced by other SST-related factors are negligible at the L- and C-bands.

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.

We employ the second-order small slope approximation (SSA-II) and the method of moment (MoM) to investigate the roughness scale effect on ocean radar scattering in both three- (3-D) and two-dimensional (2-D) cases. Various roughness scales of the ocean surface are represented by truncating the Kudryavtsev wave spectrum. Criteria of full spectrum truncation are proposed for the numerical simulations of ocean scattering. Numerical results are illustrated in fully bistatic configuration at L- and C- bands. It is found that short waves with wavenumber larger than 316 rad/m have little effects on ocean scattering. The large-scale waves put more effects on scattering in the forward directions, particularly for large incidence angles. For numerical simulations of ocean scattering with incidence angle less than 60°, using small surface profiles with size about 1/6 of those accounting for full spectrum yields result with errors less than 2dB.

A new remote sensing approach is developed to estimate soil moisture vertical profile utilizing the Global Navigational Satellite System (GNSS) signal of opportunity. The direct GNSS signal and its reflected counterpart from the air/soil interface interfere with each other, and such multi-path interference generates unique features in the angular pattern of the observed signal to noise ratio (SNR). The SNR angular patterns are sensitive to the variation of the near-surface soil moisture vertical profile and the height of the antenna phase center above the air/soil interface. In this paper, we developed a rigorous mathematical and physical basis to predict the signal received by a GNSS antenna placed above ground at a certain height. The vertical profile of soil moisture is parameterized with three parameters based on the physical solution to the Richards' equation for unsaturated flow in soils. The Fresnel reflection coefficients from the soil with moisture profiles are derived from Maxwell's equations on flat multi-layered media. The Mironov soil permittivity model is used to link the soil permittivity at L-band to its moisture content and clay fraction. The polarization coupling of the GNSS antenna is carefully incorporated in the interference model by characterizing the antenna with both the gain pattern and the phase pattern for both the right-hand circular-polarized (RHCP) and the left-hand circular polarized (LHCP) signals. Besides the rigorous forward physical model, a least-mean-square-error (LMSE) based retrieval algorithm is developed to retrieve the soil moisture profile by matching the received GNSS SNR angular patterns with model predictions. Both synthesized data and measured data are used to test the retrieval algorithm performance.

The roughness scale effects on ocean radar scattering are studied using the second-order small slope approximation (SSA-II) and the method of moments (MoM). The KHCC03 spectrum is employed to represent 2-D and 1-D sea surfaces in the above two scattering methods, respectively. Criteria of full spectrum truncation are proposed for the numerical simulations of ocean scattering. Numerical results are illustrated in fully bistatic configuration at L- and C-bands. It is found that scattering at higher frequency is relatively more sensitive to the small-scale roughness but less sensitive to the large-scale roughness. At L- and C-bands, short waves with wavenumber larger than 316 rad/m have little effect on ocean scattering. The large-scale waves put more impacts on scattering in the forward directions, especially for large incidence angles. Other than the specular direction, the effects of large-scale roughness on ocean scattering are in general smaller at VV-pol than HH-pol. The bistatic scattering at cross polarizations is less sensitive to the roughness scale as compared to the copolarizations. For numerical simulations of ocean scattering with incidence angle less than 60°, using small surface profiles with size about 1/6 of those accounting for full spectrum yields results with errors less than 2 dB. Results also indicate that the incoherent parts dominate the scattered power from ocean surfaces with large-scale roughness.

Arctic and Antarctic sea ice covers are in a sharp contrast in terms of characteristics, distributions, and processes with a drastic decrease in the Arctic versus the opposite increase in the Antarctic in a changing climate. In quantifying polar sea ice differences to address the contrasted sea ice behaviors, two key parameters are sea ice thickness and melt pond fraction, which remain challenging to measure extensively in time and in space with a sustainable approach. Here, we present a new paradigm for such measurements using bistatic radar reflectometry, thanks to developments of low-cost receivers to acquire reflected signals from numerous existing transmitter systems operated at multiple frequencies to be replenished and sustained indefinitely into the future. For sea ice thickness measurement to determine ice volume, reflected signals likely come from the bottom ice-water interface avoiding large errors inherent in current altimetry techniques due to uncertainty in free-board height and snow cover. Regarding melt pond faction on sea ice to estimate albedo and insolation, the bistatic reflection can be dominated by melt pond water with permittivity that is one order of magnitude larger compared to that of snow or ice. These are examined by a combination of numerical Kirchhoff (KA) simulator and Numerical Maxwell Model of 3D simulations (NMM3D) to preserve phase and amplitude information and thereby account for both coherent and incoherent effects. Physical insights from the rigorous theory for bistatic radar reflectometry will be valuable to develop future satellite missions to resolve cryospheric science issues concerning the polar sea ice differences.

The concept of wideband autocorrelation radiometry has recently been proposed and applied for the remote sensing of snow and lake ice. Such instruments measure the microwave emission from a scene of snow and ice over a wide and low frequency band where volume scattering within the snow/ice layer is negligible. Experiments have demonstrated that such wideband brightness temperature spectra can show oscillatory features. These features arise from coherent interference among the direct upward emission and its replicas from multiple reflections, are related to the layer thickness of snow or ice, and can be affected by interface roughness or any above snow vegetation canopy. The latter is therefore an important factor affecting the application of wideband autocorrelation radiometry in terrestrial snow remote sensing. In this paper, we analyze the effects of an above snow vegetation layer on brightness temperature spectra, particularly the possible decay of wave coherence arising from volume scattering in the vegetation canopy. In our analysis, the snow layer is assumed to be flat, and its upward emission and surface reflectivities are modeled by a fully coherent model, while the volume scattering from the vegetation layer is described by an incoherent radiative transfer model. The solution to the radiative transfer equation is obtained through an interative approach accounting for multiple scattering effects. The angular and polarization coupling arising from volume scattering and the emission contributed by the vegetation layer all cause smoothing of oscillatory patterns in the observed brightness temperature spectra.

An ultrawideband radiometer was used to measure microwave brightness temperature spectra over Arctic sea ice in the Lincoln Sea near the north coast of Greenland. Spectra over the range of 0.5-2 GHz were compared to thermal infrared images collected during the airborne campaign and also compared to nearly concurrent Sentinel-1 C-band synthetic aperture radar (SAR) data. Based on those comparisons, spectral signatures were associated with thick multiyear ice and thin ice. A radiative transfer (RT) model consisting of a homogeneous slab of sea ice bounded by sea water and air was then used to invert the spectra for sea ice thickness and salinity. Inferred thicknesses were consistent with ice thickness climatology for ice floes in the Lincoln Sea. Salinities are higher than expected which may be a consequence of neglecting surface and volume scattering contributions in the models.

There are multiple existing microwave radiative transfer models (RTMs) to simulate the brightness temperature (Tb) of snowpacks. It is still challenging to have consistent Tb responses from RTMs due to individual physical formulations of the snowpack scattering process. This article examines three of the widely-used multi-layer RTMs: 1) the microwave emission model of layered snowpacks (MEMLS); 2) the dense media radiative transfer based on the quasi-crystalline approximation (QCA) of Mie scattering of densely packed sticky spheres (DMRT-QMS); and 3) the Helsinki University of Technology (HUT) model. Interestingly, these models yield slightly different Tb responses when driven by the same physical snowpack properties. Tb variations, dependent on the choice of RTMs, are then evaluated to improve the understanding of model differences in microwave emission from a snowpack. We first perform a sensitivity study of the Tb predictions from the three RTMs as a function of snow grain sizes, densities, and depths. While Tb from all three RTMs decreases with increasing snow grain sizes, it is found that a scaling factor is required to have the same amount of Tb attenuation for small grain sizes within the Rayleigh scattering regime. For larger grain sizes, however, a scaling coefficient is not enough to match the model outputs due to the different scattering assumptions of the RTMs. For a single snow layer with increasing snow depths and densities, all three RTMs exhibit Tb attenuations arising from the increase in path lengths and optical depths. Further evaluations are conducted by feeding the three RTMs with the output of a snow physics model driven by in situ weather forcing in a coupled simulation. Outputs of this coupled model include snowpack physical properties and Tbs. By using snow stratigraphy observations, another set of Tb simulation is also conducted with RTMs driven by in situ snowpit observations. The snow physics outputs from the coupled case are compared against in situ snow stratigraphy observations. And both Tb simulations are compared against ground-based microwave observations from the European Space Agency (ESA) Nordic Snow Radar Experiment (NoSREx) 2009-2012. For three consecutive years, the in situ driven Tbs have 21.0-K root-mean-squared error (RMSE) while the coupled simulations have 24.7-K RMSE. However, after isolating the dry snow period and excluding diurnal melting snow conditions, 12.2- and 6.3-K RMSEs are achieved from in situ and coupled cases, respectively, in the 2011 water year.

The Ultra-Wideband Software Defined Microwave Radiometer (UWBRAD) measures scene brightness temperatures from 0.5-2 GHz. UWBRAD was deployed in a September 2017 airborne campaign in Greenland, and observed brightness temperatures of the ice sheet as well as sea ice, the ocean surface, and land regions during the transit to and from Calgary, Canada (the aircraft base of operations). This presentation will review the campaign and datasets collected. Spectral features of thermal emissions from the ice sheet and other geophysical regions are also examined to obtain insight into the utility of 0.5-2 GHz thermal emission measurements for remote sensing applications.

We apply the analytical fully coherent model to bicontinuous media for applications in microwave remote sensing of snow cover. In our model, snow is represented by bicontinuous media which is generated by a Gaussian random process. The statistical moments and correlation functions of bicontinuous media can be calculated. With the correlation functions, we apply the strong permittivity fluctuation (SPF) theory to derive the analytical solutions for calculation of scattering properties and effective permittivity of bicontinuous meida. The SPF theory is under the bilocal approximation. Effective permittivity and extinction coefficient from the analytical solutions are compared with those of the numerical solution of Maxwell's equation in 3D (NMM3D). The real part of effective permittivity of SPF is also compared with solutions of Maxwell-Garnett formula.

An ultra-wideband radiometer has been developed to measure subsurface properties of the cryosphere including ice sheets and sea ice. The radiometer measures brightness temperature spectra from 0.5 to 2 GHz using 12 channels, each of which measures scene brightness temperatures over an ~88-MHz bandwidth resolved into 0.24-MHz intervals. The instrument was flown over northwestern Greenland in September 2016 and acquired the first, wideband, low-frequency brightness temperature spectra over the ice sheet and coastal region. The results reveal strong spatial and spectral variations that correlate well with the physical properties of the surface encountered along the flight path, which started over ocean, then passed the rock near the coast, and then up onto the ablation, wet, percolation, and dry snow zones of the interior ice sheet. In particular, strong spectral responses in percolation and dry snow zones are observed and plausibly explained by varying the distribution of horizontal density layers and isolated icy bodies in the upper portion of the firn. The success of the airborne deployment of the instrument and subsequent implementation of algorithms to limit radio frequency interference in unprotected bands is motivating continued airborne investigations as well as stimulating research into the feasibility of a spaceborne instrument.

In this paper, we develop a radar snow water equivalent (SWE) retrieval algorithm based on a parameterized forward model of bicontinuous dense media radiative transfer (Bic-DMRT). The algorithm is based on retrieving the absorption loss of the snowpack which is directly proportional to the SWE. In the algorithm, Bic-DMRT is first applied to generate a lookup table (LUT) of snowpack backscattering at X- and Ku-band. Regression training is applied to the LUT to transform the dual-frequency backscatter into functions of two parameters: the scattering albedo at X-band and SWE. The background scattering is subtracted from the SnowSAR data to give the volume scattering of snow. Classification of SnowSAR data is applied to provide a priori information. Based on the obtained volume scattering and the priori information, a cost function is established to find SWE. Performance of the retrieval algorithm was tested using three sets of airborne SnowSAR data acquired over mixed areas in Finland and open tundra landscape in Canada. It is shown that the retrieval algorithm has a root-mean-square error below 30 mm of SWE and a correlation coefficient above 0.64.

The Ultra-Wideband Microwave Radiometer is a novel pseudo-correlation radiometer design measuring scene brightness temperatures from 0.5-2 GHz created under NASA's Instrument Incubator Program. This document analyzes the design and operation of the radiometer, the accuracy and stability of the brightness temperatures it produces, and presents initial results from a field campaign conducted in Greenland in September 2016.

A fully coherent snowpack scattering and emission model is developed by numerically solving Maxwell's equations over the entire snowpack on a bottom half-space. The scattering matrix of the snowpack is directly obtained including both amplitude and phase. Both bistatic scattering coefficients and brightness temperatures of the snowpack are derived from full wave simulations. Simulation results demonstrate backscattering enhancement effects and coherent thin layer effects. The model is applied to study microwave signatures of the Arctic sea ice where the snow cover thickness has rapidly decreased. Microwave signatures are important in classification of sea-ice types and in quantitative characterization of snow cover properties. Both have strong impacts on the thermodynamics of sea ice. In the fully coherent model, a half-space dyadic Green's function is used in the volume integral equation to represent the effects of the underlying sea ice. Discrete dipole approximation is used to solve the volume integral equations, where parallel fast Fourier transform technique is utilized to accelerate the matrix-vector multiplications. The snowpack is represented as a bicontinuous medium. Periodic boundary conditions are applied in the two horizontal dimensions to simulate an infinite lateral extent of the snowpack.

We have been engaged in Numerical Solutions of Maxwell equations (NMM3D) for more than fifteen years [1-2]. In this paper, we report on the recent progress of 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. We describe the numerical methodologies and the simulation results. Comparisons are also made with experimental measurements.

We validate an absorption based radar retrieval algorithm of snow water equivalent (SWE) using X- and Ku-band backscatter with airborne SAR data. The bicontinuous dense media radiative transfer (Bic-DMRT) model is first applied to generate a look-up table of snow properties against backscattering at X- and Ku-bands. In the retrieval algorithm, the background scattering is subtracted from the total scattering giving the volume scattering of snow. With the look-up table, we generate regression equations between multiple and single scattering and correlations between the scattering albedo and optical thickness at the two bands. With these relationships and the volume scattering of the snowpack, the best solution for the radar observation is found using a priori constrained least-squares cost function. Next, the absorption loss of the snowpack is derived from the solution, which is directly proportional to the SWE. We have applied the algorithm to airborne SAR observations from Finland and Canada. The retrieval algorithm is shown to be effective, achieving root mean square error (RMSE) of ~19 mm for both SnowSAR data, which is smaller than the 20mm RMSE requirement of SCLP.

The second-order small perturbation method is applied to investigate brightness temperature corrections caused by the rough interfaces of a two-layer medium. The spectral weighting functions of the two rough interfaces are extracted from the solution, and their properties examined. It is found that the functions are identical for the two interfaces as the spectral variable approaches zero, indicating an identical weighting of the surface height variance on each interface and an additive effect on the brightness temperature at nadir. Sample results for some realistic scenarios show that surface roughness in a two-layer medium can increase or decrease the observed brightness temperature at shallower angles, and in the case of a wideband measurement, can shift the interference pattern in frequency.

The Ultra-wideband Software Defined Radiometer (UWBRAD) for ice sheet internal temperature sensing is designed to provide observations of ice sheet brightness temperatures from 500-2000 MHz. This presentation reports on current status of the instrument development, experimental results obtained to date, and plans for a September 2016 airborne deployment over Greenland.

We apply computer generation of anisotropic bicontinuous media with different vertical and horizontal correlation functions. We then use NMM3D (Numerical solutions of Maxwell equations in 3-Dimensions) to calculate the uniaxial effective permittivities and the effective propagation constants of V and H polarizations. The co-polarization phase differences (CPD) between VV and HH backscattered signal are derived. The CPD has recently been applied to the retrieval of snow water equivalent (SWE) and snow depth. The NMM3D simulation results are also compared with the results from that of the strong permittivity fluctuations (SPF) in the low frequency limit.

Snowpack consists of ice grains that are densely packed in the wavelength scale at microwave frequencies so that the coherent microwave interactions among the ice grains are important in microwave signatures. We have used Numerical Maxwell Model of 3D simulations (NMM3D) of random media / discrete scatterer to study such interactions. In the partial coherent model of Dense Media Radiative Transfer (DMRT), we use NMM3D to calculate the effective propagation constants, the extinction coefficients and the phase matrices. These are then used in radiative transfer equations to calculate the emission and backscattering signatures. In the fully coherent model, we use NMM3D to calculate the bistatic scattering and emissivity for a layer of snow pack over the ground. Using the fully coherent approach, we calculate the complex scattering amplitudes from the snowpack, including both magnitude and phase. In microstructure characterization of snow, we have used 2 models a) densely packed scatters of sticky particles or multiple sizes, and b) computer generated bicontinuous media. Both models can be characterized by correlation functions. In this paper, we also describe the recent simulated results for tomography and co-polarization phase differences of anisotropic dense media.

A partially coherent low frequency microwave emission model for polar ice sheet is developed to operate from 0.5GHz to 2.0GHz predicting brightness temperatures. The emission from polar ice sheet over the wide frequency band is shown to be correlated with its temperature profile and affected by its density fluctuations. The density fluctuations creating weakly reflective internal interfaces cause the decay of wave coherence so that the ice sheet can be divided into blocks. The coherent wave interaction are accounted for within the block by full wave simulations while inter-block wave interaction are taken incoherently by cascading boundary conditions in radiative transfer. The layer thickness / correlation length of the density fluctuation cause distinct frequency spectrum of the brightness temperature. The air/ snow interface and intermediate snow layer interfaces are rough causing angular coupling and polarization coupling in microwave emissions, and affect the angular patterns of the brightness temperature.. We apply the small perturbation method to study the roughness effects of multiple interfaces. Results of vertical and horizontal emissivities are illustrated as a function of observation angles.

In this letter, we generate anisotropic bicontinuous media with different vertical and horizontal correlation functions. With the computer-generated bicontinuous medium, we then use numerical solutions of Maxwell equations in 3-dimensions (NMM3D) to calculate the anisotropic effective permittivities and the effective propagation constants of V and H polarizations. The copolarization phase difference (CPD) of VV and HH is then derived. The CPDs have recently been applied to the retrieval of snow water equivalent, snow depth, and anisotropy. The NMM3D simulation results are also compared with the results of the strong permittivity fluctuations in the low frequency limit and compared against the Maxwell-Garnett mixing formula.