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Ice sheet subsurface temperature is important for understanding glacier dynamics, yet existing methods to obtain the temperature of the ice sheet column are limited to in situ sources 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.

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.

Snow-depth retrieval from passive microwave observations without a priori information is a highly undetermined problem. Achieving accurate snow-depth retrievals requires a priori information on the snowpack properties, such as grain size, density, physical temperature, and stratigraphy. On a practical level, however, retrieval algorithms must consider prior information, while minimizing the dependence on it, as accurate ancillary data are not globally available. In this study, we build on the previously published Bayesian Algorithm for Snow Water Equivalent Estimation (BASE) to retrieve snow depth using an airborne passive microwave data set over the tundra snow in the Eureka region. The method computes the optimal estimates of snow depth, density, grain size, and other variables, given the brightness temperature observations and prior information, using Markov chain Monte Carlo (MCMC). The airborne data set includes passive microwave brightness temperature ( $T_{b}$ ) at 18.7 and 36.5 GHz. The in situ measurements of the snow depth provide validation data for 464 sensor footprints. The microwave radiative transfer (RT) model used is the Dense Media RT-Multilayered (DMRT-ML) model. We use a two-layer wind slab and depth hoar assumption based on the local snow cover knowledge from the previous research on the study area. To improve our understanding of the results using the airborne $T_{b}\text{s}$ , the inversion was also applied using the synthetic observations, where $T_{b}\text{s}$ were generated from the RT model. For the case with synthetic observations, the snow-depth RMSE was 0.07 cm. When the airborne $T_{b}\text{s}$ are used, the snow-depth RMSE was 21.8 cm. This discrepancy is due to the large spatial variability in the MagnaProbe snow-depth measurements and the fact that not all physical processes affecting the airborne $T_{b}\textrm {s}$ are represented in the RT model. Our work verifies the feasibility and applicability of the proposed methodology regionally for the airborne retrievals and reinforces the tractable applicability of a physics-based RT model in the SWE retrievals.

Microwave emission models are a critical component of snow water equivalent retrieval algorithms applied to passive microwave measurements. Several such emission models exist, but their differences need to be systematically compared. This paper compares the basic theories of two models: the multiple-layer Helsinki University of Technology (HUT) model and the microwave emission model of layered snowpacks (MEMLS). By comparing the mathematical formulation side by side, three major differences were identified: 1) by assuming that the scattered intensity is mostly (96%) in the forward direction, the HUT model simplifies the radiative transfer equation in $4\pi$ space into two one-flux equations, whereas MEMLS uses a two-flux theory; 2) the HUT scattering coefficient is much larger than the one of MEMLS; and 3) MEMLS considers the trapped radiation inside snow due to internal reflection by a six-flux model, which is not included in HUT. Simulation experiments indicate that the large scattering coefficient of the HUT model compensates for its large forward scattering ratio to some extent, but the effects of one-flux simplification and the trapped radiation still result in different $T_{B}$ simulations between the HUT model and MEMLS. The models were compared with observations of natural snow cover at Sodankyla, Finland; Churchill, Canada; and Colorado, USA. No optimization of the snow grain size was performed. It shows that the HUT model tends to underestimate $T_{B}$ for deep snow. MEMLS with the physically based improved Born approximation performed best among the models, with a bias of −1.4 K and a root-mean-square error of 11.0 K.

Applying passive microwave (PM) remote sensing to estimate mountain snow water equivalent (SWE) is challenging due in part to the large PM footprints and the high subgrid spatial variability of snow properties. In this paper, we linked the land surface model Simplified Simple Biosphere version 3.0 (SSiB3) with the radiative transfer model Microwave Emission Model of Layered Snowpacks, and we forced the coupled model with the disaggregated North American Data Assimilation System phase 2 (NLDAS-2) meteorological data to simulate the snow properties and the 36.5-GHz microwave brightness temperature $(T_{b})$ at a spatial resolution of 90 m. The modeled SWE and $T_{b}$ were used to interpret the radiance observed by the Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) and to explore the impact of snow spatial variability on the microwave radiance in a mountain environment. The modeling was carried out over the Upper Kern Basin, Sierra Nevada. We developed new methods for modeling the effect of large snowfall events on the snow grain size. We aggregated the modeled radiance to the satellite scale using the AMSR-E 36.5-GHz antenna sampling pattern. The methods were calibrated for water years (WYs) 2004–2006 and validated for WYs 2003, 2007, and 2008. The coefficient governing the grain growth rate was also calibrated. The modeling results showed that the new snow grain estimation scheme reduced the error in the modeled radiance by 55.2% during the calibration period. The $T_{b}$ root-mean-square error was 3.1 K during the snow accumulation season for the validation period. The modeling results showed that, in the study area, the microwave signal saturated for SWE values between 0.3 and 0.5 m. It was found that the subfootprint-scale SWE variability has a significant impact on the saturation of spaceborne PM observations. The experiments demonstrate that this modeling system improves the accuracy of the radiance modeling, which is critical for estimating the mountain SWE via PM remote sensing either for informing direct retrieval algorithms or for data assimilation. We plan to use the modeling framework in future radiance assimilation studies.

Two sets of experiments were performed to identify, respectively, the impacts of using different grain size models and simplified representations of snowpack stratigraphy on the predicted grain size evolution and the resulting radiance predictions. Three different grain size models were examined with the grain size prediction used as inputs to the Microwave Emission Model of Layered Snowpacks (MEMLS) model for predicting radiobrightness (at different frequencies) from the snowpack. The varying mechanisms and treatment of grain size growth lead to differences between the three models. Despite the differences, when using best-fit relationships between grain size and the exponential correlation length parameter needed by MEMLS, the predicted brightness temperatures are similar. For all three models, it was found that a proportional model between grain size and correlation length outperformed a more physically based model and that the regression coefficients differed from those in previous studies. The predicted V-pol brightness temperature measurements from the three grain size models showed good agreement with each other, with inter-model differences on the order of ~ 5 K. At H-pol the biases significantly increase, which is most likely due to errors in predicted density and grain size in melt-freeze layers. In the experiments aimed at assessing the impact of stratigraphy on predicted radiances, it was found that there were limited additional errors introduced in using a pre-specified one-, three-, or five-layer scheme at 18.7 and 36.5 GHz (V-pol), while sizeable errors were introduced at 89 GHz (V-pol). The additional errors at H-pol were relatively small, yet the overall errors were still larger than V-pol.

A microwave radiance assimilation (RA) scheme for the retrieval of snow physical state variables requires a snowpack physical model (SM) coupled to a radiative transfer model. In order to assimilate microwave brightness temperatures (Tbs) at horizontal polarization (h-pol), an SM capable of resolving melt-refreeze crusts is required. To date, it has not been shown whether an RA scheme is tractable with the large number of state variables present in such an SM or whether melt-refreeze crust densities can be estimated. In this paper, an RA scheme is presented using the CROCUS SM which is capable of resolving melt-refreeze crusts. We assimilated both vertical (v) and horizontal (h) Tbs at 18.7 and 36.5 GHz. We found that assimilating Tb at both h-pol and vertical polarization (v-pol) into CROCUS dramatically improved snow depth estimates, with a bias of 1.4 cm compared to -7.3 cm reported by previous studies. Assimilation of both h-pol and v-pol led to more accurate results than assimilation of v-pol alone. The snow water equivalent (SWE) bias of the RA scheme was 0.4 cm, while the bias of the SWE estimated by an empirical retrieval algorithm was -2.9 cm. Characterization of melt-refreeze crusts via an RA scheme is demonstrated here for the first time; the RA scheme correctly identified the location of melt-refreeze crusts observed in situ.