A physical-statistical framework to estimate Snow Water Equivalent (SWE) and Snow depth (SD) from SAR measurements was implemented and applied to SnowSAR flight-line data collected during the SnowEx’2017 field campaign in Grand Mesa, Colorado, USA and averaged to 90 m resolution. The physical (radar) model is used to describe the relationship between snowpack conditions and volume backscatter. The statistical model is a Bayesian inference model that seeks to estimate the joint probability distribution of volume backscatter measurements, SWE and SD and physical model parameters. To reduce the number of physical parameters, the snowpack is represented by two layers only. Retrievals compare well with pit observations with good performance in deep snow and residual errors less than 8% for SnowSAR incidence angles > 30°.

Snow water equivalent (SWE) is an important characteristic of a terrestrial hydrological cycle that needs to be retrieved in any global snow satellite mission. Many retrieval algorithms have been proposed based on microwave backscattering of snow packs. And X and Ku bands have been a focus on many of these past and future missions. In this paper we analyse the airborne X(9.6 GHz) and Ku (17.2 GHz) band data of the SnowSAR 2017 campaign and the University of Massachusetts InSAR Ku (13.3 GHz) band data using the bi-continuous dense media radiative transfer (DMRT) model. In-situ measurements of density, temperature and specific surface area (SSA) from the snow pits are used as physical parameters and are used in estimating the numerical parameters ($\zeta$) and$b$which characterizes the model. The background effects such as rough surface scattering are also removed from the airborne data and only the volume scattering is analyzed. Overcoming limitations in other models such as the sticky sphere model, the bi-continuous media model gives a more realistic representation of snow microstructure and has a weaker frequency dependence.

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.

This article presents a new algorithmic framework for multilayer inversion of the dense media radiative transfer (DMRT) equations of snowpack emission, with particular emphasis on the role of high-frequency microwave channels above 60 GHz. The approach relies on dictionary matching and locally constrained least squares. The results demonstrate that the algorithm can invert the DMRT model and retrieve depth, density, and grain size of a single-layer snowpack when dependencies of density and grain size on depth are properly accounted for. However, as the number of layers increases, the sensitivity of the inversion to observation noise grows markedly. Using observations, over the Great Plains in the United States, from the microwave imager onboard the global precipitation measurement (GPM, 10–166 GHz) core satellite, the initial results demonstrate that under a clear-sky condition and no vegetation canopy, the algorithm is capable to retrieve the snow depth and water equivalent of seasonal snow with a mean absolute error (MAE) of less than 0.15 m—when compared to the high-resolution analysis data from the SNOw Data Assimilation System (SNODAS).

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.

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 (Tb) 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 Tbs, the inversion was also applied using the synthetic observations, where Tbs were generated from the RT model. For the case with synthetic observations, the snow-depth RMSE was 0.07 cm. When the airborne Tbs 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 Tbs 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.

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.

Remote sensing of hydrology provides the key to one of the longest-standing problems in hydrology: ungaged basins. The global network of river discharge measurements available publicly accurately captures overall streamflow into global ocean, but coverage for smaller tributaries upstream, is vanishingly small. The forthcoming Surface Water and Ocean Topography (SWOT) mission will vastly expand measurements of global rivers. However, converting the SWOT measurements of height, width and slope into river discharge is non-trivial. SWOT discharge algorithms will provide discharge for all SWOT-observed rivers, but at lower accuracy than what is possible at a gage. In this paper, we answer the question of where and how SWOT discharge will be valuable. We show that median river discharge accuracy will be on the order of 50%, in terms of normalized root mean squared error (nRMSE), whereas unbiased nRMSE will be on the order of 10-20%. We discuss how SWOT discharge will contribute to global hydrologic science in the coming decade.

We carried out two aerial surveys using a weather balloon as the platform to measure the snow depth in the Wolverton watershed, CA, USA: one when the site was snow covered and the other one after the snow melted out. We reconstructed the 3-D surfaces of the site using the structure-from-motion (SfM) photogrammetry of the photographs taken in the surveys and differenced the heights of the two surfaces to obtain the snow depth. The snow depth estimates corresponded well with 32 manual measurements of snow depth, with R = 0.87 (p <; 0.05) and a root-mean-square error (RMSE) of 7.6 cm, the majority of which is a 6-cm systematic bias due to the vegetation rebound in the snow-off measurements. The relative depth error is 17% in the extremely dry year of sampling (i.e., 2015) and is expected to decrease for deeper snow because the absolute error of SfM is relatively static. The processed snow depth is able to capture the snow spatial variability at submeter scale. This study suggests that balloon photogrammetry is a repeatable, flexible, economical, and safe method for continuous snow depth measurement at small scales and could complement existing remote sensing platforms (e.g., aircrafts, satellites, and drones) for snow observations in open areas by providing spatial continuity, long observation time, and customizable resolution.

An ensemble of land surface models and forcing data was developed to assess variability in SWE estimation over North America. In this study, the ensemble output was used to assess how SWE uncertainty impacts streamflow estimation. The analysis was conducted by major basins of North America over the 2009-2017 time period.

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.

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.

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.

The ultra-wideband software-defined microwave radiometer (UWBRAD) is designed to provide ice sheet internal temperature by measuring low frequency microwave emission. A Bayesian framework is designed to retrieve the ice sheet internal temperature from simulated UWBRAD brightness temperature (Tb). Experiment results showed feasibility to estimate ice sheet internal temperature and improvement of priors.

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.

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 4π 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 TBsimulations between the HUT model and MEMLS. The models were compared with observations of natural snow cover at Sodankylä, Finland; Churchill, Canada; and Colorado, USA. No optimization of the snow grain size was performed. It shows that the HUT model tends to underestimate TBfor 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.

We investigate the degree to which ultrahigh frequency radio emission can be used to estimate subsurface physical temperature in the polar ice sheets. We combine electromagnetic emission forward models with plausible models of depth-dependent physical properties in the ice sheet. Temperature models are parameterized with variables including accumulation rate, geothermal heat flux, and surface temperature. Scattering is parameterized using empirical observations of grain growth combined with measured densities. Electromagnetic absorption is modeled using dielectric dispersion processes and semiempirical models based on observations. Our models illustrate that information about East Antarctic ice sheet temperature from near the surface to near the base can be gleaned from ultrawideband radiometer data. Based on our modeling study, we illustrate an instrument concept to measure ice sheet temperature profiles comprising a novel ultrawideband radiometer.

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 (Tb) at a spatial resolution of 90 m. The modeled SWE and Tbwere 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 Tbroot-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.

Applying passive microwave (PM) remote sensing to estimate mountain snow water equivalent (SWE) is challenging due to the complex interaction between the microwave radiance and the mountain environment; a better knowledge of the interaction is requisite to improve the characterization of mountain SWE via PM. In this study, we modeled the 36.5GHz V-Pol microwave radiance at 90m spatial resolution over the Upper Kern Basin. We replicated the AMSR-E observations with the modeling results, and used the modeled radiance to interpret the satellite observations, as well as to explore the impacts of the mountain environment on microwave radiance. We found snow grain size, model stratigraphic representation, liquid water content and intense snowfall event close related with the modeling accuracy; the calibration to these parameters reduced the error in the modeled radiance by 81%. We aggregated the modeled radiance to AMSR-E footprint scale using the antenna sampling pattern to facilitate the comparison between the modeled radiance and the AMSR-E observations. The RMSE of the basin-scale modeling was 3.1K during the dry snow season. Using the modeling results, we classified the environmental variables in terms of their influence on microwave radiance in the study area; from high to low: SWE (significant only when snowpack is deep), vegetation, elevation, aspect, slope.

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.

Large-scale snow hydrology has been studied via spaceborne passive microwave (PM) measurements for decades. Forward and inverse radiative transfer (RT) models of snow are utilized in this context but typically neglect snow stratigraphy. Our objective in this paper is to characterize the expected model error in PM brightness temperature (Tb) predictions due to neglecting stratigraphy over a range of snow cover conditions. For 191 snowpits ranging from prairie to alpine, we performed side-by-side RT model runs including and ignoring stratigraphy via mass-weighted averages across stratigraphic layers; error was estimated by comparing the two RT model runs. Neglecting stratigraphy at 37 GHz led to approximately 10-K root mean square error (RMSE) for moderately deep (alpine) snow cover and to approximately 5-K RMSE for shallower (prairie) snow. RMSE across all types of snow was 1.67 and 26.9 K at 18.7 and 89 GHz, respectively. At 37 GHz, there was a low bias for deep snowpacks and a high bias for moderate-to-shallow snowpacks. Bias magnitude bias was dependent on vertical grain size variability. Based on these results and estimates of sensitivity of Tbto snow depth, we estimated that snow depth RMSE due to neglecting stratigraphy approaches 50%.

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.

The elevation of the ocean surface has been measured for over two decades from spaceborne altimeters. However, existing altimeter measurements are not adequate to characterize the dynamic variations of most inland water bodies, nor of ocean eddies at scales of less than about 100 km, notwithstanding that such eddies play a key role in ocean circulation and climate change. For terrestrial hydrology, in situ and spaceborne measurements of water surface elevation form the basis for estimates of water storage change in lakes, reservoirs, and wetlands, and of river discharge. However, storage in most inland water bodies, e.g., millions of Arctic lakes, is not readily measured using existing technologies. A solution to the needs of both surface water hydrology and physical oceanography communities is the measurement of water elevations along rivers, lakes, streams, and wetlands and over the ocean surface using swath altimetry. The proposed surface water and ocean topography (SWOT) mission will make such measurements. The core technology for SWOT is the Ka-band radar interferometer (KaRIN), which would achieve spatial resolution on the order of tens of meters and centimetric vertical precision when averaged over targets of interest. Average revisit times will depend upon latitude, with two to four revisits at low to mid latitudes and up to ten revisits at high latitudes per$\sim$20-day orbit repeat period.

Merging microwave radiances and modeled estimates of snowpack states in a data assimilation scheme is a potential method for snowpack characterization. A radiance assimilation scheme for snow requires a land surface model (LSM) coupled to a radiative transfer model (RTM). In this paper, we explore the degree of model fidelity required in order for radiance assimilation to yield benefits for snowpack characterization. Specifically, we characterize the uncertainty of Microwave Emission Model for Layered Snowpacks (MEMLS) radiance predictions by quantifying model accuracy and sensitivity to the following: (1) the LSM snowpack layering scheme and (2) the properties of the snow layers, including melt-refreeze ice layers. MEMLS was consistent with the measured brightness temperatures at 18.7 and 36.5 GHz with a bias (mean absolute error) of 0.1 K (3.1 K) for the vertical polarization and 3.4 K (9.3 K) for the horizontal polarization. An error in the predictions at horizontal polarization is due to uncertainty in ice-layer properties. It was found that in order for predicted brightness temperatures from the coupled LSM and RTM to be adequate for radiance assimilation purposes, the following must be satisfied: (1) the LSM snowpack layering scheme must accurately represent the stratigraphic snowpack layers; (2) dynamics of melt-refreeze ice layers must be modeled explicitly, and the predicted density of melt-refreeze layers must be accurate within ; and (3) the MEMLS correlation length must be predicted within 0.016 mm, or effective optical grain diameter must be predicted within 0.045 mm. Recommendations for future field measurements are made.