The Use of a Monte Carlo Markov Chain Method for Snow-Depth Retrievals: A Case Study Based on Airborne Microwave Observations and Emission Modeling Experiments of Tundra Snow

Abstract

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> ) 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> s, the inversion was also applied using the synthetic observations, where T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> 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.