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Accelerating Numerical Electromagnetic Scattering Models for Snow Microwave Emission Using Machine Learning Surrogates

Xudong Li,Chuan Xiong

Published 2026 in IEEE Transactions on Geoscience and Remote Sensing

ABSTRACT

Accurate retrieval of snow properties such as snow depth (SD) and snow water equivalent (SWE) from passive microwave remote sensing requires robust physical models that can simulate the interactions between microwave and snow microstructure. The bicontinuous model has demonstrated high fidelity in characterizing snow microstructure, but its high computational cost limits its practical application. In this study, we develop a fast surrogate model, dense media radiative transfer theory with a neural-network-accelerated bicontinuous model (DMRT-Bic-NN), by training artificial neural networks (ANNs) on a training dataset generated from bicontinuous model simulations, thereby reducing the runtime for processing a representative case from approximately 20.1 h with the original DMRT-Bic model to about 0.54 s. Cross validation demonstrates that the trained model accurately reproduces snow scattering parameters at the three key frequencies (10.65, 18.7, and 36.5 GHz). Using snowpit data from the Altay snow experiment and Nordic Snow Radar Experiment (NoSREx), combined with the snow grain size (<inline-formula> <tex-math notation="LaTeX">$D_{\max }$ </tex-math></inline-formula>) conversion formula and optimized scaling coefficients, we comprehensively validate the DMRT-Bic-NN model. The results show that the simulated brightness temperatures (<inline-formula> <tex-math notation="LaTeX">$T_{B}$ </tex-math></inline-formula>) exhibit root-mean-square error (RMSE) of approximately 3.4 and 4.67 K for the Altay snow experiment and NoSREx, respectively. The sensitivity analysis reveals that the simulated <inline-formula> <tex-math notation="LaTeX">$T_{B}$ </tex-math></inline-formula> of DMRT-Bic-NN, DMRT based on the quasi-crystalline approximation (QCA) for Mie scattering of densely packed Sticky spheres (DMRT-QMS) model, and the microwave emission model of layered snowpacks (MEMLS) models respond similar to variations in snow grain size, although the magnitudes of their responses differ. For variations in snow density, the models exhibit distinct responses in <inline-formula> <tex-math notation="LaTeX">$T_{B}$ </tex-math></inline-formula>, both in terms of the overall trend and the magnitude of the change. The simulated analysis of <inline-formula> <tex-math notation="LaTeX">$T_{B}$ </tex-math></inline-formula> frequency differences suggests that, within the scope of the validation data and experimental configuration adopted in this study, the DMRT-Bic-NN model yields average unbiased RMSE (ubRMSE) values of 2.85 and 5.45 K for V- and H-polarizations, respectively, with marginally lower errors than the DMRT-QMS and MEMLS models. The frequency dependence tests show that the DMRT-Bic-NN model produces a weaker frequency dependence, which aligns more closely with experimental observations. This study highlights the potential of combining numerical electromagnetic models and machine learning to enhance the speed and performance of snow radiative transfer simulations.

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