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

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 bi-continuous 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 bi-continuous model (DMRT-Bic-NN), by training artificial neural networks (ANNs) on a training dataset generated from bi-continuous model simulations, thereby reducing the runtime for processing a representative case from approximately 20.1 hours with the original DMRT-Bic model to about 0.54 seconds. 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 (Dmax) conversion formula and optimized scaling coefficients, we comprehensively validate the DMRT-Bic-NN model. The results show that the simulated brightness temperatures (TB) exhibit root mean square error (RMSE) of approximately 3.4 K and 4.67 K for the Altay snow experiment and NoSREx, respectively. Sensitivity analysis reveals that the simulatedTBof the DMRT-Bic-NN, the DMRT based on the Quasi-crystalline Approximation of Mie scattering of densely packed Sticky spheres model (DMRT-QMS), and the Microwave Emission Model of Layered Snowpacks (MEMLS) models respond similarly to variations in snow grain size, although the magnitudes of their responses differ. For variations in snow density, the models exhibit distinct responses inTB, both in terms of the overall trend and the magnitude of the change. The simulated analysis ofTBfrequency 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 K 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.