NUMERICAL 3D MAXWELL’S EQUATIONS PATHWAYS TO SNOW MICROPHYSICS: WET SNOW EFFECTIVE PERMITTIVITY FOR L-BAND RADIOMETRY

H. Jiang¹, F. Borah¹, L. Tsang¹, Z. Huang¹, A. Colliander², A. Hossan³

¹Radiation Laboratory, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA, ²Finnish Meteorological Institute, Helsinki, Finland, ³Jet Propulsion Laboratory, California Institute of Technology

Global climate change and the accelerating cryosphere melt are reshaping Earth’s water cycle, with profound implications for water resources, flood hazards, and sea-level rise. A central challenge in this context is to monitor snow water equivalent (SWE) and melt dynamics, which determine freshwater availability, hydropower potential, and climate feedbacks in polar and alpine regions. Among the governing factors, the liquid water content (LWC) of snow is especially critical: even small amounts of liquid water can drastically alter energy balance, absorption, and runoff processes, thereby controlling the timing and magnitude of meltwater release. However, accurate monitoring of LWC in snowpacks remains a major challenge. The effective permittivity of wet snow provides the fundamental electromagnetic link between snow microphysics and its radiometric signature, enabling satellite radiometry to infer these key parameters. Accurately quantifying the LWC through effective permittivity is thus essential for reliable retrievals of SWE and melt dynamics, ultimately improving predictions of water security, flood risks, and climate feedbacks. Recently, L-band brightness temperatures of SMAP and SMOS have been proposed for inferring snow/firn wetness [1], which further underscores the need for accurate estimates of wet snow effective permittivity.

Wet snow is a complex three-phase medium consisting of air, ice, and liquid water.

Traditional dielectric mixing formulas attempt to approximate the effective permittivity of snow either by using classical mixing formulas based on idealized particle shapes such as spheres or ellipsoids, or by fitting measurement data with empirical power laws [2]. However, these methods are problematic: real snow microstructures consist of irregular, aggregated ice grains that deviate significantly from simple geometrical shapes, while empirical power laws are ad hoc, lacking direct physical foundations.

The absorption and scattering of microwaves in wet snow are governed exactly by Maxwell’s equations. In this study, we adopt a physics-based approach that directly solves Maxwell’s equations to characterize the electromagnetic responses of wet snow [3], [4].

Specifically, we employ a tri-continuous model to generate quasi-realistic wet snow microstructures and solve the 3D Maxwell’s equations using numerical methods [5]. The advantage of the tri-continuous representation is that it naturally captures the irregular and aggregated morphology of ice crystals. From the simulated electromagnetic fields, we then apply Mie scattering theory by treating the wet snow sample as an equivalent homogeneous body, thereby extracting its effective permittivity with both real and imaginary components [3]. The results from this Maxwell-based framework are compared against classical mixing formulas in the literature, and the derived effective permittivity is further applied to compute brightness temperature at L-band.

References

1. A. Hossan, A. Colliander, N.-J. Schlegel, J. Harper, L. Andrews, J. Kolassa, J. Z. Miller, and R. Cullather, “Evaluation of wet snow dielectric mixing models for l-band radiometric measurement of liquid water content in greenland’s percolation zone,” EGUsphere, vol. 2025, pp. 1–39, 2025.

2. A. Sihvola and I. of Electrical Engineers, Electromagnetic Mixing Formulas and Applications, ser. IEE electromagnetic waves series. Institution of Electrical Engineers, 1999.

3. L. Tsang, J. Kong, and K. Ding, Scattering of Electromagnetic Waves: Theories and Applications, ser. Wiley Series in Remote Sensing and Image Processing. Wiley, 2000.

4. L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations, ser. Wiley Series in Remote Sensing and Image Processing. Wiley, 2004.

5. Z. Huang, H. Xu, F. Borah, L. Tsang, B. Medley, J. T. Johnson, and R. D. De Roo, “L-band full-wave simulations of the effective permittivity of bi/tri-continuous media with applications to firn aquifer in polar regions and terrestrial wet snow,” IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1–12, 2024.