Energy conservative solutions for coupled heat-mass transport in frozen soils and snow

Physically based frozen soil models are essential for understanding hydrological processes in cold regions, particularly snowmelt infiltration into seasonally frozen soils and permafrost thaw. While significant progress has been made in modeling coupled heat and mass transport in frozen soils, and several sophisticated physically based models exist, practical applications require robust coupling between snow and soil models. Although we have well-developed physically based snow models, state-of-the-art soil models are typically not integrated with them. Notable exceptions include the Cold Regions Hydrological Model (CRHM) and various land surface models such as CLASS, CLASSIC, SVS, and SUMMA. However, these models are often applied with coarse vertical resolution and, in some cases, rely on oversimplified process representations. The objective of this study is to develop a simple, point scale mass- and energy-conservative coupled snow-soil model that can be used to systematically evaluate the numerous implicit and explicit assumptions embedded in existing models. A particular focus is to evaluate various approaches for representing the upper boundary condition of the soil, which plays a critical role in governing heat and mass fluxes and, consequently, the thermal and hydrological behavior of the soil.