Governing Equations for Heat Transport and Energy Conservation in Frozen Soils

Application of the energy conservation equation to soils is a source of confusion and subject to inconsistency of approaches in the literature. In this paper we explain some important concepts in a clear and simple manner, in the hopes this will lead to better understanding of the unstated assumptions that are embedded within most models. We derive the governing equation for mass and heat transport in frozen soils in a tractable form, and compare our governing equation with others in the literature, explaining the differences and where they arise. We find our equations are largely consistent with those presented by Voss et al (2024) in SUTRA (version 4.0), but there are differences with other models. The most important outstanding challenges for the frozen soil community are to fully understand the consequences of these differences between models, establish a model or suite of models that have been rigorously validated against field observations, and use these models to predict climate change impacts on the cryosphere.