Analyses and development of a hierarchy of frozen soil models for cold region study

Numerous frozen soil models currently in use differ in the complexity of their governing equations or/and in the processes being considered. It is important to comprehensively examine and categorize these on the basis of physical principles, assumptions, and relationship to each other. In this paper frozen soil models are classified into different levels according to the complexity of the governing equations. On the basis of scale analysis, models with different levels of complexity were derived from the most complicated frozen soil model. Rationales for the simplification of models at different levels are discussed. To overcome the difficulties in achieving numerical solutions, a new method of substituting soil enthalpy and total water mass for soil temperature and volumetric liquid water content in governing equations is introduced for each level of the frozen soil models. Models with different complexity levels are assessed with observational data. The preliminary monthly and seasonal evaluation shows that the results from the models with different complexity are generally similar but with substantial differences at the Tibetan D66 site during the melting and freezing period. The model including the contribution of vapor flux due to the matric potential gradient to the water balance performs the best at the D66 site. Compared to the corresponding original models, the frozen soil model versions with enthalpy and total water mass for governing equations appear to produce consistently better performance. Furthermore, the rationale of different methods for the freezing-melting process in frozen soil is discussed. It has been noted that the model derived from the freezing point depression equation and the soil matric potential equation is supported by both thermodynamic equilibrium theory and the simulation results.