An Analytical Model of Active Layer Depth under Changing Ground Heat Flux

Improved modeling of permafrost active layer freeze-thaw plays a crucial role in understanding the response of the Arctic ecosystem to the accelerating warming trend in the region over the past decades. However, modeling the dynamics of the active layer at diurnal time scale remains challenging using the traditional models of freeze-thaw processes. In this study, a physically based analytical model is formulated to simulate the thaw depth of the active layer under changing boundary conditions of soil heat flux. Conservation of energy for the active layer leads to a nonlinear integral equation of the thaw depth using a temperature profile approximated from the analytical solution of the heat transfer equation forced by ground heat flux. Temporally variable ground heat flux is estimated using non-gradient models when field observations are not available. Validation of the proposed model conducted against field data obtained from three Arctic forest and tundra sites demonstrates that the model is able to simulate both thaw depth and soil temperature profiles accurately. The model has the potential to estimate regional variability of the thaw depth for permafrost related applications. The seasonally thawed layer on top of the permafrost (active layer) is a key component of the Arctic system affected by the strong warming trend over the past decades. This soil layer experiences a pronounced seasonal cycle of freezing and thawing processes caused by the availability of Sun's energy. Mathematical modeling of the thaw depth of the active layer has remained challenging. This study formulates a novel model for the simulation of the diurnal cycle of thawing process. The formulation is developed using innovative models of heat flux that goes into the soil and soil temperature profile. Ground heat flux is derived from available energy at the land surface using a theory of surface heat flux partition. The soil temperature profile is expressed using ground heat flux within the active layer. The proposed model has been validated against field observations during thawing season. The model simulation and field observations of the thaw depth are in a good agreement at three Arctic study sites with forest and tundra surface conditions. The proposed formulation can be used for modeling freeze-thaw cycles of the active layer at the regional scales since data on surface available energy can be obtained from remote sensing observations. The proposed model is highly effective in modeling thawing depth at higher time resolution and representing the soil energy budget Non-gradient models demonstrate a strong capability to model soil energy budget in data-sparse harsh environments