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

The ground surface soil heat flux (G(0)) is very important to simulate the changes of frozen ground and the active layer thickness; in addition, the freeze-thaw cycle will also affect G(0) on the Tibetan Plateau (TP). As G(0) could not be measured directly and soil heat flux is difficult to be observed on the TP in situ due to its high altitude and cold environment, most of previous studies have directly applied existing remote sensing-based models to estimate G(0) without assessing whether the selected model is the best one of those models for those study regions. We use in-situ observation data collected at 12 sites combined with Moderate Resolution Imaging Spectroradiometer (MODIS) data (MOD13Q1, MODLT1D, MOD09CMG, and MCD15A2H) and the China meteorological forcing dataset (CMFD-SRad and CMFD-LRad) to validate the main models during the freeze-thaw process. The results show that during the three stages (complete freezing (CF), daily freeze-thaw cycle (DFT), and complete thawing (CT)) of the freeze-thaw cycle, the root mean square error (RMSE) between the models' G(0) simulated value and the corresponding G(0) measured value is the largest in the CT phase and smallest in the CF phase. The simulated results of the second group schemes (SEBAL, Ma, SEBAL(adj), and Ma(adj)) were slightly underestimated, more stable, and closer to the measured values than the first group schemes (Choudhury, Clawson, SEBS, Choudhury(adj), Clawson(adj), and SEBSadj). The Ma(adj) scheme is the one with the smallest RMSE among all the schemes and could be directly applied across the entire TP. Then, four possible reasons leading to the errors of the main schemes were analyzed. The soil moisture affecting the ratio G(0)/R-n and the phase shift between G(0) and net radiation R-n are not considered in the schemes directly; the scheme cannot completely and correctly capture the direction of G(0); and the input data of the schemes to estimate the regional G(0) maybe bring some errors into the simulated results. The results are expected to provide a basis for selecting remote sensing-based models to simulate G(0) in frozen ground dynamics and to calculate evapotranspiration on the TP during the freeze-thaw process. The scheme Ma(adj) suitable for the TP was also offered in the study. We proposed several improvement directions of remote sensing-based models in order to enhance understanding of the energy exchange between the ground surface and the atmosphere.

Increase of surface temperatures has long been recognized as an unequivocal response to radiative forcing and one of the most important implications for global warming. However, it remains unclear whether the variation of ground surface temperature (GST) and soil temperatures is consistent with simultaneous changes of the near-surface air and land (or skin) surface temperatures (T-a and LST). In this study, a seven-year continuous observation of GST, T-a, and surface water and heat exchange was carried out at an elevational permafrost site at Chalaping, northeastern Qinghai-Tibet Plateau. Results showed a distinct retarding of warming on the ground surface and subsurface under the presence of dense vegetation and moist peat substrates. Mean annual T-a and LST increased at noteworthy rates of 0.22 and 0.32 degrees C/a, respectively, while mean annual GST increased only at a rate of 0.057 degrees C/a. No obvious trends were detected for the four radiation budgets except the soil heat flux (G), which significantly increased at a rate of 0.29 W.m(-2).a(-1), presumably inducing the melting of ground ice and resulted in much higher moisture content through the summers of 2015 and 2016 than preceding years and subsequent 2017 at the depths between 80 and 120 cm. However, no noticeable immediate variations of soil temperatures occurred owing to the large latent heat effect (thermal inertia) and the extending zero-curtain period. We suggest that a better protected eco-environment, particularly the surface vegetation, helps preserving the underlying permafrost, and thus to mitigates the potential degradation of elevational permafrost on the Qinghai-Tibet Plateau.