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Abstract Previous studies discovered a spatially heterogeneous expansion of Siberian larch into the tundra of the Polar Urals (Russia). This study reveals that the spatial pattern of encroachment of tree stands is related to environmental factors including topography and snow cover. Structural and allometric characteristics of trees, along with terrain elevation and snow depth were collected along a transect 860 m long and 80 m wide. Terrain curvature indices, as representative properties, were derived across a range of scales in order to characterize microtopography. A density-based clustering method was used here to analyze the spatial and temporal patterns of tree stems distribution. Results of the topographic analysis suggest that trees tend to cluster in areas with convex surfaces. The clustering analysis also indicates that the patterns of tree locations are linked to snow distribution. Records from the earliest campaign in 1960 show that trees lived mainly at the middle and bottom of the transect across the areas of high snow depth. As trees expanded uphill following a warming climate trend in recent decades, the high snow depth areas also shifted upward creating favorable conditions for recent tree growth at locations that were previously covered with heavy snow. The identified landscape signatures of increasing tall vegetation, and the effects of microtopography and snow may facilitate the understanding of treeline dynamics at larger scales. 

Snow cover plays a key role in the water and energy budgets over cold regions. Understanding and parameterizing water and heat exchange over snow surfaces in hydrologic models remains a major challenge. An innovative approach based on the theory of maximum entropy production (MEP) was developed for modeling energy budgets for snow-covered surfaces. This study generalizes the MEP model to simulate surface water vapor (latent heat) fluxes over an entire snowpack lifecycle, including snow accumulation and melting during the early growing season. The expanded MEP model combines soil evaporation, canopy transpiration, and snow sublimation to evaluate snow water loss during the lifecycle of the snowpack. Two hypotheses are tested: (1) sublimation becomes negligible during snowmelt when snowpack is isothermal (0°C) and (2) transpiration is progressively activated as a function of the air temperature during vegetation awakening. The proposed approach is shown to be effective for modeling the total surface water vapor fluxes over the snowpack's lifecycle. Both the hypotheses are supported by field observations. 

The Maximum Entropy Production (MEP) method for modeling surface energy budget has been developed and validated at local, regional and global scale including the Arctic regions. The MEP model has solid theoretical foundation built on the Bayesian probability theory, information theory, non-equilibrium thermodynamics and boundary layer turbulence theory. Its formulation has advantageous features including closing energy budget at any space-time scales, independence of moisture and temperature gradient, wind speed and surface roughness, and free of tunable empirical parameters. Application of the MEP model has been covering all types of land covers including Arctic permafrost tundra, sea ice and snow surfaces. Recent tests using field experimental observations suggest that the MEP model using fewer input data and model parameters is able to simulate surface energy budget accurately. It is a more efficient alternative to the classical Penman-Monteith model of potential evapotranspiration. The MEP method has potential to influence the study of Arctic water-energy cycles and climate change. 

A physically based model is formulated for the active layer depth of permafrost under changing boundary condition instead of constant boundary condition considered in the traditional Stefan problem. Time-varying ground heat flux is obtained from net radiation and surface temperature using the Maximum Entropy Production (MEP) model as the driver of the active layer melting process. Conductive heat flux at the melting front is approximated in terms of an analytical function of ground heat flux. The simulated active layer depth is in good agreement with the field observations.