Alpine permafrost environments are highly vulnerable and sensitive to changes in regional and global climate trends. Thawing and degradation of permafrost has numerous adverse environmental, economic, and societal impacts. Mathematical modeling and numerical simulations provide powerful tools for predicting the degree of degradation and evolution of subsurface permafrost as a result of global warming. A particularly significant characteristic of alpine environments is the high variability in their surface geometry which drives large lateral thermal and fluid fluxes along topographic gradients. The combination of these topography-driven fluxes and unsaturated ground makes alpine systems markedly different from Arctic permafrost environments and general geotechnical ground freezing applications, and therefore, alpine permafrost demands its own specialized modeling approaches. In this work, we present a multi-physics permafrost model tailored to subsurface processes of alpine regions. In particular, we resolve the ice-water phase transitions, unsaturated conditions, and capillary actions, and account for the impact of the evolving pore space through freezing and thawing processes. Moreover, the approach is multi-dimensional, and therefore, inherently resolves the topography-driven horizontal fluxes. Through numerical case studies based on the elevation profiles of the Zugspitze (DE) and the Matterhorn (CH), we show the strong influence of lateral fluxes in 2D on active layer dynamics and the distribution of permafrost.

Climate warming and anthropogenic impact causes transformation of geocryological conditions in the river basins of the North-East of Russia. Changes in the thickness of the active layer, configuration of taliks, types of landscapes and other factors lead to transformation of water exchange processes between surface and groundwater runoff. This is manifested in the seasonal redistribution of the components of the water balance, accelerated melting of aufeis, change in the ratio of waters of different genesis in the structure of river runoff. As a result, natural and anthropogenic risks that affect the safe and efficient development of infrastructure and socio-economic processes are increasing. At the same time the system of observations developed in the Soviet period has been practically destroyed in the region. This paper offers a vision of organizing complex multidisciplinary research to assess and project the changes in the conditions of underground and surface water interaction in natural and disturbed river basins of the cryolithozone of the North-East of Russia, including for solving applied problems, based on permafrost, hydrology. hydrogeology, landscape science and geophysics with applications of remote sensing and field research integrated through mathematical modeling methods. To achieve the goal, the identification of natural and disturbed landscapes using remote sensing data. and key areas for detailed research will be selected. Geophysical and drilling works will be carried out within the sites to establish permafrost-hydrogeological conditions, monitoring stations will be equipped to determine hydrogeological, hydrometeorological and geocryological characteristics, including sampling for isotopic and hydrogeochemical studies. As the main key sites, it is proposed to use the area of the Kolyma water-balance station and the site on Anmangynda aufeis, for which there are long-term observation series in the 20th century. Field data will become the basis for improving the mathematical model of runoff formation, considering the relationship between groundwater and river runoff in the conditions of permafrost. Mathematical modeling will make it possible to quantitatively analyze the water balance of rivers considering various factors and project water availability both for specific industrial facilities and for the region as a whole.

Results of modeling of the dynamics of the seasonally thawing layer in the twenty first century made for two polar points (the Svalbard Archipelago and the Antarctic Peninsula) are discussed in the paper. The loss of thermal stability of a permafrost is usually associated with the formation of non-merging layer that transforms then into a talik. This occurs when the seasonal thaw layer is not fully frozen due to a rise in air temperature and an increase in the snow cover thickness. Climate change (warming) causes an increase in the thickness of the seasonal thaw layer. From 2001 to 2018, the rise of summer air temperature at the Barentsburg weather station was about 0.05 degrees C/year, while in winter -0.21 degrees C/year, and at the Bellingshausen weather station (Antarctic) in the summer period a slight cooling was observed. On the island of West Svalbard in 1968-2000, the average daily summer and winter air temperatures were equal to +3.74 and -9.9 degrees C, respectively, while in 2001-2018 these values were significantly higher, especially in winter: +4.83 and -7.12 degrees C, respectively. On the Antarctic Peninsula, similar values were equal to: +1.03 and -4.05 degrees C (1968-2000) and +0.83 and -3.60 degrees C (2001-2018). Calculations for the conditions of the Bellingshausen weather station did show that if the snow cover thickness exceeded 0.72 m (the average climatic value) but the average values of other parameters were not changed, formation of the non-merging permafrost became possible. With regard for a possible dynamics of the air temperature, the non-merging permafrost may be frozen through at the snow cover thickness lower 0.9 m. According to calculations for the conditions of the West Svalbard Island, it follows that when the snow cover thickness exceeds 1.5 m on the ground with its humidity higher 25% and the absence of moss cover, incomplete freezing of the seasonal thaw layer and the formation of non-merging permafrost becomes possible even at present time. Using data on rates of the air temperature rise and the regional model of the climate change, we show that at the soil moisture of 18% (it corresponds to measured values of air humidity) and the snow cover thickness of 1.5 m formation of a layer of non-merging permafrost may take place in 12 years, while at the thickness of 1 m - in 24 years.

Thaw and liquid precipitation retard cooling of snow cover and soil surface and so may be a factor of heating. This slows down the soil freezing due to more active freezing of the wet snow, and, thus, promotes cooling and re-cooling of the soil. However, there are a number of factors which intensify the soil freezing after thaw. With thaw, the thickness of the snow cover decreases, and its density increases. In addition, after freezing wet snow improves the contact between the ice crystals, which increases the hardness and thermal conductivity of the snow As a result, after the thaw, the thermal protection ability of the snow decreases, and this can accelerate freezing of the soil. The dynamics of snow accumulation in Russia is considered in the paper. Using data obtained in the Western Svalbard, we demonstrate the increase in the number of thaws and liquid precipitation and influence of them on the snow cover and soil freezing. The influence of thaw on the growth of thermal resistance of snow cover is also considered. Calculations have shown that in the absence of a thaw, the depth of soil freezing is 1.26 m. With a thaw lasting 10 days, which begins on the 40th day from the start of soil freezing, the depth of freezing is reduced down to 1.2 m without considering changes in snow cover. When taking into account changes in the thermal resistance of snow cover, the depth of soil freezing by the end of the cold period increases up to 1.32 cm. With a thaw in the mid-winter, i.e. on the 70th day, the depth of freezing decreases down to 1.22 m, that is smaller than the depth of freezing without thaw This scenario is in accordance with changes in snow accumulation dynamics under the present-day climate, as in many areas most of the solid precipitation falls in the first half of the cold period. As a result, for a period after a thaw the smaller volume of snow will be deposited, and this will retard increasing in thermal resistance of the snow cover.