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This article presents a numerical solution of the one-dimensional Stefan problem with two phase transitions, which is implemented on a non-uniform grid. The system of equations is written in a general form, i.e. it includes not only conductive, but also convective and dissipative terms. The problem is solved numerically by the front-fixing method on a non-uniform grid using an implicit finite-difference scheme, which is implemented by the sweep method. This algorithm can also be used to create more complex mathematical models of heat and mass transfer, as well as to describe glacial and subglacial processes. The mathematical apparatus proposed in the article was used to solve a specific problem of water freezing in a glacial crevasse. The presence and progression of crevasses, in turn, is a demonstrative factor indicating the dynamic activity of the glacier. Crevasses formed in one way or another can not only expand, but also decrease in size until they completely disappear. One of the reasons for their closure is the freezing of near-surface meltwater in the crevasse. Such a process was observed on glaciers near Mirny and Novolazarevskaya stations (East Antarctica). This process is modeled as an example of solving the Stefan problem. It is believed that all media are homogeneous and isotropic. The temperature of the water in the crevasse corresponds to the melting temperature of the ice. Modeling has shown that for the coastal part of the cold Antarctic glacier with an average temperature of –10°C and below, crevasses 5–10 cm of width freeze in less than a week. Wider ones freeze a little longer. 30 cm wide crevasses close in about two to three weeks, depending on the temperature of the glacier.

Airbase Novo Runway has the status of the largest transport hub in the northern part of Antarctica, which can land large airlifter on wheeled chassis. However, the unsteady flow of the glacier leads both to the formation of hazardous glacial crevasses and changes the configuration of the runway. The purpose of this study was to investigation the state of the Novo Runway and to identify the degree of uneven flow of the glacier in this area. The article shows the results of research carried out from late October to mid-December 2021. Field work included GPR profiling, tacheometric survey, mechanical drilling, and downhole thermometry. The tacheometric survey was carried out at the beginning and at the end of the field work (in 42 days) to determine the displacements of pickets fixed on the glacier and then to calculate the glacier deformation rates. The results of the studies showed that there are no open crevasses in this area, which pose a danger to aircraft. There are non-hazardous healed crevasses at the beginning and end of the runway. At the same time, GPR data indicate that in the central part of the runway (at the distances from 1720 meters to 2240 meters from its beginning), there is a zone of junction of glacial flows. This zone is traced on parallel profiles for more than one kilometer. Calculation results indicate that the strain rates in this area in the transverse direction (across the runway) reaches -0.183 year-1. This corresponds to deformations (compressions) of more than 1.4 meters over 42 days of observations in absolute terms. Although these values significantly exceed the threshold values, there were no open crevasses in the glacier. It can be assumed that relatively recently the glacier flowed more slowly than now. This research should be continued to draw broader conclusions about the dynamics of the glacier in the area of the Novo Runway.

The Russkaya station (Marie Byrd Land, West Antarctica) was one of the wintering stations of the Russian Antarctic Expedition (RAE) before its conservation in 1990. Starting from the field season of the 65th RAE (2019/20), work is under way at Russkaya station to put it into operation as a functioning wintering station. Due to its significant distance from other RAE infrastructure sites and also due to severe climate, organization of logistical operations in this area requires a special approach. For the most effective transport communication with the station, it is planned to organize an airstrip to receive planes on ski landing gear on the surface of the outlet glacier. Glaciers of this type are oſten characterized by crevasses, which are not traceable on the surface, which makes it necessary to study the structural sub-surface features of the glacier. For this purpose, geophysical survey in the field season of the 65th RAE were carried out with usage of the GPR-method. GPR profiling at a frequency of 900 MHz allowed us to identify the crevasses and assess their morphometric characteristics, in particular the width and depth. The widest crevasses were examined in detail to improve the interpretation of GPR data. Based on the results of geophysical works, the boundaries of zones were determined, within which the crevasses are either absent, or their width does not exceed 0.6 m. In addition, by means of core drilling, values of ice density to a depth of 5 m from the surface were obtained, which correspond to the normative data on preparation of airfields for operation of airplanes on ski landing gear. Based on the results of geophysical and glaciological investigations, a site on the glacier suitable for runway preparation was identified. An area safe for organization of transport communication between the airfield and Russkaya station was also identified. It is adjacent to the hills of the oasis, as the glacier in this part is the most stationary.

In recent years, when organizing works of the Russian Antarctic Expedition (RAE), considerable attention is given to the safety of logistics operations carried out at Russian stations and field bases. The main factors that threaten polar explorers are extensive systems of cracks and water breakthroughs, confined to the marginal, the most dynamic part of the outlet glaciers, in the area of which the most part of stations are located. One example of the impact of these processes on transport communications in Antarctica is the breakthrough of an intraglacial reservoir in the Dolk glacier near the station Progress (Larsemann Hills, Eastern Antarctica) in the season of the 62nd RAE (2016/17). The outburst resulted in the formation of a huge hole in the glacier body and an extensive system of cracks directed towards its flanks. This took place on the part of the route connecting the Progress Station with the point of organization the sledge-tractor train marches to inner regions of the Antarctic continent. Thus, this destroyed the transport links between these points. That is why during the seasonal works of the 63rd RAE (2017/18) geophysical surveys were carried out around the hole by means of the GPR profiling for the purpose to find the best way and organize a new all-season route. The GPR soundings performed at frequencies of 900 and 150 MHz, made possible to fix numerous cracks and large volumes of melt water accumulations in the near-surface part of the ice layer. The analysis of the obtained time sections and the assessment of the depths of cracks and watered areas did show that the detected objects in the glacier body were not dangerous for advancing of the sledge-caterpillar equipment passing by the hole. These surveys allowed planning the optimal new route, after which it was rolled up and put into operation. The logistical connection between the station and the airfield has been restored. Until the end of the field season, the new all-season route was actively used for transportation.

Glaciers and numerous glacial lakes that are produced by glacier melting are key indicators of climate change. Often overlooked, supra-glacial lakes develop in the melting area in the low-lying part of a glacier and appear to be highly variable in their size, shape, and location. The lifespan of these lakes is thought to be quite transient, since the lakes may be completely filled by water and burst out within several weeks. Changes in supra-glacial lake outlines and other surface features such as supra-glacial rivers and crevasses on the glaciers are useful indicators for the direct monitoring of glacier changes. Synthetic aperture radar (SAR) is not affected by weather and climate, and is an effective tool for study of glaciated areas. The development of the Chinese GaoFen-3 (GF-3) SAR, which has high spatial and temporal resolution and high-precision observation performance, has made it possible to obtain dynamic information about glaciers in more detail. In this paper, the classical Canny operator, the variational B-spline level-set method, and U-Net-based deep-learning model were applied and compared to extract glacial lake outlines and other surface features using different modes and Chinese GF-3 SAR imagery in the Mount Everest Region of the Himalayas. Particularly, the U-Net-based deep-learning method, which was independent of auxiliary data and had a high degree of automation, was used for the first time in this context. The experimental results showed that the U-Net-based deep-learning model worked best in the segmentation of supra-glacial lakes in terms of accuracy (Precision = 98.45% and Recall = 95.82%) and segmentation efficiency, and was good at detecting small, elongated, and ice-covered supra-glacial lakes. We also found that it was useful for accurately identifying the location of supra-glacial streams and ice crevasses on glaciers, and quantifying their width. Finally, based on the time series of the mapping results, the spatial characteristics and temporal evolution of these features over the glaciers were comprehensively analyzed. Overall, this study presents a novel approach to improve the detection accuracy of glacier elements that could be leveraged for dynamic monitoring in future research.

Glaciers and numerous glacial lakes that are produced by glacier melting are key indicators of climate change. Often overlooked, supra-glacial lakes develop in the melting area in the low-lying part of a glacier and appear to be highly variable in their size, shape, and location. The lifespan of these lakes is thought to be quite transient, since the lakes may be completely filled by water and burst out within several weeks. Changes in supra-glacial lake outlines and other surface features such as supra-glacial rivers and crevasses on the glaciers are useful indicators for the direct monitoring of glacier changes. Synthetic aperture radar (SAR) is not affected by weather and climate, and is an effective tool for study of glaciated areas. The development of the Chinese GaoFen-3 (GF-3) SAR, which has high spatial and temporal resolution and high-precision observation performance, has made it possible to obtain dynamic information about glaciers in more detail. In this paper, the classical Canny operator, the variational B-spline level-set method, and U-Net-based deep-learning model were applied and compared to extract glacial lake outlines and other surface features using different modes and Chinese GF-3 SAR imagery in the Mount Everest Region of the Himalayas. Particularly, the U-Net-based deep-learning method, which was independent of auxiliary data and had a high degree of automation, was used for the first time in this context. The experimental results showed that the U-Net-based deep-learning model worked best in the segmentation of supra-glacial lakes in terms of accuracy (Precision = 98.45% and Recall = 95.82%) and segmentation efficiency, and was good at detecting small, elongated, and ice-covered supra-glacial lakes. We also found that it was useful for accurately identifying the location of supra-glacial streams and ice crevasses on glaciers, and quantifying their width. Finally, based on the time series of the mapping results, the spatial characteristics and temporal evolution of these features over the glaciers were comprehensively analyzed. Overall, this study presents a novel approach to improve the detection accuracy of glacier elements that could be leveraged for dynamic monitoring in future research. [ABSTRACT FROM AUTHOR]