Despite the importance of thermokarst (thaw) lakes of the subarctic zone in regulating greenhouse gas exchange with the atmosphere and the flux of metal pollutants and micro-nutrients to the ocean, the inventory of lake distribution and stock of solutes for the permafrost-affected zone are not available. We quantified the abundance of thermokarst lakes in the continuous, discontinuous, and sporadic permafrost zones of the western Siberian Lowland (WSL) using Landsat-8 scenes collected over the summers of 2013 and 2014. In a territory of 105 million ha, the total number of lakes >0.5 ha is 727,700, with a total surface area of 5.97 million ha, yielding an average lake coverage of 5.69% of the territory. Small lakes (0.5–1.0 ha) constitute about one third of the total number of lakes in the permafrost-bearing zone of WSL, yet their surface area does not exceed 2.9% of the total area of lakes in WSL. The latitudinal pattern of lake number and surface coverage follows the local topography and dominant landscape zones. The role of thermokarst lakes in dissolved organic carbon (DOC) and most trace element storage in the territory of WSL is non-negligible compared to that of rivers. The annual lake storage across the WSL of DOC, Cd, Pb, Cr, and Al constitutes 16%, 34%, 37%, 57%, and 73%, respectively, of their annual delivery by WSL rivers to the Arctic Ocean from the same territory. However, given that the concentrations of DOC and metals in the smallest lakes (<0.5 ha) are much higher than those in the medium and large lakes, the contribution of small lakes to the overall carbon and metal budget may be comparable to, or greater than, their contribution to the water storage. As such, observations at high spatial resolution (<0.5 ha) are needed to constrain the reservoirs and the mobility of carbon and metals in aquatic systems. To upscale the DOC and metal storage in lakes of the whole subarctic, the remote sensing should be coupled with hydrochemical measurements in aquatic systems of boreal plains.

Randomized machine learning focuses on problems with considerable uncertainty in data and models. Machine learning algorithms are formulated in terms of a functional entropy-linear programming problem. We adapt these algorithms to forecasting problems on an example of the evolution of thermokarst lakes area in permafrost zones. Thermokarst lakes generate methane, a greenhouse gas affecting climate change. We propose randomized machine learning procedures using dynamic regression models with random parameters and retrospective data (climatic parameters and remote sensing of the Earth’s surface). The randomized machine learning algorithm developed below estimates the probability density functions of model parameters and measurement noises. Randomized forecasting is implemented as algorithms transforming the optimal distributions into the corresponding random sequences (sampling algorithms). The randomized forecasting procedures and technologies are trained, tested, and then applied to forecast the evolution of thermokarst lakes area in Western Siberia.

The article deals with the problem of reconstructing missing data in data collections for machine learning problems. We propose a new randomized method for missing data reconstruction based on the technology of entropy-robust estimation and generation of ensembles of random variables. The method is similar to the use of an auxiliary regression to reconstruct missing values, but unlike the latter, no additional constraints are imposed on the likelihood function of errors in the sample in the case of entropy estimation and small amounts of data are permissible; this becomes extremely relevant in problems where the amount of data for training is limited and the omissions are not systematic. The proposed method is used to reconstruct missing data on the areas of thermokarst lakes in the Arctic zone of the Russian Federation as measured from satellite images.

Subject of research: article is the time series of changes in the area of thermokarst lakes in the Arctic under the conditions of modern climatic changes. Purpose of research: to analyze the time series of satellite measurements of lake areas for studying the dynamics of lakes in the West Siberian Arctic. Methods and objects of research: we present the results of formation and analysis of time series of lake areas intended for studying the dynamics of thermokarst lakes in the Arctic zone of Western Siberia over a 36-year period. The time series were obtained based on the results of remote measurements of the lake areas on the territory of 627 thousand km2 using 688 Landsat satellite images, sampled in the period 1985-2021. The study area was divided into three ecoregions to analyze the territorial features of the vast Arctic zone of Western Siberia. The analysis of the time series showed that the change in the average lake area in the territory of the Arctic zone of Western Siberia exhibits a marked negative linear trend. Main results of research: based on the comparison of the trends in the time series of lake areas in the territories of the three ecoregions of the West Siberian Arctic, it was found that the thermokarst lakes of Yamal exhibit the highest rate of change in the areas compared to the other Arctic ecoregions.

The article is devoted to remote studies of the size distribution of thermokarst lakes in the eastern part of the Russian Arctic. The studies are carried out in the Arctic territories of the Northeastern tundra (NET) (Yakutia) and the Chukotka tundra (CT), which are relatively homogeneous areas in terms of their natural properties (referred to here as ecoregions). Remote studies of the distribution of thermokarst lakes by area are conducted using satellite images from Kanopus-V and Sentinel-2 (with spatial resolutions of 2.1 and 20 m, respectively), obtained in the summer months of 2017–2021. The lakes are interpreted using a Sentinel-2 satellite image mosaic, which provides full coverage of the study territories; Kanopus-V images at 12 test sites; and QGIS 3.22 tools. We briefly describe the method of integration (combination) of data from Kanopus-V and Sentinel-2 images for plotting synthesized histograms of lakes distribution by their sizes. This technique allows us to get histograms of lake distribution in a very wide range of their sizes from 50 to 10⁸ m² in the studied Arctic ecoregions. The histogram plots show a similar behavior in both ecoregions, manifesting itself in an increase in the number of lakes as their size decreases. It is shown that the main contribution to the number of lakes in the NET is made by much larger lakes than in the CT, which may indicate a significant difference in the geocryological conditions in different Arctic territories of the eastern part of the Russian Arctic. The degree of the lake cover of the territories is assessed. It is shown that the lake cover of the NET is 7 times higher than in the studied territories of Chukotka.