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There is an exceptional opportunity of achieving simultaneous and complementary data from a multitude of geoscience and environmental near-earth orbiting artificial satellites to study phenomena related to the climate change. These satellite missions provide the information about the various phenomena, such as sea level change, ice melting, soil moisture variation, temperature changes and earth surface deformations. In this study, we focus on permafrost thawing and its associated gravity change (in terms of the groundwater storage), and organic material changes using the gravity recovery and climate experiment (GRACE) data and other satellite- and ground-based observations. The estimation of permafrost changes requires combining information from various sources, particularly using the gravity field change, surface temperature change, and glacial isostatic adjustment. The most significant factor for a careful monitoring of the permafrost thawing is the fact that this process could be responsible for releasing an additional enormous amount of greenhouse gases emitted to the atmosphere, most importantly to mention carbon dioxide (CO2) and methane that are currently stored in the frozen ground. The results of a preliminary numerical analysis reveal a possible existence of a high correlation between the secular trends of greenhouse gases (CO2), temperature and equivalent water thickness (in permafrost active layer) in the selected regions. Furthermore, according to our estimates based on processing the GRACE data, the groundwater storage attributed due to permafrost thawing increased at the annual rates of 3.4, 3.8, 4.4 and 4.0cm, respectively, in Siberia, North Alaska and Canada (Yukon and Hudson Bay). Despite a rather preliminary character of our results, these findings indicate that the methodology developed and applied in this study should be further improved by incorporating the in situ permafrost measurements.