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The research on changes in the spatial-temporal dynamics of carbon in natural ecosystems on land is explored. The works of Russian and foreign authors on the analysis of the depositing ability of the cover are presented. Works on biomass reserves and primary production of biogeocenoses, research in the field of mathematical modeling of the carbon cycle in terrestrial ecosystems using remote sensing data are described. The article discusses modern approaches to mathematical modeling of productive processes and biological cycles of elements in plant ecosystems. The contribution of Russian and foreign authors to the spatial-temporal dynamics of carbon is analyzed. The research data in the assessment of the sequestration capacity of plant ecosystems, as the role of an ecosystem function, performing the function of a climatic ensemble of the state of the atmosphere is given. The various modeling-based methods for assessing and forecasting carbon stocks in forests, which have received international recognition, are presented, and the role of climate in managed forests in mitigating changes and predicting their carbon storage potential for the period up to 2050 under different forest management scenarios is examined. Among them: ISIS IIASA (Austria), EFIMOD+ ROMUL (Russia), ROBUL (Russia), Information System for Determination and Mapping of Carbon Deposition by Forests (Russia, UGFTU), CBM-CFS3 (Canadian Forest Service), FORCARB2 (US Forest Service). The works based on the spatial model of the carbon cycle in the “atmosphere-plant-soil” system (AM Tarko) of the Computing Center of the Russian Academy of …