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This study is focused on the specific features of ocean-air interaction in the Laptev Sea, in the late summer, on the basis of recurrent measurements during four expeditions in the 2000s and 2010s, atmospheric reanalysis products, and satellite ice concentration data. It was established that in the icy years, the accumulation of heat in the upper ocean layer is insignificant for the subsequent ice formation. In the ice-free years, the accumulated heat storage in the upper mixed layer depends on the duration of open water and the distance of the point of interest to the nearest ice edge. In a broader context, we considered possible links between the average ice area/extent in the August-September-October (ASO) period, and in the December-January-February (DJF) period, for two representative Arctic regions; that is, the Eurasian segment, defined within the bounds 60-120 degrees E, 65-80 degrees N, and the American segment, defined within the bounds 150 degrees E-150 degrees W, 65-80 degrees N. Significant seasonal memory, characterized by the consistent change of the ice cover parameters in sequential seasons, was revealed in the Eurasian segment between 2007 and 2017. No linkage on a seasonal time scale was found in the American segment. A possible explanation for the distinguished contrast between the two geographical regions is proposed.