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One of the most interesting features on the East European Plain is the net of dry valleys and hollows. Dense vegetation usually covers their bottoms and slopes, so the modern erosion here is negligible in the pristine conditions. Coring in these valleys showed the features and deposits of at least two erosion events, first during late MIS-6 and the second during late MIS-3. The both periods were characterized by periglacial conditions with low air temperatures and deep permafrost, as well as very high surface runoff. The structure of these systems of dry valleys and hollows is well described with power-law magnitude-frequency relationships, close to determinations of the fractal theory. These power-law relationships don’t act only near and within the belt of no erosion, where probability distribution functions of morphometric characteristics takes another form. The same type of the erosion landscape is typical for the Arctic regions with the modern periglacial conditions, especially for Yamal, Gydan and Tazovskiy peninsulars. The size, density and structure of such valleys and gullies is quite similar to those on the East European Plain, but these features are active there (especially in the conditions of natural or anthropogenic vegetation cover deterioration). Therefore, the landscape and hydrological conditions at the modern belts of no erosion in Arctic, can be used to reconstruct the same characteristics of the erosion landscape in former periglacial conditions, first of all, typical values of the critical velocities of erosion initiation. Gully erosion and thermoerosion model was used to find the most suitable values of these critical velocities, which can explain the structure and density of dry valleys systems on the East European Plain.