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THE RELATIONSHIP OF THE FRACTAL DIMENSION OF THE ROWS OF MULTI-YEAR RIVER RUNOFF AND THE NORMS OF SURFACE AIR TEMPERATURE
Abstract
The article deals with the regularity connecting the correlation type of the fractal dimension of the series of river flow with the climatic norm of the surface air temperature. The identified patterns in the increased fractal dimension of long-term river flow series at extremely low (sub-Arctic climatic zone) and high (sub-equatorial zone) climatic norms of surface air temperature are linked with its significant influence on the selective value of evaporation in comparison with the river flow. A map of the location of topologically equivalent areas for the formation of river flow is shown. The use of two-dimensional manifolds made it possible to visualize the manifestation of topological nonequivalence of phase spaces for different selective values of runoff and evaporation in the form of the Whitney fold, which is one of the types of typical catastrophes. This research allows to allocate regions with the tendency to instability of modeling of a runoff, that the most dangerous, from the point of view, of reliability of work of hydraulic engineering constructions.
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