Fractal properties of river systems and their use in hydrological calculations

Possibilities of river systems fractal properties use in hydrological calculations are considered. Fractal properties of channel systems, possibilities of their use in hydrological calculations are studied for this purpose. It is established that differences of river systems from ideal fractal objects are determined by drawing of interface of the main river and its inflows. 13 types of river network drawings depending on existence or lack of inflows at the main river, symmetry of arrangement of inflows, and uniformity of arrangement of inflow mouths on the length of the main river are allocated. The method of elements formalization of this network of the river network structure based on definition of the river orders is reasonable. The order of the river establishes similarity of river systems structure elements. It is proved that the most convenient way of its definition is A. Sheydegger's method, putting an order of the river in dependence on the quantity of water currents of the first order in a river basin. On the basis of dependences studying between average hydrological characteristics and orders of the rivers the option of large-scale effects identification of hydrological characteristics change is offered and coefficients of their large-scale changes on the length of the rivers are estimated. The coefficient of large-scale changes shows the frequency rate of hydrological characteristics change with the growth of the order of the river on a unit. It is established that for some characteristics of the rivers the coefficient of large-scale changes is identical to all river basins, and for others - changes depending on physiographic position of the basin. Close compliance of large-scale coefficient changes of the hydrological characteristic and its fractal dimension is defined. Data processing on basins of the Upper Volga River, the Pechora and the Amur (the Russian part) showed that for any river basin there is a strict compliance between the main hydrographic characteristics (river order, the area of the basin and density of the river network). The order of any river is in close dependence (coefficient of multiple correlation is more than 0.95) on the area of the basin and density of the river network.

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