Simulation of the maximum flow hydrograph as a part of the problem of flood transformation through ahydraulic system

Modeling ofthe maximum flow hydrographs during spring flood is interpretedas part of a more general task as extreme floods transit throw spillway structures accounting the cutting of maxima in flood control reservoirs. A general statement of the problem related to solving the problem of floods and related economic and environmental damages requiring carrying out complex compensatory and protective water management and hydraulic engineering measures is formulated. The solution of the general problem is not considered, but the authors’ link to the relevant publications is given. The presence of important infrastructure facilities, industrial enterprises and agricultural land can significantly reduce the class of structures. The method of modeling a maximum hydrograph using the Pearson type I differential distribution function for the cases of single-peak and two-peak hydrographs is proposed. Taking into account previous studies of research, the coefficients of completeness of hydrograph form and asymmetry are accepted as criteria for the correspondence of full-scale and simulated hydrographs. A theoretical justification is given and formulas are derived for the functions of maximum flow and flood volumes depending on time. The modeling algorithm is implemented in an Excel environment using built-in statistical beta distribution functions and an optimization procedure “solver”. Excel program is presented for a set of average parameter values, outlines of hydrographs are constructed depending on the shape coefficient, as well as nomograms of the relationship of the asymmetry coefficient with the shape coefficient depending on the ratio of the maximum flow rate and the volume of the flood. Methodology for a two-peak hydrograph is also considered, which is illustrated by the example of the Sursky hydroelectric complex on the Sura River.

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