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The Pearson Type IV distribution function employed to describe the parametric flow hydrograph

Baziak Beata, Gądek Wiesław

Acta Geophysica

2019

Vol. 67, no. 5

1419--1433

The gamma distribution functions with one shape parameter, employed to describe the parametric hydrograph, proved ineffective for the upper Vistula River and the middle Oder River water regions. It was therefore necessary to fnd a diferent function. The Pearson Type IV distribution functions proposed by Strupczewski with one and two shape parameters were analyzed for their applicability based on the data acquired from 60 water gauges, 30 of which were located on the Vistula River and the other 30 were on the Oder River. The shape parameter (parameters) and the time of rising limb were optimized based on the calculated hydrograph widths at 50% and 75% of peak flow (W50 and W75) as well as on the skewness coefcient s. The calculated parametric hydrographs were compared with the nonparametric input hydrographs with regard to the closeness of their volumes and the position of their centers of gravity. Both Pearson Type IV distribution functions proved to ft well. However, the function with two shape parameters did not yield the exact solution since the condition of the assumed objective function was met by a very large group of pairs of m and n shape parameters. It was therefore assumed that the recommended function is the Pearson Type IV distribution with one shape parameter. This function has an additional advantage of having an infection point located between the W50 and W75, which allows to use the exponential function for the rising or recession limb that better describes either part of the hydrograph.