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Flow descriptors for parametric hydrographs accounting for afforestation of the catchment

Baziak Beata, Gądek Wiesław, Bodziony Marek, Tokarczyk Tamara

Meteorology Hydrology and Water Management. Research and Operational Applications

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2020

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Vol. 8, Iss. 1

36--45

EN

Parametric flow hydrographs are used for design and management purposes in such fields as water management and aquatic engineering. They describe a theoretical hydrograph based on such parameters as maximum flow, time to peak, and surge duration. They are used to forecast flood risk and to evaluate the impact of land use on the run-off hydrograph. In Western Europe for many years methods have been used in which parametric hydrographs are determined based on physical catchment descriptors (PCDs), which are divided into three groups describing the physical features of a catchment. These descriptors are used to derive formulae enabling the determination of parametric flow hydrographs for any computational crosssection. In this work, such formulae are derived for the catchment of the Raba River, using the principles of design hydrology applied in Western European countries. The parametric hydrograph is described using Baptista’s gamma density function. The input hydrograph was a nonparametric flow hydrograph determined by Archer’s method. For nine gauging stations located in the Raba catchment, physical catchment descriptors were obtained for two 30-year periods: 1961-1990 and 1983-2012. Based on the nonparametric flow hydrograph and the PCDs, two groups of formulae were derived to describe the parametric hydrograph. Analysis of agreement between the computed parametric flow hydrographs and the input hydrograph indicated a high quality of fit. It should be noted that the formulae and analysis presented here refer only to the Raba catchment. However, the results confirm the possibility of applying these methods to the determination of parametric flow hydrographs for any river cross-section.

2

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

Baziak Beata, Gądek Wiesław

Acta Geophysica

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2019

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Vol. 67, no. 5

1419--1433

EN

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.

3

Nonparametric design hydrograph in the gauged cross sections of the Vistula and Odra basin

Gądek W. J., Baziak B., Tokarczyk T.

Meteorology Hydrology and Water Management. Research and Operational Applications

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2017

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Vol. 5, Iss. 1

53--61

EN

The Archer method for construction of nonparametric hydrographs was regarded as the basic one for constructing design hydrographs in gauged cross sections. The hydrographs designed using this method belong to a group of non-formalized hydrology. Unlike the commonly used formalized methods, where a nonparametric hydrograph is strictly determined and defined, the hydrographs defined in this way are constructed on the assumption, that flow is the main determined parameter. On the other hand, the Archer method assumes that the basic parameter is time, which is determined for assigned standardized flow, called a flow percentile. Hydrographs constructed using this method are the basis for constructing parametric design hydrographs used for engineering computations. The Archer method is relatively new and should be verified for various regions. Presented manuscript compares the results obtained using this method in the middle Odra and upper Vistula basins with the nonparametric method developed at the Cracow University of Technology, called the Cracow method. The obtained results show, that four highest registered flood waves are sufficient to construct a nonparametric design hydrograph, whereas semi-standardized volumes above descriptors W75 and W50 and the duration time of the descriptors are bigger than the volumes and duration times calculated by means of the Cracow method in the Vistula River basin, and approximate with regard to the values in the Odra River basin.

4

Strupczewski Method for Parametric Design Hydrographs in Ungauged Cross-Sections

Gądek W., Baziak B., Tokarczyk T.

Archives of Hydro-Engineering and Environmental Mechanics

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2017

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Vol. 64, nr 1

49--67

EN

Nonparametric hydrographs, constructed by the method suggested by Archer, are usually used for developing parametric design hydrographs. Flow changes in time are described by the UPO ERR Gamma complex function, which denotes a Gamma curve reformulated to have a Unit Peak at the Origin (abbreviated to UPO), supplemented by the Exponential Replacement Recession (ERR) curve. It may be observed, that this solution does not work in some areas of the upper Vistula and middle Odra catchments when the times of the rising limb of a hydrograph are higher than the times of the falling limb, i.e. when the skewness coefficient approximates 0.5 or higher values. Better results can be achieved with the function suggested by Strupczewski in 1964. It is a solution which uses two parameters of the flood hydrograph. The objective of the present paper is to assess the Strupczewski method by comparing it with a complex UPO ERR Gamma function for gauged cross-sections in the upper Vistula and middle Odra catchments. The assessment was carried out for 30 gauged cross-sections (15 in each river catchment). The parameters were optimized for width-hydrograph descriptors W75 and W50, designed by the Archer method, and for the skewness coefficient s. Optimization using only two width-hydrograph descriptors aims to test how the Strupczewski method works for cross-sections for which the values of width-hydrograph descriptors W75 and W50 are known. The assessment of both methods was carried out with reference to a nonparametric hydrograph constructed by the Archer method. The results of these assessments suggest that the Strupczewski method may be used not only for gauged cross-sections, but also for ungauged ones.