A comparison of three parameter estimation methods of the gamma distribution of annual maximum low flow duration and deficit in the Upper Vistula catchment (Poland)

Cracow University of Technology, Department of Environmental Engineering, Institute of Water Engineering and Water Management, ul. Warszawska 24, 31-155 Cracow, Poland

^* Corresponding author: Katarzyna.Baran-Gurgul@iigw.pk.edu.pl

Abstract

Based on 30-year 24-hour flow sequences at 69 water gauging stations in the Upper Vistula catchment, it was determined that the probability distributions of the low flow duration and its maximum annual deficit can be described by the gamma distribution with the estimated parameters by the methods: MOM, the method of moments, LMOM, the method of linear moments, and MLE, the method of maximum likelihood. The stationarity of the time series was tested by the Mann-Kendall correlation using the Hamed and Rao variance correction. The low flows were defined by the SPA method, with the limit flow Q_70%. The quality of the match was tested by the Anderson-Darling goodness of fit test. This test allowed accepting the gamma distribution in all analysed cases, regardless of the method used to estimate the distribution parameters, since the p_v (p-values) values were greater than 5% (over 18% for T_max and 7.5% for V_max). The highest p_v values for individual water gauging stations, as well as the highest 90% T_max and V_max quantiles were noted using LMOM to estimate the gamma distribution parameters. The highest 90% T_max and V_max quantiles were observed in the uppermost part of the studied area.