Comparison of Three-Parameter Distributions in Controlled Catchments for a Stationary and Non-Stationary Data Series

Abstract

Flood Frequency Analysis (FFA) and the non-stationary FFA approaches are used in flood study, water resource planning, and the design of hydraulic structures. However, there is still a need to develop these methods and to find new procedures that can be used in estimating simple distributions in controlled catchments. The aim of the study is a comparison of three-parameter distributions in controlled catchments for stationary and non-stationary data series and further to develop the procedure of the estimation the simple distributions. Ten rivers from the Czech Republic and Poland were selected because of their existing or planned reservoirs as well as for flood protection reasons. The annual maximum method and the three-parameter Weibull, Log-Normal, Generalized extreme value, and Pearson Type III distributions were used in this study. The analyzed time series are stationary and non-stationary. The methodology used in this study, which makes use of the Maximum Likelihood Estimation, allows one to simplify the analysis whenever there is a series of data that is both stationary and non-stationary. The novelty in our research is the standardization and development of a new procedure for a stationary and non-stationary data series, taking into account to read a specific value of the maximum flow with a given exceedance probability from the lower or upper tail. It determines the optimal choice of the theoretical distribution that can be used, for example in the design of weirs in rural areas (lower quantiles) or in the design of hydrotechnical structures in areas at risk of flooding (upper quantiles).

Keywords

• flood frequency analysis
• non-stationary
• three-parameter distribution
• GEV distribution
• Weibull distribution
• Log-Normal distribution