Non-stationary approach to at-site flood frequency modelling I. Maximum likelihood estimation

For dealing with hydrological non-stationarity in flood frequency modelling (FFM) and hydrological design, it is necessary to account for trends. Taking the case of at-site FFM, statistical parametric techniques are discussed for investigation of the time-trend. The investigation entails (1) an identification of a probability distribution, and (2) development of a trend software. The Akaike Information Criterion (AIC) was used to identify the optimum distribution, i.e. the distribution and trend function, which enabled an identification of the optimum non-stationary FFM in a class of 56 competing models. The maximum likelihood (ML) method was used to estimate the parameters of the identified model using annual peak discharge series. A trend can be assumed in the first two moments of a probability distribution function and it can be of either linear or parabolic form. Both the annual maximum series (AMS) and partial duration series (PDS) approach were considered in the at-site frequency modeling.