A unified statistical model for hydrological variables including the selection of threshold for the peak over threshold method

Abstract

This paper explores the use of a mixture model for determining the marginal distribution of hydrological variables, consisting of a truncated central distribution that is representative of the central or main‐mass regime, which for the cases studied is a lognormal distribution, and of two generalized Pareto distributions for the maximum and minimum regimes, representing the upper and lower tails, respectively. The thresholds defining the limits between these regimes and the central regime are parameters of the model and are calculated together with the remaining parameters by maximum likelihood. After testing the model with a simulation study we concluded that the upper threshold of the model can be used when applying the peak over threshold method. This will yield an automatic and objective identification of the threshold presenting an alternative to existing methods. The model was also applied to four hydrological data series: two mean daily flow series, the Thames at Kingston (United Kingdom), and the Guadalfeo River at Orgiva (Spain); and two daily precipitation series, Fort Collins (CO, USA), and Orgiva (Spain). It was observed that the model improved the fit of the data series with respect to the fit obtained with the lognormal (LN) and, in particular, provided a good fit for the upper tail. Moreover, we concluded that the proposed model is able to accommodate the entire range of values of some significant hydrological variables.