Statistical Properties of Partial Duration Series: Case Study of North Island, New Zealand

Abstract

The partial duration series (PDS) model is preferable for hydrological frequency analysis when dealing with values exceeding a certain threshold, and the model is capable of capturing more information about extreme events than the rival annual maximum series (AMS) model. However, the use of PDS in hydrological application encounters the difficulty of determining the exceedance threshold attributable to physical and statistical complexity. An inverse relationship exists between the threshold value and the number of peaks selected above a threshold, and a fixed number of average peaks per year is an option to define the threshold value. Additionally, a PDS is generated under the assumption that the series is best described by a generalized Pareto (GP) distribution. To date, the question arises as to how many peaks should be appropriate for modeling the PDS. This paper investigates the optimum number of peaks for integer values on the basis of the variability of the GP/PDS parameters with an increase in the number of peaks. This paper uses daily rainfall data from 36 stations across the North Island region of New Zealand, with record length varying between 31 and 105 years.