Non-Stationary Rainfall Intensity-Duration-Frequency Relationship: a Comparison between Annual Maximum and Partial Duration Series

Abstract

The rainfall Intensity-Duration-Frequency (IDF) relationship is the primary input for storm water management and other engineering design applications across the world and it is developed by fitting an appropriate theoretical probability distribution to annual maximum (AM) series or partial duration series (PDS) of rainfall. The existing IDF relationship developing methods consider the extreme rainfall series as a stationary series. There exist few studies that compared AM and PDS datasets for developing rainfall IDF relationship in a stationary condition. However, during the last few decades, the intensity and frequency of extreme rainfall events are increasing due to global climate change and creating a non-stationary component in the extreme rainfall series. Therefore, the rainfall IDF relationship developed with the stationary assumption is no longer tenable in a changing climate. Hence, it is inevitable to develop non-stationary rainfall IDF relationship and to understand the differences in non-stationary rainfall IDF relationships derived using AM and PDS datasets. Consequently, the objectives of this study are: (1) to develop non-stationary rainfall IDF relationships using both AM and PDS datasets; (2) to compare them in terms of return level estimation. In particular, the non-linear trend in different durations’ PDS and AM datasets of Hyderabad city (India) rainfall is modeled using Multi-objective Genetic Algorithm (MGA) generated Time based covariate. In this study, the PDS datasets are modeled by the Generalized Pareto Distribution (GPD) while the AM datasets are modeled by the Generalized Extreme Value Distribution (GEVD). The time-varying component is introduced in the scale parameter of the GPD and the location parameter of the GEVD by linking the MGA generated covariate. In addition, the complexity of each non-stationary model is identified using the corrected Akaike Information Criteria (AICc) and the statistical significance of trend parameter in the non-stationary models is estimated using the Likelihood Ratio (LR) test. Upon detecting significant superiority of non-stationary models, the return levels of extreme rainfall event for 2-, 5-, 10- and 25-year return periods are calculated using non-stationary models. From the results, it is observed that the non-stationary return levels estimated with PDS datasets are higher than those estimated with AM datasets for short durations and smaller return periods while the non-stationary return levels estimated with AM datasets are higher than those estimated with PDS datasets for long durations and higher return periods.