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The infrastructure design is primarily based on rainfall intensity–duration–frequency (IDF) curves, and the existing IDF curves are based on the concept of stationary extreme value theory (EVT) (i.e. the occurrence probability of extreme precipitation is not expected to change significantly over time). But, the extreme precipitation events are increasing due to global climate change and questioning the reliability of our current infrastructure design. Based on recent developments in the EVT, recent studies proposed a method for developing non‐stationary rainfall IDF curve by incorporating linear trend in the location parameter of the generalized extreme value (GEV) distribution. Upon detecting a significant trend in the extreme rainfall series, directly applying the linear trend to develop non‐stationary IDF curves may increase the bias of the non‐stationary model. Hence, it is important to develop non‐stationary GEV model which has less bias than the stationary model by modelling nonlinear trend in the series. In this study, we try to develop non‐stationary GEV models with less bias by modelling nonlinear trend in the series using multi‐objective genetic algorithm (MOGA). In addition, the proposed GEV model is compared with the stationary GEV model and the linear trend‐based non‐stationary GEV model. Furthermore, the Wilmington city and the Hyderabad city non‐stationary IDF curves are developed and compared with stationary IDF curves. From the study results, it is observed that the proposed MOGA‐based method is able to build the good quality and less bias non‐stationary GEV models by modelling nonlinear trend in the series. In addition, it is also observed that the usage of linear trend for modelling non‐stationarity in the time series sometimes increase the bias of non‐stationary model.

ABSTRACT:Since the substantial evidence of non-stationarity in the extreme rainfall series is already reported, the current realm of hydrologic research focusing on developing methodologies for a non-stationary rainfall condition. As the rainfall intensity duration frequency (IDF) curve is primarily used in storm water management and infrastructure design, developing rainfall IDF curves in a non-stationary context is a current interest of water resource researchers. In order to construct non-stationary rainfall IDF curve, the probability distribution's parameters are allowed to change according to covariate value and the current practice is to use time as a covariate. However, the covariate can be any physical process and the recent studies show that the direct use of time as a covariate may increase the bias. Moreover, the significance of selecting covariate in developing non-stationary rainfall IDF curve is yet to be explored. Therefore, this study aims to find the uncertainties in rainfall return levels due to the choice of the covariate (covariate uncertainty). In addition, since the uncertainty in parameter estimates (parameter uncertainty) is the major source of uncertainty in the stationary IDF curve, the relative significance of covariate uncertainty, when compared to the parameter uncertainty, is also explored. The study results reveal that the covariate uncertainty is significant, especially when a number of covariates produce significantly superior non-stationary model and, remarkably, it is nearly equivalent to the parameter uncertainty in such cases.