Uncertainty of stationary and nonstationary models for rainfall frequency analysis

Abstract

The development of nonstationary frequency analysis models is gaining popularity in the field of hydro‐climatology. Such models account for nonstationarities related to climate change and climate variability but at the price of added complexity. It has been debated if such models are worth developing considering the increase in uncertainty inherent to more complex models. However, the uncertainty associated to nonstationary models is rarely studied. The objective of this article is to compare the uncertainties in stationary and nonstationary models based on objective criteria. The study is based on observed rainfall data in the United Arab Emirates (UAE) where strong nonstationarities were observed. In this study, a nonstationary frequency analysis introducing covariates into the distribution parameters was carried out for total and maximum annual rainfalls observed in the UAE. The generalized extreme value (GEV) distribution was used to model annual maximum rainfalls and the gamma (G) distribution was used to model total annual rainfalls. A number of nonstationary models, using time and climate indices as covariates, were developed and compared to classical stationary frequency analysis models. Two climate oscillation patterns having strong impacts on precipitation in the UAE were selected: the Oceanic Niño Index and the Northern Oscillation Index. Results indicate that the inclusion of a climate oscillation index generally improves the fit of the models to the observed data and the inclusion of two covariates generally provides the overall best fits. Uncertainties of estimated quantiles were assessed with confidence intervals (CIs) computed with the parametric bootstrap method. Results show that for the small sample sizes in this study, the width of the CIs can be very large for extreme nonexceedance probabilities and for the most extreme values of the climate index covariates. The weaknesses of nonstationary models revealed by the bootstrap uncertainties are discussed and words of caution are formulated.

Uncertainty of Rate of Change in Korean Future Rainfall Extremes Using Non-Stationary GEV Model

“…Traditionally, the GEV distribution assumes that observations are independent and identically distributed. However, in order to model non-stationarity in the AMR time series, many researchers allowed the parameters of the GEV distribution to change depending on the co-variate [10,22,[27][28][29]31,32,36,39]. In theory, all parameters of the GEV distribution can be applied as a function of various co-variates, but in this study, a co-variate was applied only to the scale parameter alpha, as shown below, in order to intuitively understand the effect of the co-variate.…”

“…However, the AIC (where AIC = 2 × (# of parameters) + 2 × nllh) reflecting the parsimony point of view recommends that it is more appropriate to apply the stationary model s for both AMRs of both sites. That is, as applied in Lee et al [10] and Ouarda et al [36], if an optimal model is selected using the AIC, which mainly considers the aspect of fitness of the observed AMR, the stationary model s is selected as the optimal model for the AMR at Chuncheon and Cheonan sites. The fundamental purpose of performing a frequency analysis is to estimate the rainfall quantile.…”

“…Therefore, they argued that it was not essential to adopt a non-stationary model. On the other hand, studies showing that a co-variate-based non-stationary frequency analysis is more appropriate to convincingly project rainfall extremes in the future have also been actively proposed [10,12,15,31,36].…”

“…The smaller the uncertainty of the estimated quantiles, the more reliable the model can be recognized as [39]. Ouarda et al [36] pointed out that uncertainty is likely to act as a major weakness in the applicability of non-stationary models through stationary and non-stationary frequency analyses of annual maximum rainfall in the UAE. However, studies suggesting a methodology that can reduce uncertainty are still difficult to find.…”

Uncertainty analysis of the rate of change of quantile due to global warming using uncertainty analysis of non-stationary frequency model of peak-over-threshold series

“…Agilan and Umamahesh (2018) investigated the effect of covariate selection on uncertainty in the covariate-based non-stationary analysis using annual maximum series. Ouarda et al (2020) indicated that uncertainty is likely to work as a major weakness in the applicability of the non-stationary model through the analysis of UAE annual maximum rainfall series.…”