Uncertainty in nonstationary frequency analysis of South Korea's daily rainfall peak over threshold excesses associated with covariates

Several methods have been proposed to analyze the frequency of nonstationary anomalies. The applicability of the nonstationary frequency analysis has been mainly evaluated based on the agreement between the time series data and the applied probability distribution. However, since the uncertainty in the parameter estimate of the probability distribution is the main source of uncertainty in frequency analysis, the uncertainty in the correspondence between samples and probability distribution is inevitably large. In this study, an extreme rainfall frequency analysis is performed that fits the peak over threshold series to the covariate-based nonstationary generalized Pareto distribution. By quantitatively evaluating the uncertainty of daily rainfall quantile estimates at 13 sites of the Korea Meteorological Administration using the Bayesian approach, we tried to evaluate the applicability of the nonstationary frequency analysis with a focus on uncertainty. The results indicated that the inclusion of dew point temperature (DPT) or surface air temperature (SAT) generally improved the goodness of fit of the model for the observed samples. The uncertainty of the estimated rainfall quantiles was evaluated by the confidence interval of the ensemble generated by the Markov chain Monte Carlo. The results showed that the width of the confidence interval of quantiles could be greatly amplified due to extreme values of the covariate. In order to compensate for the weakness of the nonstationary model exposed by the uncertainty, a method of specifying a reference value of a covariate corresponding to a nonexceedance probability has been proposed. The results of the study revealed that the reference covariate plays an important role in the reliability of the nonstationary model. In addition, when the reference covariate was given, it was confirmed that the uncertainty reduction in quantile estimates for the increase in the sample size was more pronounced in the nonstationary model. Finally, it was discussed how information on a global temperature rise could be integrated with a DPT or SAT-based nonstationary frequency analysis. Thus, a method to quantify the uncertainty of the rate of change in future quantiles due to global warming, using rainfall quantile ensembles obtained in the uncertainty analysis process, has been formulated.