Abstract
Extreme value modeling for extreme rainfall is one of the most important processes in the field of hydrology. For the improvement of extreme value modeling and its physical meaning, large-scale climate modes have been widely used as covariates of distribution parameters, as they can physically account for climate variability. This study proposes a novel procedure for extreme value modeling of rainfall based on the significant relationship between the long-term trend of the annual maximum (AM) daily rainfall and large-scale climate indices. This procedure is characterized by two main steps: (a) identifying significant seasonal climate indices (SCIs), which impact the long-term trend of AM daily rainfall using statistical approaches, such as ensemble empirical mode decomposition, and (b) selecting an appropriate generalized extreme value (GEV) distribution among the stationary GEV and nonstationary GEV (NS-GEV) using time and SCIs as covariates by comparing their model fit and uncertainty. Our findings showed significant relationships between the long-term trend of AM daily rainfall over South Korea and SCIs (i.e., the Atlantic Meridional Mode, Atlantic Multidecadal Oscillation in the fall season, and North Atlantic Oscillation in the summer season). In addition, we proposed a model selection procedure considering both the Akaike information criterion and residual bootstrap method to select an appropriate GEV distribution among a total of 59 GEV candidates. As a result, the NS-GEV with SCI covariates generally showed the best performance over South Korea. We expect that this study can contribute to estimating more reliable extreme rainfall quantiles using climate covariates.
Highlights
Extreme value modeling for hydrological extreme events is an essential task for the design of hydraulic structures
It is necessary to determine the relationships between model parameters and covariates prior to model parameter estimation to deal with the ergodicity issue
In nonstationary extreme value modeling, it is essential to reflect the trend in statistical characteristics, such as the mean and variance of the observations, because nonstationarity is generally considered by the time-dependent location and/or scale parameters of the probability distribution model
Summary
Extreme value modeling for hydrological extreme events (e.g., heavy rainfall and floods) is an essential task for the design of hydraulic structures. One popular approach applies a variety of candidate nonstationary models to the nonstationary data and selects an appropriate model based on model diagnostics It generally employs the maximum likelihood estimation (MLE) method to estimate nonstationary model parameters due to its adaptability to changes in model structures [1]. This approach has been studied extensively and can be referred to as a “user-friendly” method. It is necessary to determine the relationships between model parameters and covariates prior to model parameter estimation to deal with the ergodicity issue This is an important issue that needs to be addressed in terms of statistical hydrology, but hydrological applications mostly accept nonstationary models, as we mentioned earlier. We apply the standardized approach in this study, and the limitations regarding ergodicity will be discussed in the discussion section later
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