Improvement of Extreme Value Modeling for Extreme Rainfall Using Large-Scale Climate Modes and Considering Model Uncertainty

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.

An Index-Flood Statistical Model for Hydrological Drought Assessment

Modelling of hydrological extremes and drought modelling in particular has received much attention over recent decades. The main aim of this study is to apply a statistical model for drought estimation (in this case deficit volume) using extreme value theory and the index-flood method and to reduce the uncertainties in estimation of drought event return levels. Deficit volumes for 133 catchments in the Czech Republic (1901–2015) were simulated by hydrological model BILAN. The validation of severity, intensity and length of simulated drought events revealed good match with the available observed data. To estimate return levels of the deficit volumes, it is assumed (in accord with the index-flood method), that the deficit volumes within a homogeneous region are identically distributed after scaling with a site-specific factor. The parameters of the scaled regional distribution are estimated using L-moments. The goodness-of-fit of the statistical model is assessed by Anderson–Darling test. For the estimation of critical values, sampling methods allowing for handling of years without drought were used. It is shown, that the index-flood model with a Generalized Pareto distribution performs well and substantially reduces the uncertainty related to the estimation of the shape parameter and of the large deficit volume quantiles.

Incorporating spatial dependence in regional frequency analysis

The efficiency of regional frequency analysis (RFA) is undermined by intersite dependence, which is usually ignored in parameter estimation. We propose a spatial index flood model where marginal generalized extreme value distributions are joined by an extreme-value copula characterized by a max-stable process for the spatial dependence. The parameters are estimated with a pairwise likelihood constructed from bivariate marginal generalized extreme value distributions. The estimators of model parameters and return levels can be more efficient than those from the traditional index flood model when the max-stable process fits the intersite dependence well. Through simulation, we compared the pairwise likelihood method with an L-moment method and an independence likelihood method under various spatial dependence models and dependence levels. The pairwise likelihood method was found to be the most efficient in mean squared error if the dependence model was correctly specified. When the dependence model was misspecified within the max-stable models, the pairwise likelihood method was still competitive relative to the other two methods. When the dependence model was not a max-stable model, the pairwise likelihood method led to serious bias in estimating the shape parameter and return levels, especially when the dependence was strong. In an illustration with annual maximum precipitation data from Switzerland, the pairwise likelihood method yielded remarkable reduction in the standard errors of return level estimates in comparison to the L-moment method.

Nonstationary precipitation Intensity-Duration-Frequency curves for infrastructure design in a changing climate

Extreme climatic events are growing more severe and frequent, calling into question how prepared our infrastructure is to deal with these changes. Current infrastructure design is primarily based on precipitation Intensity-Duration-Frequency (IDF) curves with the so-called stationary assumption, meaning extremes will not vary significantly over time. However, climate change is expected to alter climatic extremes, a concept termed nonstationarity. Here we show that given nonstationarity, current IDF curves can substantially underestimate precipitation extremes and thus, they may not be suitable for infrastructure design in a changing climate. We show that a stationary climate assumption may lead to underestimation of extreme precipitation by as much as 60%, which increases the flood risk and failure risk in infrastructure systems. We then present a generalized framework for estimating nonstationary IDF curves and their uncertainties using Bayesian inference. The methodology can potentially be integrated in future design concepts.