As the environment changes, the stationarity assumption in hydrological analysis has become questionable. If nonstationarity of an observed time series is not fully considered when handling climate change scenarios, the outcomes of statistical analyses would be invalid in practice. This study established bivariate time-varying copula models for risk analysis based on the generalized additive models in location, scale, and shape (GAMLSS) theory to develop the nonstationary joint drought management index (JDMI). Two kinds of daily streamflow data from the Soyang River basin were used; one is that observed during 1976-2005, and the other is that simulated for the period 2011-2099 from 26 climate change scenarios. The JDMI quantified the multi-index of reliability and vulnerability of hydrological drought, both of which cause damage to the hydrosystem. Hydrological drought was defined as the low-flow events that occur when streamflow is equal to or less than Q80 calculated from observed data, allowing future drought risk to be assessed and compared with the past. Then, reliability and vulnerability were estimated based on the duration and magnitude of the events, respectively. As a result, the JDMI provided the expected duration and magnitude quantities of drought or water deficit.The GAMLSS framework has been applied to hydrological frequency analysis to provide the design criteria for managing future drought risk [11,12]. Bivariate frequency analysis based on the GAMLSS-copula model was also conducted and proved useful in hydrological prediction [13][14][15]. GAMLSS can be useful to estimate nonstationary index. For example, Wang et al. [16] proposed the time-dependent standardized precipitation index and Bazrafshan and Hejabi [17] suggested using the nonstationary reconnaissance drought index.This study performed statistical analyses with 26 climate change scenarios for the Soyang River basin in South Korea to construct the bivariate time-varying copula models based on GAMLSS theory. Copula functions were used to combine the drought information estimated from low-flow events, which were reliability and vulnerability. Then a new drought index, joint drought management index (JDMI), was developed based on the nonstationary copula model. The potential drought or water supply failure events were quantified as durations and magnitudes by JDMI-based risk assessment.
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