Drought analysis framework based on copula and Poisson process with nonstationarity

Droughts have been occurring with increased frequency and bringing with them considerable losses. Due to its nature, the best approach to monitoring and assessing droughts is in terms of stochastic theories. As a consequence, this study applied SPI in the hydrological drought detection, and examine/interpret drought-related phenomena. The 3-month SPI is used to decide the drought development and terminate phases based on the coincidence of hydrological drought and anomalies in precipitation. Four primary characteristics were determined to clarify the descriptions of drought magnitude and occurrence: duration, deficit, occurrence time and recurrence year. A stochastic process of drought is established to take account these characteristics using the copula function and a Poisson process as well as non-stationarity. Case study on the Shihmen and Zengwen reservoir watersheds in Taiwan revealed that hydrological drought events often coincide with meteorological drought, but some inconsistencies due to unusual hydrological hysteresis in rainfall and runoff. Our analysis raised several issues, including the choice of drought identification parameters and SPI time scale/threshold, which should take into account anthropogenic activity and hydrological characteristics. A positive correlation between drought duration and drought deficit and a negative correlation between them and occurrence time were identified. It was also observed that subsequent drought event may be more severe due to the partial recovery of hydrological condition. In terms of non-stationarity, our results do not show strong evidence of long-term trend for drought characteristics. Some limitations could be due to the percentile-to-percentile basis of copula. This issue may need to be examined using non-stationary copula analysis or time-variant correlation-covariance models. In the end, we demonstrated that this framework can apply in forecasting drought conditions and generating synthetic droughts for use in the formulation of water resources management strategies and the development of drought preparedness plans.