Probabilistic hydrological drought index forecasting based on meteorological drought index using Archimedean copulas

Hydrological drought forecasting is considered a key component in water resources risk management. As sustained meteorological drought may lead to hydrological drought over time, it is conceptually feasible to capitalize on the dependency between the meteorological and hydrological droughts while trying to forecast the latter. As such, copula functions are powerful tools to study the propagation of meteorological droughts into hydrological droughts. In this research, monthly precipitation and discharge time series were used to determine Standardized Precipitation Index (SPI) and Standardized Hydrological Drought Index (SHDI) at different time scales which quantify the state of meteorological and hydrological droughts, respectively. Five Archimedean copula functions were adopted to model the dependence structure between meteorological/hydrological drought indices. The Clayton copula was identified for further investigation based on the p-value. Next, the conditional probability and the matrix of forecasted class transitions were calculated. Results indicated that the next month's SHDI class forecasting is promising with less than 10% error. Moreover, extreme and severe meteorological drought classes lead to hydrological drought condition with a more than 70% probability. Other classes of meteorological drought/wet conditions lead to normal hydrological (drought) condition with less than 50% probability and to wet hydrological condition with over 20% probability.