Three dimensional characterization of meteorological and hydrological droughts and their probabilistic links

Meteorological and hydrological droughts are inherently correlated, but with a time lag. A prolonged precipitation deficiency propagates to surface water bodies and may give rise to hydrological drought in the subsequent time period. Establishing links between these two drought types is of great significance for water resources planning and for developing drought resistant measures. This study proposes a copula-based method employing conditional probability distribution to depict the structure of dependence between the characteristics of meteorological and hydrological droughts. The time series of grid-based standardized precipitation evapotranspiration index (SPE1) and standardized runoff index (SRI) were derived from the simulations of the variable infiltration capacity (VIC) model over the Yellow River basin (YRB) during 1961-2012. Then, using a three-dimensional (time-latitude-longitude) drought identification method, three drought characteristics, including duration, area and severity, were extracted for meteorological and hydrological droughts. For analyzing drought characteristics, return periods and connection between meteorological and hydrological droughts, a probabilistic framework using the copula function, was developed. Results showed that there was a general drying tendency both for meteorological and hydrological droughts with longer duration and larger spatial extent. According to the trivariate joint distribution of duration, area and severity, the most severe meteorological and hydrological droughts over the YRB occurred around 1998-2000, with return periods exceeding 50 years. In terms of establishing the dependence between characteristics of meteorological and hydrological droughts, traditional statistical models like the linear, exponential, and power functions presented significant deviations, especially for severe or extreme drought conditions. In contrast, the copula based conditional distribution method provided a satisfactorily probabilistic prediction of hydrological drought characteristics given the information of meteorological drought characteristics. The stability test suggested compared to the length of data sample, the incorporation of typical major drought events with long persistence and wide spatial extent is more important for reliable drought prediction.