Bi-site Analysis of Meteorological Drought Duration: Theoretical Modeling and Application

Droughts are regional incidents that threat the environment and limit most of the socio-economic activities. Given the dry and wet state sequences for two sites, X_t^{( 1 )}X_t^{\left( 1 \right)} and X_t^{( 2 )}X_t^{\left( 2 \right)} , this paper presents a procedure to reduce the two sequences X_t^{( 1 )}X_t^{\left( 1 \right)} and X_t^{( 2 )}X_t^{\left( 2 \right)} to one sequence Z _t for the purpose of simplifying the analysis of drought duration at two sites jointly. Theoretical models to evaluate the expected value and the variance of the process Z _t and the occurrence probability of the dry state at two sites jointly are presented and verified using simulation experiments. Historical data for the period 1939–2005 and generated rainy season precipitation data for two gauging sites in Central Jordan, namely Amman Airport and Madaba, is used in the present study to investigate the occurrence of droughts. The joint analysis of drought duration obtained using the historical precipitation at the two sites appears to be inconsistent especially for droughts of duration longer than 3 years. On the other hand, the joint analysis of drought duration obtained theoretically by employing the characteristics of the process Z _t are found to match well with the more reliable drought statistics obtained empirically by analyzing the long generated precipitation. Considering 25 years planning horizon, droughts of 1, 2, and 3 years duration are the most frequent droughts in the region of Central Jordan. The return period of such regional droughts ranges from 8–30 years.