Improving stochastic dynamic programming for reservoir operation using drought severity and the copula function

Study region Marun Dam reservoir, southwestern Iran. Study focus Reservoir operation under droughts remains challenging because traditional Stochastic Dynamic Programming (SDP) estimates inflow transition probabilities using Markov chains, without explicitly considering drought severity or nonlinear dependence between hydrological variables. This study reformulates the transition probability matrix (TPM) of SDP by integrating inflow and drought severity into the TPM using copula functions, specifying more realistic reservoir operation policies under drought conditions. To achieve this, the Copula-Hybrid Drought Index (CHDI) is proposed, based on the predicted rainfall projections acquired from the results of modeled climate-change simulations under the SSP3.70 scenario. New hydrological insights for the region Historical analysis of Marun Dam reservoir shows that the implementation of the proposed SDP, integrating inflow with the drought severity for the previous period using copula-based transition probabilities (TPM C ), yields greater sustainability and conserves more water in the reservoir for future ‎droughts‎, compared with the SDP method using the conventional Markov-chain transition probabilities (TPM M ). However, this improvement comes with a higher objective ‎function value. The proposed approach is also examined using three suggested scenarios, named S1, S2, and S3, to update the operation policies under droughts, and shows a reduction in drought severity and duration of drought spells by reserving more water for the drought periods, albeit at the cost of lower sustainability and objective function values. This research confirms that incorporating inflow with drought through TPMs enhances the robustness of reservoir operation policies under drought conditions, particularly for arid and semi-arid regions facing increasing climate variability.