Equipping stochastic dynamic programming with copula function to determine reservoir operation rule curves and risk assessment for current and future conditions

Abstract

In this study, a novel approach is proposed in which the transition probability matrix (TPM) of stochastic dynamic programming (SDP) methods is determined based on the copula function (TPM-C) by calculating the conditional probability. The obtained results are compared with the TPM based on the Markov Chain method (TPM-M). Here, the Marun dam reservoir, in southwestern Iran, is selected as a case study. In addition, for the historical period, the best values of reliability, resilience, vulnerability, sustainability, a minimum of water deficit as an objective function are obtained, and the average reservoir storage value of TPM-C is better than TPM-M. Finally, to update the reservoir operation rule curves, three different scenarios are proposed depending on the historical and future conditions. For this purpose, the water inflow values into the dam reservoir are predicted using a Multi-Layer Perceptron (MLP) model depending on the predicted precipitation of the climate change model. Therefore, the inflows, reservoir storage volumes, and water demand values are used to simulate and forecast the water release values into the reservoir. The results show the superior performance of the proposed TPM-C compared to the TPM-M approach to determine the reservoir operation rule curves at uncertain future conditions. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.