Theoretical Foundations of Chance-Constrained Programming for Water Resources Management Under Hydrological Uncertainty in the Benue River Basin

Water resources management in the Benue River Basin of North Central Nigeria confronts severe hydrological uncertainty arising from climate variability, upstream dam operations in Cameroon, and measurement limitations that render deterministic optimization models inadequate for policy decision-making. This dissertation develops theoretical foundations for chance-constrained programming formulations applied to water resources management under hydrological uncertainty in the Benue River Basin, making original contributions to optimization theory and applied water resources operations research. The theoretical framework is grounded in a formal characterization of deep uncertainty using imprecise probability theory, which subsumes classical probabilistic uncertainty as a special case. Original results are established regarding the convexity, differentiability, and tractable approximation of chance constraints under a novel class of elliptical-log-normal mixture distributions estimated from historical flow data. A multi-period chance-constrained water allocation model is formulated for the Benue River Basin, incorporating agricultural, municipal, hydropower, and ecological flow requirements with probabilistic constraint satisfaction at specified reliability levels. An original sequential convex approximation algorithm for solving the non-convex chance-constrained optimization model is developed and proven to converge to a local optimum satisfying first-order optimality conditions. Empirical application generates water allocation policies for five downstream states with formal probability guarantees on demand satisfaction, providing a rigorous basis for transboundary water governance discussions. The dissertation contributes original theoretical results in chance-constrained optimization with significant implications for water resources planning methodology. Keywords: chance-constrained programming, water resources, hydrological uncertainty, Benue River Basin, stochastic optimization