Economic Valuation of Inter-Annual Reservoir Storage in Water Resources Systems: Theory, Development, and Applications

UoM administered thesis: Phd

  • Authors:
  • Majed Khadem


This thesis develops and applies methods that blend physical science, engineering and economics to the management of water resources. The core intuition of the work is that multi-disciplinary models of water systems which integrate hydrological, engineering and economic dimensions of the problem will be most effective at identifying best modes of management at system scale. The problem area of focus in the thesis is the question of inter-annual reservoir operation in large-scale multi-reservoir systems. Excessively generous releases will threaten future supplies but exaggerated pre-emptive saving of water supplies will create unnecessary economic hardship downstream. What’s the appropriate amount of water to carry-over from one year to the next? How can effective and efficient carry-over storage strategies be determined? This thesis proposes to address this question with a generalised approach for large-scale water resource systems using end-of-year carry-over storage value functions, i.e., curves that quantify the economic value of maintaining various amounts of water storage for subsequent years. The proposed approach uses hydro-economic optimisation models to simulate the economic allocation of water over space and time within human managed water systems. The model breaks up the simulated period of study into shorter periods and performs sequential runs of the optimisation model which allocates water from source nodes to water demands or storage nodes. The final state from the previous year provides the initial condition to each year-long problem and COSVF acts as a terminal condition representing the value of stored water for future use. These COSVFs have a concave shape to reflect the fact that the value of stored water is high when water is scarce and low when abundant. COSVF parameters that optimise performance can be determined using an external multi-objective evolutionary algorithm (EA), thus enabling to estimate the storage valuation which brings the highest overall regional economic benefits from water use. The scholarly contribution of the thesis includes investigating how hydro-economic model features impact their results, a new method for optimising water storage strategies in large complex non-convex managed water systems, and an investigation of how historical reservoir release data can be used to reveal the implicit economic value attributed to stored water. Existing approaches for valuation of carryover storage either suffer from curse of dimensionality, i.e. they fail as the size of the problem increases, or are unable to handle non-convexity (nonlinearity) of the natural phenomena. Above contributions are applied to a large-scale California Central Valley hydro-economic system where groundwater head-dependent pumping costs make the problem non-convex. Initially, it is investigated how an improved groundwater formulation that considers non-linear groundwater pumping costs leads to reduced overdrafting of aquifers. Also, it is shown that use of shadow prices for water marginal values, does not lead to an efficient management practice, especially in case of conjunctive use with non-linear groundwater pumping representation. This finding contradicts to what was being used in similar existing approaches for valuation of water storage e.g. Stochastic Dual Dynamic Programming. The hydro-economic optimisation model is then used to find COSVFs that lead to economically efficient management of the water system. Results show improved scarcity management evidenced by a reduction of scarcity (80% in scarcity volume and 98% in scarcity costs) compared to historical estimates. Finally, COSVF are calibrated to derive historical valuation of end-of-year storage for the region. This application reveals the implicit over-year storage values for 30 reservoirs in California’s Central Valley; results are discussed. The economic valuation of storage estimated in our case-studies can help inform water storage management decisions. Conclusions and a discussion of the three contributions are included.


Original languageEnglish
Awarding Institution
Award date31 Dec 2019