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Kyoto University (2016)

Stochastic Modeling of Hydrological Events for Better Water Management

Erfaneh, Sharifi

Titre : Stochastic Modeling of Hydrological Events for Better Water Management

Auteur : Erfaneh, Sharifi

Université de soutenance : Kyoto University

Grade : Doctoral Thesis 2016

Résumé
Alteration of the hydrological cycles caused by climate change is increasingly affecting water resources. Offering sustainable solutions to the water management problems require hydrological process studies. The goal of this thesis is to provide a mathematical and numerical modeling framework for assessing hydrological events, deducing optimal control strategies, and studying their real world applications for better water management. This thesis focuses in particular on stochastic modeling and optimal control of reservoirs as well as rainfed agriculture. In the first part of the thesis a hydrologic model is proposed based on the Langevin equation, which is a stochastic differential equation governing zero-reverting Ornstein-Uhlenbeck (OU) processes. The optimal control problem is formulated in the context of dynamic programming to deduce the optimal strategies for better water management. Then, computational methods are presented to numerically approximate the relevant equations. Considering the level of drought severity as the zero-reverting OU process, optimality of rainfed agriculture is investigated in the context of stochastic control theory. Occurrence of drought terminating growth of crops is modelled with the concept of first exit time. Next, a novel type of hydraulic structure is proposed for rainwater harvesting in arid area. Design, construction, and operation of the actual rainwater harvesting system are presented with model parameters identified from observed data. Finally, a mathematical model is proposed to deduce optimal operational rules for reservoirs harvesting stochastic surface water flows to meet the demand from command areas. The mathematical model defines stochastic control problems in terms of dynamic programming, involving (Hamilton-Jacobi-Bellman) HJB equation systems. Then, the real life application is discussed with numerical solutions to a HJB equation. The zero-reverting OU process is applied to representing the stochastic surface water flows and the demand from command areas. The numerical solutions of the HJB equation yield optimal irrigation strategies represented in terms of rule curves prescribing water withdrawal limits.

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