Hydroeconomic Conjunctive Use Model Formulation for California's Central Valley Using Response Functions

Water resource system planning models that include surface and groundwater have often represented aquifers as simplified lumped sub-basins. Recently, systems models increasingly embed groundwater flow equations or stress response functions to enable the study of spatially distributed groundwater phenomena. This is especially important for environmental restoration models, since spatial information is essential to managing eco-hydrologic systems. This paper describes the formulation and design of a hydrologic-economic monthly planning model of California's Sacramento Valley. The model uses deterministic optimization with a non-linear formulation. The proposed optimization model includes a network-like structure to represent surface water and compiled response functions to model spatial groundwater processes. The response function method uses an external groundwater simulation model as a pre-processor to build a database of the aquifer's responses to unit stresses. This allows relatively detailed modeling in areas of interest (such as river and wetland locations) and coarser modeling where only regional groundwater elevations are required. Water allocation in the proposed model is driven by minimizing costs associated with system operation and water scarcity at demand sites. Water scarcity costs are estimated from urban and agricultural water demand curves derived externally using economic models. Dynamic pumping costs require the model to be non-linear, because pumping cost is a function of groundwater elevation, itself a decision variable.