COUPLED WITHDRAWAL AND SAMPLING DESIGNS FOR GROUNDWATER SUPPLY MODELS

A coupled formulation of withdrawal and sampling designs for groundwater supply models is presented. The withdrawal design is described as a discrete time optimal control problem and solved using a closed loop stochastic control (CLSC) method. Two main features of the CLSC method are the anticipation of the future observation program and decomposition of the objective function into the deterministic and stochastic part. The former characteristic indicates the necessity for coupling the withdrawal and sampling designs, while the later feature allows a decision maker to estimate the uncertainty in the objective function if certain withdrawal rates are applied. The sampling network is sequentially developed, with the design criterion defined as a sensitivity of the objective function stochastic part to the uncertainty in the hydraulic head distribution multiplied with the variance of the hydraulic head. The concept of minimizing the stochastic part of the objective function with respect to the hydraulic head uncertainty provides a convenient way to couple the withdrawal design objectives with the monitoring network development weighted with the magnitude of the prediction error in the hydraulic head distribution. The Bayesian concept of measurement conditioning is employed to sequentially adjust the withdrawal rates and sampling network development by accounting for the information conveyed in field observations. Between the sampling sessions the uncertainty in the hydraulic head prediction is evaluated using the first- and second-moment analysis applied to the discretized groundwater flow model. The uncertainty in the hydraulic head prediction is assumed to come from the natural uncertainty in the hydraulic conductivity and uncertainty in the boundary condition values and other external fluxes (e.g., leakages and recharge). A hypothetical example is included to demonstrate the application procedure and to illustrate the main features of the proposed coupled formulation.