The accuracy of model prediction depends on the reliability of the estimated model parameters as well as on the accuracy of the prescribed initial and boundary conditions. In general, parameters used in deriving the governing equations are not directly measurable from the physical point of view. In practice, model parameters are required to be estimated from historical input-output observations using an inverse procedure of parameter estimation.
The inverse problem of parameter estimation in distributed-parameter systems has been studied extensively during the last three decades. The term distributed system implies that the response of the system is governed by a partial differential equation [(Eq. (8) or (13)] and parameters embedded in the equation (Txx, Tv} . S) are spatially dependent. A review of the inverse problem of parameter identification in groundwater hydrology was presented by Yeh (1986), Carrera (1988), Sun (1994a), and McLaughlin and Townley (1996). In general, the inverse problem seeks to identify the model parameters by observing the output of the dependent variable (head) in the spatial and time domain. Frequently, point estimates of transmissivity and storage coefficient are also available and they can be used as prior information to regulate the inverse solution.
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