An extended Kalman filter model for characterizing minimum variance estimates of the piezometric heads and coefficients defining an unconfined aquifer subject to artificial recharge is developed. The system evolution model employs Hantush's (1967) model. Sensitivity analyses are used to test the estimation capability of the technique. The ability of the extended Kalman filter to use all available information from both the system model and measurements of the state to provide approximate minimum variance estimates of the state and confidence limits is shown. The extended Kalman filter version of Hantush's model is applied to a record data length of one year obtained at the study area located in Norwood, Ontario. INTRODUCTIONIn many regions, increases in demand for water have been met by groundwater extractions resulting in the 'mining' of the water. Concurrently, the quality of the surface water body receiving the increased effluent has deteriorated. To halt or even reverse these trends, artificial groundwater recharge is receiving increased attention. In some situations the water source for use in the recharge is secondary sewage effluent '[e.g., Bouwer, 1976]. The basis of the recharge concept is that the vadose zone and the aquifers purify the water chemically and biologically, thereby, allowing its reuse.Groundwater systems are unique •in water resources managemerit because they can only be observed and controlled indirectly, using measurements obtained from the surface. Many deterministic mathematical models to infer the groundwater system response and parameters have been developed, all of them essentially being based on hydrologic and geologic information such as the soil characteristics, infiltration, and pumpage rates. The parameter estimates for the majority of the models are obtained either directly in the field or from disturbed samples in a laboratory. These model parameters are then assumed to be constant and perfectly known. However, these parameters exhibit large temporal and spatial fluctuations due to the heterogeneity and anisotropy of the aquifer, the stochastic meteorological conditions, and other changing environmental factors. In addition, due to the measurement errors there is always some uncertainty implicit in assignment of parameter magnitudes at any point in time or space. As well, any model represents only an abstraction of the real system. As a consequence the modeling of a stochastic process by a deterministic model may be subject to significant errors. Therefore the development of methodologies to interpret the observable information and thereby provide more accurate estimates of the responses of the system is of increasing interest. Only recently have the uncertainties of hydrologic system parameters been incorporated into a groundwater modeling technique. Wilson et al. [1978] utilized a state estimation technique, the extended Kalman filter, which combines an uncertain system model and noisy measurements of system Paper number 2W0709. 0043-1497/82/002 W-0709505.00 behavior to dete...
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