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In recent years, ground-water hydrologists have become increasingly aware of the need to describe the spatial variability of aquifer characteristics in statistical terms. This has led to the development of new theoretical models whose parameters, representing the aquifer characteristics, are treated as stochastic variables rather than deterministic functions of space. In this paper, the state of the art in stochastic modeling is reviewed, and the experience and new knowledge gained with these models are summarized. Many of the stochastic models developed to date allow the parameters to fluctuate with equal amplitude at every point in space, including points at which the material properties have actually been measured. A more recent trend has been to try to reduce the variance of the computed hydraulic head values by conditioning the model on measured values of aquifer transmissivities. It is argued that a further reduction in this variance could be effected by conditioning the model not only upon measurements of the aquifer characteristics, but also upon historical data relating to the prevailing flow regime. This additional conditioning can be achieved by estimating the model parameters with the aid of inverse methods that are compatible with the stochastic interpretation of spatial variability. Two such inverse methods are described in this paper. It is suggested that in the future, the output from inverse models should be used as input into stochastic models of groundwater flow. In addition to the need for interphasing inverse models with stochastic models, additional research is required to improve the reliability, versatility, and computational efficiency of these models.

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