Water Resources Research Center, University of Minnesota
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Modelling groundwater flow can be viewed as two separate problems. The first is identification of the transmissivity of the porous medium. This property fully describes the medium when the type of flow does not vary with time. The second problem is the prediction of the response (output) of the system under different stimuli (inputs), which are given as boundary conditions such as known values of flow, discharge (leakage, pumping, infiltration, etc.), and piezometric head. The research reported here
I addresses both of these problems. The theory of random fields provides a powerful method to model the complex variability of transmissivities observed in nature. Choosing this geostatistical approach implies that the other two fields (heads and
velocities) must be described as random fields as well. Under this assumption, the natural question to ask is: how can we obtain the best description of the random fields, given all available information? To
answer this question, this work presents a new method to estimate the random fields involved in groundwater flow. Its relevant feature is to make maximum use of all available information. The method is based on
conditional probability formulas, derived for the case of a Gaussian distribution.
A gaussian random field is completely specified by its first two moments:
mean and covariance. It is customary to describe the mean as a spatially variable function and the covariance as a function that depends solely on the distance between two points in the field. Both functions depend on parameters that must be estimated from the data. The method of maximum likelihood is used to estimate covariance parameters, while the mean parameters are filtered out by linear transformation of the transmissivity data. A new method was developed to solve the prediction problem. Basically, it estimates the conditional densities of the three random fields using all available data. For this purpose, the flow equation was linearized about a conditional mean of the transmissivity field. Numerical simulations wereI used to test this method; and results are quite satisfactory. A better description of the spatially variable fields was achieved, as manifested by a reduction of the mean squared error of estimation of both the log transmissivity and head fields. The error reduction is directly proportional to the degree of heterogeneity of the log-transmissivity field.
Kitanidis, P.K. Quinodoz, H.A.M. 1988. Estimation of Transmissivities, Heads and Velocities in Steady-State Groundwater Modeling. Water Resources Research Center.
Water Resources Research Center
Kitanidis, P.K.; Quinodoz, H.A.M..
Estimation of Transmissivities, Heads and Velocities in Steady-State Groundwater Modeling.
Water Resources Research Center, University of Minnesota.
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