Data from 31 regional aquifers are analyzed to identify the horizontal spatial correlation structure of transmissivity, hydraulic conductivity, and storage coefficient. Three parameters are estimated: the variance of small-scale variability (or nugget) and the variance and integral scale (range) of an exponential covariance function. The assumption of normality of the aforementioned geohydrologic parameters and their logarithmic transformations is also examined. Results are obtained which indicate that the logarithms of these properties generally pass normality tests.

The geostatistical approach to the estimation of transmissivity from head and transmissivity measurements is developed for two‐dimensional steady flow. The field of the logarithm of transmissivity (log‐transmissivity) is represented as a zero‐order intrinsic random field; its spatial structure is described in this application through a two‐term covariance function that is linear in the parameters θ1 and θ2. Linearization of the discretized flow equations allows the construction of the joint covariance matrix of the head and log transmissivity measurements as a linear function of θ1 and θ2. In this particular application the coefficient matrices are calculated numerically in a noniterative fashion. Maximum likelihood estimation is employed to estimate θ1 and θ2 as well as additional parameters from measurements. Linear estimation theory (cokriging) then yields point or block‐averaged estimates of transmissivity. The approach is first applied to a test case with favorable results. It is shown that the application of the methodology gives good estimates of transmissivities. It is also shown that when the transmissivities are used in a numerical model they reproduce the head measurements quite well. Results from the application of the methodology to the Jordan aquifer in Iowa are also presented.

The Netherlands has faced unique water management challenges. Much of the western part of this country is covered by compressible peat or clay soils. Historic land use practices resulted in loss, decay, and consolidation of these soils and subsequent land subsidence. This, along with the sea level rise, tides, and storms, resulted in a country where one-third of the land lies below mean sea level and without dunes, dikes, and pumps, 65% would be under water at high tide.Over many centuries the Dutch have fought against this loss of land. Three stages in the historical development of land drainage and reclamation activities are presented.The first stage was in the sixteenth and seventeenth centuries when many lakes north of Amsterdam were drained and reclaimed for agricultural use. Windmills were used to pump these lakes dry. Next, in the nineteenth century, Lake Haarlem became the largest lake drained in the Netherlands and the one of the first to be drained using steam-powered pumps alone. Finally, in the twentieth century the Zuiderzee tidal estuary was drained and reclaimed, resulting in an additional 1650 km 2 of new land for agriculture, recreation, and urban expansion.

In geological settings where the water table is a subdued replica of the ground surface, cokriging can be used to estimate the water table elevation at unsampled locations on the basis of values of water table elevation and ground surface elevation measured at wells and at points along flowing streams. The ground surface elevation at the estimation point must also be determined. In the proposed method, separate models are generated for the spatial variability of the water table and ground surface elevation and for the dependence between these variables. After the models have been validated, cokriging or minimum variance unbiased estimation is used to obtain the estimated water table elevations and their estimation variances. For the Pits and Trenches area near Oak Ridge National Laboratory, water table estimations along a linear section, both with and without the inclusion of ground surface elevation as a statistical predictor, illustrate the advantages of the cokriging model.

Two separate applications of the geostatistical solution to the inverse problem in groundwater modeling are presented. Both applications estimate the transmissivity field for a two-dimensional model of a confined aquifer under steady flow conditions. The estimates are based on point observations of transmissivity and hydraulic head and also on a model of the aquifer which includes prescribed head boundaries, leakage, and steady state pumping. The model used to describe the spatial variability of the log-transmissivity describes large-scale fluctuations through a linear mean or drift intermediate and small-scale fluctuations through a two-parameter covariance function. The first application presented estimates the log-transmissivities using Gaussian conditional mean estimation. The second application uses an extended form of cokriging. The two methods are compared and their relative merits discussed. The extended cokriging application is applied to the Jordan Aquifer of Iowa. A comparison is also made between the conditional mean application and an analytical approach. based on all available information, including (1) point observations of the piezometric head, (2) measurements of transmissivity (usually from pumping tests), (3) estimates of the areal extent and boundary features of the aquifer, (4) estimates of the rate of water removal from the aquifer, and (5) estimates of the leakage characteristics of confining layers. The most recent efforts in the solution of the inverse problem presuppose the piezometric head and transmissivity fields to be realizations of random functions. Regression procedures or statistical estimation can then be applied to solve the problem.The scope of this work is that of estimating the transmissivity field for a two-dimensional model of a confined aquifer under steady flow conditions. The estimation procedure will be based on the five types of information described above. The emphasis here is on regional aquifer models. For this reason the measured values of transmissivity are assumed to represent aquifer behavior at a scale smaller than the dimension of a typical model discretization element.The geostatistical approach to the inverse problem is described in detail in the works by Kitanidis and Vomvoris [1983] and Vomvoris [1982]. An application of the geostatistical solution is presented in the work by Hoeksema and Kitanidis [1984], and a similar technique is presented in the work by Dagan [1985]. The geostatistical solution can be viewed as a five-step procedure. First, a model for the statistical spatial variability of the transmissivity field is proposed. Second, the differential equation of groundwater flow is used to relate the spatial variability of the piezometric head to that of the transmissivity. Third, the observed values of head and transmissivity are used to estimate the unknown parameters in the transmissivity spatial variability model. Fourth, the validity of the fitted spatial variability model is tested. If the model passes the validity test then, finally, linear ...