## 1. Introduction

[2] Although stochastic theories of subsurface flow and transport for applications involving heterogeneous geologic media have existed for several decades, field attempts at validating these theories in a variety of sediments are limited. To enable a quantitative assessment of the validity of the stochastic approach, it is not sufficient to only observe the spatial patterns of a dissolved tracer plume. It is also critical that the controlling hydraulic conductivity variations be mapped in detail sufficient to elucidate the geostatistical structure of the aquifer through which the tracer migrated. Such exercises have to date been limited to relatively simple hydrogeological settings, where the results of controlled tracer tests are available. Much less attention has been paid to demonstrate whether or not the spread of a large-scale plume such as that emanating from a landfill is consistent with the underlying geostatistical structure of the host aquifer.

[3] One of the first focused attempts at characterizing the spatial variability of hydraulic conductivity in a sandy aquifer where an intensively monitored tracer test had been conducted was performed by *Sudicky* [1986]. His work at the tracer test site at Canadian Forces Base (CFB) Borden, Ontario, has lead to much optimism concerning the workability of stochastic theories such as those developed by *Dagan* [1982, 1984, 1988], *Gelhar and Axness* [1983], *Neuman et al.* [1987], *Neuman and Zhang* [1990], *Zhang and Neuman* [1996], *Di Federico and Neuman* [1998], among others. While the theories are typically based on the assumption of small perturbations of hydraulic conductivity, *Rubin* [2003] indicates they are fairly robust, even for *Ln*(*K*) variances above 2.0. The analyses performed by *Sudicky* [1986] suggested that an exponential covariance model can suitably describe the log-transformed hydraulic conductivity, *Ln*(*K*), variations in the CFB Borden aquifer. Simple least squares fitting of the exponential model to spatial autocorrelation data based on 1279 regularly spaced hydraulic conductivity measurements yielded a horizontal *Ln*(*K*) correlation length equal to 2.8 m and a vertical correlation length equal to 0.12 m. The variance of the *Ln*(*K*) process was estimated to be 0.29 after the removal of a nugget value equal to 0.09. Bulk hydraulic conductivity values and macrodispersion parameters calculated by *Sudicky* [1986] on the basis of stochastic theories of groundwater flow and transport proposed by *Dagan* [1982] and *Gelhar and Axness* [1983] were shown to be consistent with the large-scale transport parameters deduced by *Freyberg* [1986] from his analysis of the tracer plume characteristics (through the moment analysis).

[4] A more thorough geostatistical interpretation of the structure of the *Ln*(*K*) variations in the CFB Borden aquifer was later performed by *Woodbury and Sudicky* [1991]. Using the hydraulic conductivity data measured by *Sudicky* [1986] and performing a detailed analysis of experimental variogram data calculated using various estimators, they estimated a horizontal correlation length equal to 5.1 m, a vertical correlation length equal to 0.2 m, and a nugget-corrected *Ln*(*K*) variance of 0.17. The nonlinear variogram fitting procedure also revealed that considerable uncertainty can exist in the values of the geostatistical parameters, which, in turn, will lead to uncertainty in the values of effective, large-scale transport parameters predicted by stochastic theory. Other discussions pertaining to the Borden tracer experiment and subsequent interpretations are given by *Sudicky* [1988a, 1988b, 1988c], *Kemblowski* [1988], *White* [1988], *Molz and Güven* [1988], *Naff et al.* [1988, 1989], *Dagan* [1989], *Zhang and Neuman* [1990], *Rajaram and Gelhar* [1991], *Ritzi and Allen-King* [2007], *Woodbury and Sudicky* [1992], and others.

[5] A similar study has been performed at Cape Cod, Massachusetts, within a geostatistical framework as part of a large-scale natural-gradient tracer experiment [*Garabedian et al.*, 1991; *LeBlanc et al.*, 1991] and at the Columbus site [*Boggs et al.*, 1992]. Other field studies of the nature of hydraulic conductivity variations in geological deposits have been performed in the past, although only a few have been carried out where detailed plume concentration data are available. Such studies include the work by *Pickens and Grisak* [1981], *Sudicky et al.* [1983], *Killey and Moltyaner* [1988], *Moltyaner and Killey* [1988a, 1988b], and *Yeh et al.* [1995].

[6] The purpose of this paper is to present the results of an intensive field study conducted in a sandy aquifer at North Bay, Ontario, that elucidates the three-dimensional (3-D) nature of the hydraulic conductivity variations. The data are analyzed in a geostatistical framework in order to quantify the statistical structure of the variations. We then use the geostatistical parameters to obtain the effective hydraulic conductivity tensor and macrodispersivity values using the theoretical expressions developed by *Gelhar and Axness* [1983] and *Dagan* [1982]. Finally, we utilize the geostatistically derived effective hydraulic conductivity and macrodispersivity in a numerical groundwater flow and transport model to assess the predictability of ambient hydraulic head and concentration distributions of the chloride plume at the North Bay site.