Mapping Hydraulic Conductivity: Sequential Conditioning with Measurements of Solute Arrival Time, Hydraulic Head, and Local Conductivity

We present a method for estimating the spatial pattern of aquifer hydraulic conductivity from three types of measurements: solute arrival time quantiles, hydraulic heads, and direct local measurements. Results indicate that arrival times and heads provide different, but complementary, information about the large features of the conductivity field which serve as flow paths and barriers. We compare the information provided by head and arrival time measurements by plotting the correlation between measurement and conductivity over the entire domain. We also compare the value of head and arrival time data by estimating the conductivity with only one type of data, and by incorporating the different data types into the estimation procedure in different sequences. Using quantiles of arrival time, rather than concentrations, has three advantages: (1) Arrival times are independent of the amount of dilute solute introduced into the aquifer. (2) Under some conditions, by measuring the median arrival time, the accuracy of the conductivity field estimate is not degraded by poor knowledge of the local dispersivity. (3) The estimation procedure is greatly simplified by relying on a single quantile to represent the critical information contained in a breakthrough curve that is constructed from many concentration measurements. For the case examined here, incorporating arrival time quantiles that describe the tails of the breakthrough curves did not significantly improve our estimate of the conductivity field. An accurate map of the hydraulic conductivity of an aquifer is vital for predicting groundwater flow and solute transport through the aquifer. Typically, the spatial pattern of conduc- tivity is qualitatively inferred from a few local values of con- ductivity, head, and concentration measured at wells which are sparsely distributed, leaving large volumes of the aquifer un- sampled. When monitoring wells fail to penetrate important flow channels or barriers, these features must be deduced from measurements of head and concentration at nearby wells. A number of studies (Kitanidis and Vomvoris, 1983; Hoek- sema and Kitanidis, 1984; Dagan, 1985; Sun and Yeh, 1992) have shown how measurements of hydraulic head can be used in conjunction with measurements of local transmissivity to estimate the spatial pattern of aquifer transmissivity. These studies solve the inverse problem with a procedure that com- bines solution of the flow equation with linear estimation. Some recent studies (Graham and McLaughlin, 1989a, b; Ru- bin, 1991a, b) describe how measurements of solute concen- trations can be used to predict or estimate concentrations at other times and locations. Although spatially variable conduc- tivity is the underlying cause of uncertainty in these studies, the procedures are not directed toward estimating the conductivity field. Wagner (1992) used both head and concentration mea- surements to estimate the value of conductivity within pre- scribed zones. Woodbury and Smith (1988) combined steady state temperature and head measurements to estimate spa-