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Effects of Measurement Error on Horizontal Hydraulic Gradient Estimates

During the design of a natural gradient tracer experiment, it was noticed that the hydraulic gradient was too small to measure reliably on an ∼500‐m2 site. Additional wells were installed to increase the monitored area to 26,500 m2, and wells were instrumented with pressure transducers. The resulting monitoring system was capable of measuring heads with a precision of ±1.3 × 10−2 m. This measurement error was incorporated into Monte Carlo calculations, in which only hydraulic head values were varied between realizations. The standard deviation in the estimated gradient and the flow direction angle from the x‐axis (east direction) were calculated. The data yielded an average hydraulic gradient of 4.5 × 10−4±25% with a flow direction of 56° southeast ±18°, with the variations representing 1 standard deviation. Further Monte Carlo calculations investigated the effects of number of wells, aspect ratio of the monitored area, and the size of the monitored area on the previously mentioned uncertainties. The exercise showed that monitored areas must exceed a size determined by the magnitude of the measurement error if meaningful gradient estimates and flow directions are to be obtained. The aspect ratio of the monitored zone should be as close to 1 as possible, although departures as great as 0.5 to 2 did not degrade the quality of the data unduly. Numbers of wells beyond three to five provided little advantage. These conclusions were supported for the general case with a preliminary theoretical analysis.