Estimating the horizontal gradient in heterogeneous, unconfined aquifers: Comparison of three-point schemes

At least two approaches may be used to estimate observation points. First, the gradient may he estimated by passing a plane through the measured heads (h-method). Second, if the elevation of the base of the aquifer is known to be spatially constant, an estimate of the gradient may be obtained using the squares of the measured heads (h(2)-method). In the present study. these methods are examined in application to a heterogeneous system, Using Monte Carlo analysis, we demonstrate that the magnitude of the gradient estimated via the h-method involved significant bias, which increased when the distance separating the walls increased. in contrast, bias in the estimated magnitude of the gradient based on the h(2)-method decreased with increasing separation among the wells. Estimation variances for both the magnitude and orientation of the gradient also decreased with separation distance. Tftr: variance in the orientation was observed to remain relatively high, however, even at relatively large separations among the wells (e.g., 10 integral scales). These results an interpreted as implying that the best estimate of the gradient for steady flow in an unconfined aquifer is derived from the h(2)-method with the wells separated by significant distances. These results also demonstrate the uncertainty inherent in estimating the gradient based on limited field data.