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Estimating the Horizontal Gradient in Heterogeneous, Unconfined Aquifers: Comparison of Three‐Point Schemes
Author(s) -
Cole Bryce E.,
Silliman Stephen E.
Publication year - 1996
Publication title -
groundwater monitoring and remediation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.677
H-Index - 47
eISSN - 1745-6592
pISSN - 1069-3629
DOI - 10.1111/j.1745-6592.1996.tb00128.x
Subject(s) - magnitude (astronomy) , aquifer , hydraulic head , orientation (vector space) , mathematics , plane (geometry) , geology , geometry , soil science , physics , groundwater , geotechnical engineering , astronomy
At least two approaches may be used to estimate the horizontal components of the hydraulic gradient based on measured heads from three observation points. First, the gradient may be 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 wells 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. The 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 are 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.