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The Effect of Measurement Error on Estimating the Hydraulic Gradient in Three Dimensions
Author(s) -
Silliman S.E.,
Mantz G.
Publication year - 2000
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.2000.tb00208.x
Subject(s) - consistency (knowledge bases) , observational error , geodesy , horizontal plane , field (mathematics) , elevation (ballistics) , piezometer , standard deviation , mathematics , statistics , geology , orientation (vector space) , geometry , geotechnical engineering , groundwater , aquifer , pure mathematics
Based on a series of analyses of published data sets, it was observed that there is a consistent problem in the estimation of the vertical component of the hydraulic gradient. In most cases investigated, data collected for a single field site led to individual estimates of the orientation of the gradient that fell close to both +90 degrees and ‐90 degrees relative to the horizontal plane (i.e., the gradient was estimated to be oriented both vertically upward and vertically downward at the same site). Being consistent across most field sites analyzed, but inconsistent with our basic knowledge of hydrology (the impact of heterogeneity is distinct from the behavior presented here), alternative explanations for these observations were sought. Analysis using a simple numerical study showed that this behavior could be attributed to the presence of measurement error in the field data. The consistency of the field observations with the numerical study shows that errors in measuring the elevation of water in a well or piezometer may result in estimates of the vertical component of the gradient that are unreliable, effectively being measures of the difference in measurement error among wells. It is noted that this measurement error is in addition to local variations in the vertical component of the gradient that are related to heterogeneity or transients in the flow field. A formula is presented for the standard deviation of the error of the estimated vertical gradient as a function of both the measurement error and the relative location of the data points used in completing the estimate.