Estimating the Precision of Ground‐Water Elevation Data

1. Abstract A common problem in ground‐water monitoring and hydrogeology in general is determining the precision with which to plot ground‐water elevation contours. If ground water represented a completely static system and could be measured without error, the choice would simply be a function of the ambition of the graphic artist or the capabilities of the available computer algorithm. Since contour maps involve an interpolation from a set of irregularly spaced points (i.e., wells or piezometers) to a grid or mesh of evenly spaced points, which in general contains far more points or “nodes” than the original dataset, virtually any level of “graphical precision” is possible (e.g., one‐tenth of a foot). However, ground‐water elevation measurements represent the results of a dynamic process that, in general, does not affect all wells equally. Furthermore, as in any measuring process in which humans are involved, errors of measurement must certainly exist. The natural consequence, of course, is that one component of the total variation in ground‐water elevation data represents random sampling fluctuations. The magnitude of these random sampling fluctuations can in turn be used to make probabilistic statements regarding the precision of ground‐water elevation data such that ground‐water elevation contours may be determined at meaningful intervals. The importance of empirically determining ground‐water elevation precision is that it assures us that the plotting interval will never be less than the precision of the generating ground‐water elevation data. Without this assurance, which of course is the typical case in practice, structure and even gradients that are observed in a contour plot may be nothing more than the effects of random sampling variability.