| Abstract: | ABSTRACT: In geohydrology, three-dimensional surfaces are typically represented as a series of contours. Water levels, saturated thickness, precipitation, and geological formation boundaries are a few examples of this practice. These surfaces start as point measurements that are then analyzed to interpolate between the known point measurements. This first step typically creates a raster or a set of grid points. In modeling, subsequent processing uses these to represent the shape of a surface. For display, they are usually converted to contour lines. Unfortunately, in many field applications, the (x, y) location on the earth's surface is much less confidently known than the data in the z dimension. To test the influence of (x, y) locational accuracy on z dimension point predictions and their resulting contours, a Monte Carlo study was performed on water level data from northwestern Kansas. Four levels of (x, y) uncertainty were tested ranging in accuracy from one arc degree-minute (± 2384 feet in the x dimension and ± 3036 feet in the y dimension) to Global Positioning Systems (GPS) accuracy (± 20 feet for relatively low cost systems). These span the range of common levels of locational uncertainty in data available to hydrologists in the United States. This work examines the influence that locational uncertainty can have on both point predictions and contour lines. Results indicate that overall mean error exhibits a small sensitivity to locational uncertainty. However, measures of spread and maximum errors in the z domain are greatly affected. In practical application, this implies that estimates over large regions should be asymptotically consistent. However, local errors in z can be quite large and increase with (x, y) uncertainty. |
