THE INFLUENCE OF (X,Y) UNCERTAINTY ON PREDICTION ERROR AND CONTOUR LINES FROM A 3-DIMENSIONAL SURFACE

In geohydrology, three-dimensional surfaces are typically represented as a series of contours. Water levels, saturated thickness, precipitat ion, and geological formation boundaries are a few examples of this pr actice. These surfaces start as point measurements that are then analy zed to interpolate between the known point measurements. This first st ep typically creates a raster or a set of grid points. In modeling, su bsequent processing uses these to represent the shape of a surface. Fo r 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 t est the influence of (x,y) locational accuracy on z dimension point pr edictions and their resulting contours, a Monte Carlo study was perfor med on water level data from northwestern Kansas. Four levels of (x,y) uncertainty were tested ranging in accuracy from one arc degree-minut e (+/- 2384 feet in the x dimension and +/- 3036 feet in the y dimensi on) to Global Positioning Systems (GPS) accuracy (+/- 20 feet for rela tively low cost systems). These span the range of common levels of loc ational uncertainty in data available to hydrologists in the United St ates. This work examines the influence that locational uncertainty can have on both point predictions and contour lines. Results indicate th at overall mean error exhibits a small sensitivity to locational uncer tainty. However, measures of spread and maximum errors in the z domain are greatly affected. In practical application, this implies that est imates over large regions should be asymptotically consistent. However , local errors in z can be quite large and increase with (x,y) uncerta inty.