Sampling and isometric mapping of continuous geographic surfaces

Analysis and isometric mapping of continuous geographic surfaces often require estimation of values at points on the surface from a sample of known values. Five factors influence accuracy of these intermediate value estimates: Data measurement accuracy, control point density, spatial distribution of sample points, intermediate value estimation procedures, and spatial variability of the surface represented.While holding data measurement, data location procedures, and interpolation methods constant, the relationship between sample size and value estimation accuracy was examined for six terrain surfaces. A functional relationship with consistent slope was found between sampling intensity and value estimation error. As sampling intensity increased, both the error of intermediate value estimates and the randomness of the spatial distribution of that error decreased at a decreasing rate. Absolute value of error varied with surface variability. These results were demonstrated to be applicable to determining minimum acceptable isometric intervals. Findings indicate that some state-wide digital databases are being constructed with data resolutions unsuitable for their intended uses.