On the use of dimensioned measures of error to evaluate the performance of spatial interpolators

Spatial cross-validation and average-error statistics are examined with respect to their abilities to evaluate alternate spatial interpolation methods. A simple crossvalidation methodology is described, and the relative abilities of three, dimensioned error statistics - the root-mean-square error (RMSE), the mean absolute error (MAE), and the mean bias error (MBE) - to describe average interpolator performance are examined. To illustrate our points, climatologically averaged weather-station temperatures were obtained from the Global Historical Climatology Network (GHCN), Version 2, and then alternately interpolated spatially (gridded) using two spatial-interpolation procedures. Substantial differences in the performance of our two spatial interpolators are evident in maps of the cross-validation error fields, in the average-error statistics, as well as in estimated land-surface-average air temperatures that differ by more than 2 degrees C. The RMSE and its square, the mean-square error (MSE), are of particular interest, because they are the most widely reported average-error measures, and they tend to be misleading. It (RMSE) is an inappropriate measure of average error because it is a function of three characteristics of a set of errors, rather than of one (the average error). Our findings indicate that MAE and MBE are natural measures of average error and that (unlike RMSE) they are unambiguous.