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 cross‐validation 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°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.