Figure 3.

Effects of covariance model parameters on expected prediction loss. (a) Kriging MSE (eq 4) was calculated for 1 mm spacing, unit variance, and zero noise over a Matérn parameter space. MSE was monotonic in both range and smoothness parameters. Our threshold for predictability was 10% MSE relative to process variance (blue isocontour). Predictability was limited by a low value of either parameter. Smoothness had a weak influence on predictability when range was below a limit, and vice-versa. (Exact limits depended on the sampling geometry.) (b) The 10% predictability threshold for 1 mm grid pitch was computed under increasing levels of sample noise. In higher noise, predictability was restricted to smoother and longer range fields. (c) Predictability thresholds at 20% noise and varied grid pitch from 0.5 to 2.5 mm. Increasing or decreasing pitch had a similar effect on predictability as increasing or decreasing noise. By reducing pitch to 0.5 mm, approximately the same fields were predictable in 20% noise as were predictable in 0% noise and 1 mm pitch.