Measuring forecast skill: is it real skill or is it the varying climatology?

It is common practice to summarize the skill of weather forecasts from an accumulation of samples spanning many locations and dates. In calculating many of these scores, there is an implicit assumption that the climatological frequency of event occurrence is approximately invariant over all samples. If the event frequency actually varies among the samples, the inetrics may report a skill that is different from that expected. Many common deterministic verification metrics, such as threat scores, are prone to mis-reporting skill, and probabilistic forecast metrics such as the Brier skill score and relative operating characteristic skill score can also be affected. Three examples are provided that demonstrate unexpected skill, two from synthetic data and one with actual forecast data. In the first example, positive skill was reported in a situation where metrics were calculated from a composite of forecasts that were comprised of random draws from the climatology of two distinct locations. As the difference in climatological event frequency between the two locations was increased, the reported skill also increased. A second example demonstrates that when the climatological event frequency varies among samples, the metrics may excessively weight samples with the greatest observational uncertainty. A final example demonstrates unexpectedly large skill in the equitable threat score of deterministic precipitation forecasts. Guidelines are suggested for how to adjust skill computations to minimize these effects.