Skill, as ever, is defined as improvement over an optimal naive prediction. We show that the optimal naive prediction depends on both the base rate (the climatology) of the event being forecasted, and the loss one would incur if one were to make an incorrect decision based on the forecast.

Here, we take the climate skill score and extend it to the case where the predicted series is first-order Markov in nature, of which, again, precipitation occurrence series are an example. We show that Markov skill is different and more demanding than is persistence skill. Persistence skill is defined as improvement over forecasts which state that the next value in a series will equal the present value. We also define the optimal naive prediction in the Markov case.

Surprisingly, it turns out that the form of the Markov skill score is identical to the climate skill score, making calculations simple. The distribution of the Markov skill is more complex than is the distribution of the climate skill score, however. The distribution for the Markov skill score is presented, and examples of hypothesis testing for precipitation forecasts are given. We graph these skill scores for a wide range of forecast-user loss functions, a process which makes their interpretation simple.

Supplementary URL: http://wmbriggs.com/public/weathermarkov.pdf