Forecasts of "normal"

The difficulty of forecasting “normal” weather and climate conditions is demonstrated in the context of bivariate normally distributed forecasts and observations. Functional relationships are derived between many deterministic and probabilistic verification scores and the skill of the forecasts in the bivariate normal setting as measured by Pearson's correlation. The deterministic and probabilistic skill scores for the “normal” category are less than for the outer category for all but perfect models. There are two important mathematical properties of the normal category in a three-category climatologically equiprobable forecast system that affect the scores for this category. Firstly, the normal category can achieve the highest probability less frequently than the outer categories, and far less frequently in contexts of weak to moderate skill. Secondly, there are upper limits to the probability the normal category can reach.