Explicitly accounting for observation error in categorical verification of forecasts

Given an accurate representation of errors in observations it is possible to remove the effect of those errors from categorical verification scores. The errors in the observations are treated as additive white noise that is statistically independent of the true value of the quantity being observed. This method can be applied to both probabilistic and deterministic verification where the verification method uses a categorical approach. In general this improves the apparent performance of a forecasting system, indicating that forecasting systems are often performing better than they might first appear.