Measure of skill - the anomaly correlation coefficient

Another way to measure the quality of a forecast system is to calculate the correlation between forecasts and observations. However, correlating forecasts directly with observations or analyses may give mislead­ingly high values because of the seasonal variations. It is therefore established practice to subtract the climate average from both the forecast and the verification and to verify the forecast and observed anomalies according to the anomaly correla­tion coefficient (ACC), which in its most simple form can be written:

The WMO definition also takes any mean error into account:

The ACC can be regarded as a skill score relative to the climate. It is positively orientated, with increasing numerical values indicating increasing “success”. It has been found empirically that ACC=60% corresponds to the range up to which there is synoptic skill for the largest scale weather patterns. ACC=50% corresponds to forecasts for which the error is the same as for a forecast based on a climatological average, i.e. RMSE = A_a. An ACC of about 80% would correspond to a range where there is still some skill in large-scale synoptic patterns.