The 500 hPa geopotential height anomaly correlation is a key indicator of the skill of numerical weather prediction.
Patterns of 500 hPa heights reveal short- and long-wave troughs and ridges. Surface low pressure tends to develop (or strengthen) to the east of 500 hPa short-wave troughs, while surface high pressure tends to form (or strengthen) to the east of 500 hPa short-wave ridges.
The correlation is between the observed and forecast 500 hPa geopotential height anomaly. A higher value is better, indicating a forecast that was closer to the observed situation.
A correlation of 0.6 is considered to represent a useful forecast. For the ECMWF model, forecasts fell below 0.6 at about 5.5 days in 1980, whereas by 2010 they did not fall below 0.6 until about 8.5 days - this represents an improvement in skill of one day per decade. The forecast for which the value falls to 0.8 is approaching 6.5 days.