Absolute Error is the absolute value of the statistical difference between a forecast value ($F$) and the observed value ($O$): $|F – O|$. Because it uses an absolute value, the result is always positive, regardless of whether the forecast was too high or too low, providing a direct measure of the magnitude of the error without considering its direction.
In the weather industry, MAE is often used over Root Mean Square Error (RMSE) because it is more intuitive and less sensitive to “outliers” or extreme “Busts.” While RMSE squares the errors—thereby penalizing large misses more heavily—MAE provides a linear average of the forecast’s “closeness” to reality. Professionals search for MAE benchmarks to compare the baseline consistency of different model providers across a specific season.
While Absolute Error tells you how far off a forecast was, it does not tell you how it was off. For example, a forecast that is consistently 2 degrees too high and a forecast that is consistently 2 degrees too low both have the same Absolute Error (2.0), but they have opposite biases. Forecasters look at both to determine if their “off” days are random or part of a systemic model trend.
In many verification systems, Absolute Error is calculated after rounding both the forecast and the observation to the nearest whole degree. This is critical for industry standard-setting, as a forecast of 74.5°F for an observation of 75.4°F might technically be nearly a degree off, but after rounding, both are 75°F, resulting in an Absolute Error of 0.