Glossary of Verification Statistics Terms

Error

Is the difference between the forecast and the obsered. Error: E = Forecast - Observed

Bias

Is the difference between the mean of the forecasts and the mean of the observations. Could be expressed as the percentage of the mean observations. Also known as overall bias, systematic bias, or unconditional bias. This is not a good statistic for tidal influence stage forecasts. Relative Bias is computed as: RB = Mean Error / Observed Mean. Percent Bias: PB = 100 x (Σ (Fcst - Obs) / Σ Obs)

Mean Absolute Error (MAE)

The average of the absolute differences between forecasts and observations. A more robust measure of forecast accuracy than Mean Square Error that is sensitive to large outlier forecast errors. Perfect score: 0. Mean Absolute Error: MAE = Σ |Fcst - Obs| / N, where N is number of observations.

Mean Error (ME)

The average difference between forecasts and observations. Note: it is possible to get a perfect score if there are compensating errors. Perfect score: 0. Mean Error: ME = Σ (fcst-Obs) / N, where N is number of observations.

Root Mean Square Error (RMSE)

The square root of the average of the squared difference between forecasts and observations. It puts a greater influence on large errors than smaller errors, which may be good if large errors are especially undesirable, but may also encourge conservative forecasting. Perfect score: 0. Root Mean Square Error: RMSE = √ (Σ (Fcst - Obs)²) /N, where N is number observations.

Uncertainty

The degree of variability in the observations. Most simply measured by the variance of the observation. Important aspect in the performance of a forecasting system, over which the forecaster has no control.