RMSE (Root Mean Square Error)

The Root Mean Square Error (RMSE) (also called the root mean square deviation, RMSD) is a frequently used measure of the difference between values predicted by a model and the values actually observed from the environment that is being modeled. These individual differences are also called residuals, and the Root Mean Square Error serves to aggregate them into a single measure of predictive power. Root Mean Square Error measures how much error there is between two data sets. In other words, Root Mean Square Error compares a predicted value and an observed or known value.

where X(Obs,i) is the observation value and X(model,i) is the forecast value.