User Guide 026
15 Appendix E: Goodness of Fit Statistics Brier Skill Score The Brier Skill Score (BSS) is defined as (A1) where the angled brackets indicate averaging, subscripts m, c, and 0 indi-cate measured, calculated, and initial values, respectively. The BSS ranges between negative infinity and one. A BSS value of 1 indicates a perfect agreement between measured and calculated values. Scores equal to or less than 0 indicates that the mean observed value is as or more accurate than the calculated values. The following quantifications are used for de-scribing the BSS values: 0.8<BSS<1.0 = excellent, 0.6<BSS<0.8 = good, 0.3<BSS<0.6 = reasonable, 0<BSS<0.3 = poor, BSS<0 = bad. Room Mean Squared Error The Root Mean Squared Error (RMSE) is defined as (A2) The RMSE has the same units as the measured data. Lower values of RMSE indicate a better match between measured and computed values. Normalized Root Mean Squared Error The Normalized Root Mean Squared Error (NRMSE) is (A3) The NRMSE is often expressed in units of percent. The measured data range can be estimated as . Lower values of NRMSE indicate a better agreement between measured and computed values. Mean Absolute Error The Mean Absolute Error (MAE) is defined as (A4) Normalized Mean Absolute Error Similarly, the Normalized Mean Absolute Error (NMAE) is given by (A5) The NMAE is often expressed in units of percent. Smaller values of NMAE indicate a better agreement between measured and calculated values. Correlation Coefficient Correlation is a measure of the strength and direction of a linear relation-ship between two variables. The correlation coefficient R is defined as (A5) A correlation of 1 indicates a perfect one-to-one linear relationship and -1 indicates a negative relationship. The square of the correlation coefficient describes how much of the variance between two variables is described by a linear fit. The interpretation of the correlation coefficient depends on the context and purposes. For the present work, the following qualifications are used: 0.7<R2<1 = strong, 0.4<R2<0.7 = medium, 0.2<R2<0.4 = small, and R2<0.2 = none. Bias The Bias is defined as (A6) Positive values indicate over-prediction and negative values indicate un-der-prediction.