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Both the root mean square error (RMSE) and the mean absolute error  (MAE) are regularly employed in model evaluation studies.  Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator  of average model performance and might be a misleading indicator of  average error, and thus the MAE would be a better metric for that  purpose.  While some concerns over using RMSE raised by Willmott and Matsuura (2005) andWillmott et al. (2009)  are valid, the proposed avoidance of RMSE  in favor of MAE is not the solution.  Citing the aforementioned papers,  many researchers chose  MAE over RMSE to present their model evaluation  statistics when presenting or adding the RMSE measures could be more beneficial.  In this technical note, we demonstrate that the RMSE is not  ambiguous in its meaning, contrary to what was claimed byWillmott et al. (2009).  The RMSE is more appropriate to represent model  performance than the MAE when the error distribution is expected to  be Gaussian.  In addition, we show that the RMSE satisfies the  triangle inequality requirement for a distance metric,  whereas  Willmott et al. (2009) indicated that the sums-of-squares-based  statistics do not satisfy this rule.   In the end, we discussed  some circumstances where using the RMSE will be more beneficial.  However, we do not contend that the RMSE is superior over the MAE.  Instead, a combination of metrics, including but certainly not limited  to RMSEs and MAEs, are often required to assess model performance

Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature