On the use of the normalized mean square error in evaluating dispersion model performance

Abstract

A widely used air quality model performance index, the normalized mean square error, NMSE, is analyzed in detail. It is shown that the main purposes of the index, i.e. avoiding bias towards model overestimate or underestimate and giving an overview of the model performance over the entire data set of sampled concentrations, are not fulfilled. It is also shown that in certain situations, that have not to be considered as limit cases, the “best” condition to get the lowest value of the NMSE is completely different from what one would expect by simple logical considerations. A proposal is then made to obtain the desired results by the use of different indices.