Generalized approach for using unbiased symmetric metrics with negative values: normalized mean bias factor and normalized mean absolute error factor

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Abstract
Unbiased symmetric metrics provide a useful measure to quickly compare two datasets, with similar interpretations for both under and overestimations. Two examples include the normalized mean bias factor and normalized mean absolute error factor. However, the original formulations of these metrics are only valid for datasets with positive means. This article presents a methodology to use and interpret the metrics with datasets that have negative means. The updated formulations give identical results compared to the original formulations for the case of positive means, so researchers are encouraged to use the updated formulations going forward without introducing ambiguity. Copyright © 2012 Royal Meteorological Society

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