The Relative Mean Error (RME, sometimes called relative bias) measures the average difference between a set of forecasts and corresponding observations, relative to the mean of the latter,

\begin{equation} \textrm{RME} = \dfrac{\sum_{j=1}^{J} \left( \bar{S}_j - q_j \right)}{\sum_{j=1}^{J} q_j} \textrm{,} \end{equation}

where $q$ is the observation and $\bar{Q}$ is the mean of the ensemble forecast. The RME thus provides a measure of relative, first-order bias in the forecasts. RME may be positive, zero, or negative. Insofar as the mean of the ensemble forecast should match the observed value, a positive RME denotes overforecasting and a negative RME denotes underforecasting. Zero RME denotes the absence of relative bias in the mean of the ensemble forecast.