In ATMES II exercise there is a wide range of magnitude of observed and predicted concentrations, due to the use of field data with distances from 100 to 2000 km from the source. This suggests the use of the geometric mean bias (MG) as an extra index for the determination of model overestimation or underestimation.

The geometric mean bias is defined as:

When a data set contains several pairs of data with M_i/P_i or P_i/M_i equal to 10, 100 or more, this logarithmic form of bias is appropriate because underpredictions and overpredictions receive equal weight (Hanna et al., 1993).

A "perfect" model would have MG=1, but MG=1 does not mean that predictions coincide with measurements. An MG greater than 1 implies that the model overestimates and an MG less than 1 that the model underestimates.

The same filter as for scatter is applied on data before the calculation of this index. Moreover, since the logarithm of concentration is considered, all zero concentrations are raised to a minimum concentration (same order of the background).

The confidence interval for the geometric bias is computed with the bootstrap technique. The idea of bootstrapping consists in re-sampling the set of pairs with possible repetitions for a number of times, every time computing the MG of the new sample. From the distribution of resulting geometric mean biases, the 5^th and 95^th percentiles are taken as the limits of the confidence interval.