The n^th percentile of a distribution of values is defined as the cumulative probability in percent, that is the value that bounds the n% of values below and the (100-n)% above it. In this report the box plot consists of a plot where 25^th, 50^th, and 75^th percentiles are drawn.

In ATMES II, for each model, the global box plot and the time dependent box plot are reported and graphically compared with the measured ones in the 11 selected stations.

Looking at the box plot the general features of the distribution can be evinced. For instance, if all the percentiles of the model that are drawn in the box plot are lower than the percentiles of the corresponding measurements, it means that the lower 75 % of the predictions is lower than the lower 75 % of measurements. This might probably correspond to a modelled distribution everywhere lower than the measured one or, less likely, to a model distribution much more peaked in the 25 (or less) % of higher values.

In this context it must be pointed out that this comparison does not couple values. Thus, in the case of the global box plot the values are completely unpaired, while in the time dependent box plot they are, obviously, paired in space. However, in both cases, the frequency distribution is evaluated with the same data filter as in the scatter diagram calculation. For each station, both measurements and predicted values are kept only if included between two time intervals before the arrival of the tracer and two time intervals after the departure of tracer, in this way eliminating most of the zero measurements. Thus, only the part of predicted distribution included in the ‘accepted window’ is analysed.

Another type of global box plot is the one based on the distribution of the differences between predictions and measurements in the same location, at the same time. In this case data are paired both in space and time.

An example of box plot for one of the participants to ATMES II is shown in Figure 1.

Figure 1. Global box plot for one of the models participating to ATMES II. Percentiles are reported for measurements, the model, and for the difference of predicted and measured values of each pair.