The dispersion of pollutants in the atmospheric boundary layer is a stochastic process but many approaches make use of deterministic models, such as the advection-diffusion equation, that determines average values. Comparison between observation and model prediction show a significant spread of values due to the stochastic character of the pollution dispersion phenomenon. Measured data though represent only one sample of an unknown distribution. Thus, the present article is a first attempt to reconstruct at least some of the pollutant concentration distribution properties from the comparison of deterministic predictions to observed concentrations under specific micro-meteorological conditions. The experimental data are the findings of the Copenhagen campaign. We show the scatter plot of observed versus predicted ground level concentrations from which distributional properties are extracted by determining the distance of each plot point from the bisector, proposing a parametrization for the probability function and fit the discrete set of data points. The probability density function obtainde from the probability distribution shows a narrow peak centered at zero besides a second smaller but displaced contribution. A reconstructed distribution symmetrically around zero signifies, that the model describes the average values of the distribution with fairly good fidelity and the width could be used as an approximation for the second statistical moment. The distribution which is not centered at the origin indicates either missing physics in the model, or failures in the measuring procedure. The reconstructed distribution with correlation less than one shows the aforementioned stochastic character of the phenomenon. Although applied to a specific experiment and using one deterministic model the reconstruction method is general and can be applied to other scenarios in an analogue fashion
