Long-range atmospheric dispersion models calculate concentration values over a relatively short period of time (hours or days). Models of this type are often used to deal with accidental releases.

Two categories of long-range atmospheric dispersion models can be distinguished, Eulerian and Lagrangian. Eulerian models describe the dispersion of pollutants in a fixed frame of reference (fixed with respect to a point on the earth surface). In Lagrangian models, the evolution of a pollutant air parcel is described relative to a mobile reference system associated with the parcel from its initial position as it moves along its trajectory. Both descriptions are equivalent, since the wind velocity u(x,t) in the Eulerian frame of reference is equal to the Lagrangian velocity dx/dt (if, for simplicity, only one dimension is considered).

The choice of model category depends on the various aspects of the desired application, such as the numerical facilities available. Both Eulerian and Lagrangian models are based on the definition of the mass conservation equation, in which a balance is made between what is created, destroyed, enters and leaves each air volume.

As most air pollutants are emitted at or near the surface of the earth, long range atmospheric dispersion models must deal in detail with a thin layer about 2 km in depth, called the atmospheric boundary layer (ABL).

A description of the evolution of ABL depth due to the diurnal solar energy cycle and ground surface characteristics is therefore included in the long-range atmospheric dispersion models. Its physical properties are derived from the input state variables to the models, which are the three-dimensional wind and turbulence fields (with appropriate time and space resolution).

In ETEX real-time modellers were asked to forecast both the meteorological field and the long-range dispersion to calculate the concentration field evolution. For this reason, discrepancies between concentration forecasts made by different models implemented in computer codes could be caused by the initialisation of the meteorological model and by the characteristics of the meteorological and dispersion model used. For example, some modellers used wind fields from the ECMWF, others employed a limited area model, and still others a hemispherical or global model.

The use of different time resolutions and different grids for flow and dispersion calculations could also contribute to increasing the expected differences in model results. While some modelling systems are configured with a coarse grid in the flow model and interpolate flows to a finer grid for their dispersion model, others do not exploit all the information the flow model provides.

More on: Mathematical concepts in atmospheric dispersion modelling