Statistical models of air pollution have been developed primarily to provide a simpler and less data-demanding approach to estimating atmospheric concentrations, either for the purpose of air quality management (e.g. as screening models) or for exposure assessment in epidemiological studies.  A range of approaches have been devised, so that statistical models take many different forms.  Amongst these, two approaches are of particular utility in exposure assessment:

1. simplified dispersion models, in which the dynamic transfer equations have been reduced to a series of formulae;
2. GIS-based models, where associations between source and receptor are represented by empirically defined equations, derived using regression analysis or similar techniques.

Simplified dispersion models

These typically represent an attempt to reduce the complex, dynamic equations inherent in a true dispersion model to a simpler, and generally static, form.  Simplification is achieved primarily by ignoring the local, time-varying processes that affect short-term air pollutant concentrations (e.g. associated with variations in meteorology), and modelling instead the average (net) long-term patterns.   Models thus comprise a series of formulae or statistical equations, which can be solved either arithmetically (e.g. using spreadsheet functions) or through the use of look-up tables and graphs.  

Amongst many examples, two of the most widely used in Europe are the Calculation of Air pollution from Road traffic (CAR) model and the Design Manual for Roads and Bridges (DMRB) model.  The original CAR model was developed for use as a screening tool for air quality management in the Netherlands, but a more generic version (CAR-International) was later devised.  The DMRB model was designed to support air quality management in Britain, and likewise has undergone several revisions; the most recent provides the means to run it within a GIS.  Both models have been widely tested and compared against other, more sophisticated appraoches, and have generally been shown to work well when used within their intended operating conditions (i.e. to assess locally-derived concentrations of traffic-related air pollutants in relatively simple source-receptor environments).  They are, however, inevitably limited in that they are not designed to deal with non-transport emissions, and in terms of the sources number of sources and receptors that can easily be analysed, or their ability to model long-range transfers of pollutants.

GIS-based models

Geographical information systems (GIS) have become important tools for air pollution modelling, due to their capability to extract and process the spatial data needed as inputs to air pollution models, and then to map the results of the models. 

In recent years, however, GIS have also been used to develop air pollution models in their own right.  One such approach has been termed 'land use regression' (LUR), because it is based on empirically-derived regression equations linking land use (or more strictly land cover) to measured air pollutant concentrations at a set of monitoring sites.  Other predictors are usually selected to represent traffic-related emissions (e.g. road length, traffic flows) in the surrounding area, and the effect of local topography (e.g. altitude).  Optimal models (in terms of the correlation between measured and predicted concentrations) can often be obtained using stepwise regression techniques, in a somewhat unconstrained way.  This, however, carries the danger of developing models which are inherently counter-intuitive, and which may not be generally applicable.  Ideally, therefore, LUR models should be developed according to strict rules on variable selection, designed to reflect the real-world processes and dependencies that determine air pollutant concentrations. 

An alternative to LUR modelling has recently been devised, using focalsum techniques in GIS.  This explicitly uses measures of source intensity or emissions as inputs, and applies inverse-distance functions to weight these according to their contribution to air pollution at the monitoring sites.  The weights may be determined a priori (e.g. on the basis of results from dispersion modelling under typical conditions), or by using regression modelling. 

In both cases, model development requires a dense network of monitoring sites, so has usually been done using purpose-designed monitoring campaigns (e.g. employing passive samplers).  In both cases, also, model performance has been shown to be good (and comparable to dispersion models) when used to analyse relatively long-term (e.g. seasonal, annual) concentrations of locally-derived pollutants.  These methods also have an advantage of relative ease of application, and less demanding processing requirements, than dispersion models.  On the other hand, a major limitation is that the models do not directly represent the processes determining air pollution concentrations, so cannot be guaranteed to provide reliable estimates of changes in concentration associated with policy or other interventions.  Their use in integrated assessments, therefore, is mainly as screening tools.