Impacts of air pollution: general relationships and site dependence

We analyze the structure of the impact pathway methodology and show that, for the important problem of calculating the expectation value of the marginal damage from a point pollution source, the equations can be simplified greatly. In particular, in a uniform world (uniform receptor density and uniform atmosphere. they can be integrated in closed form to yield a very simple formula for the total damage Duni in a uniform world. The generalization to secondary pollutants is straightforward. We then test the relevance of this simple formula in the real world, by using curve fits to the results of detailed models for atmospheric dispersion and chemistry and by varying the receptor density according to typical patterns. We also compare Duni with the output of a software package that carries out an accurate numerical integration of atmospheric dispersion results over geographic data for population and other receptors. Evaluating a set of five sites in France that appear generally representative, ranging from rural to extremely urban, we find that the true damage is within a factor of three of Duni. This remarkably small sensitivity to geographical detail can be explained by the conservation of matter. We provide guidelines for several questions that are relevant for environmental policy: what are the functional relations and key parameters, as input to an uncertainty analysis? How does the damage vary with key parameters, e.g. stack height? How much accuracy and resolution is needed, in the atmospheric modeling and in the data for receptor distribution? How large is the error if one uses typical average values rather than detailed calculations?