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Report n°4: How Much to Spend for the Protection of Health and Environment

UWM: a Simple Model for Damage Cost Estimation

A simple and convenient tool for the development of typical values is the "uniform world model" (UWM), first presented by Curtiss & Rabl [1996] and further developed, with detailed validation studies, by Spadaro [1999] and Spadaro & Rabl [2002]. More recently Spadaro & Rabl [2004] have extended it to toxic metals and their pathways through the food chain. The UWM is a product of a few factors; it is simple and transparent, showing at a glance the role of the most important parameters of the impact pathway analysis. It is exact for tall stacks in the limit where the distribution of either the sources or the receptors is uniform and the key atmospheric parameters do not vary with location. In practice the agreement with detailed models is usually within a factor of two for stack heights above 50 m. For policy applications one needs typical values and the UWM is more relevant than a detailed analysis for a specific site - better approximately right than precisely wrong!

The UWM for the damage cost Duni in €/kg of a particular impact due to the inhalation of a primary pollutant is shown in Eq.1

Duni= p sCR r/vdep (1)

where
p = cost per case ("price") [€/case],
sCR = CRF slope [(cases/yr)/(pers·(mg/m3))],
r = average population density [pers/km2] within 1000 km of source, and
vdep = deposition velocity of pollutant (dry + wet) [m/s].

For secondary pollutants the equation has the same form, but with an effective deposition velocity that includes the transformation rate of the primary into the secondary pollutant. With this model it is easy to transfer to the results from one region to another (assuming that CRF and deposition velocity are the same): simply rescale the result in proportion to the receptor density and the cost per case.