Estimating the uncertainty of damage costs of pollution: A simple transparent method and typical results

Whereas the uncertainty of environmental impacts and damage costs is usually estimated by means of a Monte Carlo calculation, this paper shows that most (and in many cases all) of the uncertainty calculation involves products and/or sums of products and can be accomplished with an analytic solution which is simple and transparent. We present our own assessment of the component uncertainties and calculate the total uncertainty for the impacts and damage costs of the classical air pollutants; results for a Monte Carlo calculation for the dispersion part are also shown. The distribution of the damage costs is approximately lognormal and can be characterized in terms of geometric mean μg and geometric standard deviation σg, implying that the confidence interval is multiplicative. We find that for the classical air pollutants σg is approximately 3 and the 68% confidence interval is [μg / σg, μgσg]. Because the lognormal distribution is highly skewed for large σg, the median is significantly smaller than the mean. We also consider the case where several lognormally distributed damage costs are added, for example to obtain the total damage cost due to all the air pollutants emitted by a power plant, and we find that the relative error of the sum can be significantly smaller than the relative errors of the summands. Even though the distribution for such sums is not exactly lognormal, we present a simple lognormal approximation that is quite adequate for most applications.