Relating error bounds for maximum concentration estimates to diffusion meteorology uncertainty

Abstract

The intent of this paper is to relate the magnitude of the error bounds of data, used as inputs to a Gaussian dispersion model, to the magnitude of the error bounds of the model output, which include the estimates of the maximum concentration and the distance to that maximum. The research specifically addresses the uncertainty in estimating the maximum concentrations from elevated buoyant sources during unstable atmospheric conditions, as these are most often of practical concern in regulatory decision making. A direct and quantitative link between the nature and magnitude of the input uncertainty and modeling results has not been previously investigated extensively. The ability to develop specific error bounds, tailored to the modeling situation, allows more informed application of the model estimates to the air quality issues. In this study, a numerical uncertainty analysis is performed using the Monte-Carlo technique to propagate the uncertainties associated with the model input. Uncertainties were assumed to exist in four model input parameters: (1) wind speed, (2) standard deviation of lateral wind direction fluctuations, (3) standard deviation of vertical wind direction fluctuations, and (4) plume rise. For each simulation, results were summarized characterizing the uncertainty in four features of the ground-level concentration pattern predicted by the model: (1) the magnitude of the maximum concentration, (2) the distance to the maximum concentration, and (3) and (4) the areas enclosed within the isopleths of 50% and 25% of the error-free estimate of maximum concentration. The authors conclude that the error bounds for the estimated maximum concentration and the distance to the maximum can be double that of the error bounds for individual model input parameters. The model output error bounds for the areas enclosed within isopleth values can be triple the error bounds of the input. It was not our intent to cover all possible combinations for the error in the input parameters. Ours was a much more limited goal of providing a lower bound estimate of model uncertainty in which we assume the input is reasonably well characterized and there is no bias in the input. These results allow estimation of minimum bounds on errors in model output when considering reasonable input error bounds.