A comparison of hazard area predictions based on the ensemble-mean plume versus individual plume realizations using different toxic load models
The most common way for a T&D model to calculate toxic effects is based on the total inhaled dose. These effects are independent of the manner in which this dose was accumulated (i.e., they are independent of the exposure history). But for many chemicals, it has been observed that the time dependence of the concentration is important – for instance, inhaling a dose of chlorine over a short period of time has much stronger effects than inhaling the same dose over an extended period of time. Toxic load modeling tries to account for this effect by utilizing the toxic load exponent n (approximately 2.75 for chlorine). While the experimental data supporting toxic load modeling were derived using concentration exposure profiles in the form of a rectangular pulse, the actual exposures from hazardous plumes are not well-described by rectangular pulses. There are several proposed generalizations of the toxic load model to the case of time-varying exposure profiles, none of which have been validated using animal experiments. One of these extensions, the generalized ten Berge model, involves calculating the temporal integral of the concentration raised to the power n, while several other extensions can be expressed in a general form as D^n T^(1-n), where D is the dosage (time-integrated concentration) and T is a generalized exposure duration. In this work, a total of four toxic load models are considered that cover the full spectrum of conservatism in casualty and hazard area estimation.
The majority of present-day T&D models used for consequence assessment estimate a “mean” plume that approximates the ensemble average over a large number of plume realizations. The few T&D models that utilize the toxic load model apply toxic load casualty estimation using this mean plume. By its definition, the “mean” plume “smears out”, in both time and space, the high concentration regimes that would be expected within individual plume realizations. The question arises whether the casualties estimated from the “mean plume” could differ from the mean of the casualties estimated from individual plume realizations.
The National Center for Atmospheric Research (NCAR) Virtual Threat Response Emulation Test Bed (VTHREAT) modeling system is composed of a suite of models designed to provide a virtual environment for meteorological modeling and T&D modeling. A key feature of VTHREAT is the potential to produce realistic, statistically representative hazardous materials plumes that include turbulence-induced fluctuating and meandering components. VTHREAT actually predicts individual realizations of the plume and not a “mean” plume.
We are assisting with the validation of VTHREAT, and as part of this work we have obtained a high resolution (in space and time) set of predictions that contains 20 plume realizations for a continuous release of a neutral-buoyancy tracer gas over flat terrain under stable atmospheric conditions. This data set is an ideal candidate for comparing toxic load calculations based on a “mean” plume with calculations based on individual plume realizations in order to assess the potential effect on casualty estimation. Preliminary results indicate that: a) the toxic load hazard areas for individual plume realizations have a wide spread around the ensemble mean hazard area, especially at higher levels of interest; b) the toxic load calculations based on the “mean” plume significantly under-estimate hazard areas compared to toxic load calculations based on the average of individual plume realizations for three out four toxic load models considered in this study.