Over the past several decades, the development of computer models to predict the atmospheric transport of hazardous material across a local (on the order of 10s of km) to mesoscale (on the order of 100s of km) region has received considerable attention, for both regulatory purposes, and to guide emergency response teams. Wind inputs to these models cover a spectrum of sophistication and required resources. At one end is the interpolation/extrapolation of available observations, which can be done rapidly, but at the risk of missing important local phenomena. Such a model can also only describe the wind at the time the observations were made. At the other end are sophisticated numerical solutions based on so-called Primitive Equation models. These prognostic models, so-called because in principle they can forecast future conditions, contain the most physics, but can easily consume tens of hours, if not days, of computer time. They may also require orders of magnitude more effort to set up, as both boundary and initial conditions on all the relevant variables must be supplied. The subject of this report is two classes of models intermediate in sophistication between the interpolated and prognostic ends of the spectrum. The first, known as mass-consistent (sometimes referred to as diagnostic) models, attempt to strike a compromise between simple interpolation and the complexity of the Primitive Equation models by satisfying only the conservation of mass (continuity) equation. The second class considered here consists of the so-called linear models, which purport to satisfy both mass and momentum balances. A review of the published literature on these models over the past few decades was performed. Though diagnostic models use a variety of approaches, they tend to fall into a relatively few well-defined categories. Linear models, on the other hand, follow a more uniform methodology, though they differ in detail. The discussion considers the theoretical underpinnings of each category of the diagnostic models, and the linear models, in order to assess the advantages and disadvantages of each. It is concluded that diagnostic models are the better suited of the two for predicting the atmospheric dispersion of hazardous materials in emergency response scenarios, as the linear models are only able to accommodate gently-sloping terrain, and are predicated on several simplifying approximations which can be difficult to justify a priori. Of the various approaches used in diagnostic modeling, that based on the calculus of variations appears to be the most objective, in that it introduces the fewest number of arbitrary parameters. The strengths and weaknesses of models in this category, as they relate to the activities of Sandia's Nuclear Emergency Support Team (NEST), are further highlighted.
