Editor’s note: This is the final article in a four-part series on exposure modeling. Other articles in the series are “
Patterns of Exposure
” (January 2017), “
Easy Modeling
” (April 2017), and “
Downstream Modeling
” (September 2017).

“May you live in interesting times.” While the origin of this familiar saying is unclear, it is commonly understood to be a kind of curse. And it's true—even though we may lament the mundaneness of life on occasion, there’s nothing like a crisis to make a person long for those “normal” days. My career thus far has thrown me into more than a few interesting situations, where critical decisions hinge on the quickness and accuracy of mathematical modeling. Let’s explore a few lessons learned, and propose a framework for effective emergency response exposure modeling.
To begin, a little groundwork must be laid to demonstrate the most useful type of dispersion model for emergencies. The quantitative principles of Gaussian air dispersion modeling were effectively established in the 1950s in what is colloquially known as the “Prairie Grass Experiments.” In these, scientists released a tracer gas in central Kansas to see if any relationship could be established between release rate and downwind concentration. They knew the release rate and measured the downwind concentration. They did it 68 times, and found that the further downwind they measured, the lower the concentration was. Furthermore, the further the crosswind was from the centerline of where the wind was blowing, the lower the concentration was. These results were, of course, intuitive. What was novel about the experiments was the attempt to quantify how much lower that concentration was. From these efforts, a relationship was established between release rate and downwind concentration, which is the Gaussian Plume Equation: 
This basic equation is what most dispersion models today are built on. The experiments confirmed that the concentration profile both vertically and horizontally across these tracer gas plumes followed a Gaussian profile. The extent of dispersion depended on weather conditions summarized by the dispersion coefficients, which basically apply physical dimensions to these concentration profiles. Further dressed-up versions of the equation above include adjustments for inversions, reflection of emissions at the ground, removal by rainout, dry deposition, thermal buoyancy, terrain effects, and any other number of physical phenomena; but the basic principles remain the same: downwind dispersion happens according to some fairly reliable relationships.  I used this equation during graduate school, and it suited just fine for static situations (fairly constant wind direction and speed, emission rate and conditions, and so on). I spent my time studying transport and dispersion of power plant plumes in central Texas, and their propensity to form ozone, for my master’s thesis. I used an Eulerian urban airshed model, which is basically a bunch of box models linked together. A unique feature of the model, and the feature I turned most of my attention to, was the Lagrangian plumes allowed to migrate through this box model scheme. This was the most realistic way to represent these plumes, both conceptually and mathematically. How does a Lagrangian model use the Gaussian scheme? Think of a puff, represented by a cylinder, in a cubical box. During each time step, the puff is permitted to grow in physical size, according to the physical dimensions represented in the Gaussian equation by the dispersion coefficients, and is moved from box to box according to the wind speed. Figure 1 portrays Lagrangian plume transport through an Eulerian box model.
After graduation, I turned to near-field dispersion (think hundreds of feet, not tens of miles) to begin my career in emergency response. My first project was a response to a train derailment in Minot, N.D., where a large release of anhydrous ammonia occurred. It was there that I was faced with a basic question: “Should we evacuate more people?”
Nearly every emergency for which I’m called requires that a decision be made about evacuation. The question that’s really being asked is “How do we protect people from exposure?”  But this question isn’t correctly phrased. The general population, and in some cases the first responder community, tends to default to evacuation as the primary protective action of choice. However, in many emergency situations, shelter-in-place is preferred, whether it is due to the nature of the chemical (Is it easily removed by  simple processes like absorption?), or due to the nature of the release (Is the resulting cloud so transient that “waiting it out” would be better than running out into the cloud?).  The “Emergency Response Guidebook” published by the United States Department of Transportation is a ubiquitous, familiar, and oft-looked-to reference for first responders. It provides a clear summary of chemical hazards, classified logically by the properties of those chemicals. A ready-reference is given to suggested distances within which protective action should be taken. The key words here are “protective action.” As noted, too many people leap to evacuation as the protective action of choice. In the case of my first emergency response, shelter-in-place was by far the most protective action. Anhydrous ammonia is an extremely hygroscopic (water-loving) chemical, and research published in the
Journal of Occupational and Environmental Hygiene
has shown that breathing through a wet cloth can eliminate up to 95 percent of an air concentration of 1,000 ppm ammonia, whose NIOSH IDLH (Immediately Dangerous to Life and Health) value is 300 ppm. Thanks to the quick thinking of 911 operators, the residents of Minot were instructed to shelter-in-place and the effects of the high concentrations of ammonia were limited, relative to what might have occurred had residents evacuated their homes and entered the vapor cloud. The ERG makes it clear that protective actions include both evacuation and shelter-in-place, as well as a combination of the two. The distances to protective actions are based on dispersion modeling, using a model called CASRAM. CASRAM essentially uses a Monte Carlo simulation approach, where multiple release scenarios are considered across a wide range of meteorological conditions, based on actual incidents. These incidents are compiled statistically, and the downwind distance to a set threshold is calculated for each incident. The set threshold is the ERPG-2—the Emergency Response Planning Guideline, second level—which is a level (promulgated by AIHA) below which it is believed nearly all individuals could be exposed for up to one hour without experiencing effects that would impair their ability to seek protective action. Thus, it is frequently viewed as the level that indicates the need for either evacuation or shelter-in-place. How close can first responders get to the hazard without endangering their health? The ERG recommends that the distance to hazard should be the 95th percentile of the calculated distances arrived at through the Monte Carlo simulation. So essentially, the ERG provides first responders a distance that will cover 95 percent of all conceived scenarios, based on experience. Therefore, for a typical incident, the ERG will provide a fairly conservative estimate of the potential downwind distance to hazard.  The objective of real-time, emergency response dispersion modeling is to take the assessment from this stochastic, risk-based modeling of the ERG to a more site-specific modeling scenario that might be used in decision making. There is a critical distinction between the two approaches: the statistical modeling used in the development of the ERG is useful for a broad-brush approach in the absence of site-specific information; however, as soon as site-specific information becomes available, the ERG recommendations become obsolete. As the ERG guidelines themselves state, the ERG is intended for first responders’ use within the first 30 minutes of the response.  Looking forward to how emergency modeling should be approached, then, depends largely on the philosophy of that approach—namely, what is the objective? The objective ought to be to provide decision makers within the incident (for example, the incident commander) with the information necessary to make life-protective decisions. This must be done accurately and quickly. The remainder of this article will deal with strategies through which the above science may be implemented with speed and accuracy.
When confronted with a real hazardous materials release, your first step should be to run your emergency dispersion model. Don’t overthink it: run it immediately. Put the model into a visually compelling format and provide it to the decision makers. Include text that summarizes what you know, along with what you don’t know. But don’t make it too long—no more than four sentences.  We are in the 21st century and have extremely fast computers; therefore, run a thousand variations of the model if you must. A supercomputer will not have to grind out a new set of results over hours. But you will have another bit of information to consider: what should you change in these various iterations? If you doubt some of the inputs of the model, test their outer boundaries. Here are some of the typical uncertainties:
Release rate.
This may be determined for evaporative liquids, for example, from the surface area of the spill. What is the spill surface area? This question may lead to a much better estimate of the potential downwind impact than could be inferred from the ERG alone.
Temperature of release.
If a plume is thermally buoyant (hot air tends to rise), then the potential downwind impact may be reduced due to the tendency of those emissions to disperse at an elevated height, prior to impact to ground-level receptors. 
Duration of release.
A short-duration release is a good candidate for shelter-in-place, as summarized above. While the emissions pass by the shelter, the receptors reduce their potential exposure indoors; after the emissions have been transported away from the shelter, receptors can move outside into the now-clear air. 
Meteorological conditions.
What happens when the sun goes down and the atmospheric stability changes? Prepare for changing site conditions by modeling the difference between dispersion of the release during stable and unstable atmospheric dispersion (which will be drastically different). Provide this information to incident command personnel so that the responders are not caught off guard by these changes. 
Each of the above conditions can be easily summarized in an emergency dispersion model, to be provided within a few minutes of the release. Unknown parameters should be tested repeatedly, essentially providing a statistical analysis of the potential scenarios. For example, a hydrochloric acid release may be represented by solution strengths ranging from pure, anhydrous HCl to a 5 percent muriatic acid solution. Each solution strength possesses a significantly different vapor pressure and, therefore, potential airborne concern. Until site-specific information is known regarding the particular chemical involved, a range of potential downwind impacts should be presented, with relevant assumptions summarized. In this case, further visual observations may help determine the strength of the solution: an anhydrous HCl release will yield a yellow-greenish cloud, while a weak HCl solution of 40 percent or less will yield a whitish vapor cloud composed primarily of water vapor and a weak acid mist. In either case, the presence or absence of an odor may aid in the validation of modeling provided for the incident. 
Many emergency dispersion models are available, and many people are available to conduct them. Some are free, and bear along with them the technical limitations described in this article. In general, a Lagrangian puff model will better represent the rapidly changing conditions often encountered in an emergency. Keep in mind that the models will need to be changed to match site observations, including air monitoring or odor observation results; this is important when considering model selection.  Other tools have been discussed in previous
articles. These tools involve considering the maximum exposure concentrations that receptors might encounter. A first step is to determine the saturated vapor concentration, which is simply the vapor pressure of the pure component divided by standard atmospheric pressure. This provides a high-bound estimate of potential exposure concentration. A well-mixed box model is useful for static exposures in an indoor environment. In the case of an outdoor exposure to a release of an unconfined chemical, the use of the Gaussian plume equation will yield an estimate of potential exposure that may be a more refined high-bound estimate of exposure to downwind receptors. This equation may be easily implemented into a spreadsheet, and receptors may be evaluated at varying distances downwind. Beyond these tools, air dispersion modeling software is available to further refine estimates given site-specific information, including wind direction and speed, terrain, and the properties of released chemicals.  Another question sometimes encountered is “Will this container blow up?” Whether a container is suitable to contain the pressure of a sudden ignition of flammable material depends on basic principles captured in the ideal gas law (which defines the relationship among the pressure, volume, and thermodynamic temperature of a gas) along with some simple combustion stoichiometry—specifically, does the combustion of the material produce enough byproducts to generate an increase in gas volume sufficient to overcome the pressure rating of the vessel? The use of the ideal gas law, some simple chemical relationships, and a knowledge of the vessel pressure rating is sufficient to make a well-educated estimate as to the potential of an overpressure scenario. 
The primary considerations for emergency modeling are speed and accuracy: how quickly can site-specific information be distilled into a sound scientific analysis that helps decision makers recommend a protective action? Over the years, our ability to guide these decisions has improved dramatically, such that site-specific information, including air monitoring data, is typically available by the time the 30-minute window of applicability for the “Emergency Response Guidebook” has run its course. The earlier this tool can be engaged during an emergency response, the earlier this site-specific information can be used to guide decisions regarding protective action, for the ultimate protection of human life during emergencies.   
DYRON HAMLIN, CIH, is a professional chemical engineer with GHD in Little Rock, Ark. He can be reached at (501) 224-1926 or via

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Figure 1.
Lagrangian plume transport through an Eulerian box model. Recreated based on EPA graphic on the agency's
web page on photochemical modeling
Tap on the graphic to open a larger version in your browser.
Tap on the equation to open a larger version in your browser.
Exposure Models for Emergency Response
Decision Time
Photochemical Modeling
Journal of Occupational and Environmental Hygiene
: “Effectiveness of Common Shelter-in-Place Techniques in Reducing Ammonia Exposure Following Accidental Release” (April 2009).  Pipeline and Hazardous Materials Safety Administration: “
Emergency Response Guidebook
” (November 2017).