Site-Specific Vertical Dispersion Coefficient Development

Most USEPA dispersion models used in regulatory application are of the Gaussian type.  The Gaussian or normal distribution, familiar in statistics, is used to describe the crosswind (horizontal) and vertical distributions which result from the turbulent mixing known as dispersion.  (The degree of mixing is generally governed by the temperature profile of the atmosphere in the 10 meters or so closest to the ground.) 

Dispersion coefficients (both vertical and horizontal) are identified which describe the shape of the plume as it advects along in the mean wind direction.  They define the distance one must move away from the plume centerline, at some specified downwind distance, before the concentration is reduced by a factor of 1/e.  A Gaussian distribution implies that the pollutant concentration profile forms a bell-shaped curve centered about the plume centerline in both the horizontal and the verical. 

In the models, dispersion coefficients are used to parameterize the atmospheric stability.  Atmospheric stability can be thought of simply as a property governing the up and down movement of air parcels relative to the surrounding air.  For convenience, a total of six discrete stability categories are identified.  Assignment of the appropriate category is made based on in-field measurements of various combinations of meteorological parameters, including solar radiation, wind speed, and delta temperature (change of temperature with height).  Each stability class category is associated with a unique set of curves defining the vertical and horizontal dispersion coefficients as functions of distance downwind of the source.  The set of curves yielding the greatest dispersion coefficients (at a given downwind distance) describe the most unstable situation (referred to as Stability Class A); in this case, the plume spreads out as it advects along, thus dispersing the pollutant the most.

On the other hand, the set of curves yielding the smallest dispersion coefficients describe the most stable situation (referred to as Stability Class F); in this case, the plume remains largely intact as it advects along, thus dispersing the pollutants the least.  In modeling, we are generally concerned with these stable conditions, as they lead to the highest downwind concentrations owing to the lack of turbulent mixing. 

In the real world, atmospheric stability, of course, is not a step-function; instead, like most everything else, it is a continuum.  The approximation of ascribing a discrete category of atmospheric stability when it is actually a continuous function is fine for most dispersion modeling applications, as the error introduced by the uncertain assignment of the emission-rate term generally exceeds the error introduced by this stability approximation.  However, when great care is exercised in the design and execution of field-measurement programs for back-calculating emission rates -- as is the case for our work at the New York City municipal wastewater treatment plants -- other sources of error are minimized and the atmospheric stability approximation becomes the dominant source of error. 

With employment of the area-source technique for emissions estimation, the error introduced by the approximation of atmospheric stability is much more significant with respect to vertical than horizontal dispersion.  This is largely because the technique involves measurement along an entire downwind measurement path.  Therefore, we generally concern ourselves only with development of site-specific vertical dispersion coefficients (also known as sigma-z or σz values). 

Site-specific sigma-z values are developed for the express purpose of replacing the equations in the model which limit atmospheric stability to the six discrete categories.  By measuring these vertical dispersion coefficients directly, a site-specific equation is developed for use with each particular emission-rate measurement event.  This representation of atmospheric stability recognizes the continuous nature of the function and eliminates the need to even consider stability class, as the purpose of stability class in the models is solely to facilitate default to the appropriate set of dispersion coefficient equations.  Emission rates which are back-calculated using these default equations can differ from those back-calculated using site-specific equations by several factors, especially when the observed stability class is marginal with respect to the neighboring class.


The tracer method involves the cross-plume, path-integrated measurement of a tracer gas released in a controlled manner in the vicinity of the source of concern.  This method provides actual sigma-z measurements over durations coincident with the source-attribution measurements for use in the area-source technique for emissions estimation.  It takes advantage of the following equation, in which sigma-z is derived by integrating, in the crosswind direction, Turner's general Gaussian equation for ground-level concentration downwind of a continuously emitting, ground-level point source.  This yields:

                                                                                          σz   =  (2π)2 Q (πCu) -1

where:

σz         =          vertical dispersion coefficient at the particular downwind distance (m)

Q         =          uniform tracer-gas emission rate (mg/s)

C         =          ground-level crosswind-integrated tracer-gas concentration (mg/m2)

u          =          mean wind speed (m/s)

Click onto Use of Open-Path FTIR Spectroscopy at a New York City Municipal Wastewater Treatment Plant to access a technical publication presented at the Air & Waste Management Association's 95th Annual Conference and Exhibition (June 2002) in Baltimore.  This article is a case study where the technology was used to support development of refined estimates of H2S emissions through development of unique, site-specific sigma-z curves for each of 77 separate monitoring events.  These curves were then substituted directly into the dispersion model for H2S emissions back-calculation.


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