AERMOD Tech Guide

Gaussian Plume Air Dispersion Model

4.2 Vertical Inhomogeneity in the Boundary Layer as Treated by the Interface

AERMOD, unlike existing regulatory models, is designed to treat the effects on dispersion from vertical variations in wind and turbulence. This treatment is needed to properly handle releases that are near the ground (the gradient of the variables is strongest here) and to provide a mechanism by which sources that exit the top of the mixed layer and penetrate into an elevated stable layer can re-enter the CBL further downwind. Since AERMOD uses a single value of the meteorological parameters to represent a layer through which these parameters are varying, AERMOD "converts" the inhomogeneous values (as measured or estimated) into equivalent (effective) homogeneous value. The averaging procedure used to create effective boundary layer parameters is discussed here. This technique, in general, is applied to u, vT, wT, and TLy . Wind vT wT Ly direction is treated separately.

Fundamental to this approach is the concept that the primary layer of importance, relative to receptor concentration, is the one through which plume material travels directly from source to receptor. Transport and diffusion of plume material located outside of this layer is assumed to be relatively unimportant until the reflected plume contributes significantly to the receptor concentration. Therefore, the effective parameters, which are denoted by an underscore throughout the document (e.g., effective wind speed is denoted by u ), are determined by averaging their values over that portion of the layer between the plume centroid height (Hp {x} ) (a simplified surrogate for the height of the plume’s center of mass) and the receptor height (zr ) that contains plume material. In other words, the averaging layer is determined by the vertical half-depth of the plume but is bounded by the Hp {xsr } and zr . The values used in the averaging process are taken from the vertical profiles generated in the AERMOD interface (Section 4.a.).

Since z {xsr } depends on the effective values of wT and u, the plume size is estimated using the initial values of wT {Hp } and u {Hp } to calculate z {xsr }. z {xsr } is then used to determine the layer over which wT {xsr } and u {xsr } are calculated. Figure 9 illustrates this approach.

Figure 9

Figure 9: AERMOD’s Treatment of the Inhomogeneous Boundary Layer

The specific procedure for calculating any effective parameter (denoted here generically as ) is as follows:

Equation (46)
Equation (47)

For all plumes, both limits are bounded by either the zr or Hp .

In stable conditions, Hp is always set equal to the plume centerline height. That is,

Equation (48)

The stable source plume rise h is calculated from eq.(126). s

In the CBL, the specification of Hp is somewhat more complicated. Because of limited mixing in p the CBL the center of mass of the plume will be the plume height close to the source and the mid-point of the PBL at the distance where it becomes well mixed. Beyond final plume rise, Hp is varied linearly between these limits.

Prior to plume stabilization, i.e., x < xf (distance to plume stabilization)

Equation (49)

and hd is estimated from eqs. (116) and hp is hep - hs where hep is calculated from eq. (119).

The distance to plume stabilization, xf , is determined as follows (Briggs, 1971, 1975) :

Equation (50)

where the buoyancy flux (Fb ) is calculated from eq.(117). b

However, for Fb = 0 the distance to final rise is calculated from the ISC3 (U.S.EPA, 1995) expression as:

Equation (51)

and the stabilized rise due to momentum alone is:

Equation (52)

Beyond plume stabilization ( x>x f), Hp varies linearly between the stabilized plume height f p (H{xf }) and the mid-point of the mixed layer (zi /2). This interpolation is performed over the distance range xf to xm , where xm is the distance at which pollutants first become uniformity mixed throughout the boundary layer. The distance xm is taken to be the product of the average mixed layer wind speed and the mixing time scale, zi/wT That is,

Equation (53)

where the averaging of u and wT are taken over the depth of the boundary layer. For distances beyond xf , Hp is assumed to vary linearly between the plume's stabilized height, H {xf }, and z i/2 such that:

Equation (54)

Furthermore, for all xf, Hp is limited to a maximum value of zi .

Note that in the CBL, both the direct and indirect source will have the same (effective parameter) values. In eq. (47) z is the average of the updraft z and the downdraft z , the maximum value of ht is zi , and when hb zi , = {zi}.

As discussed previously, when multiple vertical measurements of wind direction are available a profile is constructed by linearly interpolating between measurements and persisting the highest and lowest measurements up and down, respectively. The approach taken for selecting a transport wind direction from the profile is different from the above. The transport wind direction is selected as the mid point of the range between stack height and the stabilized plume height.