AERMOD Tech Guide

Gaussian Plume Air Dispersion Model

6.1 General Structure of AERMOD including Terrain

AERMOD incorporates, with a simple approach, current concepts about flow and dispersion in complex terrain. Generally, in stable flows, a two-layer structure develops in which the lower layer remains horizontal while the upper layer tends to rise over the terrain. This two-layer concept was first suggested by theoretical arguments of Sheppard (1956) and demonstrated through laboratory experiments, particularly those of Snyder et al. (1985). These layers are distinguished, conceptually, by the dividing streamline, denoted by Hc . In neutral and unstable conditions, the lower layer disappears and the entire flow (with the plume) tends to rise up and over the terrain.

A plume embedded in the flow below Hc tends to remain horizontal; it might go around the hill or impact on it. A plume above Hc will ride over the hill. Associated with this is a tendency for the plume to be depressed toward the terrain surface, for the flow to speed up, and for vertical turbulent intensities to increase. These effects in the vertical structure of the flow are accounted for in models such as the Complex Terrain Dispersion Model (CTDMPLUS). However, because of the model complexity, input data demands for CTDMPLUS are considerable. EPA policy (Code of Federal Regulations, 1995) requires the collection of wind and turbulence data at plume height when applying CTDMPLUS in a regulatory application. As previously stated, the model development goals for AERMOD include having methods that capture the essential physics, provide plausible concentration estimates, and demand reasonable model inputs while remaining as simple as possible. Therefore, AERMIC arrived at a terrain formulation in AERMOD that considers vertical flow distortion effects in the plume, while avoiding much of the complexity of the CTDMPLUS modeling approach. Lateral flow channeling effects on the plume are not considered by AERMOD.

AERMOD deals with the two-layer concept in the following way. AERMOD assumes that the value of the concentration on a hill lies between the values associated with two possible extreme states of the plume. One of these states is the horizontal plume that occurs under very stable conditions when the flow is forced to go around the hill. The other extreme state is when the plume follows the terrain vertically (terrain following state) so that its centerline height above terrain is equal to the initial plume height. AERMOD calculates the concentration at a receptor,.51 located at a position (xr ,yr ,zr), as the weighted sum of the two limiting estimates. Figure 12 presents a schematic of the two state concept.

Figure 12

Figure 12:AERMOD Two State Approach. The total concentration predicted by AERMOD is the weighted sum of the two extreme possible plume states.

The relative weighting of the two states depends on: 1) the degree of atmospheric stability; 2) the wind speed; and 3) the plume height relative to terrain. In stable conditions, the horizontal plume "dominates" and is given greater weight while in neutral and unstable conditions, the plume traveling over the terrain is more heavily weighted. The specific approached used to calculate this weighting function is presented below and illustrated in Figure 13.

The concentration, estimated by AERMOD, in the presence of the hill is given by.

Equation (59)

The concentration subscripts (c, s) in eq. (59) relate to the total concentration during convective conditions “c” and stable conditions “s”. It is important to note that for any concentration calculation all heights (z) are referenced to stack base elevation.

The formulation of the weighting factor draws on the concept of the dividing streamline height, Hc . Using the hc from AERMAP as the receptor specific height scale (“hill height”) Hc is calculated from the same algorithms found in CTDMPLUS (Perry, 1992). That is:

Equation (60)

We first define p , the fraction of the plume mass below Hc , as

Equation (61)

where CT ={xr , yr, zr} refers to the concentration in the absence of the hill. Then, the weighting factor, f, which relates to the fraction of plume material (p ) that is below the height of the p dividing streamline (Hc ), is given by

Equation (62)

Defined this way, when the plume is entirely below the critical dividing streamline, p = 1.0, and f = 1, and the terrain concentration is only affected by the flat plume. On the other hand, when the plume is entirely above the critical dividing streamline height, p = 0, and f = 0.5. This means that we never allow the plume to approach the terrain responding state completely. That is, even as the plume encounters the terrain and rises up, there is a tendency for some plume material to spread out around the sides. Thus, under purely neutral or unstable conditions, the plume state is half way between the horizontal state and the terrain responding state.

The first term on the right side in eq. (59) is the contribution from the horizontal plume state. The second term is the contribution from the terrain responding state, in which the concentration is calculated at the receptor flag pole height, zp , zp = zr - zt as where zr is the receptor height (above stack base elevation), and zt is the terrain height (above mean sea level). Therefore, zp is defined as the height above terrain. If z = 0.0, the terrain responding state sees the receptor on p the hill as a ground-level receptor. Although a complete terrain responding state is not likely to occur in practice, even under very unstable conditions, its associated concentration value sets one of the possible limits. As seen in eq. (62), we do not allow the actual plume to completely attain this state. Note that in flat terrain (i.e., zt = 0 ), the concentration equation eq. (59) reduces to the form for a single horizontal plume.

Figure 13 illustrates how the weighting factor is constructed and its relationship to the estimate of concentration as a weighted sum of two limiting plume states.

Figure 13

Figure 13:Treatment of Terrain in AERMOD. Construction of the weighting factor used in calculating total concentration.

The general form of the expressions for concentration in each term of eq. (59) for both the CBL and the SBL can be written as follows:

Equation 63

where Q is the source emission rate, u is the effective wind speed, and py and pz are probability y z density functions (p.d.f.) which describe the lateral and vertical concentration distributions, respectively. AERMOD assumes a traditional Gaussian p.d.f. for both the lateral and vertical distributions in the SBL and for the lateral distribution in the CBL. The CBL’s vertical distribution of plume material reflects the distinctly non-Gaussian nature of the vertical velocity distribution in convectively mixed layers. The specific form for the concentration distribution in the CBL is found in eq. (66) which uses the notation Cc {x,y,z}. Similarly, in the SBL, the c.55 concentration takes the form of eq. (77) and used the notation C {x.y.z}. s

AERMOD simulates five different plume types depending on the atmospheric stability and on the location in and above the boundary layer: 1) direct, 2) indirect, 3) penetrated, 4) injected and 5) stable. All of these plumes will be discussed, in detail, throughout the remainder of this document. During stable conditions, plumes are modeled with the familiar horizontal and vertical Gaussian formulations. During convective conditions (L<0) the horizontal distribution is still Gaussian; the vertical concentration distribution results from a combination of three plume types: 1) the direct plume material within the mixed layer that initially does not interact with the mixed layer lid; 2) the indirect plume material within the mixed layer that rises up and tends to initially loft near the mixed layer top; and 3) the penetrated plume material that is released in the mixed layer but, due to its buoyancy, penetrates into the elevated stable layer.

During convective conditions, AERMOD also handles a special case referred to as an injected source where the stack top (or release height) is greater than the mixing height. Injected sources are modeled as plumes in stable conditions, however the influence of the turbulence and the winds within the mixed layer are considered in the inhomogeneity calculations as the plume material passes through the mixed layer to reach receptors.