# AirWare User Manual

# AERMOD: A Dispersion Model

for Industrial Source Applications

This documentation is extracted from Perry et al. (1998).

AERMOD MODEL FORMULATION

This section describes the basic formulation of the
AERMOD dispersion model as it is structured at the time of this writing
(January, 1994). Included are: the general form of the concentration
equation with adjustments for terrain, plume rise and dispersion algorithms
appropriate for the convective boundary layer and for the stable boundary
layer, handling of boundary layer inhomogeneity, and algorithms (interfacing
between AERMET and AERMOD) for developing vertical profiles of the necessary
meteorological parameters. As will be discussed later, the model will go
through a developmental evaluation, after which some changes in the algorithms
are likely.
In sections where two options are being considered for a given algorithm,
both are described.

General Structure of AERMOD including Terrain Handling

AERMOD (like ISC2) is a steady-state, plume model.
That is, it is designed to apply to source releases and meteorological
conditions that are assumed to be steady over individual modeling periods
(typically one hour or less).
AERMOD has been designed to handle the computation of pollutant impacts in
both flat and complex terrain within the same modeling framework.
In fact, with the AERMOD structure, there is no need for the specification
of terrain type (flat, simple, or complex) relative to stack height since
receptors at all elevations are handled with the same general methodology.
To define the form of the AERMOD concentration equation, it is necessary to
simultaneously discuss the handling of terrain.

AERMOD incorporates, with a simple approach,
current concepts about flow and dispersion in complex terrain.
In very stable conditions, the flow, and hence the plume embedded in it,
tends to remain horizontal as it encounters a terrain obstacle.
Generally, in stable flows, a two-layer structure develops in which the lower
layer remains horizontal while the upper layer tend to rise over the terrain.
This two-layer concept was first suggested by theoretical arguments of
Sheppard^{0} and demonstrated through laboratory
experiments, particularly those of Snyder et al^{0}.
These layers are distinguished by the concept of a dividing streamline.
In neutral and unstable conditions, the lower layer disappears and
the entire flow (with the plume) tends to rise up and over the terrain.
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 as well as others (flow horizontally around the terrain) are accounted
for in models such as the Complex Terrain Dispersion Model
(CTDMPLUS)^{0}.
However, because of the model complexity, input data demands for
CTDMPLUS are considerable.

As stated before, our model development goals for AERMOD
include having methods that capture the essential physics, provide reasonable
estimates, and demand reasonable model inputs while remaining as simple as
possible.
Therefore, AERMIC arrived at terrain formulations in AERMOD that consider
the important concept of a dividing streamline, while avoiding much of
the complexity of the CTDMPLUS modeling approach.

AERMOD deals with the two-layer concept in the following way.
The model assumes that the plume exists in two states and that the
concentration at a receptor, located at a position (*x,y,z*),
is the weighted sum of the two concentration estimates:
one where the plume is horizontal (representing plume material below the
dividing streamline) and the other where the plume travels over
the terrain (representing plume material above the dividing streamline).
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 important (heavily weighted).
In flat terrain, the concentration equation reduces to the form for
a single plume. The general form for the total concentration at any
terrain elevation is:

where *f* is the weighting factor related to the fraction
of plume material that is below the height, *H*_{c},
of the dividing streamline, C(*x,y,z*) is the flat-terrain
concentration equation appropriate for given stability conditions (defined in
subsequent sections), *z* is the height of the receptor
(this includes the height above local terrain), and z_{eff}
is an "effective" receptor height (which is equal to *z* in flat terrain)
to be defined later in this section.
The first term on the right-hand side of equation (1) represents the
contribution from the horizontal plume and is evaluated at a receptor height,
*z*, while the second represents the contribution from the plume
adjusted by terrain and is evaluated at an effective receptor height.

The weighting factor, *f*, is a function of the fraction
of plume mass that is below *H*_{c} at the downwind distance of
the receptor. The fraction, f ,
of mass below *H*_{c} is calculated as:

*H*_{c} is a function of the wind speed
, vertical potential temperature gradient, and the height of the terrain
influencing the flow. In neutral to unstable conditions (or in flat terrain
for all conditions), *H*_{c} = 0, and thus
f = 0.

Two options are being considered by AERMIC for defining the
effective receptor height, *z*_{eff}, and the relationship
between *f* and f .
Both will be included in the developmental evaluation to be discussed later.

**OPTION ONE**. In this option, *f* is set equal to
f as calculated in equation (2).
Therefore, the two states of the plume are directly weighted by the fraction
of plume material below *H*_{c}.

The plume is allowed to react to the terrain in a manner
similar to that in the Rough Terrain Diffusion Model
(RTDM)^{0} where (for representation of the
plume above *H*_{c}) a half-height correction is made to the
plume centerline.
With the RTDM approach, the reflecting surface is effectively brought closer
to the plume center which may result in unrealistically high concentrations.
To avoid this, option one in AERMOD applies a correction to the receptor
height above base elevation that is equivalent to the half-height plume
correction;
that is, AERMOD elevates the receptor onto a pole by an amount equivalent to
that which RTDM would have reduced the plume height for the same terrain.
This gives an increased concentration due to terrain without an inappropriate
increase in plume reflection at the surface.

The AERMOD modified half-height approach yields an effective
receptor height of:

where *h*_{p} is the plume height above base elevation,
*z*_{t} is the height of the terrain at (*x,y*),
and (*z*-*z*_{t}) represents the height of the receptor
above the local terrain (when the original receptor is on a pole).

For example, when the receptor is on the hill surface
(*z* = *z*_{t}) and at an elevation above the plume height,
AERMOD models (based on equation (3)) the concentration in the second
term of equation (1) as if the terrain was absent and the receptor was on
a pole at one-half the plume height.
If the receptor is at an elevation below the plume height,
then the effective pole height is one-half the receptor height in this
example.

**OPTION TWO**. In this option, the weighting function is a
function of f such that *f* ranges
between 0.5 and 1 (in contrast to option one where *f* ranges from 0 to
1).
This insures that both states of the plume as defined in equation (1)
contribute to concentrations in all stability conditions. In this option the
horizontal plume is the same, but the plume representing the flow over the
hill is exactly terrain-following. In other words, the effective receptor
height is unaffected by the terrain height. With this concept *f* and
*z*_{eff} have the form:

and

Equation (5) shows that, in option two, the effective receptor
height is only a function of the receptor height above local terrain
(since *z* is the sum of the terrain height at the receptor and the
height of the receptor above the local terrain).
In neutral to unstable conditions, *H*_{c} = 0,
f = 0, so *f* = 0.5.
In these conditions, the concentration at an elevated receptor is the
average of the contributions from the horizontal plume state and the
terrain-following state.