How AERMOD works: from inputs to concentrations

AERMOD — the AMS/EPA Regulatory Model, the U.S. Environmental Protection Agency's (EPA) preferred model for near-field dispersion — is a steady-state plume model: for each hour of meteorology it computes, at every receptor, the concentration a continuous plume would produce under that hour's boundary-layer conditions. This page walks the path from inputs to a concentration; the two pages after it go deeper on plume rise and terrain. Everything quoted here comes from EPA's model formulation document for the current model version.

One equation, two atmospheres

At its core the model evaluates one expression per hour and receptor:

C{x, y, z} = (Q/ũ) Py{y; x} Pz{z; x}, where Q is the source emission rate, ũ is the effective wind speed, and py and pz are probability density functions (pdf) which describe the lateral and vertical concentration distributions, respectively.

Source · AERMOD Model Formulation (EPA-454/B-26-003) §5, eq. 51 — quoted word-for-word from the source document.

Everything interesting lives in those two distribution functions, because the atmosphere the plume disperses into has two fundamentally different modes (see The boundary layer & the parameters that drive dispersion):

In the stable boundary layer (SBL), it assumes the concentration distribution to be Gaussian in both the vertical and horizontal. In the convective boundary layer (CBL), the horizontal distribution is also assumed to be Gaussian, but the vertical distribution is described with a bi-Gaussian probability density function (pdf).

Source · EPA-454/B-26-003 §2.

Why the convective vertical distribution isn't Gaussian: daytime plumes ride "a traveling train of convective elements - updrafts and downdrafts" (§5.2), and because downdrafts occur more often than updrafts, the vertical velocity distribution is skewed — the plume's most concentrated material drifts downward on average. A symmetric Gaussian cannot represent that; the bi-Gaussian can.

The convective day: three plumes in one

For a buoyant daytime release, AERMOD splits the plume into three mathematical sources (§5.2):

…there are three main mathematical sources that contribute to the modeled concentration field: 1) the direct source (at the stack), 2) the indirect source, and 3) the penetrated source. The strength of the direct source is fpQ, where Q is the source emission rate and fp is the calculated fraction of the plume mass trapped in the CBL (0 ≤ fp ≤ 1).

The direct plume is the mass that downdrafts carry to the ground. The indirect plume handles material that first reaches the top of the mixed layer — with a rise adjustment that "mimics the plume's lofting behavior, i.e., the tendency of buoyant plumes to remain temporarily near zi and resist downward mixing" (§5.2). The penetrated plume accounts for material that punches through the elevated inversion entirely "but is subsequently re-entrained by and disperses in the growing CBL" (§5.2). A tall, hot stack on a summer afternoon may put most of its mass in the third category at sunrise and the first by noon — the model tracks the split hour by hour.

A steady-state model that respects a varying atmosphere

Wind and turbulence change with height, but a steady-state plume equation can hold only one value of each. AERMOD resolves this with effective parameters (§4.2):

…the model "converts" the inhomogeneous values into equivalent effective or homogeneous values. This technique is applied to u, σvT, σwT, ∂θ/∂z, and the Lagrangian time scale.

The averaging runs over "that portion of the layer that contains plume material" between the plume's centroid height and the receptor (§4.2) — so a ground-level receptor under an elevated plume is governed by the winds the plume experienced, not the winds at the receptor's own height.

Two more pieces of physics round out the hourly calculation:

• Meander. At long travel times and light winds, a plume stops being a coherent ribbon: "AERMOD accounts for meander by interpolating between two concentration limits: the coherent plume limit … and the random plume limit, (which assumes an equal probability of any wind direction)" (§5.4). This is a large part of how the model behaves realistically in the light-wind hours that often control design values.
• Terrain, always on. Every concentration is computed as a weighted combination of a horizontal-plume state and a terrain-following state (§5.1, eq. 48) — flat terrain is just the case where the two states coincide. The next-but-one page unpacks this.

What the model needs to do all this

The hourly boundary-layer parameters come from AERMET's surface and profile files; receptor elevations and hill-height scales come from the terrain preprocessor AERMAP; source data (emission rate, stack parameters, building dimensions where downwash applies) come from the modeler. The model's data appetite is deliberately modest — a single wind, temperature, and cloud-cover record plus a morning sounding suffices (Formulation §2; see the meteorology pages) — because the similarity-theory profiles fill in the rest.

In PlumeSmart

Runs execute the current regulatory AERMOD version with the regulatory options, and results carry the hour-by-hour design-value bookkeeping the standards require — so what this page describes is exactly what produced the numbers on a results page.