Terrain: the dividing streamline & the two-state plume

Older regulatory models forced a choice: a "simple terrain" model when receptors sat below stack top, a "complex terrain" model when they sat above it. AERMOD replaced that split with a single treatment that works everywhere — built on one physical idea and one weighting equation.

The physical idea: stable flow splits at a height

Watch stably stratified air approach a hill and it divides into two layers:

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. The concept of a two-layer flow, distinguished at the dividing streamline height (Hc), was first suggested by theoretical arguments of Sheppard (1956) and demonstrated through laboratory experiments, particularly those of Snyder et al. (1985). In neutral and unstable conditions Hc = 0.

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

The consequence for a plume is direct: "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" (§5). The nightmare case for elevated terrain — a stable nighttime plume held flat at hillside height — is exactly the below-H_c state.

The weighting: every receptor gets both answers

Rather than deciding which state applies, AERMOD computes both and blends:

In general, AERMOD models a plume as a combination of two limiting cases: a horizontal plume (terrain impacting) and a terrain-following plume. Therefore, for all situations, the total concentration, at a receptor, is bounded by the concentration predictions from these states. In flat terrain the two states are equivalent. By incorporating the concept of the dividing streamline height, in elevated terrain, AERMOD's total concentration is calculated as a weighted sum of the concentrations associated with these two limiting cases or plume states.

Source · EPA-454/B-26-003 §5.1 (the weighted sum is eq. 48: C_T = f·C{z_r} + (1−f)·C{z_p}).

The weight f moves with the physics: it "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" (§5). Because the total is always bounded by the two limiting states, the treatment degrades gracefully — there is no cliff where a receptor switches regimes and the answer jumps.

Where the terrain numbers come from

The terrain data enters through the model's terrain preprocessor:

The AERMOD terrain pre-processor (AERMAP) uses gridded terrain data to calculate a representative terrain-influence height (hc) for each receptor with which AERMOD computes receptor specific Hc values. Through this approach, AERMOD handles the computation of pollutant impacts in both flat and elevated terrain within the same modeling framework, thereby removing the need to differentiate between the formulations for simple and complex terrain (as required with previous regulatory models).

Source · EPA-454/B-26-003 §5.1.

So every receptor carries three terrain numbers: its location, its ground elevation, and its hill height scale — a measure of the terrain that actually influences flow at that receptor, computed by AERMAP from digital elevation data. The regulatory default requires exactly this: the DFAULT option demands "the use of terrain elevation data processed through the AERMAP terrain processor" (40 CFR 51 App. W, Addendum A, A.1, Regulatory Use — see Rule — Regulatory Default (DFAULT)).

What this means in practice

• Terrain matters most on stable nights. H_c is zero in neutral and unstable conditions — the two-state machinery engages precisely in the stable hours when a flat-riding plume can meet rising ground.
• "Flat" is a modeling claim, not a convenience. Running flat terrain where real elevations exist removes the horizontal-plume state's encounter with the hillside — which is why elevation handling is part of the regulatory default rather than a stylistic choice.
• Receptor elevations deserve the same scrutiny as emission rates. The controlling receptor in elevated terrain is often the one where plume height and hillside height converge; a wrong elevation there moves the design value directly.

In PlumeSmart

Terrain processing runs through AERMAP automatically for projects with elevated terrain: receptor elevations and hill height scales come from digital elevation data, user-supplied or imported elevations take precedence where provided, and the run records show which elevations each receptor actually used.