Gaussian Plume, Pasquill Stability & Effective Stack Height

Quick Answer: Use the NCEES Handbook Gaussian plume equation with Pasquill-Gifford σy and σz for the stated stability class, effective stack height H = hs + Δh, and uniform wind speed u. Stability controls dispersion — unstable air mixes vertically faster, often lowering peak ground impacts near the stack.

Atmospheric dispersion predicts downwind concentrations from point, line, or area sources. The FE Environmental exam tests conceptual plume behavior and plug-and-chug application of the steady-state Gaussian plume model.

Gaussian Plume Assumptions

The model assumes:

1. Continuous, constant emission rate Q (mass/time).
2. Uniform steady wind u at stack height (direction along x).
3. Flat terrain, no chemical decay unless a decay term is given.
4. Gaussian distribution in crosswind (y) and vertical (z) directions.
5. Reflection at ground surface (image source method for elevated releases).

Violations — complex terrain, building downwash, calm winds, reactive chemistry — invalidate simple Gaussian results; exam problems usually state when to use handbook formulas.

Pasquill Stability Classes

Pasquill-Gifford classes A (very unstable) through F (stable) combine wind speed with solar insolation (day) or cloud cover (night):

Exam trap: Stable night conditions (F) produce smaller σz — plumes stay narrow vertically. Peak ground-level concentrations can occur farther downwind and sometimes higher than under unstable conditions for the same source.

Handbook curves give σy(x) and σz(x) as functions of downwind distance and stability. Always select class from the weather narrative before reading σ values.

Effective Stack Height

[ H = h_s + \Delta h ]

• hs — physical stack height above ground.
• Δh — plume rise from buoyancy (warm flue gas) and momentum (high exit velocity).

Briggs equations in the Handbook estimate rise for buoyant and momentum-dominated plumes. Hot combustion stacks often rise tens of meters above the release point before leveling.

Building downwash lowers effective height when stacks are too short relative to building width — a design error that increases ground-level impacts on the downwind roof wake.

Centerline Ground-Level Concentration

For an elevated release, handbook forms give concentration at ground level (z = 0) on the plume centerline (y = 0). General structure:

[ C(x,0,0) = \frac{Q}{\pi u \sigma_y \sigma_z} \exp!\left(-\frac{H^2}{2\sigma_z^2}\right) ]

(Constants and exponent forms vary slightly by handbook edition — use the exact NCEES form on exam day.)

Maximum ground-level concentration for elevated stacks occurs where the plume impinges on the ground — not at the stack. Downwind distance to maximum increases with H and depends on stability.

Superposition and Multiple Sources

Concentrations from independent stacks emitting the same pollutant add linearly at a receptor:

[ C_{total} = \sum_i C_i ]

Different pollutants are not combined for standard comparison — compare each to its NAAQS or hazard limit separately.

Fugitive, Area, and Line Sources

Point sources — stacks (Gaussian form above).

Area sources — landfills, stockpiles; often treated as ground-level area integration.

Line sources — highways; line-source integral perpendicular to wind.

FE items most commonly use point-source Gaussian with given Q, u, H, and stability.

Worked Example Framework

Given: Q = 25 g/s; u = 4 m/s; physical stack 20 m; plume rise 15 m; stability D; find ground-level centerline concentration at x = 800 m.

Steps:

1. H = 20 + 15 = 35 m.
2. From handbook, read σy(800 m) and σz(800 m) for class D.
3. Substitute into Gaussian equation.
4. Convert units to µg/m³ or ppm if comparing to a standard (use MW and 24.45 L/mol at 25°C for ppm from µg/m³).

Unit discipline: Q in g/s, u in m/s, σ in meters → concentration in g/m³; multiply by 10⁶ for µg/m³.

Inversions and Fumigation

Radiation inversions trap pollutants near the surface at night. Lofting occurs when a plume releases above the inversion base. Fumigation — rapid vertical mixing when the inversion breaks in morning — can spike ground concentrations briefly.

Meteorological Inputs

• Wind rose — prevailing direction for receptor siting.
• Mixing height — caps vertical dilution in inventory screening models.
• Turbulence class from stability — never skip this step.

FE Exam Strategy

Practice one full problem: weather → stability → σ → H → concentration. Flag the Handbook dispersion section during the tutorial. Verify whether the question asks centerline, off-centerline, or at height z (breathing zone on a hill).

Exam trap: Using physical stack height without plume rise when Δh is provided or calculable from Briggs formulas underestimates H and overpredicts ground-level concentration.

Gaussian plume mechanics connect emission rates to ambient impacts — the quantitative bridge between stack design and NAAQS compliance demonstrations.

Briggs Plume Rise and Building Wake Effects

Briggs formulas estimate buoyant and momentum plume rise as functions of stack diameter, exit velocity, temperature difference, and atmospheric stability. On exam problems, plume rise may be given directly — still compute H = hs + Δh before dispersion. Building downwash lowers effective height when stacks are shorter than 2.5 times building height; EPA guidance recommends raising stacks or relocating to avoid cavity recirculation zones that increase ground-level concentrations on the building lee side.

Fumigation occurs when an elevated plume mixes down to ground during morning inversion break — transient high concentrations. Stable nocturnal conditions with light winds often produce the worst-case scenarios for short stacks near receptors.