Question 2 of 5: Dispersion Models and Plume Behaviour

Problem 2: Dispersion Models and Plume Behaviour (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (i) — Gaussian dispersion model. A widely used example is AERMOD (the U.S. EPA's regulatory Gaussian plume model, successor to the older ISCST3). Basic approach: the model assumes the pollutant plume travels downwind along the mean wind direction from an effective stack height (physical stack height plus plume rise), and that concentration is distributed normally (Gaussian) about the plume centreline in both the crosswind (y) and vertical (z) directions, with the spread described by dispersion coefficients σ_y and σ_z that grow with downwind distance according to the atmospheric stability class. Information required to run it: pollutant emission rate Q, stack parameters (height, diameter, exit velocity, exit temperature) to compute plume rise, wind speed and direction, atmospheric stability class (derived from insolation/cloud cover and wind speed via the Pasquill–Gifford scheme, or boundary-layer parameters in AERMOD's more modern formulation), ambient temperature, terrain elevation, and receptor locations. Two assumptions: (1) steady-state emissions and meteorology over the averaging period, i.e. wind speed, direction and stability do not change during plume travel; (2) the pollutant is conservative — no chemical reaction, deposition, or removal occurs between the stack and the receptor, and the terrain is relatively flat/open with no building-downwash or complex-terrain effects. One limitation: the model performs poorly under low wind speed / calm conditions, since the Gaussian formulation divides concentration by wind speed and assumes a well-defined transport direction — near-calm conditions make the predicted concentration unrealistically large and the assumed straight-line transport unreliable.

Part (ii) — plume behaviour types. Four (of the six classically named) plume behaviours are looping, coning, fanning, and fumigation (lofting and trapping are the other two). Three are described below, each governed by how the environmental lapse rate (ELR) compares to the dry adiabatic lapse rate (DALR, ≈9.8 °C/km):

Looping occurs under a strongly unstable (superadiabatic) lapse rate — a clear, sunny day with strong surface heating and light wind. Large thermal eddies loop the plume up and down chaotically; close to the stack a downward loop can briefly bring high concentration to ground level, but the same strong turbulence dilutes the plume rapidly, so ground-level concentration falls off quickly with distance beyond that near-source zone. Coning occurs under near-neutral stability — overcast, windy conditions (day or night) where the temperature gradient neither strongly enhances nor suppresses turbulence. The plume spreads in a smooth, symmetric cone about the centreline, and ground-level concentration increases gradually and predictably with downwind distance — this is the regime the standard Gaussian model represents most faithfully. Fanning occurs under stable conditions or a temperature inversion (typically a clear, calm night with strong radiative surface cooling, ELR < DALR or even a temperature increase with height). Vertical turbulence is strongly suppressed, so the plume stays thin and nearly flat while spreading laterally (side to side) as it travels; it can carry pollutant far downwind with little ground-level impact directly beneath it, but poses a hazard wherever it intersects elevated terrain or an elevated receptor at plume height.

Part (iii) — a non-dispersion air quality model. A receptor model, such as Chemical Mass Balance (CMB), works in the opposite direction to a dispersion model: instead of starting from a source's emission rate and predicting concentration downwind, it starts from measured ambient pollutant concentrations and chemical "fingerprints" (elemental, organic-tracer, or isotopic composition) at a monitoring site, together with known emission profiles for each candidate source category, and solves a mass-balance system to apportion how much each source contributed to the measured concentration. It is especially useful for source apportionment (e.g. splitting ambient PM₂.₅ into traffic, wood-smoke, and industrial contributions) when source emission rates are poorly characterised but good ambient monitoring data and source profiles exist — the reverse of the information Gaussian, Eulerian, or Lagrangian dispersion models require.