Gaussian Plume Simulator — Atmospheric Dispersion Model

The Gaussian plume model assumes a steady point source whose pollutant is advected by the mean wind in the x direction and spreads laterally and vertically following Gaussian profiles. With ground reflection at z = 0 the centerline concentration is $C(x,0,0)=\dfrac{Q}{\pi u\sigma_y\sigma_z}\exp\!\left(-\dfrac{H^2}{2\sigma_z^2}\right)$. This tool uses the Pasquill D class simplified spread $\sigma_y(x)=0.10\,x^{0.92}$ and $\sigma_z(x)=0.08\,x^{0.92}$. With the defaults Q = 10 g/s, u = 5 m/s, H = 50 m and x = 2 km the result is about 56.6 μg/m³. Note that the denominator is $\pi$ rather than $2\pi$ because the ground reflection has been folded into the exponential.

Environmental impact assessment (EIA): When designing new stacks for power plants or factories, regulators require that ground level concentration stays below standards across the full Pasquill A to F range. This tool gives quick D class sensitivity, the standard reference case.

Effective stack height design: Geometric stack height plus plume rise (Briggs formula) gives the effective H. Engineers minimise capital cost by finding the lowest stack that still meets WHO or national air quality limits.

Emergency response: After a chemical plant leak, a Gaussian plume estimate of the downwind impact zone can be produced in seconds, long before a full CFD run is available. It supports evacuation planning.

Urban air quality monitoring: Networks of point sources (roads, plants) are summed using Gaussian plume kernels to estimate annual mean and 1 hour peak concentrations. It remains the workhorse formula behind many regulatory codes.

First, the Gaussian plume model assumes a steady state and a time-averaged concentration. Short bursts and rapidly varying wind directions cannot be reproduced. When wind direction variance is large, switch to a puff model or a CFD simulation for higher fidelity.

Second, the $\sigma=a\,x^{0.92}$ form used here is a simplified Pasquill D representation. Production codes such as AERMOD and CALPUFF use class-specific coefficients and functions (Briggs open country, ASME formulation, etc.). Treat the absolute value as illustrative and the trend as the takeaway.

Third, terrain and buildings are ignored. A tall building near the stack causes downwash and the model will underestimate the near-field ground concentration. In practice apply the GEP rule (stack at least 2.5 times the tallest nearby building) and add building wake corrections.