Stack Emissions Dispersion Calculator

The Gaussian plume equation predicts the steady-state concentration downwind of a continuous point source by assuming pollutant mass spreads with a normal distribution in the crosswind and vertical directions while advecting at the mean wind speed. Concentration is inversely proportional to wind speed and to the product of the two dispersion coefficients, sigma y and sigma z, both of which grow with downwind distance. The exponential term in minus H squared over twice sigma z squared accounts for the elevation of the plume centerline above the receptor. H should be the effective stack height, the physical stack plus plume rise from buoyancy and exit momentum, which can add 50 to 200 meters for a hot utility stack. The dispersion coefficients used here follow the Briggs open-country forms for stability class A, strongly unstable daytime conditions, with sigma y equal to 0.22x divided by the square root of one plus 0.0001x; Briggs gives sigma z as 0.20x alone, so applying the same denominator to it slightly understates vertical spread far downwind. The model assumes flat terrain, steady wind above about 1 meter per second, no chemical decay, and no building downwash, and it is unreliable in calm air, in complex terrain, and beyond roughly 20 kilometers.

Atmospheric diffusion theory began with the turbulence work of G. I. Taylor in 1921 and was turned into practical plume formulas by Oliver Graham Sutton, whose papers of the 1930s and 1940s gave the first widely used expressions for spread from a continuous source, developed partly for British chemical defence research. The Gaussian form gained its modern empirical footing from field campaigns of the 1950s, notably the Project Prairie Grass tracer experiments conducted in Nebraska in 1956, which supplied the concentration data against which spread parameters were fitted. Frank Pasquill proposed the familiar six stability classes A through F in 1961, keyed to wind speed, insolation, and cloud cover; Franklin Gifford converted them into the dispersion curves usually called the Pasquill-Gifford scheme, and D. Bruce Turner's 1970 Workbook of Atmospheric Dispersion Estimates put them in a form engineers could apply by hand. Gary Briggs published the algebraic fits reproduced in this calculator in the early 1970s, replacing graphical reading of the curves. The approach entered US regulation through the Industrial Source Complex models of the 1980s and 1990s and was superseded in 2005 by AERMOD, which keeps the Gaussian core but derives dispersion from boundary layer similarity theory rather than discrete stability classes.