Question

Why is including the mirror-image plume important in the Gaussian dispersion equation? Now suppose z = 4H. How much does including the mirror-image plume affect the final downwind concentration at this height?

Answer 1

There is one modification done to equation 1. Unlike a plume spreading in free air, most plumes will be emitted close to the ground, like the case of the chimney shown above. Hence, as the plume spreads downwards (as well as upwards) as it moves downwind from the source, it will eventually hit the ground. The plume cannot continue to spread into the ground, it is reflected back into the air above the ground. The effect of the ground boundary is included in the concentration equation mathematically by using a mirror-image source Si of the same strength Qi placed at the same distance from the ground (hs) but on the other side of the bound at any point P there is a contribution to the concentration C(x,y,z) from both the real source (S) and the imaginary source (Si ) as well. The vertical distance to P from the centre-line of the real plume is (z-H). The vertical distance to P from the centre-line of the imaginary source is (z+H) so the modified equation is

for z=4H comparing eq.1 and eq.2 concentration has been increased in case 2