Why are two exponential terms present in the centerline concentration expression along the vertical axis?

Why are two exponential terms present in the centerline concentration expression along the vertical axis?

• A. They represent two separate plumes from different stacks.
• B. They are used to correct for humidity.
• C. They have no physical meaning.
• D. They account for the reflection at ground (image source) leading to a mirrored term.

Answer: (D)

The centerline concentration along the vertical axis includes two exponential terms because the ground acts like a mirror for the plume. In the standard Gaussian plume model, enforcing the boundary condition at the ground (no net flux through the surface) is most conveniently done with the method of images: place an image source below the ground at the mirror height (-H) with the same strength as the real source at height H. The concentration on the vertical line is then the sum of the contributions from the real source and its image, giving terms that involve (z − H) and (z + H) in the exponent. This reflected (image) term represents the reflected portion of the plume and is essential for accurately modeling how the ground affects dispersion near the surface. It’s not due to humidity, and it isn’t because there are two separate real plumes; it’s the mathematical representation of the ground reflection.

The centerline concentration along the vertical axis includes two exponential terms because the ground acts like a mirror for the plume. In the standard Gaussian plume model, enforcing the boundary condition at the ground (no net flux through the surface) is most conveniently done with the method of images: place an image source below the ground at the mirror height (-H) with the same strength as the real source at height H. The concentration on the vertical line is then the sum of the contributions from the real source and its image, giving terms that involve (z − H) and (z + H) in the exponent. This reflected (image) term represents the reflected portion of the plume and is essential for accurately modeling how the ground affects dispersion near the surface. It’s not due to humidity, and it isn’t because there are two separate real plumes; it’s the mathematical representation of the ground reflection.