What is the typical ground-level concentration expression for y=0 and z=0?

What is the typical ground-level concentration expression for y=0 and z=0?

• A. C = Q/(π u σ_y σ_z)
• B. C = (Q/(π u σ_y σ_z)) exp(-H^2/(2 σ_z^2))
• C. C = exp(-H^2/(2 σ_z^2))
• D. C = Q/(u σ_y)

Answer: (B)

This uses the Gaussian plume model with ground reflection. For a continuous point source, the concentration at downwind distance x, crosswind y, and height z is C = Q/(2π u σ_y σ_z) · exp(-y^2/(2 σ_y^2)) · [ exp(-(z−H)^2/(2 σ_z^2)) + exp(-(z+H)^2/(2 σ_z^2)) ]. Setting y = 0 and z = 0 gives C = Q/(2π u σ_y σ_z) · [ exp(-H^2/(2 σ_z^2)) + exp(-H^2/(2 σ_z^2)) ] = Q/(π u σ_y σ_z) · exp(-H^2/(2 σ_z^2)). So the ground-level, centerline concentration includes the ground-reflection effect and has the form Q/(π u σ_y σ_z) times the exponential factor exp(-H^2/(2 σ_z^2)).

This uses the Gaussian plume model with ground reflection. For a continuous point source, the concentration at downwind distance x, crosswind y, and height z is

C = Q/(2π u σ_y σ_z) · exp(-y^2/(2 σ_y^2)) · [ exp(-(z−H)^2/(2 σ_z^2)) + exp(-(z+H)^2/(2 σ_z^2)) ].

Setting y = 0 and z = 0 gives

C = Q/(2π u σ_y σ_z) · [ exp(-H^2/(2 σ_z^2)) + exp(-H^2/(2 σ_z^2)) ]

= Q/(π u σ_y σ_z) · exp(-H^2/(2 σ_z^2)).

So the ground-level, centerline concentration includes the ground-reflection effect and has the form Q/(π u σ_y σ_z) times the exponential factor exp(-H^2/(2 σ_z^2)).