In the expression 1/√f = 4 log(3.7 D / e), what does e represent?

In the expression 1/√f = 4 log(3.7 D / e), what does e represent?

• A. Surface roughness
• B. Wind speed
• C. Emission rate
• D. Temperature difference

Answer: (A)

The quantity e is a length scale that represents surface roughness. In atmospheric dispersion, how rough the ground is (its roughness length, often denoted z0) shapes the wind profile right above the surface and the turbulence that mix pollutants. The log term inside the equation comes from using a logarithmic wind profile near the ground, where a small change in the ground’s roughness length changes how quickly the wind speed increases with height. Since e sets that length scale in the log, it controls the relationship between the downwind distance D and the dispersion parameter f. That’s why e being a surface roughness length makes this equation behave the way it does. The other options—wind speed, emission rate, and temperature difference—are not the length scale that appears inside this logarithmic relationship.

The quantity e is a length scale that represents surface roughness. In atmospheric dispersion, how rough the ground is (its roughness length, often denoted z0) shapes the wind profile right above the surface and the turbulence that mix pollutants. The log term inside the equation comes from using a logarithmic wind profile near the ground, where a small change in the ground’s roughness length changes how quickly the wind speed increases with height. Since e sets that length scale in the log, it controls the relationship between the downwind distance D and the dispersion parameter f. That’s why e being a surface roughness length makes this equation behave the way it does. The other options—wind speed, emission rate, and temperature difference—are not the length scale that appears inside this logarithmic relationship.