Mixed Layer Depth Calculation

From the previous sections, we found that both the computation of the stability and the estimate of the resulting turbulence was a function of the mixed layer or boundary layer depth (used interchangeably in these discussions). The default approach is to use the mixed layer depth that is output from the meteorological model. This field is not always available and if missing, the depth is computed from the temperature profile as the height at which the potential temperature exceeds the surface temperature by two degrees. The mixed layer depth can also be estimated from the TKE profile as the height when the TKE value first becomes less than 0.20.

1. To compute the plume using a different mixed layer depth method, open menu #7 and check the radio-button (press Reset first) marked From Temperature Profile, save the change, run the model, the display batch file, and then compare the resulting plume with the base calculation. It is narrower and the air concentrations are much higher.


2. Repeat the above sequence again, but this time select Compute from TKE Profile radio-button from Menu #7 and the resulting plume shows a concentration pattern very similar to the previous calculation.


3. During the earlier trajectory analysis discussion, we determined that the mixed layer depth for this case was 1756 m. We can force the calculation to use a constant mixed layer depth by setting the Set as Constant radio-button and entering the value 1750. The button highlight will disappear when the value is changed from its default, but the calculation will use this value and not unexpectedly the resulting plume looks very much like the base calculation.


4. To contrast the previous calculation, reduce the mixed layer depth to half its previous value. Change the Set as Constant field to 875, rerun the model, and now the resulting plume is a little smaller, but nowhere near a factor of two smaller in area. However at any one location, air concentrations may be a factor of two higher only if the original plume growth was restricted by the mixed layer. The mixed layer depth directly affects air concentrations but the effect on the plume size is more indirect, related more to other factors such as the wind shear through the depth of the plume.

In summary, the results show that the magnitude of the air concentration prediction is directly proportional to the mixed layer depth. However, this conclusion only applies in situations of strong vertical mixing, when the particles interact with this mixing boundary. The effect on plume size depends upon how much the wind direction and speed change with height. If there is little wind shear with height, then plume size will be much less sensitive to vertical mixing.