9.4 Stability Computation Method


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If you are not continuing from the previous section, first retrieve conc_case_control.txt and conc_case_setup.txt. The base calculation from the previous sections used the meteorological model predicted fluxes of heat (H) and momentum (M) to compute the stability, expressed as a Monin-Obukhov length. Many of the meteorological data files contain estimates of the fluxes. However, if these fields are missing there is an option to use the vertical profile of wind and temperature to estimate the stability.

  1. The default computation uses the momentum flux to the surface (M) to compute the friction velocity, the sensible heat flux (H) to compute the friction temperature, and the mixed layer depth to compute the convective velocity scale. Using these three values, the height normalized Monin-Obukhov (z/L) stability parameter is computed.

    • u* = (∣M∣ / ρ)0.5
    • t* = -H (ρ Cp u*)-1
    • z/L = Z2k g t*(u*2T2)-1

  2. When no fluxes are provided by the meteorological model, z/L can be estimated from the wind and temperature profiles by first computing the bulk Richardson Number from the two lowest data levels and the z/L can be computed using several different functional forms that depend upon the stability.

    • Rb = g Δθ ΔZ {θ12 [(Δu)2+(Δv)2]}-1
    • z/L = f(Rb)

    The plume prediction should be recalculated using the wind and temperature profile by opening Configuration Setup / Concentration / Turbulence Method Menu #7, press Reset, and then select the Computed from U/T profile radio-button for the boundary layer stability section. When the run has completed, execute the display batch file and open the resulting graphic which shows a much different plume structure than the base calculation.

    In this case using the wind and temperature profiles to compute stability caused a significantly different calculation result. Stability from profiles are instantaneous values valid at the model time step, while flux derived stabilities are based upon time-averaged heat and momentum fluxes. There is no single right answer that applies to all data files but it depends upon the frequency of the meteorological data and the time duration of the flux integral.

  3. There is one other option in this section. Normally the vertical turbulence profile varies with height, approaching zero near the ground, increasing to a peak in the mid-boundary layer, then decreasing again to the top of the mixed layer. This is the default approach. However, the height varying profile can be replaced by a single boundary layer average value. This approach would only be used when trying to configure the model to match the Gaussian analytic solution, where the vertical diffusivity is constant with height. The effect of this change can be compared with the previous calculation by selecting the Menu #7 radio-button Replaced by PBL average, save, run the model, display script, and then the resulting graphic shows a result very similar to the profile method.

The results shown in this section suggest that there may be considerable sensitivity to the selection of how the stability is computed from the meteorological data. The key is understanding the sources of the data and their limitations. For instance, hourly fields generated by a mesoscale meteorological model may show more similarity between the flux and profile calculation than computations performed using regional or global model output that may only be available at 3- or 6-h intervals.