9.7 Velocity Variances and Puff Growth


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If you are not continuing from the previous section, first retrieve conc_case_control.txt and conc_case_setup.txt. There are a few namelist file options left in menu #7 that are more appropriate for certain customized applications. One of these would be when dealing with user defined data files, an example of which, stndata.bin, should have already been created in the working directory (or the working.??? backup directory after the cleanup step). This file contains only the minimum number of meteorological fields required to run HYSPLIT.

  1. Recall from the previous sections that the puff growth is computed from the velocity variances,
    • h/dt = σu

    a field which is not available in most meteorological model output files and must therefore be computed from the atmospheric stability and various turbulence parameterizations. However, a stability value was defined when the User Defined data file was created. This stability was immediately converted to a velocity variance using an empirical relationship that matched each stability category with a wind fluctuation. Therefore, to use this data file, open the Concentration / Setup Run menu and clear the meteorology file and Add Meteorology File and select stndata.bin. Save and then open the Configuration Setup menu #7, press Reset, and select the measured variances radio-button. Save, exit, run model and the display batch file, to see the graphical result. In this simulation, the wind speed and direction were constant with height throughout the boundary layer, and the resulting narrow plume illustrates the importance of wind variation to plume growth.

  2. These constant wind simulations would not normally be applied over such long distances, but at much shorter ranges where the stability as well as the winds would not be expected to change. In these circumstances, it might be desirable for the plume growth to more closely match the empirical estimates that are found in published plume growth graphs. Most of these indicate a growth with time to a power of slightly less than one. This relation can be expressed in differential form and applied in the model calculation.
    • σh = σu T0.9
    • h/dt = 0.9 σu dt / T0.1

    Open menu #7 and select the empirical puff growth, leave the other settings as before, save, run, and display the graphical result. The plume width appears to be about 50 km, which suggests a "σy" of about 10-15 km (4σ ~ 95th percentile), consistent with published values, but much smaller than the reality indicated by the aircraft sampling.

The results shown here, using a Gaussian plume model approach with winds constant in space and time should be compared to the previous calculations where the winds varied in space, time, and height above ground. The various parameter sensitivity tests reviewed in the last few sections probably leave a residual sense of uncertainty as to the best approach to use in a particular situation. However, these simple test results were only compared to a few samples at one downwind distance. The best approach is to at least run each test through the entire experiment and then the results should be compared to the measurement data as was discussed in the statistics section.