17.2 Volume or Mass Mixing Ratios


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In all previous examples, the pollutant release was specified by a mass emission rate and the resulting air concentrations by mass over volume. Another frequently used air concentration unit is a volume mixing ratio. This is especially common for gaseous pollutants where concentrations may be specified in units such as ppm (parts per million) or ppb (parts per billion). There is an option in the Advanced / Configuration menu to facilitate these conversions. All the original CAPTEX measured tracer concentration data were reported in units of fL/L (f=femto=1.0E-15) and were converted to mass/volume concentrations for model comparison applications. If continuing from the previous example, first delete LAGSET.CFG from the working directory.

  1. First, the mass to volume conversion is based upon the perfect gas law (PV = nRT):
    • V/n = RT/P = (0.0821 L atm / K mole) * 273 K / 1 atm = 22.40 L/mole (at 273 K), then
    • POL [g/m3] = POL [L/L] * [g/mole] * (1/22.4) [mole/L] * 1000 [L/m3]
    • POL [g/m3] = POL [L/L] * [g/mole] * 44.64 [mole/m3]

    where L is liters and the conversion factor between mass and volume units is just based upon the molecular weight of the pollutant (POL). To compute the conversion factor for PMCH, which has a molecular weight of 350, from fL/L to pg/m3, substitute the following values:
    • PMCH [pg/m3] 1.0E-12 [g/pg] = PMCH [fL/L] * 1.0E-15 [L/fL] * 350 g/mole * 44.64
    • PMCH [pg/m3] = PMCH [fL/L] * 15.624

    One of the model options divides the pollutant mass by the air density prior to summing the mass to the concentration grid. This in effect replaces the constant temperature perfect gas law conversion with a dynamically changing value based upon height as well as temperature. The units of air density within the model are kg/m3, therefore if the pollutant emission units are in kg, the effect of dividing the pollutant mass by air density is the same as dividing the final air concentration kg-pol/m3 by air density kg-air/m3, resulting in a mass mixing ratio of kg-pol/kg-air. To convert the mass mixing ratio to a volume mixing ratio:
    • (liter-pol/liter-air) = (kg-pol/kg-air) * (kg-air/mole) / (kg-pol/mole) * (liter-pol/mole) / (liter-air/mole)

    Because the liters per mole is the same for all ideal gases, the conversion from a mass mixing ratio to a volume mixing ratio is simply proportional to the ratio of the molecular weight of air (29) to that of the pollutant. For the case of the PMCH tracer, the conversion factor to get the model simulation output in fL/L would be:
    • [fL/L] = 29/350 [L/L] * 1.0E+15 [fL/L] = 8.3E+13
    • or 8.3E+10 if the emissions are in grams rather than kg

  2. To demonstrate the use of the model to generate mixing ratio output, go back and retrieve the control file settings from conc_case_control.txt and the namelist file parameters from conc_case_setup.txt saved in the Base Configuration Optimization tutorial. If these files are not available, follow the instructions in that section to modify the run duration to 13 hours and start the sampling at 83 09 26 03 00 so that only one output frame is created. Save the changes and open the Advanced / Configuration / Concentration / Conversion Modules Menu #10 and check the Divide output by air density radio-button. Save the changes, and then run the model.

  3. Before opening the display menu, we already know that the default label options are insufficient to describe this case. Open the borders label menu and set the mass units to fL and the volume to /L. If you are continuing from the previous example, the mass field may still contain the REM label. The other descriptive fields are optional. Now open the Display / Contour menu, select the 1000 m level, and set the concentration multiplier to 8.3E+10. Because we already know that the volume contours will be more than a factor of 10 less than the mass contours (15.6 to be precise), we can force a more realistic contour interval than the order-of-magnitude default. Check the User Set radio-button and enter 2000+1000+500+200+100 in the contour text field, then Execute Display.

  4. Although the results look reasonable, it would be better to do a more quantitative comparison by showing the aircraft measurements in fL/L on the same graphic. The CAPTEX data report contains a tabulation of all collected samples in fL/L. To save a little time, the relevant data were transcribed to the file data_orig.txt in the \Tutorial\captex directory. This is identical to the data file that was used in the case study tutorial, except sampling units are in fL/L. Use the browse button to set this file name in the DATEM text entry box. The resulting graphic shows an excellent correspondence between model and measurements in the native reporting units.

A model feature was demonstrated that facilitates the conversion of model output air concentration units from mass/volume to either mass or volume mixing ratios. On your own try a more realistic example, perhaps for SO2 with emissions in kg and output in ppm. For instance, the Kilauea volcano in Hawaii emits about 2000 tons of SO2 per day. Assuming no conversion to SO4, what concentrations might be expected?