FEDERAL LAND MANAGERS' AIR QUALITY RELATED VALUES WORKGROUP (FLAG)
PHASE I REPORT
(December 2000)

Appendix 2.C

Example Problem

Example applications for coherent plumes that are viewed against a scenic background are provided in the Workbook for Plume Visual Impact Screening and Analysis (USEPS, 1992a), so no specific example needs to be supplied here. The analysis of a plume or aggregation of plumes that affects the appearance of a scene does involve some new concepts, so an example application is being provided. The example is given for two cases, first for a general model application where a visibility post processor is not available, and a second case for the CALMET/CALPUFF/CALPOST modeling system.

General Model Application

For the purposes of general application, let us assume that a dispersion model has been run and yielded daily (24-hour) concentrations of SO₄⁼ (sulfate) and soot (elemental carbon). From these concentrations the analyst can calculate a change in extinction from some specified reference level using the procedures given in Appendix 2.A. The first step is to calculate the visibility reference level for the Class I area of interest from the information provided in Appendix 2.B. Then, one calculates the new source's contribution to extinction and the expected change in extinction from the reference level. This example will only address one 24-hour time period. The calculation would, of course, have to be repeated for the other 24-hour time periods as well as, accounting for the seasonal differences.

Calculation of the Reference Level

The determination of the reference level for a single 24-hour period in January visibility condition can be made by examining the example table below (for an actual case, the applicant would turn to Appendix 2.B). While the reference extinction for Acadia NP is provided in the table (21.1 Mm^-1), it is useful to go through the calculation to see how to apply the different numbers in the table.

The reference extinction (b_ref), expressed in the form of Equation 6 (Appendix 2.A) would be b_ref = 0.9 f(RH) + 8.5 + 10.0 (see Equation 6, Appendix 2.A). The f(RH) term in the example table (for January) is 2.9, yielding an extinction coefficient of 21.1 Mm^-1. If one were using site specific, hourly relative humidity data, one would have to calculate the average f(RH) for that 24-hour period. To do this, one needs to look up the f(RH) value corresponding to each hour's relative humidity in Table 2.A-1 (Appendix 2.A) and take the average of those f(RH) values. One can not take the average of the relative humidity and look up the f(RH) in the table; that would yield an incorrect result. (Similarly, the f(RH) values shown in the example table and in Appendix 2.B are generated using annual and seasonal average relative humidity estimates and the empirical curve for f(RH) given in IMPROVE 2000. Annual and seasonal averages of f(RH) do not directly correspond to the relative humidity values in Table 2.A-1.)

Calculation of Single-Source Contribution

In a typical modeling analysis, IWAQM recommends, and the FLMs endorse, the use of five years of meteorological data. This will produce a corresponding number of block 24-hour averaging periods, which will each need to be compared with the reference condition.

Again for purposes of illustration we will only show the calculation of extinction for one modeled 24-hour period in January. This calculation would then have to be repeated for all other 24-hour periods. For this example we will assume that the sources in the analysis contributed 0.3 µg/m³ of sulfate (SO₄⁼) and 0.10µg/m³ of soot (elemental carbon), 24-hour average. The first step is to convert the mass of SO₄⁼ to ammonium sulfate ((NH₄)₂SO₄), which is accomplished by multiplying by the ratio of the molecular weights of (NH₄)₂SO₄ to SO₄⁼, which is 1.375. This yields a concentration of (NH₄)₂SO₄ of 0.4 µg/m³. This is then multiplied by the "dry" scattering efficiency of (NH₄)₂SO₄ (which is 3, from Appendix 2.A, Equation 3), yielding an extinction coefficient for the sulfate of 1.2 Mm^-1; the relative humidity adjustment has not yet been applied.

In this example our modeling does not require any conversion of the mass of soot, so we will just multiply the soot concentration (0.10 µg/m³) by the extinction efficiency of elemental carbon (which is 10, from Appendix 2.A, Equation 4). This yields an extinction coefficient of 1.0 Mm^-1. Therefore, following the form of Equations 3 and 5 (Appendix 2.A), the source contribution would be:

b_source = 1.2 f(RH) + 1.0

A representative relative humidity adjustment term, f(RH), must be applied. It is important that the same adjustment be made to both the source contribution to extinction and the reference level. For a screening level analysis, the relative humidity adjustment factors listed in Appendix 2.B can be applied to the source contributions. For example, if we are analyzing for Acadia NP, the average winter f(RH) is 2.9. With the winter quarterly average relative humidity adjustment factor (f(RH)) of 2.9, b_source would be 4.5 Mm^-1.

Calculation of the Change in Extinction

The resulting percent change in extinction is found from:

Δb_ext = (b_source/b_ref) x 100%

For the example here, b_source = 4.5 Mm^-1 and b_ref = 22.1 Mm^-1, yielding Δb_ext = 20%. This calculation must be repeated for each 24-hour averaging period. To portray the frequency, magnitude, and geographic extent of expected impairment, this calculation will have to be repeated for all days and many receptors in the modeling domain. FLAG expects a robust selection of model receptor locations in the Class I area be included in the analyses, i.e., one receptor representing the entire area, or just the nearest boundary, will not be sufficient.

Example using the CALMET/CALPUFF/CALPOST modeling system

For the refined analysis, it is necessary to calculate the change in extinction for the relative humidity conditions on a specific day. To accomplish this, the representative, hourly RH values for this day need to be obtained. For each hour, the corresponding f(RH) must be obtained from Table 2.A-1. These f(RH) values are then averaged together. These calculations would have to be repeated for each 24-hour average concentration, at each receptor, in the analysis, using the corresponding average f(RH), and be applied to both the aerosol data in Table 2.B-1 (to determine the reference level) and the source contribution to extinction.

In the case of a CALPUFF application, the post-processor, CALPOST, has been set up to directly calculate the combined visibility effects from different visibility impairing pollutants. Refer to Figure 2.C-1 for an example of the visibility parameters to set in the CALPOST input file. Most of the parameters set in CALPOST are application specific. The pollutants in the example are sulfate and soot (elemental carbon). CALPOST allows for the specification of sulfate (SO4), but not elemental carbon in the source portion of the visibility calculation. (This should be rectified in the next update of the modeling system.) Therefore elemental carbon will be modeled as PM fine (PMF). In CALPOST the variables LVSO4 and LVPMF are set to true. Since elemental carbon is being modeled as PMF, the extinction efficiency for PMF must be set to that for elemental carbon (EEPMF = 10.0). FLAG is recommending that the default f(RH) values in Appendix 2.B be used for screening analyses for each Class I area. Therefore, MVISBK would be set to 6. When MVISBK is set to 6, RHFAC would be set to the f(RH) value in Appendix 2.B or in this example, it would be set to 2.9 for the winter months (Dec, Jan, Feb). CALPOST does not explicitly allow for the input of the hygroscopic and non-hygroscopic components to extinction at this time; it only allows for the input of the concentrations of particulate species. To properly input the components to extinction, the hygroscopic component of extinction is divided by 3 (the extinction efficiency of sulfate and nitrate) and is input to the variable BKSO4. In this example the hygroscopic component of extinction is 0.9; after dividing by 3 we get a value of 0.3, which is input to CALPOST (BKSO4 = 0.3). For the non-hygroscopic component, enter its value into the variable BKSOIL (BKSOIL = 8.5) (also make sure that EESOIL is set to 1.0). All other background concentrations must be set to zero (0.0). Finally, a value for the extinction due to Rayleigh scattering must be entered (BEXTRAY = 10.0).

If MVISBK=2 (hour-by-hour calculation of f(RH)) in the above example, the hour-by-hour relative humidity values from CALMET would be used to calculate the 24-hour average extinction, rather than the long-term average f(RH) values supplied in Appendix 2.B. The only modification to the input would be that the value of RHMAX (set to 98.0 in the example) would be used to cap the maximum f(RH) used in the averages, and the value of RHFAC would not be used. A "vis.dat" file (not shown in Figure 2.C-1) would also be specified. It must be generated when CALPUFF is run.

Figure 2.C-1. Segment of CALPOST input file corresponding to example problem.