Kentucky Energy and Environment Cabinet 

Kentucky Division for Air Quality 

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Appendix M.2 

Procedures for Developing and 

Displaying AoI Back-trajectory 

Residence Time GIS Data 

 

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Procedures for Developing and Displaying AoI Back-trajectory Residence Time GIS Data 

29 August 2007 

The development of the GIS databases for the VISTAS Area of Influence (AoI) analyses were 

accomplished through the application of a set of Linux Perl scripts and Arc Macro Language 

(AML) scripts executed within ESRI’s Arc/INFO GIS. Specific steps in the development of the 

GIS data and the associated displays are provided below: 

Back-trajectory Residence Time GIS Coverages

1) Back-trajectory Residence time data were received from ARS as ASCII GRID formatted 

data files. Included were the raw counts in each grid cell as well as extinction weighted 

residence time counts. Residence time data weighted by total extinction, as well as 

constituent species extinction, were provided on a uniform 1 degree by 1 degree unprojected (i.e. geodetic) coordinate system. 

2) Linux Perl scripts are used to re-format the ARS back-trajectory residence time datasets 

for import to Arc/INFO 

3) A polygon coverage was defined in Arc/INFO to represent the geodetic 1 degree by 1 

degree gridded domain for the residence time data. The reformatted datasets are then 

joined to this polygon coverage using the I and J cell indices as the join item. 

4) The residence time polygon coverage is then re-projected to the RPO Unified Grid 

Lambert Conformal Projection coordinate system. The RPO LCP coordinate system is 

defined as follows: 

 Projection LAMBERT 

 Datum NONE 

 Units METERS Spheroid SPHERE 

 Parameters: 

 1st standard parallel 33 0 0.000 

 2nd standard parallel 45 0 0.000 

 central meridian -97 0 0.000 

 latitude of projection's origin 40 0 0.000 

 false easting (meters) 0.00000 

 false northing (meters) 0.00000 

 Figure 1 displays the result of re-projecting the raw back-trajectory residence time data. 

 Displayed are the raw counts (bcnt) in each 1 degree by 1 degree grid cell. 

5) The resulting polygon coverage is then aggregated to 36-km grid cells on the RPO LCP 

coordinate system using an area-weighting interpolation scheme using the Arc/INFO 

STATISTICS command. Figure 2 displays the associated result of step 4 overlayed with 

the 36-km modeling grid cells. The area fractions for each polygon are also displayed, 

and in Figure 3, the raw trajectory counts are also displayed for each re-projected 1 

degree by 1 degree grid cell. Area fractions are defined as the ratio of the area of each 

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polygon resulting from the intersection of the two grids to the area of the 36-km 

modeling grid cells. Note that for modeling grid cells that lie entirely within the 1-degree 

by 1-degree cell, the area fraction is equal to 1.0. The result of the area-weighted 

interpolation is displayed in Figure 4. For the grid cell in the center of the display, the 

calculation is as follows: 

 761*0.5208 + 1798*0.4792 = 1257.95 

 Other back-trajectory data (total extinction-weighted residence time, sulfate extinction-

 weighted residence time, etc.) are treated similarly to obtain a 36-km gridded data set in 

 the RPO LCP coordinate system. 

 

6) Residence time back trajectory data (raw counts and extinction-weighted data) are further 

weighted by inverse distance (1/r) from each grid cell to the location of the corresponding 

IMPROVE monitor site. The distances are calculated as the linear distance from each 

grid cell center to the IMPROVE monitor. The grid cell corresponding to the IMPROVE 

monitor location is given a weight of 1/9. The value of 1/9 was chosen, somewhat 

arbitrarily, to represent the nominal distance a trajectory travels across the grid cell 

containing the monitor. Although the exact location of the monitor is known, because the 

gridded datasets are representative of grid cell averages across the 36-km by 36-km cells, 

the decision to use a value of 9 (i.e., 1⁄4 of the distance across a grid cell) was made in 

order to be fairly consistent with the distances to the center of all other grid cells. The 

distance weighting factors are displayed in Figure 5. Note that the distance factor for grid 

cell with the monitor is set to 9 internally in the processing script, over-riding the distance 

as displayed in Figure 5. Note also that the distance weighted back-trajectory residence 

time are not displayed; these data are calculated at this processing step in order to export 

the data as text files for further processing and analysis outside of the GIS. 

7) The resulting coverage is then over-layed with county boundaries and the following data 

fields are exported to an ASCII comma-delimited text files for further processing and 

analyses: 

 I, J, County FIPS, raw count, total extinction-weighted RT, sulfate extinction- 

 weighted RT, total extinction-weighted, distance-weighted RT, and sulfate 

 extinction-weighted, distance-weighted RT. 

Displaying Back-Trajectory Residence Time Data

Displays of back-trajectory residence times are generated from the GIS coverage described 

above using Arc/INFO as follows: 

1) In the current analysis, only sulfate extinction-weighted back-trajectory residence times 

are considered. For each grid cell, the sulfate extinction-weighted back trajectory is 

scaled by the maximum value of total extinction-weighted residence time across the 

entire domain. The result is re-cast as a percentage by multiplying by 100. Note that 

these data, as displayed, are not weighted by distance. In the example shown, the 

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domain-wide maximum total extinction-weighted back-trajectory residence time has a 

value of 176620. This value is used as a scaling factor for the data displayed. Figure 6 

displays the sulfate extinction-weighted, back-trajectory residence times, re-projected and 

allocated to the 36-km modeling grid cells, and scaled by the maximum value of total 

extinction-weighted residence time. Therefore the plots display the sulfate extinctionweighted back-trajectory residence times as a percentage of the domain-wide maximum 

total extinction-weighted back-trajectory residence times. 

2) The boundaries of the extent of the sulfate extinction-weighted back-trajectory residence 

time, scaled by the maximum total extinction-weighted residence times (as computed 

above), for values greater then 2%, 5% and 10% are generated using the RESELECT 

command in Arc/INFO by extracting all grid cells meeting the specified criteria (i.e., > 

2%; > 5%; and > 10% of the maximum total extinction-weighted residence time across 

the domain) 

3) Graphical displays are generated of the sulfate extinction-weighted residence times based 

on the coverages described above. The boundaries of the 2%; 5% and 10% contours in 

these data are drawn on the displays in red (>10%), orange (5%) and blue (>2%) and 

shaded with varying degrees of grey. These data are plotted using intervals of 2, 5, 10, 

20, 30, 40 and 60%. 

4) The location of the IMPROVE monitor for each Class I Area is noted by drawing 

concentric circles centered on the monitor with radii of 100 and 200 kilometers. A 

separate point coverage defining the location of the IMPROVE monitors is used to 

facilitate this step. 

5) Finally, county boundaries are over-layed and various labels are added to the displays. 

The final sulfate extinction-weighted back-trajectory residence times are displayed in 

Figure 7 for Everglades National Park. Note the maximum total extinction-weighted 

back-trajectory residence time value (176620) and the maximum values of the data 

displayed (43%) shown in the legend. 

Gridded Emissions x Back-Trajectory Residence Time GIS Coverages

1) The VISTAS 36-km gridded point source emissions data are imported into Arc/INFO as 

a polygon coverage at 36-km resolution in the RPO LCP coordinate projection system. 

Figure 8 displays the gridded SO2 point source emissions on the 36-km modeling 

domain. 

2) For each species in the emission data file, and for each extinction-weighted residence 

time value, new items are added to the coverage and the product of emissions times 

extinction weighted back-trajectory residence times is computed on a grid-cell by gridcell basis. Both distance-weighted and non-distance-weighted data are calculated and 

added to the polygon coverages. Figure 9 displays the total extinction-weighted backAppendix M.2 - 5 

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trajectory residence time data, re-projected and interpolated to the 36-km grid cells. Also 

displayed in Figure 9 are the values from the 1-degree by 1-degree raw data (labeled in 

blue). Figure 10 displays these data weighted by distance. The cell-by-cell product of 

SO2 emissions and total extinction-weighted residence times are displayed in Figure 11, 

while Figure 12 displays these data weighted by inverse distance from the monitor. 

3) The sum of each of these items across the entire modeling domain is computed (using 

STATISTICS) and used to normalize each grid-cell value and re-cast as a percentage by 

multiplying by 100. In the example, this sum is computed as 53512390. The final result 

of this normalization step is displayed in Figure 13. The calculation is as follows, for the 

sample grid cell displayed in the center of Figure 13: 

 100 * [BEXT_RT *(1/R)*SO2] / Sum(BEXT_RT*(1/R)*SO2) 

 

 100 * [113191.56 * (1/50.91) * 8989.56] / 53512390 = 37.34 

Displaying Normalized Emissions x Distance-Weighted Back-Trajectory Residence Time Data

Displays of emissions x back-trajectory residence times are generated from the GIS coverage 

described above using Arc/INFO as follows: 

1) In the current analysis, only total extinction-weighted back-trajectory residence times are 

considered. For each grid cell, the total extinction-weighted, distance-weighted back 

trajectory data is multiplied by the VISTAS point source SO2 emissions on a grid-cell by 

grid-cell basis. 

2) The result of the previous step (SO2 * total extinction-weighted, distance-weighted backtrajectory residence times) is normalized by the sum across the entire domain. The result 

is re-cast as a percentage by multiplying by 100. 

3) The maximum value of the resulting data of 2) above is computed using the 

STATISTICS command in Arc/INFO. This value is displayed in the legends of the plots. 

4) Graphical displays are generated of the normalized SO2 emissions * total extinctionweighted, distance-weighted back-trajectory residence times based on the coverages 

described above. The boundaries of the 2%; 5% and 10% contours from the residence 

times data, as described above, are drawn on the displays in red (>10%), orange (5%) and 

blue (>2%) and shaded with varying degrees of grey. The emissions * residence times 

data are plotted using intervals of 0.2, 0.3, 0.4, 0.6, 0.8, 2.0 and 10. 

5) The location of the IMPROVE monitor for each Class I Area is noted by drawing 

concentric circles centered on the monitor with radii of 100 and 200 kilometers. A 

separate point coverage defining the location of the IMPROVE monitors is used to 

facilitate this step. 

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6) Finally, county boundaries are over-layed and various labels are added to the displays. 

The final distance-weighted, normalized point source SO2 emissions * total extinctionweighted back-trajectory residence times are displayed in Figure 14 for Everglades 

National Park. Note the maximum value of the data displayed, from Step 3 above, (37%) 

shown in the legend. 

Figure 1. Raw back-trajectory residence time counts – re-projected to RPO LCP 

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Figure 2. Area fractions used in interpolation scheme. 

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Figure 3. Area fractions used in interpolation scheme with raw counts displayed in blue text. 

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Figure 4. Result of area-weighted interpolation of raw counts to the 36-km modeling grid cells. 

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Figure 5. Distance weighting factors. 

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Figure 6. Result of area-weighted interpolation of sulfate extinction-weighted back-trajectory 

residence times to the 36-km modeling grid cells, scaled by the maximum total extinctionweighted back-trajectory residence time. 

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Figure 7. Final display of sulfate extinction-weighted back-trajectory residence time for 

Everglades National Park. 

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Figure 8. Gridded point source SO2 emissions. 

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Figure 9. Interpolated total extinction-weighted residence times. 

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Figure 10. Distance-weighted, total extinction-weighted residence times. 

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Figure 11. SO2 emissions times total extinction-weighted residence times. 

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Figure 12. Distance-weighted, SO2 emissions times total extinction-weighted residence times. 

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Figure 13. 100 * Distance weighted, normalized, SO2 emissions times total extinction-weighted 

residence times. 

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Figure 14. Final display of normalized distance-weighted, SO2 point source emissions * total 

extinction-weighted back-trajectory residence time for Everglades National Park. 

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