This first map shows visibility stations (red dots) and their coverage areas (orange lines) based only on distance. Wilderness areas are drawn in green. The map projection here is an Albers optimized for the contiguous U.S., which is nice looking but not ideal for the distance calculations we're doing. For that matter, distance-to-station is just one factor to consider when finding a representative air quality station for a locality.
Be careful in the insets and at the edge of the earth. Polygons for the station coverage areas are calculated before the Alaska, Hawaii, and Puerto Rico insets are moved into the map frame. Lines are correctly placed, but the ones from the mainland should draw underneath the insets.
This second graphic shows all of the visibility data for all 176 stations. Lower values mean better visibility -- MOZI1 at Mount Zirkel Wilderness has less haze and better visibility than NEYO1 at New York City or FRES1 at Fresno. We might confirm some assumptions by binning these in various ways, but before we get into that we can clean up the graphic by plotting the trends instead of the jaggy lines through data points.
Visibility data is released as 5-year moving averages rather than actual observations, so there is no need to calculate a window and do further smoothing.
This bundle of pickup sticks shows linear trend lines through the available 5-year moving averages for each station from the above graph.
Visibility stations can be grouped by one of 28 regions, which even for me is too much for one graphic. We'll move on to visibility at a single wilderness for now and revisit these groups and the differences between them later.
This map is similar to our first map above, but zoomed in on some arbitrary wilderness area (the Frank Church–River of No Return). Stations are still red dots, and the three nearest are drawn with a dotted circle to show relative distance to the center of the wilderness. Looks like the middle of the wilderness is closest to the SAWT1 station.
This wilderness area is pretty big, and obviously parts of it are closer to SULA1 at Sula Peak to the north than to SAWT1 at Sawtooth to the south. Our orange coverage areas are still here, so we can see the ratio of wilderness in each station area.
Finally getting somewhere with all this, we have one last graph showing, for each of the three nearest stations, the observed visibility (hollow circles) and the Theil-Sen slope (dotted line) though them.
Captions below the graph give the trend and p-value for each of our stations. For the wilderness character visibility measure at the Forest Service, we choose one station as best representative of the wilderness area and leave it at that.