A bit of searching later found the right incantation to make gnuplot adjust
color based on a third value (signal level in my case). It isn't very complicated:
set size square
set angles degrees
set polar
set grid polar 30
set xtics axis 0,30
set ytics axis 0,30
unset border
unset param
set xrange[-90:90]
set yrange[-90:90]
set rrange[0:360]
set trange[0:90]
set title "GPS satellite tracks"
set xlabel "Azimuth"
set ylabel "Elevation"
set terminal png size 600,600
set output "gpsazelsig.png"
plot "gpsazelsig.dat" using 1:2:3 palette notitle
But the
resulting plot
isn't very helpful for my original question: in which direction radio
signals are obstructed. There are some obstructions in the Southwest, but they
are comparable to what is in the Northeast.