Some possible approaches

• r.angle.sh (see image below and attached script)

  r.mapcalc "$GIS_OPT_output = atan( ($GIS_OPT_elev - $z) / sqrt( (x() - $x)^2 + (y() - $y)^2) )"

  Angle Map: Vertical angle (degrees) from starting point (yellow point) to each cell.

• Compute percent of visible terrain that is above 10 degrees vertical elevation at each cell, using r.los.
  # setup:
  #
  # 30 m resolution takes about 4.5 minutes on my laptop
  # g.region res=30 -ap
  # 10 m resolution takes about 19 minutes on my laptop
  # g.region res=10 -ap
  
  # dump x,y,z values from DEM
  r.out.xyz elev10m > ~/temp/xyz
  
  
  # setup coordinate file
  echo -n "" > stats.xyp
  g.remove --q rast=MASK
  
  # loop through each cell
  for cell in `cat ~/temp/xyz`
  do
  
  los_cmd=`echo $cell | awk -F"|" '{print "r.los --q --o in=elev10m out=los coordinate="$1","$2}'`
  
  angle_cmd=`echo $cell | awk -F"|" '{print "r.mapcalc \"ang = if( los >= 100, 1, null())  \""}'`
  
  eval $los_cmd
  eval $angle_cmd
  
  p=`r.stats -p -N ang | awk '{print $2}' | sed 's/\%//g'`
  echo $cell | awk -v p=$p -F"|" '{ if(p != "") {print $1"|"$2"|"p}}'  >> stats.xyp
  
  done
  
  # load results when done:
  # r.in.xyz in=stats.xyp out=angp --o

  Percent of visible terrain obscuring the sky above 10 degrees