WIthin QGIS you can use Grass tool r.horizon.height to calculate sun height for desired bearings. Result is raster map representing horizon height for each point. However, since you need this for each bearing (I presume 360?) this would mean you would have to generate 360 maps. One way i was thinking of for similar problem could be to create viewshed, vectorize it, to get vector line of horizon, break it into points, read DEM valuse on points and then calculate their angular elevation..

WIthin QGIS you can use Grass tool r.horizon.height to calculate sun height for desired bearings. Result is raster map representing horizon height for each point. However, since you need this for each bearing (I presume 360?) this would mean you would have to generate 360 maps.

One way is by using Viewshed Analysis plugin avalible in QGIS which can be used to calculate horizon. If you vectorize result of that you could calculate height angles in combination with DEM.