I think, that's not a back-of-the-envelope calculation, it is more a good way to verify things and not believe everything...
But, back to my problem: Yes, you are right. PVGIS values are real-sky values => http://re.jrc.ec.europa.eu/pvgis/solres/solrespvgis.htm.
So, if I build the ratio of real-sky to clear-sky (PVGIS/r.sun) I get for february 0.5628, that means ~56% of the solar radiation doesn't reach the earth, right?
Let's do the same calculation for a summer day. If I take mid of july (day=196) using r.sun (with lin=4.4) I get a global radiation of 7651 KWh/m² per day, PVGIS shows an average value of 4730 KWh/m² per day for july. The ratio for july (PVGIS/r.sun) is 0.6182....hmm, in summer more radiation losses in percent as in winter, could this be right?
Hamish schrieb:
ok, this is probably the worst back of the envelope calc you'll ever come
across, but it gives me an idea, maybe the PVGIS value takes average cloud
cover into account while r.sun (by default) does not? I don't know if
Germany's winter is anything like England's, if it is this might explain
the difference... ?lat = 52.267
day_of_year = 45
% lat_tropic: 23 + 26/60 + 16/3600 = 23.438
% so crudely:
[0 -23.438
45 -11.719
90 0
180 +23.438 ]sun_angle_noon = 52.267 + 11.719 = 63.986
solar_constant = 1367 % W/m^2
peak_rad = cos(sun_angle_noon * pi/180) * solar_constant
mean_rad = peak_rad * 2/pi % more crudenesssunlight_hrs = 7 % rough guess
sunlight_hrs * mean_rad
= 2671.8 Wh/m^2 /day [Clear sky]