I'm posting here for the first time, so I hope not to violate any community-specific rules.
In Allen et al. (1998): FAO-56 an equation is presented to estimate extraterrestrial radiation Ra for different latitudes from the solar constant, the solar declination and the time of the year:
This works quite well to replicate most of the pre-computed values given in Annnex 2, table 2.6 - except for the values in the 70-deg-lat row.
I already noticed the computation fails at this point because of the sunset hour angle equation for latitudes > 66.5° N/S, where you end up with
-tan(phi) * tan(delta) > 1:
While FAO-56 does not seem to mention any restrictions or alternative equations, Neitsch et al. (2011): SWAT Theoretical Documentation at least mention the following (p. 32):
At latitudes above 66.5° or below -66.5°, the absolute value of
-tan(phi) * tan(delta)can exceed 1 and the above equation cannot be used.
Maybe I'm just lacking some basic math knowledge to notice the obvious for a workaround, but from my point of view the limitation makes sense insofar, as there can't be a sunset hour angle by definition if there is no sunset during certain times of the year.
However, I guess another equation might be applicable in this case in order to determine Ra for high latitudes which I'm not aware of yet?
Thank you very much in advance!