Calculating the incidence angle of the Sun

[jones123]

Hi all,

I have some difficulties understanding a formula for calculating the incidence angle for incoming solar radiation on a sloping surface. I found that:

angle of incidence calculated as cos(j) = sin((pi/2)-surface slope)*sin(altitude angle) + cos((pi/2)-surface slope)*cos(altitude angle)*(cos(surface aspect - azimuth angle))

However, in my textbook it says "The angle between the sun’s projection on the horizontal plane and the plane of the gridcell’s slope is calculated as: azimuth angle * tan(surface slope + cos(azimuth angle - surface aspect))"

Can anyone explain me what the difference between these two formulas is and how they are related?

Thanks in advance!

 

[sophiecentaur]

Without looking very deeply into those formulae, it looks to me that they are calculating different things. The angle of incidence relates to the normal and the incident ray but the second formula gives the angle between the Sun's projection on the ground and a "plane". The only unique angle relative to a plane has to be relative to the normal. Your textbook may have a diagram that it's referring to.