Applications Solar_zenith_angle

1 applications

1.1 sunrise/sunset
1.2 albedo
1.3 summary of special angles

applications
sunrise/sunset

sunset , sunrise occur (approximately) when zenith angle 90°, hour angle h0 satisfies

cos
⁡

h

0


=
−
tan
⁡
Φ
tan
⁡
δ
.


{\displaystyle \cos h_{0}=-\tan \phi \tan \delta .}

precise times of sunset , sunrise occur when upper limb of sun appears, refracted atmosphere, on horizon.

albedo

a weighted daily average zenith angle, used in computing local albedo of earth, given by

cos
⁡

θ

s



¯


=




∫

−

h

0





h

0




q
cos
⁡

θ

s



d

h



∫

−

h

0





h

0




q

d

h





{\displaystyle {\overline {\cos \theta _{s}}}={\frac {\int _{-h_{0}}^{h_{0}}q\cos \theta _{s}{\text{d}}h}{\int _{-h_{0}}^{h_{0}}q{\text{d}}h}}}

where q instantaneous insolation.

summary of special angles

for example, solar elevation angle is :

90° if on equator, day of equinox, @ solar hour of twelve
near 0° @ sunset or @ sunrise
between -90° , 0° during night (midnight)

an exact calculation given in position of sun. other approximations exist elsewhere.