en>Melcombe: remove cat, no "probability interpretation" here

2010-12-23T16:19:23Z

remove cat, no "probability interpretation" here

New page

The '''solar zenith angle''' is the angle measured from directly overhead to the geometric centre of the sun's disc, as described using a [[horizontal coordinate system]]. The '''solar elevation angle''' is the altitude of the [[sun]], the angle between the horizon and the centre of the sun's disc. If we write ''θ''''s'' for the solar zenith angle, then the solar elevation angle ''α''''s'' = 90° – ''θ''''s''.<ref>{{cite doi|10.1016/B978-012369407-2/50005-X}}</ref>

==Formulas==

===Solar zenith angle===
The solar zenith angle, ''θ''''s'' is estimated using results from [[spherical trigonometry]] by<ref>{{cite book | page = 317 | title = Fundamentals of Atmospheric Modeling | first = Mark Z. | last = Jacobson | publisher = Cambridge University Press | year = 2005 | isbn = 0521548659 | edition = 2}}</ref><ref name="hartmann">{{cite book | title = Global Physical Climatology | first = Dennis L. | last = Hartmann | publisher = Academic Press | page = 30 | year = 1994 | isbn = 0080571638}}</ref>
:<math> \cos \theta_s = \sin \varphi \sin \delta + \cos \varphi \cos \delta \cos h</math>
where
* ''θ''''s'' is the ''solar zenith angle''
* ''h'' is the [[hour angle]], in the local [[solar time]].
* ''δ'' is the current [[declination of the Sun]]
* ''φ'' is the local [[latitude]].

===Solar elevation angle===
The solar elevation angle is the altitude of the sun, the angle between the horizon and the centre of the sun's disc. The approximate value can be calculated with the following formula:
:<math>\sin \alpha_\mathrm{s} = \cos h \cos \delta \cos \varphi + \sin \delta \sin \varphi</math>
where
* ''α''''s'' is the ''solar elevation angle'', ''α''''s'' = 90° – ''θ''''s''
* ''h'' is the [[hour angle]], in the local [[solar time]].
* ''δ'' is the current [[declination of the Sun]]
* ''φ'' is the local [[latitude]].

===Caveats===
The values calculated above are approximations due to the distinction between [[Latitude#Geodetic and geocentric latitudes|common/geodetic latitude]] and [[Latitude#Geocentric latitude|geocentric latitude]]. However, the two values [[Latitude#Comparison of selected types|differ]] by less than 12 [[minutes of arc]].

The formulas neglect the effect of [[atmospheric refraction]].

The formula for solar elevation angle was derived using the [[trigonometric addition formulas]] from the solar zenith angle formula<ref>{{cite journal | title = On the computation of solar elevation angles and the determination of sunrise and sunset times | page = 3 | first = Harold M. | last = Woolf | journal = NASA technical memorandu, X-1646 | year = 1968 | location = Washington, D.C.}}</ref>

==Applications==

===Sunrise/Sunset===
The approximate times of sunset and sunrise occur when the zenith angle is 90°, where the hour angle ''h''0 satisfies<ref name="hartmann" />
::<math>\cos h_0 = -\tan \phi \tan \delta.</math>

Precise times of sunset and [[Sunrise#Angle|sunrise]] occur when the upper limb of the Sun appears, as refracted by the atmosphere, to be on the horizon.

===Albedo===
A weighted daily average zenith angle, used in computing the local [[albedo of the Earth]], is given by
::<math>\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}</math>
where ''Q'' is the instantaneous [[insolation]].<ref name="hartmann" />

===Summary of special angles===
For example, the solar elevation angle is :
* 90° if you are on the equator, a day of equinox, at a solar hour of twelve
* near 0° at the sunset or at the sunrise
* between -90° and 0° during the night

An exact calculation is given in [[position of the Sun]]. Other approximations exist elsewhere.<ref>{{cite web|last=livioflores-ga|url=http://answers.google.com/answers/threadview/id/782886.html|publisher=Google|title=Equation to know where the Sun is at a given place at a given date-time|accessdate=9 March 2013}}</ref>

== See also ==

* [[Altitude (astronomy)]]
* [[Horizontal coordinate system]]
* [[Solar azimuth angle]]
* [[Sun]]
* [[Sun path]]
* [[Position of the Sun]]
* [[Sunrise]]
* [[Sunset]]

==References==

<references/>

{{DEFAULTSORT:Solar Elevation Angle}}
[[Category:Horizontal coordinate system]]
[[Category:Sun]]
[[Category:Solar energy]]

Combs method - Revision history

en>Melcombe: remove cat, no "probability interpretation" here