The solar zenith angle is defined as the angle between the zenith and the Sun's disc centre. The solar elevation angle refers to the altitude of the Sun, which is the angle between the horizon and the Sun's disc centre. These two angles are complementary, so the cosine of one equals the sine of the other and vice versa and both can be calculated with the same formula
is the solar zenith angle
is the solar elevation angle or solar altitude angle, = 90° –
h is the hour angle, in the local solar time.
is the current declination of the Sun
is the local latitude.
Elevation Angle effects
Sunset and sunrise approximately happen when the zenith angle is equal to 90°, and the hour angle h0 satisfies
Precise times of sunset and sunrise happen when the upper extremity of the Sun appears on the horizon, as refracted by the atmosphere.
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 (midnight)
The elevation angle - which can be used interchangeably with altitude angle as explained- is sun’s angular height in the sky measured from the horizontal plane. The elevation equals Zero at sunrise and 90 deg when the sun is directly above (for example during spring and fall equinoxes at the equator).
The elevation angle depends on the latitude of a particular location and the day of the year and it varies during the day.
The maximum elevation angle is an important parameter in the design of photovoltaic systems.
The following formula for the elevation angle at solar noon can be determined:
φ is the latitude of the required location (positive for the northern hemisphere and negative for the southern hemisphere).δ is the declination angle, depending on the day of the year.
At the Tropic of Cancer on the summer solstice, the sun is directly overhead and the elevation angle is 90°. In summer at latitudes between the equator and the Tropic of Cancer, the elevation angle at solar noon is greater than 90°, implying that the sunlight is coming from the north rather than from the south as in most of the northern hemisphere. Similarly, at latitudes between the equator and the Tropic of Capricorn, during some periods of the year, sunlight is incident from the south, rather than from the north.
While the maximum elevation angle is used even in very simple PV system design, more accurate PV system simulation requires the knowledge of how the elevation angle varies throughout the day.