![]() S0: Solar constant in W/m^2, will try to read from constants.pyĭay_type: Convention for specifying time of year (+/- 1,2). Long_peri: longitude of perihelion (precession angle) (degrees) Orb: a dictionary with three members (as provided by orbital.py) Orbital parameters can be computed for any time in the last 5 Myears withĮcc,long_peri,obliquity = orbital.lookup_parameters(kyears)ĭay: Indicator of time of year, by default day 1 is Jan 1. $$ Q = S_0 \left( \frac, S0=None, day_type=1)Ĭompute daily average insolation given latitude, time of year and orbital parameters. Substituting the expression for solar zenith angle into the insolation formula gives the instantaneous insolation as a function of latitude, season, and time of day: At the poles, six months of daylight alternate with six months of daylight.Īt the equator day and night are both 12 hours long throughout the year. In the winter, $\phi$ and $\delta$ are of opposite sign, and latitudes poleward of 90º-$|\delta|$ are in perpetual darkness. Right at the pole there is 6 months of perpetual daylight in which the sun moves around the compass at a constant angle $\delta$ above the horizon. Latitudes poleward of 90º-$\delta$ are constantly illuminated in summer, when $\phi$ and $\delta$ are of the same sign. Near the poles special conditions prevail. Where $h_0$ is the hour angle at sunrise and sunset. Sunrise and sunset occur when the solar zenith angle is 90º and thus $\cos\theta_s=0$. If $\cos\theta_s < 0$ then the sun is below the horizon and the insolation is zero (i.e. $$ \cos \theta_s = \sin \phi \sin \delta + \cos\phi \cos\delta \cos h $$ Sunrise and sunset ¶ With these definitions and some spherical geometry (see Appendix A of Hartmann's book), we can express the solar zenith angle for any latitude $\phi$, season, and time of day as The hour angle $h$ is defined as the longitude of the subsolar point relative to its position at noon. $\delta$ currenly varies between +23.45º at northern summer solstice (June 21) to -23.45º at northern winter solstice (Dec. The seasonal dependence can be expressed in terms of the declination angle of the sun: the latitude of the point on the surface of Earth directly under the sun at noon (denoted by $\delta$). This means we have the least direct solar radiation of the year on the first day of winter, resulting in colder temperatures because there’s less heating of the Earth’s surface.Just like the flux itself, the solar zenith angle depends latitude, season, and time of day. The solar-noon sun angle is the lowest and farthest south in the sky on the winter solstice. ![]() In the winter, the sunrise is in the southeastern sky and the sunset is in the southwestern sky – a much shorter path across the Northern Hemisphere sky – so days are short and nights are long. This provides the most direct solar radiation of the year, resulting in more heating of the Earth’s surface and, therefore, warmer temperatures. local time due to daylight saving time) on the summer solstice. The sun reaches its highest and northernmost point in the sky at solar noon (around 1 p.m. In the summer, the sun rises in the northeastern sky and sets in the northwestern sky, providing long days and short nights. Therefore, everywhere on Earth experiences an equal 12 hours of day and night because the sun rises due east and sets due west. On the vernal equinox in March and the autumnal equinox in September, the equator (0 degrees latitude) is aligned directly with the sun. On June's summer solstice, the most direct rays of sunlight are in alignment with the Tropic of Cancer (23.5 degrees north latitude). On the winter solstice in December, the sun's most direct rays are positioned over the Tropic of Capricorn (23.5 degrees south latitude).
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