![]() ![]() ![]() During the June solstice (marked between June 20 and June 22), solar declination is about 23.5°N (the Tropic of Cancer). On Earth, solstices are twice-yearly phenomena in which solar declination reaches the Tropic of Cancer in the north and the Tropic of Capricorn in the south. On our planet, solstices are defined by solar declination-the latitude of Earth where the sun is directly overhead at noon. S65 = orbital.A solstice is an event in which a planet’s poles are most extremely inclined toward or away from the star it orbits. to compute the timeseries of insolation at 65N at summer solstice over the past 5 Myears This is automatic if computed from _parameters()Į.g. Orbital arguments should all have the same sizes. Not linearly related because, by Kepler's Second Law, Earth'sĪngular velocity varies according to its distance from the sun.ĭefault values for orbital parameters are present-dayįsw = Daily average solar radiation in W/m^2.ĭimensions of output are (lat.size, day.size, ecc.size)Ĭode is fully vectorized to handle array input for all arguments. Note that calendar days and solar longitude are Longitude is the angle of the Earth's orbit measured from springĮquinox (21 March). The calendar is referenced to the vernal equinoxĭay_type=2: day input is solar longitude (0-360 degrees). ĭay_type=1 (default): day input is calendar day (1-365.24), where day 1 ![]() 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 $\delta$). Just like the flux itself, the solar zenith angle depends latitude, season, and time of day. ![]()
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