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I know that the Axial Tilt of Earth is about 23.4° - 23.5°. And I would like to know how much this change effects Solar Radiation for particular geo-location.
What is the Axial Tile change rate? How often or how fast does it change? How much precision do we need when we calculate Solar Radiation for Weather forecast?
What could be difference between 1920, 1939. 1945, 1950 or 2017 Axial Tilt and it's effect on Solar Radiation at particular geo-location?
Check out this matlab program that is presented in a paper by Kostadinov and Gilb, 2014. The paper is worth reading, and they have their full matlab code in the "supplement" link (top right corner under downloads).
The code launches a GUI. From it you can control the values of obliquity, eccentricity, precession, total solar irradiance, day of year, calendar start year and end year, and latitude. Section 2.1 in the paper explains the coordinate system.
I don't think anyone could answer off the top of their heads the question "what is the difference between 1920, 1939, etc... of solar radiation at a particular geo-location". But with this program, you can mess around with the data and find out. So let us know what you discover! (ps, if you don't have Matlab, you can probably use this in octave which is free).
Here's a screenshot of the gui
And here's what some of the output looks like
Here's some alternatives to matlab:
1) nasa has online calculator that spits out raw text tables of insolation.
2) If you are savvy with fortran then you may like this fortran code.
3) The fortran code above also has an online interface
4) If you like python, then you may like this python code, climlab, where there are detailed instructions here on how to use the code and visualize the information.
5) If you like R, then try palinsol which has a little documentation here.
"Obliquity of the ecliptic for 20,000 years, calculated by Laskar (1986) reflects change from 24.2° to 22.5°.
Until 1983 the obliquity for any date was calculated from work of Newcomb, who analyzed positions of the planets until about 1895: ε = 23° 27′ 08″.26 − 46″.845 T − 0″.0059 T2 + 0″.00181 T3 where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question.[13]
From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated:
ε = 23° 26′ 21″.45 − 46″.815 T − 0″.0006 T2 + 0″.00181 T3
where hereafter T is Julian centuries from J2000.0.
JPL's fundamental ephemerides have been continually updated. The Astronomical Almanac for 2010 specifies:[15]
ε = 23° 26′ 21″.406 − 46″.836769 T − 0″.0001831 T2 + 0″.00200340 T3 − 0″.576×10−6 T4 − 4″.34×10−8 T5
These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps ± several centuries.[16] J. Laskar computed an expression to order T10 good to 0″.04/1000 years over 10,000 years.[12] All of these expressions are for the mean obliquity, that is, without the nutation of the equator included. The true or instantaneous obliquity includes the nutation.[17]"
Source: Wikipedia - Obliquity of the ecliptic
From historical Total Solar Irradiance records there is evident, that the great changes of TSI doesn't correspond to the Axial Tilt.
I could not found how much local solar radiation can be affected by Obliquity. But I have found that local solar radiation is called insolation. "Factors affect insolation (without the effect of the atmosphere): Angle of the sun Distance between the sun and the earth Duration of daylight The longer the duration of daylight, the more the insolation received per day."
