How much is Solar Radiation effected by Axial Tilt or Obliquity?

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?

• What I have found so far is that Total Solar Radiation changes in 11 year cycles arxiv.org/ftp/arxiv/papers/1606/1606.05258.pdf and the minimal and maximal values are 1364 and 1367.9 Wm-2 . However in history it changes significantly: lasp.colorado.edu/lisird/tsi/historical_tsi.html – user1141649 Jul 24 '17 at 15:47
• en.wikipedia.org/wiki/Ecliptic#Obliquity_of_the_ecliptic has a possibly helpful formula to answer at least one of your questions. – user967 Jul 24 '17 at 17:28
• As far as variations in the last few decades, when it comes to weather forecasting, the differences will get swamped by all the other uncertainties – 410 gone Jul 24 '17 at 17:36
• @Barry Carter: This is great source and you could use the text as an answer. Thank you! – user1141649 Jul 24 '17 at 18:47
• @user1141649 Go for it. I shun the bourgeoisie point system. – user967 Jul 25 '17 at 0:14

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.

• Hi, I am not sure if I can run Octave, I have installed octave-4.2.1.exe and client. The Gui version is not possible to run because of error. The client version runs only. But IDK to use it. Running Windows XP. – user1141649 Jul 24 '17 at 20:11
• @user1141649 ah that is a bummer! So there is a free trial of Matlab you can download. A second option is, if you're okay with reading code, you could look at the individual m-files to determine the steps taken in calculating insolation values. This might be tedious, but you would have to do this anyways if you were to calculate insolation yourself. – Z W Jul 24 '17 at 20:31
• I can run it with Java server on. With the Octave I tried to open and run the files but only the orbit.m have show some 3D graf. The next files did not run to me or did not show anything. – user1141649 Jul 24 '17 at 22:01
• I'm not sure exactly how the operation of the program might differ in octave, but what I do in matlab is the following. First I make sure that I'm in the directory of the folder containing all the files. Then I type "Earth_orbit_v2_1.m" and this launches the graphical user interface (the first screenshot I posted). Are you able to launch the GUI or have you only had luck launching the function files it calls upon? – Z W Jul 24 '17 at 22:09
• uh oh, looks like octave does not have the program gui_mainfcn which this program uses... unfortunately in this case, this does look to be a matlab specific program. I'll let you know if i find any other options – Z W Jul 24 '17 at 22:12

"Obliquity of the ecliptic for 20,000 years, calculated by Laskar (1986) reflects change from 24.2° to 22.5°.

Diagram

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.

[14]

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."

• The total solar radiation doesn't change much, it's the seasonal variation that changes. Higher tilt (24.2 degrees), Summers are hotter in both hemispheres and winters are colder. Lower tilt, less seasonal variation. The effect is greatest near the polls, smallest near the equator. Calculations would need to be based on latitude and season and over decades, would be quite small. – userLTK Jul 25 '17 at 10:42