|Solar Power at TOA||W/m2|
|Obliquity (axis tilt)||degrees||Tilt with respect to the ecliptic, between 22.1 and 24.5 degrees|
|Day of Year||Used with the obliquity to determine the declination|
|Declination||degrees||Angle of the sun with respect to the equator|
|Local Time of Day||hours||Used to determine the rotation of the Earth with respect to midnight|
|Power normal to the surface||W/m2|
|Daily average insolation||W/m2|
|Surface Albedo||% Reflected|
All albedos are approximate - many tables give a range, not a single value.
There are 2 different calculations for the average daily temperature.
The Annual Average is computed by finding the average power for the specified latitude and using that value to compute a temperature.
The Global Average is computed by finding the average power in a single day for each latitude, from -90 to +90 in one degree steps, and using that value to compute a temperature. There is a small change between seasons which I don't understand. However, the fact that the result is close to the -18°C everyone talks about is sufficient verification that the formulas are close - very close.
All albedos are approximate - many tables give a range, not a single value. For the planets (and Moon), I used the Bond Albedos - the Geometric Albedos are a bit larger. However, you can type in any value you want.
Even on the moon, after 14 days of night, the temperature is still significantly above 0.0K, but, since the Moon has no atmosphere, this is because the surface actually holds a lot of heat and because radiation slows down a lot at low temperatures.
Part I: Introduction and history of the Earth's climate > Paleoclimate > Problem 2 - Milankovitch cycles
The equations are pretty straight forward for the sun shining on a sphere where the solar zenith angle is given by,
cos(θ) = sin(Φ)sin(δ) + cos(Φ)cos(δ)cos(h)
|θ||The solar zenith angle for a given time and position on the Earth|
|δ||The solar declination - the angle between the sun and the plane of the equator
This varies between plus and minus the obliquity and depends on the day of the year.
At the summer solstice, the declination is equal to the obliquity.
|h||The hour angle - varies between -π and π throughout the day (0 to 24 in the calculator above)|
I(Φ,δ,h) = S0cosθ, where cosθ>0
Declination refers to the sun with respect to its position relative to the equator. This changes depending on the position of the Earth in its orbit around the sun.
Other Calculators and References