The Planet Mean Surface Temperature Equation: Tmean=[Φ(1-a)S(β*N*cp)¹∕ ⁴ /4σ]¹∕ ⁴

+0,0225 °C temperature rise

“Temperature doesn’t infinitely rise, however, because atoms and molecules on Earth are not just absorbing sunlight, they are also radiating thermal infrared energy (heat). The amount of heat a surface radiates is proportional to the fourth power of its temperature. If temperature doubles, radiated energy increases by a factor of 16 (2 to the 4th power). If the temperature of the Earth rises, the planet rapidly emits an increasing amount of heat to space. This large increase in heat loss in response to a relatively smaller increase in temperature—referred to as radiative cooling—is the primary mechanism that prevents runaway heating on Earth.”


“Effect on Surface Temperature

The natural greenhouse effect raises the Earth’s surface temperature to about 15 degrees Celsius on average—more than 30 degrees warmer than it would be if it didn’t have an atmosphere. The amount of heat radiated from the atmosphere to the surface (sometimes called “back radiation”) is equivalent to 100 percent of the incoming solar energy. The Earth’s surface responds to the “extra” (on top of direct solar heating) energy by raising its temperature.”


“The absorption of outgoing thermal infrared by carbon dioxide means that Earth still absorbs about 70 percent of the incoming solar energy, but an equivalent amount of heat is no longer leaving. The exact amount of the energy imbalance is very hard to measure, but it appears to be a little over 0.8 watts per square meter. The imbalance is inferred from a combination of measurements, including satellite and ocean-based observations of sea level rise and warming.”


Very well, let’s now check the above by a simple calculation with the help of the old blackbody effective temperature equation:

Te = [ (1-a) S / 4 σ ]¹∕ ⁴

Te = 255 K

Tmean = 288 K

σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant

So = 1.361 W/m² (So is the Solar constant)

a = 0,306 The Earth’s average albedo

“The exact amount of the energy imbalance is very hard to measure, but it appears to be a little over 0.8 watts per square meter.”

Let’s assume the Tmean = 288 K is the Earth’s mean surface temperature due to the radiative forcing (from both the sun plus the greenhouse effect)

288 K = [ (1-a) S / 4 σ ]¹∕ ⁴

Let’s calculate the radiative forcing S (from both the sun plus the greenhouse effect):

6.878.707.136 = (1 – 0,306) S /4 σ

S = 6.878.707.136 * 4 σ / (1 – 0,306) =

S = 6.878.707.136 * 4* 5,67*10⁻⁸ W/m²K⁴ / 0,694 =

S = 2.248,3 W/m²

Let’s add this 0,8 W/m² to the S = 2.248,3 W/m²

So we shall have

0,8 W/m² + 2.248,3 W/m² = 2.249,1 W/m²


For the new radiative forcing the calculated Earth’s mean surface temperature will be:

Tmean = [ (1-a) S / 4 σ ]¹∕ ⁴

Tmean = ( 0,694 * 2.249 W/m² /4*5,67*10⁻⁸ W/m²K⁴ )¹∕ ⁴ =

Tmean = ( 6.881.860.670 )¹∕ ⁴ = 288,0225 K

Tmean = 288,0225 K

or 0,0225 °C temperature rise.