"The simplest assumption possible"
Here it is a very interesting article, which is based on the mistaken assumption that the Stefan-Boltzmann emission Law can be applied for the estimation of the irradiated surface's temperature.
Here it is the interested us abstract:
"The thickening of the blanket has added 3 Wm-2 to the IR energy to the planet. In response, the planet will warm and radiate this energy to restore the energy balance between the net solar energy flowing in and the infrared energy flowing out.
We will begin this discussion by making the
simplest assumption possible, which is that the surface and the atmosphere behave like Max Planck’s black body, in which case it will radiate energy to space as a black body, which is given by σT4 , where σ is a fundamental constant derived by Max Planck and T4 denotes the fourth power of temperature T.
Based on this law, the surface and the atmosphere will radiate
3.3 Wm-2 per 1°C of warming. In other words, the planet can get rid of 3.3 Wm-2 for every degree warming. So to get rid of the 3 Wm-2 energy trapped by manmade greenhouse gases, the planet will warm by (3/3.3=) 0.9°C.
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236 Complexity and Analogy in Science: Theoretical, Methodological and Epistemological Aspects
"simplest assumption possible, which is that the surface and the atmosphere behave like Max Planck’s black body, in which case it will radiate energy
to space as a black body"
A planet surface in radiative equilibrium with the sun has NOT any resemblance with the radiative equilibrium in the cavity with a small hole.
The planet average surface temperature (Tmean) is not a blackbody’s temperature.
Planet does not have a blackbody temperature, because planet has not a uniform temperature, and because planet is not a blackbody.
A blackbody planet surface is meant as a classical blackbody surface approaching.
Here are the blackbody's properties:
1. Blackbody does not reflect the incident on its surface radiation. Blackbody absorbs the entire incident on its surface radiation.
2. Stefan-Boltzmann blackbody emission law is:
Je = σ*Τe⁴
Te is the blackbody's temperature (surface) at every given moment.
When the blackbody is not irradiated, the classical blackbody gradually cools down, gradually emitting away its accumulated energy.
The classical blackbody concept assumes blackbody's surface being warmed by some other than incoming irradiation source of energy - see the Sun's paradigm.
Sun emits like a blackbody, but it emits its own inner energy source's energy. Sun is not considered as an irradiation receiver. And sun has a continuous stable temperature.
Therefore we have here two different blackbody theory concepts.
a. The blackbody with the stable surface temperature due to its infinitive inner source (sun, stars).
b. The blackbody with no inner energy source. This blackbody's emission temperature relays on the incoming outer irradiation only.
Also in the classical blackbody definition it is said that the incident on the blackbody irradiation is totally absorbed, warms the blackbody and achieves an equilibrium emission temperature Te.
It is an assumption.
This assumption, therefore, led to the next assumption: the planet like a blackbody emitting behavior.
And, consequently, it resulted to the planet's Te incomplete formula, in which it is assumed that planet's surface is interacting with the incoming irradiation as by being in a uniform equilibrium temperature.
Consequently it was assumed that planet's surface had a constant equilibrium temperature (which was only the incident solar irradiation dependent value) and the only thing the planet's surface did was to emit in infrared spectrum out to space the entire absorbed solar energy.
3. When irradiated, the blackbody's surface has emission temperature according to the Stefan-Boltzmann Law:
Te = (Total incident W /Total area m² *σ)¹∕ ⁴ K
σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant.
This emission temperature is only the incoming irradiation energy depended value.
Consequently, when the incoming irradiation on the blackbody's surface stops, at that very moment the blackbody's emission temperature disappears. It happens because no blackbody's surface accumulates energy.
4. Blackbody interacts with the entire incident on the blackbody's surface radiation.
5. Blackbody's emission temperature depends only on the quantity of the incident radiative energy per unit area.
6. Blackbody is considered only as blackbody's surface physical properties. Blackbody is only a surface without "body".
7. Blackbody does not consist from any kind of a matter. Blackbody has not a mass. Thus blackbody has not a specific heat.
Blackbody's cp = 0.
8. Blackbody has surface dimensions. So blackbody has the radiated area and blackbody has the emitting area.
9. The entire blackbody's surface area is the blackbody's emitting area.
10. The blackbody's surface has an infinitive conductivity.
11. All the incident on the blackbody's surface radiative energy is instantly and evenly distributed upon the entire blackbody's surface.
12. The radiative energy incident on the blackbody's surface the same very instant the blackbody's surface emits this energy away.
But what happens there on the rotating real planet's surface?
The rotating real planet's surface, when it turns to the sunlit side, is an already warm at some temperature, from the previous day, planet's surface.
Thus we, when assuming the planet's surface behaving as a blackbody, face the combination of two different initial blackbody surfaces.
a. The one with an inner energy source.
b. The one warmed by an outer irradiation.
Planet is not a blackbody.
Planet reflects the (1-Φ + Φ*a)S part of the incident on the planet's surface solar irradiation "S".
Here "a" is the planet's average albedo and "Φ" is the planet's solar irradiation accepting factor.
For smooth planet without thick atmosphere, Earth included,
The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean:
Tmin↑→ T↑mean ← T↓max