Recently in a discussion thread a warming proponent suggested we read this paper for conclusive evidence. The greenhouse effect and carbon dioxide by Wenyi Zhong and Joanna D. Haigh (2013) Imperial College, London. Indeed as advertised the paper staunchly presents IPCC climate science. Excerpts in italics with my bolds.

IPCC Conception: Earth’s radiation budget and the Greenhouse Effect

The Earth is bathed in radiation from the Sun, which warms the planet and provides all the energy driving the climate system. Some of the solar (shortwave) radiation is reflected back to space by clouds and bright surfaces but much reaches the ground, which warms and emits heat radiation. This infrared (longwave) radiation, however, does not directly escape to space but is largely absorbed by gases and clouds in the atmosphere, which itself warms and emits heat radiation, both out to space and back to the surface. This enhances the solar warming of the Earth producing what has become known as the ‘greenhouse effect’. Global radiative equilibrium is established by the adjustment of atmospheric temperatures such that the flux of heat radiation leaving the planet equals the absorbed solar flux.

The schematic in Figure 1, which is based on available observational data, illustrates the magnitude of these radiation streams. At the Earth’s distance from the Sun the flux of radiant energy is about 1365Wm−2 which, averaged over the globe, amounts to 1365/4 = 341W for each square metre. Of this about 30% is reflected back to space (by bright surfaces such as ice, desert and cloud) leaving 0.7 × 341 = 239Wm−2 available to the climate system. The atmosphere is fairly transparent to short wavelength solar radiation and only 78Wm−2 is absorbed by it, leaving about 161Wm−2 being transmitted to, and absorbed by, the surface. Because of the greenhouse gases and clouds the surface is also warmed by 333Wm−2 of back radiation from the atmosphere. Thus the heat radiation emitted by the surface, about 396Wm−2, is 157Wm−2 greater than the 239Wm−2 leaving the top of the atmosphere (equal to the solar radiation absorbed) – this is a measure of ‘greenhouse trapping’.

Why This Line of Thinking is Wrong and Misleading

Principally, the Earth is not a disk illuminated 24/7 by 1/4 of solar radiant energy. 

That disk in the cartoon denies the physical reality of a rotating sphere, and completely distorts the energy dynamics.  Christos Vournas addresses this issue directly in deriving his planetary temperature equation that corresponds to NASA satellite measurements of planets and moons in our solar system.  Previous posts provide background for this one focusing on the radiant heating of the rotating water planet we call Earth (though Ocean would be more accurate).  See How to Calculate Planetary Temperatures and Earthshine and Moonshine: Big Difference.  

Φ – is the dimensionless Solar Irradiation accepting factor. It recognizes that a sphere’s surface absorbs the incident solar irradiation not as a disk of the same diameter, but accordingly to its spherical shape. For a smooth spherical surface Φ = 0,47

The classical blackbody surface properties

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 radiation incident on its surface.

2. Stefan-Boltzmann blackbody emission law is:   Je = σ*Τe⁴

Notice:

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 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 relies on the incoming outer irradiation only.

Also in the classical blackbody definition it is said that the irradiation incident on the blackbody 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 equation, in which it is assumed that planet’s surface is interacting with the incoming irradiation as 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.

Notice: 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 capacity.  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.

A Real Planet is Not a Blackbody

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, when assuming the planet’s surface behaving as a blackbody, we face the combination of two different initial blackbody surfaces.

a. The one with an inner energy source.

And

b. The one warmed by an outer irradiation.

The Real Planet’s Surface Properties:

1. The planet’s surface has not an infinitive conductivity. Actually the opposite takes place. The planet’s surface conductivity is very small, when compared with the solar irradiation intensity and the planet’s surface infrared emissivity intensity.

2. The planet’s surface has thermal behavior properties. The planet’s surface has a specific heat capacity, cp.

3. The incident on the planet solar irradiation is not being distributed instantly and evenly on the entire planet’s surface area.

4. Planet does not accept the entire solar irradiation incident in planet’s direction. Planet accepts only a small fraction of the incoming solar irradiation. This happens because of the planet’s albedo, and because of the planet’s smooth and spherical surface reflecting qualities, which we refer to as “the planet’s solar irradiation accepting factor Φ”.

Planet reflects the (1-Φ + Φ*a) portion of the incident on the planet’s surface solar irradiation.  And  Planet absorbs only the Φ(1 – a) portion of the incident on the planet’s surface solar irradiation.

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, Φ=0,47

5. Planet’s surface has not a constant intensity solar irradiation effect. Planet’s surface rotates under the solar flux. This phenomenon is decisive for the planet’s surface infrared emittance distribution.

The real planet’s surface infrared radiation emittance distribution intensity is a planet’s rotational speed dependent physical phenomenon.

Φ factor explanation

The Φ – solar irradiation accepting factor – how it “works”. It is not a planet specular reflection coefficient itself.

There is a need to focus on the Φ factor explanation. Φ factor emerges from the realization that a sphere reflects differently than a flat surface perpendicular to the Solar rays.

It is very important to understand what is really going on with planets’ solar irradiation reflection.

There is the specular reflection and there is the diffuse reflection.

The planet’s surface Albedo “a” accounts for the planet’s surface diffuse reflection. Albedo is defined as the ratio of the scattered SW to the incident SW radiation, and it is very much precisely measured (the planet Bond Albedo).

So till now we didn’t take in account the planet’s surface specular reflection. A smooth sphere, as some planets are, are invisible in space and have so far not been detected and the specular reflection not measured . The sphere’s specular reflection cannot be seen from the distance, but it can be seen by an observer situated on the sphere’s surface.

Thus, when we admire the late afternoon sunsets on the sea we are blinded from the brightness of the sea surface glare. It is the surface specular reflection that we see then.

Jsw.absorbed = Φ*(1-a) *Jsw.incoming

For a planet with albedo a = 0 (completely black surface planet) we would have

Jsw.reflected = [1 – Φ*(1-a)]*S *π r² =

Jsw.reflected = (1 – Φ) *S *π r²

For a planet which captures the entire incident solar flux (a planet without any outgoing specular reflection) we would have Φ = 1

Jsw.absorbed = Φ*(1-a) *Jsw.incoming

Jsw.reflected = a *Jsw.incoming

And

For a planet with Albedo a = 1 , a perfectly reflecting planet

Jsw.absorbed = 0 (no matter what is the value of Φ)

In general:  The fraction left for hemisphere to absorb is  Jabs = Φ (1 – a ) S π r²

We have Φ for different planets’ surfaces varying  0,47 ≤ Φ ≤ 1

And we have surface average Albedo “a” for different planets’ varying  0 ≤ a ≤ 1

Notice:

Φ is never less than 0,47 for planets (spherical shape).

Also, the coefficient Φ is “bounded” in a product with (1 – a) term, forming the Φ(1 – a) product cooperating term. Thus Φ and Albedo are always bounded together.

The Φ(1 – a) term is a coupled physical term.

The Φ(1 – a) term “translates” the absorption of a disk into the absorption of a smooth hemisphere with the same radius.

When covering a disk with a hemisphere of the same radius the hemisphere’s surface area is 2π r². The incident Solar energy on the hemisphere’s area is the same as on the disk:  Jdirect = π r² S

But the absorbed Solar energy by the hemisphere’s area of 2π r² is:  Jabs = Φ*( 1 – a) π r² S

It happens because a smooth hemisphere of the same radius “r” absorbs only the Φ*(1 – a)S portion of the directly incident on the disk of the same radius Solar irradiation.

In spite of hemisphere having twice the area of the disk, it absorbs only the Φ*(1 – a)S portion of the directly incident on the disk Solar irradiation.

Gaseous Planets

Φ = 1 for gaseous planets, as Jupiter, Saturn, Neptune, Uranus, Venus, Titan.

Gaseous planets do not have a surface to reflect radiation. The solar irradiation is captured in the thousands of kilometers gaseous abyss. The gaseous planets have only the albedo “a”.

Heavy Cratered Planets

Φ = 1 for heavy cratered planets, as Calisto and Rhea ( not smooth surface planets, without atmosphere ).

The heavy cratered planets have the ability to capture the incoming light in their multiple craters and canyons. The heavy cratered planets have only the albedo “a”.

That is why the albedo “a” and the factor “Φ” we consider as different values. Both of them, the albedo “a” and the factor “Φ” cooperate in the

Energy in = Φ(1 – a) left side of the Planet Radiative Energy Budget.

Conclusively, the Φ -Factor is not the planet specular reflection portion itself.

The Φ -Factor is the Solar Irradiation Accepting Factor (in other words, Φ is the planet surface shape and roughness coefficient).

Bottom Line

What is going on here is that instead of Jabs.earth = 0,694* 1.361 π r² ( W ) we should consider Jabs.earth = 0,326* 1.361 π r² ( W ).

Averaged on the entire Earth’s surface we obtain:

Jsw.absorbed.average = [ 0,47*(1-a)*1.361 W/m² ] /4 =

= [ 0,47*0,694*1.361W/m² ] /4 = 444,26 W/m2 /4 = 111,07 W/m²

Jsw.absorbed.average = 111,07 W/m² or 111 W/m²

Example:  Comparing Earth and Europa

Earth / Europa satellite measured mean temperatures 288 K and 102 K comparison
All the data below are satellites measurements. All the data below are observations.

Planet	Earth	Europa
Tsatmean	288 K	102 K
R	1 AU	5.2044 AU
1/R²	1	0,0369
N	1	1/3.5512 rot/day
a	0.3	0.63
(1-a)	0.7	0.37
coeff	0.91469	0.3158

We could successfully compare Earth /Europa ( 288 K /102 K ) satellite measured mean temperatures because both Earth and Europa (moon of Jupiter) have two identical major features.

Φearth = 0,47 because Earth has a smooth surface and Φeuropa = 0,47 because Europa also has a smooth surface.

cp.earth = 1 cal/gr*°C, it is because Earth has a vast ocean. Generally speaking almost the whole Earth’s surface is wet. We can call Earth a Planet Ocean.  Europa is an ice-crust planet without atmosphere, Europa’s surface consists of water ice crust, cp.europa = 1cal/gr*°C.

The table below shows how well the universal equation estimates temperatures of planets and moons measured by NASA.

Planet	Φ	Te.correct	[(β*N*cp)¹∕ ⁴]¹∕ ⁴	Tmean	Tsat
Mercury	0.47	364	0.8953	325.83	340
Earth	0.47	211	1.3680	287.74	288
Moon	0.47	224	0.9978	223.35	220
Mars	0.47	174	1.2270	213.11	210
Io	1	95.16	1.1690	111.55	110
Europa	0.47	78.83	1.2636	99.56	102
Ganymede	0.47	88.59	1.2090	107.14	110
Calisto	1	114.66	1.1471	131.52	134 ±11
Enceladus	1	55.97	1.3411	75.06	75
Tethys	1	66.55	1.3145	87.48	86 ± 1
Titan	1	84.52	1.1015	96.03	93.7
Pluto	1	37	1.1164	41.60	44
Charon	1	41.9	1.2181	51.04	53

My Comment:

This post explains why it is an error to treat Earth (or any planetary body) as a classic blackbody in either the absorption of incident energy or in the emission of radiation.  Thus the typical energy balance cartoons are not funny, they are false and misleading.  A further error arises in claiming that greenhouse gases like CO2 in the atmosphere cause surface warming by trapping Earth radiation and slowing the natural cooling.  This fallacy is addressed directly in a previous post Why CO2 Can’t Warm the Planet.

The table above and graph below show that Earth’s warming factor is correctly calculated despite ignoring any effect from its thin atmosphere.

A previous post elaborated a rigorous equation from Christos Vournas for calculating surface temperatures of planets or moons, for comparison with NASA satellite measurements of such bodies in our solar system.  That post is How to Calculate Planetary Temperatures.

The image above presents the huge disparity in day and night temperatures between Earth and its Moon, and notes the role of ocean heat transport.  But as I have learned from Christos, there is much more to the story, and this post discusses these deeper implications.  He adds the rotational factor and its impact upon the radiation emitted by both bodies, ie. Earthshine and Moonshine (though obviously it is not simply visible light).  Excerpts from Vournas are in italics with my bolds.

Moon and Earth – so close to each other – and so much different…

Moon is in our immediate neighborhood

Moon rotates around its axis at a slow rate of 29.5 days.  The day on the Moon is 14.75 earth days long, and the night on the Moon is also 14.75 Earth days long. 

Moon is in our immediate neighborhood. So Moon is at the same distance from the sun, as Earth, R=1 AU (astronomical unit).  The year average solar irradiation intensity on the top of atmosphere for Moon and Earth is the same

So = 1361 W/m².

We say “on the top of the atmosphere”, it means the solar intensity which reaches a celestial body and then falls on it. For certain then, during these 14.75 earth days long lunar day the Moon’s surface gets warmed at much higher temperatures than the Earth.

There is the Planet Surface Rotational Warming Phenomenon

I’ll try here in few simple sentences explain the very essence of how the planet rotational warming Phenomenon occurs.

Lets consider two identical planets F and S at the same distance from the sun.  Let’s assume the planet F spins on its axis Faster, and the planet S spins on its axis Slower.  Both planets F and S get the same intensity solar flux on their sunlit hemispheres. Consequently both planets receive the same exact amount of solar radiative energy.

The slower rotating planet’s S sunlit hemisphere surface gets warmed at higher temperatures than the faster rotating planet’s F sunlit hemisphere. The surfaces emit at σT⁴ intensity – it is the Stefan-Boltzmann emission law.

Thus the planet S emits more intensively from the sunlit side than the planet F.  There is more energy left for the planet F to accumulate then.  That is what makes the faster rotating planet F on the average a warmer planet.

That is how the Planet Surface Rotational Warming Phenomenon occurs.

And it becomes very cold on the Moon at night

Moon gets baked hard during its 14,75 earth days long lunar day.  And Moon also emits hard from its very hot daytime surface.  What else can the very hot surface do but to emit hard, according to the Stefan-Boltzmann emission Law.  The very hot surface emits in fourth power of its very high absolute temperature.

Jemit ~ T⁴

A warm object in space loses heat via emission. The hotter is the object, the faster it loses heat.  So there is not much energy left to emit during the 14.75 earth days long lunar night.

The Table below shows the implications:

Planet	Tsat mean	Rotations	Tmin	Tmax
Mercury	340 K	1/176	100K	700K
Earth	288 K	1
Moon	220 Κ	1/29.5	100K	390K
Mars	210 K	0.9747	130K	308K

Comparing Mars and Mercury

The closest to the sun planet Mercury receives 15.47 times stronger solar irradiation intensity than the planet Mars does.  However on the Mercury’s dark side Tmin.mercury = 100 K, when on the Mars’ dark side Tmin.mars = 130 K.

These are observations, these are from satellites the planets’ temperatures measurements.  And they cannot be explained otherwise but by the planet Mars’ 171.5 times faster rotation than planet Mercury’s spin.

Earth-Moon temperatures comparison -why the differences

The faster (than Moon) Earth’s rotation smooths the average heat. The higher (than Moon) Earth’s surface specific heat capacity(oceanic waters vs dry regolith), also smooths the average heat. Consequently the daytime Earth’s surface temperature (compared to Moon) lessens, and the nighttime Earth’s surface temperature (compared to Moon) rises. Earth receives the same amount of solar heat (per unit area) from sun as Moon – for the same albedo. And Earth emits the same amount of solar heat, as the Moon does.

But something else very interesting happens.

It is the difference between Earth’s and Moon’s emitting temperatures. At the daytime Earth’s surface is warmed at a much lower temperatures and therefore at the daytime Earth’s surface emits IR radiation at a much lower intensities. So the intensity of Earth’s daytime IR radiation is much lower (than Moon’s).

As a result, there is a great amount of energy – compared to Moon – “saved” on Earth during the daytime emission..  This “saved” energy should be emitted by Earth’s surface during the nighttime then. At the night-time Earth’s surface is warmer than Moon’s and therefore Earth’s surface at night-time is at a higher temperatures.  So the intensity of Earth’s night-time IR radiation is higher.

There is always a balance.  The energy in = the energy out

But again something else very interesting happens.

In order to achieve that balance Earth’s night-time IR emitting intensity should be much higher than the night-time IR emitting intensity of the Moon.  Now we should take notice of the nonlinearity of the Stefan-Boltzmann emission law. Consequently the night-time temperatures on Earth rise higher (compared to Moon) than the daytime temperatures on Earth lessens.

So the average Earth’s surface temperature is warmer (compared to the Moon). Thus Earth’s Tmean.earth = 288 K and Moon’s Tmean.moon = 220 K

The faster rotation and the higher specific heat capacity does not make sun to put more energy in the Earth’s surface. What the faster rotation and the higher specific heat capacity do is to modify the way Earth’s surface emits, the same amount as Moon, of energy (per unit area).

Earth emits IR radiation at lower temperatures during the daytime and at higher temperatures at night-time. Because of the nonlinearity of this process according to the Stefan-Boltzmann emission law, Earth ends up to have on average warmer surface than Moon.

The night-time temperatures on Earth rise higher (compared to Moon) than the day-time temperatures on Earth lessens. Earth receives (for the same albedo and per unit area) the same amount of solar energy as the Moon . This energy is “welcomed” on each planet and processed in a unique way for each planet.

To illustrate the above conclusions I’ll try to demonstrate on the Earth-Moon temperatures comparison rough example:

Surface temperatures

.min……mean……max

Tmin↑↑→T↑mean ←T↓max

Moon…100 K…220 K …390 K

Δ………..+84 K +68 K….- 60 Κ

Earth…184K↑↑.288 K↑.330 K↓

So we shall have for the faster rotating Earth, compared to the Moon:

Tmin↑↑→ T↑mean ← T↓max

+84↑↑→ +68↑mean ← -60↓

The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean.

Note:  To emphasize we should mention that Moon’s max and min temperatures are measured on Moon’s equator, and Earth’s max and min temperatures are not.  Earth’s max and min temperatures are measured on continents, and not on oceanic waters. Otherwise the Δmin would have been even bigger and the Δmax would have been much smaller.

This rough example nevertheless illustrates that for the faster rotating and covered with water (higher cp) Earth compared with Moon the average temperature should be higher.

The planet’s faster rotation and the planet’s higher specific heat capacity “cp” not only smooths, but also processes ( Δmin > Δmax ), the same incoming solar heat, but in a different emission pattern.

Earth is warmer because Earth rotates faster and because Earth’s surface is covered with water

We had to answer these two questions:

1. Why Earth’s atmosphere doesn’t affect the Global Warming?

It is proven now by the Planet’s Mean Surface Temperature Equation calculations. There aren’t any atmospheric factors in the Equation. Nevertheless the Equation produces very reasonable results:

Tmean.earth = 287,74 K,  calculated by the Equation, which is the same as the Tsat.mean.earth = 288 K, measured by satellites.

Tmean.moon = 223,35 K, calculated by the Equation, which is almost identical with the Tsat.mean.moon = 220 K, measured by satellites.

2. What causes the Global Warming then?

The Global Warming is happening due to the orbital forcing.

And… what keeps Earth warm at Tmean.earth = 288 K, when Moon is at Tmean.moon = 220 K? Why Moon is on average 68 oC colder? It is very cold at night there and it is very hot during the day…

Earth is warmer because Earth rotates faster and because Earth’s surface is covered with water.

Does the Earth’s atmosphere act as a blanket that warms Earth’s surface?

No, it does not.

.