A Matter of Some Gravity

Guest Post by Willis Eschenbach

A couple of apparently related theories have been making the rounds lately. One is by Nikolov and Zeller (N&Z), expounded here and replied to here on WUWT. The other is by Hans Jelbring, discussed at Tallblokes Talkshop. As I understand their theories, they say that the combination of gravity plus an atmosphere without greenhouse gases (GHGs) is capable of doing what the greenhouse effect does—raise the earth at least 30°C above what we might call the “theoretical Stefan-Boltzmann (S-B) temperature.”

So what is the S-B temperature, theoretical or otherwise?

A curious fact is that almost everything around us is continually radiating energy in the infrared frequencies. You, me, the trees, the ocean, clouds, ice, all the common stuff gives off infrared radiation. That’s how night-vision goggles work, they let you see in the infrared. Here’s another oddity. Ice, despite being brilliant white because it reflects slmost all visible light, absorbs infrared very well (absorptivity > 0.90). It turns out that most things absorb (and thus emit) infrared quite well, including the ocean, and plants (see Note 3 below). Because of this, the planet is often treated as a “blackbody” for IR, a perfect absorber and a perfect emitter of infrared radiation. The error introduced in that way is small for first-cut calculations.

The Stefan-Boltzmann equation specifies how much radiation is emitted at a given temperature. It states that the radiation increases much faster than the temperature. It turns out that radiation is proportional to absolute temperature to the fourth power. The equation, for those math inclined, is

Radiation = Emissivity times SBconstant times Temperature^4

where the Stefan-Boltzmann constant is a tiny number, 0.0000000567 (5.67E-8). For a blackbody, emissivity = 1.

This “fourth-power” dependence means that if you double the absolute temperature (measured in kelvins), you get sixteen (2^4) times the radiation (measured in watts per square metre, “W/m2”). We can also look at it the other way, that temperature varies as the fourth root of radiation. That means if we double the radiation, the temperature only goes up by about 20% (2^0.25)

Let me call the “theoretical S-B temperature” the temperature that an evenly heated stationary blackbody planet in outer space would have for a given level of incoming radiation in W/m2. It is “theoretical”, because a real, revolving airless planet getting heated by a sun  with the same average radiation will be cooler than that theoretical S-B temperature. We might imagine that there are thousands of mini-suns in a sphere around the planet, so the surface heating is perfectly even.

Figure 1. Planet lit by multiple suns. Image Source.

On average day and night over the planetary surface, the Earth receives about 240 W/m2 of energy from the sun. The theoretical S-B temperature for this amount of radiation (if it were evenly distributed) is about -18°C, well below freezing. But instead of being frozen, the planet is at about +14°C or so. That’s about thirty degrees above the theoretical S-B temperature. So why isn’t the planet a block of ice?

Let me take a short detour on the way to answering that question in order to introduce the concept of the “elevator speech” to those unfamiliar with the idea.

The “elevator speech” is simply a distillation of an idea down to its very basics. It is how I would explain my idea to you if I only had the length of an elevator ride to explain it. As such it has two extremely important functions:

1. It forces me to clarify my own ideas on whatever I’m discussing. I can’t get into handwaving and hyperbole, I can’t be unclear about what I’m claiming, if I only have a few sentences to work with.

2. It allows me to clearly communicate those ideas to others.

In recent discussions on the subject, I have been asking for that kind of “elevator speech” distillation of Jelbring’s or Nikolov’s ideas, so that a) I can see if whoever is explaining the theory really understands what they are saying and, if so, then b) so that I can gain an understanding of the ideas of Jelbring or Nikolov to see if I am missing something important.

Let me give you an example to show what I mean. Here’s an elevator speech about the greenhouse effect:

The poorly-named “greenhouse effect” works as follows:

• The surface of the earth emits energy in the form of thermal longwave radiation.

• Some of that energy is absorbed by greenhouse gases (GHGs) in the atmosphere.

• In turn, some of that absorbed energy is radiated by the atmosphere back to the surface.

• As a result of absorbing that energy from the atmosphere, the surface is warmer than it would be in the absence of the GHGs.

 OK, that’s my elevator speech about why the Earth is not a block of ice. Note that it is not just saying what is happening. It is saying how it is happening as well.

I have asked, over and over, on various threads, for people who understand either the N&Z theory or the Jelbring theory, to give me the equivalent elevator speech regarding either or both of those theories. I have gotten nothing scientific so far. Oh, there’s the usual handwaving, vague claims of things like ‘the extra heat at the surface, is just borrowed by the work due to gravity, from the higher up regions of the atmosphere‘ with no mechanism for the “borrowing”, that kind of empty statement. But nothing with any meat, nothing with any substance, nothing with any explanatory value or scientific content.

So to begin with, let me renew my call for the elevator speech on either theory. Both of them make my head hurt, I can’t really follow their vague descriptions. So … is anyone who understands either theory willing to step forward and explain it in four or five sentences?

But that’s not really why I’m writing this. I’m writing this because of the claims of the promoters of the two theories. They say that somehow a combination of gravity and a transparent, GHG-free atmosphere can conspire to push the temperature of a planet well above the theoretical S-B temperature, to a condition similar to that of the Earth.

I hold that with a transparent GHG-free atmosphere, neither the hypothetical “N&Z effect” nor the “Jelbring effect” can possibly raise the planetary temperature above the theoretical S-B temperature. But I also make a much more general claim. I hold it can be proven that there is no possible mechanism involving gravity and the atmosphere that can raise the temperature of a planet with a transparent GHG-free atmosphere above the theoretical S-B temperature.

The proof is by contradiction. This is a proof where you assume that the theorem is right, and then show that if it is right it leads to an impossible situation, so it cannot possibly be right.

So let us assume that we have the airless perfectly evenly heated blackbody planet that I spoke of above, evenly surrounded by a sphere of mini-suns. The temperature of this theoretical planet is, of course, the theoretical S-B temperature.

Now suppose we add an atmosphere to the planet, a transparent GHG-free atmosphere. If the theories of N&K and Jelbring are correct, the temperature of the planet will rise.

But when the temperature of a perfect blackbody planet rises … the surface radiation of that planet must rise as well.

And because the atmosphere is transparent, this means that the planet is radiating to space more energy than it receives. This is an obvious violation of conservation of energy, so any theories proposing such a warming must be incorrect.

Q.E.D.

Now, I’m happy for folks to comment on this proof, or to give us their elevator speech about the Jelbring or the N&Z hypothesis. I’m not happy to be abused for my supposed stupidity, nor attacked for my views, nor pilloried for claimed errors of commission and omission. People are already way too passionate about this stuff. Roger Tattersall, the author of the blog “Tallbloke’s Talkshop”, has banned Joel Shore for saying that the N&Z hypothesis violates conservation of energy. Roger’s exact words to Joel were:

… you’re not posting here unless and until you apologise to Nikolov and Zeller for spreading misinformation about conservation of energy in their theory all over the blogosphere and failing to correct it.

Now, I have done the very same thing that Joel did. I’ve said around the web that the N&Z theory violates conservation of energy. So I went to the Talkshop and asked, even implored, Roger not to do such a foolish and anti-scientific thing as banning someone for their scientific views. Since I hold the same views and I committed the same thought-crimes, it was more than theoretical to me. Roger has remained obdurate, however, so I am no longer able to post there in good conscience. Roger Tallbloke has been a gentleman throughout, as is his style, and I hated to leave. But I did what Joel did, I too said N&Z violated conservation of energy, so in solidarity and fairness I’m not posting at the Talkshop anymore.

And more to the point, even if I hadn’t done what Joel did, my practice is to never post at or even visit sites like RealClimate, Tamino’s, and now Tallbloke’s Talkshop, places that ban and censor scientific views. I don’t want to be responsible for their page views counter to go up by even one. Banning and censorship are anathema to me, and I protest them in the only way I can. I leave them behind to discuss their ideas in their now cleansed, peaceful, sanitized, and intellectually sterile echo chamber, free from those pesky contrary views … and I invite others to vote with their feet as well.

But I digress, my point is that passions are running high on this topic, so let’s see if we can keep the discussion at least relatively chill …

TO CONCLUDE: I’m interested in people who can either show that my proof is wrong, or who will give us your elevator speech about the science underlying either N&K or Jelbring’s theory. No new theories need apply, we have enough for this post. And no long complicated explanations, please. I have boiled the greenhouse effect down to four sentences. See if you can match that regarding the N&K or the Jelbring effect.

w.

NOTE 1: Here’s the thing about a planet with a transparent atmosphere. There is only one object that can radiate to space, the surface. As a result, it is constrained to emit the exact amount of radiation it absorbs. So there are no gravity/atmospheric phenomena that can change that. It cannot emit more or less than what it absorbs while staying at the same temperature, conservation of energy ensures that. This means that while the temperature can be lower than the theoretical S-B temperature, as is the case with the moon, it cannot be more than the theoretical S-B temperature. To do that it would have to radiate more than it is receiving, and that breaks the conservation of energy.

Once you have GHGs in the atmosphere, of course, some of the surface radiation can get absorbed in the atmosphere. In that case, the surface radiation is no longer constrained, and the surface is free to take up a higher temperature while the system as a whole emits the same amount of radiation to space that it absorbs.

NOTE 2: An atmosphere, even a GHG-free atmosphere, can reduce the cooling due to uneven insolation. The hottest possible average temperature for a given average level of radiation (W/m2) occurs when the heating is uniform in both time and space. If the total surface radiation remains the same (as it must with a transparent atmosphere), any variations in temperature from that uniform state will lower the average temperature. Variations include day/night temperature differences, and equator/polar differences. Since any atmosphere can reduce the size of e.g. day/night temperature swings, even a transparent GHG-free atmosphere will reduce the amount of cooling caused by the temperature swings. See here for further discussion.

But what such an atmosphere cannot do is raise the temperature beyond the theoretical maximum average temperature for that given level of incoming radiation. That’s against the law … of conservation of energy.

NOTE 3: My bible for many things climatish, including the emissivity (which is equal to the absorptivity) of common substances, is Geiger’s The Climate Near The Ground, first published sometime around the fifties when people still measured things instead of modeling them. He gives the following figures for IR emissivity at 9 to 12 microns:

Water, 0.96

Fresh snow, 0.99

Dry sand, 0.95

Wet sand, 0.96

Forest, deciduous, 0.95

Forest, conifer, 0.97

Leaves Corn, Beans, 0.94

and so on down to things like:

Mouse fur, 0.94

Glass, 0.94

You can see why the error from considering the earth as a blackbody in the IR is quite small.

I must admit, though, that I do greatly enjoy the idea of some boffin at midnight in his laboratory measuring the emissivity of common substances when he hears the snap of the mousetrap he set earlier, and he thinks, hmmm …

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Paul Dennis
January 15, 2012 10:20 pm

Willis,
You state:
“Finally, I think (sadly) that Dr. Roy is wrong about the eventual distribution at equilibrium being isothermal. That would put the maximum total energy (kinetic plus potential) at the top of the atmosphere. I see no reason why that uneven energy distribution would be favored over the even energy distribution reflected by the normal lapse rate. I see no reason why the normal lapse rate would not obtain.”
This statement seems to imply that the lapse rate is a result of the loss of kinetic energy with height in a gravitational field. Surely the lapse rate is determined by the adiabatic expansion of the atmosphere and requires the motion of air parcels. If you remove convection from the thought model (and I don’t see why convection will occur on your evenly heated sphere) you are simply describing the Loschmidt effect. This paradox is dealt with by Coombes and Laue, 1985, Am. J. Phys. A paradox concerning the temperature distribution of a gas in a gravitational field.
What you see as an uneven energy distribution is not the case. The temperature is determined by the average kinetic energy of the ensemble of molecules in a given volume element. Whilst both the number of molecules and kinetic energy of molecules decreases with height, the average kinetic energy remains the same and thus the temperature is constant with height. A similar proof has also been given by Roman, White and Velasco, 1996, Eur. J. Phys., On a paradox concerning the temperature distribution of an ideal gas in a gravitational field.
None of this affects your argument about gravity effects and surface temperature. However, there are some who believe the Loschmidt effect is the origin of the lapse rate and I believe they are wrong.
Finally, I’m amazed this thread has such legs. There again there are some who believe in perpetual motion!

wayne
January 15, 2012 10:33 pm

jjthom says:
January 15, 2012 at 4:59 pm
A brilliant site for the physics:
http://www.patarnott.com/atms749/
The presentations are clear – from First Course in Atmospheric Radiation: Second Edition, by Grant W. Petty.
— — —
jjthom, that is hugely appreciated and exactly at the right time. I sure needed that! Hope Willis and others a bit confused also read it. So… N2 does have rotational lines after all… just what I expected! Thanks again.

Alexander Harvey
January 15, 2012 11:00 pm

The thought experiment given by Willis is sound.
The question of whether the resultant atmosphere will conform to the DALR or become isothermal is not relevant to his argument.
There is a disagreement on that point but although it is not crucial to his argument it is interesting in its own right.
I think I can show that conformation to the DALR as opposed to the isothermal state is not mandated.
In his model the atmosphere is only coupled to the surface, that is its only boundary where energy transfer can take place, i.e. it is not coupled radiatively or by any other means, via its upper boundary with deep space
1) Should the atmosphere become isothermal, for any reason, a spontaneous move towards adopting the DALR would require a transfer of energy from the atmosphere in a way that promotes a temperature gradient. The atmosphere would then be transfering energy up that temperature gradient. That is a problem with repsect to the 2nd Law. This does not say that it must become isothermal but that conversion to the isothermal state is irreversible without doing work.
2) A DALR conforming atmosphere is open to a perpetual motion exploit in that the bottom and top of the atmosphere have the potential to be used as a thermal source and a thermal sink. In practice this could be achieved by constructing a heat engine using a gas with a differnt Cp to the atmosphere, as a working fluid, or by coupling using a rod with high thermal conductivity, but thermally insulated along its length, to bridge the distance. I suspect other methods could be devised. Work could be extracted and heat would be transfered in the manner promoting a move towards an isothermal distribution. A requirement for the temperature profile to adhere to the DALR would require that the energy be returned up the temperature gradient again problematic with regard to the 2nd Law.
3) Similarly any “substantive” move towards the isothermal state caused spontaneously due to thermal conduction/diffusion would be irreversible without doing work. Here substantive is to be understood as more than the inevitable random fluctuations.
None of those points says it must be isothermal but do argue that the isothermal state is preferred due to entropic considerations.
It is clear that the DALR is stable in the respect that any tendency to increase the slope of the profile away from the DALR will be conteracted by increasing convention and hence the thermal coupling. A tendency to decrease the slope of the profile away from the DALR will tend to inhibit convection reducing the coupling. If this progresses the profile will move towards the isothermal and ever greater stability as the atmosphere becomes incresingly stratified. This describes the DALR as being the maximum slope limiting condition. The isothermal profile being the other limiting condition.
None of this gives an indication of to what degree or over what timescale a move towards the isothermal would take place but it does suggest that a profile conforming to the DALR is not a thermodynamically preferred option.
Alex

JimF
January 15, 2012 11:00 pm

C says:
January 14, 2012 at 12:45 am
Thank you for that reference to Joseph Postma’s work. I went and read “The Model Atmospheric Greenhouse Effect”, found here:
http://www.tech-know.eu/uploads/The_Model_Atmosphere.pdf
Very informative. Basically, this says that the Radiative Greenhouse Effect model is completely wrong, and if you pick the wrong boundary conditions, then this kind of thinking occurs: “…On average day and night over the planetary surface, the Earth receives about 240 W/m2 of energy from the sun. The theoretical S-B temperature for this amount of radiation (if it were evenly distributed) is about -18°C, well below freezing….” (This is not intended to criticize Willis; his words simply met my needs, and do in fact represent the “consensus” thinking. Postma shows how these numbers come about, and gives a strong case as to why they are wrong).
One should read this and consider what I think are valid points regarding the physical model we’re dealing with, and see how this might lead one into making calculations that are silly (like the numbers quoted above). Dr. Brown, who recently started looking at Earth’s baseline black-body model – “a damn hard problem” – would surely find it of interest.
This ongoing discussion is really interesting, because it addresses the fundamental basis of the radiative greenhouse effect, which Postma says is garbage. I’m just learning as I go. I think Willis’ “elevator speech” approach is a good one that we all can adopt to use.

lrshultis
January 15, 2012 11:14 pm

Willis:
This is a simplified view of the GHG-free atmosphere with solar input according to my understanding.
Some solar energy is transferred to the Ar, O2, and N2 by absorption at various frequencies, mainly high in the atmosphere, and by momenta transfer by scattering of photons. The remaining solar energy is absorbed by the local surfaces giving them local temperatures (not necessarily the same as the local weather temperature of the air several feet above the surface). Some of that surface kinetic energy is radiated to space as IR. Some more is conducted to the atmosphere causing it to do work by expansion decreasing its density and convecting to higher altitude. Gravity then causes cooler dense air to fall to the surface and doing work on it equivalent to the work done by the surface heating by increasing its density and temperature. A lapse rate is established by gravity as pressure*volume/ mole decreases and thus temperature decreases with increased height. The amount of surface heat to the atmosphere determines what the equilibrium lapse rate will be. Thus the kinetic energy transfer which causes convection does work against gravity and does not need to be radiated to space.
With GHGs the lapse rate will change due to the increase in atmospheric temperature due to the transfer of energy from GHG molecules by transferring kinetic energy ( due to absorption of IR from the local surfaces) from the GHG molecules to the Ar, O2, and N2 atoms and molecules.
Larry

JIsbert
Reply to  Willis Eschenbach
January 16, 2012 9:52 am

Willis,
I think N&Z are getting a bit carried away with their conclusions, which is also reflected in their abstract.
Their model is a 2 layer model (surface + emission layer). Heat is transferred from the surface to the emission layer by radiation only (in the Penn State model) and by radiation + convection in their “unified” model.
They show solutions for the equations describing either model (Fig. 2 and 3). And their finding is that their “unified” model carries the day, i.e fits with the atmospheres of many solar system planets and moons.
The important point here is that their model requires the 2nd layer. They never explore what influence the composition of the atmosphere has in creating this situation.
Your “dry air model” takes away this condition and changes the model into a 1 layer model (the surface only). This change in model makes the different conclusions not applicable to their case.
Since they do not explore what mechanisms this 2nd layer requires and how the composition of the atmosphere might change their case, their claim that the composition does not matter is just that – an unexplored and thus unproven claim.
Cheers,
JI

January 16, 2012 12:00 am

I’d like to hear Willis’s further comments on the last version of my post which was as follows:
1) Willis knows that his non GHG atmosphere will produce a dry adiabatic lapse rate with the warmest temperature at the surface.I am assuming some movement via convection to achieve it.
2) The warmth at the surface is NOT due to gravitational compression ( although a tiny fraction of it would be) but gravity IS responsible for placing the maximum density of non GHG molecules at the base of the atmospheric column.
3) That maximium density causes the greatest number of molecular collisions to occur just above, or in contact with, the surface.
4) Such collisions transfer energy between themselves by conduction and not radiation. The surface converts incoming solar shortwave radiative energy into kinetic energy and the non GHG gases in contact with or in close proximity to the surface retain that kinetic energy by exchanging the energy via conduction between themselves and between themselves and the surface until it can be released upward by the surface as outgoing longwave IR.
5) It is that delay that allows the surface temperature to rise as energy accumulates within the system and most particularly at or just above the surface.
6) The greater the density of the non GHG atmosphere, the more molecular collisions occur, the longer the delay and the higher the equilibrium temperature must become. The increased density does NOT slow down the rate of conduction. Instead it increases the proportion of radiation that is retained for longer within the system in the form of slower moving conduction leading to an average net reduction in energy flow through the system at any given level of input.
7) At equilibrium we now have solar shortwave hitting the surface at 240W/m2 and IR longwave leaving the surface at 240W/m2 but additionally we now have a backed up pool of kinetic energy bouncing between air molecules at the surface and between those molecules and the surface giving the necessary temperature boost at the surface.
It sounds somewhat like a pressure bulge in a hosepipe when there is a weakness in the wall which then stretches under pressure of increasing throughput. It comes and goes with the speed of flow. Water for the hose, solar energy for the non GHG atmosphere. In the non GHG atmosphere it is the pressure and temperature at the surface which changes in response to changes in solar input and atmospheric density.
I don’t see how one could accept a slowing down of the energy throughput without some sign of higher temperature somewhere in the system and by virtue of the dry adiabatic lapse rate it has to be in the air where it contacts the solid surface.

Bart
January 16, 2012 12:10 am

Willis Eschenbach says:
January 15, 2012 at 10:55 pm
shawnhet says:
January 15, 2012 at 8:22 pm
“The main one being: how can the surface of a planet such as Earth emit more energy than the planet as a whole emits to space?”
And, when did you stop beating your wife?
You have to show it is necessary that more energy be emitted by the planet for non-GHG heating to work before discounting the idea on that basis. SB does not demonstrate it. SB is not a fundamental law – it has loopholes. And, the widespread neglect of these loopholes is just plain sloppy.

PhilC
January 16, 2012 12:21 am

I’m interested in Reed Coray’s question and I had a look at the links you gave him, and I think that there is something missing from the elevator speech for the “Greenhouse Effect”. That is that Infra Red absorption can raise the temperature of the atmosphere higher than that of the radiating surface.
This apparent breaking of the 2nd law of thermodynamics is possible because the energy is transmitted from the surface to the atmosphere as radiation, not heat. IR absorbing molecules in the atmosphere lose energy to the atmosphere as heat, by collision with other molecules.
Because this disturbs the radiation budget of the planet, and energy can only escape the planet by radiation, this can only be restored by an increase in temperature of the surface, until the equilibrium set the the Stefan-Bolzmann curve is restored. There is downward welling energy transfer, but it’s mostly heat rather than radiation. All the IR photons do eventually escape, but they may be absorbed and re-emitted many times in the atmosphere on the way.
This effect of energy (not heat) being transmitted from a cooler to a hotter body is not unique to the atmosphere. The Sun’s corona is another instance. It has a temperature of a million K because of energy transmitted from a body of 6000 K (the surface of the Sun).
It seems to me that is how the atmospheric “Greenhouse Effect” actually works.

RobB
January 16, 2012 12:27 am

I asked this further up the thread, and this is a change to the model that Willis proposed. But, does anyone know the state of an otherwise identical model if the atmosphere did emit radiation at some rate? I think this is a very good analogy to a GHG free Earth. The surface conducts/convects energy into the atmosphere but any IR emitted goes straight out to space. The atmosphere itself emits radiation at some rate, either up or down, down hits the ground and up goes to space, so the radiation physics are very simple still in this case. The down radiation heats the surface which either gets emitted as IR into space or warms the atmospere by conduction.
Any idea that the surface air temperature is in this slightly altered model?

Editor
January 16, 2012 12:33 am

Willis
For what it’s worth I was unhappy with the initial banning of Joel by tall bloke and said so. Equally the amount of snipping here is prodigious, surely the first time in climate history that anything has actually genuinely been ‘unprecedented’
However what has become clear is that no one has managed to make the elevator speech you asked for even though there are plenty of people here who could,if such a device were possible to explain the theories. That leaves a bystander such as me fairly sure that such a speech is not possible. The theories that have been postulated are radical and important and it would be interesting to rerun this thread in a months time when hopefully less heat and more light can be shone on the subject by people who have had more time to think about it
All the best
Tonyb

Martin A
January 16, 2012 12:34 am

Willis – I can see no fault in your argument by contradiction.
For your model, you said “we add an atmosphere to the planet, a transparent GHG-free atmosphere.”
Its surprising how many commenters insist that the atmosphere in your model will radiate nonetheless – ie they insist that the atmosphere is NOT a transparent GHG-free atmosphere, despite your explicitly stating the assumption that it is.
However –
” How many comments like mine didn’t even make it past moderation?
My dear, there are no comments like yours, so the answer is none.”
Am I alone in finding this reply sexist, condescending and unworthy of W.E. ?

gbaikie
January 16, 2012 12:37 am

shawnhet says:
“The main one being: how can the surface of a planet such as Earth emit more energy than the planet as a whole emits to space?”
Not sure of question being asked.
how can surface of earth emit more energy than entire earth emits to space?
So obviously surface of earth is part of earth. So you asking does surface emit energy which doesn’t go into space, and how could these surface emission [not going into space be greater.
Otherwise It makes no sense.
Don’t what has do anything, but see if I can answer.
We could assume you mean by earth emits, that this different then earth reflecting sunlight.
Or we can assume anything come from the direction of the earth [includes reflected sunlight and anything else].
If we address the latter [which should the greatest amount], how much energy comes from the direction of earth. We have forest fires and geothermal heat but the big number is the sunlight- so we focus of that number. Wiki says “The Earth receives 174 petawatts (PW) of incoming solar radiation (insolation) at the upper atmosphere.”.
So question is how can surface emit more energy than 174 petawatts?
174 petawatts is 174 10^15 watts or 1.74 10^17 joules per second.
Now, what is surface. Do we mean top 1 mm of land or water which meets air of atmosphere,
do mean the troposphere. Or first couple miles of land and/or ocean.
No idea.
Anyways, the surface area of earth is 510 million square kilometers, or 5.1 10^14 square meters, and this approximation of surface area probably is what is meant. So, let’s see, 1740 10^14
divided by 5.1 10^14 is 374 joules per second. So question is are 374 Joules per sq meter being emitted or transfered somewhere other than space per second.
Do powerlines count as surface? Humans emit about 100 joules per second.
Well atmosphere is warmed [requires energy to emit] and cooled [requires energy to emit].
Oh so is it this cooling and warming that you mean?
The atmosphere is 5.1 x 10^18 kg. Nah, let’s do 10 tonnes per square a one C degree change in 10 tonnes of air is 1.0 kJ/kg.K so 10,000 times 1000 is 10 million joules. Say 10 C per nite
And 12 hours times 3600 is 43200 seconds. 100 million divided by 43200 is 2314 joules per second per square meter. 2314 is 6 times more than 374 Joules.
And of course it warms up during day, and so has same scale of joules in energy is being emitted.
So guess answer is yeah.
Dew which is 1 mm thick per square meter is how much energy involved? so meter is 100 cm square, so 10,000 square cm. And mm is 1/10 of cm, so 1000 cubic cm or 1000 grams. And Latent heat of evaporation – 2,270 kJ/kg. So 2.7 million joules. That’s not much.
How about campfire? it warms air, and air molecules warm other air molecules and they each emit energy to other molecules and they do this zillions of times.
Or actually even if air stays same temperature one of the zillions molecules are exchanging energy every fraction of nanosecound- it and all the rest of them are constantly averaging the molecular speed.
But the exchange velocity or exchange of heat could be said not to be what is called the energy emitting.
Perhaps you mean only photons. I don’t know number photons. Sun is emitting a lot of them.
And standard greenhouse theory is all about photons. CO2 absorbs photons, and emits photons.
Is CO2 absorption and emission of photon what you asking? Consider the theory on this, seems shortage of discussion on how photons are involved.
I wonder many photons to a watt:
What is the energy in a single photon of light at 500nm?
a single photon is 0.039756 × 10-17 J
Or one joule/watt equals 25.15 × 10^17 photons
http://reefkeeping.com/issues/2006-02/sj/index.php
Every wavelength has different energy, but ignoring that
Sunlight: 1.74 10^17 joules times 25.15 × 10^17 photons
So 4.4 10^34 protons per second from the Sun.
So, don’t know how many photons a CO2 or H2O molecule can absorb and emit per second.
Ok so “As the frequency of the radiation increases (wavelength gets shorter), the amount of energy in each photon increases”
Which means the hotter something the less photons used per joule. double 500nm to 1000 nm
and per watt it’s twice the photon [or so it seems to this idiot].
So since Sun is hotter, it’s energy uses less photons, and colder objects to emit same energy need more photons.
So original question was:
“The main one being: how can the surface of a planet such as Earth emit more energy than the planet as a whole emits to space?”
So since earth is colder it will need to emit more photons to equal the energy.
Every grain of sand is emitting photons. Does every atom in rock emit photons?
I would guess, since there more joules of energy on earth then is delivered by the Sun in a second [or nanosecond] and any thing isn’t mostly facing the sky and gases are suppose absorb and emit some of these photons going towards space and things are warming and cooling, that is how.

Julian Braggins
January 16, 2012 12:42 am

Willis has proved his point, that under his specified conditions, multiple suns, no IR sensitivity of atmosphere, etc. the temperature would not exceed S-B level.
This does not disprove N&Z’s theory as these very conditions prohibit the mechanism of the gravity heat engine of atmospheres, convection.
Surface warming of the atmosphere would cause convection. Heat produced by a falling atmosphere that has lost some of that heat by radiation at height will will cause a higher temperature at the surface than the average of the atmosphere, as long as there is a differential in heating to prevent equilibrium, and that there is a day/night cycle sufficiently rapid to enable a reset of conditions for the heat engine cycle.
This is not to say that the temperature will necessarily exceed S-B, but in the case of the moon it seems the average temperatures can exceed this level.

gbaikie
January 16, 2012 1:09 am

“Willis Eschenbach says:
January 15, 2012 at 11:50 pm
gbaikie says:
January 15, 2012 at 8:34 pm
“I don’t accept that it is windy on the hypothetical planet we are discussing. ”
In the million sun world? Yeah, no wind.
You sure you understand how this whole “thought experiment” deal works?”
Yeah you think million suns uniformly across the sky of a planet which each has solar flux of 240 Watts per square meter. Is the a same as one sun with solar flux of 1300 watts per square meter.
I don’t think if you had a planet which extremely high “geothermal” heat of 240 watts per square meter it would cause the planet to get above -18 C. I don’t a greenhouse effect which adding 240 watts per square would increase the planet above -18 C.
So a million suns, high geothermal heat, super greenhouse gases and still only -18 C
And you want someone to explain how the N&Z theory will increase it the surface temperature above -18 C
Of course with million suns and billion or more years you would get a “geothermal” heat of 240 watts per square meter. So the only remaining point is why would greenhouse gas add any heat?

Paul Dennis
January 16, 2012 1:22 am

Willis,
thank you for your considered response. I can only quote from Coombes and Laue, 1985:
“Question: If a vertical column of air which is adiabatically enclosed is in thermal equilibrium, is the temperature the same throughout the column or is there a temperature gradient along the direction of the gravitational field? – Let us assume an idealized model in which there are no interactions between air molecules and no collisions once the equilibrium distribution has been established. The resolution of the paradox below is unrelated to this assumption. Energy conservation mplies that the kinetic energy (KE) of a molecule decreases with its height z above the Earth’s surface according to the formula:
KE = (KE)o – mgz
where m is the mass of the molecule and g is the acceleration due to gravity. Now, the two conflicting answers to the above question are as follows.
(1) There is no temperature gradient because a system which is in thermal equilibrium has the same temperature throughout.
(2) The temperature decreases as one goes up the column for the following reasons. (a) Since Eq (1) implies that every molecule loses kinetic energy as it moves upward, the average kinetic energy of all molecules decreases with height. (b) Temperature is proportional to the average molecular kinetic energy. Combining (a) and (b) establishes statement (2) above.
Which of the statements (1) or (2) is correct? Where lies the mistake? Note that the argument is short and that it is hard to find anything wrong with any of the statements. In fact, the second arguments seem so convincing that one begins to doubt the validity of state,ent (1) in the presence of a gravitational field. We recommend that the students be made to wait from one period to the next before the solution is given. We also recommend that the reader of this Note spend some time carefully thinking about the problem before continuing.
The answer is that statement (1) is right and statement (2) wrong. Statement (2) is wrong because the conclusion in statement 2(a) is wrong. The seemingly paradoxical truth is that the average kinetic energy of all molecules does not decrease with height even though the kinetic energy of each individual molecule does decrease with height”
Willis, I urge you to read Coombes and Laue and then the other paper I referred to upthread to read the proofs of these assertions. Of course they are counter to your elegant description above and suggest the atmosphere will be isothermal.

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