Greenhouse Thought Experiment – Id’s Answer

I waited until my answer was posted in the WUWT thread.  I have replicated it here as well.

Ok, so the point of this thought experiment was to engage the public in a consideration of the differences between the greenhouse effect and an actual greenhouse.  Most here already know that the name itself is a misnomer, but by considering the physics of what is going on we can better understand the argument and better present our opinions on the subject.  The majority of the answer below was emailed to Anthony yesterday before he ran the post at WUWT with the note- just to make sure I can’t back out!  I wrote the reply in terms of energy Joules, it would be more accurate to say power Joules/Sec or Watts but since the system is stabilized the answer works  fine.

I know everyone is wondering what my answers will be to the two greenhouse situations, we’ll see how many will be convinced to change their opinions  – or insist that I change mine 😉 .  It turns out that both problems are fairly straightforward when considered from an engineering standpoint. In the thermally stabilized systems of the example where temperature is not changing, energy into the system is equal to energy out.    We’ll cover the greenhouse vs free air plant situation first.  Both plants receive the same energy but the ability to remove heat from the system is limited in the greenhouse plant through convection and evaporation.   So in the case of the free air plant, although it is receiving the same energy it has 3 methods of cooling: convection, evaporation and radiation.  In the case of the greenhouse, we can consider evaporation and convection negligible so the only option to release the energy is through radiation.   Since our camera is only measuring radiation, and since both plants must emit the same energy they receive, the free air plant radiation will sum like this:

Measured EM radiation = Energy in – convection energy – evaporation energy

the greenhouse will sum like this

Measured EM radiation = Energy in – zero convection energy – zero evaporation energy

Therefore the camera will show the greenhouse plant as warmer (brighter) than the free air plant.  This holds true even if we include non-zero convection and evaporation for the greenhouse because they are still reduced values requiring a higher EM emission to balance the energy equations.

So now we have the situation where we have two planets, one with more CO2 than the other. We know that CO2 absorbs certain outgoing wavelengths of light. We also know energy in is equal to energy out for both planets.  Although this is called the greenhouse effect, it is actually quite different.  For both the high and low CO2 planets, the only available cooling mechanism is EM radiation.  All the energy coming in has to escape by EM radiation to space, so the equations balance like this.

Measured EM radiation = Energy in

That’s it really.  Both planets will measure exactly the same to our camera yet one has a higher surface temperature.  The reason this works is that the average energy emission altitude has gone up, allowing a warmer surface yet the net flow is the same.

Caveats:  Now I warned that some will get tied in knots over the nuance of this example.  There are all kinds of subtleties of the situation which cause minute differences in the planet example.  For instance, increasing CO2 will increase the albedo to incoming light, reducing reflected energy and we get a microscopically higher energy in and therefore were our camera of perfect accuracy we could measure a very slightly higher measured radiation from the warmer planet.  If this is your explanation, we are in agreement.  There are other details as well, but in bulk the answers are A – greenhouse plant is brighter, and B – both are the same.

I read several comments which got the right answer, Carrick was the first to write the correct answer in the comments at tAV, although he kept the answers subtle enough that people had to read it carefully.  If you were one who got them both, congratulations.  If you are unconvinced by my explanations, ask away and I’ll do my best.


13 thoughts on “Greenhouse Thought Experiment – Id’s Answer

  1. Until the plants on the high CO2 planet eat the gas down to starvation levels like the other one, there will be less energy available for radiation. So the high CO2 planet will be cooler (while the CO2 lasts). 🙂

  2. Jeff.
    I am relieved that I got the same answer as you by the same reasoning. It strains the mind to follow some of the discussions over at scienceofdoom but it is gratifying that in my dotage, at least I can muddle my way through some of these thought experiments.

  3. Nice Robert. There was all kinds of complaining about the clarity of the problem. Some was certainly justified as it is difficult to make an ideal experiment which has simple definable answers but still quite a few people got the correct answers without a lot of extra work.

  4. Jeff,

    For instance, increasing CO2 will increase the albedo to incoming light, reducing reflected energy and we get a microscopically higher energy in and therefore were our camera of perfect accuracy we could measure a very slightly higher measured radiation from the warmer planet.

    Don’t think so. CO2 absorbs incident solar radiation in the near IR. The surface absorptivity is pretty close to 1 for those wavelengths (the surface of the ocean for example) so increasing CO2 just changes where the sunlight is absorbed, not how much.

  5. Ignoring Dewitt’s point (he is correct about CO2 in the near IR), the albedo statement does not make sense to me. If albedo increases then the amount of reflection increases (from the camera point of view), not decreases. Your camera will read this as outgoing energy – as you state.

    But the energy in is the same regardless.

  6. Since you like thought experiments and are comfortable with regem and imputting, here is a little thought experiment challenge.

    Multidecadal, possibly longer natural temperature anomalies exist. These oscillations in recent history appear to have cycles ranging from 15 to 70 years. Before the instrumentation era, there is some evidence that oscillations or combination of oscillations may have had longer periods. That anecdotal evidence is generally dismissed as regional anomalies. The Medieval Warm period is one such anomaly that is considered regional and down played as not important in influencing global temperature averages by many scientist attempting to reconstruct past global temperatures. Is there any valid reason to accept their reasoning?

    With the recent shift in the Pacific Decadal Oscillation, shifts in temperature in the arctic and near arctic are producing much higher than normal “regional” temperature patterns that some could argue are similar to patterns that could be associated with Medieval Warm period like climate.

    While global average temperatures have remained relatively flat during this period, arctic and near arctic temperatures have produced interesting and to some frightening red blobs on global temperature maps. Are these regional red blobs inconsequential like similar Medieval Warm period temperatures are assumed to be inconsequential?

    Just as a mental experiment, what would happen regionally should the end of a cool AMO be synchronized with the beginning of a cool PDO? Intuitively, global average temperatures would be stable or slightly cooling while arctic and near arctic temperatures would be considerable warmer, a regional anomaly.

    For extra credit: Conversely, try a warm warm scenario.

    Would press releases in 1100 AD emphasize catastrophic global warming or would adds for real estate sales in Greenland be the headlines? A new medieval real estate bubble set to burst within a century.

  7. Kan, I agree with you on DeWitt’s point. I did consider your answer about reflected light as well. You have two options choose that you are integrating only the thermal portion of the spectrum for outgoing light or assume you are unable to separate the spectra. Both lead to the same answer.

  8. Dallas,

    I don’t think we can use any of the proxies for temperature. They all stink, and I’m unconvinced there is signal in any of them. Ljungqvist’s data, the history in particular, may be able to change my opinion but I think the pre-processing and a particular quirk of CPS may have something to do with its self similarity.

    The big red splotches on the graphs haven’t been around long enough to deflect a Mannian style reconstruction.

    While I don’t mind discussing the basics of AGW, the reality of the magnitude is a complete unknown to me. IMO Climate science has no clue of historic natural variability. They’ve built historic stability into the climate models and backcast them against BS low variance reconstructions to confirm the low historic variance result. It’s all crap and nobody knows the truth but that can’t negate that there is a chance that they are right. If they are right, it would be proof of god’s sense of humor b/c it all reads like a lotto ticket to me.

  9. Most of the winning numbers are on cooling tickets, Jeff. That’s why I’m a lukewarming cooler.

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