Guest Post by Willis Eschenbach
I’ve been considering the effect that temperature swings have on the average temperature of a planet. It comes up regarding the question of why the moon is so much colder than you’d expect. The albedo (reflectivity) of the moon is less than that of the Earth. You can see the difference in albedo in Figure 1. There are lots of parts of the Earth that are white from clouds, snow, and ice. But the moon is mostly gray. As a result, the Earth’s albedo is about 0.30, while the Moon’s albedo is only about 0.11. So the moon should be absorbing more energy than the Earth. And as a result, the surface of the moon should be just below the freezing temperature of water. But it’s not, it’s much colder.
Figure 1. Lunar surface temperature observations from the Apollo 15 mission. Red and yellow-green short horizontal bars on the left show the theoretical (red) and actual (yellow-green) lunar average temperatures. The violet and blue horizontal bars on the right show the theoretical Stefan-Boltzmann temperature of the Earth with no atmosphere (violet), and an approximation of how much such an Earth’s temperature would be lowered by a ± 50°C swing caused by the rotation of the Earth (light blue). Sunset temperature fluctuations omitted for clarity. DATA SOURCE
Like the Earth, averaged over its whole surface the moon receives about 342 watts per square metre (W/m2) of solar energy. We’re the same average distance from the sun, after all. The Earth reflects 30% of that back into space (albedo of 0.30), leaving about 240 W/m2. The moon, with a lower albedo, reflects less and absorbs more energy, about 304 W/m2.
And since the moon is in thermal equilibrium, it must radiate the same amount it receives from the sun, ~ 304 W/m2.
There is something called the “Stefan Boltzmann equation” (which I’ll call the “S-B equation” or simply “S-B”) that relates temperature (in kelvins) to thermal radiation (in watts per square metre). It says that radiation is proportional to the fourth power of the temperature.
Given that the moon must be radiating about 304 W/m2 of energy to space to balance the incoming energy, the corresponding blackbody lunar temperature given by the S-B equation is about half a degree Celsius. It is shown in Figure 1 by the short horizontal red line. This shows that theoretically the moon should be just below freezing.
But the measured actual average temperature of the lunar surface shown in Figure 1 is minus 77°C, way below freezing, as shown by the short horizontal yellow-green line …
So what’s going on? Does this mean that the S-B equation is incorrect, or that it doesn’t apply to the moon?
The key to the puzzle is that the average temperature doesn’t matter. It only matters that the average radiation is 304 W/m2. That is the absolute requirement set by thermodynamics—the average radiation emitted by the moon must equal the radiation the moon receives from the sun, 304 W/m2.
But the radiation is proportional to the fourth power of temperature. This means when the temperature is high, there is a whole lot more radiation, but when it is low, the reduction in radiation is not as great. As a result, if there are temperature swings, they always make the surface radiate more energy. As a result of radiating more energy, the surface temperature cools. So in an equilibrium situation like the moon, where the amount of emitted radiation is fixed, temperature swings always lower the average surface temperature.
For confirmation, in Figure 1 above, if we first convert the moment-by-moment lunar surface temperatures to the corresponding amounts of radiation and then average them, the average is 313 W/m2. This is only trivially different from the 304 W/m2 we got from the first-principles calculation involving the incoming sunlight and the lunar albedo. And while this precise an agreement is somewhat coincidental (given that our data is from one single lunar location), it certainly explains the large difference between simplistic theory and actual observations.
So there is no contradiction at all between the lunar temperature and the S-B calculation. The average temperature is lowered by the swings, while the average radiation stays the same. The actual lunar temperature pattern is one of the many possible temperature variations that could give the same average radiation, 304 W/m2.
Now, here’s an oddity. The low average lunar temperature is a consequence of the size of the temperature swings. The bigger the temperature swings, the lower the average temperature. If the moon rotated faster, the swings would be smaller, and the average temperature would be warmer. If there were no swings in temperature at all and the lunar surface were somehow evenly warmed all over, the moon would be just barely below freezing. In fact, anything that reduces the variations in temperature would raise the average temperature of the moon.
One thing that could reduce the swings would be if the moon had an atmosphere, even if that atmosphere had no greenhouse gases (“GHGs”) and was perfectly transparent to infrared. In general, one effect of even a perfectly transparent atmosphere is that it transports energy from where it is warm to where it is cold. Of course, this reduces the temperature swings and differences. And that in turn would slightly warm the moon.
A second way that even a perfectly transparent GHG-free atmosphere would warm the moon is that the atmosphere adds thermal mass to the system. Because the atmosphere needs to be heated and cooled as well as the surface, this will also reduce the temperature swings, and again will slightly warm the surface in consequence. It’s not a lot of thermal mass, however, and only the lowest part has a significant diurnal temperature fluctuation. Finally, the specific heat of the atmosphere is only about a quarter that of the water. As a result of this combination of factors, this is a fairly minor effect.
Now, I want to stop here and make a very important point. These last two phenomena mean that the moon with a perfectly transparent GHG-free atmosphere would be warmer than the moon without such an atmosphere. But a transparent atmosphere could never raise the moon’s temperature above the S-B blackbody temperature of half a degree Celsius.
The proof of this is trivially simple, and is done by contradiction. Suppose a perfectly transparent atmosphere could raise the average temperature of the moon above the blackbody temperature, which is the temperature at which it emits 304 W/m2.
But the lunar surface is the only thing that can emit energy in the system, because the atmosphere is transparent and has no GHGs. So if the surface were warmer than the S-B theoretical temperature, the surface would be emitting more than 304 W/m2 to space, while only absorbing 304 W/m2, and that would make it into a perpetual motion machine. Q.E.D.
So while a perfectly transparent atmosphere with no GHGs can reduce the amount of cooling that results from temperature swings, it cannot do more than reduce the cooling. There is a physical limit to how much it can warm the planet. At a maximum, if all the temperature swings were perfectly evened out, we can only get back to S-B temperature, not above it. This means that for example, a transparent atmosphere could not be responsible for the Earth’s current temperature, because the Earth’s temperature is well above the S-B theoretical temperature of ~ -18°C.
Having gotten that far, I wanted to consider what the temperature swings of the Earth might be like without an atmosphere. Basic calculations show that with the current albedo, the Earth with no atmosphere would be at a blackbody temperature of 240 W/m2 ≈ -18°C. But how much would the rotation cool the planet?
Unfortunately, the moon rotates so slowly that it is not a good analogue to the Earth. There is one bit of lunar information we can use, however. This is how fast the moon cools after dark. In that case the moon and the Earth without atmosphere would be roughly equivalent, both simply radiating to outer space. At lunar sunset, the moon’s surface temperature shown in Figure 1 is about -60°C. Over the next 30 hours, it drops steadily at a rate of about 4°C per hour. At that point the temperature is about -180°C. From there it only cools slightly for the next two weeks, because the radiation is so low. For example, at its coolest the lunar surface is at about -191°C, and at that point it is radiating a whopping two and a half watts per square metre … and as a result the radiative cooling is very, very slow.
So … for a back of the envelope calculation, we might estimate that the Earth would cool at about the lunar rate of 4°C per hour for 12 hours. During that time, it would drop by about 50°C (90°F). During the day, it might warm about the same above the average. So, we might figure that the temperature swings on the Earth without an atmosphere might be on the order of ± 50°C. (As we would expect, actual temperature swings on Earth are much smaller, with a maximum of about ± 20-25 °C, usually in the desert regions.)
How much would this ±50° swing with no atmosphere cool the planet?
Thanks to a bit of nice math from Dr. Robert Brown (here), we know that if dT is the size of the swing in temperature above and below the average, and T is the temperature of the center of the swing, the radiation varies by 1 + 6 * (dT/T)^2. With some more math (see the appendix), this would indicate that if the amount of solar energy hitting the planet is 240 W/m2 (≈ -18°C) and the swings were ± 50°C, the average temperature would be – 33°C. Some of the warming from that chilly temperature is from the atmosphere itself, and some is from the greenhouse effect.
This in turn indicates another curiosity. I’ve always assumed that the warming from the GHGs was due solely to the direct warming effects of the radiation. But a characteristic of the greenhouse radiation (downwelling longwave radiation, also called DLR) is that it is there both day and night, and from equator to poles. Oh, there are certainly differences in radiation from different locations and times. But overall, one of the big effects of the greenhouse radiation is that it greatly reduces the temperature swings because it provides extra energy in the times and places where the solar energy is not present or is greatly reduced.
This means that the greenhouse effect warms the earth in two ways—directly, and also indirectly by reducing the temperature swings. That’s news to me, and it reminds me that the best thing about studying the climate is that there is always more for me to learn.
Finally, as the planetary system warms, each additional degree of warming comes at a greater and greater cost in terms of the energy needed to warm the planet that one degree.
Part of this effect is because the cooling radiation is rising as the fourth power of the temperature. Part of the effect is because Murphy never sleeps, so that just like with your car engine, parasitic losses (losses of sensible and latent heat from the surface) go up faster than the increase in driving energy. And lastly, there are a number of homeostatic mechanisms in the natural climate system that work together to keep the earth from overheating.
These thermostatic mechanisms include, among others,
• the daily timing and number of tropical thunderstorms.
• the fact that clouds warm the Earth in the winter and cool it in the summer.
• the El Niño/La Niña ocean energy release mechanism.
These work together with other such mechanisms to maintain the whole system stable to within about half a degree per century. This is a variation in temperature of less than 0.2%. Note that doesn’t mean less than two percent. The global average temperature has changed less than two tenths of a percent in a century, an amazing stability for such an incredibly complex system ruled by something as ethereal as clouds and water vapor … I can only ascribe that temperature stability to the existence of such multiple, overlapping, redundant thermostatic mechanisms.
As a result, while the greenhouse effect has done the heavy lifting to get the planet up to its current temperature, at the present equilibrium condition the effect of variations in forcing is counterbalanced by changes in albedo and cloud composition and energy throughput, with very little resulting change in temperature.
Best to all, full moon tonight, crisp and crystalline, I’m going outside for some moon-viewing.
O beautiful full moon! Circling the pond all night even to the end Matsuo Basho, 1644-1694
w.
Stephen Rasey says:
January 10, 2012 at 1:31 pm
“There has to be a typo here somewhere. Totals don’t match.”
No typo. That’s how climatre boffin accounting works.
The totals actually match. 390W out, 320W in, for a NET radiative out of 70W. Net radiative in is 170W. The rest leaves by evaporation and conduction not radiation. The actual numbers aren’t right. Actual heat budgets obtained from ocean studies (use google=scholar for “ocean heat budget”) put evaporative (latent) heat loss at about 150W/m2, radiative loss at 50W/m2, and conductive at less than 10W/m2.
Latent heat loss is the big Kahuna. Willis needs to somehow get a mental grasp on the fact that evaporative cooling is about 3 times more efficient than radiative cooling. Thermal radiation is a bit player over the ocean because of evaporative efficiency. Greenhouse gases are therefore also a bit player over the ocean because their modus operandi is thermal radiation. I have explained the physics involved many times in many ways. It is explained by theoretical physics and it is evidenced in ocean heat budget studies. There is no possible informed dispute. One has to be ignorant of the material properties of water (i.e. the physics), in denial of the observations made in myriad ocean heat budget studies, or just bullheaded and incapable of admitting an error.
Willis Eschenbach says:
January 11, 2012 at 1:42 am
David says:
January 10, 2012 at 11:40 pm
Robert Brown says:
January 10, 2012 at 9:19 am
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Thank you for your educational comments. I have a question if you are willing. …
… 2. It therefore follows that any effect which increases the residence time of LW energy in the atmosphere, but reduces the input of SW and LWIR energy entering the oceans, (such as clear sky water vapor and clouds) causes a net reduction in the earth’s energy balance, proportioned to the energy change involved, relative to the residence time of the radiations involved. (To paraphrase an old maxium, one unit of energy absorbed into the oceans is worth two in the atmosphere)
I’m not Robert Brown, David, and I hope he answers you. My problem with what you say is that I have no idea what you are calling the “residence time” of energy. It would be extremely useful if you could answer the following two questions:
How do you measure the residence time of energy, and in what units is it measured?
All the best w.
—————————————————————
Thanks for the questions Willis. By rsidence time I am referring to how long energy stays within a defined area. For earth that area is the ocean, the land, and the atmosphere. As for energy I am referring to heat, as measured in W/m 2, which of course can be latent heat as in the evaporation – condensation process. Each wavelength of incoming TSI has a different residence time within the atmosphere, land and ocean. This residence time is of course affected by it own inherent properties as well as all of the material it encounters. This can be very short, almost instant in the case of some SWR reflecting from a cloud and again lost in space, to very long for some photons of SWR which reach deep into the ocean from 660 to 3,000 feet (200 to 900 meters), where only about 1 percent of sunlight penetrates. This layer is known as the dysphotic zone (meaning “bad light”). http://www.scienceclarified.com/
How much the particular W/L of energy which comprises this 1% changes from solar cycle to solar cycle is unknown. I think that the long-term balance of these flows across the ocean surface partially determines the oceanic (and therefore the atmospheric) temperature. As a result, small sustained imbalances can cause gradual temperature shifts of the entire system. Solar spectrum energy mostly goes deep into the oceans which reflect only2-3% of sunlight; and the part of the earth which is mostly oceans is in the tropics where most of the solar energy arrives.
Absorption by the the H2O in the atmosphere does warm the atmosphere; in fact it is one of the major warming influences; and that results in long wave Ir radiation in an isotropic pattern, so only half of that radiative LWIR energy comes down to the surface. The other half goes upwards to space; so there is a net energy loss to the surface of about 1/2 of the amount that H2O vapor absorbs from the solar input. Reducing the total amount of solar energy that reaches the earth surface results in it getting cooler.; that can be seen instantly in a partial eclipse of thes sun; or standing in the shadow zone of a cloud. There is no H2O vapor, liquid or solid phase phenomenon anywhere in the atmopshere where an increase in water results in an increase in the ground level solar energy. Additionally evaporation conduction of latent heat may vary far more then realized and would decrease the ability of LWIR to warm the oceans. (Newell & Dopplick’s (1979) calculations that tropical temperatures cannot rise any further.) I hope this answers your questions. A simple analogy given below perhaps help clarify.
1. On a highway if ten cars per hour enter the highway, and the cars are on the road for ten hours before exiting, there will be 100 cars on the road and as long as these factors remain the same the system is in balance. If you change the INPUT to eleven cars per hour, then over a ten hour period the system will increase from 100 cars to 110 cars before a balance is restored and no further increase occurs. The same effect as the increase in INPUT achieves can be realized by either slowing the cars down 10% or by lengthening the road 10%. In either case you have increased the energy in the system by ten percent by either increasing the residence time or the input.
2. Now lets us take the case of a very slow or long road with the same input. Ten cars per hour input, 1000 hours on the road, now you have ten thousand cars on the road. Now lets us increase the input to eleven cars per hour just as we did on the road with a ten hour residence time. Over a 1,000 hour period we have the same 10% increase in cars (energy) However, due to the greater capacity on that road, the cars (energy) have increased 100 times relative to the 10 hour road with a 10% increase in input. (1,000 car increase verses a 10 car increase.) Any change in the input or the residence time of this 1,000 hour road will have a 100 times greater effect then on the 10 hour road if the input change endures for 1,000 hours. The ocean of course is the 1000 hour road, the atmosphere is the 10 hour road.
mkelly says:
January 10, 2012 at 10:50 am
“Why is the air “very thin”?”
Because there isn’t enough of it to stay dense all the way to the moon.
“And my bet is you would freeze before you melted at the altitudes you are talking about. A molecule may be “hot” but there are so few of them you would neverfeel it.”
You’d lose that bet because the same sun that heats that rarefied air would boil you in your own juices. We’re talking 1500W/m2 up there IIRC. That’s why satellites and such that have to maintain a fixed orientation have highlyt reflective foil all over them and/or must rotate so that they are not frozen on one side and roasted on the other.
You appear to be confusing heat capacity with absolute temperature. The air there is rarefied so it has little heat capacity and thus little ability to transfer heat to solid objects with far higher heat capacities. That’s the saving grace which allows the International Space Station, for instance, to orbit through air with a temperature in the thousands of degrees. But it still is very hot and that fact still isn’t explained within the context of Huffman’s or Nikolov’s gravitational hypothesis.
Izen says
http://wattsupwiththat.com/2012/01/08/the-moon-is-a-cold-mistress/#comment-859566
Henry@Izen & Stephen Wilde
Hi Izen. Thx. The comparison of my own terrestial data (in RH) with that of the upper troposhere is a bit of a problem. It is not very likely to be comparable. As far as your 2nd reference is concerned, is seems the report is heavily biased towards ACC (AGW) and in this respect their own findings are actually somewhat contradictory.
Namely, for example, why then blame the increase in CO2 (your carbon footprint) rather then the increase in water (vapor) in the atmosphere CC?
I have posed this very possibility of an increase in water vapor due to human activities as a cause for man made warming,
http://www.letterdash.com/HenryP/more-carbon-dioxide-is-ok-ok
as very much more likely and probable than it being caused by an increase in carbon dioxide.
Both you Izen and the report say that the water content of the atmosphere has increased by 0.41 kg per m2 per decade since 1988. The units that are used here are a bit of a problem to me. How much is that in kg/m3?
1m3 air is about 1.2 kg so I don’t think the unit used is a mistake on the part of the report.
(0.41 kg per m3 per decade would mean the entire atmosphere being added with water in 3 decades and that is unlikely).
I also could not access the measuring- and standardisation procedures.
I must say that I doubt the results and I will tell you why.
I have looked very carefully at my own datasets \ 20 weather stations
http://www.letterdash.com/HenryP/henrys-pool-table-on-global-warming
and in my opinion I think that the warming is caused by more heat being slammed into the SH (oceans) due to a lesser appearance of clouds there, rather than more intense heat from the sun….
Does Stephen Wilde agree with me on that?
That being the case, (is it correct?) then my reported esitmate of -0.02% RH/ annum globally since 1974 actually makes sense (to me).
By the way Willis it was this understanding…”Solar spectrum energy mostly goes deep into the oceans which reflect only2-3% of sunlight; and the part of the earth which is mostly oceans is in the tropics where most of the solar energy arrives.” which promted me to question your assertion that albedo is greater in the tropics. ( By greater I mean the % of radiation affected) Yes the earths albedo is higher then the moons on average, but I support the possibility that it is relatively lower in the tropics and the SH. In general the oceans are a blackbody, absorbing whatever radiation reaches the surface with little reflectivity. The NH has a great deal of landmass north of the tropics, as well as year round snow and ice in the artic, as well as tremendous winter albedo beyond year round ice. The polar SH of course has antarctia with its very high albedo. Additionally the incident angle of sunligh creates ever greater reflectance as one moves further from the tropics. A further factor is the poles appear to have a great deal of consistent.cloud cover as I look at the global map on the right side of WUWT home page. For these reasons I would have to see actual meauserment to accept your assertion here, as I suspect that the tropics. especially the southern tropics have the lowest albedo as well as the greatest TSI, especially in January when the earth is thee million miles closer to the sun and TSI is close to 100 W/m2 greater then in July. Therefore the earths albedo varies far more then the moons, and may be lowesest as a % of TSI, where that energy enters the earths largest heat capacity, the oceans. This may indeed be a great factor in the earths relative warmth compared to the moon’s, despite the moons lesser but evenly distributed albedo.
Willis Eschenbach says:
January 10, 2012 at 11:31 am
“True, Joules, and there’s a good discussion of the subject here. At the salinity of most sea water (around 35 psu), the maximum density is at slightly below freezing.”
Of course it’s true. I wouldn’t have written it down if it weren’t. But that’s just an interesting factoid. The $64,000 question it raises is how the global ocean can possibly have an average temperature of 3.9C with 90% at a constant temperature of 3C with just a comparatively thin surface layer any warmer than that. It isn’t because the rocks underneath are cold. Those get up to millions of degrees G (degrees Gore).
The only explanation I can come up with is tha 3.9C is the average temperature of the surface taken over a complete glacial/interglacial cycle. IMO what we have to worry about is the fact that the Holocene interglacial and our civilization is a thin warm temporary skin floating on a bucket of icewater. Any disturbance in the force which keeps the thin warm layer from mixing too fast with the cold layer will plunge the globe back into the freezer in no time flat. Interglacials tend to have steep shoulders on them: http://en.wikipedia.org/wiki/File:Ice_Age_Temperature.png
Stephen Wilde says:
January 10, 2012 at 11:39 am
“The sun heats the surface, the surface heats the atmosphere, and the farther away from the source of heat the colder it gets. It’s the same “lapse rate” principle you experience as you move further away from a campfire.”
The heat near the campfire gets higher with more molecules
——————————————————————————
It was an analogy. Don’t try to pick it apart into quantum mechanics please. Energy tends to dissipate with distance from the source usually because it is expanding into a larger volume and where this implies an inverse square relationship between distance and intensity. The energy source is the earth. It is expanding into a sphere of infinitely larger volume. Energy density will therefore decrease with distance. Gravity has nothing to do with it. It could be a vacuum and this will still hold true so it has nothing to do with air pressure or density either.
@Robert G. Brown
So did you have time to digest the fact that seawater increases in density all the way down to its freezing point yet?
This puts a whole different spin on ocean temperature and how it got that way. A lot of people, even physics professors at Duke University, just assume it got that way because 3C is the highest density point so it sinks and becomes isolated because nothing colder can sink below it. Au contraire. Colder seawater is quite free to below it. So this must be the equilibrium temperature instead of the highest density point. Unless I’m wrong but so far no one jhas explained any other way for the ocean to be a relatively constant 3C everywhere below a few hundred meters deep. I’d really like to hear the opinion of a newly enlightened Duke University physics professor on this matter.
Izen says
http://wattsupwiththat.com/2012/01/08/the-moon-is-a-cold-mistress/#comment-859566
Henry@Izen & Stephen Wilde
Hi Izen. Thx. The comparison of my own terrestial data (in RH) with that of the upper troposhere is a bit of a problem. It is not very likely to be comparable. As far as your 2nd reference is concerned, is seems the report is heavily biased towards ACC (AGW) and in this respect their own findings are actually somewhat contradictory.
Namely, for example, why then blame the increase in CO2 (your carbon footprint) rather then the increase in water (vapor) in the atmosphere CC?
I have posed this very possibility of an increase in water vapor due to human activities as a cause for man made warming,
http://www.letterdash.com/HenryP/more-carbon-dioxide-is-ok-ok
as very much more likely and probable than it being caused by an increase in carbon dioxide.
Both you Izen and the report say that the water content of the atmosphere has increased by 0.41 kg per m2 per decade since 1988. The units that are used here are a bit of a problem to me. How much is that in kg/m3?
1m3 air is about 1.2 kg so I don’t think the unit used is a mistake on the part of the report.
(0.41 kg per m3 per decade would mean the entire atmosphere being added with water in 3 decades and that is unlikely).
I also could not access the measuring- and standardisation procedures.
I must say that I doubt the results and I will tell you why.
I have looked very carefully at my own datasets \ 20 weather stations
http://www.letterdash.com/HenryP/henrys-pool-table-on-global-warming
and in my opinion I think that the warming is caused by more heat being slammed into the SH (oceans) due to a lesser appearance of clouds there, rather than more intense heat from the sun….
Does Stephen Wilde agree with me on that?
That being the case, (is it correct?) then my reported estimate of -0.02% RH/ annum globally since 1974 actually makes sense (to me).
AAAARgh
it (the system) does not want to notify me of follow up comments
I try again
Willis,
The adiabatic lapse rate fixes the relationship of pressure to volume, PV^γ = constant. The value of γ is determined by the ratio of the gas heat capacity at constant pressure to the heat capacity at constant volume, which in turn is related to the degrees of freedom of movement of the gas molecules or atoms. So if the atmosphere must have an adiabatic lapse rate, or indeed any fixed lapse rate, then the surface temperature determines both pressure and density of the atmosphere at any altitude.
Joules Verne,
The ocean behaves like the atmosphere only it’s much less compressible. If the temperature decreases with depth, you don’t get convection because the warmer water above is less dense than the colder water below. At the poles, the surface water becomes colder with higher salinity because of evaporation so it’s denser than the water below and it sinks. That forces upwelling everywhere else, more some places than others. But the surface of the ocean in the tropics and mid-latitudes is warmed by sunlight. Turbulent convection, also called eddy diffusion, carries that heat from the warm surface toward the colder depths. But since you also have upwelling cold water, you get a steady state where the warm surface water transitions to the cold deep water. That’s the thermocline. The depth of the thermocline varies seasonally, but the average depth remains constant.
DeWitt Payne says:
January 11, 2012 at 7:57 am
Good points. Thanks. I wonder how high up those effects would reach. The jet stream is currently located just below the tropopause, a feature that is created by greenhouse gases. Perhaps a similar stream would occur at the top of the nightly temperature inversion. Or perhaps the inversion would be more permanent because cold air might tend to flow from one pole (winter) to the other (summer).
DeWitt Payne says:
January 11, 2012 at 7:57 am
“Absent greenhouse gases, the atmosphere would not be isothermal. The surface temperature at the poles would still be colder than the surface temperature at the equator. That means the pressure will decrease less rapidly with altitude at the equator than at the poles. That causes what’s called a pressure gradient force which in turn causes air circulation. Any air circulation will move heat around and force the lapse rate towards the adiabatic rate. ”
Very true, DeWitt. Even on Venus with a practically opaque atmosphere (the opposite condition) the convection bands are clearly visible, and there heating would be from near the top of the atmosphere. It seems that in the real world with a fluid atmosphere convection is ubiquitous and you can’t escape the adiabatic lapse rate. Probably even true of the ocean. I’d caution Nicol that composition does affect lapse rate tho’.
Joules Verne says:
January 11, 2012 at 6:43 am
@Robert G. Brown
So did you have time to digest the fact that seawater increases in density all the way down to its freezing point yet?
This puts a whole different spin on ocean temperature and how it got that way. A lot of people, even physics professors at Duke University, just assume it got that way because 3C is the highest density point so it sinks and becomes isolated because nothing colder can sink below it. Au contraire. Colder seawater is quite free to below it. So this must be the equilibrium temperature instead of the highest density point. Unless I’m wrong but so far no one jhas explained any other way for the ocean to be a relatively constant 3C everywhere below a few hundred meters deep.
As far as I’m aware it’s always been explained by the high density, cold salty water produced in the North Atlantic and Southern Ocean descending to the ocean floor and circulating, it takes about 1500 years to return to the surface if I recall.
I would suggest that a non-GHG atmosphere could make the moon much warmer than it is now on average.
I think that I agree, although I’m still working on just how and why. However, one has to be careful — Willis proposes a perfect non-GHG atmosphere, which is probably self-contradictory — matter is made up of charge, charged matter interacts with the electromagnetic field and has a heat capacity, and surrounding the earth with a neutral dielectric material with a heat capacity would suffice to trap some radiation and warm the surface, I think. I suspect that this is probably the reason that there is (if the NZ curve is correct — I do not have any easy way to check that it is) that there is an heuristic/empirical relationship between density of atmosphere and surface temperature. The GHE simply takes into account nonlinear gain due to the nonlinear susceptibility of real gas components, but I suspect there would be some linear gain without it. But I haven’t worked out the algebra, so I’m not certain.
I also don’t know about the word “much”. Without a physical argument in mind, it is difficult to estimate an order of magnitude, don’t you think?
The reason I think that it would increase surface temperatures (on average) is simple enough. Sunlight comes in (warming the atmosphere and the surface in some differential way, we’ll assume warming the surface a lot more than the atmosphere because the latter is “transparent”. As the surface warms, it further warms the atmosphere, setting up convection rolls that lift heat from the surface up and bring cold “air” down to be warmed, gradually mixing to distribute the heat in the atmosphere. The surface has a low albedo; the atmosphere doesn’t really have much albedo. The surface has a high emissivity, the atmosphere has an emissivity (it is made up of dielectrically polarizable charges) but we’ll assume that it is relatively low as well, see “transparent” to first order.
This daytime cooling of the surface reduces its peak temperature and hence lowers (on average) its loss of energy during the day, while at the same time storing some of the energy in the atmosphere. Quite possibly a lot of energy (a significant fraction of the total incident heat, that is). Nighttime falls, and the cycle reverses. The surface radiatively cools until it is cooler than the air, but the vast convective rolls established during the day have an inertia and air continues to flow over the surface, warming it, especially if there is differential cooling (regions with different emissivity and albedo and hence different temperatures during the day) to continue to help drive convective heat transfer. Even a non-GHG will also return some of the heat absorbed during the day to the ground (slowly, sure, with its lower emissivity) in the absence of convection, just as the non-GHG will slowly cool via radiation on its own while still absorbing some of the heat given off by the ground and slowing its transit out of the system.
Even without this, however — even if the wind stops and one straight up radiatively cools the surface, chilling a surface layer of air by (slow) conduction — one cools from a lower initial temperature and so the cooling is slower, less net energy is lost than would have been otherwise. Temperature inhomogeneity favors cooling, and by storing heat in the atmosphere it acts as “thermal ballast” to reduce the daytime peak temperature and nighttime minimium temperature by absorbing and storing some of the heat in the day and giving it back at night.
Make the air wet air, add water to the mix, even ignoring its GHG properties, and things change once again. Oceans act as major thermal reservoirs that do two things. One is drive trade winds and climate oscillations — large scale thermal imbalances, sustained over long times, cause huge chunks of atmosphere to get caught up moving in giant closed loops. These loops enormously enhance the process above, again quite independent of GHE per se. You have two big reservoirs for solar thermal energy buffering the daytime-nighttime fluctuation, reducing (mostly) thermal variation, and hence (mostly) increasing the global mean temperature. You’ve put the planet in a blanket (the atmosphere) with a hot water bottle that warms more during the day than it cools at night) the oceans compared to the land, buffering surface temperatures on a decadal timescale on Earth.
I don’t remember who it was — Willis, Crosspatch, somebody — who suggested on this or some other thread that the ocean was the elephant in the room that was being carefully ignored compared to the GHE. I’d say it is one of an entire menagerie — there are multiple reservoirs of heat, all of which contribute to net warming outside of the GHE, so that the warming we observe from the theoretical “vacuum Earth” estimate is not all CO_2 based GHE warming, it has to be split up. I’m guessing — guessing in moderate ignorance, mind you — that it should probably be split up roughly in thirds — if the anomaly in the mean is 30C, 10C of that is probably due to the ocean, 10C is probably due to the fact that we have an atmosphere, and 10C is due to GHGs. But it could be 15, 10, 5; 10, 5, 15, or some other split — without solving a complete coupled hydrodynamic radiative model including the ocean and continental structure and solar coupling including any GCR variation-linked effects and… it would be very difficult, I think, to soundly justify one split or another outside of pulling numbers out of your ass. Maybe not — its the kind of thing were I’m open to argument.
But any assertion that Earth lacking CO_2 altogether would suddenly revert to the same mean temperature as the moon seems as though it would be obviously false. It might kick us into permanent glaciation, but I can’t see the tropics ever permanently freezing. We probably got close to this in the last glacial epoch, where it is asserted (based on evidence) that atmospheric CO_2 dropped to 180 ppm, roughly 1/2 what it is today. Again, if there were a hole pointing downward toward true coldside catastrophe, atmosphere freezing out and all that, this sort of event would likely have triggered it. Negative feedback from the ocean and the rest of the atmosphere very likely blocked that kick; clearly the Earth was able to warm back to interglacial (current) average temperatures.
rgb
“I have looked very carefully at my own datasets \ 20 weather stations
http://www.letterdash.com/HenryP/henrys-pool-table-on-global-warming
and in my opinion I think that the warming is caused by more heat being slammed into the SH (oceans) due to a lesser appearance of clouds there, rather than more intense heat from the sun….
Does Stephen Wilde agree with me on that?”
Hi Henry.
I agree that the data does seem to show that cloudiness globally did decrease during the late 20th century warming spell.
I put it down to more poleward/zonal jetstreams. Svensmark thinks it is due to less cosmic rays but I think he is wrong.
Since the late 90s the jets started to become more equatorward/meridional and global cloudiness is on the rise again. Meanwhile ocean heat content has stopped rising.
Interesting that the sun is less active too !!!
“You’ve put the planet in a blanket (the atmosphere) with a hot water bottle that warms more during the day than it cools at night) the oceans compared to the land, buffering surface temperatures on a decadal timescale on Earth.
I don’t remember who it was — Willis, Crosspatch, somebody — who suggested on this or some other thread that the ocean was the elephant in the room that was being carefully ignored compared to the GHE”
Yay !!!
http://climaterealists.com/index.php?id=1487&linkbox=true&position=5
“The Hot Water Bottle Effect”
It has taken nearly four years but is now entering the vernacular.
The tides slow down the rotation they don’t lock it into any specific configuration. This loss in angular momentum is of course translated into heat. If it weren’t for mass distribution asymmetry what would determine which half of the moon would come to rest facing toward us? And if there is no preference for any particular face how can a particular face be the chosen one? In other words why isn’t it the other side of the moon that’s facing us?
Consider a pendulum with a frictionless pivot. Give it a kick strong enough to make it rotate. It will rotate forever, because gravity points down and exerts no torque, and we made the pivot frictionless so that won’t slow it down either.
Now add damping — damping that is strictly due to oblate deformation in the case of the moon as both I and all of the textbooks assert and as you can easily understand by looking at simple mechanical pictures and can even test by comparing to a derived equation, but we might as well damp from the pivot for our pendulum example, or if you want a less extreme example a rotating disk with one side heavier than the other. As long as the pivot exerts a damping torque, it slows down, until eventually the energy needed to rotate the heavy side up and over the top is less than the energy available in the system, The heavy side rises one final time and — a-l-m-o-s-t — makes it over the top, but then it falls back. It now behaves like an ordinary damped oscillator until it comes to rest, heavy side down.
In the specific case of the moon, the tidal forces on the near side and far side of the moon aren’t quite symmetric. They are only symmetric to leading order. If you want, I’ll either derive or point you to a derivation of the effective tidal force/field on the near side vs the far side, but I assure you that they aren’t identical and that the near side field is slightly stronger. Given that the moon is still (probably) internally molten at this point — remember, the damping force that slowed it down was plastic deformation that heated the interior of the moon right up to the point where the moon was fully tidally locked — slow oscillations as it came to rest “shook” a small surplus onto the side facing the Earth.
Personally I doubt very much that there was much average azimuthal asymmetry in the mass distribution of the moon throughout the damping process. The moon was far closer to the Earth, and the tidal forces acting on it were far stronger (perhaps 8x stronger or thereabouts, again, can’t remember the number and am too lazy to look it up, but it is known because it is computable from current observations and models). The moon was almost certainly still a relatively thin and uniform crust surrounding a more or less equilibrated interior of hot squishy rock, kept uniform by the fact that it was literally turning on a spit that exposed the entire moon to the same deforming forces, day after day after day as the tidal bulge chased the Earth-centered antipodes. So I think that most of the asymmetry was created during the cooling process. But I don’t much care — the simple, easy to understand, and obviously correct physical argument above shows you how the heavy side would always end up “down”, facing the earth, even though “down” is an inverse fourth-order down compared to gravity (second order) and tide (third order).
rgb
David says: (a bunch of stuff).
Yeah, sounds very reasonable, and I pretty much agree. Both the ocean and the atmosphere without considering GHGs contribute to the net warming of the surface relative to an atmosphere-free planet, both by doing nonlinear stuff that traps heat (in the case of oceans) on their own and by acting as thermal ballast in a vast circulatory model that stores some of the heat that would otherwise “just” warm the surface and radiate back to space.
Personally I have little feel for the relative magnitudes (as I just mentioned on another thread) but the total “anomaly” of the Earth above the “vacuum Earth” purely radiative temperature really needs to be split up among GHGs, atmospheric convection (for a wet atmosphere with all sorts of complexity including vast decadally-sustained patterns of atmospheric heat and moisture transport) and the ocean, or maybe between GHGs, Water, Air (GH neutral, mostly), and GHGs with a strong absorption in the IR. There is no way that all 30C (or whatever) is “just” due to CO_2. It may well be that most of it is not due to CO_2. As I said, I don’t have a good idea of the physics here — I’m still a, what was the word my Ph.D. advisor used after prelims, oh, yeah dilletante of climate science, learning as I go.
rgb
The only explanation I can come up with is tha 3.9C is the average temperature of the surface taken over a complete glacial/interglacial cycle. IMO what we have to worry about is the fact that the Holocene interglacial and our civilization is a thin warm temporary skin floating on a bucket of icewater. Any disturbance in the force which keeps the thin warm layer from mixing too fast with the cold layer will plunge the globe back into the freezer in no time flat. Interglacials tend to have steep shoulders on them: http://en.wikipedia.org/wiki/File:Ice_Age_Temperature.png
Just to show that I don’t always argue with you, I agree about the Holocene being a warm skin floating on a bucket of icewater, and the Younger Dryas is evidence (if hypothesized Oceanic Conveyor Belt explanations are correct) that disturbing the surface transport of stored heat can quickly kick the Earth back into the deep freeze. I also think that there is considerable cause for 40,000 year concern — the general trend of glaciation seems to be getting colder during the glacial eras, and it doesn’t need to get much colder at the coldest to enable various catastrophes that seriously compromise the human race’s ability to survive at current population levels with anything like our current technology.
As for the 3.9C — oceanic ice forms in a complex way, because salt water has a lower freezing point than fresh water. Hence ice nucleation is around fresh-direction fluctuations and both grows preferentially with fresher water (increasing the salinity of what it leaves behind) and actually sheds salt, which remains liquid, more dense, and melts its way through the ice. Icebergs are hence (mostly) fresh water, and I’m guessing that they precipitate out at the point where the greatest freshwater density occurs (nucleation point) as that is where there would begin to be a chemical potential favoring separation. The heat of fusion goes back into the ocean, carried by the (more saline) salt water. Ocean ice still floats, which forms a nice insulating layer with more or less fixed temperature on the lower surface of the ice. So the ocean still doesn’t freeze from the bottom up, but from the top down, and otherwise I agree about the downwelling and upwelling and OCB and all that.
I would expect that another contributor to bottom temperatures — possibly weak, but not necessarily negligible — is outgoing heat from the Earth. Yes, the energy flux is low, but the energy released at the bottom doesn’t go anywhere in a hurry, so there a long time for heat to accumulate. It might be enough to keep the bottom above freezing even if the ocean otherwise froze all the way down to near the bottom.
I don’t think that it is “just” the average temperature over the entire glacial cycle. For one thing, it doesn’t really match the average surface temperature during glaciation, let alone during the warmer glaciation. Also, IIRC the timescale for oceanic equilibration is supposed to be roughly 1000 years. That means (if true) that it is well-equilibrated as far as things like average temperature are concerned during the Holocene, and the rapid plunge is somewhat more likely to be due to flipping from one global pattern of heat transport (primarily confined to the surface) to another more than major bulk alteration of overall heat content.
But I’m happy to be educated, here, if you know better.
rgb
The adiabatic lapse rate fixes the relationship of pressure to volume, PV^γ = constant. The value of γ is determined by the ratio of the gas heat capacity at constant pressure to the heat capacity at constant volume, which in turn is related to the degrees of freedom of movement of the gas molecules or atoms. So if the atmosphere must have an adiabatic lapse rate, or indeed any fixed lapse rate, then the surface temperature determines both pressure and density of the atmosphere at any altitude.
Ah, this is exactly what I was missing in this discussion. OK, assuming I know what \gamma is and all about these relations (true enough) where can I learn about it in the direct context of the atmosphere and convection? Also assume that I can do algebra and calculus and even PDEs and all that (I’m a theorist and can do serious math if my interest motivates it). Ideally a reasonably easy introduction — baby steps first…
By the way, your replies are cogent and clearly well-founded. I appreciate it. I’m guessing that this is directly related to the way the atmosphere stores dayside/tropical heat and moves it in all-scale convective rolls north and south, coriolis and continent deflected into major surface patterns, which is the way even a GHG-free atmosphere would reduce the moon-like rates of cooling by establishing more uniform overall temperatures, right?
rgb
Robert Brown,
My introduction to Physical Meteorology was by reading Rodrigo Caballero’s Lecture Notes on Physical Meteorology ( http://maths.ucd.ie/met/msc/PhysMet/PhysMetLectNotes.pdf (big, 28 MB pdf). He’s located at University College Dublin. This is something of a work in progress and has expanded over the years. I presume that it will eventually end up as a textbook. If you have access to a University library, you could probably find other textbooks like Curry and Webster’s Thermodynamics of Atmospheres and Oceans, Ray Pierrehumbert’s Principles of Planetary Climate or Grant Petty’s A First Course in Atmospheric Thermodynamics. If I were going to buy one myself, I would go with Grant Petty because I find his A First Course in Atmospheric Radiation indispensable. It may not be as rigorous as Goody and Yung, but it’s very accessible. Both of Petty’s books can be ordered direct from the publisher, Sundog Publishing, at a significant discount.
As to your question on circulation, I think that’s correct, but I’m still learning about this stuff too.
Robert Brown says:
January 11, 2012 at 12:16 pm
“Consider a pendulum with a frictionless pivot. “
Bad analogy, unless you specify where the pivot is located. In space, the “pivot” is at the CG. A better analogy would be a dumbbell supported at the midpoint. There is no preference for heavier or lighter side to end up facing the Earth. It is a flip of the coin.
The theory for this is exceedingly well-established, as hundreds of satellites relay upon gravity gradient stabilization (which you can google for voluminous references) for attitude control or attitude assist.
“…rely upon…” a
I should have mentioned, what happens is, the minimum energy configuration is one in which the object ends up rotating about its major axis of inertia, whereas the minor inertia axis ends up parallel to the Earth-to-satellite vector.