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.
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The estimate of 4C an hour for cooling at the surface over a desert on earth is a pretty good one, but probably not realistic for the cooling seen at the lunar surface when the sun sets. Measurements during lunar eclipses indicate peak rates of about 30C an hour or around 100C during the full length of the eclipse (around 4.5 hours).
Noted. I looked to see if I could find an online computation of the cooling rate T(t) of an ideal spherical surface layer subject to some reasonable assumptions — largely because I am too lazy to WILLINGLY compute it myself, it’s a fair amount of work — just to see if one can get an order of magnitude feel for what it “should” be. Basically integrating Stefan-Boltzmann, taking the heat capacity of the surface up to some depth as the reservoir. Since linear (in T) loss would produce an exponential, the T^4 suggests T(t) is much faster than exponential, so that it loses a lot of heat very quickly, but the rate of heat loss drops dramatically with the temperature. So it isn’t completely crazy for the cooling rate to be down to 4C/hour at the terminator, if the temperature there is already down close to 0C.
I have so very much to do, and this is so very entertaining and distracting, but if I actually finish some good fraction of my chore list I’m thinking seriously of building a model of my own. I downloaded rttm so that I could take a look at it and might use it as a base, but sometimes there is virtue in trying something on your own first and then looking at what others have done — it’s easier to find something they might have missed or a mistake they might have made if you aren’t “trapped” into following their reasoning.
Hopefully rttm does the full computation “right” — spatially and temporally inhomogeneous, with emissivity a function of temperature and wavelength, and so on. I’m still very curious about how they manage the interaction between convection and GH — bulk convective cooling leading to vertical heat transport is roughly the same order as radiative cooling (more, if there is a wind) and carries hot air up through the densest layer of atmosphere near the ground to where it can radiatively cool more efficiently, an effect that should be strongly enhanced by water vapor carrying heat of vaporization up above that dense layer. In other words, I’m curious as to whether they correctly integrate in the vertical direction and hence end up with too much GHE trapping.
I suppose the best analogy is that the atmosphere isn’t like a “greenhouse”, a ground surface and an IR absorber over head. It is more like a ground surface and a large collection of very thin (much weaker) IR aborbers placed so that air and moisture can easily convect up through them, while their integrated thickness is the same as that of the original IR absorber in the glass house model. Convection carries warm air from the ground up through most of the plates to create a warm layer at the top that cools much faster via radiation than the air or ground at the bottom, then falls back both cooling the plates themselves in an irregular pattern (reducing surface trapping of the heat) to pick up still more heat from the surface and lift it, warming the plates where it lifts. This would very quickly create inhomogeneous surface temperatures fed by semistable convective rolls that cools the surface with a wind much faster even than the initial convection, and much faster than radiation. To make matters even more complicated, the “plates themselves” are just CO_2 molecules and get lifted up to cool faster than pure radiative transport in a static atmosphere would would allow, so there is a constant turnover of the plates as they absorb down low and emit up high.
The point — consistent with the entire discussion so far and Willis’ analysis above — is that any system with an atmosphere self-organizes(creating hot and cold differential) to lose heat faster than any static model (or model with the wrong transport dimensionality) predicts. The entire “greenhouse” is turning over all the time it is functioning, cooling the ground by direct wind-driven convection and evaporation and carrying heat to the top to be lost through a much thinner greenhouse than one expects just looking at lower troposphere. The correlation of the current not-so-warming trend with a surprising drop in stratospheric H_2O seems to add some weight to the possibility that this isn’t being done right. As the stratosphere dries, it could significantly enhance cloud-top cooling — even “resonantly” enhance, as it leaves a growing hole right where water vapor is radiating.
rgb
@Robert brown –
even more outrageous than the survey on the quad about the moon-
ask around to see what color people think the sun is – and it’s not like they had no acquaintance with it.
but most of em will grab the yellow crayon.
Tidal locking (the more commonly used term than gravitational locking) is a little misleading as it has nothing to do with tides on the earth. It begins with a mass distribution asymmetry in a smaller rigid body. The earth’s moon is large enough to form a gravitationally shaped sphere but the mass distribution won’t be perfect even if the spheroid shape is perfect. The heavier side of the smaller body will eventually come to constantly face the larger body.
Joules, you are dead right about your cynicism exceeding your IQ. I tend to think that it isn’t a matter of formal education being “a racket” as much as it is due to a mix of a distribution in abilities plus the fact that most humans — and I’ll include myself in this — are not Holmesian in our powers of observation or inference. Also, for most people using their brain seems to hurt, or tire them out, or something. It isn’t pleasant. Not entirely unreasonable — the brain burns between 1/4 and 1/3 of one’s daily calorie intake, and we are bio-programmed to conserve energy (the reptile within is a lazy bastard that wants only to bask on a rock, get laid, and eat, in complete safety).
As for your remark, it has nothing to do with tides on the Earth, it has everything to do with tidal “force” on the moon where I’m pretty sure you understand why I put the word force in quotes, as the “tidal force” is just the (negative of the) difference between the actual gravitational force and the total force acting on different mass points in an extended object accelerating in some way relative to the attracting body. Points on the tidally locked moon (good catch, I was just trying to convey the idea but you are right) that are closest to the Earth experience too much gravitational attraction to be in “orbit” and hence require less force to oppose the moon’s gravitational attraction in the opposite direction. Points on the opposite side from the earth experience too little Earth gravitation to be in orbit, the difference is again made up by Moon gravity at expense of the e.g. normal force holding them up. Hence a bulge in both directions, that isn’t quite symmetric (in higher order than third), so indeed the heavier side ended up facing the Earth.
However, tidal forces also likely contributed to the bulge and mass asymmetry in the first place. The moon isn’t (or wasn’t, as it became locked) a completely rigid body.
Tidal force from the moon (and sun, much larger but much farther away) acting on the earth is very, very slowly slowing it down so that at some point in the very distant future the Earth and the Moon, given time, they would be mutually tidally locked. I can’t remember if the Sun will have done the red giant thing or not by then, so this may not happen before there is no more Earth or Moon to lock. In any event, human-derived life forms will either be extinct or have moved on by then to other worlds, and the molecules that currently make “me” up will probably not even be locally contiguous any more, so I suppose it isn’t worth worrying about:-)
rgb
Willis, I don’t know if you’re still reading the comments. But this is simple, straightforward, thank you. It may be stating the obvious, but often the obvious is overlooked. The bigger the temperature difference (slower the rotational speed), the lower the AVERAGE temperature.
Would make for an interesting hypothesis for partially explanating the “small sun, warm earth” paradox of the early solar system.
Septic Matthew says:
January 9, 2012 at 1:54 pm
Joules Verne: One of the most crucial facts to understand is that the ocean cools primarily through evaporation not radiation. If the ocean doesn’t cool by giving off longwave thermal radiation then it wont’ be warmed that way either. Therefore greenhouse gases that produce downwelling longwave radiation have little effect on the ocean.
“What exactly does the downwelling longwave radiation do to the surface of the water?”
It is completely absorbed in the first few microns of depth. It raises the evaporation rate and in most cases is not propagated downward. The result is called the cool skin layer which is approximately one millimeter deep and is 1-2C cooler than the water below it. The cool skin layer is the predominant condition of the ocean surface. Breaking waves can obliterate it but it reforms in about 10 seconds.
Someone in this thread mentioned that the greenhouse effect is caused by increased residence time of insolation due to the variable properties of the earth’s surface. The global ocean is actually the big kahuna in this regard. The ocean is transparent to incoming shortwave which penetrates at the speed of light to a depth of about 100 meters depending on water clarity. Water is opaque to longwave so the solar energy absorbed at depth must be mechanically transported to the surface for emission. This increases the residence time of the insolation and causes the ocean to warm up higher than its S-B temperature in order to attain equilibrium. The majority of greenhouse warming is accomplished by a liquid ocean that covers 70% of the earth’s surface not the tenuous and far less effective greenhouse gases in the atmosphere. Take away the ocean and leave everything else equal and the earth would be a giant deep freezer.
“I’m trying to see the various reasons why the earth stays so much warmer than its S-B temperature.”
Basically, you assume the “blue dot” is a black body with no atmosphere and no gravity, i.e., the only contribution to the thermodynamics is the radiative piece – while ignoring the “elephant in the room”, namely, the atmosphere and gravity.
Yet it’s trivial to estimate the effect of gravitation on the atmosphere and it’s influence on the Earth’s surface temperature by using the equations of state starting at the -18C degree surface (roughly 40km above the Earth) and dropping down to the surface.
Then there’s the single point temperature measurement on the Moon which clearly shows a constant “nightly” decay in temperature which is only interrupted by “dawn”. Do you have any idea what the data is telling you?
@rgb
You have the cart before the horse. The fixed tidal bulge only emerges after tidal lock has occured. Before that point the tidal bulge travels along the surface. And yes the moon isn’t completely rigid but it’s pretty darn close and in the context of my missive it is completely rigid as higher density features within it don’t migrate. A small tidal bulge occurs as it flexes but the ellipsoid shape today happened after it became tidally locked not before. In its early history it was presumably a perfect sphere and was not tidally locked with the earth so the tidal bulge that, if fixed, could serve as a torque point to keep it tidally locked, was free to migrate across the surface. It is density asymmetry that produced the initial torque and established exactly which portion of the moon came to permanently face the earth. After that it became ellipsoid to the degree that it isn’t quite a completely rigid body.
From Mike Maxwell on January 9, 2012 at 6:42 pm:
Thanks for catching that. I should have gone with the rotational speed, not the actual speed. Geostationary orbit does seem boring though, with the Moon always directly above about the same spot always, thus depriving about half of the planet from ever seeing it at all, with nights that are exceptionally dark. An additional complication, there are also biological cycles that appear tied to the Moon’s transit around the Earth, such as the menstrual cycles of human females, and many predators and other creatures are nocturnal and need that limited amount of moonlight to see. With a fixed moon, who knows how such would be disrupted.
The mass of the satellite factors out, so that wouldn’t be an issue. What could be important is the exosphere, Earth’s highest atmospheric layer. The upper boundary in theory is about 190,000 km from Earth, about half the distance to the Moon. With the considerably closer position of a geostationary Moon, this could lead to atmospheric drag and the Moon eventually spiraling into the Earth if we don’t speed it up again. That would also be close enough that the Moon could start trapping particles from the Earth’s atmosphere.
Except in a geostationary orbit there wouldn’t be any lunar-influenced tides, as the moon would be in a fixed location relative to the surface of the Earth. No moving Moon, no such tides. The constant fixed pull would draw water to “under” the Moon leading to a fixed amount of rise, eventually the Earth itself would distort into a bulge. But we wouldn’t have those tides, and we likely would have less earthquakes and volcanic activity without the regular lunar-induced flexing of the Earth’s thin crust, although geological forces may become more pent-up leading to more powerful events.
…reduces the Albedo
I believe you meant to say that clouds increase the albedo, reflecting more heat away during the day and trapping more heat at night.
Clouds are a source of great controversy — and uncertainty — in climate models. Catastrophic models all assume that warmer temperatures leads to more water in the atmosphere leads to more net heat trapping, positive feedback. However, this is a vastly oversimplified statement. A number of studies have shown that a wetter environment cools faster because evaporation is a very efficient heat loss mechanism. One of the big factors in UHI effects is the lack of green plants, that cool the ground as they absorb energy, store some of it, use some of it to pull water out of the ground, and then respire, releasing water vapor. Warm water vapor gets carried up in convective rolls to the cooler upper atmosphere where it condenses, releasing the heat of vaporization into the air far above most of the greenhouse effect, and eventually falls as rain that is usually cooler than the ground or ocean it falls on, cooling it by conduction. Clouds over the polar circle regions at night trap heat so that they cool more slowly (net warming). Clouds over the tropics tend to reflect more heat and have a net cooling effect.
This all isn’t simple and cannot be reduced to a sound bite that should convince us that it is “settled science” that more water vapor in response to enhanced CO_2 GHE produces net positive feedback and a higher climate sensitivity, independent of the state of the sun. Nor should it blind skeptics to the possibility that it could lead to positive feedback and a higher climate senstivity. The fact is that at the moment we do not know for certain what it does, in part because the major oscillations have a major effect on the distribution of clouds at different times of the year. Spencer argues, not unconvincingly, that negative-to-neutral is most consistent with the data, but we really don’t have very good data for even a single whole cycle of many of the major oscillations, and one would really want to observe them over several cycles (or come up with really good models that match and predict them) before calling anything settled. Or both. Say, 100 years or so more observation and computational work and we’ll “settle” this, maybe, depending on what we eventually conclude about the role of the Sun and how chaotic everything turns out to be.
But I do think that by far the most plausible suggestion is that the Earth nearly always self-organizes in response to additional forcing to increase, not decrease, its differential rate of cooling. That is, there are good empirical reasons to think that overall feedback is consistently negative — as Willis has noted, the total temperature variation we’re seeing over the entire Holocene (excluding the Younger Dryas) is order of a couple of degrees C, order of 1% of the mean temperature of the Earth, with variations per century that are only rarely half as large and are usually smaller. Hard to imagine this without negative feedback — one would expect much larger and more violent excursions of temperature in the past. To put it another way, if the system were near a “critical point” one symptom that is expected is a gradual divergence in the response to fluctuations (fluctuation-dissipation theorem). The “susceptibility” of the system should increase. This is the warmist prediction of “more violent storms” and the like — a strong and rapid increase if we were near a “catastrophe” (or “phase” transition to a much warmer phase).
The data, however, shows nothing of the sort. There has been basically no statistically significant change in the frequency or violence of storms, or in the total energy being dissipated in storms. What variation there is is reasonably well understood as response to the major climate oscillations, notably ENSO and factors such as rainfall in West Africa and tropical SSTs and the prevalence of upper atmospheric shear. In a way, it is almost surprising — storms arise from temperature differentials and cool the planet faster than it would cool without the storm (they consume free energy, if you like). The flatness in the total energy dissipated in tropical storms actually argue for the flatness of tropical temperatures across a suprisingly long period. Even given a very simple linear response model one would expect at least a linear growth in strength.
This argues for strong negative feedback, or perhaps more likely confounding factors that have nothing to do with global temperature. Complex system, not well understood, not settled science.
rgb
Agile Aspect says:
January 10, 2012 at 9:10 am
If it’s all about gravity then why does the lapse reverse and the atmosphere become increasingly warmer with increasing altitude past the thermopause?
Gravity does not cause heating once the compressive and expansive forces become equal. Since the acceleration of gravity here is constant at 32 feet/sec^2 and the composition of the atmosphere, and indeed the surface pressure, is relatively constant, there is nothing that gravity is doing to cause a temperature gradient in the atmosphere. 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 lapse rate reverses at altitude even though pressure keeps on decreasing because very energetic portions of solar spectrum which don’t penetrate to lower altitudes are absorbed by the very thin air and heat it up to thousands of degrees at the farthest reaches of the atmosphere.
This increases the residence time of the insolation and causes the ocean to warm up higher than its S-B temperature in order to attain equilibrium. The majority of greenhouse warming is accomplished by a liquid ocean that covers 70% of the earth’s surface not the tenuous and far less effective greenhouse gases in the atmosphere. Take away the ocean and leave everything else equal and the earth would be a giant deep freezer.
Well said (and quite correct), sir!
Add to that the fact that water achieves its greatest density around 4C, not coincidentally the mean temperature of the ocean and the actual temperature of nearly all of the oceans, starting a few hundred meters below the surface. If water achieved the greatest density like “normal” fluids, at its freezing point of 0C, the oceans would freeze from the bottom up, not the top down, and the earth would be a giant deep freezer because once the surface froze (at the poles) it would never, ever melt to the depths, and the high albedo of ice would slowly, surely, cover the entire planet with ice.
Much of the surface cooling away from the oceans involves water as well, especially where there are green plants, lots of trees, that sort of thing. Changes in land use (cutting down vast stretches of forest, introducing goats to e.g. the Sahara) very likely did in the past and continues to have today a profound anthropogenic effect on the local warming or cooling of comparatively large areas of the planet’s surface, the UHI effect being just the tip of the iceberg, so to speak, in this regard. There’s also the “cultivated field vs forest full of trees” effect, the “didn’t this desert used to have plants on it?” effect, the “let’s irrigate the hell out of things” effect, the “let’s dam this river and make a big lake” effect, the “Oh hell, it’s too much of a hassle to site our weather station out in the middle of a forest-surrounded field, let’s just put it here next to the building on the southwest side” effect, and many more effects that all contribute to measured warming and cooling.
That’s why UAH rocks. Satellites rock. We can’t trust anything global about temperature data before roughly 1979, and have to take local data with several well-considered grains of error-bar salt. Even the satellite data is worrisome (for well-enough understood reasons) but at least there is a chance that we can build up a century’s worth of consistently measured data with the same general systematic and random errors over time.
In the meantime, the ocean is this enormous reservoir of slowly turning over heat, with timescales ranging from hourly to a thousand years all contributing. It is thermal ballast that both dampens major temperature fluctuations and (via evaporation) self-organizes in response to increased heating and coupling with atmospheric circulation into structures with increased net cooling — like hurricanes, thunderstorms, plain old rain, large patches of cumulus clouds, updrafts, downdrafts, high and low pressure center circulations that take heat and move it around, generally to cool the hot spots, warm the cool spots, and increase the rate of over all cooling as it does so.
rgb
Willis,
Very nice exposition on T^4. I’m not at all disturbed that you got some details wrong. That will be (and is being) corrected. The essence of your argument is the important thing.
@rgb
There are two great attractors in the earth’s climate system. One is a completely frozen world and the other is a completely unfrozen world. Antarctica was covered by temperate forest more than several million years ago. The warm attractor historically dominates over the cold attractor by time factor of about 10:1. It’s all about albedo. Ice and snow breed more ice and snow by reflecting solar energy which would be absorbed if it was ocean or rocks instead of snow and ice. Non-condensing greenhouse gases probably take on their main role in the climate when the cold attractor is in force. On a frozen world the sinks that normally scrub volcanic CO2 from the atmosphere are missing in action thus the gas is free to accumulate. Dark volcanic ash lighter than water is also free to accumulate on the snow/ice surface during any partial melt turning it darker and darker as time goes on. Then all in a rush the worm turns and snow/ice being retreating in positive feedback situation. CO2 sinks don’t reactivate as quickly so the system overcompensates and we get back to the “normal” state of affairs where CO2 level is several times greater than today, global average temperature several degrees C higher, and green plants love those conditions which is why there are temperate forest remains under the Antarctic ice sheet.
At this point in history we are at the precipice between one or the other attractor taking over. If it weren’t for the sun being hotter today than it was during the last big ice age hundreds of millions of years ago there wouldn’t be any interglacials today – it would be all glacial all the time until volcanic activity described above could work long enough to throw the system into the other state.
Robert Brown says:
January 10, 2012 at 9:40 am
“Add to that the fact that water achieves its greatest density around 4C
That’s not true for saltwater. A very common mistake that I constantly have to correct.
Seawater at modern salinity level keeps on increasing in density until it reaches its freezing point of about -2C.
The ocean below the thermocline is a relatively constant 3C. This constant temperature water comprises about 90% of the mass of the ocean. The average temperature of the global ocean is 3.9C.
So the deep ocean is 3C not because that’s the low density point. Think again. I can’t think of any way for the ocean to be that temperature except for that being the average of its surface temperature over timespans long enough to cover a complete glacial/interglacial cycle.
Feel free to offer a different explanation. I’m all ears.
After that it became ellipsoid to the degree that it isn’t quite a completely rigid body.
Don’t mind me, I just teach this stuff. Or if you prefer, can you provide evidence to back your description?
The correct description for the cause of tidal locking is breathing mode deformations that transforms angular momentum into heat, because the lobes lag the point of greatest tide and create a net torque. An asymmetric perfectly rigid rotator in orbit, OTOH, experiences no net torque IIRC as it rotates. Similarly, the thing slowing the earth today is again the asymmetric lagged tidal deformation, which cannot transform (axial) rotational angular momentum to the locked moon any more and is therefore transferred to the (orbital) angular momentum of the moon, increasing its orbital radius by a few cm a year as the earth’s rotation slows.
See, in particular, the description in:
http://en.wikipedia.org/wiki/Tidal_locking
or
http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/tides.html
which has simple, easy to understand pictures that permit you to directly see the vector lines of effective force responsible for the net torque.
So I would have to assert that your description does not correspond to the accepted physics of tidal locking, nor does it make sense. Obviously, since this elastic bulge is directly responsible for the torque leading the tidal locking in the first place, the moon was ellipsoidal right up to where the locking occurred, and sufficiently elastic for some time afterwards for the moderate transfer of additional mass to the fourth order “stronger” tide, on the side facing the earth.
Note well that this all probably happened a long time ago when the moon was much closer and tidal heating was correspondingly much greater (and where the moon may have still had substantial heat left over from its formation). The Earth, OTOH, will not become tidally locked to the moon before the sun goes Red Giant. I couldn’t remember the timescales, but they are apparently order of 10^10 years for tidal locking of the Earth, and the sun won’t last that much longer.
rgb
Robert Brown says:
January 10, 2012 at 6:58 am
“I am most skeptical about “heating” of the atmosphere due to pressure and PV=NkT — that is nonsense, frankly.”
Then you must be skeptical that the atmospheric pressure and density decreases exponentially with height too.
If you ignore gravity, then the pressure of the atmosphere would be constant (from the surface to x equals infinity.)
Try doing the math.
@RGB
“Much of the surface cooling away from the oceans involves water as well, especially where there are green plants, lots of trees, that sort of thing.”
Not as much as you might think. Half the surface (higher latitudes) half the time (winter months) is too cold for much transpiration to occur. Another interesting tidbit there is that plants transpire less as CO2 level rises. That’s because evaporation occurs during gas exchange. Stomata iris open and closed in response to need to take in CO2. Water evaporates from the plant when the stomata are open. Higher level of CO2 in the atmosphere makes the gas exchange happen faster and stomata spend less time open and thus water use is conserved.
This is important because the way I see it we’re going to run out of fresh water for agriculture before we run out of diesel for the farm equipment. What a happy coincidence it is, and the height of irony for global warming boffins, that burning fossil fuel to grow more plants lowers the fresh water requirements for growing those plants. A positive feedback in beneficial consequences! The benefits of higher atmospheric CO2 are legion and the downside practically nil as far as I can determine. If we weren’t raising atmospheric CO2 through fossil fuel consumption we’d need invent some other way to do it. Just sayin’.
Joules Verne says:
January 10, 2012 at 9:31 am
“…altitudes are absorbed by the very thin air and heat it up to thousands of degrees at the farthest reaches of the atmosphere.”
Why is the air “very thin”? 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.
CRISP says:
January 9, 2012 at 10:12 pm
You are correct about heat, because heat is the net flow of energy.
However, what you seem to have missed is that energy (not net energy, but energy) can certainly flow from a cooler object to a warmer object by radiation. Surely you don’t think that when radiation hits an object, it only transfers its energy to the object if it is warmer than whatever emitted the radiation, do you? Whatever the radiation is absorbed by, it increases the energy of that object, regardless of the relative temperatures of the emitter and the absorber. And no, this doesn’t violate the 2nd Law. The second law is discussing heat flow, not energy flow.
w.
“ferd berple says: “It does seem remarkable that the emissivity of N2/O2 would be 0.0000. That would seem imply that N2/O2 would never cool in space. Hardly seems possible.”
Then it is a good thing that science is not limited by your imagination. Or my imagination. Or Willis’s imagination.
The simple fact is that N2 has a MUCH lower emissivity than CO2, and consequently N2 would cool MUCH slower than CO2 out in space. Just like a polished piece of aluminum would cool MUCH slower than the same piece of Al painted black. (Actually any color paint would do, since the IR properties are mostly independent of the visible properties).”
Most of space in this galaxy has little light from stars, and average value of the universe is dark.
The other aspect is there is a lot time. Blackness, lots of time, so anything which is going radiate any energy it could have radiated it.
BUT the energy of any gas in the vast darkness of space or the gas in our bright world we living in
is mostly related to it’s velocity. how fast is it going relative to something else.
So in vast area of darkness, gases which have no energy to radiate, can form a galaxy of light and energy- and not only can this occur, this is what has already occurred- hundreds of billions of times.
Dennis Ray Wingo says:
January 9, 2012 at 10:42 pm
They get rid of the excess energy the same way that they picked it up, by conduction. Do you think they can’t get rid of it and thus the atmosphere will end up warmer than the surface?
That’s the part where heat flows from cold to hot … you’ll have to think about that part a bit more. The mere fact that something being warmed may not lose energy easily does not mean that it can be heated to 90°C by an object at 80°C, doesn’t work that way …
w.
Doug Cotton says:
January 10, 2012 at 4:26 am
And if anyone reads Prof. Nahle’s work they might do well to remember that Nahle’s claims are nonsense. People measure DLR around the planet all the time. There’s hundreds of papers on the subject. Nobody gets results like Nahles. I don’t know whether he can’t read the instructions on his instruments or what, but his results are way, way, way out of line with the rest of the global researchers.
He (and Doug Cotton, I guess) also subscribe to the foolish theory that DLR can’t warm the ocean … but neither he nor Doug have explained how, if their claim is true, the ocean doesn’t freeze. The ocean emits about 390 W/m2 of thermal (infrared) radiation. It gains about 170 W/m2 from the sun, and about 320 W/m2 from DLR. Total gained equals total lost, so the temperature doesn’t change and the ocean is in general equilibrium?
If you don’t believe in DLR … then where is the 320 W/m2 coming from to keep the ocean in equilibrium?
w.
Can anyone tell me why there is a lapse rate with the greenhouse effect, it is not something that I dispute but I don’t know why it should be.How can a few molecules absorbing and emitting I R radiation lead to this?
Bruce says:
January 10, 2012 at 8:52 am
Thanks, Bruce. I know that it is somewhat simplistic, but I wanted to clarify that an atmosphere can warm a planet independent of GHGs by reducing the temperature swings. I’d never thought much about that.
w.
Joules Verne says:
January 10, 2012 at 9:31 am
“If it’s all about gravity then why does the lapse reverse and the atmosphere become increasingly warmer with increasing altitude past the thermopause?”
But it’s not all about gravity.
The Stefan-Boltzmann Law gets you -18 C or roughly 40km below the TOA. To get to the surface from 40km, you need the equation of state of the atmosphere.
The radiative piece and the gravity piece are only 2 terms in the full Navier-Stokes equation.
And the goal is explain the surface temperature.
If you actually calculated the gravity piece in the thermopause starting at the top of the thermosphere then you would notice it’s contribution is insignificant. 80% of the atmosphere is below the tropopause.
In addition, the molecules are so far apart and there is virtually no mixing so it’s hard to define a temperature. It’s argued by some that this is the cause of the temperature inversion.