## Thursday, May 13, 2010

### Venus: Chris Colose vs Steve Goddard

Chris Colose (click) thinks that Steve Goddard - and, to a lesser extent, your humble correspondent - are reinventing climatology as well as astrophysics.

"Venus and Cupid" by Lorenzo Lotto, late 1520s

Well, you can say it in this way: after these fields, especially the first one, have been contaminated by an ideological pseudoscience, the only way to proceed is to reinvent the disciplines.

Unfortunately, the flooding of the disciplines by poorly verified and "morally driven" myths has already begun in the modern, rather than postmodern, era, and it was initiated by as likable characters as Carl Sagan. He was nice but very far from infallible.

One must carefully check which insights are legitimate science and which things were politically imported myths - and when it's necessary, you have to start from scratch. But I don't want to degenerate into these moralist rants, so let's jump onto the physics of the problem.

Colose's criticism is simple: he claims that Goddard and I do not realize that the linear functions (of one variable) have two terms (rather than one), the slope term and the intercept:
y = mx + b
We think that there is one term only, we learn. That's a nice hypothesis and it's always nice to learn new things about my own brain :-) but thank you, I understood linear functions when I was 3 years old.

More seriously, Colose agrees that the slope - the lapse rate - is large on Venus - at 8 °C per km, it is comparable to the Earth. But Colose's thesis is that it's the absolute term that would be completely different if the atmosphere of Venus were not dominated by a greenhouse gas (CO2, in this case). If the atmosphere were mostly made out of nitrogen, the surface couldn't be close to 400 °C, he seems to think.

Well, it's not hard to see that Colose's statement is incorrect. We can show that even with a different composition, a very heavy atmosphere would imply a warm surface. (However, we will also see that for an excessively IR-transparent atmosphere, e.g. a pure-nitrogen atmosphere, no stationary state could actually be found at all, so the atmosphere would shrink by various mechanisms.)

Look e.g. at the Wikipedia article about the atmosphere of Venus. The article says a lot of interesting things (besides some out-of-place nonsense inserted by the likes of William Connolley) and I recommend you to read it. But it also contains some hard data such as the following picture:

In the text as well as the chart, you may see that about 50-55 km above the surface of Venus, the temperature as well as pressure are close to the values we know from the Earth's surface: around 1 atmosphere and approximately 0-50 °C. That would be a nice place for (flying) NASA/ESA/RUSA/ChinSA colonies in the future. ;-)

So beneath this Earth-like layer, you still have 50-55 km of extra "air". Because the basic laws of adiabatic heating (without heat transfer) - whose origin will be debated later - imply that the temperature gradient is around 8 °C per kilometer in average, what a shock that the Venus' surface will be found to be 400 °C warmer than what humans like to experience on the Earth. Recall that 50 times 8 equals 400.

The graph above also shows that the temperature keeps on decreasing up to the altitude 100 km where the pressure is just a few Pascal and the temperature is -112 °C or 160 Kelvin or so.

Why is the temperature decreasing so nicely - but it stops decreasing above some point? Well, it's because of circulation that drives the "air" in various directions. And the circulation exists everywhere below the 100-km altitude, but not above it. As a ton of "air" is going up where it can occupy more space, it expands, does work, loses energy, and therefore cools itself. That's why the air ends up cooler at higher altitudes.

Note that this adiabatic mechanism, which works up to the 100-km altitude on Venus, doesn't depend on the greenhouse effect or infrared radiation: it's a mechanical effect. What it depends upon is the circulation, the freedom of the air to move up and down. The winds are ultimately driven by pressure gradients which are caused by the temperature differences which are induced by the changing solar radiation during the seasons and the "day". They're changing because the Venus is revolving around the Sun and spinning around its axis. And the dependence of the pressure (and therefore temperature) on the altitude is a purely gravitational effect. The infrared radiation is not important here.

(The orbital time of Venus around the Sun is 224 [our] days. Venus is the only planet whose spinning goes in the opposite direction than the spinning of the Earth. The spinning is very slow, however, and the solar day on Venus takes 117 [our] days. The spinning is so slow that some winds are faster than the Venus' spinning and can run in the opposite direction relatively to the cosmic reference frame!)

So the circulation, ultimately driven by the Sun (and, at most, the absorption of the visible and ultraviolet light from the Sun which shouldn't be confused with the infrared radiation), guarantees that the adiabatic lapse rate is applicable in a vast majority of the atmosphere - and because the atmosphere is quite heavy, "a vast majority of the atmosphere" means up to the altitudes of 100 km or so.

Even if you assumed that the temperature at those 100 km is 0 Kelvin, which is the lowest allowed temperature, it would still imply that the surface temperature has to be 400 °C or so higher and therefore not hospitable for life (well above 100 °C). However, you can be more accurate than that.

The temperature of the "air" about 80 km above the Venus' surface is higher than 0 Kelvin. At the 80-km altitude, the temperature is actually -76 °C, almost 200 Kelvin, and this value is much higher than 0 Kelvin for a good reason. What is it? Imagine how Venus looks like from a point in the upper atmosphere:

Venus lightning, by a NASA artist

There is a lot of stuff even in the atmosphere that exchanges the incoming and outgoing thermal radiation. In particular, the stuff absorbs a part of the solar radiation. And we don't need to talk about the carbon dioxide at all. The matter of fact is that Venus is covered by sulfuric acid clouds which are opaque (not transparent). That's why we can't see "inside" Venus. A part (2/3) of the solar radiation is reflected, a part of it is absorbed, and very little gets to the surface.

The lower portions of the atmosphere are only heated adiabatically, by convection, as the circulating gas warms up as it drops down and gets compressed, and by heat conduction.

Believe me or not but sulfur that is abundant as much as 80 km above the surface is not made out of carbon dioxide. ;-) Even though the density of CO2 on Venus is something like 300,000 times higher than it is on the Earth, and it constitutes 95 percent of the atmosphere, it is not enough for this gas that we call life to dominate optics on the planet.

And believe me or not, the sulfuric clouds are often at the altitude of 80 km above the surface of Venus (at "night"). They're able to get that high, without any help from the greenhouse effect. Again, mechanics and winds should be credited with getting such material to these places.

And this material is damn able to absorb a notable fraction of the sunlight. So it follows that at these very high altitudes, you may match the outgoing thermal and incoming solar radiation (the solar radiation doesn't get too much deeper to the atmosphere, because of these clouds). When you do so, you may estimate the temperature at those altitudes to be 200 K, well above 0 K, and by extrapolating to the surface using the known slope (lapse rate), you will get to something like 700 K on the surface.

The greenhouse effect is not needed for the qualitative explanation of any of these things, up to a ten-percent accuracy or so. The greenhouse effect still does exist but it is just a relatively small enhancement of the pre-existing lapse rate, and a relatively small lifting of the tropopause (here, defined by the place where the cooling with height stops) to higher altitudes.

In a more detailed discussion, we must be careful about the definitions of the tropopause: on the Earth, several definitions nearly agree. On Venus, they may be at different altitudes. Here, I need the tropopause defined by the point where the cooling-with-height ends. But don't get carried away: the tropopause as defined in the previous sentence is so high because the atmosphere of Venus is so heavy and because the Sun- and mechanically driven "air" circulation mixes most of it, not because of some infrared emission or absorption.

As we have mentioned, the 300,000 times higher CO2 concentration on Venus, relatively to ours, means that they're just 18 CO2 doublings above our levels which only adds 20 °C or so (there are no H2O-related feedbacks over there worth talking about). You know, powers of 2 increase very quickly (2^18 = 262,144), so the logarithms of large numbers are still reasonably small.

The bulk of the surface warmth on Venus - those extra "unwanted" 400 °C - is caused by things that don't depend on CO2's being CO2 or on the greenhouse effect i.e. on the absorption or emission of the infrared radiation. In the same way, the solid interior of the Earth is warming up by 30 °C per kilometer (near the surface, where you can still find some fast enough and adiabatic circulation of the lava etc.) and going up to thousands of degrees (and even millions of degrees according to the leader of the AGW movement) and this fact is gravitational in origin, completely independent on the emissivity of the rocks in the infrared spectrum. There's no important infrared radiation going through the rocks in either direction. ;-)

Much like on Venus, the infrared radiation trying to get through the medium (either rocks on Earth, or the atmosphere of Venus) is almost immediately absorbed - and even a tiny portion of the infrared-absorbing radiation would be enough to absorb it (and to re-emit it). So there is no puzzle why the emissivity is so low (why so small a part of the thermal radiation from the surface gets out). Because the atmosphere is almost completely opaque in the infrared, the radiation everywhere inside the atmosphere is simply in thermal equilibrium with the material around: the properties of this radiation follow the temperature gradients - they're not their cause. The cause of most of the temperature gradients is mechanical (lapse rate) rather than infrared-radiative.

Just one more number: 90 km above the Venus' surface, the CO2 concentration (in molecules per unit volume) matches the concentration near Earth's surface. And you know that CO2 in a few km above the Earth's surface manages to absorb a big part of the IR radiation. So the lower 60 km of the atmosphere may be thought of as "as IR-opaque as a rock".

By the way, even if you believed that the height of the tropopause (where the adiabatic cooling-with-height stops) is linked to a value of the CO2 concentration more accurately than to a value of the total density of the atmosphere, you should notice (see the Wikipedia table below the graph I included) that above 50 km of the altitude, the pressure decreases 10 times for each 10 km. So even if you kept 10% of the CO2 only, "your relevant tropopause" would be just about 10 km lower and the temperature of the surface would only be by 8 x 10 = 80 °C lower.

(The real figure is smaller than that, about 20-40 °C, because the height of Venus' tropopause is linked to all the gases, not just greenhouse gases, and this difference may be attributed to the greenhouse effect from 18 CO2 doublings "above the Earth". But the bulk of the 400 °C extra warmth on the surface has a gravitational origin so it is independent on whether the greenhouse gases dominate the atmosphere.)

Rabbit and Pig

Pig and Rabbit, animals of the year 2009. Do you know who is who?

If you enjoy alarmists' texts about Venus, try also the essays by Pig and Rabbit. If I understand the Rabbit well, he has just penetrated deeply into Goddard's article, namely the second line with the name of the author: Rabbit just realized that Goddard's first name is Steve, not Richard. 100 more years and Rabbit may get to the second sentence.

Rabbit also reveals that "scientist" Gavin Schmidt thinks that the adiabatic lapse rate is impossible due to the energy conservation. ;-) Moreover, proposing a blasphemy such as a temperature gradient that is induced adiabatically would "topple a century of science". Gavin Schmidt clearly has a nuclear weapon against me and Goddard. Ouch. It gotta hurt. For a Planck time; well, I am willing to topple billions of years of such shoddy "science". I choose not to comment on this opinion because the understanding that the adiabatic lapse rate follows from energy conservation, rather than contradicts it, is probably essential to earn a paragraph of response on this blog. Schmidt is a crackpot.

(Hint for Gavin: "adiabatic" means that there is no heat transfer from a hotter object to a warmer object, and "adiabatic" is therefore "reversible". However, "adiabatic" doesn't prevent a body of gas from doing work, and losing kinetic energy and temperature in this way, or regaining it when it compresses back. The temperature therefore depends on the density or pressure and there's no contradiction with the energy conservation.)

Concerning Pig, I do agree that the effective emissivity is (220/735)^4 = 0.008 in the self-explaining sense. But the correct way to calculate this figure is to calculate the numerator, the denominator, and the fourth power: notice that the emissivity comes out very low despite the fact that the atmosphere is "flooded" with a highly-emitting carbon dioxide. The emissivity comes out so tiny because the atmosphere is so heavy, not because it contains a lot of high-emitting CO2! ;-)

Also note that Pig doesn't propose his own alternative of the temperature profile, "T(z)", for the "nitrogen-filled" Venusian atmosphere because he probably realizes that every significantly different alternative would be manifestly absurd. Such an alternative temperature would either violate the adiabatic rules for the lapse rate in corners where this approximation has to work, due to the circulation; or it would have to go below 0 K - or to otherwise crazy low temperatures - at higher altitudes.

Pig also seems to misunderstand that Goddard's thought experiment (and mine) was to replace CO2 by a non-greenhouse gas with similar mechanical and thermal properties. He replaced CO2 by an equally opaque and equally heavy gas which is why he shouldn't expect too much change.

Pure nitrogen atmosphere

Let me mention that I, and apparently also Steve Goddard, agree that the warm surface of Venus couldn't be sustained if the atmosphere were made out of pure nitrogen. The huge thermal radiation of the surface would escape into space without any suppression because the atmosphere would be completely transparent. Because this would be much bigger output than the fixed incoming solar energy, the whole atmosphere would be cooling: it couldn't stay in any "nearby" stationary state.

Eventually, the temperature at some point of the atmosphere would approach the boiling point of nitrogen (very low) and the dry adiabatic lapse rate would be replaced by the "wet" adiabatic lapse rate which is much slower because the work from expansion/contraction is mostly spent to the latent heat of condensation/evaporation of the liquid/gas that moves up/down the atmosphere.

Because the lapse rate would drop, that would also reduce the predicted "hot" temperature of the surface, assuming a fixed thickness of the atmosphere. If a temperature calculated/obtained after these processes would be enough to match the outgoing thermal and incoming solar energy, fine: a stationary state would be found. If it were not enough, the cooling would continue so that the temperatures below the liquid point would ultimately reach the surface (from above). A part of the atmosphere would condense into nitrogen oceans. The remaining atmosphere would be thinner and it would therefore lead to a less dramatic surface-troposphere temperature difference. If there were other gases left that would cause troubles, they could eventually condense, too. After a few steps like that, a stationary state would inevitably be found.

So even for a pure-nitrogen very heavy atmosphere, it's correct to say that the large mass transparent atmosphere would imply a hot surface. However, it's also true that for a pure-nitrogen transparent atmosphere, no nearby stationary state could be found. The atmosphere itself would cool down and/or condense and eventually we would find a different state either with a colder surface and a smaller atmosphere, or a similarly warm atmosphere with IR-absorbing materials in the atmosphere that would develop - where the energy budget would be restored.

On the real Venus, however, there's more than enough stuff to absorb those 99.2% of the surface's thermal radiation. The atmosphere is opaque. There's a lot of CO2 but there is other opaque sulfur-related dirty stuff, too. For example, the Galileo probe showed that the sulfuric clouds appear black at 2.3 microns:
Even so, the high temperatures on Venus are only partially caused by carbon dioxide; a major contributor is the thick bank of clouds containing sulfuric acid [7]. Although these clouds give Venus a high reflectivity in the visible region, the Galileo probe showed that the clouds appear black at infrared wavelengths of 2.3 microns due to strong infrared absorption [8]. Thus, Venus's high temperature might be entirely explainable by direct absorption of incident light, rather than by any greenhouse effect. The infrared absorption lines by carbon dioxide are also broadened by the high pressure on Venus [9], making any comparison with Earth invalid.
The detailed profile is always controlled by the lapse rate - while the overall one-number energy balance does depend on the transparency of the atmosphere.

The importance of the lapse rate is similar to the solid Earth which absorbs infrared radiation so perfectly that the "optical thickness" would be de facto infinite - and predict an infinite rate of geothermal warming as a function of depth.

In reality, the warmth in the geothermal holes is limited and controlled by the adiabatic rate calculated from thermal expansion rather than by the absorption of the thermal radiation (which is de facto perfect).

Rabbit and Pig may join their forces but it doesn't guarantee success.

An off-topic discussion at RealClimate, under the article "Solar", contains the word "Motl" 56 times so far, so the word even beats "Goddard", 56 to 19. If you like to read positive or negative texts with this word, help yourself. :-) I don't like reading texts about myself at all.

See also older articles, Hyperventilating on Venus and Tamino vs Goddard, on The Reference Frame.

AFP (click) brings us news about Rev James Hansen who says that the climate dice is now dangerously loaded, much like the Flash applet above. If you throw it 10 times, you will get a higher-than-average result (4,5,6) either 7 times or 6 times or 5 times or 4 times or 3 times.

It's very likely, about 90% odds, try it by clicking at the dice above. ;-) Isn't it impressive? That must be a signal from God, Rev James Hansen tells us. If you happened to get 4,5,6 in fewer than 3 attempts, it was just weather and there's no reason why your weather should ever be repeated. In the asymptotic future, you will only be getting 6,6,6. Try it. If you're sufficiently patient so that the short-term variability goes away, you will only be getting 6,6,6 all the time.

You have heard the word of Devil. Amen.

1. I believe the isothermal profile is the configuration of maximum entropy for a gas in a gravitational field and the adiabatic profile is a nonequilibrium configuration requiring a constant flux of energy to sustain it as a steady state.

If Venus has an adiabatic lapse rate upwards from the surface, does this not imply a steady-state energy flux upwards from the surface and, if solar energy does not penetrate to the surface, then whence the energy source for this flux?

2. Dear kjemiker,

a nice question but not quite a realistic one for Venus because the winds not only exist, even in the lower atmosphere, but they're often faster than the rotation of the planet around its axis.

The sunlight doesn't penetrate near the surface of Venus but the energy - originally solar energy - needed for the non-equilibrium configuration (as you nicely say - it is needed for the gas to go up and down, expand and contract, and reproduce the lapse rate curve) surely does, by convection and conduction.

Radiation is not the only way how thermal energy can move from one place to another. Does it solve the problem?

Cheers
LM

3. Dear Lubos,

Thank you for your excellent work explaining atmospheric physics.

I read the comments to Tamino's attack on Goddard last night and it was obvious that not one of the posters had even skimmed Goddard's blog (or yours, when you were referenced) to see what was said, so I tried to post this comment:

"Goddard's point seems to be lost on all of you.

That point being that if you use any of your estimates of temperature increase for a doubling of CO2, and apply it to the atmosphere of Venus, you won't even get close to the Venusian surface temperature.

BWD"

Needless to say, that didn't make it through.

It seems that no matter how one tries to explain it, the AGW congregation can't bring themselves to recognize that Gravity is a force that is acting on gas molecules to pressurize the atmosphere from the inside.

Dave

4. Lubos, in your answer to kjemiker you seem to be saying that the adiabatic lapse rate is the natural temperature profile for a non-static atmosphere. But in general an isothermal atmosphere is stable, and not just a static one. Horizontal winds will not distribute energy vertically and vertical convective flow will not occur (a parcel of gas displaced up or down will tend to move back towards it's original height). So I still don't understand why there is an adiabatic lapse rate on Venus below the level of the clouds if the incoming solar radiation is nearly all absorbed at the cloud level.

5. Dear Lubos,
Afraid not. My point concerns the source for the energy maintaining the adiabatic profile not its transport mechanism which is surely convection. Without a 2nd Law exemption, I see no means by which solar energy thermalization in the upper troposphere can lead to higher temperatures at the surface. With solar energy excluded, only internal planetary thermal energy seems a possibility. But one would then have to compare the rate of thermal leakage through the planetary crust with a thermodynamic estimate of the flux required to maintain the adiabatic profile.

While Venus provides an interesting exercise, closer to home we have the "Convective Equilibrium" assumption basic to much of climate science wherein one asserts an adiabatic profile supported by zero net convective flux. Deprived of an adjustable lapse rate dependent on convection, ... but I digress.

6. Dear rtuv3,

the answer is that there can't be any circulation of the air - or planetary atmosphere - or the oceans that would stay purely horizontal all the time.

It's just impossible in any realistic or semi-realistic setup. The circulation of the oceans on Earth is of course very complex, because of changing salinity and complex shapes of the continents etc. Up, down, Gulf stream. Similarly for winds on the Earth.

But even on Venus' atmosphere which looks simpler, the circulation is complex (click) and surely contains lots of vertical motion.

Horizontal motion inevitably sometimes brings bodies of lighter, warmer air beneath the heavier, cooler masses - so they exchange positions by vertical flows. Sometimes, variations and inversions are produced by Bernoulli's law, friction, or other mechanisms. Vertical flows follow.

Most horizontal flows have the tendency to "end somewhere" (the major, unrealistic, exception being a uniform orbiting of the air around an axis). When they end somewhere, you create a source/sink and the air must flow vertically to conserve mass. ;-)

So if there's a significantly fast horizontal motion, and at least some irregularity of the motion that makes it differ from a uniform "cylindrical" rotation around an axis, it is inevitable for the vertical flow to occur as well, and this vertical motion will guarantee that the adiabatic profile of the temperature is the only sustainable one, or at least the real one is closer to the adiabatic profile than the isothermal one.

The frequency and importance of the vertical motion decides how close you are to the adiabatic result: the more frequent the vertical flows are, the more unsustainable the isothermal profile is.

Cheers
LM

7. Dear kjemiker, I don't share the perception of a "problem" in getting the information about the temperature to the lower atmosphere if the atmosphere is opaque.

Do you agree that in your example, there will be different temperatures at different parts of the upper troposphere? Do you agree that there will be variations of pressure over there, too? Do you agree that pressure variations are spreading through gases in all directions, including the vertical one, essentially by the speed of sound - very quickly? So there will be motion and variations in the lower atmosphere, too. Moreover, there's viscosity of the fluids (which is also independent on the transparency/opacity). It's hard to isolate the winds - whose existence you seem to agree with in the upper atmosphere - from the lower atmosphere.

I may be wrong but I don't think you're right that you can isolate the lower atmosphere from the impact of the Sun just by making it opaque. The atmosphere is not "opaque" relatively to mechanical and conventional thermal influences that go beyond radiation.

It's like the ostrich who doesn't want to see the Sun so he hides the head to the sand. It's still there and it will get to him.

8. By the way, rtuv3, I mentioned the oceans and the atmosphere as examples where the complex flows including the vertical ones are inevitable.

But there's one more, historically even more important example of such a vertical motion: plate tectonics and geothermal energy.

Recall that geothermal energy leads to temperature gradients inside the Earth. They're immediately large beneath the surface - so appropriate for geothermal power stations - at the edges of the tectonic plates. That's where the "liquid" material flows vertically, bringing the profile towards the adiabatic curves.

Elsewhere, you must go deeper to see geothermal energy but eventually you'll find it because deeper layers of the Earth are "effectively liquid" at all places.

Your intuition is what prevented Wegener from defending the continental drift in a clear way. He really didn't know about the vertical motion although he knew the right answer concerning all of the horizontal consequences.

But the vertical motion is inevitable whenever you have something that effectively behaves as fluids.

Note that the plate tectonics is also creating huge temperature profiles - geothermal energy - yet it is arguably not driven by the solar energy. ;-) It's just there.

Why on Earth, using your logic based on the 2nd law, after 4.7 billion years, thermalization hasn't eliminated the temperature gradients inside the Earth? It just hasn't happened. The thermalization by heat diffusion is just too slow - and the macroscopic fluxes have simply survived because there's always been large enough energy in them, and the entropy growth from the uniformization was simply slow.

Just calculate the friction of the magma and how quickly it tries to slow down the relative motion. The motion is so slow and the thermal-energy/entropy produced by the friction is so small (as a rate) that billions of years are not enough to stop it.

If you ever have a 400-degree temperature difference between the surface and upper atmosphere, and it is not uniform, it implies that there is some vertical motion in the system, bringing the profiles towards the adiabatic ones. There's also heat diffusion, increasing the entropy. But just try to compare them which of them is more important for setting the vertical profiles of the temperature.

You might think that the vertical motion will stop soon - except that it won't. Yes, you may say that the useful energy that drives the flows in the dark atmosphere ultimate derives from the Sun's oscillating inflow of radiation.

Except that the Sun doesn't have to pump the energy to the lower atmosphere directly, by "sunlight". It gets there through the circulation that doesn't want to disappear. ;-)

These are academic models, and I am not 100% sure. They're academic because we don't have planets with atmospheres that are completely dark towards the sunlight.

Best wishes
Lubos

9. Dear Lubos,
It would be well for us to distinguish energy and temperature. A chart in this blog shows an upper troposphere temperature 200-300C and a 500C surface temperature. My copy of the 2nd Law indicates the former can not be responsible for the latter. This in no way precludes tempests on high initiating surface zephyrs.

10. Dear Lubos,

You asked: "Why on Earth, using your logic based on the 2nd law, after 4.7 billion years, thermalization hasn't eliminated the temperature gradients inside the Earth?"

Isn't this because there is a heat source within the Earth (fission of uranium, thorium, etc) to maintain the temperature gradient?

If the lower Venusian atmosphere is heated ultimately by the Sun, then the energy does not get there by thermal diffusion (conduction) from higher layers of the atmosphere because they are colder. It also does not get there by convection, which will only work as a mechanism to transport heat upwards. Radiation is all that is left, but that suggests that it arrives directly from the Sun, re-radiated IR radiation from higher atmospheric layers that absorbed the incoming solar radiation won't create the temperature gradient we see. I may be wrong but I can't see how to arrive at a hot lower atmosphere without either most of the solar radiation being absorbed lower down, or the heat source being the planet itself (fission again perhaps, or tidal heating of the planet's interior due to closer proximity to Sun, such as occurs on Io, but that seems unlikely).

11. Dear rtuv3,

the nuclear reactor at Earth's core is a pretty cool hypothesis, see e.g. this article to get a hint why I am far from the only one who considers it a crackpottery.

I think it's a misunderstanding of the continental drift and all related things. Even the mantle etc. sometimes behaves as a fluid and the much deeper core etc. is literally liquid - the outer core is liquid although the inner core looks solid (all these things are obtained by looking at the propagation of seismic waves through the Earth).

It's just completely normal for the flowing material going through different pressures to change its temperature, and the friction is sufficiently small for the slowing down not to be brought to a halt after billions of years.

It's a priori plausible there's also radioactive decay and we have this "moderate star" inside our planet except that I find it useless given Occam's razor and I tend to believe that the right isotopes just can't be there.

You know, an obvious question is what is the lifetime of the hypothetical isotope that heats it up. The primary isotopes that make it work must be long-lived but you don't get almost any energy from isotopes whose lifetime is in hundreds of millions of years, so that they're still around, especially because there can't be too big a concentration of the uranium etc. The real energy can only be obtained from the faster-decaying ones, but they're quickly gone and the reactor could no longer work once again.

So the reactor would actually have to produce its own fast-decaying isotopes - by some neutrons or alpha radiation or something like that is running around. I am convinced that any such convoluted reaction depending on radiation exciting new reactions would either quickly stop or quickly explode out of control, if the concentration were above critical. It's not easy to sustain a "moderated" reactor, at least for us, and I think that similar rules hold for Nature, too.

Of course, you can imagine pockets of uranium that explode now and then over there - maybe, it just looks too dramatic and there are too many things I've never heard of for me to quickly accept such a convoluted explanation.

Concerning the cooler Venus' interior, I don't think that you can just start with this assumption. You must start with the hot planet from the times when it was created, and use the evolution equations to see whether the planet and the lower atmosphere had the opportunity to cool down. I am not sure. It depends on the environment. It could just stay warm all the time, approaching the stationary state whose stationarity can be explained by other arguments, including the adiabatic lapse rate.

There is not necessarily just "one correct answer". Such complex systems may have many "points on the landscape", many stationary points that you can approach with the same material at the beginning.

Cheers
LM

12. RE the Earth's interior, it's a bit of both. Certainly the process of cooling since formation has not ended, and certainly much of the heat now present has been has contributed by natural decay of uranium etc. The best estimates suggest that the rate of heating by fission is currently close to the rate at which heat is leaving through the surface. The exact percentages are not known for sure, but wikipedia (http://en.wikipedia.org/wiki/Earth#Heat) is somewhere near the current consensus "best guess" in putting it at 20% residual heat from Earth's formation, 80% heat from nuclear fission.

Re Venus, are you suggesting that the lower atmosphere is hot because it started out that way and hasn't had time to cool? Well maybe, but I suspect an atmosphere cools a lot faster than the interior of a planet. I think the interiors of the Moon and Mars have had time to cool since their formation.

13. Dear rtuv3,

this 20:80 attribution is clearly just a completely unscientific flapdoodle. Someone took all kinds of literature and decided to make a compromise, mixing apples, potatoes, and tomatoes, not to speak about oranges, so that everyone likes him a bit and she doesn't insult anyone.

That's not how science runs and the statement is unlikely.

In reality, the possible temperatures and energy flows from various sources may span so many orders of magnitude that it is very unlikely for two sources to be of the same order-of-magnitude, almost equal.

So it's plausible that the radioactive decay is there and needed, although I find it unlikely, but if it is so, then the "residual heat" is almost certainly and almost completely gone.

Best wishes
Lubos

14. I forgot to answer the second point. Venus' atmosphere is in a quasi-stationary state these days, and has been in such a state for billions of years, so it's not cooling anymore, and it hasn't been cooling for some time.

I just made my comment to point out that your assumption that the Venus' interior had to be cold (and had to warm up later) is not necessarily correct, and it actually probably incorrect.

15. Atmospheric convection from absorbed Solar energy at high altitudes is the main source of transport of energy through the atmosphere to maintain the lapse rate. However, there is some longwave radiation downward (not shortwave Solar direct radiation) also from the absorption region. The longwave radiation is re absorbed and re radiated many times, but some flux down occurs (as well as some radiation flux up). There is no need for planetary internal heating to explain anything, although a very small amount may exist.

I also want to comment on the all N2 atmosphere case. The absorption and radiation from the surface would initially totally determine the surface temperature. The lapse rate due to gravity and decreasing pressure with altitude would still exist. However, since the N2 would be much colder from the surface up for this case, the density would be much higher to maintain the pressure. This would result in a much thinner atmospheric height and this shorter distance would limit the total temperature drop considerably (about a factor of two). If the condensation temperature of the N2 were reached, droplets (clouds) would form. Even lower temperatures could eventually cause frozen N2 clouds. These would decrease the amount of Sunlight reaching the surface by reflection and result in more cooling. I doubt the feedback would reach a point where the liquid N2 temperature reached the surface, but more likely would result in a somewhat cooler surface than otherwise, with some N2 clouds.

16. Why is the adiabatic lapse rate stopped at 100 km altitude above the surface? I did not understand the explanation in your text. Isn't it related to the transparency of the layer above that altitude, for IR radiation?
My view is that the adiabatic lapse rate is only an upper limit at which the atmospheric temperature may vary with height. If the atmospheric energy transfer by conduction and radiation would not be enough to transfer the absorbed heat, then the convection is easily started and the temperature is kept exactly at the adiabatic lapse rate (so one part of the heat is transferred by convection, other part by radiation and also a small part by conduction). On the other side, if the transfer of heat by radiation is enough to emit all the absorbed heat, then the temperature can vary with altitude at lower rates. This is what happens on the altitude about 100km above Venus surface, because the atmosphere is transparent enough to allow simply radiate the heat out to the space (no convection is necessary more).
Indeed, the adiabatic lapse rate of Venus is 9.8 degrees/km, but we observe only 8 degrees/km (according to your text). Why?

17. Lubos,

I didn't replace the CO2 with an equal weight of my hypothetical gas, I replaced 93 atm of CO2 with 1/4 atm of hypotheticum.

I consider the nitrogen case here, with a quite different conclusion than that you and Steve reach:

18. Hello Lubos,
What is your estimate of the stationary state of the pure nitrogen atmosphere? How do you assess the lapse rate in atmosphere completely free of greenhouse gases? Will be there an ocean of nitrogen on Venus's surface, and over the ocean less dense atmosphere than it is today? Do you assume also a complete layer of clouds (not necessarily made of N2)?
On the contrary, I think that the Venus is too close to the Sun and thus surface temperature with no warming effect of the atmosphere (not the greenhouse effect) is well above the critical temperature of nitrogen (126K), Therefore the nitrogen is not able to be in liquid state with a surface tension effects (ocean). Above the critical temperature only a supercritical fluid is possible. So the density is changing continuously (no phase transitions). But the supercritical fluid is not a gas too, the state equation of such phase is much different from ideal gas equation and thus the "adiabatic" lapse rate is significantly changed from the ideal gas rate. An example would be deep layers of Jupiter's atmosphere.
By the way, the today's Venus atmosphere is on the surface in the supercritical state rather than ideal gas. Check better the lapse rate near the surface! The rate differs from the ideal gas rate more on the surface than at higher altitudes.

19. Lubos,
I do not know exactly how you came to the conclusion, that the higher surface temperature of Venus is not caused by greenhouse effect but only by adiabatic lapse rate? Seems like a playing with words. Because of that, I would have a question. What should be the atmosphere of Venus that we can say that the greenhouse effect is significant? I mean specially the temperature change with the altitude.
According to my point of view the temperature lapse rate plays significant role in the greenhouse effect alone (in general, not just only on the Venus and with CO2).
For a proper understanding of the greenhouse effect is important fact that the radiation absorbing layer is sufficiently thick. Greenhouse atmosphere absorbs radiation from the surface at considerably lower altitude than it radiates out to the space. Emission is therefore done at a lower temperature than absorbing precisely because of the existence of adiabatic lapse rate (the heat is transferred within the layer by radiation and convection). Without this lapse rate, the surface temperature and the energy equilibrium would be equal to the black body temperature, that is, just as if it were no greenhouse effect. On this basis, I think adiabatic lapse rate is a part of the greenhouse effect. The temperature lapse rate is the reason for the logarithmic dependence of the temperature increase on the quantity of greenhouse gas (what else reason could it be?).
Therefore, it makes no sense to separate the adiabatic lapse rate from the greenhouse effect.

20. Maybe this is a bit too late, but...

The thing I'm struggling with is not how the lower Venusian atmosphere got hot, it's why it remains hot if nearly all the solar radiation is absorbed higher up. You have suggested that the mechanism could be circulation causing mixing and the adiabatic lapse rate, but I don't see it. It's true that if the lapse rate is less than adiabatic and you displace a parcel of gas either up or down (adiabatically) and hold it there until it reaches the temperature of its new surroundings, then the effect will be to move heat down (because a parcel moved down adiabatically will be initially hotter than its new surroundings, and one moved up will be initially colder than them). The point is that you have to do mechanical work to raise or lower parcel of gas in the first place. For it to happen spontaneously you need some other mechanism at work. The situation when the lapse rate is greater than adiabatic is quite different. Then mechanical work is done by the rising (or falling) parcel of air, so the atmosphere is unstable - convection will spontaneously move heat upwards until the lapse rate is brought back to adiabatic. The natural state for an atmosphere heated from below is an adiabatic lapse rate, but the natural state for one heated from above is to be isothermal.