I’ve been looking at the Nikolov and Zeller paper again. Among other things, they claim to be able to calculate the surface temperature Ts of eight different planets and moons from knowing nothing more than the solar irradiation So and the surface pressure Ps for each heavenly body. Dr. Zeller refers to this as their MIRACLE equation. He says:
Why aren’t you all trying to disprove our MIRACLE equation rather than banging your heads against walls trying to prove or disprove who knows what and exclaiming you have problems with this or that? The question is how can we possibly have done it – there is no question that our equations work – if you haven’t verified that it works, why haven’t you? […] Why aren’t you thinking: “hmmmm, N&Z have given us an equation that lo-and-behold when we plug in the measured pressures and calculate Tgb as they suggest, gives us a calculated Ts that also matches measured values! You can’t disprove the equation? So maybe we are cooking the data books somehow, but how?
This is supposed to be evidence that their theory is correct, and people keep telling me ‘but they’ve got real evidence, they can make predictions of planetary temperatures, check it out”. Plus it’s hard to ignore an invitation like Dr. Zellers, so I checked it out.
Figure 1. These are not the equations you are looking for.
They first postulate something called the “Near-surface Atmospheric Thermal Enhancement” or “ATE” effect that makes the earth warmer than it would be without an atmosphere.
The “ATE effect” is measured by something called Nte(Ps), which is defined and estimated in their paper as follows.
where Nte(Ps) is a measure of the “Near-surface Atmospheric Thermal Enhancement” effect.
Nte(Ps) is defined as the actual average surface air temperature of the planet Ts divided by the theoretical “graybody” temperature of the planet Tgb calculated from the total solar insolation So of the planet. Nte(Ps) is estimated using a fitted function of the surface pressure of the planet Ps.
Let me simplify things a bit. Symbolically, the right part of equation (7) can be written as
Nte(Ps) = e^(t1 * Ps ^ t2 + t3 * Ps ^ t4) (7Sym)
where “e” is the base of natural logs and Ps is the surface pressure on the planet or moon. There are four tunable parameters (t1 through t4) that are “fitted” or tuned to the data. In other words, those values are repeatedly adjusted and tuned until the desired fit is obtained. This fitting can be easily done in Excel using the “Solve…” menu item. As you’d expect with four parameters and only eight datapoints, the fit is quite good, and their estimate is quite close to the actual value of Nte(Ps).
Amusingly, the result of equation (7) is then used in another fitted (tuned) equation, number (8). This is:
where So is total solar irradiation.
This is their piece de resistance, their MIRACLE equation, wherein they are saying the surface temperature of eight different planets and moons can be calculated from just two variables— Pr, the surface pressure, and So, the total Solar irradiation. This is what amazes the folks in the crowd so much that they write and tell me there is “evidence” that N&Z are right.
Obviously, there is another tuned parameter in equation (8), so we can rewrite this one symbolically as:
Ts = t5 * (Solar + adjustment ) ^ 1/4 * Nte(Ps). (8Sym)
Let me pause a minute and point something out about equation (8). The total solar irradiation Solar ranges from over 9,000 W/m2 for Mercury down to 1.51 W/m2 for Triton. Look at equation 8. How will adding the adjustment = 0.0001325 to any of those values before taking the fourth root make the slightest bit of difference in the result? That’s just bizarre, that is. They say they put it in so that the formula will be accurate when there is no solar, so it will give the background radiation of 3 Kelvins. Who cares? Truly, it changes Ts by a maximum of a thousandth of a degree for Triton. So for the moment let me remove it, as it makes no practical difference and it’s just confusing things.
Back to the tale. Removing the adjustment and substituting equation 7 into equation 8 we get:
Ts = t5 * Solar^0.25 * e^(t1 * Ps ^ t2 + t3 * Ps ^ t4) (eqn 9)
This is amazing. These guys are seriously claiming that with only eight datapoints and no less than five tunable parameters , they can calculate the surface temperature of the eight planets knowing only their surface pressure and solar irradiation. And with that many knobs to turn, I am sure they can do that. I did it on my own spreadsheet using their figures. I get about the same values for t1 through t5. But that proves nothing at all.
I mean … I can only stand in awe at the sheer effrontery of that claim. They are using only eight datapoints and five tunable parameters with a specially-designed ad-hoc equation with no physical basis. And they don’t think that’s odd in the slightest.
I will return to this question of the number of parameters in a bit, because even though it’s gobsmacking what they’ve done there, it’s not the best part of the story. Here’s the sting in the tale. We can also substitute equation (7) into equation (8) in a slightly different way, using the middle term in equation 7. This yields:
Ts = t5 * Solar^0.25 * Ts / Tgb (eqn 10)
This means that if we start out by knowing the surface temperature Ts on the right side of the equation, we can then calculate Ts on the left side … shocking, I know, who would have guessed. Let’s check the rest of the math in equation (10) to see why that works out.
Upon inspection it can be seen that the first part of the right side of equation (10),
t5 * Solar^0.25
is an alternate form of the familiar Stefan-Boltzmann equation relating temperature and radiation. The S-B equation can be written as
T = (Solar / c1) ^ 0.25.
where T is temperature and c1 is a constant equal to the S-B constant times the emissivity. We can rewrite this as
T = 1/(c1^0.25) * Solar^0.25
Setting another constant c2 equal to 1 / (c1^0.25) gives me the Stefan-Boltzmann equation as:
T = c2 * Solar^0.25
But this is exactly the form of the first part of the right side of equation 10. More to the point, it is an approximation of the graybody temperature of the planet Tgb.
We can check this by observing that if emissivity is .9 then constant c1 is 5.103E-8, and c2 is therefore about 66. However, that value will be reduced by the rotation of the planet. Per the N&Z formula in their latest post, that gives a value of about 27.
Their fitted value is 25, not far from the actual value. So curiously, what it turns out they’ve done is to estimate the Stefan-Boltzmann constant by a bizarre curve fitting method. And they did a decent job of that. Actually, pretty impressive considering the number of steps and parameters involved.
But since t5 * Solar^0.25 is an estimation of the graybody temperature of the planet Tgb, that means that Equation 10 reduces from
Ts = t5 * Solar^0.25 * Ts / Tgb (eqn 10)
to
Ts = Tgb * Ts / Tgb.
and finally to
Ts = Ts
TA-DA!
CONCLUSION
Let me recap the underlying effect of what they have done. They are looking at eight planets and moons.
1. They have used an equation
e^(t1 * Ps ^ t2 + t3 * Ps ^ t4)
with four free parameters to yield an estimate of Ts/Tgb based on surface pressure. As one would expect given the fact that there are half as many free parameters as there are data points, and that they are given free choice to pick any form for their equation without limit, this presents no problem at all, and can be done with virtually any dataset.
2. They have used an equation
t5 * Solar^0.25
with one free parameter in order to put together an estimate of Tgb based on total planetary insolation. Since Tgb does depend inter alia on planetary insolation, again this presents no problem.
3. They have multiplied the two estimates together. Since the result is an estimate of Tgb times an estimate of Ts/Tgb, of course this has the effect of cancelling out Tgb.
4. They note that what remains is Ts, and they declare a MIRACLE.
Look, guys … predicting Ts when you start out with Ts? Not all that hard, and with five free parameters and a choice of any equation no matter how non-physically based, that is no MIRACLE of any kind, just another case of rampant curve fitting …
Finally, there is a famous story in science about this kind of pseudo-scientific use of parameters and equations, told by Freeman Dyson:
We began by calculating meson–proton scattering, using a theory of the strong forces known as pseudoscalar meson theory. By the spring of 1953, after heroic efforts, we had plotted theoretical graphs of meson–proton scattering. We joyfully observed that our calculated numbers agreed pretty well with Fermi’s measured numbers. So I made an appointment to meet with Fermi and show him our results. Proudly, I rode the Greyhound bus from Ithaca to Chicago with a package of our theoretical graphs to show to Fermi.
When I arrived in Fermi’s office, I handed the graphs to Fermi, but he hardly glanced at them. He invited me to sit down, and asked me in a friendly way about the health of my wife and our newborn baby son, now fifty years old. Then he delivered his verdict in a quiet, even voice. “There are two ways of doing calculations in theoretical physics”, he said. “One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither.
I was slightly stunned, but ventured to ask him why he did not consider the pseudoscalar meson theory to be a selfconsistent mathematical formalism. He replied, “Quantum electrodynamics is a good theory because the forces are weak, and when the formalism is ambiguous we have a clear physical picture to guide us. With the pseudoscalar meson theory there is no physical picture, and the forces are so strong that nothing converges. To reach your calculated results, you had to introduce arbitrary cut-off procedures that are not based either on solid physics or on solid mathematics.”
In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?”
I thought for a moment about our cut-off procedures and said, “Four.”
He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” With that, the conversation was over. I thanked Fermi for his time and trouble, and sadly took the next bus back to Ithaca to tell the bad news to the students.
The Nikolov and Zeller equation contains five parameters and only eight data points. I rest my case that it is not a MIRACLE that they can make the elephant wiggle his trunk, but an expected and trivial result of their faulty procedures.
My regards to everyone,
w.
PS—There is, of course, a technical term for what they have done, as there are no new mistakes under the sun. It is called “overfitting”. As Wikipedia says, “Overfitting generally occurs when a model is excessively complex, such as having too many parameters relative to the number of observations.” Five parameters is far, far too many relative to eight observations, that is a guaranteed overfit.
PPS—One problem with N&Z’s MIRACLE equation is that they have not statistically tested it in any way.
One way to see if their fit is even remotely valid is to leave out some of the datapoints and fit it again. Of course with only eight datapoints to start with, this is problematic … but in any case if the fitted parameters come out radically different when you do that, this casts a lot of doubt on your fit. I encourage N&Z to do this and report back on their results. I’d do it, but they don’t believe me, so what’s the point?
Aother way to check their fit is to divide the dataset in half, do the fit on one half, and then check the results on the other half. This is because fitted equations like they are using are known to perform very poorly “out of sample”, that is to say on data not used to fit the parameters. Given only eight data points and four parameters for equation 7, of course this is again problematic, since if you divide the set in half you end up with as many parameters as data points … you’d think that might be a clue that the procedure is sketchy but what do I know, I was born yesterday. In any case I encourage N&Z to perform that test as well. My results from that test say that their fit is meaningless, but perhaps their test results will be different.
[UPDATE] One of the commenters below said:
Willis – go ahead – fit an elephant. Please!
Seriously N&Z are only demonstrating in algebra what has been observed in experiments, that heating a gas in a sealed container increases both pressure and temperature.
OK, here’s my shot at emulating the surface temperature using nothing but the data in the N&Z chart of planetary body properties:
Figure 1. Willis’s emulation of the surface temperature of the planetary bodies.
My equation contains one more variable and two less parameters than the N&Z equation. Remember their equation was:
Ts = 25.3966 * Solar^0.25 * e^(0.233001 * Pressure ^ 0.0651203 + 0.0015393 * Pressure ^ 0.385232)
My equation, on the other hand, is:
Ts = 0.8 * Tgb + 6.9 * Density + 0.2 * Gravity)
Note that I am absolutely not making any claim that temperature is determined by density and gravity. I am merely showing that fitting a few points with a few variables and a few parameters is not all that difficult. It also shows that one can get the answer without using surface pressure at all. Finally, it shows that neither my emulation nor N&Z’s emulation of the planetary temperatures are worth a bucket of warm spit …
[UPDATE 2] I figured that since I was doing miracles with the N&Z miracle equation, I shouldn’t stop there. I should see if I could beat them at their own game, and make a simpler miracle. Once again, their equation:
Ts = 25.3966 * Solar^0.25 * e^(0.233001 * Pressure ^ 0.0651203 + 0.0015393 * Pressure ^ 0.385232)
My simplified version of their equation looks like this:
Ts = 25.394 * Solar^0.25 * e^(0.092 * Pressure ^ 0.17)
Curiously, my simplified version actually has a slightly lower RMS error than the N&Z version, so I did indeed beat them at their own game. My equation is not only simpler, it is more accurate. They’re free to use my simplified miracle equation, no royalties necessary. Here are the fits:
Figure 2. A simpler version of the N&Z equation 8
Again, I make no claim that this improves things. The mere fact that I can do it with two less tuned parameters (three instead of five) than N&Z used does not suddenly mean that it is not overfitted.
Both the simplified and the complex version of the N&Z equations are nothing but curve fitting. This is proven by the fact that we already have three simple and very different equations that hindcast the planetary temperatures. That’s the beauty of a fitted equation, if you are clever you can fit a lot using only a little … but THAT DOESN’T MEAN THAT PRESSURE DETERMINES TEMPERATURE.
For example, I can do the same thing without using pressure at all, but using density instead. Here’s that equation:
Ts = 25.491 * Solar^0.25 * e^(0.603 * Density ^ 0.201)
And here’s the results:
Figure 3. An emulation of the planetary temperatures, using density instead of pressure.
Does this now mean that the planetary temperature is really controlled by density? Of course not, this whole thing is an exercise in curve fitting.
w.
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Tilo Reber says:
What do you expect that effect to be? And, what do you expect all other effects to be? How do YOU explain it?
Sorry…That is not how the game is played. It is not my job to tell you what some experiment some random person on the web means. I think it means nothing. If you guys think it means something, it is up to you to intelligently explain what it means. And, if the explanation calls for overturning all conventional understanding of atmospheric physics, then it is up to you to make a really, really convincing case, including discussing how you carefully eliminated all possible other explanations using conventionally-understood physics.
I feel so stupid now that I am getting old and realize I cannot – any longer (and I am obviously the only one who cannot) – use the numerical values for irradiation (So) and for the surface pressure (Ps) and end up with surface temperature (Ts)
And as if I am not already confused enough – the ”Near-surface Atmospheric Thermal Enhancement” or “ATE” effect that makes the earth 33 Kelvin warmer than it would be without an atmosphere, I – (using the values for the Earth) end up with (1 bar = Earth’s Ps): 33 K * 1 Bar = 33 – But which “value” is correct 33 K or 33 Bar? – And, furthermore, if a “grey-body temperature” is anything like a “Blackbody temperature” then Ts should equal Tgb and as then Ts/ Tgb = 1. (This time the answer is T or 1 Kelvin) – Therefore the first part of their equation; “Nte(Ps) = Ts/ Tgb” – should simply look like this: (33 = 1) which, to me does not look very equal at all and has no value, either in heat or weight. So, I still do not know temperature from pressure!
Sorry Willis, I am lost long before (8)
But then as I said, I have probably got too old and “feeble of mind” – I probably cannot even explain myself! –
John Day says:
January 26, 2012 at 2:02 pm
Look, I said you should let Ned answer. You said no, you could answer for Ned, because answering for other people happens all the time. Now, after answering for Ned, you say you didn’t want to answer for Ned.
OK …
I can’t even figure out whether Ned is talking about the earth or the moon. So I haven’t a clue if I’m wrong yet, and I won’t until Ned answers. To date neither you nor I nor anyone can make heads or tails of Ned’s numbers, so until his explanation, I’m not sure about anything.
I understand perfectly that you don’t know, John, you have very publicly exhibited your surprising lack knowledge for all to marvel at.
My concern is that you don’t seem to realize that you don’t know.
w.
Joel Shore: “What do you expect that effect to be? ”
Well, if we buy your greenhouse gas assumption, for the sake of argument, and just look at CO2, then we have a 40% increase that has produced less that 1C of warming. And that change would be the result of miles of the stuff. Now you want to attribute 2C to about four inches of the suff. And only to the delta amount of it that results from a small pressure change. LOL. Come on!
“It is not my job to tell you what some experiment some random person on the web means.”
You already did. You said that it was ill conceived and poorly executed. And while it may not be your responsibility to explain what it means, it is your responsibility to explain why it is ill conceived and poorly executed. So far all that you have given us is handwaving and opinion. Your opinion is that only you understand the laws of physics and how they apply to this experiment. Unfortunately, as I said before, I have no interest in your opinions. I’m going to need a better explanation than just your opinion before I believe that the experiment is ill conceived and poorly exectued.
Tilo Reber says:
January 26, 2012 at 4:10 pm
So this is the new science? Konrad does an experiment without understanding the theory he’s testing. I told him that to test the theory by experiment, he needs to understand the mechanism that he is testing first. How can you design an experiment to verify a mechanism you don’t understand?
That was too high a mountain for Konrad. He replied:
Nope, that “understand the theory first” nonsense is far too twentieth century for Konrad, he did the experiment anyway. He didn’t bother to state what he expected to find in advance, or what kind of finding would support the N&Z theory, because he can’t explain the N&Z theory.
So Konrad did the experiment, without forethought or even afterthought. Now Joel points out that Konrad doesn’t know how to intelligently interpret the results, and in response you bust Joel because he can’t interpret the results?
Not Joel’s job, Tilo. Not my job or yours. That’s Konrad’s job, and from all appearances he is too foolish to know how to design an experiment, and too proud to find out. He just says empirical testing will confirm some unknown mechanism, and off he goes to test the mechanism by … by … by doing something or other, which shows … something or other.
w.
DeWitt Payne:
“How do you know the diameter increase was tiny?”
How do you know if the diameter increase was of any significance at all? You are simply shooting in the dark with that one. But if you are really concerned, why not ask Konrad to measure it. The answer, of course, is that you are simply throwing stuff at the wall hoping it will stick.
“You mean if he compared two bottles with different diameters? Of course the temperature would be different.”
You did the experiment?
“The larger bottle would have a higher effective surface area exposed to sunlight than the smaller bottle.”
Good example of one dimensional thinking. It would also have a larger internal volume and it would have a larger surface area through which to conduct heat back outside the bottle.
“Given that polyester is opaque to thermal IR, a large enough bottle might actually melt if it was well insulated.”
But the bottles in his experiment where not insulated. So an increase in surface area would also mean an increased area through which to loose heat.
“I’ve melted a box constructed from EFP with a black painted metal plate on the bottom exposed to sunlight and the box covered with a polyethylene film.”
How nice. Was this a controlled experiment? Did you try it with a small box and a large box? Or is this conclusion of yours simply based on your faith in your one dimensional thinking?
“Here’s some more. Was the temperature inside the hot water bottle monitored?”
Good point. I’m sure that it wasn’t. We know that he allowed the system to come to equilibrium before exposing the bottles to the sun. As the temperature warmed, I suppose there could have been some convection between the solar bottle and the hot water bottle. But that would only mean that the solar high pressure bottle was heating it’s own air as well as that in the hot water bottle. And to some extent, that hot air could then have used the walls of the hot water bottle to conduct away some of the heat. So his 2C increase might actually have been larger.
Got any more maybes that you want to run up the flag pole? Of course if you are truely interested in doing more that destroying the experiment with implausible maybes you could simply ask Konrad some of these things.
And the Universe didn’t even explode 🙂
Tilo Reber said @ur momisugly January 26, 2012 at 5:07 pm
OK:
And
And The Git is still completely and utterly bewildered… Divided by a common language I guess 😐
Willis: “So Konrad did the experiment, without forethought or even afterthought.”
I’m not sure what you are going on about here, Willis. It seems pretty obvious to me that the idea is to test the amount of solar warming of a gas with the only variable being pressure. And he designed an experiment whose objective was to control and equalize all the elements but pressure. And the concept he is testing seems equally clear. He wants to know if more gas in a given volume will capture more radiative energy. It strikes me as intuitive that it would. I can’t see your or anyone else’s problem with that idea. And I can’t see what laws of physics you think that idea breaks.
Tilo Reber says:
January 26, 2012 at 9:27 pm
Tilo, thanks for the reply. I have never found anyone who could give me an “elevator speech” about how the N&Z effect is supposed to work. Konrad could not do so. Well that’s not true. He said he could give me an elevator speech, but wouldn’t.
Now, if you could give me the elevator speech, that would be a first. How is the dang thing supposed to work?
Then, we can see if what Konrad is doing has any relevance to whatever the N&Z claims might be. You seem to think that somehow their claim involves the idea that the sun will warm a gas under pressure faster than it will warm a gas that is not under pressure.
Or perhaps the claim is that the sun will warm a gas under pressure more than it will warm a gas that is not under pressure.
Or perhaps the claim is that the sun will warm a gas under pressure to a higher equilibrium temperature than it will warm a gas that is not under pressure.
Now, I don’t know which of these Konrad is testing. I don’t know if Konrad knows. I don’t know what he thinks will happen in any of these cases. And that is a huge hole.
If you don’t have a clear physical picture of what you think will happen, how can you interpret your results?
But the bigger hole is, what do any of these questions have to do with N&Z? Here’s an example of the two holes together:
If he finds that a more dense gas heats faster, is that what you’d expect, and if so, exactly how does that tend to confirm or falsify N&Z?
To support or falsify N&Z, you need to specify your experiment very carefully so it answers important questions or establishes important data points. You can’t do that by just picking an experiment at random.
w.
.” You can’t do that by just picking an experiment at random.”
Too true.
I once shared an office with a physical chemist whose was designing a complicated experiment – nothing to do with climate science – it was to measure an obscure electro-optical effect. Before he took a single measurement he sat at his desk and firstly calculated the magnitude expected for this effect, then calculated the sensitivity his apparatus would need to make the measurement, then considered the materials which would be required, the electronics needed for the data analysis, and the likely error bars. This took 3 months. Then he built the apparatus and took the measurements. It worked first time, and exactly as he had predicted.
The point of this little anecdote? Well that’s how you do experiments properly – you do not just stick some gas in a bottle and put it in the sun without knowing what you are trying to measure or why.
Jimmi_the_dalek and Willis Eschenbach,
are you trying to tell us that the only good experiment is one where you already know everything about what you are working on and are just going to confirm it?? Are you guys for real?!?!?!?! How many of our best scientists had to redesign their experiments numerous times before they reached that level of understanding?!?!? Did the LHC folk find what they expected, er HOPED, to find?? How about the CLOUD experiment. I believe the AMMONIA result was just a little surprising. Try to contact the ground occasionally won’t you? My opinion is that a good experiment is any one where the experimenter actually LEARNS something without it costing too much!!
@John Day
> Will you admit you were wrong on that?
@Willis
> I can’t even figure out whether Ned is talking about the earth or the moon.
It doesn’t make any difference (else why would Ned use the Moon as reference?). The Stefan-Boltzmann equation doesn’t have a term for area, time or mass. You plug in an absolute temperature and emissivity and it spits out power per area. Ned wanted to know the absolute temperature corresponding to a certain watts/m². You said it was impossible (thinking you could expose his stupidity). You were wrong. Case closed.
@Willis
> John, you have very publicly exhibited your surprising lack knowledge for all to marvel at.
I’m here to learn and not too proud to admit my ignorance.
You’re a talented and brilliant guy, but you have a few things to learn about controlling the snark and venom in your words. Its not necessary and turns people against you. Haven’t you figured that out?
Joel Shore says:
January 26, 2012 at 9:10 am
Tilo Reber says:
Okay, let’s move on. Why do you consider Konrad Hartmann’s experiment “ill conceived and carried out”.
The main problem with the experiment is it doesn’t show what people are claiming it shows. Assuming he did the experiment correctly, he showed that a box filled with air at elevated pressure and exposed to sunlight was at a higher temperature than the box not at elevated pressure.
Have you even read the write up? The box contained two bottles. One at higher pressure than the other.
However, he has not in any way bothered to figure out what conventional physics would predict for this case. His boxes contain air that has greenhouse gases in it, for example. The one at higher pressure will have more greenhouse gases…and will also have broader absorption bands.
You’re kidding me. You think higher pressure air bottle’s water vapour or co2 is going to lift the bottle temperature 2 Celcius because it’s at a slightly elevated pressure?? Jericho would be cooking.
One does not abandon a century of physics because someone does an experiment and doesn’t know how to intelligently interpret the results!
Lol. You gravity deniers are floating off into lala land.
Tallbloke sez
It’s the albedo for rocky planets without an atmosphere. Assumed to be the same for all the bodies tested. So, Moon: measured albedo 0.12 Earth with no atmosphere, about the same, etc. So, not tuned; measured from the Moon, and applied elsewhere.
Willis sez
My point exactly. It’s actually has nothing to do with the various planetary bodies:
It’s not the even albedo from the moon. Here are the albedos from the paper, along with the corresponding t5 parameter if we used that albedo …
Body, Bond Albedo, Parameter t5
Mercury, 0.12, 25.4
Venus, 0.75, 18.6
Earth, 0.3, 24.0
Moon, 0.11, 25.5
Mars, 0.18, 25.0
Europa, 0.64, 20.3
Titan, 0.22, 24.7
Triton, 0.75, 18.6
These albedos range from a low end of 0.11 for the moon’s albedo to 0.75 for Triton’s albedo. The corresponding value for your parameter t1 ranges from 24.5 down to 18.6. And as a result, your value for t5 of 25.3966 is, as I said, a tuned parameter and not the “result of combining 4 constants” as you claim.
You seem to be having comprehension difficulties Willis. I’ve bolded the bit you need to re-read. Bear in mind Earth with no atmosphere won’t have any oceans either.
So the same value is used for all the rocky planets, the value of the albedo doesn’t change, and it is not a tuned parameter but an empirical measurement, no matter how many times you tell yourself, (and anyone still daft enough to listen to you) that it is.
I have been greatly intrigued by the N&Z theory and would really to learn more about it from its inventors, Drs. Nikolov and Zeller, whom we’re fortunate to have on board as mentors.
I would like to start by presenting my version of the N&Z ‘elevator’ speech. Probably shouldn’t do this because Willis has already revealed my “surprising lack [of] knowledge” in these areas. Shouldn’t butt in where you’re not welcome etc.
But you learn by teaching others what you have learned from others. Hopefully one teaches what is correct. But if not, you should expect to be corrected (politely) by others with corre t knowledge.
Let’s start off with a question: “Without using the S-B equation (that’s ‘cheating’) how would you determine the surface temperature, illuminated by a nearby star, of an airless planet?”
Well, you might say, it has to depend on the kinetic energy of the molecules in the surface. We could apply statistical mechanics and sum up the energies of the molecules over all their degrees of freedom and distributed motion and computer NkT. Pretty messy, all those solid bonding and vibration DOF’s to deal with. But it would have to work because of energy and momentum conservation principles.
Yes, I would say, but certainly an intractable computation (wiggling my fingers rapidly). Isn’t it therefore surprising that the S-B equation does that job so well, given two parameters: energy per unit area and emissivity? We don’t need to know anything about mass, compostition, chemistory or molecular motions and still get a reasonably good estimate of the surface temperature. It’s scary, almost magic in its simplicity.
It works because of the Gas Law, not the Ideal Gas Law (IGL) for paritcles made of fermions, but the Photon Gas Law for bosons. Very similar to IGL, in fact, except bosons don’t collide with each other. But photons do interact with matter. Keep listening, I’m still many floors my destination.
The S-B equation is really Planck’s Equation (look it up when you get to your office) integrated over all the frequencies in the radiation of that nearby star. Planck’s equation, in turn, uses the statistical distribution of photons to compute power by frequency. (Planck’s equation, BTW, was purely empirical, conceived to mitigate the ‘ultra-violet’ disaster and later derived from quantum principles by Bose and Einstein). Turns out the Bose-Einstein distribution squelches the radiation energy perfectly in the sense of predicting how warm an airless planet will get with a nearby start shining on it.
The ‘take away’ here is that the airless temperature can be predicted with knowing the mass or specific heat capacities of the solids on the surface. So ‘surface heat capacity’ in formal sense be ignored for this purpose. We don’t need it to determine temperature, do we?
You say, but, but that’s not right. You can’t ignore …
Shush! Let’s add transparent air (N2, O2, not GHG’s) to cover the planet. Now how much warmer does the planet get?
That’s easy, you say. Willis already proved that the planet can’t get any warmer because that would violate the conservation of energy law. Sure the heat will diffuse into the atmosphere and warm the gas. But it will all come to equilibrium at the same temperature. It has to because Willis said so!
But I’ll say you haven’t proven anything, because we didn’t have to compute kinetic energy of molecules in the ground to get the surface temp. All determined by the Photon Gas Law where photons interact with matter (aka S-B equation).
Furthermore, the temperature of the gas will also be determined by the Ideal Gas Law. But this time we look at the average kinetic motion of gas molucles because they do collide together, producing a change in momentum (“force”) from which we can compute pressure. The temperature follows simply by applying the IGL (PV=nkT). Since pressure depends on the density of collisions at a particular altitude, we see that temperature goes down as the air gets thinner.
Unlike the surface case, where photons interact strongly with matter, they don’t have that much effect on gas molecules. So the effects of GHG’s are not as great as supposed.
So (waving my hands) you see I’ve shown you that it really hasn’t been proven that ‘enhanced temperature’ due to this pressuration would violate energy. In fact the N&Z theory explains how the temperature increase due to the so-called Green House Effect can be explained entirely in terms of pressure from the Ideal Gas Law.
You might say then: But exactly how does this Atmospheric Temperature Enchancement (ATE) actually work?
[Ding] Sorry. This is my floor. Say, why not just talk to Ned and Karl. They’re just down the hall and would be glad to explain it to you.
😐
This laymans view is that gravity does not create the temperature of the air column.
Gravity provides the “structure” for the lapse rate up the air column.
The surface temperature at the bottom of the column defines the start temperature.
Hence the tropopause is much lower at the poles, start temperature maybe -30C whereas
at the equator the start temperature could be +30C. At ten degrees per kilometre
this seems to fit.
You can pump up a divers air bottle to a few atmospheres and the bottle gets warm.
It soon cools but does not lose pressure.
Willis: “You seem to think that somehow their claim involves the idea that the sun will warm a gas under pressure faster than it will warm a gas that is not under pressure.
Or perhaps the claim is that the sun will warm a gas under pressure more than it will warm a gas that is not under pressure.
Or perhaps the claim is that the sun will warm a gas under pressure to a higher equilibrium temperature than it will warm a gas that is not under pressure.”
Okay, let’s try an analogy. This is how I see it – basically in Newtonian kinetic energy terms. Let’s say that we throw a rubber ball at the target. The ball has a certain kinetic energy and the target will absorb or disipate some of that energy. Now, let’s hit the target with two rubber balls, each moving as fast as the earlier ball. Now we would expect the target to have to absorb twice the energy. I look at the gas molecules in the bottle as rubber balls and the thermometer as a target that measures the kinetic energy of those molecules. The analogy isn’t perfect of course, but that’s the basic idea. Now, when the sunlight enters the bottle it releases a certain amount of energy to those molecules, and the longwave radiation coming back from the black surface releases more energy to those molecules. The energy entering the bottle in both cases is the same. The longwave coming off the black surfaces is the same. But all of it is not captured by the gas in the bottle. Some of it leaves the bottle as radiant energy. My point is that the bottle with the higher pressure has more molecules in the same volume. This means that there are more molecules to absorb the radiation energy going through the volume. Each molecule, taken alone, does not end up with more kinetic energy in the high pressure bottle. The kinetic energy of the individual molecules in both bottles should be about the same. But the temperature that is measured within the bottle is a measure of the summed kinetic energy of the molecules. And the content of the higher pressure bottle has more kinetic energy simply because it has more molecules. So I would expect less radiant energy to leave the higher pressure bottle. This means that the internal temperature will rise until the extra conduction through the walls of the bottle bring the bottle to equilibrium. So the higher pressure bottle would loose less energy through radiation and more energy through conduction, but at a higher equilibrium point. Think about empty space where the temp is near 0K. It’s not that there is no radiation passing through that space. It’s that there are no gas molecules to capture its energy. Until someone can explain what I am missing, that’s my take.
Nick Stokes says:
January 26, 2012 at 5:35 pm
[Richard M says: January 26, 2012 at 5:20 am
‘And, if you read what I actually wrote you’ll see the word “discovered” and not the word “produced”. Nick, this is one reason why you have such low credibility at WUWT. You tried to change the meaning of what I said…’]
You said:
“You mean like Miskolczi’s 230 observations over 25 years…”
and then later
“My only reference was to the empirical data he discovered.”
Sounds to me like you’re trying very hard to suggest that Miskolczi produced some experimental observations, instead of just looking up numbers in a standard database (TIGR).
Sounds to me like you’re making up things as you go along. Did I say “experimental observations” … nope, those are your words. Miskolczi did “discover” a relationship in real empirical data/observations. Why would anyone care who made the direct experimental observations? It’s not relevant to the discussion. And, why do you come unglued at something that’s not relevant? Are you worried that Miskolczi is onto something?
All I’m doing is pointing out there are multiple cases which would be explained if there was a limit to the GHE. Could they all be coincidences? Well, from a purely logical point of view that is unlikely. So, I’m simply pointing out that more effort should be put into understanding these issues. That’s all.
@Tilo
> Now, when the sunlight enters the bottle it releases a certain
> amount of energy to those molecules, and the longwave radiation
> coming back from the black surface releases more energy to those
> molecules.
Tilo, if you’re trying to defend the N&Z theory, then you can’t use warming caused by absorbed radiation. That is the counter theory.
In general the sunlight will warm the solid walls of container, which will then diffuse into gas in contact with surface, eventually mixing through the gas until equilibrium is reached. Yes, any GHG’s in the gases will absorb a small amount. But N&Z, I believe, claim that this is neglible if present in trace amounts.
Yes, a gas under pressure has higher heat capacity because of the increased mass density. But if I’ve gleaned correctly, this particular experiment wasn’t set up very carefully (i.e. adiabatically) and is somewhat useless because the container will try to come into equilibrium with its contents and surroundings, so I wouldn’t expect to see temperatures rising because the pressure it higher. Would lead get hotter than aluminum, both exposed to sunlight in the same sealed container?
To defend N&Z you have to show how the Ideal Gas Law is creating the so-called “ATE” effect.
How would you design an experiment to show that? Well, why not pick 8 or so planets, with and without atmospheres and show that you can predict their termperatures from pressure alone.
Of course that’s what N&Z already did. But they did it empirically. They need to run this experiment again, but this time deriving the results from first principles, not empirical fitting. (Thanks Eli).
😐
@John Day
> Of course that’s what N&Z already did. But they did it empirically.
I should have added that there is really nothing wrong with their emprirical fitting, since it produced a very smooth curve with a small number of parameters, suggesting a natural law lurking in the background. There was no ‘overfitting’ in the sense of contrived contortions or gymnastics to make a regression line wiggle through a random set of points. But this will never please the critics, so they must at least show how their power law can be derived from first principles, in the same way Boltzmann derived Stefan’s Law and Bose & Einstein derived Planck’s Equation.
There is an interesting footnote on the Bose-Einstein derivation. Bose couldn’t get his paper published on his new quantum-insprired statistcal distribution of spin states because it was rejected by his peers who claimed it was mathematically unsound (plus he didn’t have a PhD). Einstein read the paper, saw that Bose was right and submitted it in German under both their names. It became one of the great theoretical physics achievments of the 20th century.
😐
John Day says:
January 27, 2012 at 3:31 am
That interpretation of Ned’s words proves beyond a doubt that you don’t have a clue about what you are raving about. If you plug in Ned’s 14,800 W/m2, as I said above, you don’t get a 133° temperature rise as Ned says.
No, you’re not. See your pathetic nonsense immediately above regarding W/m2. You are here childishly attempting to school people who, unlike you, actually know what they are talking about.
John, you are right. I am overjoyed to talk science with folks, but I don’t suffer puffed-up fools gladly. I give them a couple chances, and if they continue to be arrogant idiots who want to answer questions for others, questions that they don’t have a clue about, I call them on it. Consider yourself called.
w.
PS–For those keeping score, Ned had said:
That statement, by itself, makes no sense at all. Ned also said:
I have no clue what Ned means. I have asked him. He hasn’t answered. His court jester, John Day, claimed he knew the answer and would answer for Ned. Except then he claimed he wouldn’t answer for Ned. Now, John again claims to know the answer. Now he says this was Ned’s meaning:
The temperature corresponding to 14,800 W/m2 is 442 degrees. That’s 133 degrees above 309 degrees. That’s why Ned’s statement makes no sense. John’s statement also makes no sense.
tallbloke says:
January 27, 2012 at 7:56 am
So your claim is that the temperature of Venus, with an albedo of 0.88, is secretly controlled by the surface albedo that you think Venus might have if there were no clouds?
We are talking about the surface albedo of Venus, where hardly any light makes it because of the clouds, yes? And you are claiming that the surface albedo is the regulating factor in the Venusian surface temperature?
Here’s the deal. You are seriously making the argument that the temperature of the earth can be simply calculated by making the following assumptions:
1) The albedo of the Earth without oceans is exactly equal to the albedo of Venus without clouds, which in turn is kinda like the albedo of the moon, but oh, my, it’s much less than the albedo of Mars.
2) The albedo of the Earth’s ocean floor is a critical factor in the Earth’s current temperature.
Really? That’s your serious claim? That to calculate the Earth’s temperature, what we need to do is to assume that if the oceans weren’t there, the ocean floor would have an albedo about two-thirds that of Mars, and that that assumed ocean floor albedo rules the final temperature?
Do you really read this stuff over before you send it off?
Tallbloke, the exact number they used is 25.3966. This is ((1-alpha)/(epsilon*sigma))^0.25. Assuming that they used epsilon (emissivity) of 0.95 gives the most reasonable numbers. This solves to alpha (albedo) equal to about 0.125.
Note that this is not the empirically measured albedo of any of the planets or moons. It is just a number. It’s kinda like the moon’s albedo, but it’s not the moon’s albedo, or Mercury’s albedo. Mar’s albedo is about 50% higher than that, so your claim that somehow it applies to “all the rocky planets” is seen to be totally unsupportable.
So no, it’s not an “empirical measurement” from their list of planetary albedos, tallbloke, and even if it were, it loses that aspect when you use that identical albedo for all of the planets regardless of their actual albedo.
At that point, it becomes just a parameter that they picked to make the whole thing work. More to the point, there is no theoretical reason to think that it has the slightest meaning to Venus. The surface albedo of Venus itself has little to do with Venus’s temperature. The surface albedo of the earth ocean floor has little do with Earth’s temperature.
The temperature of Venus is not controlled or set by some random number that is two-thirds the surface albedo of Mars, TB, that’s a joke that even you “gravito-thermal” advocates should be able to see through.
w.
PS—But heck, suppose you are right and the (assumed) planetary albedo of 0.125 it is a, what did you call it, an “empirical measurement”. We’ll ignore the fact that you can’t tell us which empire is being measured.
But that still leaves four tunable parameters, which is half the number of data points. So even if you were right, TB, that doesn’t help at all. With four parameters you can still fit an elephant, and with four parameters, full choice of equations, and only eight data points, you are out in statistical fairyland.
Go ask a real statistician, TB, whether the whole four-parameter fit nonsense carries the slightest weight. You’re a long ways off the statistical reservation here, and you don’t seem to even have noticed.
John Day says:
January 27, 2012 at 8:16 am
Are we reading the same thread? N&Z have steadfastly refused to give an elevator speech explaining how their theory works. Your elevator speech ends where it should start, with the explanation of how it works. I can’t even get Ned to explain his calculations on the 14,800 W/m2 … and yet you think they would be “glad to explain it”? Are we on the same planet here?
Because if they are glad to explain it, their continued silence is a curious expression of just how glad they are …
w.
Tilo Reber says:
January 27, 2012 at 8:54 am
No, let’s not try an analogy. Unless you can tell me which claim N&Z are making, an analogy is worse than useless, because it convinces you that we’re moving forwards.
But we can’t move forwards if we don’t understand what the theory is saying. You lay out a whole line of reasoning … so what? Until we know what N&Z are talking about, what good does it do? Your whole layout may have nothing to do with what N&Z are talking about, we don’t know.
And that’s the problem with setting up an experiment now. How can we design the experiment if we don’t have a clue what we are trying to either falsify or support?
w.
John Day says:
January 27, 2012 at 10:28 am
John, I can’t tell you how truly silly your claim is, that because what results is “a very smooth curve with a small number of parameters” there is “nothing wrong”. That is truly eye-popping, gob-smacking, jaw-dropping cataclysmic level foolishness.
You appear to have no clue that with eight data points, five parameters is a VERY VERY LARGE NUMBER of parameters. You make the idiotic claim that a smooth curve indicates a lack of overfitting. You think that if you can fit eight data points with five parameters and a free choice of equations it suggests “a natural law lurking in the background”.
Any one of these claims is enough to earn you a resounding “F” in a statistics class. Combined, they indicate an almost superhuman ability to be oblivious to statistical concepts.
In short, John, once again you have revealed yourself to be beyond clueless. Your claims would have a first-year statistics class rolling in the aisles, and yet you are delivering your nonsensical ideas as though they were pearls of wisdom.
Truly, my friend, I don’t know how to put this nicely, but you are making a monumental arse of yourself. You do not understand statistics. You do not understand what the issues are here. You do not understand what Ned meant with his 14,800 W/m2. You do not understand what you are talking about. You do not understand overfitting.
My suggestion is that you stop acting like you do understand. But heck, that’s just me. If you want to continue prancing around passionately declaiming statistical inanities and spouting mathematical impossibilities, by all means, don’t let me hinder you, play on through …
w.