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Discussion > Numerical calculation of Planetary Black Body Temperature

Roger,

I did exactly what you say and computed the temperature at every point on the surface as a function of the fourth root of the incident radiation and then averaged that temperature across the surface. The resulting average is 266K. This is probably a little high (I know it is because I recalculated it as closer to 250K) because the albedo changes dramatically with incident angle. The S-B temperature is the temperature that would be required were the planet at a single temperature such that outgoing IR radiation balances the incoming solar radiation. This is different to the arithmetically averaged surface temperature.

It turns out that the average and the S-B temperature are actually very close.

Be careful with the Diviner data. It is not the last word and is but one set of results. It also shows a surface mean over a diurnal range of 213K which is lower than the temperature at the isothermal surface. This indicates to me that the surface is not in thermal equilibrium possibly as a result of small seasonal effects. For me the 240K temperature is more representative. Read also the other paper I sent you which estimates regolith temperatures at the equator and along a meridian.

The Chinese paper has a meridional transect and models the temperature as a function of latitude as

T(theta) = T(equator)* cos^0.25(theta)

Integrating this function between -Pi/2 and Pi/2 and dividing by Pi should give you a good estimate of average temperature.

Jan 8, 2013 at 10:16 PM | Unregistered CommenterPaul Dennis

Roger,
the functional dependence I gave you is wrong. The cos is raised to the power 0.2 (based on their observational data).

I've done the integration and the average temperature based on the 240K equilibrium equatorial temperature is 212K.

Further to my comment about the Diviner data there are long term measurements of subsurface temperature at Apollo sites. Temperatures were recorded at ca. 1m depth over 5 year periods. At this depth there is no diurnal or seasonal fluctuation. The temperatures are between 252 and 256K. At 0.4 m depth at the Apollo 15 site the temperature cycles between 250 and 260K. These temperatures must be very close to the equilibrium surface temperature as the internal heat flow is on the order of mW only. Apollo 15 is at 26 degrees North and 17 at about 20 degrees N. (see LONG-TERM WARMING OF SURFACE AND SUBSURFACE TEMPERATURES OBSERVED AT APOLLO 15 AND 17 SITES: IMPLICATIONS FOR FUTURE LUNAR GEOPHYSICAL MISSIONS. S. Nagihara1, P. T. Taylor2, D. R. Williams2, and Y. Saito3, 1Texas Tech University, Lubbock, TX 79409 (seii- chi.nagihara@ttu.edu), 2Goddard Space Flight Center, Greenbelt, MD 20711, 3Institute of Space and Astronautical Science, Sagamihara, Japan.)

These 'tropical latitude' temperatures are greater than those estimated by the Diviner mission. Since the data is measured in-situ there is no reason to doubt them. If we use 256K as the temperature at these latitudes and use the function I drew attention to above then the average temperature is 230K.

If there's any moral to this story it is that the S-B temperature estimated as BB recommends (and I concur) is 268-269K. The average surface temperature based on an area weighted assessment of local temperatures (calculated) is 266K. The empirical data based on (i) satellite measurements and (ii) in situ observations suggests that an area weighted average temperature is somewhere between 212 and 230K.

Given the great paucity of data, uncertainties in albedo and emission, difficulties with calibration of radiometer instruments etc. I don't think there is anything to say there is anything wrong with our current understanding of the radiative balance of the moon.

After reading N&Z I have to confess I still have no idea what they are trying to do. I can't follow their integration and their model of ATE makes no physical sense to me. I'm done with lunar temperatures. It's been an instructive experience to spend some time looking at this issue and thanks to everyone who has contributed, especially BB who drew my attention to the SoD site and through his gentle persistence highlighted the difference between the S-B temperature and that estimated from averaging the temperature field.

Jan 8, 2013 at 10:50 PM | Unregistered CommenterPaul Dennis

Thanks Paul,

But I don't think we are going to agree on this. Logic tells me that as the Diviner results seem to agree with the theoretical, equilibrium SB temperatures then your calculation must be incorrect.

I will try to find the time to write a numerical code this weekend.

Cheers, Roger.

Jan 8, 2013 at 10:52 PM | Unregistered CommenterRoger Longstaff

Step away for a minute and it all goes wild. I was about to post the sane as Roger, that Paul's number is too high, higher than the diviner figures allow. Then Roger posited that the arithmetic mean of each point and its anitpode, integrated is one thing and the incoming solar diveded by the spherical area them converted to an S_B temp is another. And that is the answer. They are different things. They key is that the concept of an average temperature is already broken so we have two different concepts of what it is. The numerical method gives lowest average at zero rotation and probably approaches the other result as the rate increases (my speculation). The standard method is independent of rotation rate. That's why we are in dispute over the rate making a diffenece. It does for one way but not the other. Which is right? They both are, and neither. They are different concepts.They cannot be compared with any validity. And that is why you can't compare the earth mean temp by the standard method with some figure mashed up from thermometers by dodgy methods on behalf of national weather services. The so-called 33K difference is completely irrelevant, apples and staircases would be a more valid comparison. That is one of the favourite memes of the settled science, and it is rubbish.


Please don't ask me to explain that again!

Jan 8, 2013 at 10:53 PM | Registered Commenterrhoda

Thanks again Paul, our last posts crossed. I also need to move on. Perhaps a final thought from BB, Martin and BigYin?

Jan 8, 2013 at 10:59 PM | Unregistered CommenterRoger Longstaff

Final thoughts? Well, I've had the odd experience of a few people agreeing with me (or to be more honest, agreeing with SoD) and, since I only come here for a good argument, this has therefore been somewhat disappointing ☺

Jan 8, 2013 at 11:52 PM | Unregistered CommenterBitBucket

The Christmas and New Year period is my busiest time of the year, quickly followed by the Jan/Feb period which should be my quietest, but is taken up with getting essential maintenance work and stupid stuff like bookwork done, thereby becoming almost as busy. So time is tight, but I’d just like to jump in here and say what an absolutely fascinating couple of threads this one and Rhoda’s have been so far. I’ve been leaving the laptop on all day and just popping in and out to read the various comments when I‘ve had a minute or two spare. Congrats to all those who’ve taken part. Big Yin, I don’t know if you’ve ever taught, but I sure could have done with you when I was doing physics at school. Even I could (mostly) understand your explanations and, believe me, that’s saying something. Great to see Paul Dennis here and good stuff from Martin, Roger, Rhoda and the others too. I think the best compliment I can pay is to say it’s reminded me of the old days at CA.

BB, respect breeds respect. Nice to see you asking questions and making comments without (on this thread at least) the silly little “digs” you all too often include. Keep it up and I might have to change my mind about you ;)

Jan 9, 2013 at 2:31 AM | Registered CommenterLaurie Childs

Final thought?

This has been somewhat of a schizophrenic thread for me, as my figures oscillated between N&Z and IPCC. In the end I got them to match Paul Dennis, who then discovered something at SoD that I still don't get the consequences of... were we right or wrong? And why won't Roger agree? All confusing and not a totally satisfying result.

I'm not sure I can go much further with the numerical solution, I had hoped it would prove something one way or the other, but it just seems to have polarised the two 'sides'. There is scope for adding in lunar albedo, but all it would do would be to modify what I already have, not clarify it.

I think my next project will move away from numerical computation of the spherical intergration and into the simulation area - the array of global points with their own temperatures, as described earlier in the thread. But it'll have to be AFTER I get some of my real work done... :/

Thanks

Jan 9, 2013 at 8:16 AM | Unregistered CommenterTheBigYinJames

The standard method, with the disk area of inbound radiation and the sphere area of outbound, that is the beautiful theory. The Diviner measurements are the ugly facts. It is absolutely no use having a method of calculating planetary temperatures which does not match a well-described physical example.

My explanation for the mismatch is that the two 'average temperatures' are in fact different things. You can compare two planets using the standard method, or using numerical methods, or using physical measurements. If you try to compare across methods, it will not work. Because there is no such thing as an average temperature, a fact of which we are all well aware, but which we tend to ignore in practice.

Lesson learned:

Rate of rotation makes a difference to numerical and observed results, not to standard.

Local albedo makes a difference to calculated results, not to standard.

Try this with a wet planet? Forget it, only observations wil work, and if we were really really clever, maybe a GCM.

Conclusions drawn by comparing standard method temps with measured temps have no validity. (Forget that 33K. The difference is more like 100K between measured temps earth/moon. And the difference is explained by a whole heap of reasons of which GHE is only one)

Jan 9, 2013 at 10:08 AM | Registered Commenterrhoda

Since I was at least partly responsible for this thread I have been following it — at a very respectful distance and at times struggling to keep up.
One thing that Paul Dennis said yesterday worried me at the time and it was only this morning that it clicked.
Paul, you said "From the point of view of the sun all it sees is a flat disc!" and I don't think you're right.
What we would see from space would look like a flat disc but what the sun's radiation "sees" is half a sphere and I think this is where Postma, perhaps more than N&Z, argues that using average levels of radiation breaks down. The radiation is considerably greater at the equator than at the poles simply because the earth is not a flat disc. If the insolation/irradiance were equal across the the side facing the sun then, he claims, it would be spread too thinly to have the effect it does on surface temperature. (I admit I'm speaking very much in layman's terms, here!)
I don't think I explained this very clearly earlier because TBYJ's answer didn't seem to address what I was driving at. My fault, I'm sure.
The hypotheses that argue the (virtual) irrelevance of CO2 seem to be based on the idea that the IPCC, and presumably the 'mainstream' climate community, argument falls down on this point, namely that (a) the earth is not a flat disc,and (b) you cannot simply average incoming radiation. I am seduced by this argument when I look at the (admittedly extreme) case of the Sahara Desert which can be 45C at 2pm and -10C 12 hours later. To treat it as if it were 17.5C all the time surely cannot be the right way to look at heat transfer.
Perhaps I should just stick to gardening!

Jan 9, 2013 at 10:55 AM | Registered CommenterMike Jackson

Thanks to all for a lively and good natured discussion. But I think we all need to go now for work reasons. I think it is half time, with a score of one all (joke!!).

I am going to investigate collaborating with a university to code this up. If I can do this I will post the results. I think this is worth doing as The Diviner results agree with SB physics but disagree with IPCC physics, and I want to know why. Some final thoughts that could be of interest to modellers:

A first estimate of surface conductance can be made from the "heat leak" from the darkside measured by Diviner (approx 1.5K per day).

There is no isothermal boundary under the surface at 240 - 250K, as spacecrfat have measured temperatures of 25K in lunar craters at the poles, so this is clearly latitude dependent.

Best to all, Roger

Jan 9, 2013 at 10:55 AM | Unregistered CommenterRoger Longstaff

...Well, I've had the odd experience of a few people agreeing with me

That happens when you participate constructively. Try it.

Jan 9, 2013 at 12:04 PM | Registered Commentershub

Thanks to all for a lively and good natured discussion. But I think we all need to go now for work reasons. I think it is half time, with a score of one all (joke!!).

I am going to investigate collaborating with a university to code this up. If I can do this I will post the results. I think this is worth doing as The Diviner results agree with SB physics but disagree with IPCC physics, and I want to know why. Some final thoughts that could be of interest to modellers:

A first estimate of surface conductance can be made from the "heat leak" from the darkside measured by Diviner (approx 1.5K per day).

There is no isothermal boundary under the surface at 240 - 250K, as spacecrfat have measured temperatures of 25K in lunar craters at the poles, so this is clearly latitude dependent.

Best to all, Roger

Jan 9, 2013 at 10:55 AM | Roger Longstaff>>>>>

From by own, and Perhaps Mike Jackson's and Roger Lonstaff's, point of view I think the aim of bringing the work of N&Z into the discussion on GHE has proved it's worth.

For my own part, the fact that N&Z collaborated closely with members of the NASA JPL team responsible for commissioning the Diviner instrument, who I imagine know the best way to interpret the measured results, when reaching their calculated Lunar temperature of 197.3K [NOT the previous figure of 154K from their earlier work when fewer data were available, and which seems to have caused some confusion in the thread discussions] is enough for me to accept their figures till peer review determines otherwise.

We now seem to accept that the 'accepted' 33K attributed to GHE is nonsense, and therefore the best guessed contribution of CO2 [and water vapour] based on this 33K nonsense is also wrong. So what is the REAL cause of the atmospheric greenhouse effect ,NOT radiative as radiation alone cannot explain such a large rise in temperature.

If one wishes to dismiss the contribution of Ideal Gas Laws, As proposed by N&Z and others and which was accepted for planetary warming prior the the 'radiative' GHE fad of the 70's] then a serious reworking of radiative GHE is need urgently.

Rhoda has set up the thread to explore experimental ways to measure [radiative?] GHE without much response so far, but at least an acceptance of the much larger ACTUAL contribution of GHE is another stepping stone on the way to defining a more realistic theory of climate.

Jan 9, 2013 at 12:09 PM | Registered CommenterRKS

RKS,

We now seem to accept that the 'accepted' 33K attributed to GHE is nonsense, and therefore the best guessed contribution of CO2 [and water vapour] based on this 33K nonsense is also wrong.

Really RKS, that's a bit naughty. That's not what we found.

Those of us who modelled rotation, do not accept the 33K is 'nonsense' - my final model put it at 50K, rhoda got something similar, and Paul Dennis got something even closer. Considering my considerable approximations, I would consider we've done as much as we can. Also, we've been talking about airless worlds the whole way through, mostly the moon.

The argument then split off onto the difference between SB mean temperature and arithmetic sum of temperatures, and why you can't compare them (which is what N&Z appear to have done)

I think this thread is done. Roger still thinks there is scope for N&Z to be right wrt Diviner measurements, and I won't attempt to disabuse him of that idea here, since this thread is specifically about calculating SB averages numerically, which we've done.

Can we just leave this discussion thread unsullied now? It's been one of the less fraught ones on here, and I hope a model for how we might conduct ourselves in future... the polite exchange of views, theories and ideas, with no polemicising tacked on the end and no bulldozing.

Jan 9, 2013 at 12:22 PM | Unregistered CommenterTheBigYinJames

Sorry,

My last post should have been on Rhoda's experimental GHE thread although I'll also leave it here as it has some relevance to this thread.

Jan 9, 2013 at 12:27 PM | Registered CommenterRKS

A word of warning - I have tried four times to follow the link to the SoD given by BB in his post of 8 January at 5.45. On each occasion is has crashed my computer.

Anybody else had problems?

Jan 9, 2013 at 5:34 PM | Unregistered CommenterRoger Longstaff

Get a new computer; it has clearly had its day.

Jan 10, 2013 at 12:30 AM | Unregistered CommenterBitBucket

Get a new computer; it has clearly had its day.

- Met Office, 2011

Jan 10, 2013 at 8:13 AM | Unregistered CommenterTheBigYinJames

BB Link works in Chrome, IE8 which is the last version of IE which runs in XP is now unsupported and webpages are not including it in their testing so it may not work on all websites now.

Jan 10, 2013 at 9:05 AM | Registered CommenterBreath of Fresh Air

IE8 is not unsupported! Google Apps decided to discontinue support when IE10 came out in November, but it's still a supported browser, being used by 24% of people overall. IE6 is still MS supported (on the appropriate OS and service pack) until 2014, never mind IE8!

Jan 10, 2013 at 9:21 AM | Unregistered CommenterTheBigYinJames