Roger Tattersall (aka Tallbloke) writes on his blog of a WUWT comment. Unfortunately WUWT gets so many comments a day that I can’t read them all (thank you moderators for the help). Since he elevated Dr. Robert Brown’s comment to a post it seems only fair that I do the same.
I saw this comment on WUWT and was so impressed by it that I’m making a separate post of it here. Dr Brown (who is a physicist at Duke University) quotes another commenter and then gives us all an erudite lesson. If Nikolov and Zeller feel they need to take any of the complaints on WUWT about the way they handle heat distribution from day to night side Earth seriously, they probably need to study this post carefully. this is also highly relevant to the reasons why Hans Jelbring used a simplified model for his paper, please see the new PREFACE added to his post for further elucidation.
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I can’t speak for your program, but I will stand by mine for correctly computing the ‘mean effective radiative temperature’ of a massless gray body as a perfect radiator. Remember, there is no real temperature in such of an example for there is no mass. It takes mass to even define temperature. (but most climate scientist have no problem with it and therefore they are all wrong, sorry)
I’d like to chime in and support this statement, without necessarily endorsing the results of the computation (since I’d have to look at code and results directly to do that:-). Let’s just think about scaling for a moment. There are several equations involved here:
is the total power radiated from a sphere of radius R at uniform temperature T. \sigma is the Stefan-Boltzmann constant and can be ignored for the moment in a scaling discussion. \epsilon describes the emissivity of the body and is a constant of order unity (unity for a black body, less for a “grey” body, more generally still a function of wavelength and not a constant at all). Again, for scaling we will ignore \epsilon.
Now let’s assume that the temperature is not uniform. To make life simple, we will model a non-uniform temperature as a sphere with a uniform “hot side” at temperature T + dT and a “cold side” at uniform temperature T – dT. Half of the sphere will be hot, half cold. The spatial mean temperature, note well, is still T. Then:
P’ = (4 \pi R^2) epsilon sigma ( 0.5*(T + dT)^4 + 0.5(T – dT)^4)
is the power radiated away now. We only care how this scales, so we: a) Do a binomial expansion of P’ to second order (the first order terms in dT cancel); and b) form the ratio P’/P to get:
P’/P = 1 + 6 (dT/T)^2
This lets us make one observation and perform an estimate. The observation is that P’ is strictly larger than P — a non-uniform distribution of temperature on the sphere radiates energy away strictly faster than it is radiated away by a uniform sphere of the same radius with the same mean temperature. This is perfectly understandable — the fourth power of the hot side goes up much faster than the fourth power of the cold side goes down, never even mind that the cold side temperature is bounded from below at T_c = 0.
The estimate: dT/T \approx 0.03 for the Earth. This isn’t too important — it is an order of magnitude estimate, with T \approx 300K and dT \approx 10K. (0.03^2 = 0.0009 \approx 0.001 so that 6(0.03)^2 \approx 0.006. Of course, if you use latitude instead of day/night side stratification for dT, it is much larger. Really, one should use both and integrate the real temperature distribution (snapshot) — or work even harder — but we’re just trying to get a feel for how things vary here, not produce a credible quantitative computation.
For the Earth to be in equilibrium, S/4 must equal P’ — as much heat as is incident must be radiated away. I’m not concerned with the model, only with the magnitude of the scaling ratio — 1375 * 0.006 = 8.25 W/m^2, divided by four suggests that the fact that the temperature of the earth is not uniform increases the rate at which heat is lost (overall) by roughly 2 W/m^2. This is not a negligible amount in this game. It is even less negligible when one considers the difference not between mean daytime and mean nighttime temperatures but between equatorial and polar latitudes! There dT is more like 0.2, and the effect is far more pronounced!
The point is that as temperatures increase, the rate at which the Earth loses heat goes strictly up, all things being equal. Hot bodies lose heat (to radiation) much faster than cold bodies due to Stefan-Boltzmann’s T^4 straight up; then anything that increases the inhomogeneity of the temperature distribution around the (increased) mean tends to increase it further still. Note well that the former scales like:
P’/P = 1 + 4 dT/T + …
straight up! (This assumes T’ = T + dT, with dT << T the warming.) At the high end of the IPCC doom scale, a temperature increase of 5.6C is 5.6/280 \approx 0.02. That increases the rate of Stefan-Boltzmann radiative power loss by a factor of 0.08 or nearly 10%. I would argue that this is absurd — there is basically no way in hell doubling CO_2 (to a concentration that is still < 0.1%) is going to alter the radiative energy balance of the Earth by 10%.
The beauty of considering P’/P in all of these discussions is that it loses all of the annoying (and often unknown!) factors such as \epsilon. All that they require is that \epsilon itself not vary in first order, faster than the relevant term in the scaling relation. They also give one a number of “sanity checks”. The sanity checks suggest that one simply cannot assume that the Earth is a ball at some uniform temperature without making important errors, They also suggest that changes of more than 1-2C around some geological-time mean temperature are nearly absurdly unlikely, given the fundamental T^4 in the Stefan-Boltzmann equation. Basically, given T = 288, every 1K increase in T corresponds to a 1.4% increase in total radiated power. If one wants a “smoking gun” to explain global temperature variation, it needs to be smoking at a level where net power is modulated at the same scale as the temperature in degrees Kelvin.
Are there candidates for this sort of a gun? Sure. Albedo, for one. 1% changes in (absolute) albedo can modulate temperature by roughly 1K. An even better one is modulation of temperature distribution. If we learn anything from the decadal oscillations, it is that altering the way temperature is distributed on the surface of the planet has a profound and sometimes immediate effect on the net heating or cooling. This is especially true at the top of the troposphere. Alteration of greenhouse gas concentrations — especially water — have the right order of magnitude. Oceanic trapping and release and redistribution of heat is important — Europe isn’t cold not just because of CO_2 but because the Gulf Stream transports equatorial heat to warm it up! Interrupt the “global conveyor belt” and watch Europe freeze (and then North Asia freeze, and then North America freeze, and then…).
But best of all is a complex, nonlinear mix of all of the above! Albedo, global circulation (convection), Oceanic transport of heat, atmospheric water content, all change the way temperature is distributed (and hence lost to radiation) and all contribute, I’m quite certain, in nontrivial ways to the average global temperature. When heat is concentrated in the tropics, T_h is higher (and T_c is lower) compared to T and the world cools faster. When heat is distributed (convected) to the poles, T_h is closer to T_c and the world cools overall more slowly, closer to a baseline blackbody. When daytime temperatures are much higher than nighttime tempratures, the world cools relatively quickly; when they are more the same it is closer to baseline black/grey body. When dayside albedo is high less power is absorbed in the first place, and net cooling occurs; when nightside albedo is high there is less night cooling, less temperature differential, and so on.
The point is that this is a complex problem, not a simple one. When anyone claims that it is simple, they are probably trying to sell you something. It isn’t a simple physics problem, and it is nearly certain that we don’t yet know how all of the physics is laid out. The really annoying thing about the entire climate debate is the presumption by everyone that the science is settled. It is not. It is not even close to being settled. We will still be learning important things about the climate a decade from now. Until all of the physics is known, and there are no more watt/m^2 scale surprises, we won’t be able to build an accurate model, and until we can build an accurate model on a geological time scale, we won’t be able to answer the one simple question that must be answered before we can even estimate AGW:
What is the temperature that it would be outside right now, if CO_2 were still at its pre-industrial level?
I don’t think we can begin to answer this question based on what we know right now. We can’t explain why the MWP happened (without CO_2 modulation). We can’t explain why the LIA happened (without CO_2 modulation). We can’t explain all of the other significant climate changes all the way back to the Holocene Optimum (much warmer than today) or the Younger Dryas (much colder than today) even in just the Holocene. We can’t explain why there are ice ages 90,000 years out of every 100,000, why it was much warmer 15 million years ago, why geological time hot and cold periods come along and last for millions to hundreds of millions of years. We don’t know when the Holocene will end, or why it will end when it ends, or how long it will take to go from warm to cold conditions. We are pretty sure the Sun has a lot to do with all of this but we don’t know how, or whether or not it involves more than just the Sun. We cannot predict solar state decades in advance, let alone centuries, and don’t do that well predicting it on a timescale of merely years in advance. We cannot predict when or how strong the decadal oscillations will occur. We don’t know when continental drift will alter e.g. oceanic or atmospheric circulation patterns “enough” for new modes to emerge (modes which could lead to abrupt and violent changes in climate all over the world).
Finally, we don’t know how to build a faithful global climate model, in part because we need answers to many of these questions before we can do so! Until we can, we’re just building nonlinear function fitters that do OK at interpolation, and are lousy at extrapolation.
rgb
“Arctic ice”
And so yet another potentially interesting thread is hijacked…
About time Gates had an enforced WUWT holiday IMO.
Latitude says:
January 6, 2012 at 1:34 pm
R. Gates says:
January 6, 2012 at 1:27 pm
Climate models do not predict natural variability, as that is not their intent, nor is it even possible, just as map of LA won’t tell me where the daily roadwork is or what bridge is out because of a local flash flood. Climate models can tell me however, that there will be natural variability and even how long periods of natural variability might mask underlying forcing from greenhouse gases.
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Ok, so they can’t predict it…..but they can tell when it will end……
So, when will this lack of warming end?
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You are asking for predictions about the little wiggles in the path of the water drop down the glass pane. How long will the current lower than average solar activity last? When will the next El Nino begin? How about the AMO, when will end turn higher or lower? These are all the natural variations that can mask the warming. They are the wiggles in the path of the water drop down the glass pane. Personally, I expect to see a new modern global temperature record set before 2015, simply because I think that we could get an El Nino that coincides close enough with Solar Max 24 (even though it will not be much of a max) to give the extra boost to global temps on top of the underlying greenhouse forcing. But this is just my educated “hunch”, and certainly not based on any model, as such natural variability isn’t part of them. But of course, if I right, and such a new record is set, since it will occur during a solar max and El Nino, it will be seen as a “step up” in temperatures, and undoubtedly some skeptics will want to suggest it disproves anthropogenic warming,,,when in fact, it does quite the opposite, as “step ups” to new records can’t occur without an underlying long-term increase.
R. Gates says:
January 6, 2012 at 1:38 pm
You must be assuming that the Foster & Rahmstorf 2011 study is in great error (http://iopscience.iop.org/1748-9326/6/4/044022).
I think this assumption in wrong, and that what they found shows in fact that in general the global climate models have it correct and there has not been any slowdown in warming.
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I am. FR2011 was published to explain the “missing heat” problem. There’s just one problem…well…several really, but a big one is, as Bob Tisdale says: “ENSO is not an exogenous factor”. I’m sure you’re also aware of the analysis that shows if you include the coefficients from NCDC Land Plus Ocean Surface Temperature, Hadley Centre HADCRUT Global Surface Temperature Anomalies, RSS MSU Lower Troposphere Temperature Anomalies, UAH MSU Lower Troposphere Temperature Anomalies, then there is not a continuous rise in global temperatures.
Gates: “there have been many pieces of “testable, empirical” evidence as to why natural variability has masked (to some extent) anthropogenic greenhouse forcing over the past decade”
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In other words, we don’t know………….
Gates, everything from heat hiding in the bottom of the ocean, to Chinese pollution, India pollution, volcanoes, low pressure in the Arctic, wind blowing in the wrong direction, sun too hot, sun too cold, earthquakes, ocean circulation, magnetic fields, and gravity….
….pick one
tallbloke says:
January 6, 2012 at 1:57 pm
“Arctic ice”
And so yet another potentially interesting thread is hijacked…
About time Gates had an enforced WUWT holiday IMO.
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Relax Tallbloke, I mentioned sea ice once as an example related to the topic at hand. All of my posts in this tread have been quite on topic, or answers to questions related to the topic.
RGates sets out a conclusion re a thought experiment:
“This simple thought experiment shows that we don’t need to know the details of a process to understand a great deal about it and to make useful predictions. All current global climate models tell us that the additonal greenhouse gases humans have added since 1750 tip the glass off of horizontal and are causing movement in global temperatures. They vary in how much the glass has been tipped (sensitivity) and of course the exact path the water drop will take (natural variation) but they all say the glass is tilted and the drop of water should be moving.”
Right on! BUT –
What if there is a ‘hole’ in the glass sufficient to hold the drop of water? Or a ridge which runs at an angle to the path of the drop or…. etc
So the drop of water will run down the surface if there’s nothing to stop it? But that’s the very question at issue ‘What is to stop it?”.
It is the variables we don’t know about which make all the difference – from stopping the motion completely to altering it’s rate.
But there’s more:
What if the table tilts the other way? Some counterbalancing process tends to level it again when it is tilted, or causes it to go the other way in a reaction to the original tilting?
Or, what if there is a wind blowing which is moving the drop of water and you are concluding that the surface is tilted because the drop is moving? In other words, what if the initial assumptions are wrong?
Your thought experiment is apposite. But if you consider all the possibilities, not just the ones you feel comfortable with, then other conclusions may be drawn.
It is the unkown variables and their effects which is at the heart of the problem. It is the attitude that ‘the science is settled’ i.e. we know all the variables and their effects, it is this attitude which prevents much of the science from progressing.
Kohl P
R. Gates, here’s a little thought experiment for you.
Let’s assume there exists a maximum greenhouse effect that no one yet understands. This cap would be similar to what Miskolczi claims by his constant optical depth conjecture. The GCMs do not have this limit on the greenhouse effect programmed into their models. Now, what useful information you would get out of a climate model?
The fact is there are any number of possible unknowns that might impact the climate models. Any one of them would make the models useless. Since current models have absolutely no ability to predict/project our recent climate why would any sane person expect that to change in the future?
R. Gates said @ur momisugly January 6, 2012 at 1:22 pm
“Thanks for the Langton’s Ant link and info.
Certainly the key to this “puzzle” mathematically is the shape of the basic grid cells (i.e. squares) and the nature of the basic rules for movement. The basic corner to corner symmetry of the square cell must be a key to the eventual diagonal path that emerges. It would be fun to try it with a different set of “rules”, change the basic grid shapes (i.e use hexagrams or triangles instead of squares), put it into 3D space, etc. and see what happens. The amazing complexity that can come from a few simple rules being repeated over and over is truly amazing.”
No need to change any rules. The lesson here is that even obeying a simple set of rules, the ant takes us into irreducible (so far) complexity of behaviour.
The “simple” rules quantum physics can predict the behaviour of hydrogen, but beyond that you are in “ant country”.
The “simple” rules of chemistry can predict the behaviour of only the simplest of biological chemistry. Beyond that, you are in “ant country”.
Climate depends on the “simple” rules of physics, chemistry and biology. It is well and truly into “ant country”. If a numerical model could be made predicting earth’s future climate, solving the Langton’s Ant problem would have occurred decades ago.
Steven Mosher: GHGs create a system that radiates from a higher colder place. Hence, it loses heat at a slower rate. hence the surface must “warm” or cool more slowly.
The conclusion does not follow from the analysis that precedes it. Substantial energy amounts are transferred from the surface and lower troposphere to the upper troposphere by advection and convection. It is possible for this transfer to be speeded up, and hence for the surface to cool, even as energy is accumulating in the upper layers of the atmosphere.
When you add more GHGs you increase the effective radiating height of the earth system. Raising that height results in a system that radiates from a colder place.
The second sentence does not follow; if the effective radiating height of the atmosphere is increased as a result of more CO2 absorbing and radiating energy, it isn’t necessarily the case that the increased height is cooler. If you add GHGs at a particular high altitude, and the GHGs at that altitude absorb radiation, then the mean temp at that height should increase, not decrease. Isn’t that so?
Tallbloke and the good Doctor present us with a broad brush picture of some of what is yet to be settled in the science. R. Gates takes a microscope to this landscape sketch and then tells us we are missing the point.
Then he gives us a “thought experiment” that tips a table (if the analogy to AGW is to hold true) by less than the depth of the scratches on the table surface. (By the way I got some pretty strong negative feedback from Phil’s Mum when I tried it)
Mr Gates, try this simple “thought experiment”. You’ve gathered together a bunch of data from around the world. You’ve run it through some code which gives results robustly supporting the AGW hypothesis. Settles it, if you like. Now you keep all that data and code to yourself. People will believe you, right?
R Gates: This simple thought experiment shows that we don’t need to know the details of a process to understand a great deal about it and to make useful predictions.
1. You may know and understand “a great deal” and still be unable to make accurate and useful predictions, as with climate science.
2. There is no record of climate science making useful predictions, certainly nothing like the accuracy needed to predict the climatic consequences of CO2 accumulation to 2050.
You are beating a dead horse. The questions you need to address are: (1) is climate science complete and accurate enough to make accurate predictions and (2) is there any record of making usefully accurate predictions?
R.Gates “..Now imagine that you had a “model” that told you that as you tip the glass off of horizontal toward one direction, the water drop would begin to run toward that direction with the speed of the movement to be proportional to the degree of tilt off of horizontal….Ultimately, your model predicts the drop of water will fall off the edge of the glass to the ground.”
The thought experiment fails to conserve energy – it simply assumes the tilt and then elaborates on the consequences. You seem to have hit the nail on the head by swinging the hammer a little bit too much.
For the Earth to be in equilibrium, S/4 must equal P’ — as much heat as is
For the Earth to be in equilibrium, S/4 must equal P’ — as much ENERGY as is
@ur momisugly R. Gates
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Time to stop digging, the trenches are deep enough.
Your tactics however, may need to be adjusted 🙂
You are losing this battle.
R Gates: Would it be useful for a shipping company to know that the arctic might be ice free in the summer months sometime in the relatively near future?
Which climate model predicted that. It’s a simple extrapolation of summer ice cover over the last few decades, and the shippers waited until the ice loss was confirmed before scheduling. That’s so, isn’t it? It’s also totally independent of any consideration of how much of the ice loss was caused by CO2 accumulation.
I almost hate to be “ad hom”, but you don’t seem to be thinking about what you are writing.
Excellent, clear post. If I had an applause button on my keyboard i’d press it now.
@ur momisuglyPaul Murphy
“A highly speculative possible answer ”
For a moment there I thought you were talking about CO2 😉
@ur momisugly Steve mosher,
“Raising that height results in a system that radiates from a colder place. That means the radiation loss will be slower as Brown argues.’
Raising the height also increases the surface area of the radiating area, by a factor in relation to the sSQUARE of the change in height.
Regardless of how or whether the modelers understand their models, what is important today is that policy makers view them as black boxes capable of inputting CO2 values and outputting temperatures.
Changing this misunderstanding is not easy when the world’s top science bureaucracies (AGU, APS, NAS, IPCC, etc) insist on portraying the models as reliable tools for predicting future climate.
R. Gates says:
January 6, 2012 at 9:28 am
R. Gates;
Gerry North said:
“There are so many adjustables in the models and there is a limited amount of observational data, so we can always bring the models into agreement with the data.”
So, until verified by accurate forecasting of future climate, these GCM’s have no claims on validity, especially not where vast suns of money are at stake. These models were too dubious and primitive to be included in any “gold standard” IPCC report except in an appendix, noted as a curiosity and with strong precautionary language as to assigning any significance to their constructs.
I agree Tallbloke, but the problem isn’t Gates the Troll. The problem is those feeding the Trolls. I still want to see a “climate model” built from the ground up, literally. Start with a sphere of rock, such as the moon. We could calibrate that model against the moon. Then add atmosphere (without AGW greenhouse) and then Earth’s oceans; then evaporation and clouds and rain.
This post suggests an approach to the first step.
R Gates said: This simple thought experiment shows that we don’t need to know the details of a process to understand a great deal about it and to make useful predictions. All current global climate models tell us that the additonal greenhouse gases humans have added since 1750 tip the glass off of horizontal and are causing movement in global temperatures. They vary in how much the glass has been tipped (sensitivity) and of course the exact path the water drop will take (natural variation) but they all say the glass is tilted and the drop of water should be moving.
That is somewhat delusional. Your thought experiment actually tells us that a model can mimic the real world to the extent that we can correctly factor in all the relevant variables. (This is probably not so hard for a drop of water trickling down the side of a glass.) In lieu of all the relevant variables a model can mimic the assumptions, biases, prejudices and ambitions of the programmer.
You know, if once, just *once* this “conversation” could take place without someone conflating GW, AGW, and CAGW, I would take it as a kindness.
. Remember, there is no real temperature in such of an example for there is no mass. It takes mass to even define temperature. (but most climate scientist have no problem with it and therefore they are all wrong, sorry)
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This claim is utterly wrong.
The definition of temperature has no dependency on mass whatsoever. At the microscopic level to define temperature simply requires a collection of particles whose energy distribution obeys Boltzmann statistics.
Counter examples to this claim are obvious. The temperature of the microwave background radiation for example. In this case the particles are photons and have no mass.
To Steven Mosher [Jan. 6/11:46 a.m.]: Since the issues raised in your comment have come up, I shall take the opportunity to learn something. I shall assume that you endorse all (or almost all) of Eli’s quoted remarks.
First, and this is just a question: Is my understanding of what you call the “effective radiating height” of the Earth system or what Lindzen calls the “Critical Emission Level” (CEL) correct? Namely, that level or height is the average altitude (from the surface to the TOA) at which at a given time t outgoing LW radiation just balances (if the Earth is in radiative equilibrium at t) incoming SW radiation (less reflected SW). It is not really a specific altitude, level, layer or height, but an average of many of these. Of course, the average can be higher or lower at different times.
Second, I do not fully understand two comments in your post, one from Eli and one directly from you. Eli says: “Raising the greenhouse gas concentration raises the level at which the emission to space occurs to a colder level, and thus one where emission is slower. To make up for that the surface has to warm in order to push more energy through the open window directly into space.” Your comment was: “It’s the slowing of the radiation loss at the TOA that drives the surface temperature UP. It’s not that back radiation warms the surface. . . . GHGs create a system that radiates from a higher colder place. Hence, it loses heat at a slower rate. Hence the surface must “warm” or cool more slowly.” Eli’s comment seems oddly teleological: “to make up for that the surface has to warm…”, or else what? The surface doesn’t decide to warm, so what makes it warm (or cool more slowly)? You say “GHGs create a system that radiates from a higher colder place.” OK. “Hence, it loses heat at a slower rate.” OK (but with one caveat/concern below). Finally, “hence the surface must “warm” or cool more slowly.” But why must the surface warm? You rule out “back radiation.” So how does this work? In the long before time on a blog far, far away, Leonard Weinstein tried to explain this to me, mainly in terms of changes in the lapse rate and the creation of a more energetic thermodynamic equilibrium from the surface throughout all levels of the atmosphere. If I recall correctly, it was the SW Solar that provided the necessary energy in the first place. Alas, his efforts were not altogether successful, and I’m sure this was my fault.
Third, my caveat/concern with higher/colder = slower heat loss. I do not deny that, but I nevertheless wonder whether the radiative model you endorse allows for the possibility that (a) convection, especially moist convection can provide a path around/through purely radiative transfer and (b) that the surface energy transport of this convection may have been significantly (to use G.W. Bush’s fine phrase) misunderestimated in radiative-convective models. There are a number of published papers which suggest that it has, especially in the tropics. Warm moist air rises, significantly for a time warms large portions of the upper atmosphere, then condenses releasing latent heat, which then has a much easier shot at radiating OLW ratiation to space. All this the result of the “mechanical” process of convection (at least up to the last radiative step), not of short, stepwise radiative transfers through the height of the atmosphere.
Fourth, and finally, why does Brown’s “power law” argument not work on net (taking diurnal and latitudinal changes into account) for all the OLW radiation, that is, all the levels from which it is emitted, at least to such an extent that there are important modifications needed to be made in the more standard Earth radiation budget schemes?
Lazy,
I think you’d better rethink some of your assumptions regarding mass and temperature.