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Post by glc on Jun 14, 2009 20:36:16 GMT
This is in response to queries about ~1 deg being the expected warming from a doubling of CO2. This is the easiest explanation I can come up with. As well as showing that 1 deg is a reasonable ‘ball park’ figure, I will also show why Steve Milloy’s calculation for climate sensitivity is wrong. First, though, a couple of points. (1) The forcing for 2xCO2 is assumed to be ~4 w/m2. This is generally accepted by all climate scientists including those who are sceptical of significant AGW. In any case, the amount of forcing is a separate argument which can be addressed in another post/thread. (2) Numbers used in the following are chosen for their simplicity rather than accuracy. This post is for demonstration purposes only and the resultant calculations should not be relied upon.
Okay. Let’s start by considering an earth and atmosphere with no greenhouse (IR absorbing) gases. In this case, energy emitted from the earth’s surface (G) will be the same as that emitted to the atmosphere (A), i.e. we have
G = A
In this fictitious earth, all energy is transmitted to space directly for the ground. But, of course, G ≠ A. Not all the energy is transmitted directly - some is, but a significant proportion gets absorbed and then re-emitted (roughly speaking half up – half down). In an atmosphere in which 50% of ground energy is emitted directly to space and 50% is absorbed, then a further 25% of the total would be emitted to space and 25% back towards the ground. If Λ (lamda) is the ‘absorption factor’, then it should be obvious that
Transmission (T) = 1 – 0.5Λ i.e. Total less the ½ of the absorbed energy From the known surface (G) and atmosphere (A) fluxes we can calculate a reasonable estimate for how much energy is absorbed in the atmosphere, i.e.
A = G (1 – 0.5Λ) (i)
Substituting A = ~240 w/m2; G = ~390 w/m2; we have
240 = 390 (1 – 0.5Λ)
or (1 – 0.5Λ) = 240/390 = ~0.62
This implies that ~62% is emitted to space; ~38% is emitted back towards the ground; and ~76% (Λ = 0.76) is absorbed by the greenhouse gases in the atmosphere which is not far out and close enough for our purposes.
Now then – what happens if we increase the concentration of greenhouse gases, so that the outgoing radiation is reduced by 4 w/m2. What happens to Λ and the proportion of energy transmitted. Substituting the ‘new’ flux of 236 for A, we have 236 = 390 (1 – 0.5Λ)
i.e. (1 – 0.5Λ) = 236/390 = ~0.605
So now only 60.5% is transmitted to space and Λ increases to 0.79
But now we have an imbalance. 240 w/m2 is coming from the sun but only 236 w/m2 is being emitted to space and as I’ve pointed out a number of times recently
Incoming > Outgoing = Warming
So the earth will warm until equilibrium is established. If we substitute the new value of 0.605 for Transmission into (i) we can see how it affects G as follows:
240 = G (1 – 0.5Λ) = G (0.605)
Therefore G = 240/0.605 ~ 397 w/m2
First point to note: The effect of a 4 w/m2 change in forcing at the TOA is to increase the surface radiation by 7 w/m2. This is why Steve Milloy is wrong. In his forcing calculation, Steve assumes a G:A ratio of 1-to-1, but, as shown here, this is not correct.
Now we need to find out what effect this has on temperature. For this we apply the Stefan-Boltzmann law which describes the relationship between Temperature (K) and energy as follows:
E = σT4 where σ = 5.67 x 10-8 Note for simplicity’s sake I’ve used the Blackbody expression. It makes virtually no difference for our purposes, which is to find the temperature change.
With E = G (original) = 390 w/m2 then T (original) = 288K With E = G (new) = 397 w/m2 then T (new) = 289.3K
i.e. Assuming all other factors remain the same (no feedbacks) the temperature change for a change in forcing of ~4 w/m2 is 1.3K.
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Post by northsphinx on Jun 14, 2009 21:08:09 GMT
Of course do I not agree First Substituting A = ~240 w/m2; G = ~390 w/m2; is wrong A is including the atmospheric window. A should be ~195 w/m2 Cant count that window twice. And that make : (1 – 0.5Λ) = 195/390 = ~0,5 This implies that ~50% is emitted to space; ~50% is emitted back toward the ground; and ~100% (Λ = 1) is absorbed by the greenhouse gases in the atmosphere which is not far out and close enough for our purposes. Real funny. The conlusion is that 100% is absorbed already. Any increase in greenhouse gases do not make a difference.
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Post by icefisher on Jun 15, 2009 0:03:42 GMT
First, though, a couple of points. (1) The forcing for 2xCO2 is assumed to be ~4 w/m2. This is generally accepted by all climate scientists including those who are sceptical of significant AGW. I think it would be more accurate to say that the additional forcing is not controversial because it does not result in a disaster scenario by itself. Clearly the forcing is some number, big or small, but I am not going to allow you to say the above when so many physicists are even challenging that number as correct while others simply don't see it as a controversial number (short of endorsing it as the right number).
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Post by glc on Jun 15, 2009 0:11:23 GMT
Of course do I not agree
First Substituting A = ~240 w/m2; G = ~390 w/m2; is wrong A is including the atmospheric window. A should be ~195 w/m2 Cant count that window twice.
No - you're wrong. I haven't counted it twice. Let me put the equation in another form, i.e.
G = S/(1 – 0.5Λ) where S (Solar)=~240 w/m2
If there is no greenhouse effect then Λ=0, then
G = S = A
In other words energy from the sun=energy from the surface =energy from the atmosphere. In fact we would have an "atmospheric window" of 240 w/m2. But as Λ increases the window gets smaller and more energy is absorbed. Currently ~390 w/m2 leaves the surface and ~240 w/m2 leaves the top of the atmosphere. Increasing the concentration of GHG will increase Λ, which in turn will reduce the transmission of energy through the atmosphere.
Even your revised calculation is wrong because if you ignore the IR window from A you must ignore it from G also and the substituted values become G=350; A=195 (your figure) which just tells that ~88% of the energy that can be absorbed by GHGs is already being absorbed. The IR window just means that Λ probably cannot be greater than ~0.9 (350/390).
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Post by glc on Jun 15, 2009 0:17:38 GMT
Clearly the forcing is some number, big or small, but I am not going to allow you to say the above when so many physicists are even challenging that number as correct while others simply don't see it as a controversial number (short of endorsing it as the right number).
Name one physicist who is "challenging the number as correct".
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Post by poitsplace on Jun 15, 2009 1:41:55 GMT
Heh, remember the temperature of the atmosphere relative to the temperature of the ground is the ONLY thing that's important. If the atmosphere were at the same temperature at the ground...forward and back radiation would be equal and CO2 would have no affect at all. In this case the lowest temperature is around 220k. That should hack off a fair chunk of it the potential increase in absorption.
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Post by poitsplace on Jun 15, 2009 1:45:24 GMT
Heh, remember the temperature of the atmosphere relative to the temperature of the ground is just as important as concentration of CO2 (actually more important). If the atmosphere were at the same temperature as the ground...forward and back radiation would be equal and CO2 wouldn't have any significant affect. In this case the lowest temperature is around 220k. That should hack off a fair chunk of the potential increase in absorption.
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Post by magellan on Jun 15, 2009 2:39:19 GMT
Clearly the forcing is some number, big or small, but I am not going to allow you to say the above when so many physicists are even challenging that number as correct while others simply don't see it as a controversial number (short of endorsing it as the right number).Name one physicist who is "challenging the number as correct". Which number? In another thread you asked a similar question, but edited it to include the logical fallacy of the excluded middle. solarcycle24com.proboards.com/index.cgi?action=display&board=globalwarming&thread=639&page=5This appears to be your own theory or can you name one other reputable sceptic scientist who claims that the CO2 effect does not exist. One would also note your use of the word "reputable". To some James Hansen is "reputable", so I guess to each his own. Rather than cut-and-paste formulae to impress others, I'll simply link to Norm Kalmanovitch, geophysicist www.ilovemycarbondioxide.com/pdf/THE_OTHER_HALF_OF_THE_CO2_EQUATION.pdf I've asked this before, so will again: 1) Why doesn't the tropics follow the CO2 warming curve based on your calculations? 2) What makes any warmologist think satellites won't see UHI and land use change effects? 3) Is the earth ever in equilibrium? Name a period of history when it has. 4) Why isn't the atmosphere warming more than the surface? 5) How can 10-20 ppm increase in atmospheric CO2 account for OHC rise from 1993-2003? Please include the calculations. There are others, but it would be nice to get answers to those.
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Post by icefisher on Jun 15, 2009 3:21:24 GMT
Name one physicist who is "challenging the number as correct". Don't be silly. Oh well to humor you. Heres one: biocab.org/Carbon_Dioxide_Emissivity.htmlBottom line here is it takes a rather strange sort to think he can model the climate; most aren't going to just start tearing down simplistic calculations number by number but instead just point out where observations are not supporting theory and where the biggest errors are. The 1 degree hypothetical warming from a doubling of CO2 just doesn't get a lot of attention because its sort of the "junior partner" in the asylum.
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Post by magellan on Jun 15, 2009 3:24:48 GMT
Who wants to tackle how much heat .00038L CO2/L air is required to absorb in order to raise the temperature of a 1M 3 of air with a 1cm contact layer of water (equivalent to 10,000g or ~2.6 gallons} 1 degC? The number is phenomenal. Once I can find the reference, the results will be posted. CO2 is truly a Magic Gas if it were possible, and the fact warmers cannot answer simple questions as in my previous post should raise red flags.
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Post by glc on Jun 15, 2009 9:24:09 GMT
Don't be silly. Oh well to humor you. Heres one:
biocab.org/Carbon_Dioxide_Emissivity.htmlOk - when I asked for a physicist (or scientist) I meant someone who hadn't cobbled together his own hypothesis without even a glance at the observations. This guy posts regularly on CA and while he's not an idiot he can be a bit "off the wall". His emissivity numbers when applied to the whole atmosphere are clearly wrong.
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Post by glc on Jun 15, 2009 11:19:16 GMT
Who wants to tackle how much heat .00038L CO2/Lair is required to absorb in order to raise the temperature of a 1M3 of air with a 1cm contact layer of water (equivalent to 10,000g or ~2.6 gallons} 1 degC?
Magellan (et al)
I made it clear at the outset, that the main point of this thread was to show that a change in forcing of ~4 w/m2 would, in fact, lead to a temperature increase of ~1 deg C and as, a corollary, to show why Steve Milloy's sensitivity calculation is too low. This has been done. Northsphinx is the only one that has come up with a question relating to my post. I did suggest that the issue of actual forcing should be dealt with in a separate thread once this is out of the way - and if someone can figure out a simple way of explaining it.
Anyway you have brought up a point about CO2 raising the temperature of water which is pretty much the same question you regularly ask about heating the oceans. Although I'm not entirly convinced that enhanced CO2 levels are totally responsible for the increase in OHC, the numbers do stack up.
The term 'energy' is often used incorrectly (particularly by me). In the context of heat transfer, energy is really the flux integrated over time. In electrical terms it is power integrated over time (or power x time). So, although kettle uses more power than a light, you still use more energy by leaving a light on for a few hours than by boiling a kettle for a few minutes.
If a change in ghg flux (i.e. a forcing) means that the outgoing radiative flux at the ocean surface is reduced by 1 watt/m2, then the normal rate of cooling will be reduced by that amount. The unit of energy is the Joule where 1 Joule = 1 watt-sec. So every second, 1 joule of energy is added to each square metre column of water. After a year the energy is increased by 31.5 x 106 Joules.
Now then 1 calorie = 4.19 Joules which, by definition, can raise the temperature of 1 cc of water 1 deg centigrade. One cu metre of water = 106 cc. So the energy accumulated over the year could raise the temperature of one cu metre of water as follows:
Tincrease = 31.5/4.19 =~ 7.52 deg C.
For a 100m column of water after 10 years Tincrease =~0.75 deg.
This is just to show that the numbers are plausible. I'm not going further because observations are either for the total accumulated joules in the ocean(x above figure by ocean area **) or for temperatures at various depths. But I think we need to give Hansen some credit, he's not so stupid that he would use a number for earth's imbalance that would fall over as soon as someone tried out some basic physics calculations.
** To finish off: Total ocean area ~360 x 1012 sq metre, therefore
Total Joules in 1 year = 31.5 x 106 x 360 x 1012 =~1.13 x 1022
Levitus reckons on an accumulation rate of ~0.4 x 1022 Joules since the mid-1970s, so my 1 watt/m2 forcing appears to be a bit high certainly as an average over the ~30 year period.
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Post by jimcripwell on Jun 15, 2009 11:35:07 GMT
I have never pretended to be an expert on this subject. I can however, read and understand some science. I look at Yahoo Climate Skeptics. I see today two pieces by Arthur Rosch on the Earth Climate Effect. From my reading, glc and Arthur Rosch cannot both be correct. However, I could be wrong.
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Post by magellan on Jun 15, 2009 11:41:25 GMT
Don't be silly. Oh well to humor you. Heres one:
biocab.org/Carbon_Dioxide_Emissivity.htmlOk - when I asked for a physicist (or scientist) I meant someone who hadn't cobbled together his own hypothesis without even a glance at the observations. This guy posts regularly on CA and while he's not an idiot he can be a bit "off the wall". His emissivity numbers when applied to the whole atmosphere are clearly wrong. As you did not give references in the OP, to whom should we credit the cut-and-paste job? John Finn maybe? Who's he? I've known for months, but do you? ;D No comment on Norm Kalmanovitch? There are others......
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Post by magellan on Jun 15, 2009 11:51:04 GMT
Who wants to tackle how much heat .00038L CO2/Lair is required to absorb in order to raise the temperature of a 1M3 of air with a 1cm contact layer of water (equivalent to 10,000g or ~2.6 gallons} 1 degC?Magellan (et al) I made it clear at the outset, that the main point of this thread was to show that a change in forcing of ~4 w/m2 would, in fact, lead to a temperature increase of ~1 deg C and as, a corollary, to show why Steve Milloy's sensitivity calculation is too low. This has been done. Northsphinx is the only one that has come up with a question relating to my post. I did suggest that the issue of actual forcing should be dealt with in a separate thread once this is out of the way - and if someone can figure out a simple way of explaining it. Anyway you have brought up a point about CO2 raising the temperature of water which is pretty much the same question you regularly ask about heating the oceans. Although I'm not entirly convinced that enhanced CO2 levels are totally responsible for the increase in OHC, the numbers do stack up. The term 'energy' is often used incorrectly (particularly by me). In the context of heat transfer, energy is really the flux integrated over time. In electrical terms it is power integrated over time (or power x time). So, although kettle uses more power than a light, you still use more energy by leaving a light on for a few hours than by boiling a kettle for a few minutes. If a change in ghg flux (i.e. a forcing) means that the outgoing radiative flux at the ocean surface is reduced by 1 watt/m2, then the normal rate of cooling will be reduced by that amount. The unit of energy is the Joule where 1 Joule = 1 watt-sec. So every second, 1 joule of energy is added to each square metre column of water. After a year the energy is increased by 31.5 x 10 6 Joules. Now then 1 calorie = 4.19 Joules which, by definition, can raise the temperature of 1 cc of water 1 deg centigrade. One cu metre of water = 10 6 cc. So the energy accumulated over the year could raise the temperature of one cu metre of water as follows: T increase = 31.5/4.19 =~ 7.52 deg C. For a 100m column of water after 10 years T increase =~0.75 deg. This is just to show that the numbers are plausible. I'm not going further because observations are either for the total accumulated joules in the ocean(x above figure by ocean area **) or for temperatures at various depths. But I think we need to give Hansen some credit, he's not so stupid that he would use a number for earth's imbalance that would fall over as soon as someone tried out some basic physics calculations. ** To finish off: Total ocean area ~360 x 10 12 sq metre, therefore Total Joules in 1 year = 31.5 x 10 6 x 360 x 10 12 =~1.13 x 10 22Levitus reckons on an accumulation rate of ~0.4 x 10 22 Joules since the mid-1970s, so my 1 watt/m2 forcing appears to be a bit high certainly as an average over the ~30 year period. Explain to us how reflected LW IR can warm water as it cannot penetrate beyond .015mm (to be generous). Is water more efficient at emitting or absorbing? The large jump in OHC from 2002 to 2003 doesn't even spark an interest? CO2 caused that, and also the loss of heat increase beginning in 2003? I have no doubt others read my 5 questions and wonder why they are always ignored......
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