Home/BlogUPDATE (1:20 pm. CDT 5/13/11): Since the issue of deep ocean warming (below 700 m depth) has been raised in the comments section, I have re-run the forcing-feedback model for the following two observations: 1) a net 50 year warming of 0.06 deg. C for the 0-2000 meter layer, and (2) a surface warming of 0.6 deg. C over the same period. The results suggest a net feedback parameter of 3 W m-2 K-1, which corresponds to a climate sensitivity of 1.3 deg. C from 2XCO2, which is below the 1.5 deg. C lower limit the IPCC has placed on future warming.
Weak Warming of the Oceans 1955-2010 Implies Low Climate Sensitivity
Assuming that the Levitus record of global oceanic heat content increase is anywhere near accurate, what might it tell us about climate sensitivity; e.g., how much global warming we might expect from increasing atmospheric carbon dioxide concentrations? As we will see, the oceans have not warmed nearly as much as would be expected if the climate system really is as sensitive as the IPCC claims.
The following now-familiar plot of ocean heat content change for the surface – 700 meter depth layer is the result of a layer average temperature increase of about 0.17 deg. C over the 55 year record:
In the meantime, global average sea surface temperatures have reportedly increased at about 3.5 times this rate, about 0.6 deg. C, based upon the HadSST2 data.
As Bob Tisdale has pointed out, the above plot expressing heat content in terms of gazillions of Joules sounds dramatic (if you didn’t know, 1022 is 1 gazillion) — but the 0.2 deg. C warming upon which it is based?…maybe not so much.
Nevertheless, what is useful about the heat content data is that it is relatively easy to then calculate from the yearly changes in ocean heat content how much of an energy imbalance (energy flow rate into the ocean) is required to achieve such changes.
This ends up being an average of 0.2 Watts per sq. meter for the 55 year period 1955-2010…a calculation that Levitus also made. Here’s what the yearly energy imbalances look like which are required to cause the yearly changes in ocean heat content:
Note that with considerable smoothing of the data, we see a peak imbalance around 0.6 W m-2 during the maximum warming rate around the year 2000.
Now, by way of comparison, how much radiative forcing does James Hansen (GISS) estimate the climate system has undergone during the same period of time? The following plot shows the various forcings Hansen has assumed:
Let’s assume, for the sake of illustration, that Hansen is correct for all of these forcings. In that case, the average of the all-forcings curve over the period 1955-2010 is about 0.8 W m-2.
Now let’s compare these 2 numbers for the period 1955-2010:
Average Radiative Forcing from CO2, aerosols, volcanoes: 0.8 W m-2
Average Radiative Imbalance from increasing ocean heat content: 0.2 W m-2
Assuming the ocean heat content data and Hansen’s forcing estimates are accurate, how could the average radiative forcing be 4 times the average radiative imbalance? The answer is FEEDBACK:
Radiative Imbalance = Forcing – Feedback
As the system GAINS energy (and warms) from forcing, it LOSES energy from feedbacks: e.g., changes in clouds, water vapor, and most importantly the extra loss of IR energy directly to space from warmer temperatures (which is usually not considered a feedback per se, but it is THE main climate stabilizing influence, and for purposes of discussion I will treat it as a “feedback”).
If there was no feedback (which would indicate a borderline unstable climate system), then the ocean heat content-inferred radiative imbalance (0.2 W m-2) would equal the forcing (0.8 W m-2), which it clearly doesn’t since there is a 4x difference.
Of course, some believe that CO2 forcings do not even exist (although I’m not one of them). Here I am simply trying to determine what might be concluded about climate sensitivity if we assume Hansen’s forcings and the OHC increases are correct. As we will see, the large difference between forcing (0.8) and radiative imbalance (0.2) implies an insensitive climate system.
Next, we can use these numbers to estimate the net feedbacks operating in the climate system. The simple time-dependent model of the climate system in this case looks like this:
Cp[dT700/dt] = Forcing – λTsfc
Which computes the change in temperature with time of the 700 m deep ocean layer (dT700/dt) which has a heat capacity of Cp in response to Hansen’s radiative forcings and radiative feedback in response to surface temperature changes (λTsfc).
The reason why we need to use 2 temperatures is that the surface has reportedly warmed about 3.5 times faster than the 0-700 meter ocean layer does, and radiative feedback will be controlled by changes in the temperature of the sea surface and the atmosphere that is convectively coupled to it.
If we run this model, we can adjust the feedback parameter λ until we get the kinds of radiative imbalances inferred from the ocean heat content changes. The following shows what seemed to provide a reasonable match:
The feedback parameter λ used here is 4 W m-2 K-1, which implies a climate sensitivity of only 1 deg. C warming from a doubling of CO2. This is much less than the IPCC’s estimate of 2.5 to 3 deg. C of warming.
In particular, note from the above model simulation how the strong feedback mostly offsets the forcing, leaving a small radiative imbalance, consistent with the large discrepancy between Hansen’s average forcing (0.8 W m-2) and the ocean heat content-inferred energy imbalance (0.2 W m-2).
The bottom line is that the ocean has not warmed nearly as much as would be expected based upon the climate sensitivities exhibited by all of the climate models tracked by the IPCC.
Now, what I do not fully understand is why the IPCC claims that the ocean heat content increases indeed ARE consistent with the climate models, despite the relatively high sensitivity of all of the IPCC models. While some might claim that it is because warming is actually occurring much deeper in the ocean than 700 m, the vertical profiles I have seen suggest warming decreases rapidly with depth, and has been negligible at a depth of 700 m.
Also, note that I have not even addressed any natural sources of warming. If Mother Nature was also involved in the ocean warming during 1955-2010, then this would imply an even LOWER climate sensitivity than I have estimated here.
Weak Warming of Oceans 1955-2010.
As one can see from your diagram, the ocean heat content at the very least leveled off ,if not has dropped , since late 2006- 2010.
Let’s see, around Nov.2005, the current prolong solar minimum got started. Interesting.
Also interesting, is solar activity was EXTREMELY HIGH from 1955 – late 2005.
Just some data on solar activity, versus ocean heat content. Looks to be more correlated to solar activity ,in contrast to CO2 ,which has been increasing from 2006-2010 ,while ocean heat content has,leveled off ,if not decreased during that time frame.
I will go on record by saying the ocean heat content by the end of this decade will be back to where it was in the very early 1970’s, the only weak period of solar activity from 1955-2005, but nevertheless not nearly as weak as now.
Dr. Spencer ,you don’t have to answer this, but I am curious.
My question is ,are all the postings we do on your reply message board saved ,so that say 5 years from now, you would be would be able to bring them up ,per request, in order to see who said ,what ,when ,and who seems to be correct, and who seems to be wrong?
I hope so, because I have laid it all out. Right or wrong.
I have of course many emails that express my opinions which I know I could retrive in the future to show what I said ,when I said it, but I am curious, if the same can be done with your great message boards,that we get to use,in order to express our thoughts.
thanks.
Dear Dr. Spencer,
It is nice seeing a post with some scientific content in it.
It is also nice to see you openly state:
“Of course, some believe that CO2 forcings do not even exist (although I’m not one of them).”
Most of the people who post here seem to completely dismiss the notion of positive C02 forcing (otherwise known as the greenhouse effect). A particularly vocal example is the
writer of the first three responses who is hoping you enshrine his ignorance for posterity.
But back to science, how can you justify the simple ODE for the depth at 700m? The forcing term is the forcing at the surface, not throughout 700m and simply subtracting some constant times the surface temperature doesn’t make this consistent. You have a heat equation boundary value problem, and we know the Greens function for the heat operator decays exponentially (in this case by depth). So I don’t see how this is a consistent model. I wouldn’t put too much faith in your conclusions from matching lambda.
I don’t know what the IPCC argument is:
“Now, what I do not fully understand is why the IPCC claims that the ocean heat content increases indeed ARE consistent with the climate models”
do you have a reference? I would like to see the argument.
CJ
CJ
CJ:
I’m not sure what your objection to the simple model is. It is simply conservation of energy. A change in ocean heat content for the 0-700 m layer implies a heat flux, no matter what the vertical distribution of temperature change is.
That flux, most will agree, must be radiative. Furthermore, it must be some combination of (1) forcing and (2) net feedback (what we call the radiative response to a temperature change). For feedback upon temperature, I have assumed the surface temperature change is 3.5x the 0-700 m layer average temperature change, as has been observed.
So, I don’t understand what your objection is.
I am objecting the your conservation
of energy through a quantification of feedbacks
being linearly proportional to sea surface temperature.
Your whole argument rests on this lambda, but if the
model is not consistent, then finding lambda by
matching data is meaningless.
CatrunJ:
So, when IPCC-related studies assume linear feedbacks, it’s ok, but when I do, it’s not OK? Hmmm.
Dr. Hansen,
I said I had not yet seen the IPCC argument. My mother
taught me that just because somebody else is doing something
wrong, doesn’t mean you should do it too. There are two
issues
1. Is a linear relationship correct?
2. If there is a linear relationship, what is the radiative feedback linearly proportional to?
I am sure you wouldn’t argue that radiation is linearly proportional to temperature.
What is your physical justification for the simple model (on which your whole argument rests)? Most radiated energy from the oceans is reflected back by water vapor (your favorite green house gas). Surface temperature affects latent heat loss by evaporation which affects water vapor . . .
which = lambda T_s. Hmmm.
The warming of the deeper oceans is indeed a primary counterargument. Roger Pielke Sr has argued that it doesn’t matter but I find his argument unpersuasive that he can’t think of a mechanism by which heat goes to the deep oceans. What studies have been done to support your idea that the deep oceans have not heated up, perhaps by some unknown mechanism?
MikeN,
water becomes less dense as it warms. How do you warm the lower levels without that warmer water convecting and showing up at 700m and above?? The warming would have to be extremely small and diffuse. (see underwater volcanoes and geothermal activity.)
MikeN:
As I stated, the observed warming with depth virtually disappears at 700 m depth…see from the 2007 IPCC report:
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch9s9-5.html
There is no way for warming to go deeper without it FIRST showing up in shallower layers. That would violate the 2nd Law of Thermodynamics. I find the 2nd Law quite convincing, actually.
Assuming your calculation are correct, why does the giss model with the “Hansen Forcing” reproduce an OHC increase that is comparable with Levitus data?(and lower than Lyman reconstruction)
http://www.realclimate.org/images/lyman-models.jpg
Good question, ddd. My first guess would be that Hansen’s model mixes the extra heat much deeper than the observations support (see the IPCC link above showing that warming essentially disappears by the time you reach 700 m depth).
I actually have some evidence to support that claim. I computed the equivalent mixing depths for most of the IPCC models for *interannual* temperature variations during the 20th Century (which can be computed from the models’ global surface temperature changes and top-of-atmosphere radiative imbalances). As can be seen, the GISS models are outliers, with deeper mixing than the other models:
CGCM3.1 30.2 m
CNRM-CM3 18.6 m
CSIRO-Mk3 22.2 m
GFDL-CM2.0 26.8 m
GISS-EH 42.8 m
GISS-ER 50.3 m
FGOALS 11.4 m
INM-CM3.0 25.2 m
IPSL-CM4 16.2 m
MIROC3.2(hires) 36.8 m
MIROC3.2(medres) 36.9 m
ECHAM5 20.3 m
PCM1 20.8 m
HadGEM1 26.9 m
Professor Bob Carter claims in his book that 80% of Earth’s volcanoes are on ocean floors, at mid oceanic ridges and subduction zones. Professor Carter is a geologist so perhaps he knows what he is talking about. All that heat has to go somewhere, I mean, that stuff was molten rock two minutes ago. Wouldn’t this add to the oceanic heat content? You are only measuring the top 700 metres, but warm water rises, doesn’t it. And this is not to mention that one good burp from an average volcano can match mankind’s output of CO2 from burning fossil fuels for a year. Of course its kind of difficult to express this heat as watts per square metre, but it’s still there. Cold water at high pressure can hold a lot of CO2, and it will remain dissolved until the oceanic conveyor belt brings the water up to the surface to de-gas ( years? decades? ) later, when its addition to the atmosphere can be blamed on humans.
Great work!
Your model does not fall into the pile of IPCC nonsense about “amplification”. Your model is not that of the IPCC “forcings and feedbacks” formalism which is all about “amplification” with repeated citations of Bode’s 1945 book about amplifiers.
Your use of the words “forcing and feedbacks” relies only on the energy balance equations and the designation of the “forcing” and the “feedback” is just a use of words with no dynamical physical content such as is usually implied by the circuit diagram of a feedback loop for an amplifier; yours has nothing to do with “amplification”. It is therefore not an endorsement of the IPCC usage of those words.
The stability of the earth’s energy transport process is largely due to the response of clouds secondary to the driving factors, such as increased insolation and decreased supply of cloud nuclei due to protection from cosmic rays. The reduction of clouds due to protection from cosmic rays may perhaps be part of the primary heating that has led to the increased ocean heat content over recent decades, but may perhaps have paused for now. But a most important secondary effect of the increase in atmospheric temperature is an increase in low cloud secondarily causing in increase in reflection of sunlight, and consequent stabilizing by a partial component cooling effect.
Your model uses an explicit calorimeter, the ocean, to convert from radiative effects in W m^-2, which are time rates, to temperature effects in K, which latter is not a time rate but is a steady state quantity. The IPCC doctrine does not directly provide such an explicit calorimeter and is thus just an arbitary fudge. Your model therefore is fundamentally different from the IPCC “forcings and feedbacks” formalism when the latter refers to “amplification”, the more strength to your arm and the more power to your model. Christopher Game
Dr. Roy,
Interesting analysis.
Feedbacks aside, what I fundamentally don’t get is how IPCC claims that there is a 40 year delay between forcing and final effect, specifically from the radiative forcing from CO2? This is frequently used as a justification for why we haven’t yet seen much warming.
How do they even explain seasonal change? With a 40 year delay, it seems there would not be any hemispheric seasonal change at all. Heck, there would barely be any difference even between night an day with a 40 year response time.
Have the IPCC been called upon to specifically quantify how the amount of seasonal change that occurs from a change in hemispheric ocean water and land temperature correlates to a 40 year response time?
It’s always bothered me that the heat flux from the core is not considered, in the models I’ve looked at.
That comes out over the whole surface as a heat flux out of the ground, as volcanism and as tectonic drift. I haven’t explored the physics of all that, but assume that the much of the drift, ultimately, manifests thermally.
My initial check suggests 0.065 W/m2 over land and 0.101 W/m2 on the ocean floor. i.e. at the “surface” (I’m open to correction on that, I’ve never examined it before.) (I imagine it has it’s cycles.)
From the viewpoint of a lumped earth, that’s a flux from below that will move upward as the insolation sourced energy moves downward.
With a delta of 0.2 W/m2, doesn’t that change the model quite a lot!
Hmm. I lost my connnection when I sent this the first time, let’s try again.
ddd: The “match” between the GISS model mean and the NODC’s OHC observations does not indicate the model represents reality. Much of the rise in OHC can be attributed to ENSO, changes in sea level pressure and decadal/multidecadal variations such as meridional overturning circulation. From 1975 to 2005, North Atlantic OHC rose at a rate that was three times faster than the other ocean basins. Now it’s dropping like a stone. And the GISS Model-E does not model AMOC.
Many of the ocean basins, especially the tropical Pacific and the surrounding basins, rise significantly during strong or multiyear La Nina events. The tropical Pacific warms during those La Nina events due to decreased cloud cover/increased downward shortwave radiation (that’s the way a La Nina event works. Increased strength of trade winds -> decreased cloud cover -> increased downward shortwave radiation -> warming of tropical Pacific). The tropical Pacific is also distributing those sunlight created warm waters to the adjoining ocean basins during the La Niña events. But the GISS model E doesn’t model ENSO.
So there are known reasons why the match between the GISS Model E and the observations is meaningless.
I agree with Bob that much of the warming we have seen could be natural, which would imply an even LOWER climate sensitivity than what I have estimated. I am only pointing out that, even if we assume NO natural forcings, the observed ocean warming is still less than what the IPCC would expect.
The tendency of some people to invoke some sort of magical, unobservable, deep-ocean warming which has somehow managed to completely bypass the top 700 meters of ocean seems pretty feeble and desperate.
Excellent discussion.
Catrun J- you say nothing when you post . It is just jibberish, and I am being polite. No substance at all.
Salvatore,
I am glad to hear you find my posts beyond your understanding. If I ever write something you think makes sense, then I know it will be time to retire and go fishing.
Shouldn’t you be attacking Dr. Spencer for agreeing that CO2 is warming the planet? He says 1 degree C for a doubling, you say the whole idea is total BS (and you say it about a gazillion times a month).
CJ
P.S. How are those sunspot numbers doing? Are we still in a prolonged solar minimum?
CATRUN J- I am going to point out two quick items.
On item 2, I had predicted a week prior to when the major earthquakes happened in Japan/New Zealand,that major geological activity would happen some place on the earth ,due to recent solar behavior,during late Feb/early Mar. I am saying point 2 is being set up to possibly happen again. Read point 2.
I have the emails to show when I said it and what I said,in reference to the above. I don’t spin, and I put concise clear thoughts out there,and time will tell ,not you ,if it is correct or not.
Sorry this is not about the ocean heat content,(a great discussion which I am learning much from)but it is about climate,and I just want to express two quick thoughts.
1. I argue it is the distribution of temp. rather then the absolute decline ,that sets the earth(mainly N.H.) into a cooling or warming trend.
2. Notice solar activity has fallen off. I say if this lull last for a few months, more followed by a substancial burst of solar activity earth will have another round of enhanced geological activity.
Dr. Spencer , thanks for allowing me to express my many thoughts, on your message boards.I know you don’t necessarily agree, but that is what makes the climate so interesting and challenging. So many different takes on it.
CATRUM J- Let’s not act like children. Just because we don’t agree ,we should still appreciate the efforts that are being put forth. I will admit you are putting forth ,your efforts. I will say you are knowledgeable ,we just have a different take on things.
I am no longer going to take swipes at you.
CO2 does have some effect on temp., but as it increases the effects are less and less, mainly because I subscribe to the following: CO2, is already absorbing the wavelengths of radiation bands ,it absorbs, at near saturation levels,and it overlaps with water vapor.
Secondly -I see no evidence of the positive water vapor /CO2 feedbacks.
Where is the lower tropoheric hot spot at 400mb. No evidence of this ,as of now. One of the items, at the heart of global warming ,due to increases in CO2.
Another point, the AO has not been becoming increasingly positive as was predicted by the global warmers ,another itme at the heart of their argument.
That is it for now.
I say this ,just in case my prvious post did not come out.
I appricate al the efforts everyone puts out on this board including yours Catrun J.
ALL:
See the update at the top of the article with model results for observed warming of the 0-2000 m layer.
As I understand it, the very low deep-sea temperatures are due to arctic/antarctic waters sinking and flowing into the oceans.
If increased global heating results in increased arctic melt, then this heat would be present in deep water as latent heat, with no temperature signature, as it was 0C at source.
Has anyone estimated what the heat capacity of this water would be?
Your method and results are good, but still there is a risk, while you use terms “forcing and feedback”, that your good work may seem to endorse the IPCC “forcings and feedbacks” formalism that cites the Bode 1945 feedback amplifier theory and is wrong. The key point I wish to make is that there is no amplification, properly defined, in the climate system, while the IPCC formalism is used to bluff people into thinking that there is.
It is hard to compress arguments about this. It may be useful to read the article by Makarieva, Gorshkov, Li, and Donato (2010, Proc. Roy. Soc. A, 466: 1893-1902) at
http://rspa.royalsocietypublishing.org/search?submit=yes&pubdate_year=2010&volume=&firstpage=&doi=&author1=Makarieva&author2=&title=&andorexacttitle=and&titleabstract=&andorexacttitleabs=and&fulltext=&andorexactfulltext=and&fmonth=&fyear=&tmonth=&tyear=&tocsectionid=all&subj_coll_code=&format=standard&hits=10&sortspec=relevance&submit=yes&submit=Submit
that explains for another scenario that thermodynamics asserts the impossibility of what is there called “the dissipative heat engine”. The point the article makes is that “Internal dissipation cannot increase the work output of a heat engine”. The article refers to the proposed hurricane mechanism of Emanuel, which has even found its way into a thermodynamics textbook, horrible to say. This is not quite the scenario of the IPCC “forcings and feedbacks” formalism, but the nearly the same line of argument applies.
For an amplifier, an arbitrarily controllable auxiliary power supply is needed. (Try running your amplifier without a battery!) Thermodynamically, because of the arbitrary control requirement, this may be regarded as a need for a supply of work to be used for heat transfer. There is no such work supply or auxiliary power supply in the earth’s energy transport process. This puts the IPCC “amplification” formalism in the same position as the Emanuel hurricane dissipative heat engine: in the waste bin.
Your model is like an electronic model not of an amplifier, but of a ‘capacitor’ being ‘charged’ by the energy of sunlight. The ‘capacitor’ is the land and sea body, and its ‘charging’ is increase of their temperatures. The rate of ‘charging’ is affected by the clouds, which are affected by the internal state of the system, and this might be rhetorically labeled, as it is by the IPCC, as “feedback”, but is more appropriately regarded as a non-linearity of a passive circuit element. The use of the term “feedback”, like it or not, suggests to many readers that an active circuit element (for example a transistor with a power supply) is involved, which is not so; but the IPCC revels in it, and it does them a treat. The ‘capacitor’ is discharged to space by way of passive circuit elements, which might be regarded as a ‘load’, if you like. These passive circuit elements are the components of the atmosphere. The ‘load’ is increased by adding CO2 to the atmosphere. This is like putting a ‘resistor’ in series into the discharge pathway, and slows the discharge of the ‘capacitor’, but no one in their right mind would call that “amplification” as the IPCC does. The discharge pathway also contains a non-linear passive circuit element, the water vapour column amount of the atmosphere, which increases its ‘resistance’ when the ‘capacitor’ is more ‘charged’, and also slows the discharge. Again this might be rhetorically labeled, as it is by the IPCC, as “feedback” but again is more appropriately regarded as non-linearity of a passive circuit element.
This does not impugn your calculations, but I would like to wave the flag that your use of nearly the same language as that of the IPCC “forcings and feedbacks” formalism runs the risk of seeming perhaps to endorse that IPCC formalism which uses the brilliantly diabolically persuasive rhetorical trick of talking of “amplification” where there is none.
Christopher,
Interesting comments. I’ve heard this kind argument before – that what the IPCC calls ‘amplification’ or feedback is really ‘gain’, and it’s only when ‘gain’ is separated from feedback that the true behavior of the system or the net feedback operating on the system can be determined.
In other words, the direct effect of 2xCO2 is about 3.7 W/m^2. This corresponds to only about 0.7 C of direct warming (assuming all of it is incident on the surface). The remainder of about 0.4 C is a result of system ‘gain’ – not positive feedback or ‘amplification’.
Is this kind of what you’re referring to?
Among the major uncertainities in the forcing is the solar component. Shaviv (http://phys.huji.ac.il/~shaviv/tmp/ZiskinShaviv_2column.pdf and references cited within) point to evidence of an amplification of solar forcing by a factor of 5-7 over simple TSI. This would add close to 1 W/M^2 to the GISS net forcing estimate since 1900 and further reduce the implied climate sensitivity. However Shaviv’s model, which attempts to pull all forcings together and fit both land and SST data, again finds a climate sensitivity of about 1 deg C for 2XCO2, a number that comes up again and again in various empirical studies.
“However Shaviv’s model, which attempts to pull all forcings together and fit both land and SST data, again finds a climate sensitivity of about 1 deg C for 2XCO2, a number that comes up again and again in various empirical studies.”
I think there is very simply reason for this. 1 degree C sensitivity happens to be equal to the measured response of the system to solar forcing. If the surface is currently emitting about 390 W/m^2 and 239 W/m^2 is coming in post albedo from the Sun, that yields a ‘gain’ of about 60% or 1.6 (390/239 = 1.6). 3.7 W/m^2 (from 2xCO2) x 1.6 = 6 W/m^2; 390 W/m^2 + 6 W/m^2 = 396 W/m^2, which corresponds to about a 1.1 C rise in temperature.
Yes. There is wide acknowledgement that the value of 1.1 deg C is correct for the zero feedback case. And as time goes on, the balance of empirical evidence points to a NET value of around 1 deg C (plus minus a few tenths). The question then is how do all the various feedbacks sum to near zero.
Christopher Game replying to the post of RW of May15, 2011 at 10:01AM.
Thank you, RW.
The word ‘gain’ usually implies that one one is thinking of “amplification”. It usually refers to a device in which source and load quantities have the same dimensions, and is usually expressed in decibel, because it is a dimensionless ratio. The IPCC also likes to speak of “gain” here because it works much the same rhetorical trick. The trick implies a power gain. For a purely passive device, of course there is only power loss and the usual term for a dimensionless ratio then is not ‘gain’, but is ‘attenuation’ or ‘loss’. The climate process is a purely passive process. The use of the word loss would not serve the IPCC’s rhetorical purpose.
As well as by empirical studies, science works partly by careful rational use of proper conceptual structures, expressed in proper language, what you might call ‘theory’. Science is corrupted when its theory is corrupted. The IPCC usage is an attempt to brainwash people into accepting corruption of scientific conceptual structures by getting them to accept abuses of proper scientific language. It is easy to wave one’s hands and to say “Who cares about proper use of language, we all know what is meant?” This is just the error the IPCC wants to foster, and that is why it is properly called corrupt. It is just when there are disputes that the proper use of language is most valuable, and corruption of language most destructive of scientific work.
For a ‘device’ or system with different dimensions in the source and load quantities, the more systematic term is ‘transfer ratio’, or, when the system is linear and one is thinking in the Fourier or Laplace domain, ‘transfer function’. The system of interest here has different dimensions in source and load quantities. The climate system here is not properly representable as a signal processing ‘device’ in the ordinary way because it does not have a signal defined as an energy source. In proper scientific language the increase of CO2 is to be regarded not as a signal but as a parameter change. This is not merely a trivial question of words, but refers to an important physical reality.
The usually quoted “no-feedback” figure, of 1.2 W m^-2 or so, for CO2 doubling, is touted by the IPCC as if it were a “signal”. The touted ‘output’ is the land-sea surface temperature change in response. It has the dimension of temperature, measured in C or K. The transfer ratio here is not a dimensionless ratio, and a dimensionless ‘gain’ is not an appropriate name for it.
You write “The remainder of about 0.4 C is a result of system ‘gain’ – not positive feedback or ‘amplification’”
You use the word “result”. This word gives the impression that you are talking about a real physical process of cause and effect. But that is not the case here. The distinction to which you refer, between your 0.7 C and your 0.4 C is purely a mathematical word game. There is no definite physical meaning to what you call the ‘direct warming’. The problem is that the increase in CO2 works by changing the rate of loss of energy from the system, which is a time rate, while the ‘result’ is a change in land-sea body temperature. The ‘sensitivity’ is a quantity that does not refer to a time rate, while the ratio of initiating change to final response, W m^-2 / K does refer to a time rate. Something needs to be done to reconcile that. Dr Spencer’s model does it by splitting the ‘temperature’ into two separate ‘temperatures’ not explicitly related within his model but taken only as two separate empirical inputs, and by using the ocean as a ‘calorimeter’. The use of the ocean as a ‘calorimeter’ is a proper and reasonable way to convert from rate of heating to a rate of temperature change, but Dr Spencer does not actually calculate a “no-feedback” temperature change and his model does not use a definite quantity corresponding to the “direct warming”, beloved of the IPCC, to which your remarks refer. Consequently and fortunately, the question of ‘gain’ to which you refer does not arise in his model. Your use of the word ‘gain’ here suggests that you have been gulled by the IPCC into trying to think about the problem in terms of their corrupt abuse of scientific language.
It may help to clarify this in your mind if you try to work out the physical meaning of the “no-feedback” or “direct warming” effect. You will find that it does not relate in a physical way to the main question of interest here, the value of the climate sensitivity. The “no-feedback” or “direct effect” calculation, taken as a separate calculation, does not come into calculation of the eventual “with feedback” or eventual effect including indirect effects. The “no-feedback” effect is purely a calculational artefact, with no definite physical meaning, a bit of hand-waving if you like. To try to define the “no-feedback” or “direct” effect, one can make various arbitrary assumptions and think in terms of “as if”, but these thoughts do not create a real physical meaning; they are still just hand-waving. Dr Spencer does not make the mistake of trying to produce such a “no-feedback” figure. Christopher Game
Christopher Game says:
“The distinction to which you refer, between your 0.7 C and your 0.4 C is purely a mathematical word game. There is no definite physical meaning to what you call the ‘direct warming’.”
All I meant by this is that +3.7 W/m^2 at the surface directly converted to temperature via the Stefan-Boltzman law is about 0.7 C.
I’m not sure I understand everything your saying, but I’ve heard similar things before.
“Science is corrupted when its theory is corrupted”
In fact, there is no practice of theory to speak of in climate science. There are models, for which there is not even a theory of error. People like Roy Spencer use models and data to interact with theory. That is the way it is supposed to work.
“The “no-feedback” effect is purely a calculational artefact”
Yes. It conceptually allows one to turn on and off certain physical processes in a way that a passive system cannot replciate.
” The use of the ocean as a ‘calorimeter’ is a proper and reasonable way to convert from rate of heating to a rate of temperature change..”
For more on this, see Shaviv http://www.sciencebits.com/files/articles/CalorimeterFinal.pdf . He finds the forcing due to solar variability over several sunspot cycles is much larger than one infers from simple TSI variations. This is possible to do because in this one case Mother Nature allows a Fourier representation between the stimulus (TSI) and radiative forcing, a fact that has been ignored by the climate science gang for decades.
Christopher Game replying to the post of RW of May 15, 2011 at 2:09PM.
Thank you RW.
You write: “All I meant by this is that +3.7 W/m^2 at the surface directly converted to temperature via the Stefan-Boltzman law is about 0.7 C.”
This looks impeccably innocent.
But your appeal to the Stefan-Boltzmann law uses what I mean by an arbitrary assumption, or thinking terms of “as if”. I am saying that it is just a piece of arithmetic unless you have a definite physical model. You do not specify a definite physical model. The Stefan-Boltzmann law is about the surface of an ideal black body radiating into a vacuum. An ideal black body has an ideal black interface with the vacuum. We are not dealing with that case here. So I say that your “directly converted” is hand-waving. Other people wave their hands differently and get different values for their “no-feedback” response.
I am saying that there is no way to do this except by hand-waving. The IPCC does it by hand-waving with massive computations, but still they are just hand-waving. The reason why this is so is that idea of the “no-feedback” response is not based in a proper physical model that might justify the use of the terms “gain” or “amplification”. Christopher Game
Dr Spencer uses a model:
“The simple time-dependent model of the climate system in this case looks like this:
Cp[dT700/dt] = Forcing – ?Tsfc
Which computes the change in temperature with time of the 700 m deep ocean layer (dT700/dt) which has a heat capacity of Cp in response to Hansen’s radiative forcings and radiative feedback in response to surface temperature changes (?Tsfc).”
Dr Spencer’s model relates three empirically recorded time series: for ocean temperature, for so-called “Hansen’s radiative forcing”, and for “surface temperature”. It has two empirical parameters with which to reconcile these three time series, and does a fair job of it.
All three time series are of physical variables that are largely determined by internal state variables of the earth-ocean-atmosphere system. There is no distinct and explicit (or even implicit) driver variable in this model.
Consequently, the use of the terms “forcing” and “feedback” just expresses an arbitrary choice of variables and has no strict relation to the ordinary scientific way of analysing time series for systems of this kind, in which external driver variables are considered to drive internal state variables, along with the mutual interactions of those internal state variables. The ordinary scientific way is used because it is the only reliable way to clarify cause and effect relations. The use of the terms “forcing” and “feedback” here is an arbitrary word game, not a proper use of scientific language. Dr Spencer says it is “traditional” for climatology, but other scientific disciplines would regard it merely as a corrupt abuse of language. I would say perhaps it is ‘traditional’ within the writ of the IPCC.
The true strength of the feedback cannot be found by this method, because, as Dr Spencer has often pointed out, it confounds cause and effect. The only justification for this use of terms is that its purpose is only to show that the Hansen doctrine, which uses the arbitrary word game, does not fit the measured facts of nature. This is a good purpose and justifies the usage, but only ad hoc. Christopher Game
Christopher Game says:
“But your appeal to the Stefan-Boltzmann law uses what I mean by an arbitrary assumption, or thinking terms of “as if”. I am saying that it is just a piece of arithmetic unless you have a definite physical model. You do not specify a definite physical model. The Stefan-Boltzmann law is about the surface of an ideal black body radiating into a vacuum. An ideal black body has an ideal black interface with the vacuum. We are not dealing with that case here. So I say that your “directly converted” is hand-waving. Other people wave their hands differently and get different values for their “no-feedback” response.”
I know the surface is not a perfect black body radiator, but for all practical purposes, it’s close enough. In reality it’s probably 0.99+, but how much a difference is that going to make in calculations? Not much. Also, remember, we’re talking about the surface of the Earth – not the entire thermal mass of Earth including the atmosphere, which has an emissivity of more like 0.6
Christopher Game says:
“I am saying that there is no way to do this except by hand-waving. The IPCC does it by hand-waving with massive computations, but still they are just hand-waving. The reason why this is so is that idea of the “no-feedback” response is not based in a proper physical model that might justify the use of the terms “gain” or “amplification”. Christopher Game”
I don’t disagree with this, but at some things have to be quantified through well established physics, such as the Stefan-Boltzman law.
I meant to say:
“…but at some point things have to be quantified through well established physics, such as the Stefan-Boltzman law.
Christopher Game replying to RW’s posts of May 15, 2011 at 8:42PM and of May 15, 2011 at 9:18PM.
Thank you RW.
You write: “we’re talking about the surface of the Earth – not the entire thermal mass of Earth including the atmosphere”.
Now you are beginning to start mentioning a definite model, but you have a long way to go to establish that your model is of a kind that justifies the use of the notion of “gain” or of “amplification”. The IPCC “forcings and feedbacks” formalism doesn’t justify it, and you have advanced no reason for us to expect that you will do so.
You write: “things have to be quantified through well established physics”
Yes, things have to be quantified through well established physics, and the Stefan-Boltzmann law is well established physics. But that law is well established for an ideal situation with no evaporation and no convection, not for the far-from-ideal situation of the earth’s energy transport process. My point is that you have not used a well-defined model of the earth’s process when you invoke the Stefan-Boltzmann law. So you are not quantifying anything physically real, you are hand-waving. I am saying that when you progress far enough beyond hand-waving, you will come up with a model that does not justify the use of the terms “gain” and “amplification”, because your model will have no source of work, no arbitrarily controllable auxiliary power supply, to take it out of the world of purely thermal dissipative mechanisms. That is the point of the article by Makarieva, Gorshkov, Li, and Donato (2010). Christopher Game.
Interesting post.
I have two observations:
1. The well mixed layer (more accurately, the surface convective layer) of the oceans averages ~50-60 meters in depth globally. This entire layer is thermally coupled to the troposphere, and so can be considered to have a fairly “fast response” to any radiative imbalance, positive or negative. The heat accumulated in the well mixed layer for a change of 0.6C in ocean surface temperature is ~5*10^ 22 joules, or ~1/3 of the total ~15*10^22 accumulated since 1970 (according to Levitus et al). The fraction that represents slow accumulation (rather than a fairly rapid surface response to any radiative imbalance) is only ~2/3 of the total.
2. It should be possible to independently constrain the behavior of the oceans WRT slow heat accumulation versus ocean surface temperature change. The average temperature profile of the thermocline, combined with an average value for thermohaline upwelling velocity (about 1 cm per day), provides an estimate of global average vertical diffusion/eddy down-mix constant for the oceans; that vertical diffusion constant defines the rate at which heat can be expected to “down-mix” into the thermocline due to changes in average ocean surface temperature, independent of measured heat accumulation at depth (eg. Levitus, et al). Such a simple thermal accumulation model ought to reasonably match the Levitus et al ocean heat data if fed only the ocean surface temperature history, and provide estimates of a) how ocean heat content has changed over the past 100+ years, and b) how much heat can be expected accumulate in the oceans for any postulated future change in ocean surface temperature.
Hi,
Here is a work in progress that I thought may be of interest.
http://i54.tinypic.com/2jg5o5l.png
It’s base on fitting simple cyclic functions and a linear trend to rate of change of SST. The interest of this fit is done in the energy domain rather than temperature. I then integrate analytically and plot temperature.
The linear fit becomes a quadratic with a cubic term of 0.74 K/century/century. The oscillatory fit uses just three cosines 60.2 , 58.9 and 20.6 years. These were optimised manually so as to produce the smallest residuals with no long term variation. The assumption is an attempt to model rate of change with linear plus a minimum of cosine terms. No assumption was made about the periods, they were chosen for best fit.
I found out recently that this is similar in many ways to Scafetta (2010) and the results are surprisingly similar in view of the different approaches.
Since we’re in the gross assumption game I took exponential CO2 progression to doubling (1900-2060) and grossly “attributed” the cubic term to CO2. It gave a “climate sensitivity” of 1.17
Quite close to what your model produces.
Dr Spencer,
Shouldn’t you include land surface temperature increases? A quick CruTEM3 check and looks elsewhere suggest it’s increasing at about 1.5 times the rate of ocean warming. Land surface is about 30% of the total surface, so shouldn’t your sensitivity estimate be increased by 15%?
IPCC Fig. 5.4 from section 5.2.2.3 also suggests that warming of continents & the atmosphere plus latent heat of ice adds another ~10% to the amount of heating observed. Very minor and actually within the uncertainties of the ocean measurements, but completeness shouldn’t hurt too much.
Christopher Game says:
“Now you are beginning to start mentioning a definite model, but you have a long way to go to establish that your model is of a kind that justifies the use of the notion of “gain” or of “amplification”.”
There is roughly 239 W/m^2 coming in from the Sun, 239 W/m^2 leaving at the TOA, and the surface is emitting roughly 390 W/m^2. What is the 151 W/m^2 difference if it’s not ‘gain’ (390 – 239 = 151)???
Christopher Game says:
“Yes, things have to be quantified through well established physics, and the Stefan-Boltzmann law is well established physics. But that law is well established for an ideal situation with no evaporation and no convection, not for the far-from-ideal situation of the earth’s energy transport process.”
This I do not understand. All the energy entering and leaving at the TOA is radiative. Latent heat and thermals are in kinetic form and are not part of the radiative budget of the Earth. Conservation of Energy dictates that all the kinetic energy flows from the surface into the atmosphere have to be returned to the surface in equal an opposite amounts. All latent heat and thermals are doing is moving and re-distributing energy around – mostly from the tropics to the higher latitudes.
This seems to be major source of confusion in this field, and I think it largely stems from Trenberth’s energy budget diagram that mixes together the radiative and kinetic energy flows in the atmosphere in a really confusing – and I’d argue, obfuscatory way.
Don’t misunderstand what I’m saying here. Latent heat and thermals are major players in the whole system and ultimate equilibrium temperature, but they don’t contribute to the energy budget, which is all radiative. Of course there is a significant indirect effect in that latent heat, especially, is moving water from the surface into the atmosphere in the form of water vapor and clouds, which then absorbs a large amount of outgoing surface radiation and redirects it back to the surface.
RW says: “What is the 151 W/m^2 difference if it’s not ‘gain’ (390 – 239 = 151)???”
It’s misunderstanding. Calling it “gain” does not tell us anything. What do you imagine the source of this energy is? Do you think there is a source of energy somewhere on Earth that is injecting additional power that is more than half that which we get from the Sun?
P. Solar says:
“It’s misunderstanding. Calling it “gain” does not tell us anything. What do you imagine the source of this energy is? Do you think there is a source of energy somewhere on Earth that is injecting additional power that is more than half that which we get from the Sun?”
Let me ask you then – where is the 151 W/m^2 coming from?
Dr. Roy,
You say:
“As the system GAINS energy (and warms) from forcing, it LOSES energy from feedbacks: e.g., changes in clouds, water vapor, and most importantly the extra loss of IR energy directly to space from warmer temperatures (which is usually not considered a feedback per se, but it is THE main climate stabilizing influence, and for purposes of discussion I will treat it as a “feedback”).”
Can you explain what you mean by this? What extra loss of IR energy directly to space from warmer temperatures?
RW, sorry this is not the place for me to explain the fundamentals of physics to you. You are mistaken but I don’t intend to spam Dr. Spencer’s blog with trivial explanations. Best regards.
RW: We often use energy budget calculations to determine the surface temperature.
The surface exchanges more than just radiatively – latent heat flow from evaporation & condensation is an important (and negative) feedback.
Christopher Game replying to the posts of RW of May 16, 2011 at 6:25PM and at 6:45PM.
Thank you RW.
You write: “There is roughly 239 W/m^2 coming in from the Sun, 239 W/m^2 leaving at the TOA, and the surface is emitting roughly 390 W/m^2. What is the 151 W/m^2 difference if it’s not ‘gain’ (390 – 239 = 151)???”
The actual quantities here are moieties of flow, and there are many such moieties. The basic physics is that the temperature of the land-sea body is such as to cause one moiety of the flow to be 390 W m^-2. The actual fact is a surface temperature of 288K that corresponds to the 390 W m^-2.
That 288K temperature is due to heat passively accumulated during the past, not to added power in the present. If you want to have the amplifier analogy with ‘gain’ you have to accept that it will work in real time. The the passively accumulated heat took infinitely long to accumulate and that isn’t a real time process. If you want a word form other than ‘gain’, perhaps ‘passive accumulation’ would do. Blocking the holes in the bottom of a leaky bucket doesn’t create more water, it just reduces the rate of leakage. Adding CO2 is like blocking some holes in the bottom of a leaky bucket.
You are continuing to try to work without writing down an explicit model and so you are left still waving your hands. If you won’t write an explicit model you will not get past that stage. To move ahead, you need to write an explicit model for yourself.
You write: “Conservation of Energy dictates that all the kinetic energy flows from the surface into the atmosphere have to be returned to the surface in equal an opposite amounts. All latent heat and thermals are doing is moving and re-distributing energy around – mostly from the tropics to the higher latitudes.”
Now you are talking about the atmosphere. But sad to say you misunderstand the process. It may depend how you like to use the words “kinetic energy”, but the physical fact is major non-radiative (conductive and evaporative) flow of energy from the land-sea body into the atmosphere that is not returned to the land-sea body. The amount is about 105 W m^-2 on year-round global average. The non-radiative transport moves energy to places where it is radiated to space, not to places where it returns to the land-sea body.
You are right that the exchange with space is purely radiative. You are mistaken to think that clouds return to the surface all the energy they receive from it. No, they send much of that energy to space.
Replying to your post of May 16, 2011 at 6:59 PM in reply to P.Solar:
You write: “Let me ask you then – where is the 151 W/m^2 coming from?”
It’s coming from the fact that you haven’t actually written down an explicit physical model. It is not a real physical quantity, it’s just a number from a handwaving numbers game without proper rules that would be created by a definite physical model; in a word it’s coming from the waving of your hands. Christopher Game
Christopher Game says:
“The actual quantities here are moieties of flow, and there are many such moieties. The basic physics is that the temperature of the land-sea body is such as to cause one moiety of the flow to be 390 W m^-2. The actual fact is a surface temperature of 288K that corresponds to the 390 W m^-2.
That 288K temperature is due to heat passively accumulated during the past, not to added power in the present.”
I’m referring to the system in the steady-state (energy in = energy out). The Sun is constantly adding energy to the system. If energy is still accumulating at a significant rate, why has the temperature remained so stable (i.e. fairly close to 288K) for so long?
You write:
“If you want a word form other than ‘gain’, perhaps ‘passive accumulation’ would do. Blocking the holes in the bottom of a leaky bucket doesn’t create more water, it just reduces the rate of leakage. Adding CO2 is like blocking some holes in the bottom of a leaky bucket.”
I understand this. I don’t see how anything I’ve said is in conflict with this.
You write:
“Now you are talking about the atmosphere. But sad to say you misunderstand the process. It may depend how you like to use the words “kinetic energy”, but the physical fact is major non-radiative (conductive and evaporative) flow of energy from the land-sea body into the atmosphere that is not returned to the land-sea body. The amount is about 105 W m^-2 on year-round global average. The non-radiative transport moves energy to places where it is radiated to space, not to places where it returns to the land-sea body.”
Again, I don’t see the problem here. If any of the kinetic energy moved from the surface into the atmosphere radiates into the atmosphere and is eventually radiated out to space, the amount returned to the surface will be less than the amount leaving surface (i.e. more joules leaving than joules returning). This will cool the surface, reducing surface emitted radiation by an equal an opposite amount.
All of the 390 W/m^2 emitted by the surface is radiative, and this is solely due the surface temperature and nothing else. Therefore, the surface cannot be receiving more energy than this in the steady state. Energy from latent heat and thermals leaving the surface are in addition to the 390 W/m^2 emitted at the surface, which is all photons.
You write:
“You are right that the exchange with space is purely radiative. You are mistaken to think that clouds return to the surface all the energy they receive from it. No, they send much of that energy to space.”
Again, I don’t see the conflict.
Christopher Game says:
“The amount is about 105 W m^-2 on year-round global average.”
This seems awfully high to me – at least in terms of the amount radiated to space. Most of latent heat moved from the surface into the atmosphere should be returned via precipitation, weather, etc.
I think Trenberth et. al. in their latest paper claims the total is 97 W/m^2. Trenberth then returns it to the surface as ‘back radiation’. He has none of it escaping to space (at least in the diagram depiction of the energy flows).
Christopher,
I think the confusion may lie in the fact that there are multiple exchanges many times over between radiative and kinetic and vice versa through the atmosphere. This doesn’t change the energy budget. The main point is all the energy entering from the Sun and leaving at the TOA is radiative, and all of the 390 W/m^2 emitted at the surface is radiative as well. Because the atmosphere cannot create any energy of its own and 239 W/m^2 are entering post albedo from the Sun, Conservation of Energy dictates that the additional 151 W/m^2 at the surface can only be coming from ‘back radiation’ from the atmosphere. And by ‘back radiation’, I mean the downward emitted LW radiation that last originated from surface emitted. This distinction is critical because there a lot of downward emitted LW from the atmosphere – some of which last originated from surface emitted, some of which last originated from the kinetic energy moved from the surface into the atmosphere (latent heat and thermals), and some of which last originated from the Sun.
Ultimately, 239 W/m^2 enters from the Sun and becomes 390 W/m^2 emitted at the surface through ‘back radiation’ from the atmosphere. The 151 W/m^2 is the climate system’s or surface’s ‘gain’ to incident energy. Now of course, latent heat of water is major player on how much ‘gain’ there is because the water vapor and clouds in the atmosphere largely determine the opacity of the atmosphere to outgoing surface emitted LW radiation (i.e. how much surface radiation passes through the atmosphere to space and how much is back down to the surface via ‘back radiation’).
Christopher Game replying to the post of RW of May 17, 2011 at 4:41PM.
You write: “This seems awfully high to me – at least in terms of the amount radiated to space. Most of latent heat moved from the surface into the atmosphere should be returned via precipitation, weather, etc.”
No, most of the latent heat moved from the land-sea surface into the atmosphere is radiated to space and hardly any of it is returned via precipitation, weather, etc.. You need to read a textbook or two to understand how this comes about. As long as this continues to seem awfully high to you, you are unlikely to make progress.
You write: “I think Trenberth et. al. in their latest paper claims the total is 97 W/m^2. Trenberth then returns it to the surface as ‘back radiation’. He has none of it escaping to space (at least in the diagram depiction of the energy flows).”
I am not fussed about the difference between my suggested figure of 105 W m^-2 and your citation of Trenberth et al.’s figure of 97 W m^-2. But their diagram simply means that there is so much non-radiative energy transfer from land-sea body to atmosphere. There is no explicit statement in the diagram that this goes to space. Neither is there an explicit statement in the diagram that it returns to the land-sea body. But nevertheless it is all indeed radiated to space, to the degree of accuracy of our present discussion. While you don’t believe this, you need to do some more thinking and reading and to actually write an explicit model for yourself, until you do come to believe it. Without writing an explicit model for yourself and coming to this belief you will continue to feel confused.
Dear RW, I am sorry, I cannot help you any further while you have not done these things.
You write: “I think the confusion may lie in the fact that …”
The confusion lies in the fact that you have not written yourself an explicit model and that you have not thought this through in physical terms. You are playing with words, not thinking things through with a physical model. To understand physics you need to think with a physical model. Christopher Game
Christopher Game says:
“No, most of the latent heat moved from the land-sea surface into the atmosphere is radiated to space and hardly any of it is returned via precipitation, weather, etc.. You need to read a textbook or two to understand how this comes about. As long as this continues to seem awfully high to you, you are unlikely to make progress.”
Even if all the latent heat moved into the atmosphere from the surface eventually finds its way radiated out to space, it still doesn’t change the fundamental energy budget constraints on the climate system. Also, if this is case – that it’s all radiated out to space, where is most of the kinetic energy returning to the surface in the form of precipitation coming from then?
You write:
“I am not fussed about the difference between my suggested figure of 105 W m^-2 and your citation of Trenberth et al.’s figure of 97 W m^-2. But their diagram simply means that there is so much non-radiative energy transfer from land-sea body to atmosphere. There is no explicit statement in the diagram that this goes to space. Neither is there an explicit statement in the diagram that it returns to the land-sea body.”
Not an explicit statement, no, but if you understand the constraints COE puts on the system, these things can be derived fairly easily. Trenberth’s diagram counts the energy from latent heat and thermals twice in the diagram. He also counts the post albedo energy from the Sun twice by absorbing 78 W/m^2 of it by the atmosphere and then bringing it to the surface as ‘back radiation’. Only it’s not ‘back radiation’, it’s ‘forward radiation’ that last originated from the Sun that has yet to reach the surface. The point is the full 239 W/m^2 gets to the surface, but the diagram obfuscates this. He has the surface emitting 396 W/m^2 with a 70 W/m^2 transmittance directly to space (40 W/m^2 through the clear sky and 30 W/m^2 through the cloudy sky). He then has the atmosphere emitting 169 W/m^2 up out to space for a total of 239 W/m^2 leaving at the top of the atmosphere. If the 70 W/m^2 of the 396 W/m^2 at the surface is going straight to space, the difference of 326 W/m^2 is the amount surface radiation absorbed by the atmosphere. If 169 W/m^2 is emitted up out to space, that leaves a difference of 157 W/m^2 of ‘back radiation’ (326 – 169 = 157). 239 W/m^2 post albedo from the Sun and 157 W/m^2 from ‘back radiation’ equals 396 W/m^2 received at the surface – the exact amount its emitting. The problem is the diagram depicts 333 W/m^2 of ‘back radiation’ because Trenberth just lumps in 97 W/m^2 from latent heat and thermals of 97 and another 78 W/m^2 absorbed by the atmosphere from the Sun. 157 + 97 + 78 = 332 W/m^2 of ‘back radiation’ (Trenberth purposefully has an extra watt in there to try to show there is an imbalance). The diagram makes it look like the surface is receiving 161 post albedo from the Sun and 333 W/m^2 from ‘back radiation’ from the atmosphere, but the surface cannot be receiving 494 W/m^2 as it’s only emitting 396 W/m^2.
Do you see?
Sorry for the typos and double word/number usage in my last post.
Furthermore, of the emitted surface radiation absorbed by the atmosphere, do you see how only about half is returned to or incident on the surface? Trenberth actually as greater than half emitted to space or 169 W/m^2 up and 157 W/m^2 down (52% up and 48% down), which is inaccurate. This is probably because his transmittance of 70 W/m^2 is too small. He does not reference where he’s getting 70 W/m^2 in the paper – it appears to just be a rough estimate or guess. With his numbers, 82 W/m^2 gives exactly half up/half down. Other sources I’ve seen put it more like 90 W/m^2.
At any rate, the point is only half of what the atmosphere absorbs is incident on the surface and subject to ‘gain’. The half radiated up out to space is essentially the same as surface emitted that passes straight through to space. So, using Trenberth’s numbers, if CO2 is doubled, transmittance reduces from 70 W/m^2 to 66.3 W/m^2 and the atmosphere absorbs an additional 3.7 W/m^2 – half of which goes up out to space and half of which goes to the surface.
Mixing in latent heat and thermals obfuscates this. The ultimate point is the system does not support the amount of ‘gain’ needed for a 3 C rise in temperature from the 3.7 W/m^2 of radiative forcing from 2xCO2, only half of which is incident on the surface.
Christopher Game replying to the posts of RW of May 17, 2011.
Dear RW, never mind what the Trenberth diagram makes it look like. The Trenberth diagram might not be perfect, but it provides information near enough for the present purpose, and you are familiar with it. Several of the things you say are mistaken or perhaps nearly meaningless.
You are looking at four bodies exchanging energy. They are the sun, space, the atmosphere, and the land-sea body. For a model of the steady state, total rate of gain of energy by each body is equal to its total rate of loss of energy. Each body potentially gains or loses energy in sub-total from each of the other three, by various routes or modes of transfer. One wants to know the rates of gain or loss between every pair of bodies. One wants to do this twice, once for the present CO2 level hypothetical steady state (for which one could propose that actual measured data provide the necessary information), and once for a doubled CO2 level after the system has settled to an eventual hypothetical steady state again (this is the one that is hard to calculate, and for which no actual data are adequate). I see that you persist in trying to think in terms of “gain”. Christopher Game
Christopher Game says:
“You are looking at four bodies exchanging energy. They are the sun, space, the atmosphere, and the land-sea body. For a model of the steady state, total rate of gain of energy by each body is equal to its total rate of loss of energy. Each body potentially gains or loses energy in sub-total from each of the other three, by various routes or modes of transfer. One wants to know the rates of gain or loss between every pair of bodies.”
The ‘gain’ is the just measured response of the system or surface to solar forcing. The net effect of all the various feedbacks, interactions and exchanges of energy between those four things you mention are automatically embodied in the ‘gain’. How could they not be?
“One wants to do this twice, once for the present CO2 level hypothetical steady state (for which one could propose that actual measured data provide the necessary information), and once for a doubled CO2 level after the system has settled to an eventual hypothetical steady state again (this is the one that is hard to calculate, and for which no actual data are adequate).”
This information is known. The current steady state has about 239 W/m^2 arriving from the Sun and 239 W/m^2 leaving at the TOA. The surface is emitting about 390 W/m^2. The system has a ‘gain’ of about 1.6 (390/239 = 1.6). The ‘gain’ is just the reciprocal of net transmittance to space. (390 x 0.6 = 239). The physical meaning is it takes about 1.6 W/m^2 at the surface to allow 1 W/m^2 to leave the system, offsetting each 1 W/m^2 entering the system from the Sun.
To give a numerical example, if there was a radiative imbalance (or ‘radiative forcing’) of say 3.7 W/m^2 from 2xCO2, the energy leaving at the top of the atmosphere would reduce by 3.7 W/m^2 to 235.3 W/m^2. The atmosphere would absorb an additional 3.7 W/m^2 of outgoing surface radiation, half of which is radiated up out to space and half is radiated down to the surface for a new total of 391.85 W/m^2 at the surface and 237.15 leaving at the TOA (239 – 1.85 = 237.15) for a net imbalance of 1.85 W/m^2. If the +1.85 W/m^2 incident on the surface is treated the same as the energy arriving from the Sun, it will be amplified by a factor of about 1.6, as this is the measured response of the surface to forcing of any kind (GHG or otherwise). 1.85 W/m^2 x 1.6 = +3 W/m^2 to allow an additional 1.85 W/m^2 to leave the system to restore equilibrium (239 W/m^2 in and out). The new equilibrium surface emitted radiation would be 393 W/m^2 (390 + 3 = 393 W/m^2), which corresponds to about a 0.6 C rise in temperature.
The IPCC’s claim of a 3 C rise requires the surface to emit an additional 16.6 W/m^2 (406.6 W/m^2) to restore equilibrium (to allow an additional 1.85 W/m^2 at the surface to leave at the TOA). The bottom line is the system does not support anywhere near this much ‘gain’ even if the atmosphere absorbed 100% of the surface radiation because half would escape to space anyway. The question is where is the missing 13.6 W/m^2 required for the 3 C rise coming from? COE says it can only come from the Sun via a reduced albedo. The IPCC will tell you that the 13.6 W/m^2 comes from the feedback (clouds and water vapor primarily), but why doesn’t the feedback cause this much change on solar forcing? Furthermore, if this much response is within the system’s bounds, why doesn’t it take more like 2150 W/m^2 at the surface to offset the 239 W/m^2 coming in from the Sun (16.6/1.85 = 9; 2150/239 = 9)?
The problem is what the IPCC refers to as ‘feedback’ is really ‘gain’.
Christopher, let me ask you this – do you think it’s just a coincidence the estimated sensitivity to 2xCO2 by Dr. Roy and Richard Lindzen, etc. by various means is very closely inline to the system’s response to solar forcing? I doubt it. It only confirms that they’re getting it right and the IPCC, etc. is getting it wrong.
Dr. Spencer,
This is the most interesting class I have ever attended.
The way you allow these strings to take on a life of their own
is the mark of a true educator. The math sometimes escapes me
but the discussion does not. No one on this planet has the
answers to climate variability (not change). Those like many
politicians and former VPs and UN power grabbers as well as many corrupted scientist will one day be overcome by the truth
as your student body grows. I hope this happens sooner rather then later.
Dr. Spencer, with respect, you wrote:
“Of course, some believe that CO2 forcings do not even exist (although I’m not one of them).”
Well, I am one of those that believe that CO2 forcings do not exist. Just for fun I will explain why (although I doubt it will change your mind).
All significant energy input to the surface of the Earth comes from the Sun. I am of course excluding the small small amount of energy reaching the surface from volcanoes, etc.
The Sun is a true blackbody radiator and is providing energy to the Earth by consuming fuel (hydrogen) and converting it to heat which is radiated through the vacuum of space as electromagnetic radiation (EM radiation). The spectrum of this light closely (although not exactly) follows the predictions of the theoretical blackbody radiation equations.
The Earth is most correctly considered as a quasi-blackbody RE-RADIATOR, i.e. it absorbs energy, thereafter warms and re-emits this energy as EM radiation. It thereafter cools during this process. The Earth does not provide any “Net Energy Gain” since “Energy Gain” (Net or Gross) violates the First Law of Thermodynamics (Yes Virginia; the laws of thermodynamics apply all of the time to the entire Sun/Earth/Atmosphere/Universe system).
Likewise the gases in the thin (relatively) atmosphere of the Earth act as narrow band RE-RADIATORs of the EM radiation energy they absorb. They do in fact absorb EM radiation, then warm, then re-emit some of this energy back towards the surface. They then COOL as they emit this radiation. Hence NO NET ENERGY GAIN, just a delay in the inevitable flow of energy from more energetic sources (i.e. the Sun) to less energetic destinations (i.e. the cold vacuum of the Universe).
The delay introduced by this “back-radiation” phenomena must exceed the diurnal timing of the incoming energy for any “higher equilibrium” temperature to occur. As I have posted before (probably to your annoyance) this is easily described by the “speed of heat” a.k.a. thermal diffusivity. So for “CO2 forcings” to have any meaningful impact they must slow the speed of heat in a meaningful way relative to the 24 hour cycle of the only incoming energy source (i.e. the Sun).
Have you calculated the changes in the speed of heat through the Sun/Earth/Atmosphere/Universe system caused by increases in CO2, or Water Vapor ?
Answers are very welcome,
Cheers, Kevin.
Kevin K says:
“The delay introduced by this “back-radiation” phenomena must exceed the diurnal timing of the incoming energy for any “higher equilibrium” temperature to occur. As I have posted before (probably to your annoyance) this is easily described by the “speed of heat” a.k.a. thermal diffusivity. So for “CO2 forcings” to have any meaningful impact they must slow the speed of heat in a meaningful way relative to the 24 hour cycle of the only incoming energy source (i.e. the Sun).”
So-called ‘back radiation’ from GHGs occurs 24 hours a day. The atmosphere still has the same opacity to outgoing surface radiation at night, does it not?
In Reply to RW who wrote;
“So-called ‘back radiation’ from GHGs occurs 24 hours a day. The atmosphere still has the same opacity to outgoing surface radiation at night, does it not?”
Yes indeed it does, so if you travel at 1 mph for a month or 3×10^8 meters/second (~speed of light) for a month how much further away from your starting point might you be ?
You are mistaking the speed at which an effect travels through any system with the duration of an effect in a system.
Cheers, Kevin.
I posted a full response to Dr. Spencer’s article here:
http://bbickmore.wordpress.com/2011/05/20/roy-spencers-latest-silver-bullet/
KevinK says:
“Yes indeed it does, so if you travel at 1 mph for a month or 3×10^8 meters/second (~speed of light) for a month how much further away from your starting point might you be ?
You are mistaking the speed at which an effect travels through any system with the duration of an effect in a system.”
So what exactly is your claim? That all the increased heat from anthropogenic CO2 will be lost overnight, nullifying its effect?
To RW: (May 20, 6:01 pm) who wrote:
“So what exactly is your claim? That all the increased heat from anthropogenic CO2 will be lost overnight, nullifying its effect?”
Specifically my claim is that the “increased heat” from back radiation propagates through the atmosphere at a speed that approaches the speed of light (it is delayed slightly by absorption/reemission by the “GHG” gases). Therefore it has exited the Earth/Atmosphere for the cold vacuum of space within something like a few hundred milliseconds after it arrived. It is not even necessary to wait until the sun sets.
In summary, the “missing heat” that the climate scientists are searching for should be about 20-50 light years away by now.
Cheers, Kevin.
KevinK says:
“Specifically my claim is that the “increased heat” from back radiation propagates through the atmosphere at a speed that approaches the speed of light (it is delayed slightly by absorption/reemission by the “GHG” gases). Therefore it has exited the Earth/Atmosphere for the cold vacuum of space within something like a few hundred milliseconds after it arrived. It is not even necessary to wait until the sun sets.
In summary, the “missing heat” that the climate scientists are searching for should be about 20-50 light years away by now.”
I’m not sure I even understand, but what data/evidence do you have in support of this?
RW wrote;
“I’m not sure I even understand, but what data/evidence do you have in support of this?”
It is widely understood in the fields of electrical engineering and optical engineering that it takes about 1 nanosecond (1×10^-9 seconds) for an electromagnetic wave (as “back-radiation” clearly is) to travel the distance of 1 foot. This is of course a “rule of thumb” and it varies somewhat depending on the characteristics of the materials that the electromagnetic radiation is travelling through.
In fact if you ever study how optical lenses are designed you will find that by carefully trading off “flint” glasses (lower speed of light) with “crown” glasses (higher speed of light) lens designers are able to make most of the light arrive at the final destination at the same time.
The main reason that computers continue to increase their processing speed is because the “switches”, (aka transistors) continue to shrink in size. This makes the transistors closer together and able to transfer information at a faster speed.
In my opinion (and this is only my opinion) the field of climate science has overlooked two critical facets of thermodynamics;
1 – After you have established the correct directions of energy flow through a system it is CRITICAL to also understand the speed at which this energy flows.
2- It is also imperative to consider the thermal capacities of the components of your system. If I told you my car battery (12v, ~500 amp hours) was discharged would you believe that I could recharge it with ten 1.5 volt double A batteries (15 volts)?
The “AGW” hypothesis requires that the Oceans and Rocks of the Earth (your car battery) are “forced” into thermal equilibrium with the “Double A” batteries that represent the thermal capacity of the “Greenhouse Gases” that surround the Earth.
Cheers, Kevin.
Kevin K
The earth’s atmosphere does act as a re-radiator – but it re-radiates in ALL directions; not just back into space.
Without ‘greenhouse gases’ during the day earth would heat up, but at night all the accumulated energy would radiate back into space. GHGs absorb some of the surface reflected radiation and re-radiate it all directions, including back to the surface; thus acting as an insulator trapping some heat in the atmosphere.
This is very basic physics.
I see your calculations as showing the TRANSIENT climate sensitivity is on the order of 1.3C/doubling of CO2.
So your results shouldn’t really be controversial. For example, Isacc Held of GFDL has found that the transient response of the NOAA GFDL’s CM2.1 model is about 1.5C/doubling, for time peiods between 5 and 70 years. At the same time, the equilibrium sensitivity of that model (after several hundreds of years) is estimated to be 3.4C.
His 2010 Journal of Climate paper, http://www.gfdl.noaa.gov/bibliography/related_files/ih1001.pdf has the same findings.
Note that, in the CM2.1 model at least, there is a platea in the time response to a step forcing that extends from 5 years out to around 70 years. So if their model is a reasonably accurate depiction of reality, then the 1955 to 2010 period you looked at would all be part of the “fast” response time.
Hansen’s recent self published white paper “Earth’s Energy Imbalance and Implications” also shows a similar behavior of the GISS modelE-Russel ocean. 40% response in just 3 or 4 years, still less than 60% response after 100 years. So over the 1955-2010 timeframe for response to forcing, the GISS ER model will also be showing a climate sensitivity of less than 1.5C/doubling of CO2.
Dr. Spencer — do you agree with the above observations?
Kevin O’Neill wrote (and I added):
“The earth’s atmosphere does act as a re-radiator – but it re-radiates in ALL directions; not just back into space.”
Yes indeed, it re-radiates in all directions, but this is totally irrelevant.
“Without ‘greenhouse gases’ during the day earth would heat up, but at night all the accumulated energy would radiate back into space.”
In fact all day long (and all night long) the Earth is radiating energy out to space. Also this comment of yours exactly proves my point, you are claiming that the “Greenhouse Effect” can somehow magically discern that it is nighttime and then it slows the speed of heat flowing through the atmosphere. What magical property causes this? Do greenhouse gases only re-radiate IR energy when it is dark out ?
“GHGs absorb some of the surface reflected radiation and re-radiate it all directions, including back to the surface; thus acting as an insulator trapping some heat in the atmosphere.”
Insulators SLOW THE FLOW OF HEAT, they DO NOT “TRAP” HEAT, only if this slowing of the heat flow amounts to a large reduction in the “Speed of Heat” (There’s that term again) through a system will a “Higher Equilibrium Temperature” occur.
“This is very basic physics.”
No, this is the climate scientist’s version of basic physics.
Cheers, Kevin.
Ok, I suggest a slight refinement to my previous post;
Kevin O’Neill wrote in part;
“thus acting as an insulator trapping some heat in the atmosphere”
I replied;
“Insulators SLOW THE FLOW OF HEAT, they DO NOT “TRAP” HEAT”
Please allow me to refine my statement thusly;
Thermal Insulators slow the flow of heat; this is vastly different from how Electrical Insulators function. Yes indeed an electrical insulator (like the plastic covering over the AC wiring in your house) does “TRAP” the electricity inside the wire. Even then there are still a very small number of electrons that escape from the “TRAP” and exit to a lower electrical potential. This is referred to as “leakage current”, and for most modern electrical systems is negligible.
Thermal Insulators like “Greenhouse Gases” do not offer the same effectiveness at “TRAPPING HEAT” as electrical insulators do at “TRAPPING ELECTRONS”. Thus any discussion of “GHG’s” “TRAPPING” heat is pretty much a non-starter.
Cheers, Kevin.
KevinK says:
“Thermal Insulators like “Greenhouse Gases” do not offer the same effectiveness at “TRAPPING HEAT” as electrical insulators do at “TRAPPING ELECTRONS”. Thus any discussion of “GHG’s” “TRAPPING” heat is pretty much a non-starter.”
I agree that ‘trapping’ is a bad word and not what is really happening. GHGs delay the release of surface emitted energy. An increase in GHGs will increase the delay through an increase in the opacity of the atmosphere, which will dictate a different equilibrium.
Kevin O’Neill wrote;
“GHGs delay the release of surface emitted energy.”
Exactly, they change the “SPEED OF HEAT” through the Sun/Earth/Atmosphere/Universe system. I agree completely.
Kevin O’Neill also wrote;
“An increase in GHGs will increase the delay through an increase in the opacity of the atmosphere”
Well, here is where we disagree. An increase of 100 ppm of ”GHG’s” must be displaced by a decrease of 100 ppm in “non-GHG’s”. Heat travels through the “non-GHG’s” at the “speed of heat” (aka thermal diffusivity). This is widely accepted as quite a bit slower that the speed of light at which IR radiation flows.
So if we replace ”slower” “non-GHG’s” with faster “GHG’s” what is the final effect ? I posit that due to the thermal capacities of the materials and volumes involved the gases in the atmosphere will heat up slightly faster after sunrise, and cool down slightly faster after sunset. I also posit that this effect is so small that we probably could never afford to spend enough money to measure it.
Crazy thinking isn’t it?
Cheers, Kevin.
Sorry, that last post was intended for “RW”, not Kevin O’Neill, but anybody is welcome to deconstruct it at their leisure.
Cheers, Kevin.
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