Guest Post by Willis Eschenbach
A number of people have said Hey, in your previous post, the missing forcing is going into the ocean, so it’s still “in the pipeline”. I had considered that, but it didn’t make sense. I’ve taken a closer look, and it still doesn’t make sense.
According to the IPCC calculations in that post, about 0.7 W/m2 was missing. Let us assume that it is going into the ocean. Here’s my numbers, please check them. The spreadsheet doing the calculations is here.
CONSTANTS
Specific Heat Seawater 3.85 Joules/gram/C
Ocean Volume 1.3E+18 m3
Ocean Area 3.6E+14 m2
Global Surface 5.1E+14 m2
Average Ocean Depth 3700 m
Ocean Density 1.025 tonnes/m3
Year To Seconds 3.2E+07 seconds/yr
INPUTS
"Missing" Incoming Radiation 0.7 W m-2 over earth's surface
OUTPUTS
Equiv. Incoming Radiation To Ocean 1.0 W m-2
Annual Energy 3.1E+07 Joules/yr
Warming Ability 8.2E+06 grams C-1 / yr
1 m2 Column Weight 3793 tonnes
Column Weight 3.8E+09 grams
Warming since 1850 0.11 C (from spreadsheet)
Current Warming Rate 0.22 C/century
Time To Warm 1° at current rate 465 years/C
The reason that it didn’t make sense to me is that if that is the case, if the imbalance over the last 150 has warmed the ocean a tenth of a degree, and heat in the pipeline (assuming the 0.7 W/m2 imbalance continues) is going to give us a degree of warming in just under five hundred years … I just couldn’t believe that people were seriously thinking that was an issue.
So I suppose that’s possible, that the IPCC is right, and that half of the incoming energy is going into the ocean, warming it at the rate of one measly degree every half a millennium … But if that is so, does that mean that for practical purposes (neglecting the one degree by the year 2565, which is meaningless in human terms) we cut all of the IPCC warming forecasts (excuse me, scenarios) in half? Doesn’t that make the effective climate sensitivity in the real world, for our Grandchildren, by the year 2050, half of the number promulgated by the IPCC? Because the heat in the pipeline from the 0.7 W m-2 imbalance (0.22 C/century) will give us a whopping nine hundredths of a degree of ocean warming by 2050, unmeasurably small.
What am I missing here?
[UPDATE] Bob Tisdale graciously provided a link downthread to the oceanic heat content numbers. His graph shows the global heat content increasing by 7.8 MJoules per year per square meter.
If my numbers are correct (please check), this corresponds to a heat uptake (global average) of 0.17 W/m2. That would warm the ocean by a degree in 1900 years, so I think we can neglect that … and surely that’s enough time to do the mixing.
The missing heat is on the order of 0.7 W/m2. The evidence doesn’t show anywhere near that amount of heat going into the ocean. Including the ocean warming as explaining part of the missing heat, that still leaves on the order of a half a watt per square metre missing in the IPCC-based estimate … the ongoing mathematical mystery continues. All assistance solicited.
My own feeling is that the climate sensitivity is not fixed, but is a function of T, the temperature. It decreases with increasing T. This can be seen clearly in the tropics.
In the morning the ocean is cool, and the skies are clear. As a result, the surface warms rapidly. Climate sensitivity (degrees of temperature change for a given change in forcing) is high.
By about 10:30 or so, the ocean surface has warmed significantly. As a result of the rising temperature, cumulus clouds form. Despite increasing solar forcing, the surface does not warm as fast. Climate sensitivity is lower.
In the afternoon, thunderstorms form. These bring cool air and cool rain from aloft, and move warm air from the surface aloft. They cool the surface, bringing climate sensitivity near to zero.
Finally, thunderstorms have a unique ability. They can drive the surface temperature underneath them below the starting temperature. In this case, we have local areas of negative climate sensitivity – the forcing can be increasing while the surface is cooling.
As you can see, in the real-world context the idea that the temperature is some mythical constant “climate sensitivity” times the forcing change simply doesn’t hold water. Sensitivity goes down as temperature goes up in the tropics, the area where the majority of solar energy enters our climate system.
How does a small increase in infared radiation heat the ocean it cannot penetrate beyond a few millimeters?
Even if it eventually can would not this ocean mixing occur far slower then UV, and therfore is not UV energy more effective WM2 on a planet two thirds covered in water?
What obsevational studies have been done on this?
Thanks for any response.
PS to my earlier comment: as well as heat being transformed into mechanical energy, there is also the issue of phase changes: heat energy being used up in melting ice into water, or evaporating liquid water into vapor.
I suspect the missing 0.7 W/m^2 is the result of incorrect science. The main mistake is the cloud optical physics. Present median AGW, 1.6 W/m^2, is assumed to be offset by 1.2 W/m^2 ‘aerosol cooling’, 0.5 direct and 0.7 indirect via clouds. The former is probably nearer 0.3: the latter is imaginary because the equation used to predict it, from Hansen and Lacis in 1974, is in my view as wrong as can be.
This is because it assumes diffuse internal scattering when there’s a second, pseudo-geometrical process at the upper boundary contributing the major proportion of albedo for very dark clouds. It’s strongly affected by pollution. An upper bound estimate is that changing droplet size from 15 to 5 microns reduces it by a factor of 10. So, a non-absorbing cloud with an initial albedo of 0.7 would allow 60% more energy through, a very potent form of AGW operating in parallel with any CO2 effect.
Because there’s a reversal of the sign as clouds get thinner, I’m not certain how much AGW has come from polluted clouds, but because it’s self-limiting [thick cloud albedo asymptotes to 0.5] it may account for the apparent cessation of global warming in 2003 as determined by ocean heat content. The quid pro quo is that fast ocean heating from 1985 may have been because of Asian industrialisation leading in 1999 to the observation of the ‘Asian Brown Cloud’. Soon after that, low level tropical cloud albedo may have reached its minimum level – no more cloud AGW.
So, I hope you realise by now that because of this fundamental mistake, which goes back to the physicists who devised the ‘two stream’ approximation to cloud aerosol optics, the present estimate of heating due to CO2-AGW is probably wildly exaggerated. I get to the other three major errors in the models at a later date!
PS I also strongly suspect that some in climate science know full well the basic problems. This may be why NASA puts out fake optical physics, e.g.: http://terra.nasa.gov/FactSheets/Aerosols/
‘Figure 2b. The high aerosol concentrations in these clouds provide the nucleation points necessary for the formation of many small liquid water droplets. Up to 90% of visible radiation (light) is reflected back to space by such clouds without reaching Earth’s surface.’
No professional physicist would put out such non-science yet the ‘reflection’ idea is widely believed in climate science. I’m less than impressed with the basic quality of people but that could be because of poor scientific training in the past 20 years or so.
cementafriend says:
October 23, 2010 at 9:18 pm
“It looks like my post got lost in the ether or filter. I was pointing out that measurements of evaporation point to the opposite of what is expected by IPCC and others with raising temperature ie the evaporation has been going down over the last 30 or more years.”
That is what one would expect according to Miskolczi’s theory.
Here is a chart showing how long it will take the oceans to catch up to the surface warming – 1500 years and it is still not 100% the way there yet – this is Hansen’s chart based on the slow temperature mixing which seems to be occurring so far.
http://img291.imageshack.us/img291/1200/image002.png
I guess this backs up Willis’ calculations since Hansen is still assuming 3.0C (to 6.0C) of warming in this chart so it will should take 3 X 500 years (at the current rate of 0.2C per century).
So, – either the predicted 3.0C of warming will in fact, take 1500 years (after CO2 reaches the first doubling around 2060); or,
– Hansen is trying to push that the actual equilibrium response is up to 6.0C after 1500 years per CO2 doubling; or,
– the extra heat is not, in fact, “missing”, it is just the energy the theory expects to be there but it is not. Therefore, the warming will be much less than expected and it will take much, much longer than the current theory is pushing on us.
But the conclusion must be that the heat is not missing, the theory’s correctness is missing.
I don’t know how scientists can ignore the basic math problems in this theory. I guess they must still be relying on a gut instinct “feeling” that the theory is correct and would then rather just ignore the problems or try to change the measurements so it works. Noble cause corruption.
What you are missing is the effect of aerosols. The models depress temps from 1945 thru 1978 or so due to high aerosol levels in the atmosphere. The story goes that the clean air act fixed all this and temps began to soar in the late seventies.
What you are missing is the temperature depressing effect of aerosols in the atmosphere that worked its magic from 1945 to 1978 until the clean air act fixed all that and let temps resume its upward trend.
Darren Parker says:
October 23, 2010 at 5:55 pm
Does the earth’s heat producing core have any effect on the climate?
Yes. When the the mantle breaks the surface it pumps gases and particulates in many forms and at at various altitudes and can have a profound effect on the climate.
B Buckner says October 24, 2010 at 7:24 am
Makes no sense I’m afraid. What proportion of the earths surface did clean air acts relate to? Urban areas of the US and isolated parts of Europe at best. Just the usual contrived warmist excuse, where’s the empirical correlation let alone proof of causality?
For several reasons, the atmosphere can’t heat the ocean to any great degree in comparison to the Sun.
Firstly, the ocean surface is on average warmer than the atmosphere.
Secondly, donwelling longwave IR doesn’t penetrate the ocean surface far enough to get mixed down effectivley. Because of this, the IR is concentrated in the first few molecules depth of water and simply causes prompt evaporation.
Solar energy on the other hand penetrates tens of meters into the ocean and warms it very effectively.
There is a level of insolation at which the ocean neither gains nor loses energy. Coincidentally (or not) this is the same as the average level of solar activity over the last 350 years. For much of the C20th, the Sun was putting out more than the average level of energy for most of the time, and this additional energy increased the ocean heat content, raising the surface temperature and therefore the atmospheric temperature.
There’s your global warming.
My own calcs using similar figures to Willis’ plus the satellite altimetry measurements show that the ocean was getting almost 4W/m^2 more than average in the 1993-2003 decade. This is far more than co2 could ever achieve, even if downwelling IR could penetrate and heat the ocean. It must have been due to extra insolation at the surface of the ocean. Since the sun only varies a watt or so, the amplification factor is almost certainly albedo variation due to solar activity levels – the Svensmark effect.
Empirical evidence from the ISCCP cloud project shows cloud levels fell from 1980-1998.
There’s your global warming.
Willis Eschenbach;
It was a long time ago when I went through AR4 and I’ve trashed most of my spreadsheets, but I found some notes to myself. Too bad I didn’t record where in AR4 the numbers came from so I could refer back. Bad scientist. Oh wait, I’m not a scientist. Ok, Bad skeptic. Here’s my recollection:
o The IPCC estimates doubling of CO2 to increase forcing by 3.7 w/m2 (no feedback)
o The IPCC calculates sensitivity against the EFFECTIVE black body temperature of the earth
o The IPCC estimates the effective black body temperature of the earth to be about 253K
o Hadcrut reports temperature anomalies against the SURFACE temperature of the earth
o Hadcrut estimates the average earth surface temperature to be 288K.
So to simplify matters, let’s eliminate feedbacks and just focus for the moment on the math in regard to CO2. IPCC estimates doubling co2 will increase forcing by 3.7 watts/m2, and increase temperature about 1 degree. STARTING FROM WHERE? Let’s turn to Stefan-Boltzman.
If we assume a surface temperature of 288K, then a temperature increase of 1 degree would require a change in energy input to achieve equilibrium of:
(5.67 x 10^-8 x 289^4) – (5.67 x 10^-8 x 288^4) = 5.45 w/m2
Does not compute. Can’t warm something up if it is radiating more that you are putting into it. So let’s run the numbers again using the effective black body temperature of the earth at 253K
(5.67 x 10^-8 x 254^4) – (5.67 x 10^-8 x 253^4) = 3.69 w/m2
AHA!!!!!
Thar be yer problem mate. CO2 be logarithmic and earth radiance be exponential, so we have to know sensitivity in terms of starting point. If we accept the IPCC estimate of sensitivity being doubling CO2 = 3.7w/m2 = +1 degree AT AN EFFECTIVE BLACK BODY TEMPERATURE OF 253k, we should be able to arrive at a rough approximation of the expected change in temperature at earth surface expressed as an anomaly against an earth surface average temperature of 288K.
To make it a simple back of envelope, let’s assume that small changes of 1 degree are roughly linear in relation to the starting point. That gives us an easy ratio. We should expect sensitivity at earth surface to be 3.7/5.5 of sensitivity at effective black body. So sensitivity as measured by Hadcrut would be:
3.7/5.5 = 0.67 degrees per doubling of CO2.
Using the same logic in regard to magnitude of positive feedbacks as estimated by IPCC as adding an additional 1.0 to 3.5 degrees AT EARTH EFFECTIVE BLACK BODY OF 253 we would arrive at sensitivity as expressed by Hadcrut of 0.67 to 2.35 for feedbacks. Sum total would then be CO2 doubling with feedbacks included resulting in sensitivity at earth surface being a range of 1.34 to 3.01 degrees as measured by Hadcrut, and roughly equivelant to the 2.0 to 4.5 degrees reffered to by IPCC as calculated against earth effective black body.
I suspect that if you run your numbers again in that context you’ll get a result that puts Hadcrut’s numbers more reasonably into the range. Better still would be to compare theory against actual measurement of effective black body of earth, but I have no idea how one would arrive at that from the historical record. I note however, the temperature at 14,000 feet as measured by AMSU-A averages about 253K which might make it a good proxy.
I actually found the 3.7/5.5 ration in one IPCC reference or another after I had calculated it myself, so it isn’t like this is some sort of secret. But screaming about a range of 2.0 to 4.5 is just that much more scary than screaming about a range of 1.34 to 3.01.
david says:
October 24, 2010 at 5:06 am
How does a small increase in infared radiation heat the ocean it cannot penetrate beyond a few millimeters?
Trenberth seems to be using the classic laws thermal dynamics. He is taking the gas and liquid as a two solid bodies. Water and our atmosphere are not amorphous they have two states and both states are dependent on pressure and temperature.
I believe he has underestimated SW->LW conversion at depth in the oceans and has by doing so attributed too much kinetic transfer from the atmosphere to the oceans.
(SarcOn) Is anyone else beginning to come to the conclusion that the IPCC is all a GIANT MADOFF “Slight-Of-Hand” Trick? A Gigantic Ponzi Distraction? Think about it, while the ever vigilant sheep dogs (US) have been trying to save the flock (the World) from the big, bad wolves (Them), other members of the pack (Their Buddies) have been ‘sheering’ (and doing other terrible, unspeakable things) to the poor flock while we have been distracted with this “Global Warming/Climeology” stuff. Huuuuuuuuummmmmmm… where’s BatMan, Robin ,IronMan, and the rest of the Super Heros when you need them? Think, maybe, “The Great Recession” we’re now in up to our gills is the result of what their friends have been doing while we’ve been preoccupied? I smell a rat…(SarcOff)
Very interesting, very mind-expanding, very … wrong.
Embarrassingly wrong, Shane.
Just because the climate change scientists act more like mini-Stalinists trying to depress scientific debate and nationalize major aspects of the economies of the world for their left-wing political views … doesn’t mean that every single crackpot theory, especially one reeking of creationalism, promoted by pseudoscientists is on an equal footing with questioning to what degree climate warming feedback sensitivity may have been overstated.
Is plasma an important phenomena? Yes. Might comets’ tails, for example, be more of an electrical effect than dissolving ice? Sure. Is the Sun an anode? Is that whole nuclear physics model of the Sun just nonsense?
I guess anything’s possible except that the direct measured experimental evidence supports the standard physics model.
You’re wasting your time on nuttiness. It’s your privilege, but if anyone checks out that website — and it certainly is interesting — I advise they do so with a heavily skeptical eye. There are a lots of propagandist distortions in it.
The video I watched about it was interesting, sure. But I was uncomfortable with the loosey-goosey presentation of several elements in it, particularly the idea I should take seriously several myths and goddesses around the world as if this is proof of this completely radical physics idea. Looking at the underlying science shows repeated instances where it is just plain off.
Fred, thanks for the link to the Levitus paper. Don’t you think it is a little odd that the greatest atmospheric warming 1980-1990 took place while the ocean was giving up heat? Are we supposed to believe that CO2 warmed the air, the warm air pumped heat into the ocean, and the ocean cooled less than it would have otherwise? It’s always amusing to see the linear trend argument applied in cases like this. Does the system look linear to you? The paper also did not explain how the heat moves into the lower ocean, my understanding is that the turnover rate is insufficient to explain the lack of warming in the atmosphere with the alleged sensitivity of water vapor feedback added in.
where’s BatMan, Robin ,IronMan, and the rest of the Super Heros when you need them?
Registered as democrats in Ohio. (And Texas. And Nevada. And Illinois.)
Nylo says:
October 24, 2010 at 3:21 am (Edit)
Willis, you don’t have to look for that lost heat. It doesn’t have to be somewhere, nor does it have to be “lost”. It only needs to exist in the future. At this moment, the only thing that you would need is some kind of radiative imbalance.”
yes, Nylo Thank you. After Willis post I did some calculations about the top speed of my Truck. Looking at the laws of physics I determined that the top speed of my truck would be approximately 120 Mph. I then studied the engine further and I found that the more gas I put in the carburator the more horse power I produced. I then studied the mechanism of the pedal and found that there was a direct correlation between putting the pedal down and increasing the flow of gas. So I have sensitivity number for the pedal position and I can measure it quite accurately.
My formula is very simple. the relationship is nearly linear. The pedal forcing causes the speed to increase. I decided i better test this. Much to my surprise when I slammed the pedal down and then looked up to to record the speed I had only achieved 60mph. My friends suggested that perhaps I should wait longer than 6 seconds to record the speed, but I explained that since I had a sensitivity for the forcing that was all I needed.
I therefore conclude that There is some missing velocity. where is it? further I think my simple experiment has uncovered a fatal flaw in basic physics.
My sceptic friend noted that there was a small wind at my back at the time, he thinks that the wind causes my truck to go forward, NOT the gas pedal. So much for the theory of more horsepower equals higher speed. one guy spun his tires on ice one day, and thinks traction drives the speed, not the pedal forcing. One guy claimed he can show many examples of people putting the pedal down and going in REVERSE, negative velocity!. From these incidents it clear to me that physics must be rewritten.
The other day, a few years back, on WUWT we used to talk about the ocean being a giant capacitor. That was silly talk. Some guys even tried to talk about things called ‘time constants’ I think time constants can be ignored. dont you.
/sarc off
A simple question for those arguing for a long equilibrium period due to ocean lag. Since the earth started warming a considerable time ago how much of the recent warming is just the earth working towards the imbalance from long ago? Don’t forget, the longer the time period for equilibrium to be achieved the less the warming which can be blamed on more current forcings. For those that argue for a high long term climate sensitivity I would ask the same question. The earth wasn’t created in 1979. If you wish to argue for large long term feedbacks of warming than by all means do so but don’t forget to go back and apply these principles to previous forcings.
steveta_uk says:
October 23, 2010 at 5:16 pm
Slightly off-topic, but can anyone explain why the deep oceans are so cold? They appear to be sandwiched between a surface at approx 15C, and a mantle that’s even hotter.
_______Reply;
Every winter at both poles as the sea water freezes to expand the polar sea ice area, extent, and volume, the salt in the solution is separated out and concentrated raising the density of the salt to the point that it does not freeze @ur momisugly around 0C, but sinks to the bottom. Each winter freeze cycle processes a surge of colder, denser sea water, that reaches its peak density around 3C to 4C, flows away from the poles till it covers the bottom of the total ocean floors around the world.
At sources of bottom heat the thermal gradient causes the slightly warmer water to rise and be replaced by more 3-4C dense sea water. Because this process is ongoing from both poles, there is no shortage of cold water inputs. What the Argo buoy system would show is the amount of surface warming that is getting ahead or behind the rate of sea water to freshwater ice conversion rates.
The Thermocline http://www.srh.noaa.gov/srh/jetstream/ocean/layers_ocean.htm
should reflect any long term changes in global warming or cooling, if heat is actually being stored in the oceans long term, the level of the warmest water will be seen to get deeper. So far that is not happening to a measurable amount, Judith Curry had an Antarctic sea ice paper looking for .00? temperature changes posted on here a while back.
However the temperatures at the bottom of the sea will still be the same as long as there is polar sea ice being generated, to any great extent.
jaymam says:
October 23, 2010 at 10:36 pm
jaymam, in climate science all forcings are referenced per square metre of total earth’s surface. You are right that intercepted sun is 1/4 of the earth’s surface. This is adjusted for by dividing the instantaneous top-of-atmosphere (TOA) insolation of (from memory) 1368 W/m2 by 4, to give an average TOA solar forcing of 342 W/m2.
MalagaView says:
October 23, 2010 at 3:59 pm
Charlie A says:
there are severe flaws with the quote. for one, power from stefan’s law is for a surface – so it radiates in one hemisphere. If you don’t really have a surface or assume a thin sheet, one must double that value to radiate in both hemispheres.
what has happened with the additional 3.6w/m^2 is that this amount is no longer escaping from the atmosphere (in clear skies). Since around 239w/m^2 is absorbed as incoming solar, for balance the average outgoing IR at the surface is 390w/m^2 which indicates about 150 w/m^2 is blocked in the atmosphere which means about 62% actually escapes. This of course ignores the cloudy fraction and emissions from higher up in the atmosphere. It does suggest that a 3.6w/m^2 shortfall would need to have about 5.8w/m^2 which corresponds to around 1.06 deg C rise. Of course, this includes only radiative heat transfer in a region of the atmosphere which doesn’t transfer much by radiation anyway.
Nylo,
The heat cannot be ‘nowhere.’ That is impossible. The heat from your stove is conducted into the water immediately and will start to excite the molecules, immediately.
There is no argument that the missing heat in the oceans is ‘nowhere,’ or will appear in the future. If there is a radiative imbalance (that is not the same as a forcing), then that energy must be entering the system at that rate and it’s presence must be felt by way of temperature increases.
If one wants to view the daily Solar Radiation coming in versus the Radiation actually at the Surface throughout the day, it is a little surprising.
The actual radiation at the surface is very stable compared to the solar radiation coming in (or not coming in at night). Once the Sun sets each night, about 4.5 watts/m2 per hour escapes and then once the Sun comes up, the surface radiation level rises by about the same 4.5 watts/m2 per hour (it is not quite 12 hours each way so there is a little difference in the two rates).
http://img710.imageshack.us/img710/7350/dailysolarandsurfacerad.png
If the Sun did not come up tomorrow, it would take about 86 hours for the Earth to cool down to the cosmic background radiation level (give or take a lag from the Oceans which would freeze from the top down).
Don’t forget, the longer the time period for equilibrium to be achieved the less the warming which can be blamed on more current forcings. For those that argue for a high long term climate sensitivity I would ask the same question. The earth wasn’t created in 1979. If you wish to argue for large long term feedbacks of warming than by all means do so but don’t forget to go back and apply these principles to previous forcings.
###########
thats one of the points of running GCMs to do paleo work! The issue there is the quality and granularity of forcing data.
There are two factors at play here.
1. The gain ( or sensitivity)
2. The time constant or lag.
You all know the difference between steering a jet ski and steering an oil tanker.
You apply a forcing to one and it reacts instantly.
you apply a forcing to the other and it reacts slowly.
You cannot characterize a system by simply looking at the sensitivity without looking at the time constant. well, you can, but it usually leads to crashes.
So what Willis has shown is this. If you consider the sensitivity or gain of the climate system ( its reaction to Doubling C02) to be instantaneous, then clearly
A. the sensitivity is too high OR
B. the measured temps are too High OR
C. the time constant is longer than “instantly”
Which is not showing very much at all.
There are three ways to constrain the problem. Most everyone starts with a given
B. the measured temps are just about correct. 9 you can vary this if you like as well)
Then, you can run models to figure out (ESTIMATE) the sensitivities and time constants ( like the IPCC does, and like guys who build aircraft flight controls do )
or you can look at observations IFF you have a long enough series ( Schwartz tries this, as does Lucia with her two box approach) Or you can look at some the instaneous responses ( I think spenser did this recently)
So, willis has established what we already knew. The climate doesnt respond instaneously to GHG forcing. Same way my oil tanker doesnt turn on a dime. But that sucker will turn, and once the control input is “put in”, there is no “taking it out”
And since we dont have good data on what the response time is to a increase in C02 ( like a controlled experiment) the only thing we can do is “model”.
Willis,
As with all things IPCC finding the trail of references and a straight forward answer is not… uhm… straight forward. But here are a couple of sections the illustrate the math in my previous comment:
Section 2.8.1 of WG1 states clearly that their radiative forcing calculations are taken at the tropopause, and are different from the observed forcing at surface:
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2s2-8.html#2-8-1
If you refer to figure 2.23 of WG1, you will find the graphs showing various forcings at the tropopause versus at surface. The total of all LLGHG’s is shown at just over 2 w/m2 which is about right for a 40% of doubling increase on a logarithmic function using 3.7 for doubling, but the surface forcing is only about 0.5 w/m2.
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/figure-2-23.html
Interestingly, they show the combined forcing at surface of LLGHG+Ozone+Aerosols+LandUse as NEGATIVE 1.4 w/m2. Not certain why they grouped them like that but the logical conclusion would be to expect COOLING at the surface over the last few decades, not warming. How they reconcile that with the surface temperature records they spout is beyond me.
But there you have it. Their sensitivity is calculated at the tropopause, and per their own documentation, doesn’t relate to the surface temps.