Guest Post by Willis Eschenbach
ABSTRACT
The IPCC says that the expected change in temperature arising from a change in forcing is equal to the change in forcing times the climate sensitivity. The IPCC provides values we can use to estimate the total human and natural forcing change since 1850. The IPCC also proves estimates for the climate sensitivity. These can be multiplied to provide the IPCC expected temperature change since 1850. The value derived (best estimate per IPCC numbers = 1.4 °C warming since 1850) is twice the observed warming (HadCRUT best estimate = 0.7°C warming since 1850).
Recently I became puzzled by what seems to be a glaring discrepancy in the official IPCC numbers. The IPCC estimate of climate sensitivity is +3 [+2 to +4.5] °C per doubling.
We also have the IPCC estimate of the change in forcing since 1750, in Watts per square metre (W m-2). The human contribution to that forcing is given by the 2007 IPCC Summary for policymakers as:
The understanding of anthropogenic warming and cooling influences on climate has improved since the Third Assessment Report (TAR), leading to very high confidence that the globally averaged net effect of human activities since 1750 has been one of warming, with a radiative forcing of +1.6 [+0.6 to +2.4] W m-2.
This represents the best estimate plus [lower and upper bounds].
Now, a doubling of CO2 is estimated by the IPCC to produce a change in forcing of 3.7 W m-2. So if we divide the climate sensitivity (in degrees per doubling) by 3.7, we will get the climate sensitivity expressed in units of degrees per W m-2. This gives us the result:
Climate Sensitivity = +0.8 [+0.5 to +1.2] degrees per W m-2.
Finally, we know that sensitivity times the change in forcing gives us the temperature change. Using the IPCC estimates of both, this gives us:
+0.8 [+0.5 to +1.2] degrees per W m-2 times +1.6 [+0.6 to +2.4] W m-2
= +1.3 [+0.4 to +2.2] degrees of warming from human activities since 1750. (Errors throughout have been assumed to add in quadrature.)
Now, we don’t have very good temperature data before 1850, so we need to adjust for that. However, there was very little human effect on the climate from 1750 to 1850. CO2 levels were only slightly lower in 1750 than in 1850, the industrial revolution was in its infancy, little fossil fuels were burnt, sulfur emissions were negligible, no fluorocarbons were emitted. Since the 1750-1850 anthropogenic contribution is very small compared to the total anthropogenic forcing, that IPCC based calculation of temperature change from humans of +1.3 [+0.4 to +2.2] degrees can be taken as the best estimate and bounds of the human caused temperature change since 1850.
For our final estimate, in addition to the human forcings since 1850 we need to add the natural forcings. The IPCC includes only one of these, solar forcing. The IPCC estimates that changes in solar forcing in the ~250 years since 1750 was 0.12 W m-2. For our rough calculations, we can make a crude but adequate estimate that three fifths of this change occurred since 1850. Adding solar forcing to the earlier equations makes the IPCC calculated temperature change from human and natural forcings combined since 1850 slightly greater, at +1.4 [+0.4 to +2.3] degrees.
Now, here’s the problem with that, and it’s a very big problem. According to the HadCRUT dataset (monthly dataset here, with notes here), the total temperature change 1850 – 2006 is +0.7 [+0.5 to +0.9] degrees. In other words, the world has warmed by around three-quarters of a degree (best estimate 0.7°C) since 1850. That’s nowhere near 2.3°C, the high end of what the IPCC says should have happened since 1850. It’s only half of the IPCC’s most likely number. It is just above the IPCC’s lower bound. So the IPCC method, using the IPCC numbers, way overestimates the historical temperature rise.
What can we conclude from this mismatch between observations and calculations? There are a number of possible explanations, in no particular order.
1. The sensitivity numbers are too high, and the forcing numbers are correct. If that is the case, the sensitivity is +1.5 [+0.5 to +2.4] degrees per doubling of CO2, a much lower and narrower range than the +3 [+2 to +4.5] range espoused by the IPCC.
2. The forcing numbers are too high, and the sensitivity numbers are correct. That gives us a calculated change in forcing since 1850 of +0.9 [+0.5 to +1.4] W/m2. Again this is much lower and more narrowly bounded than the canonical IPCC range of +1.7 [+0.7 to +2.5] W/m2 including solar. Note that in both this and the previous case, the relatively narrow bounds of the temperature observations have constrained narrow bounds on the underlying forcings or sensitivities.
3. Both the sensitivity and the forcing numbers are too high. This would limit possibilities to values such that the product of the two give us +0.7 [+0.5 to +0.9] degrees of warming. If the reductions were proportional, the forcing and the sensitivity would each need to be cut to about 70% of the IPCC numbers.
4. There are other mechanisms at play (e.g. cosmic rays, plankton aerosol production, thunderstorms) that the IPCC is not accounting for.
5. I’ve made a foolish mathematical mistake.
6. Climate may not obey a linear relationship between forcing and temperature change. My calculations are based on the IPCC assumption that a change in temperature can be calculated as a constant called “climate sensitivity” times the change in forcing. However, climate sensitivity may not be (and in my view is not) a constant. Instead, in my view climate sensitivity is a function of T, which changes the equation.
7. This is the “missing heat” that Trenberth referred to.
8. Something completely different that I haven’t thought of.
I couldn’t even begin to say which of those, or how many of those, if any of those, are actually going on …
Anyhow, that’s the oddity. If we multiply the IPCC historical forcing change since 1850 times the IPCC climate sensitivity to get the IPCC estimated temperature change since 1850, the result is nothing like the historical temperature change. The high IPCC estimate (2.3°C) is three times the actual change (0.7°C) since 1850. Clearly, something is wrong. Depending on which explanation we choose, we have different conclusions, none of which seems compelling.
Assistance and ideas welcome …
IPCC says “net effect of human activities,” which would assume to include aersols and their supposed cooling effects. Then again, that also would include warming from land use changes, other GHGs, etc.
At any rate, comparing “net effect” to that solely from CO2 might be a little apples-to-oranges.
The effect of CO2 is logarithmic but linear will give a decent approximation.
The old chestnut about the heat building up in the oceans doesn’t appear to be true. So where is the warming in the pipeline hiding and better yet when will it emerge !
If it is hiding at the bottom of the ocean and will emerge in 1,000 years who cares ?
Willis,
Science is so focused on temperatures that a great many other “insignificant” facts are being missed and pushed aside. CO2 itself IS changing our weather without factoring ANY heat.
This planet in being over-pressurized.
Facts:
Growth up in the mountainous areas.
Average wind speeds decreasing.
Ocean salinity changes.
Increased heavy precipitation.
Increased storm strengths.
Incorrect theory that oceans cause hurricanes and cyclones when oceans have no wind to contribute, just precipitation.
The clouds being compressed by atmospheric changes.
These all add up to the displacement of regular molecules that stay close to the planet surface with a more dense/heavier molecule CO2.
Off topic:
Scientific American reports a massive coral bleaching event off SE Asia. It’s interesting that SA has moderated its tone of cock-sure certainty (that it had a couple of years ago) about AGW being clearly to blame for all such events, and now headlines the article with the question: “Is climate change to blame?”
http://www.scientificamerican.com/blog/post.cfm?id=asian-coral-die-off-could-be-worst-2010-10-22
Willis
Thank you for your clear post and for your interest in checking the numbers.
As several commenters have said above, the error in your very basic calculation is that the sensitivity numbers are for equilibrium. Or to put it another way, the heat capacity of the oceans slows the response.
This is just another example of why the OHC (ocean heat content) is the preferred metric for global warming. Over a given period (1 year for example), the change in ocean heat content is a direct function of the overall radiative forcing over that period.
Obviously incorrect, oversimplified calculations of just multiplying the radiative forcing time the equilibrium sensitivity are counter-productive.
Trenberth did comment on this on two different papers.
One, which hasn’t been taked about much, has a more revealing chart which adds to what Willis is talking about and adds another section to the IPCC bar chart of Anthropogenic forcing – the feedbacks.
http://img638.imageshack.us/img638/8098/trenberthnetradiation.jpg
+ 1.6 W/m2 of anthro forcing;
+ 2.1 W/m2 of feedbacks which should be there;
– 2.8 W/m2 of mysterious negative radiative feedbacks that we don’t know how are occuring;
net +0.9 W/m2 which gives +0.7C (using the 0.81C/watt/m2 formula used by the IPCC)
Sometimes, the IPCC and Hansen quote a sensitivity about how much temperatures will rise for a given 1 Watt/m2 of Anthro forcing – which is usually quoted as +0.75C to +0.81C per 1 Watt/m2.
But this amount is before feedbacks (the IPCC and Hansen assume there will be 200% of additional feedbacks per 1 additional Watt/m2 of Anthro forcing – feedbacks including water vapour, ice albedo and vegetation albedo).
And these feedbacks take 25 years to fully materialize. A large amount occurs almost immediately, another large amount in the first 7 years and then the feedback factor starts to fall off (but the theory says they will continue building for up to 1000 years).
How much do temperatures actually increase per 1 Watt/m2 of forcing – there is only about a dozen numbers one could use.
– 0.18C/watt/m2 – the Stefan Boltzmann equation for the surface;
– 0.265C/watt/m2 – the Planck Response for the tropopause;
– 0.42C/watt/m2 – the short-term-less-than-one-year transient response the climate models use for a given 1 watt/m2 of Anthro forcing after feedbacks;
– 0.75C to 0.81C/watt/m2 – the medium-term equilibrium response from the theory for a given 1 watt/m2 of Anthro forcing after feedbacks have fully adjusted; and,
– 1.5C/watt/m2 – the long-long-term equlibrium response starting to be accepted as the full equilbrium response for a given 1 watt/m2 of Anthro forcing after about 1000 years.
We are actually much closer so far to the very lowest number above.
Ocean delay, aerosols, fairies; sounds like massive hand waving to me.
IPCC magic trick goes something like this:
Cup #1: 1.4° F
AND
Cup #2: 0.7° C
Shuffleshuffleshuffle . . . shuff.
Cup #1: 1.4°C
AND
Cup #2: 0.7° F
Taaa . . . Badabadabadabum . . . da.
That’s climate change live for ya’ll and that’s all folks.
My career, funding and reputation are hitched to the hysterical global warming movement.
My numbers don’t support my choice of theories to support
Gradually, science is replaced by the the need to cover my backside.
You appear to have omitted ‘aerosol cooling’ [Figure 2.4 of AR4]: 0.5 W/m^2 direct; 0.7 W/m^2 indirect [clouds]. Recent work suggests the direct effect may be 0.3 W/m^2. I believe the indirect effect is imaginary.
It’s because in 1974, Hansen and Lacis adapted an equation from Carl Sagan predicting cloud albedo from ‘optical depth’, inversely related to droplet size. Unfortunately, dark clouds, e.g. raining cumulo-nimbus, have largest droplets so Sagan’s simplification is wrong yet the calculation appears to be present in all models.
The justification seems to be that Twomey showed polluted thin clouds have higher albedo [but warned it didn’t work for thick clouds]. He also predicted 0.5 maximum cloud albedo. However, by about 2003, the cloud part of ‘global dimming’ couldn’t be proved experimentally and thick clouds were shown to have >0.5 albedo. The subject seems to have been in a quandary, retreat to sustainable science or bluff.
In 2004, Twomey was given a prize, fake physics purported polluted thick clouds have high albedo from a reflection process, e.g.: http://geo.arc.nasa.gov/sgg/singh/winners4.html , http://terra.nasa.gov/FactSheets/Aerosols/
Despite no experimental proof and no theory except for thin clouds, the ‘cloud albedo effect’ is 44% of median AGW in AR4. Without that correction, the IPCC’s predicted AGW should be nearly halved. But if you do that the models have to take into account heating from other than CO2, so in reality you must reduce it by a factor of c. three.
But, because the second optical process is strongly dependent on droplet size, the effect of pollution is to decrease albedo, another AGW. As it’s self-limiting, it may explain why as measured by ocean heat content, global warming stopped in 2003. So, net CO2-AGW may be still lower, even zero as predicted by Miskolczi.
Willis,
Very educational for me. Thanks.
Nice touch at the end of your post to invite assistance & ideas. I will try.
John
Willis, Are you aware of the following http://www.rsbs.anu.edu.au/Profiles/Graham_Farquhar/documents/271RodericketalPanreviewIGeogCompass2009_000.pdf
Here, is something measured which has a greater impact than CO2!
Observations always trump models! Ergo ………………….
Aerosol cooling is supposed to mask much of the underlying warming. See for example Stephen Schwartz http://www.bnl.gov/bnlweb/pubaf/pr/PR_display.asp?prID=1067
However, regardless of whether this is correct, we can say that the observed warming since 1850; the calculated forcings of all GHGs, aerosols, albedo, solar variabilty, etc., as provided in AR4, are not consistent with a sensitivity of 3 [2-4.5] deg. Something is indeed wrong, but the system has too many variables to determine what it is.
I think this reveals how simplistic and naive is this equation. The warmistas are just trying to blind the masses with scientific bafflegab.
I’m not saying it’s the right one, but I like your inclusion of possibility #8. It’s often the unknown unknowns that come and bit you in the butt. Your “math” looks correct to me, but let’s be clear: It’s just arithmetic. Too often people invoke “math” when what they mean is that they did some arithmetic. Not the same thing.
1) Does the IPCC believe that the warming since 1750 is all manmade. The planet gets no credit for coming out of a mini-ice age?
2) The IPCC altered (unilaterally and for no reason) a thermodynamic constant for CO2 (I cannot remember its name), bumping it up 12-fold, while lauding (some misdirection here) how constant this value had been in the literature (pretending it had been high the whole time).
If we go back to the real value for CO2, the 3 degC becomes 0.25 degC, making this a whole new ball game.
3) Do they assume CO2 has a linear effect? Is Beer’s Law being included in their fantasies about warming due to CO2 increase?
4) They say that they have a much better understanding of man caused warming when in fact they know virtually nothing as their assumptions are invalid from the beginning.
According to detailed estimates prepared by NASA-GISS (http://data.giss.nasa.gov/modelforce/RadF.txt) anthropogenic radiative forcings during the 20th century amounted to 1.8 watts/sq m, with almost all of this occurring after 1970.
According to my reconstruction of the global surface temperature record, surface temperatures increased by 0.75C during the 20th century, with almost all of this occurring after 1970 too.
According to the IPCC, “most” of this warming was anthropogenic, and I’m going to assume that “most” means two-thirds, or 0.5C. (Scafetta and West and Solanki come up with roughly the same number after subtracting solar irradiance impacts.)
And if 1.8 watts/sq m causes 0.5C of warming, then 3.7 watts/sq m, which is what we get from a doubling of CO2, will cause a temperature increase of slightly over 1C. Therefore the climate sensitivity is +/-1C. (The Lindzen estimate).
What’s wrong with this number? Nothing. It’s a reasonably robust empirical estimate, probably the best we can make using the data we have. So why isn’t it used? Because it shows a) that there were no significant feedback mechanisms operating during the 20th century, b) that there won’t be a huge temperature increase during the 21st and c) that the climate models that predict one are wrong.
Nothing wrong with your math, Willis.
On top of all this do we have to assume all the .7C increase is CO2 or other greenhous gas.?
What about UHI?
How about measurement error?
What about various natural cycles; if we have .2C cooling in the next 25 years where does this place the already poor IPCC numbers?
test
[Note: There is a Test page at the top of the home page. ~dbs, mod.]
I’ve tried to make the same argument in the past and was assured by warmistas that there is a 30-year lag at work.
I doubt if you can starting counting at 1850. The number of weather stations was so small then that the uncertainty of the data is huge. I maintain a HadCRUT3 graph using monthly not annual data. From 1850 to 1880 the graph is all over the place. However, you still have the problem of where you start counting. The 1800s seems to have been a cold century but if you start at say late 1870s there is hardly any warming but if you start at about 1890s there is more. If we had data for the 1700s we would get much less warming as the 1700s seems to have been a warm century. Same with starting at 1910 or 1940. This is not good science it is salesmanship. There is no correct place to start counting. It is rather like these investment packages which advertise huge value growth by starting at a stock market slump and ending in a boom. Move the chart a couple of years either way and you make no money at all!!!
Solaris says: “never heard something about thermal interia of the oceans????”.
If there is thermal inertia, due to the heat capacity of the ocean, then one would expect the global temperatures to continue rising. But over the past 8-10 years they have flattened out. Sort of contradicts the laws of thermal transfer.
Maybe there’s a thermal drain in the sea floor.
In reply to Luis Dias, most IPCC reports are indeed a load of aerosols.