How Sensitive Is The Climate

Why 'Fast Feedbacks' are quite slow and 'Slow Feedbacks' might be rather fast.

I've just been reading Hansen (2007):
It has lots of interesting stuff about climate sensitivity.

The climate sensitivity is the temperature response of the whole climate to a forcing of greenhouse gases. We know that there are two basic sorts of feedback processes going on in the climate. Firstly we know that as the temperature rises, relative humidity will stay roughly constant and thus absolute humidity will increase. This leads to more water vapour in the air; and water vapour is a strong greenhouse gas. Higher temperatures also has an ambigous (to this author) effect on clouds. The sum of all these atmospheric effects yields the 'Charney' definition of the climate sensitivity which is the equilibrium temperature rise from a doubling in CO2 concentrations; assuming that the land albedo and carbon (CO2/Methane) sinks stay constant. (of course they don't stay constant; we will come to this). This has been argued to be close to 3Celsius (3C) for a doubling of CO2 or 0.75C/(W/m2)*. [*A doubling of CO2 gives an increase in radiative forcing of about 4W/m2, so multiply the C/(W/m2) by 4 to get the temperature change for doubling CO2]
Hansen et al. (1993) calculated the ice age forcing due to surface albedo change
to be 3.5 C/(W/m2). The total surface and atmospheric forcings led Hansen et al. (1993) to infer an equilibrium global climate sensitivity of 3C for doubled CO2 forcing, equivalent to 3/4 +/- 1/4 C/(W/m2). This empirical climate sensitivity corresponds to the Charney (1979) definition of climate sensitivity, in which ‘fast feedback’ processes are allowed to operate, but long-lived atmospheric gases, ice sheet area, land area and vegetation cover are fixed forcings. Fast feedbacks include changes of water vapour, clouds, climate-driven aerosols1, sea ice and snow cover. This empirical result for the ‘Charney’ climate sensitivity agrees well with that obtained by climate models (IPCC 2001). However, the empirical ‘error bar’ is smaller and, unlike the model result, the empirical climate sensitivity certainly incorporates all processes operating in the real world.

This 'fast feedback' is not all that fast however... The fast feedbacks being slow: 50% of the climate response happens in 30 years and the rest takes 1000 years. So we see in immediate terms (net of the cooling effect of aerosols) about 50% of the climate change that we are likely to see.

Now to the 'slow' feedbacks, namely the ice-albedo changes from melting ice and carbon dioxide and methane releases. How fast are they? And how serious?

In answer to the 'how fast', the simple answer is we don't know. Traditionally, ice-melting has been seen as a slow process. But the old models may not be correct; as was shown by record melt rates in the early 21st century. Paleotological evidence points to times between the ice ages where sea levels have risen metres in a single decade. Hansen suggests that the relative stability of our epoch may have been to do with the fact that there was a zone of comfort between the melting of the great Eurasian and North American icesheets and the melting of Greenland and West Antarctica.

The second question is 'how much'. One approach is bottom up: you add carbon cycle causation to the greenhouse effect.
If the effect of temperature on radiative forcing is given by s and the effect of radiative forcing on temperature by g, the feedback relation is simply:
DT(with feedback)/DT(without feedback)= 1/(1-g*s). This amounts to 15-78% more warming (Cox and Scheffer 2007):
the feedback of global temperature on atmospheric CO2 will
promote warming by an extra 15–78% on a century-scale.
This estimate may be conservative as we did not account for
synergistic effects of likely temperature moderated increase
in other greenhouse gases.
But as the authors point out, this does not include the effect of everything working together.
What evidence do we have of everything working together?

A cursory inspection of the graph of greenhouse gas forcing:

a) A very high correlation (suggesting a strong link between greenhouse gas concentrations and warming)

b) Episodes of very rapid temperature change and ice melt (over the time scale of decades - e.g. the 'Younger Dryas' event.

c) a correlation between the two variables of about 3C/(W/m2)

Now the temperature shifts at the poles by about twice the global temperature change, we can imply a correlation of about 1.5C/(W/m2).

This is about double the 'fast feedback' 0.75C/(W/m2) predicted byclimate models and would imply a temperature change of six celsius for a doubling in CO2, twice what we have already found. But this is not the same quantity. It's not clear that the figure found by dividing the standard deviation of the Temperature graph by that of the Forcing graph is the quantity that Hansen asserts it is and that we want. What is going on?

So, following Scheffer and Cox, here is some basic theory of feedback loops...

Let's assume that Forcing (in W/m2) leads to temperature increases in Celsius (C). Let's assume both processes are linear:

Forcing --> Temp
\ /

If we denote the initial change in forcing by f (before feedbacks)
and the final change in temperature by T (after feedbacks)
This gives T/f=g+g(sg)+g(sg)*(sg)...= g/(1-s*g)

What about the other direction?

Temp --> Forcing
\ /

Here we observe only the final F and the final T
We see Forcing = (s+gs+gs*gs+...)t

F = t * s / (1-gs)

And T = t(1+gs+gs*gs+...)=t/(1-gs)
So F = s * T
T/F = 1/s

So if we observe T/F = 1.5 this implies that s = 2/3.

So the overall effect all depends on the overall strength of the feedback 1/(1-gs).

So ice core evidence provides us with information about the *strength of the Temperature-CO2 feedback* not on the overall greenhouse effect, including feedbacks.

The information about the gain of the whole system will therefore be gleaned from the size of the equivalent radiative forcing change that started the whole process off. If the huge temperature change and big CO2 increase was the result of a huge temperature forcing, this would imply that the feedback from temperature to CO2 was huge, but that the greenhouse effect was small.

Hansen's paper provides some very interesting evidence of the magnitude of the forcings from precession, but does not go so far as to come to an estimate of the 'equivalent' forcing implied by the Milankovich cycles. It is clear that the forcing on a global sense is small, but as Hansen points out, the effect at the ice age boundary is larger.

My conclusion supports the methodology of Cox and Sheffer over that of Hansen. However, it suggests that it should be easy to extend Cox and Scheffer to include other greenhouse gases and ice-albedo effects (by using the data that Hansen himself uses).

What is needed is to have a rough estimate of the magnitude of the original 'equivalent temperature' forcing (already including *local* ice-albedo feedbacks - since an insolation increase at the polar rim where ice is melting is clearly very effect; but *excluding* global feedbacks) that started the whole process off.

Hansen's paper hints at it but does not profer an estimate. His guess is probably a bit better than mine. Perhaps he should guess. An approximate answer to the exactly relevant question may be as much use as the exact answer to an approximately relevant question.


TheClimatePhilosopher said...

F ---> T
\ /

Feedback factor = 1/(1-g*s)
= 1/(1-0.75*0.5)=1.6

So 3C becomes 5.4C

If F started it, T/F measures g
If T started it, T/F measure 1/s

T/F = 1.5 in the
So if F started it, then this measures g=1.5 *BEFORE feedback*
If T started it, this measures 1/s in other words s=2/3 BEFORE feedback.

It's likely to be one or the other. And most of the data (Milankovich cycles etc) suggests that T started it not F.

Assuming that T started it, then T/F measures

Greyshark said...

There is absolutely no reason to worry about higher temperatures in the future due to anthropogenic CO2-emissions. It is true that a doubling of CO2 in the atmosphere theoretically could cause a global temperature increase of about 1 degree Celsius - but a doubling of CO2 is not possible. We do not have enough oil, gas and coal to achieve a doubling of CO2. And the assumption of positive feedbacks doubling or tripling this figure are pure fantasies - in reality the feedbacks are negative.
Furthermore, there are other climate effects that dominate over the increase in CO2 and which are causing a gradual cooling of the climate. This has already progressed over a number of years, but will continue over the next 20 years at least.

TheClimatePhilosopher said...

Greyshark; thanks for your comments.

"There is absolutely no reason to worry about higher temperatures in the future due to anthropogenic CO2-emissions."
1) The Earth is about 30 Celsius warmer than it would otherwise be, due to the natural greenhouse effect. The same physics suggests that increased CO2 will increase the earth's temperature bvy around 1.6 Celsius. The warming effect of increased absolute humidity would make that increase 2-4Celsius. Further increases due to Carbon Cycle feedback increase the equilibrium warming by a further 50% or so. The total Earth System Sensitivity could be said to be 2-8Celsius, with more chance of the lower warmings but a significant and non-zero chance of warmings of 6Celsius or more.

2) In the ice ages, there was 100ppm less CO2 (180ppm) that pre-industrial level (280ppm). The temperatures were 4-5 Celsius lower. While correlation does not imply causation, it gives reason for concern.

"It is true that a doubling of CO2 in the atmosphere theoretically could cause a global temperature increase of about 1 degree Celsius - but a doubling of CO2 is not possible. We do not have enough oil, gas and coal to achieve a doubling of CO2."

For remaining CO2 reserves, please see here:

There are at least 1000GtC of easily-available fossil fuels (and probavly 2000-3000GtC including other resources). 1000GtC alone accounts for 500ppm CO2 in total or 250ppm in the atmososhere; taking the atmospheric concentration from 380 well past 550ppm.
"And the assumption of positive feedbacks doubling or tripling this figure are pure fantasies - in reality the feedbacks are negative."
Please do provide evidence for your assertions.

"Furthermore, there are other climate effects that dominate over the increase in CO2 and which are causing a gradual cooling of the climate. This has already progressed over a number of years, but will continue over the next 20 years at least."

Since the effects are not detailed here, I cannot comment.

Greyshark said...

Thanks for your answer! I appreciate that you, in contrast to others in the "warmist" camp, do not censor all comments that are critical of the IPCC agenda. In the spirit of the ancient greeks, in a debate there should always be a thesis, an antithesis and possibly a final synthesis. Censorship kills the debate, and is bad for us both since I may have something to learn from you, and likewise you may have something to learn from me.

Let me give my own answer in several parts, starting with how much coal is available as fuel, it is simpler that way.
You claim that my statement that we do not have enough reserves of oil, natural gas and coal to achieve a doubling of CO2 is wrong, and you refer to a diagram from IPCC. However, IPCC obviously do not know the real facts. I refer you first to this doctorate thesis: (first page is in Swedish, the rest is in English). Then also to this site (not a "sceptic's site" by the way): .

There is simply no way we can "easily get" as much as 1000 GtC from the proven reserves (defined as having at least 90% probability of being extracted) we have today, not even counting all the "probable" reserves (defined as having at least 50% probability of being extracted). To get as much as 1000 GtC you have to make wild guesses of vast amounts of oil, gas and coal to be found in the future, and even if they are found they may well be next to impossible to extract.

Please note also that when I use the term "doubling of CO2" I mean doubling from today's level of 385 ppm, not from the pre-industrial level of (probably) 280 ppm.

Greyshark said...

Hmm, something went wrong wit one of my links, here it is again: .

Greyshark said...

Strange, maybe if I do it this way: link .

Greyshark said...

OK, that worked. Now to the feedbacks. We are absolutely agreed on a number of issues, to wit:
1) CO2 is a greenhouse gas.
2) Without greenhouse gases the Earth would be about 33 degrees C colder than it is.
3) Increasing CO2 will decrease OLR and thus have a forcing effect on global temperatures.
4) Doubling CO2 will theoretically be equivalent to a forcing of 3.7 W/m2 (this is in the IPCC report I believe).
5) With no feedbacks, a forcing of 3.7 W/m2 results in a global temperature increase of 1.1 degrees C, error range about 0.3 degrees C.

Now, IPCC believes (with no scientific proof, really) that ANY temperature increase for whatever reason will be further increased by some multiplication factor varying from 1.5 to 3 or even higher. This effect is supposed to come from the evaporation of water caused by the initial temperature increase. We all know, of course, that water vapor is a strong greenhouse gas. This is supposedly to cause a strong positive feedback.

Hope you are with me so far. But now we have to deal with facts, not hypothesies. Recently we have been able to measure OLR (the ERBE project) and other interesting things like the humidity of the troposphere using satellites. This data has been collected for many years now, and can be used to determine what the real facts are. I refer you to this recent report: . I quote from the abstract: "The observed behavior of radiation fluxes
implies negative feedback processes associated with relatively low climate sensitivity."

Greyshark said...

Now I will come to the future cooling of the planet. It is well known that global temperatures do not precisely correlate with CO2 increases. One example is the period from 1878 to 1910, when global temperatures decreased with around 0.6 degrees C . This period is counted as pre-industrial, and CO2 emissions probably did not increase. On the other hand, they certainly did not decrease either. Another example is the period 1944 to 1976 when global temperatures decreased around 0.3 degrees C while the amount of CO2 in the atmosphere was increasing. My third example is the period of global warming 1911 to 1944 when temperatures increased by around 0.7 degrees C while the amount of CO2 in the atmosphere hardly increaed at all.

Then we of course have the period of swift global warming 1976 to 1998 when CO2 and temperatures correlated very well. But all evidence indicates that there are other forcings that are more important than that caused by increasing CO2. This is especially true at this moment, since no further warming of the planet has been seen since temperatures topped our in 1998. Actually we can se a cooling trend being established during the last five to six years, and a critical factor seems to be that the PDO turned negative in 2006. In the past this has indicated a cooling trend of approximately thirty years. Add to this a quiet sun, where similarities to past Grand Minima are seen, and planetary temperatures during Grand Minima have always been colder than during other periods.

TheClimatePhilosopher said...

OK, since we are in approximate agreement on structural points, I will deal only with the paper from Lindzen and Chou.
The full paper is available here (for public access, see previous link posted by greyshark. Since I only profess to be a climate philosopher of a sort, and not a climate scientist (ie. I am a busy non-specialist), all I wish to do here is to set out Lindzen and Chou's argument, as I perceive it. I am not going to comment on it at prewent because to do so would need more knowlege of the field than I as a climate science layman posess.

Broadly speaking, the paper aims to find the correlation between sea surface temperature and outward radiation flux. From this he aims to find an estimate of the climate sensitivity.

The paper finds a large outward flux in the tropics associated with a small change in temperature, over the timescale of a year or so. In other words, increased temperature is expected to be driving increased outwards heat flux, more rapidly than expected.

Since the outward flux is proportional to temperature and is rising more rapidly with temperature than would a black body, Lindzen infers that net feedbacks are negative; so that the temperature rises less rapidly than for a black body.

I don't know whether this paper is approximately true; has good methodology; or is reflective of the balance of scientific evidence, without much more research, which unfortunately will not be dealt with here. But it will form part of a new book that I am writing on this matter. Watch this space!

TheClimatePhilosopher said...

I had a quick look around the literature. There appears to be disagreements as to whether clouds feedbacks are positive or negative. Correlation does not imply causation; and inferring causation from correlation is tricky and requires futher assumptions! Since cloud feedbacks are the most important feedback which could be negative, it's an important one to investigate. Most of the other feedbacks (water vapour, albedo; carbon cycle, methane) are likely to be positive (ie. accelerating warming). It's possible that a strongly negative cloud feedback could compensate, but it's not clear that it does.

Greyshark said...

I admire your (and Hansen's) mathematics. But I look at things in a much simpler way, and I think the information we have about temperature changes and forcings in the last 100 years can give us a more reliable result with simpler calculations.
I agree to the idea of temperatures depending on forcings in a linear manner. But as we know, CO2 forcings depend on CO2 concentrations in a logarithmic manner. So let me repeat what I think we are in agreement on:

1) CO2 has increased from 280 ppm to 385 ppm since pre-industrial times.
2) Net forcing from this increase is 1,7 W/m2 (according to IPCC, check my numbers)
3) Total forcing for a doubling of CO2 is 3.7 W/m2 (according to IPCC, check my numbers)
4) Temperature increase during this period is 0.6 C .

So there is another 2 W/m2 and 175 ppm CO2 to go until we arrive at a CO2 doubling. The time needed for this is probably 80-90 years, if we do manage to burn enough fossil fuels.

Let us now assume that the entire temperature increase of 0.6 C is due to the 100 ppm of CO2 increase (I of course think otherwise, but for the sake of argument), giving a forcing of 1.7 W/m2. Since temperatures depend linearly on forcing, this (using regula de tri) means that another 2 W/m2 will cause a temperature increase of 0.7 C. Total is 1.3 C, not far from the theoretical value of 1.1 C for a doubling of CO2.

Now IPCC says that we need to introduce a postive feedback that is quite large, and which will cause temperatures to rise even more. This is obviously wrong, since the first increase of 0.6 C is INCLUSIVE of all feedbacks in the system. Therefore the prognosticated 0.7 C increase also is INCLUSIVE of all feedbacks. This is simply a reality check showing that no positve feedbacks can exist!

The above reasoning depends omn two things:
1) We do not reach any "tipping points" along the way, and this seems to be true.
2) There are no hidden "heat deposits" that will come into play, that is I am assuming that all feedbacks for the temperature increase of 0.6 C have played out. And this seems to be a very reasonable assumption.

So my conclusion is that the "IPCC scenario" at most can mean a temperature increase of 0.7 C over what we already have got. Which does not cause me any alarm. And in REALITY, even this will not happen - because the increase of 0.6 C was "most likely" NOT caused by CO2 alone.

TheClimatePhilosopher said...

Right, but as you (Greyshark) point out, whether the earth has a non-zero 'heat capacity' or not is crucial to whether your methodology here is approximately correct -- as you point out, your methodology largely depends on the assumption
"2) There are no hidden "heat deposits" that will come into play, that is I am assuming that all feedbacks for the temperature increase of 0.6 C have played out."

Now, unfortunately I have not managed to demonstrate conclusively whether this assumption is justified of not.

One diagnostic we could use: If the oceans are in approximate equilibrium with the applied radiative forcing then we would expect the pattern of ocean temperature increases now to be the pattern of a warmer world. Now, I am not enough of an expert to know whether or not the warming we have seen is characteristic of equilibrium or not, but in principle it could be done.

The hadley data is here:

Relevant data which might help would be the trend of the ocean heat data.
This might have to do with the vertical heat transfer. (In equilibrium, I guess the oceans would warm vertically synchronized fashion; in equilbrium, they might not be.)

Some relevant heat data is here

Here is a quote from that paper:
"Including time-variable error estimates, the linear trend in ocean heat content in the upper 700 m gives a total change of 16 plusminus 3 times 1022 J from 1961 to 2003 (equivalent to an air–sea heat flux of 0.36 plusminus 0.06 W m-2 over the ocean surface area considered, 3.3 times 10^14 m2; all error estimates quoted are one standard deviation), with about 91% stored in the upper 300 m. "

I'm not sure if this evidence can give us the answers, but it is certainly interesting.

Overall, I remain confused as to whether your assumption (2) is correct or not.

TheClimatePhilosopher said...

The nature paper continues:
"We combine our estimates of thermosteric sea level with estimates of thermal expansion in the deep ocean and of the increased mass of the ocean in an attempt to balance the sea-level budget (Fig. 3). Although observations and models confirm that recent warming is greatest in the upper ocean, there are widespread observations of warming deeper than 700 m (refs 19–21). The only global observational estimate of thermal expansion in the deep ocean13 indicates that integrating to 3,000 m gives a 20% increase on the value for the upper 700 m (or 0.07 mm yr-1). This value is probably underestimated because of the use of standard optimal interpolation techniques and the sparse deep observational database, particularly in the Southern Hemisphere14. In the ocean reanalysis from the German Consortium for Estimating the Circulation and Climate of the Ocean model, the 1962–2001 ocean thermal expansion was about 0.6 mm yr-1 in the upper 700 m, with an additional 50% (about 0.3 mm yr-1) from the ocean below 700 m (ref. 22). For estimating the sea-level budget we use a deep-ocean thermal expansion of 0.2 plusminus 0.1 mm yr-1 (Fig. 3a) but recognize that this value is uncertain. This thermal expansion rate implies additional heat storage of about 8 times 1022 J (0.2 W m-2) in the deep ocean."

TheClimatePhilosopher said...

To simplify; for the oceans, about half (50-80%) warms the upper oceans and the other half (20-50%) warms the deep oceans. It's the deep ocean heat store, if it exists, which is the tricky bit, because it could mean that the oceans are not yet in thermal equilibrium with the current level of radiative forcing.

Greyshark said...

I'm sure the paper from Nature you refer to is very interesting, but I cannot access it. Also, the data it uses is only up to 2003, in that perspective I'm sure the calculations of heat content are correct. However, since then much has happened, and particularly the ARGO buoy system has been launched, and it is certainly the best system ever for collecting temperature data from the oceans. ARGO data seems to indicate a cooling of the oceans in later years, I refer you to this analysis: . This is however not a peer-reviewed paper, so I do not find it conclusive even though I can find no direct fault with it.

Almost the best thing with this paper is the reference list, particularly: . Here I find great support for my own thinking and calculations, and especially interesting is the conclusion that CO2 is responsible for a warming of 0.07 C per decade. This is completely in accord with my own simple calculations.

TheClimatePhilosopher said...

nteresting - thanks. Here's a paper from 2005 which may or may not be relevant to our collation of evidence
K. M. AchutaRao*† et al. (2007)

BTW I don't agree or disagree with this paper I've quoted: I'm as sceptical of science as the next man - it is the job of science to persuade me! But I'm just adding it to the collection of evidence. For further evidence (of my politicization (lol) ) you can email me at steve[a]

Here's the abstract:
"Observations show both a pronounced increase in ocean heat
content (OHC) over the second half of the 20th century and
substantial OHC variability on interannual-to-decadal time scales.
Although climate models are able to simulate overall changes in
OHC, they are generally thought to underestimate the amplitude
of OHC variability. Using simulations of 20th century climate
performed with 13 numerical models, we demonstrate that the
apparent discrepancy between modeled and observed variability is
largely explained by accounting for changes in observational
coverage and instrumentation and by including the effects of
volcanic eruptions. Our work does not support the recent claim
that the 0- to 700-m layer of the global ocean experienced a
substantial OHC decrease over the 2003 to 2005 time period. We
show that the 2003–2005 cooling is largely an artifact of a systematic
change in the observing system, with the deployment of Argo
floats reducing a warm bias in the original observing system."

"A recent study by Lyman et al. (12) claimed that the 0- to 700-m layer of the global ocean experienced a heat
content decrease of 3.2 plusminus1.1 x 10^22 J over 2003–2005 and that
models cannot replicate changes of this magnitude. Our analysis
shows that the cooling found by Lyman et al. is spurious. At least
five lines of evidence support this conclusion."

Greyshark said...

All new information is of course of value. However, I tend to concentrate on observed data. The paper you refer to is only a discussion of climate model performance and is of no importance in my opinion. In addition, it is a bit old.

TheClimatePhilosopher said...

The main point of introducing this paper was to note that the introduction of the Argo floats may have created a spurious downward trend in ocean heat content.

"... some caution must be exercised in estimating global-scale OHC trends
from an observing system that has undergone large and rapid increases in coverage and whose measurement biases have not been adequately quantified."

TheClimatePhilosopher said...

On trying to determine the feedback parameter from water vapour, see this paper: This paper argues that the water vapour feedback can be inferred from the data from the Pinatubo eruption, giving approximate agreement with mid-range estimates from General Circulation Models.