Guest Post by Willis Eschenbach
In the leaked version of the upcoming United Nations Intergovernmental Panel on Climate Change (UN IPCC) Fifth Assessment Report (AR5) Chapter 1, we find the following claims regarding volcanoes.
The forcing from stratospheric volcanic aerosols can have a large impact on the climate for some years after volcanic eruptions. Several small eruptions have caused an RF for the years 2008−2011 of −0.10 [–0.13 to –0.07] W m–2, approximately double the 1999−2002 volcanic aerosol RF.
and
The observed reduction in warming trend over the period 1998–2012 as compared to the period 1951–2012, is due in roughly equal measure to a cooling contribution from internal variability and a reduced 2 trend in radiative forcing (medium confidence). The reduced trend in radiative forcing is primarily due 3 to volcanic eruptions and the downward phase of the current solar cycle.
Now, before I discuss these claims about volcanoes, let me remind folks that regarding the climate, I’m neither a skeptic nor am I a warmist.
I am a climate heretic. I say that the current climate paradigm, that forcing determines temperature, is incorrect. I hold that changes in forcing only marginally and briefly affect the temperature. Instead, I say that a host of emergent thermostatic phenomena act
quickly to cool the planet when it is too warm, and to warm it when it is too cool.
One of the corollaries of this position is that the effects of volcanic eruptions on global climate will be very, very small. Although I’ve demonstrated this before, Anthony recently pointed me to an updated volcanic forcing database, by Sato et al. Figure 1 shows the amount of forcing from the historical volcanoes.
Figure 1. Monthly changes in radiative forcing (downwelling radiation) resulting from historical volcanic eruptions. The two large recent spikes are from El Chichon (1983) and Pinatubo (1992) eruptions. You can see the average forcing of -0.1 W/m2 from 2008-2011 mentioned by the IPCC above. These are the equilibrium forcings Fe, and not the instantaneous forcing Fi.
Note that the forcings are negative, because the eruptions inject reflective aerosols into the stratosphere. These aerosols reflect the sunlight, and the forcing is reduced. So the question is … do these fairly large known volcanic forcings actually have any effect on the global surface air temperature, and if so how much?
To answer the question, we can use linear regression to calculate the actual effect of the changes in forcing on the temperature. Figure 2 shows the HadCRUT4 monthly global surface average air temperature.
Figure 2. Monthly surface air temperatures anomalies, from the HadCRUT4 dataset. The purple line shows a centered Gaussian average with a full width at half maximum (FWHM) of 8 years.
One problem with doing this particular linear regression is that the volcanic forcing is approximately trendless, while the temperature has risen overall. We are interested in the short-term (within four years or so) changes in temperature due to the volcanoes. So what we can do to get rid of the long-term trend is to only consider the temperature variations around the average for that historical time. To do that, we subtract the Gaussian average from the actual data, leaving what are called the “residuals”:
Figure 3. Residual anomalies, after subtracting out the centered 8-year FWHM gaussian average.
As you can see, these residuals still contain all of the short-term variations, including whatever the volcanoes might or might not have done to the temperature. And as you can also see, there is little sign of the claimed cooling from the eruptions. There is certainly no obvious sign of even the largest eruptions. To verify that, here is the same temperature data overlaid on the volcanic forcing. Note the different scales on the two sides.
Figure 4. Volcanic forcing (red), with the HadCRUT4 temperature residual overlaid.
While some volcanoes line up with temperature changes, some show increases after the eruptions. In addition, the largest eruptions don’t seem correlated with proportionately large drops in temperatures.
So now we can start looking at how much the volcanic forcing is actually affecting the temperature. The raw linear regression yields the following results.
R^2 = 0.01 (a measure from zero to one of how much effect the volcanoes have on temperature) "p" value of R^2 = 0.03 (a measure from zero to one how likely it is that the results occurred by chance) (adjusted for autocorrelation). Trend = 0.04°C per W/m2, OR 0.13°C per doubling of CO2 (how much the temperature varies with the volcanic forcing) "p" value of the TREND = 0.02 (a measure from zero to one how likely it is that the results occurred by chance) (adjusted for autocorrelation).
So … what does that mean? Well, it’s a most interesting and unusual result. It strongly confirms a very tiny effect. I don’t encounter that very often in climate science. It simultaneously says that yes, volcanoes do affect the temperature … and yet, the effect is vanishingly small—only about a tenth of a degree per doubling of CO2.
Can we improve on that result? Yes, although not a whole lot. As our estimate improves, we’d expect a better R^2 and a larger trend. To do this, we note that we wouldn’t expect to find an instantaneous effect from the eruptions. It takes time for the land and ocean to heat and cool. So we’d expect a lagged effect. To investigate that, we can calculate the R^2 for a variety of time lags. I usually include negative lags as well to make sure I’m looking at a real phenomenon. Here’s the result:
Figure 5. Analysis of the effects of lagging the results of the volcanic forcing.
That’s a lovely result, sharply peaked. It shows that as expected, after a volcano, it takes about seven-eight months for the maximum effects to be felt.
Including the lag, of course, gives us new results for the linear regress, viz:
R^2 = 0.03 [previously 0.01] "p" value of R^2 = 0.02 (adjusted for autocorrelation) [previously 0.03] Trend = 0.05°C per W/m2, OR 0.18 ± 0.02°C per doubling of CO2 [previously 0.13°C/doubling] "p" value of the Trend = 0.001 (adjusted for autocorrelation). [previously 0.02]
As expected, both the R^2 and the trend have increased. In addition the p-values have improved, particularly for the trend. At the end of the day, what we have is a calculated climate sensitivity (change in temperature with forcing) which is only about two-tenths of a degree per doubling of CO2.
Here are the conclusions that I can draw from this analysis.
1) The effect of volcanic eruptions is far smaller than generally assumed. Even the largest volcanoes make only a small difference in the temperature. This agrees with my eight previous analyses (see list in the Notes). For those who have questions about this current analysis, let me suggest that you read through all of my previous analyses, as this is far from my only evidence that volcanoes have very little effect on temperature.
2) As Figure 5 shows, the delay in the effects of the temperature is on the order of seven or eight months from the eruption. This is verified by a complete lagged analysis (see the Notes below). That analysis also gives the same value for the climate sensitivity, about two tenths of a degree per doubling.
3) However, this is not the whole story. The reason that the temperature change after an eruption is so small is that the effect is quickly neutralized by the homeostatic nature of the climate.
Finally, to return to the question of the IPCC Fifth Assessment Report, it says:
There is very high confidence that models reproduce the more rapid warming in the second half of the 20th century, and the cooling immediately following large volcanic eruptions.
Since there is almost no cooling that follows large volcanic eruptions … whatever the models are doing, they’re doing it wrong. You can clearly see the volcanic eruptions in the model results … but you can’t see them at all in the actual data.
The amazing thing to me is that this urban legend about volcanoes having some big effect on the global average temperature is so hard to kill. I’ve analyzed it from a host of directions, and I can’t find any substance there at all … but it is widely believed.
I ascribe this to an oddity of the climate control system … it’s invisible. For example, I’ve shown that the time of onset of tropical clouds has a huge effect on incoming solar radiation, with a change of about ten minutes in onset time being enough to counteract a doubling of CO2. But no one would ever notice such a small change.
So we can see the cooling effect of the volcanoes where it is occurring … but what we can’t see is the response of the rest of the climate system to that cooling. And so, the myth of the volcanic fingerprints stays alive, despite lots of evidence that while they have large local effects, their global effect is trivially small.
Best to all,
w.
PS—The IPCC claims that the explanation for the “pause” in warming is half due to “natural variations”, a quarter is solar, and a quarter is from volcanoes. Here’s the truly bizarre part. In the last couple decades, using round numbers, the IPCC predicted about 0.4°C of warming … which hasn’t happened. So if a quarter of that (0.1°C) is volcanoes, and the recent volcanic forcing is (by their own numbers) about 0.1 W/m2, they’re saying that the climate sensitivity is 3.7° per doubling of CO2.
Of course, if that were the case we’d have seen a drop of about 3°C from Pinatubo … and I fear that I don’t see that in the records.
They just throw out these claims … but they don’t run the numbers, and they don’t think them through to the end.
Notes and Data
For the value of the forcing, I have not used the instantaneous value of the volcanic forcing, which is called “Fi“. Instead, I’ve used the effective forcing “Fe“, which is the value of the forcing after the system has completely adjusted to the changes. As you might expect, Fi is larger than Fe. See the spreadsheet containing the data for the details.
As a result, what I have calculated here is NOT the transient climate response (TCR). It is the equilibrium climate sensitivity (ECS).
For confirmation, the same result is obtained by first using the instantaneous forcing Fi to calculate the TCR, and then using the TCR to calculate the ECS.
Further confirmation comes from doing a full interative lagged analysis (not shown), using the formula for a lagged linear relationship, viz:
T2 = T1 + lambda (F2 – F1) (1 – exp(-1/tau)) + exp(-1/tau) (T1 – T0)
where T is temperature, F is forcing, lambda is the proportionality coefficient, and tau is the time constant.
That analysis gives the same result for the trend, 0.18°C/doubling of CO2. The time constant tau was also quite similar, with the best fit at 6.4 months lag between forcing and response.
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In this case it’s the Sato paper, which provides a dataset of optical thicknesses “tau”, and says:
The relation between the optical thickness and the forcings are roughly (See “Efficacy …” below):
instantaneous forcing Fi (W/m2) = -27 τ
adjusted forcing Fa (W/m2) = -25 τ
SST-fixed forcing Fs (W/m2) = -26 τ
effective forcing Fe (W/m2) = -23 τ
And “Efficacy” refers to
Hansen, J., M. Sato, R. Ruedy, L. Nazarenko, A. Lacis, G.A. Schmidt, G. Russell, et al. 2005. Efficacy of climate forcings. J. Geophys. Res., 110, D18104, doi:10.1029/2005/JD005776.
Forcing Data
For details on the volcanic forcings used, see the Sato paper, which provides a dataset of optical thicknesses “tau”, and says:
The relation between the optical thickness and the forcings are roughly (See “Efficacy …” below):
instantaneous forcing Fi (W/m2) = -27 τ
adjusted forcing Fa (W/m2) = -25 τ
SST-fixed forcing Fs (W/m2) = -26 τ
effective forcing Fe (W/m2) = -23 τ
And “Efficacy” refers to
Hansen, J., M. Sato, R. Ruedy, L. Nazarenko, A. Lacis, G.A. Schmidt, G. Russell, et al. 2005. Efficacy of climate forcings. J. Geophys. Res., 110, D18104, doi:10.1029/2005/JD005776.
(Again, remember I’m using their methods, but I’m not claiming that their methods are correct.)
Future Analyses
My next scheme is that I want to gin up some kind of prototype governing system that mimics what it seems the climate system is doing. The issue is that to keep a lagged system on course, you need to have “overshoot”. This means that when the temperature goes below average, it then goes above average, and then finally returns to the prior value. Will I ever do the analysis? Depends on whether something shinier shows up before I get to it … I would love to have about a dozen bright enthusiastic graduate students to hand out this kind of analysis to.
I also want to repeat my analysis using “stacking” of the volcanoes, but using this new data, along with some mathematical method to choose the starting points for the stacking … which turns out to be a bit more difficult than I expected.
Previous posts on the effects of the volcano.
Prediction is hard, especially of the future.
Pinatubo and the Albedo Thermostat
Dronning Maud Meets the Little Ice Age
New Data, Old Claims about Volcanoes
Salvatore Del Prete says:
September 24, 2013 at 11:53 am
I don’t recall saying anything about the temperatures of the stratosphere or the troposphere. The discussion has all been about surface air temperature. Yes, injecting tonnes and tonnes of reflective compounds into the stratosphere changes the temperature of the stratosphere.
But the odd part is, it doesn’t change the surface temperature of the earth very much at all. That’s the curiosity.
I’ve shown elsewhere that a ten-minute shift in the average time of tropical cumulus onset is enough to totally counteract a doubling of CO2 (annual average 3.7 W/m2), and the volcanic forcing is only a tenth of that (annual average 0.3 W/m2).
Volcanoes are important because we can see the effect of a short sharp pulse. It’s an ideal way to measure the effect of a known change in forcing … which for the surface turns out to be very little, and which integrates out to zero. I say it’s because of emergent phenomena which govern the temperature. When the tropical ocean is a bit cool, the clouds don’t form until a bit later … and the balance is maintained.
In the case of volcanoes, when the surface is cold because the sun is a bit weak, the system just allows more sunshine in by delaying cloud formation. It happens automatically, since when it’s cold the clouds don’t form.
Nifty system, huh? A variable sun-shade that moves earlier or later to keep the temperature constant.
w.
Willis wrote: Thanks, Frank. Actually, the difference between Fi and Fe has nothing to do with latitude. It’s all explained in the link to the “Efficacy” paper.
The explanation I suggested came from the link under “Sato paper” in your post. That link points to here: http://data.giss.nasa.gov/modelforce/strataer/
RC Saumarez, I wanted to extend an invitation to you. Here’s the puzzle. We have the HadCRUT4 temperature dataset, and the volcanic forcings dataset. For convenience, I’ve put a simple Excel worksheet containing the Sato data (global, NH, and SH) and the HadCRUT4 data (global, NH, and SH) here. IF we make the mainstream assumption that the change in temperature is a suitably lagged linear function of the change in forcing … then what numbers do you come up with for the “climate sensitivity” and the time constant “tau” of the lag?
I guess what I’m asking is, you seem very dismissive of my method of attack on the puzzle … so here you are with a free hand. How would you numerically analyze the volcanic effect on the temperature? What methods would you use? How would you judge your success?
All the best,
w.
Repost:
Russ in Texas says:
September 23, 2013 at 8:36 am
Willis or somebody else with good science-fu… can somebody help the liberal arts major here?
It seems to me (but sometimes my ideas accidentally violate the laws of thermodynamics), that part of the equilibrium might have something to do with axial tilt? No, I’m not trolling, hear me out for a second, and then illuminate/slap-me-around as needed:
You get something like a volcano: it’s going to produce a lot of localized cooling. But then it becomes winter, and the local area gets dropped even further below what the volcano would be doing…end result being more heat circulation from the rest of the globe, bang, it’s evened out, resulting in, as measured globally the forcing mechanism is destroyed at a global energy cost that is distinct, but miniscule.
I’m assuming the 305k ocean-temp limit combined with lots and lots of summer sunlight handles the other side of said equation, but… I was a history major. You wanna know why Hugh de Beaux kidnapped Mary of Siciliy in 1350, I’m your dude…. this stuff, not so much (but interested).
What am I not getting here? Thanks in advance.
Frank says:
September 24, 2013 at 12:39 pm
Please push the “Efficacy” button as requested, Frank. All questions are answered there.
w.
Willis,
Thank you for your kind response. Have read the first installment. Very interesting. You indicate that the earth’s temp has only varied approximately +/- 3% over the last half billion years. What would your source be for this info? I found this:
http://www.physics.rutgers.edu/ugrad/140/lectures/lecture_4.pdf
Also, a thought , what is the difference between a self regulating system as you describe and simply a system in which all the feedbacks sum to negative (or zero)? And, yes I read your description of the “governor” in a previous response to another poster. The effect would be the same though would it not?
happycrow:
At September 24, 2013 at 10:54 am you say in total
OK. I will bite.
If you state what you want explained then I will try to ‘translate’ (as e.g. I did above concerning the R&C Effect).
That way you may get what you want and others can concentrate on their debate without need to to talk to anyone other than each other. Your desire and their debate are both important.
Richard
Greg Goodman: “Joe, the point is that the start of month, end of month thing only matters if you have tau=2*step as in your exaggerated example. Paul_K reported specific figures and the error is minimal in the context of this data and tau of about 6 or 7 steps.”
Well, I guess it depends on what “matters” means. It’s true that even under my assumptions as to what the data mean (i.e., the F and T values are both averages over the interval) Mr. Eschenbach’s formula will produce a curve that fits the data well; for a five-time-step time constant it produced less than 6% error in the fit when I applied fifty steps’ worth of red noise, and it was only 8% off in its equilibrium-gain (“lambda”) estimate. So in the context of Mr. Eschenbach’s post it’s certainly close enough.
Still, the time-constant estimate was off by 25%, giving an estimate of six and a quarter time steps, i.e., in the range Mr. Eschenbach saw, rather than the five it should have exhibited. To me that could justify perhaps adopting a different formula in the future, which is why I brought it to Mr. Eschenbach’s attention.
I hasten to add that the approach I generally use also seems to be something wrong; although it gets closer (fit error 2%, lambda error 0.2%, time-constant error 5%), the time-constant estimate is consistently low. So I will welcome any suggestions for improvement.
Willis,
One more thought, even if the change in temp over the past 500mm years has only been +/- 3% (the source I quoted would indicate more) we are talking about a difference in reality of five to ten thousand feet of ice right here where I live compared to cattle grazing on the slopes. Irrespective of the mechanism the governor would have little practicle use in the real world of climate as it ain’t governing enough over the “short term” of 100,000 years or so to make much difference to the viability of the environment. I will invent a term, cyclically chaotic.
Thanks again
Willis said:
“Yes, injecting tonnes and tonnes of reflective compounds into the stratosphere changes the temperature of the stratosphere.
But the odd part is, it doesn’t change the surface temperature of the earth very much at all. That’s the curiosity. ”
That is because changing the temperature of the stratosphere also changes the height of the tropopause beneath those stratospheric temperature changes. A warmer stratosphere pushes the tropopause down and a cooler stratosphere pulls it up. The products of volcanoes injected into the stratosphere absorb solar shortwave directly, warm the stratosphere temporarily and push the tropopause down regionally.
Consequently the net gradient of tropopause height changes between equator and poles, the global air circulation then changes with net latitudinal shifting of jets and climate zones which then change global albedo and the amount of ToA insolation able to enter the oceans to fuel the system.
Volcanoes have a local or regional effect on the stratosphere depending on where they erupt.
The sun has an effect on the stratosphere preferentially towards the poles when solar activity changes.
In both cases it is the alterations to the global air circulation that neutralise the thermal effects for the system as a whole.
The same for changes in GHGs. They change the circulation but not the total system energy content (after a suitable adjustment period) and the effect on the circulation of our emissions is miniscule compared to the effects of solar and oceanic influences.
One still need the baseline system energy content to be set by something that is constant over geological periods of time, Hence the significance of gravity and atmospheric mass. Anything other than those two elements is capable of varying too much for the long term stability that we observe.
The thunderstorm based hypothesis of Willis is but a small fraction of the global thermostatic process. One needs to involve the entire global circulatory system from ToA to the bottom of the oceans.
Richard,
Thanks, it’s reposted at 12:59pm just above one of Willis’ posts.
Russ in Texas:
This is my promised attempt to answer your post at September 23, 2013 at 8:36 am
http://wattsupwiththat.com/2013/09/22/the-eruption-over-the-ipcc-ar5/#comment-1425599
You say:
Axial tilt does have both hemispheric and a global temperature effects
The seasons of each hemisphere are provided by the axial tilt.
The Northern Hemisphere (NH) is covered by much more land than the Southern Hemisphere (SH). And land varies its temperature much more than ocean for a similar change to solar energy. Therefore, the NH has larger seasonal temperature variation than the SH. Summer in the NH coincides with winter in the SH, and the global temperature at any moment is the sum of NH and SH temperatures. Thus, axial tilt causes global temperature to vary. The global temperature rises by 3.8°C from January to June each year and falls by 3.8°C from June to January each year.
Clearly, any mechanism which stabilises global temperature must act to adjust global temperature towards an equilibrium temperature. But axial tilt varies that equilibrium by 3.8°C during each year.
You then say
That concurs with what Willis is arguing in his above article. He says (in my opinion, he cogently says) that the cooling effect of volcanos is much less than is often claimed. Your assumption that the volcanic cooling is localised is a possible explanation for why the global cooling from volcanism is observed to be small.
You continue saying
Firstly, the 305K limit exists to sea surface temperature in the tropics. It does not apply to all oceans and it does not apply to land.
Secondly, I don’t understand what you mean by “the other side of said equation”. I am assuming you are suggesting that the 305K limit fixes maximum temperature and “lots of summer sunlight” forces global temperature up towards that limit. Now, I may have misunderstood you and if so then I apologise, but if you did mean what I have interpreted then that is very improbable. What would be the ‘stop’ which prevents global temperature rising above a maximum limit? It cannot be the R&C Effect because that only operates for sea surface temperature in the tropics. And the ‘stop’ varies the maximum temperature it imposes by 3.8K during each year. . It is much more likely that there is a constantly changing equilibrium, and effects such as the R&C Effect and the Eschenbach Effect would then be mechanisms forcing the system towards the equilibrium it has at any moment.
Thirdly, please do NOT apologise for not knowing every subject. All subjects have their importance and your expertise in the kidnaping of Mary of Siciliy can be of interest to us as our attempts to understand climate can be of interest to you.
I hope this answer is clear, adequate and what you wanted.
Richard
Hansen, J., Mki. Sato, R. Ruedy, “Fe, which is the product of the forcing and its efficacy. Fe requires calculation of the climate response and introduces greater model dependence”
I don’t see any mention that this has anything to do with TCS/ECS.
Just more fudge factors. Take the observed data then ‘correct’ it fit the model.
Thank you, Richard, that was extensive and helps me quite a bit… including that a volcano’s effects being local is indeed a dangerous assumption. Does the fact that the northern hemisphere is mostly land have any notable effect on the heat-transfer in the atmosphere from region-to-region and day-side/night-side and winter/summer once we’re past surface temps? I can see fronts move around in my weather report, of course, but I’m not well versed on how air moves *after* it’s displaced vertically.
Thanks again,
Russ in Texas
re Paul_K’s two points and Frank’s dimensional complaint.
T2 = T1 + lambda (F2 – F1) (1 – exp(-1/tau)) + exp(-1/tau) (T1 – T0)
it seems your regression fit is:
T2 = T1 + lambda (F2 – F1) ; not the same thing.
You pointed out in an earlier thread that for a constantly rising forcing, the response will settle to a delayed image of the input where delay is equal to tau, once the transient has settled. But here we are specifically choosing to study when a transient hits. The biggest ones we can find.
The dimensions of lambda are the same as sensitivity since each term in the expression must have the same dimensions. That is not sufficient to grab any term with those dimensions and equate it with climate sensitivity. You also lose a factor of (1 – exp(-1/tau)) = 0.14
I think trying to correlate all volcanoes is a good way to reduce spurious coincidental changes that lead to false attribution. However, that are some notable problems with the implementation still.
The base relationship of all this is ;
C dT/dt = F(t) – λ *T
a multivariate regression may be one approach.
tumetuestumefaisdubien1,
Yes, I believe you and I are saying the same thing but using different words to describe what is happening at the air-water interface in an attempt to get others to see why this is so. And it very much has to do with the reflectivity and angles. Sorry for the pause but I was out of place for a while.
I have in the past used the weighted cosine integral of the angles of infrared leaving the oceans surface, it integrates to be equal to 1/pi or 31.8% that is self-absorption due to the angles, weighted that is. That take 400 * (1-0.318) to be 272.8 W/m². But you also have to allow of waters actual emissivity of about 0.96. So 272.8 * 0.96 is 262 W/m² actually leaving the air-water interface and you and I end up at the same point. I tend to call it the effective emissivity though it is really the mixture of two separate effects wrapped into one.
There are some here that just cannot see that e/m radiation is composed of waves, following the duality, and these waves can and do cancel if there is a factor of angles involved. If A sends radiation to B but B is sending the exact same amount of radiation to A and at the same frequency, it is a null operation due to the angles making them exactly oppose. The angle there is 90° and the cosine is zero. At different angles you have to weight the cosines and integrate to get the overall upward sum total passage of the infrared radiation. You can do the same inverting the angles and use sines.
Think we are saying the same thing. Think this is the basis for what you are using as the reflectivity and the optical properties.
What is important is that by using the vaue that both of us are coming up with you can actually get the T-K buget to balance with the proper window frequencies radiation taken into account.
The base relationship of all this is ;
C dT/dt = F(t) – λ *T
the solution to that ODE is (as you correctly state) :
T2 = T1 + lambda (F2 – F1) (1 – exp(-1/tau)) + exp(-dt/tau) (T1 – T0)
eg. http://rankexploits.com/musings/2011/noisy-blue-ocean-blue-suede-shoes-and-agw-attribution/
(for the data here dt=1 if tau is also in months)
for brevity let’s say
a=1-exp(-dt/tau)
then
(T1-T2)-(1-a)(T1 – T0)=a*lambda*(F2 – F1)
that can be simply regressed for a number of values of a (derived from tau) and the lag regression plot produced.
It can be seen that LHS is close to being the temperature acceleration RHS is rate of change of forcing. This should satisfy Frank and Paul_K’s criticisms and is a full solution under the assumption this this is all linear to start with 😉
I think this also removed the Joe Born “start-end” thing too.
Re: Greg Goodman
September 24, 2013 at 5:34 pm
“The base relationship of all this is ;
C dT/dt = F(t) – λ *T
a multivariate regression may be one approach.”
Hi Greg,
Well that is ONE CHOICE of base relationship and it is the one that Willis is using in his forward model of temperature. The more general base relationship is:-
Change in TOA Net flux = F(t) – λ *T
Forster and Gregory 2006 did estimate λ from a regression approach over various time periods, including a go at Pinatubo.
http://journals.ametsoc.org/doi/pdf/10.1175/JCLI3611.1
Willis: Thank you for your reply, which corrects my misunderstanding. Hansen et al don’t believe that the radiative forcing for all agents will produce the same temperature change. They have put a fixed amount of Pinatubo aerosols into their MODEL for a century and then calculated the equilibrium temperature change and the radiative forcing. The MODEL has a high climate sensitivity (that you believe is wrong) arises from feedbacks that are produced by the model. The correction factor is a fairly negligible 0.91 and you applied it to the observed forcing. So what?
An analogy: If you look for a correlation between the force applied to an object and its velocity, you may find some correlation. It may improve by including a lag. However, some of the time the force may be negative while the velocity is still positive. At a moment when zero force is being applied, the velocity can have many different values. Consider a ball thrown up into the air. The force is constant, but the velocity changes with time. Does that mean there is no relationship between force and velocity? Of course not. You need to integrate the force or take the derivative of the velocity before looking for a linear relationship. That linear relationship can be used to calculate the mass of the object.
Another analogy: You might look for a correlation between the power being applied to an object and its kinetic energy, but you won’t discover the correct relationship without integrating the applied power and taking the square root of the energy. Your analysis will work better if you include friction.
Radiative forcing “is” energy per unit time while temperature “is” energy. By analogy, you need to integrate the radiative forcing or take the derivative of the temperature before looking for a linear relationship and using it to determine lamba. However, the response to a volcano is more complicated, because a change in temperature also produces a change in outgoing radiation, which modifies the forcing. And the relationship between temperature and energy depends on the heat capacity of the mixed layer.
Hope this helps. Thanks again for your replies.
@Willis Eschenbach.
I would not attempt what you suggest through linear modelling, because all the data involved suggest that these are non-linear processes, I would think it would take several months to get my teeth into the problem properly. To do so would involve a considerably better model than you propose..
Frankly I think you are behaving very badly.
I have made substantive criticisms of your model that is based on values in the literature and on proper analysis. You tend to reply with abuse. When finally challenged you come up with some autocorrelation functions that are incompetently plotted and you say that you can’t see the significance of them.
Let me remind you that you are setting yourself up as the expert on signal processing and numerics, not I. Assuming that the ACFs are calibrated in years, then I have two comments:
a) I am suspicious about the bandwidth and I think some of the shape may be artefactual..
b) It is immediately obvious that they cannot possibly be generated by the model you propose and if you had the expertise you claim, it should have been immediately obvious to you.
You challenged me to grab some data and do some sums. As it happens, I have and this is publically available. Whether you agree with my mathematical approach or not or whether you agree with Luck et al, McIntyre, Tol or not it is quite clear from the data that your model do not conform to data.
In short I have made the argument, refuted your model and you are incapabable of making any sort of response that one might expect from a genuine “scientist”..
I have read your various posts, you come over as completely imcompetetent. You post on the periodic transform is a particularly delicious example and you will note that everyone on the thread who had a knowledge of the subject concluded that you were talking complete bollocks.
I did not comment on your “science” of treadmill exercise. Let me remind you that I am an investigative physician with 30 years experience in cardiopulmonary field. Your explanation was lamentable – do you understand the highly non-linear pressure flow relations of the lung that is dependent on lund volume? Do you understand the highly non-linear pressure flow relationships in the pulmonary circulation that is highly cardiac output dependent? Do you understand how ventilation and cardiac output is matched? I could go on for hours but the fact that you describe your presentation as science is unimpressive.
Frankly I think you are self agrandising and lack insight into your scientific limitations. While you may enjoy the admiration of the credulous you hardly enjoy the respect of the educated.. The intemperance of your responses and your failure to respond to valid criticism in an objective manner reinforces this view. I would suggest that you really learn some maths and do the work in learning about signal processing rather than producing naive calculations whose basis you do not understand.
Frank,
“If Willis was feeling nasty, he could accuse those who compiled the data that Paul_K reanalyzed of cherry-picking the record that shows Pinatubo having the biggest effect on temperature. If Paul_K had analyzed the surface temperature record, he certainly would have obtained a different ECS than he reported at The Blackboard. The confidence interval for any result should reflect the uncertainty in the data used to generate that result.”
Frank,
There are certainly some differences between the surface-measured and satellite temp datasets but the choice of dataset is less important than you might think. This is because the abstraction of parameter values is not typically dependent JUST on the peak change in temperature. If you track back through my original article (which you graciously referenced), you will see that it includes a little story about Roy Spencer using TLT data, and Troy Masters testing the result on surface-measured data. The Forster and Gregory 2006 approach was also based on surface data from Hadcrut and GISS. The results all seem to yield values in the same broad range, which includes the no-feedback Planck response. However small positive or small negative feedbacks cannot be excluded by the data.
Paul_K
Hi Greg,
Well that is ONE CHOICE of base relationship and it is the one that Willis is using in his forward model of temperature. The more general base relationship is:-
Change in TOA Net flux = F(t) – λ *T
Forster and Gregory 2006 did estimate λ from a regression approach over various time periods, including a go at Pinatubo.
http://journals.ametsoc.org/doi/pdf/10.1175/JCLI3611.1
===
re “The base relationship of all this is ;”
Thanks, I meant the base relationship of the linear model is… I was not meaning it was the only possible model.
It does appear that this has been done many times and more rigorously in the literature, so this whole thread is probably a bit of a red-herring.
Lindzen and Choi 2011 , Dessler 2010 etc. etc. It seems we can produce pretty much whatever result we would like to see !
L&C studies 20S-20N , which is what I suggested above, and finds much lower sensitivity than other studies.
One mistake they all seem to have in common is the applying linear regression to two variables with significant experimental error, which is invalid and systematically produces slope below the true value. Lower slope = higher CS.
L&C2011:
As there are many intervals, the final ∆Flux/∆SST is a regression slope for the plots (∆Flux, ∆SST) for a linear regression model.
Dessler 2010:
Fig. 2. (A) Scatter plot
of monthly average val-
ues of DRcloud versus DTs
using CERES and ECMWF
interim data. (B) Scatter
plot of monthly averages
of the same quantities
from 100 years of a control
run of the ECHAM/MPI-
OM model. In all plots,
the solid line is a linear
least-squares fit and the
dotted lines are the 2s
confidence interval of
the fit.
This maybe at least one reason why many studies are producing higher CS, simple basic processing errors. Least squares only gives the ‘best estimate’ when there is a “controlled variable” whose error/uncertainty is negligible compared to that of the dependant variable.
The number of PhDs that are apparently totally oblivious to the assumptions and rules that need to be examined before clicking the “fit trend” button is astounding.
Russ in Texas:
In your post at September 24, 2013 at 4:38 pm you ask me
Again, I am not clear what you are really asking, so I will answer what I think you mean. Please get back to me if I have misunderstood.
The Earth receives energy from the Sun and – averaged over time – must radiate the same amount of energy back to space (if the energy from space did not equal the energy to space then the Earth’s global temperature would change). ‘Hot’ air rises and contains GHGs which radiate heat. At high altitudes most of that heat will go to space. So, the greater heating of air by land than from the sea in Summer means the summer heat loss to space is greater for large land areas than for large ocean areas.
‘Hot’ air has lower pressure than ‘cold’ air. This difference induces winds and other weather. It causes heat to be moved around by winds. I think you may find a primer book on meteorology would be helpful to you. From your questions, I suspect it may interest you.
I hope this answer is some help.
Richard