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
Volcanoes: Active, Inactive and Interactive
Stacked Volcanoes Falsify Models
That data shows around a -.5c drop in global temp. following the Mt. Pinatubo eruption , for a short period of time even though an El Nino is going on. This is based on satellite temperature data from Dr. Spencer’s web-site.
WIllis wrote: “I’m using the canonical relationship of the current (and in my opinion incorrect) climate paradigm. This is that ∆T = lambda ∆F, where F is forcing, T is temperature, and lambda is climate sensitivity. As I tried to say up top, I don’t believe that’s how the world works … I’m just trying to show that by their terms the so-called “sensitivity” is very small.
∆T = lambda ∆F only applies to equilibrium situations where the temperature has had plenty of time to come into equilibrium with the change in radiation. As you can see from my calculations, the effects of volcanos don’t last for long enough for equilibrium to be reached. You need to take the heat capacity of the mixed layer into account to properly model for the temperature change after an eruption. A forcing of 1 W/m2 can’t change the temperature of the mixed layer more than 0.3 degC and it takes more than a year for half the change to occur (0.15 dgC). A transient forcing several times bigger won’t produce easily detected spikes in the historic temperature record.
Steven Schneider first became famous predicting “nuclear winter”, which he later admitted turned out to be “nuclear autumn”. Similar alarmism about volcanos has led you to expect “volcanic winter” following a major eruption (“the year without a summer”), but calculations suggest “volcanic autumn”, a cooling difficult to detect against background noise.
∆T = lambda ∆F is sensible because the earth’s temperature is controlled by the amount of energy it receives from the sun and other factors. T is a function of F. If the function is well-behaved, a linear relationship between ∆T and ∆F can be used to approximate this function. The linear relationship will breakdown breakdown if you apply it to changes that are too big. All of the negative feedbacks that you sensibly argue could control climate can be represented by a smaller lambda, climate sensitivity – you don’t need to throw away the whole equation. And you don’t need to throw it away because ∆T can be hard to detect against a background of natural climate variability.
If the function is not well-behaved, we may be in a chaotic region that can’t me approximated by a linear function. The physics of radiation doesn’t produce chaotic functions, but fluid dynamics does.
Willis says :
“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””
You’re subtracting out part of the signal – potentially a large part firstly. Secondly your results are completely dependent on the type of smoothing you’re doing for the subtraction. Where are you sensitivity tests for various forms of smoothing? I see you smoothed out the long-term signal during the late 1800s and early 1900s where volcanic aerosols were prevalent… Your thesis is ultimately going to give you the answer you like just based on methodology.
Willis Eschenbach says:
September 22, 2013 at 1:01 pm
“We are talking about the surface temperature … and as the poorly named “greenhouse effect” clearly shows, we can have identical conditions 1/4 mile above the TOA, and very very different conditions at the surface.
That is why rain is a cooling mechanism … because we’re talking, not about the heat content of the planet, but the temperature of the surface, and rain definitely cools the surface.”
Actually the conditions “above TOA” drive the conditions at the surface – if you have TSI rise it drives SST/OHC and land surface temperature/heat content directly, while at the same time changes in solar wind flux modulate GCM, you get less low-cloud seeding, while you get more water vapor in atmosphere (having considerably higher heat capacity than air) and you end up with higher both tropospheric and surface air temperatures. There’s no known “homeostasis” effect countering solar activity rising trends and its GCM/cloud cover positive feedback – if there would be something like that we wouldn’t observe the very significant rising of the SST anomaly in the 20th century – which is quite well in terms with the solar activity rise even in absolute surface heat content numbers.
The water cycle cools the sea and land surfaces by taking considerable specific and latent heat (yes both – ~85% latent heat, ~15% specific heat) from it – more than third of the energy Earth surface absorbs from solar irradiation, converting it to heat (3.8×10^24 J yearly) leaves the surface via water evaporation, subsequently the specific heat contained heats the atmosphere all the way up (humid warm air has lower density than dry cold air) and the latent heat at the point where the water condenses, both changing ALR considerably. Eventually the water falls back as rain (or snow), but how it cools the surface is not so much by the temperature-of-the raining-water with temperature-of-the-surface difference (rather almost negligible effect), but again by its subsequent evaporation, which in average “costs” the surface at least 2.5 GJ per m^2 per year (or 2.6 MJ – 2.26 MJ latent heat+0.35 MJ specific heat per kilo of water evaporated – yes in average almost 1 ton of water is evaporated from 1 square meter of Earth surface, bulk of it of course from ocean). Which btw is result of water/air interface optical properties which considerably lower the real-world sea water emissivity and for example make the Kiehl-Trenberth energy budget with the “396” W/m^2 surface radiation an utter nonsense, because 2/3rds of the Earth surface is ocean which in average doesn’t radiate more than ~264 W/m^2.
DocMartyn says:
September 23, 2013 at 3:38 pm
====
We’ve been doing this for decades….
Look for “red tide” info, Miami has the longest running air quality for the Carib, etc
wayne said:
“I, as others, do greatly appreciate your work and insight into these areas though I hope you have the flexibility to possibly be incorrect in a few of your viewpoints where we do differ, one of those being that you do not feel the mass of atmospheres matter at all, I do. Keep an open mind, stay a real scientist. I’ll always give you that same courtesy. Even here on this post.”
Seconded.
Something has to set the energy content of the system around which any thermostatic mechanism must work.
The variations in weather phenomena on Earth that Willis relies on emerge when the system diverges from that baseline energy content and operate as a negative system response rather than as the element that primes the system.
Volcanic activity undoubtedly causes a divergence and the system response is circulation changes that affect the hydrological cycle as Willis correctly observes.
If there were no water then the circulation system alone would have to achieve the thermostatic effect without the assistance of the highly efficient hydrological cycle and in that event the circulation changes would need to be far more violent to maintain system stability.
Mars is a good example, water is absent and the atmospheric circulation periodically kicks up planet wide dust storms as the Martian equivalent of Earth’s hydrology based thermostatic process.
On Mercury, the same effect is achieved by the phase changes of rock from solid to liquid and back again between the day and night sides.
On Venus, the massive surface pressure causes the atmosphere to be so dense at the surface that it is halfway to being a solid and the consequent extreme power of the winds is the Venusian thermostatic process in action.
Every planet has its own form of thermostatic process which is related to both the composition and quantity of atmospheric mass with the quantity of mass setting the baseline energy content and the composition determining the circulatory configuration required to achieve a successful thermostatic outcome.
I look forward to the day when this ‘clicks’ in the minds of Willis and others who currently deny the role of atmospheric mass (and therefore surface pressure).
Joe Born,
Hi Joe,
“As my excuse for choosing this time to pick that particular nit, all I can say is that you’ve given this formula more than once before, and each time I’ve failed to understand how it applies to the usual situation with which you’re dealing, i.e., to matching data representing averages over intervals that are potentially significant fractions of the system’s major time constant.”
We are just making slightly different starting assumptions about the nature of the input and output data, I believe. The input stimulus (forcing) is normally given as an end-period cumulative, F0,F1, F2,F3 … for years 0,1,2,3…(say).
The formula used by Willis uses the stimulus at the START of the timestep to yield the temperature value at the END of the timestep. So for year 1, your X(1) value should be set to (F1+F0)/2. For year 2, your X(2) value should be set to (F2+F1)/2 and so on. The difference term, X(2)-X(1), then approximates the estimated stimulus imposed at the start of the second timestep. The resulting temperature values on the other hand correspond to the time at the END of the timestep, not central year values.
I have just tested this against analytic solutions for your choice of parameter values. There is a maximum error of 14% for the first timestep when tau is set to just twice the timestep. This rapidly diminishes to less than 2% error after 5 timesteps, and less than 1% error after 10 timesteps. (I used a linearly increasing forcing for the tests. For a step function input, the numerical error should be zero if the step is applied at the start of the first timestep.) The errors in the other cases with higher values of tau were negligible.
Why don’t you modify your program to test this, and if you still have a problem, I will post a spreadsheet with results.
Hi Willis,
I have a couple of problems with the methodology you have applied here.
First, your method of getting to the residual temps actually puts a systematic bias into the result because the volcanic effect in the temperature domain is not itself a zero-mean effect. It should pull down your Gaussian smooth and hence reduce the magnitude of the signal you are looking for.
Secondly and more importantly, you can’t use the regression coefficient as a measure of sensitivity. The magnitude of response is frequency dependent. You can test this easily by setting up a sinusoidal forcing input and then looking at the results as you reduce the periodicity while maintaining the same amplitude.
If I recall, Pinatubo had something like a 4 W/m2 forcing, but gave rise to (only) an estimated 0.6 degrees drop in temperature. If it had happened over a longer (shorter) period of time, then the temperature drop should have been bigger (smaller).
“…Thanks, Steven. I’ve shown that I can duplicate the models’ global temperature output with a one-line equation which fits easily on the back of an envelope.
So I fear that your continual claim that it’s oh-so-complex is completely contradicted by the ultimate simplicity of what the models are doing….I got an R^2 of about 0.98 between my simple emulation and the models.”
Willis-san: I’ll respectfully remind you that it was stated (by others) at the time you posted the one-line equation that what you produced was not itself a model, but a model of a model. The 0.98 value for your r², instead of amusing you, should have raised a flag that you were not operating from first principles. It’s way too good a fit. When was climate science (or what passes for it in the world of Michael Mann) ever that precise? Never. Clearly your math, though perfectly valid, is operating at a different level than the models.
Each fine-grain cellular detail of a model is ultimately summed, averaged, and replaced by a single global number, e.g., global albedo. Those finalized composite numbers have been incorporated in your model-of-a-model, but without the cellular detail that led to them. Thus there’s a level of detail in the climate models that your one-line method does not deal with. You really, really need to comprehend this to understand exactly what you’ve achieved and what you haven’t.
RC Saumarez says:
September 23, 2013 at 7:39 am
@Tintoolman.
Thankyou for clarifying your level of maturity.
Willis writes “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.”
IMO comparisons of volcanic aerosol forcings and CO2 forcings are not comparable. They’re most certainly not equivalent.
A volcanic forcing means less energy arrives at the earth’s surface. Full stop. Its not there at the surface. On the other hand CO2 forcing is one factor in how the atmosphere moves energy from the surface out to space and the atmosphere can potentially do all sorts of things to change that rate.
jorgekafkazar “Thus there’s a level of detail in the climate models that your one-line method does not deal with. You really, really need to comprehend this to understand exactly what you’ve achieved and what you haven’t.”
What does it say to you then?
My understanding of this is simple:
THEY MAKE IT UP AS THEY GO ALONG.
Apologies for yelling.
Hi Stephen, agree with much you are saying that physics will always balance using proportionally the most effective methods available at the highest rate… but don’t want to stray too far off topic, a courtesy to Willis. We’ll discuss that later.
But would you please take the time to read tumetuestumefaisdubien1’s comment for some further discussion at talkshop. This is bringing back memories of nearly a year ago, remember my figures showing the ocean’s emissivity much lower, believe near 0.65 IIRC, that everyone so objected to as unrealistic. Don’t know tumetuestumefaisdubien1’s qualifications but he is spitting right back the same figures I came up with, ~260 W/m², not 396, and a much lower emissivity. Maybe time to revisit that area. That was when I was so complaining that the Kiehl-Trenberth energy budget was completely incorrect, could not realistically be “balanced”, and then published that spread to show what I had come up with that did balance and here are the same values again out of the blue.
tumetuestumefaisdubien1, if you happen to read this comment, thanks for your comment, I’ll take a look back on those points you are making, seems they so parallel what was found separately a year ago but I’ll have to dig back a bit.
Using calculations from “Stratospheric loading of sulfur from explosive eruptions.” Bluth et al (1977), it seems that the sulfate peak after an eruption is between 2 to 3 months later. The sulfate then sediments out in about 30 to 40 months.
In “Eruptions that shook the world”, Dr. Oppenheimer (session 8.3.2) suggests that “denser sulphur clouds grow larger particles” and, therefore, are “less effective at reflecting sunlight back to space”. Thus being, larger, explosive, (super)eruptions (like Toba’s) affect climate cooling in a proportionally lesser way than non-explosive ones, which release SO2 in finer particles which may float longer at the troposphere.
My pet idea is that Carbonyl Sulfide (OCS) can contribute to the background levels of sulphate in the Junge layer, but it’s just an idea based on the long lifetime of OCS, and that it dissociates easily in 200 nm and 270 nm light. (stratosphere).
Just some random thoughts should you wish to ruminate upon this further.
Salvatore Del Prete says:
September 23, 2013 at 3:36 pm
Provide a link, or I’m not interested. And I have shown that no, past evidence doesn’t show the contrary. If you think my evidence is wrong, QUOTE MY WORDS that you think are in error and tell us exactly what is wrong with them.
Waving your hands at some study or other won’t do it. You can’t show that they’re right, that’s not possible in science, all you can do is falsify studies. So you need to show that I’m wrong.
w.
Salvatore Del Prete says:
September 23, 2013 at 3:48 pm
Meaningless. You haven’t said where and what I’ve done wrong. You haven’t provided a scrap of data, or a link to a single study. You’re just flapping your lips … sorry, not impressed.
w.
Frank says:
September 23, 2013 at 4:34 pm
Near as I can tell, it doesn’t apply at all to the real world. However, it applies 100% to the models, that’s how they work.
w.
jorgekafkazar says:
September 23, 2013 at 7:35 pm
Since I stated from the start that it was a “black-box” analysis of a model, why on earth would you think I didn’t know that it is a model of a model?
“Operating from first principles”? I fear you truly don’t understand what a “black-box” analysis is. You might read my post “Life is like a black box of chocolates” which discusses that concept.
Best regards,
w.
Willis, when I see a post by Salvatore Del Prete I usually read as far as “Del” then skip to the next post. I suggest you save your time. Paul_K has a very good level of understanding and has raised what look like important points.
Paul_K : “If I recall, Pinatubo had something like a 4 W/m2 forcing, but gave rise to (only) an estimated 0.6 degrees drop in temperature. If it had happened over a longer (shorter) period of time, then the temperature drop should have been bigger (smaller).”
If it had lasted longer the total forcing would have been greater. I would have thought this emphasises the need to convolve the input with the laplacian impulse response (decaying exponential) or equivalent like the recursive formula Willis mentions but does not use the main analysis. This also touches Frank’s comment about dimensions: integrating the forcing is the same as differentiating the response.
Willis assures us that the results are about the same but I’d rather see a method that is dimensionally (ie physically) correct than one that is not.
He says Fe is ECS equivalent of the instant forcing, but does not explain how it is derived or what assumptions are used to get there. (His spreadsheet nearly crashes Libre Office and his formulae don’t work, so I could not see what that included.) I suggested Willis’ Fe maybe the exponential integral but he has not commented on way or the other.
Would you say that the regression coeff using the integral would give something that could be compared to sensitivity?
re. Mean zero etc.:
The gaussian high-pass filter Willis uses seems to be appropriate since several studies seem to show a time const of around 6 months. At five times that the residual will be <2% so the filter seems good. That will remove long term natural trends and steadily increasing CO2 (however big/small it may be) as well as any net downward trend induced by periodic volcanic forcing. I think that last point is your objection and makes sense. It would reduce the correlation.
Would processing the volcanic forcing (in what ever form is used) to have a mean of zero , before doing the regression, sufficiently address that problem?
Paul_K says:
September 23, 2013 at 7:35 pm
First, Paul, it’s always good to hear from you.
Next, I can see what you are getting at. It’s a valid issue. However, the effect on the results was not what I expected. The effect you’ve identified shifts the residuals vertically by the average of the volcanic effect in the temperature domain. To see how large this was, I shifted the residuals by the amount of the total effect (lambda = 0.05). All it did was slightly lengthen the time constant tau from 6.5 to 7 years, the value of lambda was almost unchanged.
Now, the average of the fitted lagged forcing is 0.02 °C, and I’ve tested it with 2.5 times that amount. So I’ll stick with 0.05 as the value for lambda, and around 7 years for the time constant.
I don’t understand this. I’m using the regression coefficient as the measure of the amount of variance in the temperature that is explained by the volcanic forcing, that is to say a measure of “goodness of fit”. I’m not sure what you mean by a “measure of sensitivity”. I’ve only used it to estimate the lag between the forcing and response. I haven’t used it at all in the lagged analysis.
According to the Sato dataset, the Pinatubo forcing (Figure 1) was 3.5 W/m2. You’ll have to point out the 0.6°C drop. Let’s play “Spot The Volcano” again. Here’s the data:
There are two major volcanoes in that graph. Can you see your claimed 0.6°C drop in there? Can you identify the time of the volcanoes?
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In any case, this should make it clearer …
I’m sure you can see the problem. Yes, there was a drop after Pinatubo … but it was only about 0.2°C, not the 0.6°C that is often claimed. That was the amount the models predicted for the drop.
In addition, there are three or four similarly-sized drops in temperature which are NOT associated with an eruption.
Finally, look at what happened after El Chichon, despite the forcing being nearly as large as that of Pinatubo … basically, nothing.
Like I said … this myth of eruptions having some big cooling effect is hard to kill …
Again, thanks for the ideas and questions,
w.
Greg Goodman says:
September 24, 2013 at 12:39 am
None of these methods are dimensionally correct, because they all use a units fudge factor. Remember we are transforming forcing (W/m2) into temperature (°C), which are incommensurate.
Greg, as I mentioned above, questions such as that one are often answered in the underlying paper. In this case it’s the Sato paper, which provides a dataset of optical thicknesses “tau”, and says:
And “Efficacy” refers to
(Again, remember I’m using their methods, but I’m not claiming that their methods are correct.)
Since the effective forcing is smaller, that gives the higher value of the ECS. If you use the larger forcing Fi, it gives you the smaller value of the transient climate response (TCR).
I should have clarified that in the head post, my bad. I’ll put it in as an update.
w.
@Willis Eschenbach
You ask do I want an R^2 of 1.5? Is this supposed to be a serious question? If have pointed out that R^2 is not a proper metric of model fit. There are other more revealing methods, starting with the ACF. As regards ill-conditioning, fitting decay curves are notoriously ill conditioned and are subject to large errors in the face of variability of objective data. I would rather trust my experience and a wide range of scientific literature than your assertions.
You have repeatedly asked me to tell you what is wrong with model, so I have told you,
I have asked you to account for the fact that your model does not give results that are compatible with well known metrics of the temperature signal, namely the autocorrelation function. The implication is that your physical assumptions in your mpdel are wrong.
You have completely failed to address this question, which is fundamental to modelling.. Instead, and forgive me if I have misunderstood you, you say that this is what other people do. I thought you claimed that this is “your” model.
In this case you are simp;ly indulging in plagiarism. If you claim originality in the model, then you should try to defend it.
On this, and several other posts, you have questioned my scientific ability as you have other people who clearly have a scientific background. I don’t give a fig what somebody like you thinks about my, or any other person’s scientific ability – you have zero authority with which to criticise any of us in the terms that you do.
Since I have a PhD and have published a substantial number of papers using the techniques in question in high level journals and being a physician who applies these techniques in real time in invasive measurements in patients, I do this subject for real and you do not.
Frankly, you come over as an opinionated, ill-educated, pretentious boor who simply rants at anybody who dares to question you..
wayne says:
September 23, 2013 at 9:41 pm
“Don’t know tumetuestumefaisdubien1′s qualifications but he is spitting right back the same figures I came up with, ~260 W/m², not 396, and a much lower emissivity. Maybe time to revisit that area. That was when I was so complaining that the Kiehl-Trenberth energy budget was completely incorrect, could not realistically be “balanced”, and then published that spread to show what I had come up with that did balance and here are the same values again out of the blue.
To explain my reasons for the claim: The Kiehl-Trenberth budget “396” (W/m2) surface radiation value is most probably based on blind theoretical calculation using Stefan-Boltzman law. But the result is physically impossible due to optical properties of water->air interface, which has average reflectivity 0.3-0.4 for the mid-IR waveleghts in question.The water simply doesn’t behave as a blackbody, to which the Stefan-Boltzman law applies – at least not without a considerable correction.
In fact there’s estimated 505 km^2 of precipitation each year on Earth. The water must evaporate before. Bulk of it from ocean. The energy needed to evaporate such amount of water is more than third of the total solar shortwave energy the Earth surface absorbs.
Given the absolute average sea surface temperature the Stefan-Boltzman law would determine the average ocean radiation to be about ~400 W/m2. But it can’t happen due to the reflectivity of the water/air interface which in average reflects 30-40% of the possible IR spectra (for liquid water at sea level pressure and possible temperatures) in question back – see here. But because the water is at the same time extremely opaque to the 290 K spectra (water transmittance for 10 micrometer spectra doesn’t allow the photons travel in the water more than ~0.1 mm) both the mid IR flux from sea and atmosphere basically keeps in the very surface skin of the water and contributes there chiefly to heating of the water to the point of evaporation – which substitutes there for direct IR radiation in direction to atmosphere. It can be calculated that ocean releases at least 34% of the heat resulting from solar shortwave radiation absorbtion this way instead of direct IR radiation into the atmosphere.
(400 W/m2 – 34% = 264Wm^2. )
Similarly it works for intermitent land water cover (well even for a water drop on a leaf), whenever it gets wet – because most of the possible water cover of land due to water surface tension is thicker than ~0.1 milimeter – a layer, which is able to absorb all over-10 micrometers mid-IR radiation encountering it. Basically all liquid water – fresh or salt, insolated or in dark evaporates due to concentration of the heat, causing IR emission in its thin skin – all caused by the optical properties of water. This properties aren’t so unique in nature, what is unique is the amount of liquid water on the surface of the Earth, which makes this effects being crucial for the surface/atmosphere complex behaviour interesting for climatology.