An article in the New Scientist says:
But Dr. Leif Svalgaard, one of the worlds leading solar physicists and WUWT’s resident solar expert has this to say:
Solar max is a slippery concept. One can be more precise and *define* solar max for a given hemisphere as the time when the polar fields reverse in the hemisphere. The reversals usually differ by one or two years, so solar max will similarly differ. The North is undergoing reversal right now, so has reached maximum. The South is lagging, but already the polar field is rapidly decreasing, so reversal may be only a year away. Such asymmetry is very common.
Here is a link to the evolution of the polar fields as measured at WSO:
http://www.leif.org/research/WSO-Polar-Fields-since-2003.png
And here’s data all the way back to 1966, note there has not been a crossing of the polar fields yet in 2012, a typical event at solar max:
http://www.leif.org/research/Solar-Polar-Fields-1966-now.png
Here is a link to a talk on this: http://www.leif.org/research/ click
on paper 1540.
Dr. Svalgaard adds:
Solar max happens at different times for each hemisphere. In the North we are *at* max right now. For the South there is another year to go, but ‘max’ for a small cycle like 24 is a drawn out affair and will last several years. To say that max falls on a given date, e.g. Jan 3rd, 2013, at UT 04:15 is meaningless.
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From Bart on October 2, 2012 at 10:18 pm:
Google does not relieve you from having to review results for relevancy. This refers to gusting strong winds yielding large deflections and snapping trunks and stalks. I am examining non-damaging gentle swaying motions in a light breeze.
Also they are simulating a “periodic gusting wind” with an equation with a sinusoidal component, while acknowledging “In reality, wind gusts are not sinusoidal and forcing amplitudes are stochastic.” Assume the unnatural and get modeled results which are supposedly reflective of results from natural processes. Sound familiar? And again, drive with an oscillating signal, get an oscillating effect. What is the driver and what is driven?
Lorentz did good math while trying to support a bad theory. Einstein derived mathematically equivalent equations.
Lorentz shows us that the math can look very good yet one can still be wrong about what underlies the math. But with the “Sun is an oscillator” belief, so far the math is not even looking good.
From Bart on October 2, 2012 at 10:34 pm:
And you have dreamed up quite an envisioning of that scenario. You should write comedy.
But once again you show your “cart before horse” tendency. The correct sequence would be first putting out the fire with whatever’s at hand, as soon as possible. Then you show Leif the evidence his hair was on fire, so he knows you didn’t just dump your coffee on his head on a lark.
As your expertise does.
“When the only tool you have is a hammer, everything looks like a nail.”
Gee, I wonder who said that…
Translation: I’m sorry but I can’t be bothered to show you the elegant divine truth that has been revealed to me, so you’ll have to wait until someone else does. But trust me, it’s beautiful and I assure you it’s all true!
The Sun is the ultimate source of the energy, but the clouds control how much of it is allowed to warm the Earth. The solar output can drop, but the cloud cover could reduce to where the Earth gets warmer. Show first that the Sun is controlling the clouds, then you may say the Sun is driving recent temperature variations on Earth.
Kadaka & Bart let me tell you a short story
About 10 years ago, my younger daughter ( then at secondary school, gradated from Oxford University last summer, MSc degree) with her homework, it was about sun and the Earth. She also had a handbook from the library with sunspot cycle. I knew about 11 year cycle, but I don’t think I’ve seen actual waveform before. Since I had lot of experience in the ‘signal processing’, I recognized a cross-modulation pattern. Within minutes I was at the Excel, running Jupiter and Saturn orbital numbers, didn’t work but it look promising, used 2xJ +S then rectified, got a bit closer, and finally 2-3 days later had a go at 2xJ +JS all rectified, looked good and that was it.
Subsequently I learned that there is whole brunch of science devoted to the sunspot cycles and a new hobby was born, from then there was only a short step to the climate change.
Should we always declare as a coincidence something that we currently do not fully understand?
The equations have been called coincidence, astrology, pseudo science, nonsense and lot more, but 10 years hence the result (the polar fields version) is still as close as you can get to the complex and the non-testable process as generation of the solar magnetic field.
http://www.vukcevic.talktalk.net/LFC2.htm
Good agreement with the contemporary science’s results:
http://www.vukcevic.talktalk.net/LFC17.htm
If you wish to understand solar ‘oscillations’ look at the polar fields first.
BTW Dr. S also uses strength of the polar fields for the SSNmax prediction.
JJ says:
At October 2, 2012 at 11:26 pm you write:
Simon and Garfunkel wrote a song about the answer you are likely to get. It is called
‘The Sound Of Silence’.
Richard
Bart says:
October 2, 2012 at 10:34 pm
And, his expertise does not extend far into the realm of signal processing and systems analysis.
Regardless [and ignoring your abusive crusade – and I shouldn’t really feed the troll], the issue is whether such extension is relevant, and the generally accepted view [with which I agree] is that it is not, as the Sun is not an oscillator with driving and restoring forces controlling solar activity. Attempts to predict solar activity along these lines have repeatedly met with failure.
It’s isn’t even really important – it’s just annoying, because it could be resolved so straightforwardly.
On the contrary, the issue of the cause and predictability of the solar cycle is of utmost importance. Of course, there is no shortage of pseudo-scientists and instant arm-chair experts who claim that this issue can be solved in a straightforward manner; the problem is that none of these folks have done so.
But, I can’t carry the world on my shoulders
But you could perhaps behave in a decent manner, or is that hoping for too much
Anyway, the actually important question is, is the Sun driving recent temperature variations on Earth? Clearly, it is, to anyone with his or her eyes open. Sadly, of those, there are remarkably few.
Perhaps there are so few because it simply isn’t so. A good illustration of the failure of the ascribing recent temperature variations to solar variations is this plot: http://www.leif.org/research/Temp-Track-Sun-Not-png where the various red curves [on top of each other] are several modern estimates of solar variability.
Leif Svalgaard says:
October 3, 2012 at 7:37 am
A good illustration of the failure of the ascribing recent temperature variations to solar variations is this plot: http://www.leif.org/research/Temp-Track-Sun-Not.png where the various red curves [on top of each other] are several modern estimates of solar variability.
kadaka (KD Knoebel) says:
October 3, 2012 at 1:31 am
“Google does not relieve you from having to review results for relevancy.”
“But with the “Sun is an oscillator” belief, so far the math is not even looking good.”
Says the guy who thinks grain stalks vibrate at 3.7 kHz. Fine, whatever you say. We’re done.
vukcevic says:
October 3, 2012 at 2:40 am
Vuk – These correlations can look compelling, but without understanding the mechanisms, it’s a hard sell in general. Just look at the resistance I am getting to something which should be a slam dunk.
I am agnostic by nature – I try to keep an open mind. I’m not going to rule out a possibility just because I do not currently see a route to it. But at the same time, I’m not going to become devoted to it, either.
I am promoting the route of taking the observed oscillations as a given, and using their obvious structure as a means of making practical predictions. When the predictions pan out, people will get interested in looking into the causes. That should be a reasonable and worthwhile endeavor in any case, but even that clearly gets considerable resistance.
Fortunately, there are people looking into it. I took my advice to kadaka that “Google is my friend” last night. There are tons of people looking into applying the very methodology I have advocated. Eventually, the truth will out.
Anyway, keep on looking. I think you’ve made some nice observations. We’ll see how the future unfolds.
From Bart on October 3, 2012 at 9:44 am:
Finally! I missed the end of the Jan P debunking event, but well, sometimes you gotta stop and clean out the stables before you go out for a ride, you know?
Vuk, it’s official, Bart threw you under the bus. Promoted your ideas, said how he ‘gave you suggestions’ to appear as a mentor with superior wisdom. Then when things didn’t work out…
“Best of luck with your future endeavors, and I wrote you a nice recommendation.”
Congratulations, you’re now a sitcom character who had a bad manager/fellow employee relationship!
Seriously Vuk, the main problem is taking the absolute values and completely ignoring the shape of the troughs. With sinusoidal curves, it looks obvious to me the SSN follows a sine curve, a complete un-rectified sine, which is then offset on the y-axis by the addition of another sine curve, which is itself offset.
That would preserve the troughs, which are the most clearly defined feature of the SSN signal, as the peaks are likely distorted as I described above. For the added lower frequency signal, use a constant for the offset, the SSN record is very short and there are many characteristics of the Sun that are basically unchanged throughout and will remain so for centuries to come.
And don’t use absolute values as that precludes the possibility of negative sunspot counts. Yes, I am serious. You are modeling the underlying processes that lead to sunspots. The SSN tracks successful sunspot eruptions. It does not track unsuccessful “squibs”. Yet those processes would yield them, so your model must allow them. Indeed, around 1810 the SSN should have been negative by the shape of the curve.
So try it that way. After correcting the SSN numbers you are using per Leif, item 1550, “Reconciliation of Group & International SSNs”. As it appears that will yield a new “standard” SSN, start with it now.
kadaka (KD Knoebel) says:
October 3, 2012 at 1:18 pm
“…the main problem is taking the absolute values and completely ignoring the shape of the troughs. “
It seems, among other things, you do not understand Fourier expansions.
“Yes, I am serious. “
We only wish you weren’t. It’s painful to see.
“Bart threw you under the bus.”
Ah, no. Vuk has nailed the major harmonic components. I merely demur at assigning a specific cause to them. Just as I do not know why Leif’s hair might be on fire, but I would still be able to see the flames.
Bart says:
October 3, 2012 at 4:22 pm
“Bart threw you under the bus.”
Ah, no. Vuk has nailed the major harmonic components. I merely demur at assigning a specific cause to them.
Talking about painful. You do not understand that the sun is not a harmonic oscillator and therefore doesn’t have harmonic components based in physics like a vibrating string. Apparently, you do not understand Fourier expansions either – just because almost any function can be expanded as a Fourier series, does not mean that those waves have any physical existence. This is typical for people that learn a skill by rote without understanding and then apply that skill over and over and over. This is the difference between a scientist and an EE: understanding versus blind application of skill. And it is time you refrain from personal nastiness.
From Bart on October 3, 2012 at 4:06 pm:
You said we were done. Yet here you are again. Why did you lie?
I had previously identified the SSN signal as having sawtooth features. A sawtooth wave can be constructed by additive synthesis using a Fourier series. Getting a good fit with sines is a good start.
If you don’t understand what I’m discussing, that’s okay. You already bowed out of any pretenses of meaningful contributions to the discussion, you can leave anytime you want, it won’t matter.
From Bart on October 3, 2012 at 4:22 pm:
Vuk has assigned their causes, Jupiter and Saturn. They are the source of the constants of his equations. So you are saying you are supporting the equations whose constants match Jupiter and Saturn, without supporting Jupiter and Saturn as the causes of those exact matching numbers?
I know I’m not stupid enough to believe those linguistic gyrations. Vuk should be insulted that you expect him to believe you.
Leif Svalgaard says:
October 3, 2012 at 4:35 pm
The oscillations are visible by inspection. The harmonics are readily evident in the PSD. You are so out of your league in this.
And, as for nastiness… you started it.
Bart says:
October 3, 2012 at 5:02 pm
The oscillations are visible by inspection. The harmonics are readily evident in the PSD. You are so out of your league in this.
To a hammer everything looks like a nail. Just because something is varying does not mean it is an oscillator. That requires two opposing forces: a driver and a restoring force. And you,should know that the Fourier expansion defined on an interval of a function generally have no predictive power outside of that interval, unless they describe actual physical forcings.
And, as for nastiness… you started it.
A childish and untrue assertion.
Leif Svalgaard says:
October 3, 2012 at 5:17 pm
“That requires two opposing forces: a driver and a restoring force.”
To be precise, it requires storage of energy, and a mechanism for conversion or transmission between specific manifestations of or reservoirs for that energy. You have that here.
“And you,should know that the Fourier expansion defined on an interval of a function generally have no predictive power outside of that interval, unless they describe actual physical forcings.”
Unless the function really is periodic, and that interval contains at least one full cycle. The SSN is not periodic. But, it is quasi-periodic, in the sense that it behaves like a sum of lightly damped oscillating modes disturbed by wideband fluctuations in forcing. Those modal oscillations have repeatable structure, and because of that, the future depends at least partially deterministically on the past, and can therefore be predicted within the bounds of that determinism.
If the SSN had no regularity at all, if the curves from one cycle to the next varied widely and essentially randomly, I would agree with you that this system would be unpredictable. But, they don’t do that.They have a very repeatable structure. You can move fairly smoothly from one peak to the next.
I do not know precisely how well I could predict the SSN after a given number of cycles. But, I know that I can predict them, and I know that I can estimate accurate error bounds for the predictions, and that in itself is something of considerable value.
Bart says:
October 3, 2012 at 7:44 pm
To be precise, it requires storage of energy, and a mechanism for conversion or transmission between specific manifestations of or reservoirs for that energy.
To be even more precise: If the system is displaced from the equilibrium, there should be a restoring force, tending to bring it back to equilibrium. and there is no such force.
The SSN is not periodic. But, it is quasi-periodic, in the sense that it behaves like a sum of lightly damped oscillating modes disturbed by wideband fluctuations in forcing.
Here is where you go wrong [the hammer and nail thing], there are no oscillating modes because the solar cycle is not an oscillator.
They have a very repeatable structure. You can move fairly smoothly from one peak to the next.
Again wrong, the conversion from toroidal field [sunspots] to poloidal fields [seeds for the next cycle] is essentially a random process, and large random jumps can occur. The small Cycle 20 following the all-time high Cycle 19 is a good example.
But, I know that I can predict them, and I know that I can estimate accurate error bounds for the predictions, and that in itself is something of considerable value.
Until you have done so, you don’t know. Nobody has ever managed to predict more than a cycle ahead every time. The error bounds are not of value per se. What is important is to have narrow error bounds, so people can act on the prediction.
Leif Svalgaard says:
October 3, 2012 at 7:59 pm
“To be even more precise…”
No, I think I’ll keep my definition. What is a “force”? What is, e.g., the “force” which produces the oscillations of an electromagnetic field? You can loosely say it is the Laplacian of the field vectors, but easier to imagine it as simply the alternating storage of energy in the E and the B fields.
“…there are no oscillating modes because the solar cycle is not an oscillator.”
There is just this incredibly regular 11-ish year cycle with a 130-ish year beat.
“Again wrong, the conversion from toroidal field [sunspots] to poloidal fields [seeds for the next cycle] is essentially a random process, and large random jumps can occur.”
If the former were so, the peaks would be scattered all over the place with no discernible pattern. As for the latter, that can happen in simulating my model here, as in this plot, in the peak before 1900, and the second one after 1950. This is due to the two modes which make up the model randomly moving in and out of sync with each other. It can be predicted well in advance of the event, as the stochastic phase modulation of each component is not particularly fast.
“Until you have done so, you don’t know. Nobody has ever managed to predict more than a cycle ahead every time. The error bounds are not of value per se.”
Fair enough on the first, at least as far as knowing how large the error bars would be. I suspect they would be reasonably tight for a reasonably long duration but,… fair enough. On the latter, knowing how much an estimate might be in error would be quite useful for, e.g., implementing contingency operations for an electrical utility, or preparing propellant budgets for the ISS, or determining whether to invest in sunscreen oil futures.
Leif, where do you get the monthly SSN data, and where are the corrections applied?
You stated here:
SIDC is available from WoodForTrees: http://www.woodfortrees.org/data/sidc-ssn
They’re showing 63.1 August, 61.5 September.
NASA-Marshall reports the International Sunspot Number from “the Solar Influences Data Analysis Center”: http://solarscience.msfc.nasa.gov/greenwch/spot_num.txt
Same as from WFT.
Where is the 66.9 and 66.8 from?
Where is the 66.9 and 66.8 from?
http://sidc.oma.be/sunspot-data/
Bart says:
October 3, 2012 at 9:48 pm
but easier to imagine it as simply the alternating storage of energy in the E and the B fields.
Imagining is one thing, reality is another
There is just this incredibly regular 11-ish year cycle with a 130-ish year beat.
Not regular at all.
If the former were so, the peaks would be scattered all over the place with no discernible pattern.
There are two processes going on: 1) the solar dynamo winds up the poloidal field. That is fairly deterministic. 2) the sunspots [the toroidal fields] fall apart and their magnetic debris is moved towards the poles by a combination of meridional circulation and random diffusion. Less than one percent of the magnetic flux makes it to the poles in a very haphazard way, so although there is some memory in the process [more spots to begin with, more field eventually to the poles in general], the random part is strong enough that the polar fields at the end of a cycle do not follow the strength of the cycle, i.e. are not predictable.
On the latter, knowing how much an estimate might be in error would be quite useful
The prediction is only useful if the error bar is small enough, and then it doesn’t really matter how small, e.g. a prediction of 100+/-50 is useless, while 100+/-10 is useful.
kadaka (KD Knoebel) says:
October 3, 2012 at 10:25 pm
Leif, where do you get the monthly SSN data,
In tracking the solar cycle one uses the smoothed [over one year] values. Last column of ‘monthly and monthly smoothed sunspot number’ from here http://www.sidc.be/sunspot-data/
Thanks Vuk, for another source. I had just gotten done figuring it out for myself when I saw your comment (which was about 2 hours ago as I’ve been researching stuff while writing this).
I got the data from this NOAA page, select “plot data” at bottom:
http://www.ngdc.noaa.gov/nndc/struts/results?t=102827&s=5&d=8,430,9
Found from this Solar Indices Data page:
http://www.ngdc.noaa.gov/nndc/struts/results?t=102827&s=1&d=8,4,9
I recalled Leif said “smoothed”. Figured out the derivation by comparing monthly and monthly smoothed and with a spreadsheet.
So it’s a 12 month running average, but to center it you take a 13 month span, and average together the 11 middle months but only half of the beginning and end months.
By the presentation, 66.9 would be the February 2012 number. The NOAA data didn’t have the September mean value yet so I grabbed it from the WFT file. That gave 66.8 for March 2012.
So did Leif misspeak when he said August and September?
Oh well, back to digesting Leif’s reference 1550, and figuring out the cryptic notation.
Rz – Relative Zurich count, aka Wolf number.
Ri – Says here that’s the ISN that replaced Rz from January 1981. So when Rz is seen referencing 1981 and later SSN data, it’s Ri.
Rg – Group Sunspot Number, by the 15 observer independent group listed on slide 15? But slide 13 says that’s 1825 to 1900. The H&S 1994 graph on slide 3 of Wolf and Group numbers is apparently showing Group data past 1900. Yep, I’m lost.
Bart says:
October 3, 2012 at 9:48 pm
If the former were so, the peaks would be scattered all over the place with no discernible pattern.
A good review of solar cycle prediction can be found here:
Pesnell, W. D. (2012), Solar Cycle Predictions (Invited Review), Solar Phys., The Sun 360, doi:10.1007/s11207-012-9997-5
kadaka (KD Knoebel) says:
October 4, 2012 at 2:21 am
So did Leif misspeak when he said August and September?
Yes, I’m sorry for that. It should have been February and March.
What I meant was that the latest smoothed value published in August was 66.9 and published in September was 66.8
Rz – Relative Zurich count, aka Wolf number.
Ri – Says here that’s the ISN that replaced Rz from January 1981. So when Rz is seen referencing 1981 and later SSN data, it’s Ri.
Yes, there are just too many names for this. As Ri was meant to be a follow-up for Rz, I use Rz for the whole time. It is too cumbersome otherwise.
Rg – Group Sunspot Number, by the 15 observer independent group listed on slide 15? But slide 13 says that’s 1825 to 1900.
Should have been 1936. Graph got updated. This is a work in progress.
Probably paper 1570 is better.
The H&S 1994 graph on slide 3 of Wolf and Group numbers is apparently showing Group data past 1900. Yep, I’m lost.
The Group numbers go to 1996 or so. I’m only concerned with the part around the jump in 1885.
richardscourtney says:
“How is it that when solar forcing is known to vary by an amount that you now argue is equivalent to 10-15 years of ‘global warming’, neither the models nor the error bands on their predictions incorprate this variation?
What else is left out of the models, and out of the uncertainty bands?”
Simon and Garfunkel wrote a song about the answer you are likely to get. It is called
‘The Sound Of Silence’.
Yes. Fellows like Perlwitz participate only so long as they are permitted to tell lies about others. When asked to tell the truth about their own beliefs, they run. They like fighting strawmen, they don’t like being shown they are one.
richardscourtney wrote in
http://wattsupwiththat.com/2012/09/28/dr-leif-svalgaard-on-the-new-scientist-solar-max-story/#comment-1098503
You can post this link as often as you want, it still won’t make appear statements in the report, which you have only made up.
Box TS.9 explains what “Committed Climate Change” is. It says:
If the concentrations of greenhouse gases and aerosols were held fixed after a period of change, the climate system would continue to respond due to the thermal inertia of the oceans and ice sheets and their long time scales for adjustment. ‘Committed warming’ is defined here as the further change in global mean temperature after atmospheric composition, and hence radiative forcing, is held constant…
(http://www.ipcc.ch/publications_and_data/ar4/wg1/en/tssts-5-1.html)
There is nothing in there that says this was only the case for the “recent 15-year temperature stasis”, compared to the “previous similar stasis” between 1980-1995 where the temperature record appeared to be “flat” in a trend analysis over that limited time period. You read something into it, which is only in your head.
Why would it be different? All the conditions listed there needed for a “committed warming” were also present in the year 1980.
You didn’t quote anything where the IPPC Report says what you assert regarding this issue above. You only post a link and try to support your assertions by asserting it is quoted under the link, which you post.
I didn’t complain anything like you assert here about what the IPCC Report presents on this page. My argument was directed against your faulty line of reasoning, which is to compare the multi-model mean results about the “committed warming” of about 0.1 K/decade until 2020 and the multi-model mean value of the scenario predictions of about 0.2 K/decade temperature increase with the one single realization of the temperature record provided by Nature, and, because both supposedly diverged from each other, to conclude the “committed warming” calculated with the models and the scenario predictions were wrong.
No, I do not agree with the first statement, and I do not claim second statement. The model do simulate the climate system of real Earth. They just don’t do it perfectly.
There are no such statements by me. I haven’t said anything about “why the IPCC prediction of ‘committed warming’ has not happened.” You are just projecting your own assertion on me, according to which it hasn’t happened. If I wanted to explain “why”, I would have to accept the presumption as true first, according to which there wasn’t any “committed warming”. The evidence is lacking for the validity of the presumption, though. Results from non-robust trend analysis, the apparent “flat” temperature trend, are not evidence for it. A failure to reject the Null hypothesis that there wasn’t any change doesn’t falsify the alternative hypothesis that states there was a “committed warming” or global warming as predicted in the scenario calculations. My response was about something else. It was about why your reasoning is faulty, based on which you claim that the real world temperature record contradicted the model results.
I haven’t said anything like the statement you assert here, according to which “the warming has ‘decreased’ to nothing” due to solar forcing, or any other cause for the matter of fact. You are making things up again. You are projecting your own assertion, according to which warming has “vanished”, but for which evidence is lacking, on me.
If you are not deliberately disseminating falsehoods, what is your problem then, since you read things that aren’t being written, both into the IPCC Report and into my comments.
As for the assertion, the temperature record was in contradiction to the “committed warming” of about 0.1 K/decade, and scenario warming of about 0.2 K/decade, one can look at the decadal averages of the globally averaged temperature anomaly.
Using the data from the GISS Surface Temperature Analysis:
http://data.giss.nasa.gov/gistemp/graphs_v3/Fig.A2.txt
These are the annually averaged anomalies in K:
For the decade of 1981 to 1990:
0.27, 0.06, 0.27, 0.10, 0.06, 0.13, 0.28, 0.33, 0.21, 0.37
mean+/-std = 0.208+/-0.113
For the decade of 1991 to 2000:
0.36, 0.14, 0.15, 0.25, 0.40, 0.30, 0.42, 0.59, 0.34, 0.36
mean+/-std = 0.331+/-0.133
For the decade of 2001 to 2010:
0.49, 0.58, 0.57, 0.49, 0.62, 0.56, 0.59, 0.44, 0.57, 0.63
mean+/-std = 0.554+/-0.061
2011:
0.51
Running decadal averages of the anomaly from end year 1991 to end year 2000:
0.217, 0.225, 0.213, 0.228, 0.262, 0.279, 0.293, 0.319, 0.332, 0.331
Running decadal averages of the anomaly from end year 2001 to end year 2010:
0.334, 0.338, 0.430, 0.454, 0.476, 0.502, 0.519, 0.504, 0.527, 0.554
Running decadal average for end year 2011:
0.556
Anomaly change between decadal averages of consecutive decades with end years from 2001 to 2011 (e.g., average of decade 1992-2001 minus average of decade 1982-1991):
0.117, 0.113, 0.217, 0.226, 0.214, 0.223, 0.226, 0.185, 0.195, 0.223, 0.222
What is supposed to have vanished again? I would say those data aren’t as far away from the about 0.2 K/decade in the scenario prediction from the model simulations. Those changes in the anomalies averaged over the decades are well within the uncertainty range up to the end year 2011.
Thanks Leif.
So from ref 1570, where is the x1.2 correction applied?
Slide 26, pre-1945 (from start to 12/1944)?
Slide 31, before 1946 (from start to 12/1945)?
Since Waldmeier took over in 1946 (slide 30) and the post 1945 Zurich numbers were 21% higher by sunspot area (slide 23), the second appears correct.