Guest essay by Johannes Herbst
There is a much discussed graph in the blogosphere from ‘Tamino’ (Grant Foster), which aims to prove that there is no delay or pause or decline in global warming.
He states: Twelve of sixteen were hotter than expected even according to the still-warming prediction, and all sixteen were above the no-warming prediction:
Let’s get a larger picture:
- We see the red HADCRUT4 graph, coming downwards a bit from 1960 to 1975, and inclining steeper beyond 2000, with a slight drop of about the last 10 years.
- We see a blue trend, rising at the alarming rate of 0.4°C within only one decade! This was the time when some scientists started to worry about global warming.
- We see the green trend, used by the blogger Tamino in the first graphic, rising less than 0.1°C per decade.
- Below we see the Sunspot Numbers, pulsing in a frequency of about 11 years. Comparing it with the red temperature graph, we see the same pattern of 11 years pulsing. It shows clear evidence that temperature is linked to the sunspot activity.
Tamino started his trend at high sun activity and it stopped at low activity. Therefore the weak increase during 18 years.
Which leads us to the question: How long should a time be for observing climate change? If we look at the sunspot activity and the clear pattern it produces in the temperature graph, the answer is: 11 years or a multiple of it.
Or we can measure from any point of:
·high sun activity to one of the following
·low sun activity to one of the following
·rising sun activity to one of the following
·declining sun activity to one of the following
to eliminate the pattern of sunspot numbers.
Let’s try it out:
The last point of observation of the trend is between 2003 and 2014, about 2008. But even here we can see the trend has changed.
We do not know about the future. An downward trend seems possible, but a sharp rise is predicted from some others, which would destroy our musings so far.
Just being curious: How would the graph look with satellite data? Let’s check RSS.
Really interesting. The top of both graph appears to be at 2003 or 2004. HADCRUT4 shows a 0.05°C decline, RSS a 0.1°C per decade.
A simple way for smoothing a curve
There is a more simple way for averaging patterns (like the influence of sunspots). I added a 132 months average (11 years). This means at every spot of the graph all neighboring data (5.5 years to the left and 5.5 years to the right) are averaged. This also means that the graph will stop 5.5 years from the beginning or the end. And voila, the curve is the same as with our method in the previous post to measure at the same slope of a pattern.
As I said before the top of the curve is about 2003, and our last point of observation of a 11 years pattern is 2008. From 2008 to 2003 is only 5 years. This downtrend, even averaged, is somehow too short for a long time forecast. But anyway, the sharp acceleration of the the 1975-2000 period has stopped and the warming even halted – for the moment.
Note: I gave the running average graph (pale lilac) an offset of 0.2°C to get it out of the mess of all the trend lines.
If Tamino would have smoothed the 11years sun influence of the temperature graph before plotting the trend like done here at WFT, his green trend would be would be the same incline like the blue 33 year trend:
Even smoother
Having learned how to double and triple smooth a curve, I tried it as well on this graph:
We learned from Judith Curry’s Blog that on the top of a single smoothed curve a trough appears. So the dent at 2004 seems to be the center of the 132 month’s smoothed wave. I double smoothed the curve and reached 2004 as well, now eliminating the dent.
Note: Each smoothing cuts away the end of the graph by half of the smoothing span. So with every smoothing the curve gets shorter. But even the not visible data are already included in the visible curve.
According to the data, after removing all the “noise” (especially the 11 year’s sun activity cycle) 2004 was the very top of the 60 years sine wave and we are progressing downwards now for 10 years.
If you are not aware about the 60 years cycle, I just have used HADCRUT4 and smoothed the 11 years sunspot activity, which influences the temperature in a significant way.
We can clearly see the tops and bottoms of the wave at about 1880, 1910, 1940, 1970, and 2000. If this pattern repeats, the we will have 20 more years going down – more or less steep. About ten years of the 30 year down slope are already gone.
One more pattern
There is also a double bump visible at the downward slopes of about 10/10 years up and down. By looking closer you will see a hunch of it even at the upward slope. If we are now at the beginning of the downward slope – which could last 30 years – we could experience these bumps as well.
Going back further
Unfortunately we have no global temperature records before 1850. But we have one from a single station in Germany. The Hohenpeissenberg in Bavaria, not influenced from ocean winds or towns.
http://commons.wikimedia.org/wiki/File:Temperaturreihe_Hoher_Pei%C3%9Fenberg.PNG
Sure, it’s only one single station, but the measurements were continuously with no pause, and we can get somehow an idea by looking at the whole picture. Not in terms of 100% perfection, but just seeing the trends. The global climate surely had it’s influence here as well.
What we see is a short upward trend of about ten years, a downward slope of 100 years of about 1°C, an upward trend for another 100 years, and about 10 years going slightly down. Looks like an about 200 years wave. We can’t see far at both sides of the curve, but if this Pattern is repeating, this would only mean: We are now on the downward slope. Possibly for the next hundred years, if there is nothing additional at work.
The article of Greg Goodman about mean smoothers can be read here:
Data corruption by running mean ‘smoothers’
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Johannes Herbst writes at: http://klimawandler.blogspot.de/
(1 + cos(signal)) * cos(carrier).
Expand it and you get the same thing : cos*cos but with more carrier added back in. That is to prevent the modulation going too deep and is why what radio calls “100%” modulation is just half amplitude modulation. If you go deeper than that you can’t recover the signal with a simple rectifier.
I also tune my guitar that way, I also explained the difference between beats and the non rectified modulation pattern. It’s because the ear is insensitive to phase so what we hear is the amplitude of the rectified cosine and we ‘count’ both the positive and negative modulation as a beat. If you look carefully each second pattern is upside down , there’s phase flip where it nips off.
The “beat frequency” is twice the real modulation signal.
It’s like the formula for planetary conjunctions. Since they count both superior and inferior conjunctions (ie they don’t care about the “phase” ) it is the same as the beats formula.
Don’t bet hung up on the term “interference pattern”. Look at the plots on the U. NSW link or do you own. Plot cos(9)+cos(10) count the peaks and calculate the period of the fast cycles. You’ll find they are neither 9 nor 10 😉
Radio sidebands are at carrier + modulation signal and carrier – modulation signal , so working back form two side bands the carrier is at the average and the separation is twice the modulation freq. Hence half the difference.
When you have exactly equal amplitude modulator and carries the carrier disappears and you get left with the two side bands. That is what the basic trig identity gives you. If they’re not equal you get the usual triplet, like I found in Arctic ice. It is obviously unlikely that the two will be the same size in climate so triplets are common.
Now I hope that’s enough because I can’t spend the rest of the night going over it. It does take a while to get your head around if you’re not familiar with the concepts so don’t scim read and expect to get it first time.
Greg.
Instead, the beat frequency is the DIFFERENCE, not the average, of the underlying frequencies.
Beats are the average (half the sum) modulated by the half the difference. We hear it rectified so what we hear is twice of (half the difference), ie the freq diff.
Greg Goodman says:
February 9, 2014 at 3:39 pm
I would expect a fast settling effect on shallow water. It’s like the small capacity part of the pot analogy. That would have minimal lag and thus equilibrate fast enough to be a direct correlation to power. <
Energy input, not power. And it is not like the pot. The pot starts cooling immediately when you remove the fire and to begin to warm instantly when the heat comes back on. No lag, no 'triangular' function.
That does not preclude a longer response in deeper reservoirs that would have significant lag, dependant on the time constant it may correlate better with integral, ie accumulated energy.
You must mean accumulated [i.e. integrated] power 🙂
That is the point I was trying to make originally, global SST may take a while to drop back to 1900 levels even if get two low cycles, having been pumped up for the last 50 years.
The run of solar activity in the 20th century has been similar to that of the 19th and of the 18th as well, so your argument is not valid, so you have no point to make.
W: “You’re asking the wrong guy. ”
I think that is what I was trying to point out to your good self. That also makes you the “wrong guy” to be telling me to toss out my formula.
Jeez, there are TWO cycles 18.0xxx and 18.6 . If you haven’t got that far yet, have a glass of humility and read up a bit before firing off.
“You must mean accumulated [i.e. integrated] power :-)”
No I mean the accumulated energy is the integral of the instantaneous power.
Greg Goodman says:
February 9, 2014 at 3:39 pm
That is the point I was trying to make originally, global SST may take a while to drop back to 1900 levels even if get two low cycles, having been pumped up for the last 50 years.
The run of solar activity in the 20th century has been similar to that of the 19th and of the 18th as well [minimum up to a maximum, then back to minimum], so your argument is not valid, so you have no point to make. Now, there are longer term variations of climate [1000 yr or so], we don’t know if they are caused by similar cycles in the sun [without any lags either] or if such cycles even exist.
Greg Goodman says:
February 9, 2014 at 4:39 pm
“You must mean accumulated [i.e. integrated] power :-)”
No I mean the accumulated energy is the integral of the instantaneous power
You didn’t notice the little smiley 🙂
Yeah, the energy input as measured by TSI is what we should concentrate on.
Willis Eschenbach says:
February 9, 2014 at 1:56 pm
“So … you say that if Greg claims that the sun is affecting the climate, the burden of proof is on Leif to show that it DOESN’T affect the climate?”
Well, in the first place, that is very poorly phrased. It is a given that the Sun is affecting the climate. It is the only significant heat source which does.
The question is whether solar variability has a significant impact on surface temperature variability. Leif, et al, are not arguing that it is not proven that the Sun has such an impact. He, in particular, is flat out claiming it does not. So, yes, he does carry the burden of proof of such a statement.
So far, his efforts to prove this are based on an extraordinarily shallow argument, made with his usual pugnacious grace and charm, one which Greg has taken him to the woodshed several times over. In a massive natural system with energy storage and retrieval mechanisms, the effect of short term input variations is generally severely attenuated, while that of long term influences is relatively amplified. The long term response can easily dominate under these circumstances, yet that input component would be lost “in the noise” of the overall input signal.
The situation here is very like AM radio. The information that is being transmitted may be bandlimited to substantially less than 20 kHz, but the carrier is at 540 kHz and above. The entire signal looks little like the waveform which is eventually going to come out at your speaker. But, the song is nevertheless there.
Greg, I officially dub you an expert…she said with a sherried tongue firmly planted in her cheeky self.
The pot starts cooling immediately when you remove the fire and to begin to warm instantly when the heat comes back on. No lag, no ‘triangular’ function.
With a large heat capacity and minimal losses , the temp increase will be near linear, dT/dt will be near constant. As you say that start to happen as soon as the heat is applies and stop wnen it is removed.
So , as I said, it is dT/dt that is in phase and correlates with the input not T(t).
Alternatively T(t) is in phase and correlates with integral { W(t) }
If you try to correlate the triangular T(t) ramp with power input it will be near zero since it is 90 degrees out of phase, despite the fact that the change in slope happens at the same time as the step in power.
Now if you’ve finished playing silly buggers, I’d rather discuss climate than play your silly games.
It may work with you 18 year old undergrads but I’m not impressed.
Bart says:
February 9, 2014 at 4:46 pm
He, in particular, is flat out claiming it does not. So, yes, he does carry the burden of proof of such a statement.
You cannot, or will not, read, what I have been saying for a long time is that there is no evidence that satisfies me that there is. There is no burden of proof of that statement.
So far, his efforts to prove this are based on an extraordinarily shallow argument, In a massive natural system with energy storage and retrieval mechanisms, the effect of short term input variations is generally severely attenuated, while that of long term influences is relatively amplified.
There is no good evidence for long-term changes of solar activity either, so your qualitatively handwringing is moot.
Willis Eschenbach says:
February 9, 2014 at 2:47 pm
“Wikipedia, on the other hand, confirms what I thought, which is that amplitude modulation is done by an equation of the form (1 + cos(signal)) * cos(carrier).”
(1 + cos(signal)) * cos(carrier) = cos(carrier) + 0.5*cos(carrier+signal) + 0.5*cos(carrier-signal)
Greg, you say:
Are “9” and “10” frequencies, periods, or what? Are they in radians, degrees, years, or what?
w.
Are “9″ and “10″ frequencies, periods, or what? Are they in radians, degrees, years, or what?
Come on Willis, you’re a bright chap , do I need to spell it, dot all the I’s and cross the T’s?
Plot a couple of cosines in whatever units you fancy and count the bumps.
Bart says:
February 9, 2014 at 4:54 pm
Yes, agreed, that’s true … but what does that have to do with Greg’s claim that “Addition of two cosines is mathematically INDENTICAL to a modulation.”
w.
Bart says:
February 9, 2014 at 4:54 pm
Thanks Bart, I’d already replied to that but that’s another way to explain it.
Folks, if there is scant evidence that it is and scant evidence that it isn’t (regardless of what “it” is), the null hypothesis must still rule. That is how science works. It is up to solar enthusiasts (and CO2 enthusiasts) to show a robust correlation and mechanism that is stronger than the null hypothesis which is rooted in intrinsic factors. Deal with it.
Yes, agreed, that’s true … but what does that have to do with Greg’s claim that “Addition of two cosines is mathematically INDENTICAL to a modulation.”
Look at it Willis. RHS is the “addition of two cosines” ; LHS is the multiplication (ie modulation).
Greg Goodman says:
February 9, 2014 at 4:57 pm
Well, one thing’s for sure. I’m too bright to play guessing games with someone who STILL hasn’t given me the citations I’ve asked for. You can continue the conversation without me.
You don’t answer questions, you don’t answer requests, you airily wave your hand at Wikipedia and tell me I should study some vague something that you don’t specify or link to. You don’t explain your terms. You don’t give the math that you claim underlies your claims. You may be knowledgeable, Greg, but if so, you sure are making every effort to hide it.
And now this. I ask you a simple question for clarification and you flat freakin’ refuse to answer, and instead you insult my intelligence because I can’t read your mind. I don’t give a damn how smart anyone is, because no one knows what you mean by “cos(9)” and “cos(10)”. Nine and ten what?
Piss off, fool, I’m done with you. There’s no cheese at the end of your maze, just more insults and no answers. Go play with someone else, it’s no fun for me. You want me to guess that you mean 9 degrees and 10 degrees so you can abuse me for not guessing right?
Son, I’m too old and too wise to play that game … I’m out. Bother someone else.
w.
lsvalgaard says:
February 9, 2014 at 4:51 pm
“You cannot, or will not, read, what I have been saying for a long time is that there is no evidence that satisfies me that there is.”
If that is your position, then I have erred, and apologize. I would suggest you persistently make your position clear, as not everyone has the time to read an entire thread to see where precisely the protagonists stand. What I stated was the vibe I got from the argument you were having with Greg.
Greg Goodman says:
February 9, 2014 at 4:48 pm
As you say that start to happen as soon as the heat is applied and stop when it is removed.
You have seen the light, yay. So we agree that the pot does not continue to warm after the heat is removed.
Alternatively T(t) is in phase and correlates with integral { W(t) }
Taken over how long? a minute [the heating-cooling cycle], a day, a month, a million years? The integral grows monotonically with time and diverges towards infinity. If you take the integral over the heating-cooling cycle it is constant, so T is constant?
No, a proper analysis uses the concept of a source-function and a loss-function and evaluates the energy balance using those, based on the energy input/loss per unit time..
Bart says:
February 9, 2014 at 5:05 pm
If that is your position, then I have erred, and apologize.
Accepted.
I would suggest you persistently make your position clear, as not everyone has the time to read an entire thread to see where precisely the protagonists stand. What I stated was the vibe I got from the argument you were having with Greg.
I have persistently done this perhaps a hundred times over the past several years. I don’t think I have an argument with Greg, I am trying to teach him something: that not everything is a nail.
Pam “That is how science works. ”
If someone said “null hypothesis” prove otherwise, it’s a fair argument. If someone says no correlation therefore I’ve proved it’s not there, I say there is a logical flaw, since no correlation is not sufficient (in mathematical use of the word) to establish that claim.
Those who lack the maths to realise can be excused if they are prepared to listen when it is explained in detail. Those who don’t lack the maths are either just trolling on a Sunday afternoon or past their sell-by date.
Greg Goodman says:
February 9, 2014 at 5:10 pm
since no correlation is not sufficient (in mathematical use of the word) to establish that claim.
I think we are not discussing mathematics, but physics – you know: cause and effect, not what might or might not be that we don’t know about…
lsvalgaard says:
February 9, 2014 at 5:10 pm
“I don’t think I have an argument with Greg, I am trying to teach him something: that not everything is a nail.”
If that is your intention, it is not coming across. Greg has been laying out a clear case for his POV, of which…
Greg Goodman says:
February 9, 2014 at 5:10 pm
“If someone says no correlation therefore I’ve proved it’s not there, I say there is a logical flaw, since no correlation is not sufficient (in mathematical use of the word) to establish that claim.”
I would personally amend that to say “no immediate 1:1 correlation”, or “no 0th order correlation” as a stated previously, or something along those lines of simple and straightforward correlation. But, it seems as if Greg is under the same impression as I, that you were arguing that solar influence is disproved to have an effect by lack of simple correlation.
If we can all agree that it is not disproved, but that the case for proving it does not, at this time at least, rise to the level to persuade Leif, then I think the argument is over.