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/
RichardLH says:
February 8, 2014 at 2:14 am
Richard, I don’t know of any lunar cycle with that periodicity. In fact, the lunar cycles only have approximate periodicity. For example, the tides kind of repeat after 18 years six months or so, but then they have a much closer repetition after 54+ years.
The best explanation of this is over at Chiefio’s blog, in his post called Lunar Cycles More Than One. Among lots of other interesting stuff is his discussion of the Saros cycle, which includes this:
The Greeks knew about this because it was important in predicting eclipses. What this means is that after that 54-year period, the sun, moon, and earth are in a straight line (thus the eclipse) and the same spot on earth is directly under the sun … except of course, only approximately the same spot, but still quite close … and that’s why the tides repeat every 54+ years.
Finally, while I’m at it, can I rail against the pernicious practice of declaring a cycle is “close to” a lunar or other astronomical cycle? I don’t care if it’s 20 years and that’s “close to” a lunar cycle. I’ve calculated tide tables. There is no 20 year cycle.
The triple Saros cycle has a real-world meaning, in that the tidal forces repeat (almost exactly) every 19,756 days. So I don’t care if you find a 60-year cycle in some random climate dataset X. Unless your cycle is 54 years 1 month, I’m not interested. The tides do NOT repeat on a 60-year cycle.
Please note that I do think the tidal cycles govern the mixing of the oceans, and that since the ocean is thermally stratified, this mixing must affect the temperature. The only question is … how much?
w.
Willis: “I hate following a link to find it’s a tease, with no data, no code, no explanation”
Fair point. I just threw it in quickly for interest, that’s why I prefixed FWIW. That graph was part of an article, I should have linked that rather than just the graph itself.
http://climategrog.wordpress.com/2013/03/01/61/
At that time I was doing the lag correlation in R , which I’ve pretty much given up using for a number of reasons. The code is not clear enough to be made public and is nothing clever enough to merit the effort of cleaning up. I presume you can do a lag correlation in R any way but if you like I could pull out the bit that iteratively does c-c in a loop and used lag() each time.
I now have an awk script to do correlation. That should be close enought to being pubishable. I have more confidence in the code doing what I asked it to do an nothing more when using awk.
For the chirp-z tranform I use some software Tim Channon was kind enough to provide me with but is not mine to hand out. I don’t know whether he could be persuaded to give you copy too. I have found it excellent.
Greg says:
February 8, 2014 at 2:28 pm
8.85 interference with 18.6/2 gives 9.06 . The interference pattern produces 9.06
Remind me where you get the 8.85 from. And 9.06 is not the 9.15 you show.
“Please note that I do think the tidal cycles govern the mixing of the oceans, and that since the ocean is thermally stratified”
If there’s any hysteresis in this process (e.g.transfer of heat between the ocean and atmosphere is faster in the positive direction versus the negative), this has the effect of a subharmonic that you can’t detect without a much longer sample period.
Almost all the discussion above appears to me to be related to the problem of – not a long enough sample means the conclusions drawn vary widely with the starting sample point or other assumption.
We simply need to collect data for another hundred years or more to be sure of what the actual underlying signals are.
Greg says:
February 8, 2014 at 2:48 pm
The code is not clear enough to be made public
If the code is not crystal clear, how can you yourself have any confidence in it?
I’ve added the following explanation under that graph now.
Power spectra are derived from auto-correlation of d/dt(SST) from the ICOADS data base.
g12m indicates a 3-sigma gaussian low-pass filter with sigma=12 months.
1400m indicates the maximum range of lag used to generated the autocorrelation function, from which the power spectra were derived.
Greg says:
February 8, 2014 at 2:28 pm
Thanks, Greg. I have to say that the “beat frequency” explanation always seems suspect to me. Yes, they are real, and yes, they exist … but they are also too easy to calculate.
In this case, however, there are other problems. First, what is “8.85”, and why would it give an interference pattern (a “beat frequency”) against the half-period of 18.6? How does that work?
Also, you seem to think that the “interference pattern” between two waves with periods P1 and P2 has the average period, since (8.85 +18.6/2) / 2 = 9.08, and you get 9.06 … or perhaps not, perhaps you are calculating it some other way.
In fact, the interference pattern between two waves with periods P1 and P2 has the period (P1 * P2) / (P1 – P2), which for 8.55 and 9.3 years gives us 182.9 years.
w.
lsvalgaard says: “If the code is not crystal clear, how can you yourself have any confidence in it?”
The code is “crystal clear” to me because I wrote it. It’s several things lashed together. It would be probably more effort that it is worth for someone else to try and decrypt it.
The bit I don’t have confidence in is what R is doing. Its an economists tool, not well behaved enough for science IMO. I caught it extending a data set once. I never understood how or why and don’t really care. A “language” that screws around like that I just drop and go elsewhere.
Willis, don’t confuse beats , which is the ‘rectified’ envelop of the interference pattern with the modulation frequency. In some cases that may be relevant, like phase insensitive human ear just picks up the change in amplitude. There may be cases like wind speed where this could apply in climate.
For more detail see here.
http://climategrog.wordpress.com/2013/09/08/amplitude-modulation-triplets/
The averaging needs to be done of frequency, not period. That’s why you got a slightly different value.
18.6/2 because this is the period of alignment of solar and lunar orientations. Tidal effects are wavenumber 2 causing equal and opposite forces on near and far side of planet.
8.85 is precession of the line of apsides. The largest difference between perigee and apogee is about 15% , in the tidal force varying as the inv. cube, that’s about 40%. A huge variability. 8.85 years is now long it takes for line of apsides to come back to the same alignment with sun-earth line.
Willis: “Finally, while I’m at it, can I rail against the pernicious practice of declaring a cycle is “close to” a lunar or other astronomical cycle? ”
I agree. When working with periods it needs to be damn close otherwise if all falls apart within a few cycles. If I use ‘close to’ in this context, I mean 9.06 is close to 9.1 . ie within the accuracy of extracting a peak by this method.
For example when trying to identify evidence of amplitude modulation by presence of spectral triplets, I like to see frequency symmetry better than 1% eg.
http://climategrog.wordpress.com/?attachment_id=757
PS in that case 27.6006d is ‘close to’ 27.55 days, the anomalistic month: the average period of the perigee cycle.
Greg says:
February 8, 2014 at 3:11 pm
So you just average the two frequencies and name the average the “modulation frequency”? I don’t understand that at all. Do you have a citation to something other than your own work for that procedure?
Are you claiming that if there is a signal with a period of 1 year, (frequency = 1 cycle/year) and another signal with a period of 10 years (frequency = 1/10 cycle per year), that when we put them together there is some kind of “modulation frequency” at the average frequency = 0.55 cycles and a period of 1/0.55 = 1.82 years? What does that even mean?
You’ll have to explain how that one works, because I sure can’t see it in the data, and I don’t understand how the physics might work …
w,
PS—Not that it matters, but when I average frequencies for 8.55 and 9.3, I get 9.07, not the 9.06 that you reported …
Greg says:
February 8, 2014 at 3:03 pm
The code is “crystal clear” to me because I wrote it.
As a one time professional programmer [ http://en.wikipedia.org/wiki/RC_4000_Multiprogramming_System ] I can tell you that what you say is not valid. Everybody says that even if the code is full of bugs. The only way to be sure the code works is to expose it to scrutiny by other programmers.
Greg says:
February 8, 2014 at 3:33 pm
If I use ‘close to’ in this context, I mean 9.06 is close to 9.1 . ie within the accuracy of extracting a peak by this method.
How about the 9.15 you actually found?
The tides come and go all the time you know. Canute tried to point out that fact. He knew but could not convince others.
a) Tides are not gravity per se.
b) Tides add an entirely predictable amount of energy to the Earth every day.
c) The amount of energy they add is pure noise compared to everything else that is going on.
d) Tides are without question not the cause of observed global warming as a source of energy although sure, they can help stir the pot just like gravity is needed for convection. They aren’t within two orders of magnitude of being sufficient as a proximate cause of warming. They are 0.002% of the Earth’s annual energy budget.
So no, sorry, gravity is a conservative force and tides are a tiny, tiny contribution to the Earth’s energy budget. In fact, there is only one significant contributor to the Earth’s energy budget — Mr. Sun. Everything else is pretty much irrelevant — all together their total contribution (if it were to double) wouldn’t explain climate variation.
rgb
“So you just average the two frequencies and name the average the “modulation frequency”? I don’t understand that at all. Do you have a citation to something other than your own work for that procedure?”
Willis, if you read about two lines above that in the text of mine you quote you will find a reference to an article that will hopefully explain to you all you are demanding an explanation of. (with refs to external sources in case you can’t follow the maths and you want to believe someone other than me).
This is pretty standard maths identities and the basic physics of optical, acoustic and many other phenomena what show wave like behaviour. It’s not my own private theorem.
If I provide you with links at least read them before coming back moaning that I need to explain it all.
BTW, if you use 8.85 I gave instead of 8.55, you may find you finally get the same answer as me. Dyslexia rules, KO 😉
“How about the 9.15 you actually found?”
9.15/9.06=1.009934 : within 1%
Greg says:
February 8, 2014 at 3:21 pm
8.85 is precession of the line of apsides. The largest difference between perigee and apogee is about 15% , in the tidal force varying as the inv. cube, that’s about 40%.
It sounds like you want to modulate the 9.3 year tidal period by the 8.85 yr cycle [multiplying the two amplitudes]. If you do that you get two periods 4.54 [half of your 9.06, ‘close’ at least] and 182.6 years. Not the 9.15 you found. If you add the amplitudes you get periods 8.84 and 9.29 [harmonic mean 9.06, but still not your 9.15]. Why should one add the amplitudes? It seems more physical to multiply as the tides presumably would be modulated by distance [inv. cube].
”
b) Tides add an entirely predictable amount of energy to the Earth every day.
…
So no, sorry, gravity is a conservative force and tides are a tiny, tiny contribution to the Earth’s energy budget. In fact, there is only one significant contributor to the Earth’s energy budget — Mr. Sun. Everything else is pretty much irrelevant — all together their total contribution (if it were to double) wouldn’t explain climate variation.”
rgb
Recognised talbes of tidal periods usually run to 18.6 years I think. The direct input of tidal energy dispersed through frictional losses is small as you correctly point out. However, if there is inter-annual to decadal scale bulk displacement of water this could cause more energy to be captured from Mr Sun:
http://wattsupwiththat.com/2014/02/07/proper-cherry-picking/#comment-1561992
There’s an interesting study here …
Greg says:
February 8, 2014 at 4:29 pm
“How about the 9.15 you actually found?”
9.15/9.06=1.009934 : within 1%
I don’t consider that ‘close’ enough and find it symptomatic that you first tried to compare with 9.1, not 9.15
Greg says:
February 8, 2014 at 4:25 pm
Greg, if you are talking about the link http://climategrog.wordpress.com/2013/09/08/amplitude-modulation-triplets/ I thought that website was yours … as are all but one of the links. That one says nothing about a “modulation frequency” that is the average of a pair of frequencies.
I find nothing saying you can just average two frequencies and claim it’s a interference phenomenon.
I believe I read them all. They explained nothing. Not one of them talked about a “modulation frequency”. Plus … it’s all you. I asked specifically:
You go on to say:
No, that was my point. The 8.55 was simply my typo in writing it up, not a math mistake. If you use 8.85 for the calculations (as I actually did, despite the typo) and 9.3, you get 9.07, not 9.06 as you claimed. Here are the results from Excel:
You’d do well to wait for the actual sunrise before you start crowing.
w.
“If you add the amplitudes you get periods 8.84 and 9.29 [harmonic mean 9.06, but still not your 9.15].”
Scafetta found 9.1 +/-0.1 . BEST estimated the spectral uncertainty at +/-0.4 which is probably rather pessimistic. Those figures are within about 0.5%. Periods close to this value are very common in many aspects of climate. The particular N.Atl cc N.Pacific example I cited is within 1%.
That’s going to drift into anti-phase after 50 x 9 year cycles. Not a worry in this context.
It is well within the accuracy of the data and the extraction method. If this was spectroscopy we would be looking a lot better than that to identify an element by atomic absorption but I think it’s good enough for SST data.
Willis Eschenbach says:
February 8, 2014 at 2:30 pm
“Richard, I don’t know of any lunar cycle with that periodicity. In fact, the lunar cycles only have approximate periodicity. For example, the tides kind of repeat after 18 years six months or so, but then they have a much closer repetition after 54+ years…..What this means is that after that 54-year period, the sun, moon, and earth are in a straight line (thus the eclipse) and the same spot on earth is directly under the sun … except of course, only approximately the same spot, but still quite close … and that’s why the tides repeat every 54+ years.”
Indeed. The only slight problem I have with that simple, near 60, cycle is that it is not divisible by 4.
Why 4? Because of Leap Years. You know, the time it takes for the Sun to be in the same position in the sky at the same place on Earth at the same time of year.
So a modulation of the 54 by the 4. Who knows. This all gets WAY too complicated.