Basil Copeland and I also found linkages between surface temperature and solar cycles in two articles we published in the last year. We were roundly criticized and ridiculed by warmists mainly due to a statistical error in the first essay, but the base premise remained and the second essay was improved due to that error. I’m pleased to see that NCAR has found other solar to earth linkages, such as this one in ENSO. This is exciting news, but by no means a complete solution to the climate puzzle. There is much more to be learned about this. This is but one connector of the hydra-like patch cable that Dr. Jack Eddy imagined – Anthony
Scientists find link between solar cycle and global climate similar to El Nino/La Nina. Credit: NCAR
Establishing a key link between the solar cycle and global climate, research led by scientists at the National Science Foundation (NSF)-funded National Center for Atmospheric Research (NCAR) in Boulder, Colo., shows that maximum solar activity and its aftermath have impacts on Earth that resemble La Niña and El Niño events in the tropical Pacific Ocean.
The research may pave the way toward predictions of temperature and precipitation patterns at certain times during the approximately 11-year solar cycle.
“These results are striking in that they point to a scientifically feasible series of events that link the 11-year solar cycle with ENSO, the tropical Pacific phenomenon that so strongly influences climate variability around the world,” says Jay Fein, program director in NSF’s Division of Atmospheric Sciences. “The next step is to confirm or dispute these intriguing model results with observational data analyses and targeted new observations.”
The total energy reaching Earth from the sun varies by only 0.1 percent across the solar cycle. Scientists have sought for decades to link these ups and downs to natural weather and climate variations and distinguish their subtle effects from the larger pattern of human-caused global warming.
Building on previous work, the NCAR researchers used computer models of global climate and more than a century of ocean temperature to answer longstanding questions about the connection between solar activity and global climate.
The research, published this month in a paper in the Journal of Climate, was funded by NSF, NCAR’s sponsor, and by the U.S. Department of Energy.
“We have fleshed out the effects of a new mechanism to understand what happens in the tropical Pacific when there is a maximum of solar activity,” says NCAR scientist Gerald Meehl, the paper’s lead author. “When the sun’s output peaks, it has far-ranging and often subtle impacts on tropical precipitation and on weather systems around much of the world.”
The new paper, along with an earlier one by Meehl and colleagues, shows that as the Sun reaches maximum activity, it heats cloud-free parts of the Pacific Ocean enough to increase evaporation, intensify tropical rainfall and the trade winds, and cool the eastern tropical Pacific.
The result of this chain of events is similar to a La Niña event, although the cooling of about 1-2 degrees Fahrenheit is focused further east and is only about half as strong as for a typical La Niña.
Over the following year or two, the La Niña-like pattern triggered by the solar maximum tends to evolve into an El Niño-like pattern, as slow-moving currents replace the cool water over the eastern tropical Pacific with warmer-than-usual water.
Again, the ocean response is only about half as strong as with El Niño.
True La Niña and El Niño events are associated with changes in the temperatures of surface waters of the eastern Pacific Ocean. They can affect weather patterns worldwide.
The paper does not analyze the weather impacts of the solar-driven events. But Meehl and his co-author, Julie Arblaster of both NCAR and the Australian Bureau of Meteorology, found that the solar-driven La Niña tends to cause relatively warm and dry conditions across parts of western North America.
More research will be needed to determine the additional impacts of these events on weather across the world.
“Building on our understanding of the solar cycle, we may be able to connect its influences with weather probabilities in a way that can feed into longer-term predictions, a decade at a time,” Meehl says.
Scientists have known for years that long-term solar variations affect certain weather patterns, including droughts and regional temperatures.
But establishing a physical connection between the decadal solar cycle and global climate patterns has proven elusive.
One reason is that only in recent years have computer models been able to realistically simulate the processes associated with tropical Pacific warming and cooling associated with El Niño and La Niña.
With those models now in hand, scientists can reproduce the last century’s solar behavior and see how it affects the Pacific.
To tease out these sometimes subtle connections between the sun and Earth, Meehl and his colleagues analyzed sea surface temperatures from 1890 to 2006. They then used two computer models based at NCAR to simulate the response of the oceans to changes in solar output.
They found that, as the sun’s output reaches a peak, the small amount of extra sunshine over several years causes a slight increase in local atmospheric heating, especially across parts of the tropical and subtropical Pacific where Sun-blocking clouds are normally scarce.
That small amount of extra heat leads to more evaporation, producing extra water vapor. In turn, the moisture is carried by trade winds to the normally rainy areas of the western tropical Pacific, fueling heavier rains.
As this climatic loop intensifies, the trade winds strengthen. That keeps the eastern Pacific even cooler and drier than usual, producing La Niña-like conditions.
Although this Pacific pattern is produced by the solar maximum, the authors found that its switch to an El Niño-like state is likely triggered by the same kind of processes that normally lead from La Niña to El Niño.
The transition starts when the changes of the strength of the trade winds produce slow-moving off-equatorial pulses known as Rossby waves in the upper ocean, which take about a year to travel back west across the Pacific.
The energy then reflects from the western boundary of the tropical Pacific and ricochets eastward along the equator, deepening the upper layer of water and warming the ocean surface.
As a result, the Pacific experiences an El Niño-like event about two years after solar maximum. The event settles down after about a year, and the system returns to a neutral state.
“El Niño and La Niña seem to have their own separate mechanisms,” says Meehl, “but the solar maximum can come along and tilt the probabilities toward a weak La Niña. If the system was heading toward a La Niña anyway,” he adds, “it would presumably be a larger one.”
Source: National Science Foundation (news : web)
h/t to Leif Svalgaard
This may be a stupid question but what guarantee is there that the models used in this formulation are more accurate than the ones used by the warmists? What parameters are used to model the forcings in order to reach this conclusion (which is very interesting if true)?
And does my question make any sense?
So it is the sun.
I hear a dying echo-like sound—
It sounds like “The science is settled.” Repeated and growing fainter.
Uhm…isn’t this describing a negative watervapor feedback from warming?
And isn’t this the exact opposite of what climate models assume (positive feedbacks) to come up with warming from CO2?
And absent positive feedbacks, doesn’t this refute CO2 as a significant driver of climate?
But Buzz didn’t see any climate on the Moon and only lunatics on Earth.
A connection between solar cycles and global climate?? A fine step forward.
So, the Sun does have something to do with climate, imagine that!
What happens in this mechanism if the solar cycle is delayed or very weak?
Do we get heavy snows where applicable instead of heavy rains?
I do agree with one thing here: Whenever I have witnessed an El Nino dump on the Western US, the next couple of years are as dry as popcorn. It shuts itself off with La Nina.
One more plug on the Eddy patch cord.
I noticed some articles on Intellicast as well that also shows 11 year cycles in the reliability and intensity of various monsoon seasons and the price of coffee.
Now that we know the possible 11 year impacts of a regular solar cycle on ENSO, but what happens in a grand minimum or a very weak cycle?
Speaking of ENSO all of the plots on the TAO site and the SOI isn’t showing anything that points to an El Nino even close to 1998 levels though SST’s are now on their way down from near-record levels, this El Nino is looking more likely now that it could be a weak one when it’s all said and done.
Very good Anthony.
Served at request!
We know the sun plays an important role.
Now we have a mechanism that explains what is going on.
We need more study, data and observations but step by step…
Eventually. despite the chaotic and dynamic character of weather turning into climate directed by the clock of time we will crack this complicated puzzle of mechanisms.
Thanks for your work.
“…The transition starts when the changes of the strength of the trade winds produce slow-moving off-equatorial pulses known as Rossby waves in the upper ocean, which take about a year to travel back west across the Pacific…”
Yabbut what causes changes of the strength of the trade winds? Do the trees in South America stop wiggling their branches?
At last some “sunlight” is being shed in the very dark corners of the AGW debate. Perhaps Henrik Svensmark has a place on the podium along with Newton, Coppernicus and Gallileo.
It is interesting that they claim the extra Sunshine heats the air which only then evaporates more water. Wouldn’t some of the extra Sunshine evaporate water directly, like maybe the IR part of the spectrum?
Now with this minimum -Nino seems to portend a Moderate to weak one.Looking at the SST charts,It is nothing like ’97/98…
Yet there are those who fervently hope..
jorgekafkazar (16:56:10) :
“Yabbut what causes changes of the strength of the trade winds?”
From the text posted: “. . . as the Sun reaches maximum activity, it heats cloud-free parts of the Pacific Ocean enough to increase evaporation, intensify tropical rainfall and the trade winds”
heat/evaporation/ xxx / trade winds
xxx = low pressure
Trade winds blow from the STHP cells toward the ITCZ. Lower pressure in the latter will “intensify” the trade winds.
“The next step is to confirm or dispute these intriguing model results with observational data analyses and targeted new observations.”
My goodness, what a novel idea – test the models with observations!
Now what are the probabilities of Hansen or the IPCC using this new procedure?
I am afraid the answer as to why the trade winds vary in both strength and slightly in position is a bit of a circular one.
Essentially the path and strength is driven by the convective processes that heat the air at the tropics and we can neglect any tiny variation in the rate at which the earth turns upon its axis.
But When the heating is less the winds become less strong and their path is more affected by the rotation of the earth.
As you might expect they move at their fastest and are more stable towards the centre of the wind zone: hence the old sailorman’s references to the ‘true trades’ as opposed to the rather inconstant winds at either edge of the zone.
Kindest Regards
The paper is filled with similes. Make sure you don’t jump over those to conclusions about ENSO and PDO that were never made in the paper. Also, it appears that this is a dynamical model, not a statistical model. You won’t find the signal in the observed statistical data, only in the model. At least not yet.
Jim (17:05:31) :
It is interesting that they claim the extra Sunshine heats the air which only then evaporates more water. Wouldn’t some of the extra Sunshine evaporate water directly, like maybe the IR part of the spectrum?
I can only provide you with a single web address on this subject:
http://www.ilovemycarbondioxide.com
More evidence on the sun’s influence on the earth. The pieces are coming together. It looks like we are at the edge pieces stage now.
All the while Al Gore is getting more desperate in his war on science. His latest comparison of his battle against us ‘deniers’ is with the battle against the Nazi’s—no, I’m not kidding.
But Richard Lindzen is right : we will win, because we are right, and they are wrong.
11. a prime number. math is a beautiful thing.
This isnt exactly revolutionary, the sun warms the sea, increases evaporation and cloud colver preventing further heating. When there is less sun there are less clouds and the sea warms more. This feature moderates the climate at the equator (and the earth to a lesser extent) and is the reason why Co2 wont cause much more than slight warming. Cloud behaviour helps maintain a ocean temperature equilibrium at the equator. This is why in previous warm periods the equator was the same or slightly cooler than today yet the northern and southern extremities where much warmer. This happens every day aswell, its just that there is a longer more subtle cycle overlaid ontop.
Just a shame the IPCC models cant include the correct behaviour of clouds at the equator and how the climate system actually functions. The climate model used in this study sounds like it better replicates the behaviour of clouds and has the correct values for ocean surface evaporation etc…
This also ties in with two studies (I dont recall the names or authors) that found baseflows in large river catchments and extreme floods correlate with solar activiity.
Certainty very interesting
UK Skeptic says:
“This may be a stupid question but what guarantee is there that the models used in this formulation are more accurate than the ones used by the warmists?”
I think we need to get one thing straight. The models used by GISS, Hadley, CSIRO etc. are not so much inaccurate as wrongly used. Those models are basically being used for the wrong purpose by the IPCC in that they are being used to predict the climate out to 2100. They shoud and still are used to test our understanding of the climate system. The use of models in gaining an understanding of a system and hypothesis development is actually what they are meant for.
In this case, the models are legitimately being used to develop an understanding of a system and the likely research directions needed to develop a full understanding of it.
It is not a matter of accuracy.
Wow, so you guys were “criticized and ridiculed by warmists mainly due to a statistical error?”
Wonder how these same people reacted when they found out about Mann’s statistical shenanigans (Mannanigans?) with the 1st hockey stick?
Sunspot Cycle Length 1800-1960
via Wavelet Analysis:
http://www.sfu.ca/~plv/SunspotCyclePeriod.PNG
Regarding the response to UK Skeptic made by Richard Steckis (18:09:59) :
Excellent response !!! Too many, including some members of science and politicians think that the ‘models’ say or mean more than what they do. UK Skeptic seems to have missed this portion ……
“The next step is to confirm or dispute these intriguing model results with observational data analyses and targeted new observations.”
Confirm or dispute with observational data. Too bad Gore, Hansen, etc. don’t think of such things. Models test hypothesis but do not prove anything.
Then there is no claim of the models to predict. The main jist is……
“The research may pave the way toward predictions”
To the no-more-money-for-them dungeons with them.
What everyone is ignoring is ALBEDO!! guys, ALBEDO!!!!
Curious that when models support AGW they are all wrong, but when they support natural variability they are all the sudden good enough…
The various people that have advocated ENSO as tied to the solar cycle find that El Nino happens at or shortly after solar minimum, not as ‘the Sun reaches maximum activity’ as this study claims…
And what happens to the cosmic ray link? The article does not refer to that [at least not in the blurb]. Now, the true enthusiasts will, of course, point out that the ‘cloud-free’ parts of the ocean at maximum are there because there are fewer cosmic rays to create clouds.
O/T
I don’t know about the rest of you all, but I was a young man all of 8 years old when I witnessed Apollo 11. I remember being dragged by my teen-aged aunt down to the school to watch the launch. I had no previous understanding about what was about to happen. I went back every day for as long as the mission lasted. This would have been the approximate time I became scientifically aware. I feel honoured to have been alive and at such a formative age when those brave Americans reached out and touched another planet for the first time. I still feel the wonder I did then.
I will never forget.
A little late to the party, but then most of the NCAR staff live in Boulder Colorado (otherwise know as the Peoples Republic of Boulder) where the citizens have a tenuous grasp on reality!
Leif,
What’s up with the sun? I thought it was going to ramp up in activity? Any thoughts?
INGSOC,
I remember the Apollo 11 launch very well [I watched it along with everyone else on the single 19″ B&W TV set we had at our firebase in Tuy Hoa, Viet Nam].
A thousand years from now, WWII will be a footnote in history — but the first men on the moon will be remembered as a major milestone for the human race, eclipsing any other event. It was the human race’s first baby step to the stars.
America’s zenith was the period from WWII through the Apollo lunar exploration program. Like you, I am proud to have witnessed it.
Climate politics changing?
Climate science changing?
Leif Svalgaard (18:55:08) :
Curious that when models support AGW they are all wrong, but when they support natural variability they are all the sudden good enough…
The various people that have advocated ENSO as tied to the solar cycle find that El Nino happens at or shortly after solar minimum, not as ‘the Sun reaches maximum activity’ as this study claims…
—
Problem appears to be these analysts’ “assumed” linkage of temperature directly to the 11 year solar sunspot cycle.
Wrong approach, in my ever-so-humble opinion. The real result (of whatever is controlling earth’s climate) is a thirty year oscilating cycle imposed on a 800-1000 year larger cycle. Thus, if the AMO is dominating the year cycle – then the question becomes: What drives (controls and causes, starts and stops) the AMO?
If a second short term temperature cycle is the PDO – which may or may not go up and down with the AMO at any given time – then, What drives the PDO?
It does NOT appear to be sunspots – certainly not directly. Several previous plots show the high’s and lows of eartherm temperature match to the relative length of the sunspot cycle, the relative peaks of ech long or short sunspot cycle – but those are a symptom, not a cause, of the (unknown) cause of the AMO and PDO changes.
There is a second long term climate cycle independent of the short-term PDO’s and AMO thirty year period: The Roman Warm Period descended down to the Dark Ages, back up to the Medival Warming Period, back down to the Little Ice Age, then back up from the mid-1600’s towards today’s – early 2000’s – warmer temperatures.
I can (and have!) thought of all sorts of things influencing those two cycles: but – whatever it turns out to actually be – finding out the SOURCE of those two patterns will be the winner.
We cannot discount the very long term 10,000 year Ice Ages and the even longer 100,000 cycles. These do get controlled by solar and earth’s orbit pertubations. But orbit and polar pertubations cannot account for the very real changes that are clearly measureable. Over 8, 80, even 800 years they only distract from, and not justify, the measured short term cyclic change.
Throw a 1/10 (or even 1/2) of one degree per century in from recent CO2 changes? Yes, it could have happened. But if we are globally rising from the mid-1600’s by 1.0? 1.5? 2.0? degrees without CO2 induced effects in the previous 2000 years, then why assume/require (other than taxes and power) that any theory needs a CO2 factor?
In fact, if you add the proven 30 cycle of 1/2 of one degree to 3/4 of one degree into the graph of temperatures and temperature proxies and their error bars as they fall then rise ever since the year 1050, you probably can account for almost all of the “false evidence” cases of temperature in most any analysis.
So, today’s homework assignment is: What drives the two short term temperature cycles?
Steven Hill (19:19:26) :
What’s up with the sun? I thought it was going to ramp up in activity? Any thoughts?
It is, it is, but slowly. If you look at http://www.leif.org/research/TSI-SORCE-2008-now.png
You’ll see that TSI [the dark blue curve on top] has started to show life. The F10.7 radio flux [the pink curve in the middle] is up, and the sunspot number [green, bottom] shows new activity. But, if the new cycle is going to be weak [as I think it is] the ‘ramp-up’ will be slow.
I’m not lobbying Congress to pass an agenda to double your gasoline, electricity, water, food, internet, etc bills.
AGW is.
They want to make life extremely expensive.
Therefore I cheer anything on that tosses cold water in the face of faked concern for the Planet.
Besides that, their dire predictions turned out no better than the Ice Age warnings late 19th and early 20th centuries. Or the warming scare of the 30’s. Or the Global Warming theory of 1952. Or the Ice Age coming in the 70’s.
I have no problem with Sci-Fi books and scary movies.
When you walk out of the movie or put the book down, nobody is in your face with the latest dire warnings they cooked up.
Excellent question UK Sceptic! The answer for me comes from a quote in the article “The next step is to confirm or dispute these intriguing model results with observational data analyses and targeted new observations.”
It’s just a theory and they plan on using the scientific method to test it. AGW sounded like a good theory when it started. As long as they don’t start passing laws based on this theory, I’ll be happy to read more about it.
@ Leif Svalgaard (18:55:08) :
Dr. Svalgaard wrote: “Curious that when models support AGW they are all wrong, but when they support natural variability they are all the sudden good enough…”
Frankly, of course, it’s human nature to respond positively to a report or in this case, analysis & interpretation that falls your way.
More important is that this analysis & interpretation explains what Man knows intuitively: When the Sun is “raging & beastly” (solar maximum) more energy is received by the Earth than when the Sun is “meek & mild” (solar minimum).
Now, this analysis makes do with the 0.1% irradiance variation you agree to and articulates why that variation does make a difference in temperature over the solar cycle.
So it disagrees with your position (although, I acknowledge you provided the heads up to Anthony).
But the fact remains those that claim Man or Science knows all there is to know about the energy transfer process between the Sun and the Earth are arrogant and liable to intellectual blindness.
And you know what they say: “Pride cometh before the fall…”
I was going to point out the double-standard of computer modeling, but then I thought I read that it fit the historical record (backtested). That doesn’t make a perfect predictor either (investment modelling, anyone?), but AGW models don’t even backtest very well at all!
Yet we continue to make policy…well, wecontinue to ALLOW our electerd officials off the hook.
Mark (18:15:35) :
Wonder how these same people reacted when they found out about Mann’s statistical shenanigans (Mannanigans?) with the 1st hockey stick?
Who knows, but note that these guys admitted, and then corrected their error. The same cannot be said for The Team.
Mark
Re: Leif,
“Curious that when models support AGW they are all wrong, but when they support natural variability they are all the sudden good enough…
The various people that have advocated ENSO as tied to the solar cycle find that El Nino happens at or shortly after solar minimum, not as ‘the Sun reaches maximum activity’ as this study claims…”
Leif,
Part of the reason I am a bit dis-trustful (and hence skeptical) of the science of AGW is due to things like the issues with Mann’s hockey stick, and some people (like McIntyre) not being able to get code and data from some science and climate organizations.
And then there are the redistributive politics tied into AGW policies that is a whole other issue…
Nah…its not like a “wow all of the sudden the dynamical models support natural variability”…when we in another breath discounted them for AGW.
More like….there are more complexities….more variables….more layers…..than any simplistic or all-or-nothing approach or analysis can ever handle.
Its the OCEANS immediately, stupid.
Its the SUNS…intermediately, stupid.
And Svensmark and his rays fit in somewhere too.
IT IS ALL THREE….and more.
Thanks Anthony for inducting these studies into the record. 🙂
Chris
Norfolk, VA, USA
To me the most interesting quote in the article was the following:
“Scientists have known for years that long-term solar variations affect certain weather patterns, including droughts and regional temperatures”.
Just curious what happened 121 years ago. Wouldn’t it be interesting if every eleventh cycle had importance too?
GISS and other temp series producers are not using models. They use adjustment codes to both scrub, correct, and smooth the data. IPCC borrowed dynamical models of CO2 driven climate from a few researchers who may not have had complete control of what they did to the models in promoting their agenda. These dynamical models take super computer strength to run them. In fact short cuts are made because there is not enough computer strength to run the kind of model they would like to run. Statistical models can be run on a PC. Dynamical models should always be compared to observations and then adjusted to reflect the addition or change to the parameters that are causing the divergence. Statistical models almost learn on their own. The longer the data history of conditions present just prior to a weather or climate event, the better it becomes at predicting climate events. But there are no long strings of calculations involved. Just whether or not the same set of pre-conditions existed before.
The paper seems to be describing the outcome of a dynamical model of a proposed mechanism for a small solar signal that may not be able to rise above the noise, not an actual observation. I question the assumptions made about the proposed mechanism and wonder if it isn’t a bit of fishing. Would like to read the entire paper.
Everyone is looking for the slam dunk on climate. When will we get a model that includes the vast variety of factors?:
1. A Heliomagnetosphere/teramagnetosphere interaction (tearing holes in teramagnetosphere?) (exposure to (protection from?) solar wind/cosmic rays, and quantified roughly by sunspot qty/SC periods under a multi decadal curve?
(this so as to explain the heat content(or lack thereof) in #2)
2. A definitive measure of the radiative balance at the limb of our atmosphere?
3. (Now I’ll really show my ignorance) An ENSO/LNSO /+/- AMO oscillation
(I’ll guess – induced by Lunar cycle and its precession COMBINED WITH solar retrograde due to Barycenter fluctuation, including precession of all planetary bodies about the sun, AND about the plane of the ecliptic) (It may be small mass, leif, but it’s there)
And I want to raise a question on this: Since Sun is a ball of ionized plasma, why can’t this (magnetic disturbance) be affected by jovian mass displacement? It isn’t as though the sun was a solid body. It isn’t necessary to move the entire mass…. Just pull on the taffy…
4. Let’s not forget Milankovitch or the solar system’s position within galaxy arms ( and exposure to cosmic rays).
5. The position of tectonic plates/continental mass/ability of oceans to circulate heat.
6. Vulcanism – possibly induced by barycenter gravitational effects on earth’s molten core. (My personal opinion is that these will coincide with other effects because they are all caused by the same thing – barycenter movement.
(BTW – YELLOWSTONE IS OVERDUE! HOLY GUACAMOLE!)
7. The consumption/expulsion of C02 by the biosphere ( how the H*@ can anyone calculate the consumption of C02 by the biomass ? We don’t really know what it is!
8. Lastly, the anthropogenic effect. UHI (including how many times Britney Spears, and all the cows of earth passed gas today.
I’m sure I forgot many things, but if you’ll just check with Britney, I think you’ll find that no-one has been keeping track.
Oh, and one more thing: even if the variance is 0.1%, who says that’s not enough to cause drastic changes in Mother Earth? (Besides Leif, that is…)
sorry…
(this so as to explain the heat content(or lack thereof) in #2)
make it #3,
a jones (17:19:48) : “…I am afraid the answer as to why the trade winds vary in both strength and slightly in position is a bit of a circular one…”
Yes, so it seems to me. Increased evaporation lowers the density of the air mass above equatorial waters, presenting less resistance to trade winds, resulting in increased velocity without much momentum change. Other mass flow factors can increase this effect by lowering pressures in this region. If the wind altitude is sufficiently low, reduced seawater viscosity may also play a part.
Re: savethesharks (20:37:05)
Don’t forget N-S asymmetry – what is “the equator” to weather/climate? And how does that thing vary?….
(Hint: Chandler wobble….)
When President Obama finds out about this finding, I imagine the NSF might get an offer it can’t refuse from Al Gore and Jim Hansen. Following the administrative manual by George Orwell given to them by Al and Jim, the NSF can publish an immediate revision entitled Carbon Cycle Linked to Global Climate. The revised article need only replace the words “solar” and “Sun” with the word “carbon” everywhere in the text, and all will once again be well in Consensusland.
Thank you Anthony, this couldn’t have come at a better time to confirm what I’ve been going on about for the last week.
The Earth’s outgoing longwave radiation varies more or less in antiphase to the solar cycle. Here’s OLR flipped against the solar cycles from 1974
http://s630.photobucket.com/albums/uu21/stroller-2009/?action=view¤t=ssn-olr-1974-2009.gif
So we have been getting up to 4W/m^2 swings in OLR upwards when the sun is quieter, downwards when it’s active.
This figure matches the calculations I did which Leif confirmed as correct a few days ago. Between 1993 and 2003 the fifference between what the oceans absorbed and emitted was around 14×10^22J of energy. This is equivalent to 4W/m^2 and is consistent with the sea level rise due to expansion measured by the satellite altimetry. It contradicts what we’ve been told by recent ocean heat studies, which I believe have had the figures fudged to be consistent with the claimed co2 radiative forcing.
The ocean strongly emits heat when the sun is quiet, that is why el nino often happens within a year of solar minimum. In the past few cycles, el nino following solar minimum has been helped along by strong new cycles adding heat to the land. However this time, the sun is still quiet. I think we will see the rise in SST’s continue for a while yet, because OLR is staying high, but all things oscillate, and once the ocean has warmed the atmosphere, the newly warmed air will suppress the oceans emission of heat and start to damp down the el nino a few months later.
The net result will be a loss of ocean heat content, and in the aftermath of the currently forming el nino, I predict temperatures will drop to below the levels of jan 2008 because of the loss of heat from the ocean.
The next question is how a 1.6W variation in TSI can cause 4W/m^2 swings in Earth’s energy budget. About a quarter of the 1366W/m^2 incident on Earth’s exosphere makes it into the climate system (Leif will correct me to the correct figure I hope), so that 1.7W variation in TSI is only around 0.4W/m^2 at the surface. This is because the sun only shines on one side of the earth at a time, and the angle of incidence polewards means less insolation there.
Nir Shaviv found in his paper on using the oceans as a calorimeter that over the solar cycle, the 0.1% variation in solar output was amplified 10 times by terrestrial feedback. He thinks the best candidates are the clouds. This study seems to be heading the same way. And it matches my findings too.
Interesting times indeed.
“a jones (17:19:48) : “…I am afraid the answer as to why the trade winds vary in both strength and slightly in position is a bit of a circular one…”
Yes, so it seems to me. Increased evaporation lowers the density of the air mass above equatorial waters, presenting less resistance to trade winds, resulting in increased velocity without much momentum change. Other mass flow factors can increase this effect by lowering pressures in this region. If the wind altitude is sufficiently low, reduced seawater viscosity may also play a part.”
The real energy transport is the evaporation off tropical seas by trade-winds as they feed TCZ Cu Nims. An index of the amount of equatorial cu-nim activity would give some idea of how much heat was being lifted into the Hadley Cells.
Maybe it would make the Nino, Nina cycle clearer?
Come on Willis, your Cu Nim heat governor effect feels very plausible and I’m sure has data to support it.
If it does hold then I’m sure control theory makes the system un-modellable?
I did an analysis once of the ENSO annual reading for the period 1876 – 2003, breaking it into 4 equal groups of 32 years.
It was striking that post 1972, the incidence of weak la Nina dropped markedly compared to the other three periods. Happy to email my Excel spreadsheet to a moderator if they are interested……..
Now that was using crude ENSO data, not the four regional coefficients used nowadays.
Has anyone else picked that kind of thing up and does anyone postulate any reasons for it??
I was just musing on the PDO.
PDO + to – , – to + 33 years.
Sunspot cycle 22 years. That seems to be an odd ratio. Although that sort of ratio (3 to 2) is seen in gravitational resonances.
I have no idea what it means or if it is even significant.
There is an interesting chart in the global temperature section of the climate4you web site (which I would recommend to anyone wanting a seemingly unbiased overview of the climate system).
I tried unsuccessfully to copy it to this post so you will have to look for yourself. It is in the subsection “outgoing radiation over the equator”
http://www.climate4you.com/
It is interesting because it shows the clear anticorrelation between outgoing longwave radiation and temperature, in the tropics. On the face of it this is what AGW predicts i.e. radiation into space reduces (they say due to greenhouse gases) and the temperature goes up. However the details of the chart tend to give a lie to this and support the more dynamic cloud models suggested in this post. Climate4you give their own view but I would make a few points.
The variation in outgoing radiation is +/- 20%. This is huge. Far greater than greenhouse gases can explain. The variation is also very dynamic (peaks every 5 years or so) whereas CO2 has been relatively stable albeit increasing gradually.
The trend in outgoing radiation since 1979 has been slightly upwards whereas increased greenhouse gases should have led to a slight decrease.
The anticorrelation was broken by the 1998 el nino suggesting that this was a cause rather than an effect and uncharacteristic of the normal pattern. The trend graphs continue to reflect the normal anticorrelation despite this shor term blip.
My assessment it that either there is a mechanism for blocking radiation which is far more powerful and more variable than greenhouse gases (clouds?)or there is big variation in the energy convected to the upper troposphere which bipasses the greenhouse blanket (Hadley cells?).
Either way we are looking for dynamic effects that could easily be triggered by variations in incoming radiation/ cloud seeding/ aerosols etc. I have no idea which of these theories proves to be the more important but given the clear fingerprint of the Milankovitch cycles my money would be our relationhip with the sun being the prime driver.
I know that we have probably had this discussion before, but I must have have skipped class that day.
I am still having a problem getting my arms around the idea that that the sun’s output variability is (as expressed in TSI) only one tenth of a percent. If we have solar maximum, or on the extreme end, stuff like an 1859 Carrington event, vs a grand minimum, isn’t the difference in energy introduced to the planet much higher than 0.1%?
Since different wavelengths have a differing effect on the atmosphere, ie higher frequencies excite atmospheric water molecules and ‘microwave’ and heat the water, shouldn’t we also be looking at spectral irradiance or maybe even intensity instead of only TSI? I am having a hard time with solar input to our planet as a near constant when there is so much variance in output. Sorry to be a simplecorn, but it doesn’t make sense to me.
O/T- Rhinelander, WI normal high for tomorrow, 79 , forecast high, 55F.
Every time we think we understand the climate system we come away a bit more humbled and a bit more wise.
The truth is our there in the data.
I too think it is probable that there is a climate-solar link, but have not been able to prove it to myself. Part of this is simply lack of time – others who I respect do think that they have found this holy grail of climate science.
James F. Evans (20:29:33) :
“But the fact remains those that claim Man or Science knows all there is to know about the energy transfer process between the Sun and the Earth are arrogant and liable to intellectual blindness.
And you know what they say: “Pride cometh before the fall…””
Excellent! My thoughts exactly. We know little about the sun so why dismiss it entirely? This is the field that needs more research, the heliogenic part of climate processes… it’s not well understood, full of different theories and the best thing is that you can observe the sun anywhere on the surface of Earth!! (except the Arctic/Antarctic in winter O_o).
I have just returned from a trip to Europe, and experienced some pretty nasty weather… in late June/early July summer was clearly not present all the way from Poland through Czech Rep, Austria and Slovenia down to Istria in Croatia. Rain and Frigid conditions persisted to the disgust of locals. Upon arrival to Croatia the clouds thinned and the rain stopped but still, according to tourist guides I spoke to, this is one of the worst summers in quite some time, Summer arrived at least two weeks late and the warm weather typical of the Mediterranean only came around the 11th of July. Anecdotal but interesting nevertheless to experience a dud summer among all this hype over global warming in the EU!
Now back in SA the weather is even colder, winter is in full force!!
(Someone asked earlier about what drives the PDO, AMO etc):
The ocean currents may very well be the drivers of climate but what drives the oceanic current cycles!? Much research will have to be done. The sun is an excellent place to start…
M. Simon (00:40:45) :
I was just musing on the PDO.
PDO + to – , – to + 33 years.
Sunspot cycle 22 years. That seems to be an odd ratio. Although that sort of ratio (3 to 2) is seen in gravitational resonances.
I have no idea what it means or if it is even significant.
Sunspot cycle 11 years
Hale cycle of solar magnetic polarity 22 year
PDO AMO 33 years ish.
Sunspot cycles compared to inverted global outgoing longwave radiation
http://s630.photobucket.com/albums/uu21/stroller-2009/?action=view¤t=ssn-olr-1974-2009.gif
cal (01:07:49) :
There is an interesting chart in the global temperature section of the climate4you web site (which I would recommend to anyone wanting a seemingly unbiased overview of the climate system).
I tried unsuccessfully to copy it to this post so you will have to look for yourself. It is in the subsection “outgoing radiation over the equator”
http://www.climate4you.com/
It is interesting because it shows the clear anticorrelation between outgoing longwave radiation and temperature, in the tropics.
The variation in outgoing radiation is +/- 20%. This is huge.
How do I get to that subsection?
Global OLR inverted compared to Solar cycles
http://s630.photobucket.com/albums/uu21/stroller-2009/?action=view¤t=ssn-olr-1974-2009.gif
nino 3.4 OLR
http://i25.tinypic.com/2035ed.png
It the water vapour innit?
A 2007 paper by Camp and Tung found a very strong temperature correlation with the 11 year cycle. Quote:
“[1] By projecting surface temperature data (1959–2004)
onto the spatial structure obtained objectively from the
composite mean difference between solar max and solar min
years, we obtain a global warming signal of almost 0.2K
attributable to the 11-year solar cycle. The statistical
significance of such a globally coherent solar response at
the surface is established for the first time. Citation: Camp,
C. D., and K. K. Tung (2007), Surface warming by the solar cycle
as revealed by the composite mean difference projection,
Geophys. Res. Lett., 34, L14703, doi:10.1029/2007GL030207.”
Unfortunately an excellent paper was marred by the last few paragraphs in which the authors, obviously realising the implications, re-affirm their touching belief in AGW. New Scientist, when reporting this paper, predictably made the bizarre claim that in some way this paper actually *proves* AGW.
The variation they found was nearly one third of the total modern global warming, which is surprisingly large.
Chris
@ cal (01:07:49) :
Variaton in quantity/severity/position of tropical storms???
I have a problem with any hypothesis that relies on events in the air driving changes in climate. That applies to many sceptical hypotheses as well as AGW.
Any such hypothesis fails to fit the whole range of observations so we are left with ‘chicken and egg’ problems.
As I see it the only solution and the one upon which my various writings have relied is the simple observation that over decades the rate of energy emission from the oceans changes due to events within the ocean and not events within the air and that in itself is enough to generate changes in the speed of the hydrological cycle which leads seamlessly to everything else we see.
For anyone who doubts that proposition just ask yourself:
How likely is it that a constantly moving liquid driven by variable solar energy input and containing many independent internal movements driven by density variations and the Earth’s rotation will maintain a constant rate of energy emission to the air ?
It only takes small variations in energy supply from a liquid such as water to have profound effects on the air above it especially when one considers the power of the evaporative process in throwing energy around.
That proposition is the distinguishing feature of my climate description as against all others.
Robert A Cook PE (19:57:53)
“So, today’s homework assignment is: What drives the two short term temperature cycles?”
Simple.
The sun is driving the multiple century scale cycles i.e. Roman Warm Period, Dark Ages, Mediaeval Warm Period, Little Ice Age, Modern Maximum.
The oceans are driving the multidecadal cycles i.e. early 20th Century warming, mid century slight cooling, late century warming and now possible cooling.
BUT ALSO bear in mind that sun and oceans can operate in and out of phase with each other AND ADDITIONLLY cycles in each ocean can operate in or out of phase with each other.
No need for any CO2 effect at all.
However to fit with the observed sequence of events on the multidecadal time frame one has to put the changes in oceanic energy emission as the first event to occur. The air then responds as it must.
Any theory that puts changes in the air as the first step in a multidecadal change of trend in global temperatures does not fit observations.
We have all seen ernough evidence that it is the multidecadal phase shifts in the oceans that impose changes in global air temperature changes.
Stephen Wilde (06:28:35) :
How likely is it that a constantly moving liquid driven by variable solar energy input and containing many independent internal movements driven by density variations and the Earth’s rotation will maintain a constant rate of energy emission to the air ?
It only takes small variations in energy supply from a liquid such as water to have profound effects on the air above it
Stephen, while I agree with most of your analysis, I think an important aspect is the way the air temperature, with a lag, feeds back to the ocean and suppresses oceanic thermal emission. The extent to which this happens will depend primarily on humidity and water vapour column levels, particularly in climate sensitive zones. Ozone, methane and, yes, to a small extent co2 levels will play supporting roles too.
Then there are winds and dust to consider, and their role in varying effective insolation.
Together, the ocean, the air and the variation in solar input amplified by changing cloud cover (GCR levels!?), and decreased by aerosols set the value at which the earth will emit Outgoing longwave radiation, which is the key value determining whether our plant will warm or cool on the decadal and multidecadal scale.
Ray B (01:45:01) :
If we have solar maximum, or on the extreme end, stuff like an 1859 Carrington event, vs a grand minimum, isn’t the difference in energy introduced to the planet much higher than 0.1%?
The ‘stuff at the extreme end’ adds up to very little compared to TSI. Even the very largest flares observed in modern times emit so little energy that they almost drown in the flood from TSI. See e.g. here: http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Chree_Analysis_for_Flares
The ‘extra’ energy was 1/4000 of the total TSI for about a quarter of an hour. And only a couple such events have ever been seen above the background. So, in the grand scheme of this, solar activity makes such a small difference to the solar output that it is not hard to understand why it is difficult to demonstrate that solar activity has any significant influence.
I’ve always liked the Hawkins statement about science:
“(Scientific) progress does not consist of replacing a wrong theory with one that is right, but in replacing a wrong theory with one that is more subtly wrong”
That imputes the proper amount of caution we should all expect in scientific analysis and is the careful way real science works. Leif Svalgaard is, I think, the living embodiment of that attitude in all of these comment threads as is Anthony in the construction and management of this site.
As far as I know, from Scafetta paper/conference to EPA, TSI followed solar cycle until somebody made corrections to some satellite data:
http://yosemite.epa.gov/ee/epa/wkshp.nsf/vwpsw/84E74F1E59E2D3FE852574F100669688/$file/scafetta-epa-2009.pdf
Slide 15 heading:
PMOD correction of Nimbus7 during the ACRIM GAP
PMOD shifts down Nimbus7 record by 0.86 W/m^2 during the ACRIM-gap
I saw the conference video and there were angry reactions…
I meant TSI/temperatures relation
tallbloke
you get to the subsection by first selecting the “global temperature” section (list on the left hand side) this provides a list of subsections with the relevant one right at the bottom of the list.
tallbloke,
Thanks for that. And yes I meant the Hale cycle re: 22 years. i.e. a “complete” solar cycle.
tallbloke (07:05:14)
I don’t have any problem with the assertion that once the ocean has set a trend then there will be variable multiple feedback responses from the air circulation systems and all variety of weather phenomena.
However those feedbacks never dominate the oceanic control of the trend although they may suppress or enhance it for a time.
Observations show that when the ocean phase changes occur the global air temperature trend changes, the air circulation systems move latitudinally and the distribution of regional climates changes.
The clouds and their inevitable feedback are an integral part of the response in the air to changes in the rate of energy released to the air by the oceans.
The clouds cannot significantly change the trend imposed by the ocean SST changes otherwise the timing of the cause and effect would not be as clear in the charts which I have seen you produce.
The air is a passenger,clouds and all, but movements in the air change the speed of the hydrological cycle which is what ultimately stabilises the system and allows the Earth to hold on to it’s oceans.
It’s now totally clear to me after a long period of reluctance to imagine that I see something that others appear not to see and I can only await verification or otherwise by real world events. In the meantime I’ll keep pushing the idea as long as it fits observations and the phenomena described in blog postings
here and elsewhere.
Stephen Wilde (09:12:07) :
Observations show that when the ocean phase changes occur the global air temperature trend changes, the air circulation systems move latitudinally and the distribution of regional climates changes.
So is there any overview of how far the air circulation systems move in relation to what sort of magnitude changes in SST?
Seems like the basis for a nice little model to me. 😉
Nogw (07:55:34) :
As far as I know, from Scafetta paper/conference to EPA, TSI followed solar cycle until somebody made corrections to some satellite data:
http://yosemite.epa.gov/ee/epa/wkshp.nsf/vwpsw/84E74F1E59E2D3FE852574F100669688/$file/scafetta-epa-2009.pdf
Heh, light the blue touchpaper, and stand well back…
tallbloke,
You’ve made some interesting comments. The next step is to explain the reversed phase relationship in the 1800s. Stephen Wilde is promoting focus on the hydro cycle. I agree – and I will suggest something a little more specific as a starting point: asymmetry in the hydro cycle. When I look at temperature ranges I see statistical relationships that do not show up when I work with means.
And SolarFlux is back to 66.
the unfixed or however you call it, just in case Leif starts chimping out…
Leif Svalgaard (18:58:58) :
And what happens to the cosmic ray link? The article does not refer to that [at least not in the blurb]. Now, the true enthusiasts will, of course, point out that the ‘cloud-free’ parts of the ocean at maximum are there because there are fewer cosmic rays to create clouds.
27-day variation in cloud amount and relationship to the solar cycle
Y. Takahashi1, Y. Okazaki1, M. Sato2, H. Miyahara3, K. Sakanoi4, and P. K. Hong5
Abstract. Linkages between solar activity and the earth’s climate have been suggested in previous studies. The 11-year cycle in solar activity evident in sunspot numbers is the most examined example of periodicity, and it is clearly recognized in variations in the thermal structure and dynamical motion of the stratospheric atmosphere. Also the variations in the stratosphere related to the period of apparent solar rotation have also been suggested; however, for such a short period, no quantitative evidence indicating a relationship to the tropospheric phenomena. We clearly demonstrate a 27-day variation in the cloud amount in the region of the Western Pacific warm pool, which is only seen in the solar maximum years of the 11-year cycle. The average spectrum in solar maximum years also shows an enhancement in the range of MJO period. Long-term variations in the tropospheric phenomena, including the 11-year cycle, are generally investigated based on monthly or even yearly averaged data, but the present results may suggest an alternative possibility: short-period variations could modulate longer periodic phenomena.
Interference ?
http://www.atmos-chem-phys-discuss.net/9/15327/2009/acpd-9-15327-2009.html
Stephen Wilde (09:12:07) : I see what you mean about the oceans dominating current weather. But if hotter ocean water causes more clouds, can’t the clouds in turn limit the amount of energy absorbed by the oceans. Maybe this cooler water goes under the surface only to come up again decades later … it just seems the Sun and especially clouds would still be in play. The way I see it, the Sun is the hammer, the Earth the anvil, and the atmosphere a mosquito. Except for clouds, which can modulate input energy from the Sun. Also, I believe it is not known if the Sun has other perhaps chaotic variations in output. The solar guys certainly couldn’t predict the length of this solar minimum and they had to revise their forecast for the peak of cycle 24 didn’t they … they don’t really understand it, do they?
tallbloke (23:52:42) : Do you have a mechanism that would inhibit or block OLW when the Sun is peaking vs when it’s quiet?
http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Chree_Analysis_for_Flares
Conclusions
“Even a simple-seeming and intuitively correct analysis technique can have tricky consequences. The Chree analysis does work in this case (see Ref. 3), but not as well as one would like. For a given SNR for the detection of a single X10-class flare, the extension to the M1 level (a factor of 100 in magnitude) would correspond to an increase in SNR of 3.6 (using the slope from Figure 1). While this is certainly not to be sneezed at – it might be just the factor needed to learn something really important about flare energetics – the weak dependence suggests that it is a difficult analysis.”
Even the author acknowledges more ambiguity than Dr. Svalgaard.
Re: maksimovich (17:47:45)
Too bad they didn’t plot the power spectrum (figs. 3 & 4) as a function of time. The way they did it (i.e. just discrete max vs. min) makes me suspicious that there might be something they would prefer us not to see… Another possibility is that they are fond of antiquated methods…
Jim (20:03:36) :
tallbloke (23:52:42) : Do you have a mechanism that would inhibit or block OLW when the Sun is peaking vs when it’s quiet?
Not certain Jim, but as the ocean emits strongly when the sun is quiet, as evidenced by the correlation between el nino’s after solar minimum and heightened OLR, maybe the el nino’s which occur at solar max don’t lose as much heat to space because the atmosphere is generally warmer and wetter. More water vapour, less OLR.
Also, since the ocean must somehow manage to store heat into areas deeper than the mixed near surface waters to account for the thermal expansion component of sea level rise, I wonder if the there is an alternating net up ward flow of warm water near solar min, as heat escapes, and a corresponding downward flow near solar max when the heat storage is occuring. If so, the circulation must bring cooler water to the surface to be warmed as it would be displaced.
Warm water going downwards is very counter-intuitive, yet it must be happening. I wonder if salinity is a factor. The surface waters will become more saline and denser as the evaporated water heads skywards.
This is all a priori rambling though, I wish an oceanography expert would come on here to tell us more.
Paul Vaughan (21:46:22) :
Re: maksimovich (17:47:45)
Too bad they didn’t plot the power spectrum (figs. 3 & 4) as a function of time. The way they did it (i.e. just discrete max vs. min) makes me suspicious that there might be something they would prefer us not to see… Another possibility is that they are fond of antiquated methods…
Here’s an interesting plot from near solar min of global troposphere temps at 4km that was posted on the Pielke prediction thread.
http://davidsmith1.files.wordpress.com/2009/07/0718091.jpg
Sure looks like solar rotation period spikes to me. At solar min not max. Dunno if there’s another explanation like it being raw data not corrected for some satellite related issue, I’ve asked for clarification.
Paul Vaughan (12:49:37) :
I will suggest something a little more specific as a starting point: asymmetry in the hydro cycle. When I look at temperature ranges I see statistical relationships that do not show up when I work with means.
No OLR data from back then. 🙂
Look forward to seeing your graphs though. The cycle length one was interesting. What does it tell us that a normal plot like Schatten’s doesn’t?
tallbloke,
I’m very curious to hear what you might propose to explain the reversed phase relationships of the 1800s.
This is absolutely key.
James F. Evans (21:11:22) :
“it might be just the factor needed to learn something really important about flare energetics – the weak dependence suggests that it is a difficult analysis.”
Even the author acknowledges more ambiguity than Dr. Svalgaard.”
Of course, he does not. All he is saying is that the signal is so weak compared to the background noise, that even the powerful Chree analysis has a hard time pulling the signal out. There is no ambiguity at all. It is a question of signal-to-noise ratio, and the signal is just so weak that it will be hard to show that there is one for weaker flares. This is not a problem with the analysis, but with the flares. They simply make such a little contribution to the total energy that they are hardly observable. I know the author [Hudson] well, we are colleagues at Berkeley [see e.g. the next nugget], and I know exactly what he meant.
\
tallbloke (22:26:41) “What does it tell us that a normal plot like Schatten’s doesn’t?”
Can you provide a link?
Anyone who studies Landscheidt, Charvatova, NAO, &/or drought severity might appreciate this one:
Fye, Falko K.; Stahle, David W.; Cook, Edward R.; Cleaveland, Malcolm K. (2006). NAO influence on sub-decadal moisture variability over central North America. Geophysical Research Letters 33(15), L15707.
http://adsabs.harvard.edu/abs/2006GeoRL..3315707F
*Please take the time to watch this youtube video showing time lapse images of solar cycle 24’s spots and the bias present in viewing these spots.*
The topic of whether these specks would have been seen 400 years ago is being discussed on solarcycle24.com and if this video shows the resolution and disc size that was analysed for spots back then it would clearly indicate a major issue that must be resolved.
Paul Vaughan (22:44:22) :
tallbloke (22:26:41) “What does it tell us that a normal plot like Schatten’s doesn’t?”
Can you provide a link?
http://www-ssc.igpp.ucla.edu/IASTP/43/image6.gif
Paul Vaughan (22:33:48) :
tallbloke,
I’m very curious to hear what you might propose to explain the reversed phase relationships of the 1800s.
This is absolutely key.
Well it’s obvious, the Oojmaflip is in anticorrelation to the wotsit.
Seriously, show me a graph or two, and I’ll throw a SWAG at you.
If you posted ’em, I missed it.
:o)
tallbloke (22:08:46) : Here is a good article on ocean currents. Some are driven by wind, some by tides, and some by changes in temperature and salinity. As water from the surface evaporates, the water becomes saltier, which in turn increases the density. It is obvious the ocean is a major player in climate, second only to the Sun which supplies the driving energy. I am still intrigued by the possibility that the Sun could be more variable than we think which would explain the paleo record. The Sun’s output could go up a bit, warming the planet and releasing CO2 from the oceans. This would explain where the warming came from and why the temp goes up first and CO2 800 years later.
http://en.wikipedia.org/wiki/Thermohaline_circulation
Anthony, I don’t know that the paper showed all that the write-up is claiming. There are too many “may pave the way tos…” and “results point to…” and “tends to…” I found the abstract along with some figures of the Pacific Ocean at Dr. G. Meehl’s site — summary of achievements: http://www.cgd.ucar.edu/research/profiles/2009/meehl.profile.html (sorry, I still can’t do links).
Didn’t want to spend the $22. The specifics are: “[We] show that dynamical coupled processes initiated by the response in the tropical Pacific to peaks in solar forcing produce wind-forced ocean Rossby waves near 5N and 5S. These reflect off the western boundary, producing downwelling equatorial Kelvin waves that contribute to transitioning the tropical Pacific to a warm event…that lags the peaks in solar forcing by a couple of years.”
You had a post some time ago that referred to Rossby waves, maybe by Bob Tisdale, or maybe my research led me to look up Rossby waves. Anyway, I think this is already “known”, but Meehl and Arblaster (2009) are linking these waves to a lag from solar maximum. Very interesting. I’d sure like to see some “proof”. Can you get the article for WUWT or does one of your readers have further information?
Wow, I actually did a link!
Paul Vaughan (18:19:39) :
Sunspot Cycle Length 1800-1960
via Wavelet Analysis:
http://www.sfu.ca/~plv/SunspotCyclePeriod.PNG
——————————————————
Paul,
So what is that showing us? Just that recent cycles have been shorter? Or that there is perhaps a centennial scale variation in cycle length?
Basil
tallbloke (22:26:41) “What does it tell us that a normal plot like Schatten’s doesn’t?”
Paul Vaughan (22:44:22) “Can you provide a link?”
tallbloke (05:28:15)
http://www-ssc.igpp.ucla.edu/IASTP/43/image6.gif
The wavelet approach gives monthly estimates of solar cycle length from monthly data …and without fussing around with “where was the max? where was the min?”
– –
Paul Vaughan (18:19:39)
Sunspot Cycle Length 1800-1960
via Wavelet Analysis:
http://www.sfu.ca/~plv/SunspotCyclePeriod.PNG
Basil (07:21:11) “Paul, So what is that showing us? Just that recent cycles have been shorter? Or that there is perhaps a centennial scale variation in cycle length?”
For now, I’ll leave it open for people to interpret themselves. One thing that struck me immediately was the timing of 11.1 year power when the period was decreasing rapidly. (This suggests other analyses which I may pursue when I have time.)
I may have more comments as time passes. In the meantime I’ve presented this result to raise awareness of what can be done with wavelets in Excel.
Also, I’ll be completely honest: I’m sick of seeing power spectra that are not plotted as a function of time. People are way too willing to assume stationarity – even when the assumption is patently untenable. [This is adding a thick layer of unhelpful distortion & confusion to discussions (that otherwise might be fruitful) about phase relations.]
– –
tallbloke (05:35:02) “[…] show me a graph or two, and I’ll throw a SWAG at you. If you posted ‘em, I missed it.”
Remember this?
http://www.woodfortrees.org/plot/hadsst2gl/from:1850/to:2009/isolate:78/mean:39/plot/sidc-ssn/from:1850/to:2010/scale:0.0005
[Note that I’ve adjusted “isolate” from 156 months to 78 to emphasize that this is still a work in progress.]
It’s not as simple as “temps follow solar cycle”. It looks like there is interaction with another (or more than one) cycle(s) that throw[s] *apparent* reversals into the phase relationship.
It looks like something that can be worked out. This doesn’t look like the “hopelessly impossible” problem some paint it to be. I’ll be working on the phasing over the weeks/months/years ahead.
This is a multi-disciplinary problem. Your comments on mechanics are appreciated – thank you for stimulating discussion.
Re: pyromancer76 (06:47:02)
Careful here …
“The important role of the 11 year cycle of solar forcing is emerging in model simulations that have been analyzed, along with observations, to confirm earlier hypotheses (Meehl et al. 2003) and model results in that the effect of enhanced solar forcing is to strengthen the climatological precipitation regimes in the tropics. This produces a La Nina-like response in the tropical Pacific with teleconnections to the North Pacific that reduce precipitation with greater solar forcing in the Pacific northwest and northern California.”
http://www.cgd.ucar.edu/research/profiles/2009/meehl.profile.html
This appears to avoid the phase reversal centred ~1931. [The PNW precipitation phase relationship with solar variables flips over.] Perhaps this point needs to be hammered repeatedly until people acknowledge what may be inconvenient.
Explaining the flip should be objective #1 for people working on the mechanics.
I’m concerned that people are going to go to great lengths to get the mechanics wrong. We all know how fond people are of their computer models after they’ve poured years of their lives into them.
Let’s do the research community (in general) a favor – without delay – by pointing out things apparently swept under-the-rug (due to inconvenience). Even an acknowledgement like, “Yeah, we know about that – we’re going to go back & work on it later,” might help other researchers avert a potentially (very) wasteful path.
Part of the reason for all of the secrecy is the scarcity of funding.
pyromancer76 (06:47:43) :
Wow, I actually did a link!
If you don’t try to do any tags but just paste the link, the wordpress software will do the rest for you.
Paul Vaughan (12:53:46) :
Paul, one thought about cycle length as that the length of the minima matter too, for timing and strength of el nino. That in turn is going to have an effect on the sampling of SST’s, and the curves we get. There’s a relationship between solar cycle amplitudes, outgoing longwave radiation, global temperature, and Stephen’s poleward expanding air circulations. I’m half way to understanding it. It may help with the phase reversal thing, at some timescales at least.
http://climatechange1.files.wordpress.com/2009/05/fig-4-olr-and-sst-0-10c2b0s2.jpg
Paul Vaughan (12:53:46) :
The wavelet approach gives monthly estimates of solar cycle length from monthly data …and without fussing around with “where was the max? where was the min?”
As solar cycles overlap by several years, the notion of THE minimum is physically dubious, no matter how the length is computed. You cannot invent physics with statistics.
tallbloke (14:35:47)
http://climatechange1.files.wordpress.com/2009/05/fig-4-olr-and-sst-0-10c2b0s2.jpg
–
Whoever produced that graph appears to have a handle on what the task is.
Where can I find the:
1) accompanying write-up?
2) OLR series? [& related references?]
I will again caution about ranges vs. means and local vs. global (since you list “global temperature”). I suspect it is going to take years before the research community’s momentum shifts far enough away from tradition & convention to embrace fruitful analyses that are not laden with spatiotemporal assumptions that dilute signals.
Anyone with mechanical insights is welcomed to comment on these observations, which relate to Agassiz, British Columbia, Canada (~49N, near sea-level, & near the west coast of North America – i.e. on the coastal side of the mountain range):
1) When Earth wobbles harder (6.4a timescale), extreme monthly maximum temperatures tend to be lowest (11a & 13a timescales).
2) When Earth wobbles harder (annual timescale), extreme monthly maximum temperatures tend to be lowest (4a timescale).
3) When Earth spins faster (annual timescale), minimum, extreme minimum, & mean monthly temperatures tend to be warmer (11a & 13a).
The most notable deviations from these (preliminary) generalizations occur in relatively recent years.
I am interested in broadening the investigation (spatially), but for now I just have results for the site I was paid to study for a year (which I at least know [first-hand] correlates strongly regionally (with some continental-coastal qualification)).
I hope to produce some presentable graphics when my schedule allows. There are so many ways to summarize this complex information visually — it is going to be a (minor) project just to figure out how to be most concise.
Leif Svalgaard (14:53:15) “As solar cycles overlap by several years, the notion of THE minimum is physically dubious, no matter how the length is computed.”
Agree.
Paul Vaughan (16:06:57) :
“THE minimum is physically dubious, no matter how the length is computed.”
Agree.
So, the quantity you are plotting has a dubious physical meaning, apt to confound any conclusions one might draw from relationships involving the cycle ‘length’ [the latter also being dubious].
Leif Svalgaard (14:53:15) “You cannot invent physics with statistics.”
One of the most brilliant statisticians I know once told me he prefers to avoid working on physics problems with physicists. I asked him, “Because of the ‘mechanism’ thing?” A grin slowly appeared on his face as he began nodding his head [yes]. It was a moment of shared humor. What to do when different disciplines, each with their own merit, see the world differently?…
I have noticed that a lot of statisticians like working with the medical/pharmaceutical community (since they get heralded as heros). Personally, that research has never interested me, even though the coin is better.
I investigate relationships, not causes. I qualify my statements about relationships; I do not claim causation. It is incumbent upon others (with the appropriate expertise) to sufficiently explain mechanisms; if/when that ever happens, climate research will no longer be needed.
This is a multi-disciplinary problem and it is crystal clear that many professing expert knowledge of the relevant physics need some lessons in statistics – and vice versa — but a human lifetime is not long enough to develop deep expertise across multiple fields, so one option appearing to have some practical merit (for society & individuals) is cooperation. If we all try to become experts in every field, the job might never get finished (for example, math is an endless world).
Cheers,
Paul.
Re: Leif Svalgaard (16:32:08)
You appear to misunderstand the method.
Paul Vaughan (19:27:53) :
Re: Leif Svalgaard (16:32:08)
You appear to misunderstand the method.
As usual, when there is misunderstanding, the onus is one the one who has something to communicate to clear it up.
The method is irrelevant if that which is supposed to be found with the method does not have much physical significance. And wavelet methods is part of any good physicists ‘cookbook’, e.g. http://www.leif.org/research/Asymmetric%20Rosenberg-Coleman%20Effect.pdf
Any statistical relationship or method is irrelevant if there is no underlying [real or a priori expected] physical relationship. ‘Hunting’ for relationships is not a valid enterprise: One looks at a hundred different things and expects by chance to find a handful, significant at the 95% level. So when you indeed find one, don’t declare it significant or undeniable.
Re: Leif Svalgaard (21:35:00)
Perhaps you misread “without” (as “with”). Otherwise: Do you seriously expect people to believe the series is stationary?
Leif Svalgaard (21:35:00) “‘Hunting’ for relationships is not a valid enterprise: One looks at a hundred different things and expects by chance to find a handful, significant at the 95% level. So when you indeed find one, don’t declare it significant or undeniable.”
This is pure distortion.
Paul Vaughan (15:01:15) :
tallbloke (14:35:47)
http://climatechange1.files.wordpress.com/2009/05/fig-4-olr-and-sst-0-10c2b0s2.jpg
–
Whoever produced that graph appears to have a handle on what the task is.
Where can I find the:
1) accompanying write-up?
2) OLR series? [& related references?]
It’s our old friend Erl Happ. Write up here; http://climatechange1.wordpress.com/2009/05/12/climate-change-a-la-naturale/
OLR for the tropics can be downloaded from;
http://www.cpc.noaa.gov/data/indices/olr
Paul Vaughan (01:26:51) :
Re: Leif Svalgaard (21:35:00)
Perhaps you misread “without” (as “with”). Otherwise: Do you seriously expect people to believe the series is stationary?
No, but the underlying phenomenon you are trying to depict is physically somewhat meaningless: the real length of a solar cycle is 13-18 years.
Paul Vaughan (01:30:33) :
Leif Svalgaard (21:35:00) “‘Hunting’ for relationships is not a valid enterprise: One looks at a hundred different things and expects by chance to find a handful, significant at the 95% level. So when you indeed find one, don’t declare it significant or undeniable.”
This is pure distortion.
But a fact, nevertheless. You say that you do not claim ‘causation’, but without such a claim, the exercise is meaningless.
Leif Svalgaard (05:03:54) “You say that you do not claim ‘causation’, but without such a claim, the exercise is meaningless.”
This statement is political.
Suggestion:
Spend a minute reproducing the transform I posted rather than wasting my time.
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Leif Svalgaard (21:35:00) “One looks at a hundred different things […]”
This is where you went wrong – so your claim of “fact” is strawman-distortion.
When someone knows exactly what they are looking for and where to find it, there is just one efficient strike (no dice rolling).
–
Conceptual Understanding of Wavelet Analysis
Based on your comments, I question your conceptual understanding of the factors that can affect wavelet power. I encourage you to think very carefully about how the choice of wave & envelope affect local correlation in the time-timescale spectrum.
–
Terminology & Cross-Disciplinary Communication
As for your comment “the real length of a solar cycle is 13-18 years”, what is the temporal spacing between these? [no need to answer – rhetorical question – readers around here know the answer]
Perhaps you can deliver a brief lesson on comparative terminology in support of efficient cross-disciplinary communication. What do solar physicists want people to call the 11.1 year (on average) thing? (A precise technical term – on which there is broad consensus – would be most useful, if such a thing exists.)
I think you may find that this is a little like my beef with “running mean” vs. “moving average” – i.e. good luck shaking established conventions, whether ‘right’ or ‘wrong’. Other good examples of (misleading) terms we are stuck with (& tolerate): “imaginary numbers” & “standard error“.
I am (& others probably are) interested in knowing what the ‘preferred’ terminology is amongst solar scientists — and perhaps you can try to get a movement started to steer the general public’s use of terminology towards what you think it should be. [My choice is to not waste my energy leading a futile revolt against “imaginary”, “running”, & “error”.] Wouldn’t the simplest solution (considering reality & momentum) be to make use of 2 different adjectives in front of “solar cycle period” or “solar cycle length”? I await comment…
Paul Vaughan (14:01:59) :
When someone knows exactly what they are looking for and where to find it, there is just one efficient strike (no dice rolling).
If you claim no causation, then how does one know exactly what to look for and where to find it?
As for your comment “the real length of a solar cycle is 13-18 years”, what is the temporal spacing between these? [no need to answer – rhetorical question – readers around here know the answer]
There is no ‘temporal spacing’ that makes sense. The closest you can get to something that makes is to talk about the number of solar cycles per millennium, and from that compute a number. But it would be misleading to say anything about what the ‘length’ of a single cycle is.
What do solar physicists want people to call the 11.1 year (on average) thing?
We call it the ‘solar cycle’ [a misleading, but accepted term]. Everybody knows that it is not a real cycle and everybody knows that the cycle begins well before the ‘statistical’ minimum and extends well beyond the next minimum. Everybody knows that the minima are fiducial and not physical. Alternatively, one could count the cycle from polar field reversal to polar field reversal [roughly from ‘maximum’ to ‘maximum’]. This would be slightly better. There are some problems with that: 1) polar fields reverse at different times in each hemisphere, 2) may reverse multiple times within a short time [so how to define ‘the’ reversal], 3) assumes that polar fields always reverses in every cycle [so model dependent].
The best is not to attach any definite physical meaning to the minimum and to acknowledge that cycles overlap and that the average real ‘length’ of a ‘cycle’ is considerably longer than M, where M is the number you get by dividing a long time interval, T [say a thousand years – enough that end effects are small enough], by the number of cycles in T. Since we all know this, no [or little confusion] arises from this sloppy usage. Like we talk about electron ‘orbital’ well knowing the electrons are not like little planets ‘orbiting’ the nucleus; no confusion arises from this.
More on the ‘extended cycle’:
http://www.nature.com/nature/journal/v333/n6175/abs/333748a0.html
There is some debate if the extended cycle should be counted from the first to the last sunspot, or [the longer] time from first ‘sign’ of the new cycle [e.g. in the corona] to the last. The bottom line is that the precise time [even as determined by wavelet analysis or any other method] between successive minima [however defined] has little physical meaning. and that therefore, any relationship or conclusion that attaches meaning to that number is on shaky and dubious ground.
I don’t see any reason to ‘educate’ the public beyond the above and to try to establish a terminology. Since it is a sloppy thing to begin with, nothing is gained by trying to be semantically over-precise; on the contrary, it may confer a sharpness to the phenomenon that is not there to begin with.
Cameron and Schuessler http://arxiv.org/PS_cache/arxiv/pdf/0806/0806.2833v1.pdf discuss some of the pitfalls that follow by ignoring the overlap between cycles.
Paul Vaughan (14:01:59) :
“You say that you do not claim ‘causation’, but without such a claim, the exercise is meaningless.”
This statement is political.
You may have a political agenda, I don’t,
Suggestion: Spend a minute reproducing the transform I posted rather than wasting my time.
I assume that your computer can add and subtract and think that you have already wasted your time computing the time variation of a near meaningless number.
To simplify the analysis by Schuessler and Cameron and making it more accessible, let’s construct a simple example: A low cycle followed by a high cycle. The ‘official’ minimum [and I bet your wavelet minimum too] would be skewed towards the low cycle, making it shorter than it should be and the high cycle longer. A similar thing happens at the other end. So the length of the ‘cycle would be ‘convolved’ with the height of the surrounding cycles and would be a strangely weighted function of three cycles. This holds no matter how you define the minimum.
The way most solar physicists deal with this is to downplay [or simply disregard] papers or theories that take their starting point in the ‘length of a solar cycle’.
P.S. may I ask why your plot of ‘cycle lengths’omits that first and last ~50 years of the sunspot record? Avoidance of end-effects doesn’t seem to dictate such an excessive ‘overhang’.
Leif Svalgaard (17:14:20) :
To simplify the analysis by Schuessler and Cameron and making it more accessible, let’s construct a simple example: A low cycle followed by a high cycle. The ‘official’ minimum [and I bet your wavelet minimum too] would be skewed towards the low cycle, making it shorter than it should be and the high cycle longer.
If the cycles are asymmetrical, this effect can actually be reversed [what C&S really is after]. The important issue is that skewing occurs, depending on the sizes and asymmetries of adjacent cycles.
Leif Svalgaard (16:44:01) “I don’t see any reason to ‘educate’ the public beyond the above and to try to establish a terminology. Since it is a sloppy thing to begin with, nothing is gained by trying to be semantically over-precise; on the contrary, it may confer a sharpness to the phenomenon that is not there to begin with.”
We agree ^here.
–
Leif Svalgaard (16:44:01) “The bottom line is that the precise time [even as determined by wavelet analysis or any other method] between successive minima [however defined] has little physical meaning. and that therefore, any relationship or conclusion that attaches meaning to that number is on shaky and dubious ground.”
Key phrase: “[…] between successive minima [however defined] […]”
Now it is 100% clear that you misread (or misunderstood) my use of “without“. A wavelet transform treats all time series points as equals.
If you reread my initial comment in response to tallbloke, you will see that I was actually taking a swipe at methods that try to define a minimum (or maximum) and then try to base ‘cycle lengths’ (not ‘extended’ ones) on that. (I’ve gone through that exercise myself – it is messy & subjective – and it produces unsatisfying results.)
–
Leif Svalgaard (16:44:01) “If you claim no causation, then how does one know exactly what to look for and where to find it?”
It’s just Acoustics 101. As indicated a number of times, we need to work on rhythm. There is sufficient focus on amplitudes, but insufficient focus on phase relations (& their impact on linear correlation). Someone working on mechanisms will not know what the task is if there is no (undistorted) empirical picture available. Paradox will not seem illogical once we master the complexity. This will be achieved via deepening awareness of conditioning.
As an anecdote:
When I first learned wavelet analysis, I used to throw it at every possible combo (generating matrices). I quickly learned that while that might generate a lot of pretty pictures, it is (largely) a waste of time (& hard-drive space) (aside from the entertainment value).
Now I only bother to produce wavelet images when I know intuitively (from conceptual understanding) that they will provide a concise summary of something I already see. I work out all of the acoustics in my head while walking on the mountain – like I said: just Acoustics 101.
Don’t underestimate the flexibility & utility of wavelet methods Leif.
–
When you have some time, try this:
1) Generate a sine wave – call it A.
2) Do a Complex Morlet transform of A at a variety of wavenumbers.
3) Take the derivative of A – call the result B.
4) Repeat step 2 – but for B.
5) Compare the phase & power across A, B, & wavenumber.
6) Look at the cross-spectra for A & B (for varying wavenumber).
7) Repeat the preceding for sine-squared, higher-powered, & other-shaped waves (including absolute values).
8) Repeat with other wavelets.
9) Repeat with time-normalization of power.
10) Explore graphical portrayal of resonance by studying phase differences for harmonics.
–
Thanks for the solar physics insider-notes – appreciated as always.
Leif Svalgaard (17:14:20) “[…] [and I bet your wavelet minimum too] […] no matter how you define the minimum.”
You need to review my other comments to overcome your misunderstanding/misreading. Again: There is no definition of a minimum in the wavelet analysis.
–
Leif Svalgaard (17:14:20) “[…] may I ask why your plot of ‘cycle lengths’omits that first and last ~50 years of the sunspot record? Avoidance of end-effects doesn’t seem to dictate such an excessive ‘overhang’.”
As explained previously (in a recent thread), Morlet 2pi is a bandwidth hog. This is the cost of frequency resolution – it is a tradeoff – basic Wavelet 101.
Elaboration:
I do not pad with zeros (or assume cyclicity or do anything else) to create “fantasy extensions” off the edges. In this case you can see that I also snipped off the edge-contamination related to the time-normalization – which is over a narrowing timescale-band towards the ends (a more serious problem at the 1800 end due to the high power at 13a) (not a problem at the 1960 end until the cone-of-influence intersects the ~10.5a power-band). I have no use for the “edge fantasies” that pollute publications – & btw editors should consider cracking down on this misleading [but seemingly conventionally accepted] [mal]practice.
A useful webpage – addressing time- vs. timescale- resolution tradeoffs:
http://www.clecom.co.uk/science/autosignal/help/Continuous_Wavelet_Transfor.htm
This becomes interesting when one starts investigating resonance using wavelet methods. For example, if there is loose resonance, a Complex Mexican Hat cross-wavelet transform will show higher frequency phase-difference variations than the corresponding cross-wavelet transform for Complex Morlet 2pi. Such comparisons provide a means of assessing robustness of findings. NO POLITICS HERE – JUST CAREFUL INVESTIGATION.
Paul Vaughan (18:14:33) :
Don’t underestimate the flexibility & utility of wavelet methods
I don’t. Use them myself, but [as it seems you do too], only as tools to confirm and quantify what I already see or know. As I said, you can’t invent physics with statistics.
When I first learned wavelet analysis, I used to throw it at every possible combo (generating matrices)
This is what I meant when I said that if one tries a hundred things, one should be surprised if a handful show significance at the 95% level.
But back to the science, since the cycle length is ill-defined [and depends on the shape of neighboring cycles], what is the purpose of doing the analysis in the first place?
Paul Vaughan (19:07:13) :
You need to review my other comments to overcome your misunderstanding/misreading. Again: There is no definition of a minimum in the wavelet analysis.
No, it is up to you to [as I always do in great detail] to elucidate [repeat ad nauseam, if necessary] the process. There may not be an explicit definition, but an implicit one, because the power depends on the values. Try this experiment: make 15 cycles [identical in amplitude and period – e.g. triangular]; then make the middle cycle twice as high, plot the resulting wavelet power.
–
“may I ask why your plot of ‘cycle lengths’omits that first and last ~50 years of the sunspot record?”
I do not pad with zeros (or assume cyclicity or do anything else) to create “fantasy extensions” off the edges.
So, you could not do the analysis if you only had 100 years of data?
Paul Vaughan (19:07:13) :
There is no definition of a minimum in the wavelet analysis.
Since it goes after the amplitude of the sunspot number, the analysis may be meaningful as an indication of the ‘recurrence’ period of solar activity, that is, the time from one maximum to the next. Since this is not what [some] people ordinarily call the solar cycle length, there is amble room for confusion here [since extended cycles overlap]. Better would be some notion of repeat time of activity ‘pulses’ [subject to some stochastic variations], instead of the fixation on the [misleading] ‘solar cycle length’.
Leif Svalgaard (19:24:27) :
Paul Vaughan (18:14:33) :
“When I first learned wavelet analysis, I used to throw it at every possible combo (generating matrices)”
This is what I meant when I said that if one tries a hundred things, one should be surprised if a handful show significance at the 95% level.
One should NOT be surprised …, of course.
Leif Svalgaard (19:32:45) “So, you could not do the analysis if you only had 100 years of data?”
You could – but you would have to use a different wavelet — for example: Morlet with a lower wavenumber. This would inevitably lead to tradeoffs. When I’ve tried this tactic for some time series, I have ended up tossing out the results (because sometimes they simply do not stand up to scrutiny).
However, I don’t think it is preferable to invent “fantasy extensions” (which is common & misleading [mal]practice).
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Leif Svalgaard (19:24:27) “This is what I meant when I said that if one tries a hundred things, one should be surprised if a handful show significance at the 95% level.”
I knew very well & exactly what you meant. I’ve taught & judged 1000s of statistics students …and my point [as I think you see now, based on your other comments] is that I’m not running “crap-shoot” “shot-in-the-dark” analyses — these comments:
Leif: “[…] [as it seems you do too], only as tools to confirm and quantify what I already see or know.”
Re: Leif Svalgaard (20:10:59)
You appear awfully eager to quote that OUT-OF-CONTEXT.
Re: Leif Svalgaard (19:53:35)
These comments are constructive. What concise labeling of the wavelet transform plot would you deem ‘acceptable’? – & balanced (given the potential for misunderstanding due to widespread perceptions that are beyond our control)?
Re: Leif Svalgaard (20:10:59)
To reiterate:
I only bother to produce wavelet images when I know intuitively (from conceptual understanding) that they will provide a concise summary of something I already see.
Paul Vaughan (20:38:33) :
Re: Leif Svalgaard (20:10:59)
You appear awfully eager to quote that OUT-OF-CONTEXT.
I think the context is very appropriate. We once had a student that discovered the usefulness of a Chree-analysis [superposed epoch analysis]. As you did, she tried it with every data set she could find [about a hundred] and did turn up a few correlations at the 95% level.
Paul Vaughan (20:47:28) :
Re: Leif Svalgaard (19:53:35)
These comments are constructive.
I strive hard to make ALL comments constructive.
What concise labeling of the wavelet transform plot would you deem ‘acceptable’? – & balanced (given the potential for misunderstanding due to widespread perceptions that are beyond our control)?
No labels at all would be acceptable to me, and minimize misunderstanding.
Paul Vaughan (20:36:12) :
that I’m not running “crap-shoot” “shot-in-the-dark” analyses
Then, since you claim no causation and only correlation, what are the criteria for selecting a correlation to try [knowing ‘exactly” what to look for]. I would ordinarily only even look for correlation if I had an idea of causation, then the correlation might or not confirm the mechanism I was toying with, thus causation comes first. To me it makes no sense to look for correlation without a mechanism in mind, then it has degenerated to [as you say] crap shots.
Leif Svalgaard (21:17:19) “[…] you claim […] only correlation […]”
Yet more distortion – note that the plot is univariate.
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Leif Svalgaard (21:09:38) “[…] did turn up a few correlations at the 95% level.”
You can do that with a random series. You are (possibly) missing the point that it is healthy for students to learn from experience. In today’s age of heavily-algorithmic & computationally-intensive analysis, it is important that students (& teachers) learn a “feel” for the performance of (& issues with) the algorithms (& software, hardware, etc.).
You may also be missing another point: Real series are not necessarily random, so you would not expect 5 in 100. (That logic holds only under the assumption of randomness.) Think about what PCA & factor analysis are all about. Those are legitimate tools.
Anyway, I think you and I both understand and that this exchange has degenerated into a show for the public (who you are worried will misunderstand something).
A physicist brought the following complaint to a judge:
“The statistician is investigating physics. This is unacceptable.”
The statistician then counter-charged:
“The physicist is using statistics without first becoming formally recognized as a member of the Statistical Society.”
And so the wise judge passed a rule requiring an army of administrators to ensure that light-bulbs be changed by electricians. Lawyers delighted in their profits.
Meanwhile – in a society with less in-fighting – problems were solved efficiently.
It’s great to see you two doing your level best to understand each other’s angle.
In support of Paul’s approach, I do think it’s a worthwhile exercise to investigate statistical correaltions regardless of a lack of obvious causative link for two reasons.
1)It may evoke a realisation that known forces not previously thought to be effective in certain ways are.
2) It may lead to the discovery of new forces. If physicists can have ‘dark energy’ and string, and climatologists can have ‘teleconnections’, then statisticians can have ‘unknown causitive links’ to chuck over the fence for physicists and climatologists to think about.
In support of Leif’s approach, a belief in the sufficiency of known forces and their effects enables progress in theory development, even if it turns out to be wrong or inadequate later. The realisation that the theory is wrong or inadequate leads us back to the a priori consideration of new frameworks for aspects of physics. Newton -> Einstein, Dalton ->Bohr, etc.
Let the physicists do physics, let the statisticians do stats, and let them both talk to each other in non-judgmental and collaborative ways.
Well done guys.
Paul Vaughan (22:06:51) :
Yet more distortion – note that the plot is univariate.
what has that to do with anything? speak English, please.
You can do that with a random series
A series with random data is not the same as a series chosen at random.
Paul Vaughan (22:06:51) :
Yet more distortion – note that the plot is univariate.
Here is how a physicist sees and solves a multivariate problem:
http://www.leif.org/research/suipr699.pdf
You may want to try your hand on that problem. The data is the am-index and the OMNI dataset.
The solar cycle is also very clearly linked to the number of Republican senators in the US Congress. The mechanism for this is just as well established as the link between the solar cycle and climate. (Completetly unknown, that is.)
Univariate = 1 variable
The plot is univariate.
It is a plot of one variable.
No claim has been made.
No correlation has been presented.
[Correlation with what??? There is only one variable!!!]
tallbloke,
Thanks for the Erl Happ link. I’m making my way through it…
Paul Vaughan (17:17:27) :
[Correlation with what??? There is only one variable!!!]
y = f(x) is a function of one variable. The functional form, e.g. the set of pairs (x,y), is [especially if errors are present] essentially, a correlation of y with x.
Re: Leif Svalgaard (18:49:01)
Thanks for another laugh.
Paul Vaughan (22:43:53) :
Re: Leif Svalgaard (18:49:01)
Thanks for another laugh.
No problem; you provide me with good material for that.
The only substantive issue you have raised is what the title of the graph should be – and you fail to offer a satisfactory alternative.
Paul Vaughan (14:38:03) :
The only substantive issue you have raised is what the title of the graph should be – and you fail to offer a satisfactory alternative.
Is this is your idea of substance? I don’t care what you call it. Having no title is perfectly satisfactory as the substance is not in the title but in the graph.
Leif Svalgaard (15:02:27) “Having no title is perfectly satisfactory as the substance is not in the title but in the graph.”
Many will irritatedly disagree, but I agree with you ^here.
The assumption of stationarity (e.g. in unwindowed-FFT) is untenable.
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The substance of the wavelet transform is SOLID.
http://www.sfu.ca/~plv/SunspotCyclePeriod.PNG
Arguments suggesting otherwise are a foolish waste of time (possibly aimed at pulling wool over the eyes of the innumerate &/or those lacking deeper conceptual understanding of wavelet methods).
My guess is that you are willing to use the weight of your stature in this community to deceitfully distort because you are worried others will misuse the result. If others misuse the result, your issue is with them.
The result on its own is purely descriptive. (No inference has been made.)
Challenging the result is as foolish as challenging a verifiable claim that a red car is red (which is a long way from claiming red paint on the car causes x & y & z).
–
If others misuse the result, I might be inclined to join you in calling them on it – but let’s cross that bridge if & when it arises.
Paul Vaughan (16:06:06) :
If others misuse the result, your issue is with them.
and if you misuse the result?
As I’ve said the (your?) concept of the length of a solar cycle is already dubious, no matter by what method you come up with a number. For another purpose I have followed the practice [because others did and I compare with them] of defining a cycle ‘length’, two ways: max-max and min-min, just using the ‘official’ sunspot numbers. Within the accuracy of the data and the [much more troubling] fuzziness of the concept, my plot of the ‘length’ as a function of time:
http://www.leif.org/research/Cycle%20Lengths%20and%20Temperatures.png if identical to yours [except extends usefully further on both sides], so there is no additional [meaningful] information in the wavelet plot, so I will agree that the result is solid.
Paul Vaughan (16:06:06) :
My guess is that you […] deceitfully distort
Your comment shows that you fit the old Danish proverb: “a thief thinks that everybody steals”.
Leif Svalgaard (18:49:01) :
y = f(x) is a function of one variable. The functional form, e.g. the set of pairs (x,y), is [especially if errors are present] essentially, a correlation of y with x.
Um, no.
Mark
Paul Vaughan (22:33:48) :
I’m very curious to hear what you might propose to explain the reversed phase relationships of the 1800s.
Paul Vaughan (20:51:53) :
I only bother to produce wavelet images when I know intuitively (from conceptual understanding) that they will provide a concise summary of something I already see
Paul I have plotted phase/period/FFTs of the chandler wobble and I see little of which you speak.
1. There are only 20 data points per year from 1890-present and 10 points prior to this date.
2. The phase/period anomalies occur during the minimum amplitude where accuracy disappears
http://img39.imageshack.us/img39/5355/chandlerwobblephaseperi.jpg
3. There is a beat frequency betwen 365.25 days and the chandler period which causes the minima.
http://img24.imageshack.us/img24/4861/chandlerperiodfft.jpg
I am rather surprised that data is recorded on a 18.26 day period. Why?
in your plot
http://www.sfu.ca/~plv/ChandlerPeriodAgassizBC,CanadaPrecipitationTimePlot.PNG
you seem to get a chandler period with a 1 day accuracy – how is this possible from a 18 day measurement period?
The above plot shows 420 day period in 1930 My 10 year averaged chandler period in 1930 is ~340 days
http://img339.imageshack.us/img339/8189/chandlerwobbleaveragepe.jpg
Notice also that this dip is not unusual.
Mark T (16:58:12) :
“y = f(x) is a function of one variable. The functional form, e.g. the set of pairs (x,y), is [especially if errors are present] essentially, a correlation of y with x.”
Um, no.
Well, in my book it is, “Um” or not. Example, geomagnetic activity is to first order a function of solar wind speed. A = k V^n. Correlating A vs. V one finds n = 2. I’m not limiting myself to linear correlation, as one would do in statistics. It is more useful to broaden the concept to any functional relationship. One can then be specific and say linear correlation, if there is chance of confusion. One can also calculate the Spearman’s rank correlation coefficient as long as the function is monotonic, but not necessarily linear. In physics and in general applications it makes sense to broaden the concept. Of course, if a statistician wears blinders he cannot get out of his box.
Re: bill (18:19:12)
Don’t confuse polar motion (in general) with the Chandler wobble. The annual wobble beats with the Chandler wobble to produce the ~6.5a polar motion group waves. (It seems you have figured this out.)
That the Chandler wobble reversed phase in ~1931 is not in dispute – see the literature. For example:
Jan Vondrak (1999). Earth rotation parameters 1899.7-1992.0 after reanalysis within the hipparcos frame. Surveys in Geophysics 20, 169-195.
http://www.yspu.yar.ru/astronomy/lib/Rotation.pdf
[See particularly section 3.2.]
J. Vondrak & C. Ron (2005). The great Chandler wobble change in 1923-1940 re-visited. In: H.-P. Plag, B. Chao, R. Gross, & T. Van Dam (eds.), Forcing of polar motion in the Chandler frequency band: A contribution to understanding interannual climate variations, Cahiers du Centre Europeen de Geodynamique et de Seismologie 24, 39-47.
Even just looking at the raw polar motion series, one can see that the group wave envelopes lengthen in period on either side of ~1931.
As for the sampling frequency: They started out with 10 per year & then doubled it to 20 per year in 1890.
To reiterate past comments:
Unwindowed-FFT is misleading (sometimes extremely so) for nonstationary time series. I recommend wavelet methods. I posted the instructions for the analysis in an earlier thread:
http://wattsupwiththat.com/2009/07/01/another-paper-showing-evidence-of-a-solar-signature-in-temperature-records/
See Paul Vaughan (19:14:38) [July 7, 2009].
Note that the variable I worked with is an index derived from the raw polar motion data.
I think you may want to read Gross (2005) and then review some of your plots.
Gross, R. S. (2005). The observed period and Q of the Chandler wobble. In: H.-P. Plag, B. Chao, R. Gross, & T. Van Dam (eds.), Forcing of polar motion in the Chandler frequency band: A contribution to understanding interannual climate variations, Cahiers du Centre Europeen de Geodynamique et de Seismologie 24, 31-37.
http://www.sbl.statkart.no/literature/plag_etal_2005_editors/gross_1_CWTQ_final.pdf
Leif Svalgaard (16:40:48) “[…] so there is no additional [meaningful] information in the wavelet plot […]”
You appear to have missed the point made above (in response to tallbloke’s original inquiry) that it provides monthly estimates.
As indicated above, I’ve (previously) done the analysis the way you did.
You are eager to label “solar cycle period” as a “dubious” term and yet you cannot provide a suitable alternative that will be understood by a general science audience.
Nonetheless, you agree that the results are solid – so case closed.
Leif Svalgaard (16:46:54) “a thief thinks that everybody steals”
Oh come on – rather than resorting to hurling unmerited insults, admit that you are worried that people might use this to (try to) pull nails out of a coffin you (believe you) have previously nailed shut. (Most folks around here are familiar with that chapter (on 90s research claims), so you are fooling very few.)
Leif Svalgaard (19:13:57) “[…] if a statistician wears blinders he cannot get out of his box.”
To make sure misunderstandings do not arise:
I’m not claiming to be a statistician. However, I do have a very solid grounding in some branches of that discipline – and I spent a number of years teaching stats.
Paul Vaughan (23:02:07) :
Oh come on – rather than resorting to hurling unmerited insults
I think the insult was here:
“you are willing to use the weight of your stature in this community to deceitfully distort…”
Paul Vaughan (22:50:35) :
You appear to have missed the point made above (in response to tallbloke’s original inquiry) that it provides monthly estimates.
If the whole concept is dubious, a monthly estimate is even more meaningless. Perhaps, if we measured the sunspot number every minute [which is feasible – and might one day be done], you could provide a minute-by-minute estimate of the length of the solar cycle…
Paul Vaughan (23:02:07) :
(Most folks around here are familiar with that chapter (on 90s research claims), so you are fooling very few.)
Most folks, perhaps, but you lost me. What chapter? And I would consider ‘fooling’ an insult, so look who is hurling. But perhaps what you hurl are merited insults in your mind.
Paul Vaughan (22:34:02) :
That the Chandler wobble reversed phase in ~1931 is not in dispute – see the literature. For example:
There is no 45 to 135 phase change in 1930s in my plot. I assume that we are talking phase between x and y offsets?. I have removed the annual cycle, I have removed the chandler cycle. The phase stubbonly refuses to change much from an average of about 90 deg in 1930s. This period is of course before the improvement of measurement in 60s when noise is much reduced.
During the nulls of the beat frequencies (1year and 1.2 years) amplitudes become negligible and phase cannot be accurately determined. But when amplitude is again usable the phase is as before the dip (I suppose one could suggest that the phase changed by 360 degress). During the minima phase differences can go to near zero.
The pahse is calulated by measuring peak to trough and trough to peak periods and dividing by the time between zero crossing pos and zero cross pos. This gives 2 measures of phase per cycle. The 10 sample/year era data were increased to 20 by interpolating. The data was obtained from the source you suggested.
I say again there is no oddity in the 1930s in my plots. A phase change of 180deg would be easily seen in the amplitude plots. No need for wavelets.
The FFT was obtained from raw unfiltered data (at 20 samples / year)
Someone somewhere is wrong. I cannot see errors in my data handling. Perhaps you could tell me where I am going wrong!
So you label the results as both dubious & solid – and you expect me to believe you are not trying to deliberately obfuscate?
You are only fooling people who lack a solid conceptual understanding of wavelet analysis.
The only substantive issue you have raised is that solar science might need to consider revising its terminology to more clearly differentiate between the different uses of the term “solar cycle”. In the meantime, don’t slander the current mainstream convention as “dubious”.
…And you know very well what study I’m referring to — I’ve seen you attack it with zeal (…& there’s a sign of it on the image to which you linked).
Paul Vaughan (08:10:06) :
So you label the results as both dubious & solid – and you expect me to believe you are not trying to deliberately obfuscate?
The statistics is solid, the physics is dubious. It is like saying that a climate that swings between only temperatures -50C and +90C is comfortable because the average temperature is 20C.
You are only fooling people who lack a solid conceptual understanding of wavelet analysis.
since what you find is no different from what everybody else finds, the people who lack a solid understanding of wavelets are no worse off.
don’t slander the current mainstream convention as “dubious”.
The convention is what it is, the dubious bit comes when one attaches too much meaning or significance to the concept, like pinning it down to a month or better and ignoring that different hemispheres and different measures [sunspots, areas, radio flux, cosmic rays, magnetic fields, TSI, etc] have minima and maxima occurring at different times.
…And you know very well what study I’m referring to — I’ve seen you attack it with zeal (…& there’s a sign of it on the image to which you linked).
And I don’t now what you are referring to. Do we have yet another [would make it #3] instance of you don’t wanting to tell me [or anyone else]?
Leif Svalgaard (09:34:48) “It is like saying that a climate that swings between only temperatures -50C and +90C is comfortable because the average temperature is 20C.”
This is not analogous. Ridiculous!
–
Leif Svalgaard (09:34:48) “[…] ignoring that different hemispheres and different measures [sunspots, areas, radio flux, cosmic rays, magnetic fields, TSI, etc] […]”
The instantaneous period can be estimated for any of these variables …and if I then ran a factor analysis, I would certainly not expect to find all of the resulting series to be orthogonal.
–
Leif Svalgaard (09:34:48) “I don’t now what you are referring to.”
More nonsense – WUWT readers know what you were trying to demonstrate with the image you attached. That paper is famous “AGW-road-kill”. I’ve seen you gunning at it more than once whenever some (poorly-informed) latecomer cites it in these forums.
Hi bill,
Of course the phase difference between x & y is relatively constant at a quarter-cycle – that is the nature of a wobble. If you review my comments in the earlier threads – and the papers to which I have linked – you will see that this is not the phase being discussed.
Question:
How are you estimating the period in this plot?
http://img339.imageshack.us/img339/8189/chandlerwobbleaveragepe.jpg
As for this plot …
http://img24.imageshack.us/img24/4861/chandlerperiodfft.jpg
… the higher frequency is nonstationary, so unwindowed-FFT is not good enough. You need to use a method that facilitates time-localization as well as frequency-localization.
–
bill (18:19:12) “you seem to get a chandler period with a 1 day accuracy – how is this possible from a 18 day measurement period?”
This will be evident once you follow the steps I have outlined.
As you will see, the first step is to estimate the polar motion group-wave period. Then the following assumption is made: The annual cycle has a period of 1 year. This facilitates application of the Helmholtz acoustic equation to arrive at a series of time-localized estimates of the Chandler period (which has a period of 432 to 433 days on average – see the literature). As you can see from your FFT power spectrum, the assumption of stationarity is not bad for the annual cycle — this, of course, is not surprising (….but note the spread for the Chandler frequency – a very strong hint to look deeper).
“higher frequency”
pardon me – should read: “higher period“
Paul Vaughan (11:16:45) :
This is not analogous. Ridiculous!
Gave me a laugh, this time. Thanks.
The instantaneous period can be estimated for any of these variables …and if I then ran a factor analysis, I would certainly not expect to find all of the resulting series to be orthogonal.
But which one would be THE solar cycle period? The point is that there is no ‘THE’ period. All cycles overlap and overlap differently and are, of course, correlated to a large degree, but with non-stationary lags, etc. So picking one and saying that that one is the one of interest must be justified on physical grounds. Statistics can’t help you here.
That paper is famous “AGW-road-kill”. I’ve seen you gunning at it more than once whenever some (poorly-informed) latecomer cites it in these forums.
Refresh my memory – I don’t recall/remember that famous paper.
Pretend you are that poorly-informed person and cite it. Even a search with Google doesn’t bring up any obvious hits.
Also bill, why the 10 year averaging?
– –
tallbloke,
Erl’s got the right idea with his equator-pole contrasts. Speculation: The Chandler wobble phase reversal (& associated phase reversals) is (are) related to pole-equator flows (meridional vs. zonal) and the NH phasing should be opposite to SH phasing (on average for some bands of latitude …and as you wisely mention “at some timescales” – indeed the higher timescales show a different phase relation).
Paul Vaughan (11:58:16) :
The Chandler wobble phase reversal (& associated phase reversals) is (are) related to pole-equator flows
It is well-established that the Chandler wobble is mostly caused by ocean-bottom pressure changes and a smaller part by fluctuations in atmospheric pressure. The effect of atmospheric winds and ocean currents on the wobble are very minor.
Leif Svalgaard (11:51:31) “Gave me a laugh, this time. Thanks.”
It’s not analogous. We are talking about periods – not ranges & averages.
–
Leif Svalgaard (11:51:31) “[…] So picking one and saying that that one is the one of interest […]”
No one is “picking one”. If this is what you have concluded, you have erred. “One” has been presented, but others have been (& will be further) explored – and analyses will be varied (…and as you acknowledge: “[…] correlated to a large degree […]” anyway …but analyses will be varied anyway – just a core ingredient in robust data analysis).
I don’t think you are thinking through the utility of the estimates. They are needed for studies of phase relations – (and the estimates I’ve seen are always in wide time-steps – usually only one per cycle). It isn’t enough to look at 2 variables at a time and ignore phase relations — that is the “linear” flaw in conventional thinking that is plaguing the research and dead-stalling progress. Once capable people work out the phase relations, then the folks with amplitude-talent might be empowered to quickly clean house. The complexity stems from the interaction of multiple nonstationary cycles. (My money is not on ‘mysterious’ forces.) I’m working on the conditioning – this is just basic Stat 400 (which very, very, very few researchers have since it is pushed aside to make room for more popular (& more theoretical) advanced stats courses).
Re: Leif Svalgaard (12:18:07)
You should consider reviewing (more of the detail of) the work of Richard Gross & other EOP experts.
Also, there you go again conflating the terms “related” & “caused”. When someone says “related to” it DOES NOT equate with “caused by”.
Such conflation is either:
a) deliberate obfuscation (strawman)
– or –
b) error (failure to read carefully & interpret words literally).
Again we see that you fail to appreciate the value of confounding. Confounding is not only a hazard; sometimes it is a blessing (like if there is an important (perhaps not-so-obvious) lurking variable that is not being measured). You might scream “unphysical”, but the “physical” might be in the lurking variable(s). All a data analyst needs to find the signal is a “related” variable (and there’s a huge & important branch of statistics known as multivariate stats, as you surely know).
Paul Vaughan (13:01:36) :
You should consider reviewing (more of the detail of) the work of Richard Gross
It is Gross that established that the Chandler wobble is mostly caused by ocean-bottom pressure changes and a smaller part by fluctuations in atmospheric pressure. And that the effect of atmospheric winds and ocean currents on the wobble are very minor.
We are talking about periods – not ranges & averages.
The conceptual error you commit is the same.
I don’t think you are thinking through the utility of the estimates.
They may seem useful to you pursuing numerology, but have little meaning and usefulness considering the nature of the physical phenomena.
They are needed for studies of phase relations […] is plaguing the research and dead-stalling progress.
Progress is not dead-stalled. It is being made on a broad front and at a good clip. Adding numerology and overly ‘precise’ estimates that ignore the physical reality are perhaps satisfying for some, but has rarely [if ever] lead to real progress, and I don’t expect it in this case either.
complexity stems from the interaction of multiple nonstationary cycles
The cycles do not interact [that is Cyclomania], the physical bodies and forces that wax and wane interact and couple.
When someone says “related to” it DOES NOT equate with “caused by”.
Then WHAT does it mean? If they both have a common cause, for example, it is still wrong to say that they are ‘related’ to each other.
a) deliberate obfuscation (strawman) ‘thief thinks everyone steals’
b) error (failure to communicate what you mean)
Again we see that you fail to appreciate the value of confounding.
A lurking variable is an extraneous variable that correlates with both the dependent variable and the independent variable and gives rise to a type 1 error: an erroneous ‘false positive’ conclusion that the dependent variables are in a causal relationship with the independent variable. I fail to see that the value of such erroneous conclusions can be anything but non-existent.
Leif Svalgaard (14:03:40) “If they both have a common cause, for example, it is still wrong to say that they are ‘related’ to each other.”
FALSE.
You also use an exceptionally narrow definition of “lurking” variable.
I will reiterate that I suggest you review the EOP literature for more detail.
–
Leif Svalgaard (14:03:40) “The conceptual error you commit is the same.”
My impression is that you do not understand the analysis-related factors that can cause (spurious) cycles in wavelet power. More generally, your inattentiveness to the convergence of phase & amplitude in linear correlation appears to be a serious blindspot – (this is what I mean when I say “narrowly linear”). Resorting to charges of “numerology” & “cyclomania” is as ridiculous as claiming the day & year are “irrelevant”. There’s no need to be blinded by the most dominant cycles and you can’t integrate-out inter-cycle signals if you don’t know periods. Pretending everything after first-order/stationary is “just noise” is a prescription for meeting a dead-end.
Paul Vaughan (15:25:41) :
“If they both have a common cause, for example, it is still wrong to say that they are ‘related’ to each other.”
FALSE.
Give an example that makes sense to me.
You also use an exceptionally narrow definition of “lurking” variable.
I don’t think so. Pearl [2000] has shown that that confounding variables cannot be defined in terms of statistical notions alone, but that some initial causal assumptions are necessary. So we are back to physics.
I will reiterate that I suggest you review the EOP literature for more detail.
May I suggest you do the same. What counts for me is that Gross have identified the main causes and influences that determine the Wobble. I’ll go with his assessment.
prescription for meeting a dead-end
What I’m questioning is that we at a a dead-end, and that your contribution is needed.
your inattentiveness to the convergence of phase & amplitude in linear correlation appears to be a serious blindspot
Nobody I know [and respect] is confounded by these problems, so I think you are overstating your case that everybody [including me] have serious blind spots in that regard.
Paul Vaughan (15:25:41) :
That paper is famous “AGW-road-kill”. I’ve seen you gunning at it more than once whenever some (poorly-informed) latecomer cites it in these forums.
Refresh my memory – I don’t recall/remember that famous paper.
Pretend you are that poorly-informed person and cite it. Or are we having yet another example [count stands at 3 now] of you not wanting to tell anybody…
Leif Svalgaard (16:11:24) “I think you are overstating your case that everybody [including me] have serious blind spots in that regard.”
Have you carefully considered why the time-normalization brings out such smooth bands? Think about wavelet shape-variation. Don’t be fooled into thinking wavelet power is objectively physical. Wavelet shape introduces spurious power-cycles. There are ways to minimize (& work around) this problem.
–
Leif Svalgaard (16:11:24) “I don’t think so.”
Now you appear to be conflating confounding with lurking. Also, understand that definitions of terms even so basic as “standard error” vary (…particularly if one gets philosophical …but no need to waste our time).
–
Don’t you think the most sensible thing to do is admit that climate is a multi-disciplinary challenge? You have a good understanding of the role a physicist can play, but you seem to fail to understand (or perhaps choose to deny) the role of others.
At present, the bottleneck in research progress appears to be a lack of awareness of conditioning factors.
Gross’ findings are impressive, but my point is that they do not constitute an end. The question just switches to “So what causes that?” and “What is related to that?” Also, it is important to understand that Gross can’t apply his methods to investigate the Chandler wobble phase reversal (because OAM & AAM records do not go back far enough).
One way I might explain the wavelet power thing to students would be with an analogy: Say 2 carpenters are working together and one complains to the other that he just can’t get any power to turn a screw. The other shows him that the heads on the screws are different shapes. (And now imagine that the heads are changing shape cyclically…)
Regarding your request. Unrelated-peoples’ daily activity cycles are related even though one is not causing the other.
Paul Vaughan (17:52:56) :
Regarding your request. Unrelated-peoples’ daily activity cycles are related even though one is not causing the other.
They are not ‘related’ in any sensible way. They may be ‘similar’ because they are driven by the same underlying factor: time of day. Not related.
Don’t you think the most sensible thing to do is admit that climate is a multi-disciplinary challenge?
Sure, there are many disciplines involved: atmospheric physics, measurement theory, solar [perhaps], etc. Statistics [like English] in this respect is not a discipline, but simply a tool, and all too often a blunt tool standing in the way of physical insight.
Chandler wobble phase reversal
Other people seem to have difficulty finding the ‘phase reversal’…
Now you appear to be conflating confounding with lurking
I can only go by mainstream established definitions. e.g. Wikipedia’s: “In statistics, a confounding variable (also confounding factor, lurking variable, a confound, or confounder) is an extraneous variable …”
Don’t be fooled into thinking wavelet power is objectively physical
Now, who in his right mind would do this? All analysis has to be taken with caution and the only real guide is one’s subjective physical insight and intuition, honed by dealing with physics for decades.
That paper is famous “AGW-road-kill”. I’ve seen you gunning at it more than once whenever some (poorly-informed) latecomer cites it in these forums.
Refresh my memory – I don’t recall/remember that famous paper.
Pretend you are that poorly-informed person and cite it. Or are we having yet another example [count stands at 3 now] of you not wanting to tell anybody…
Leif Svalgaard (18:50:08) “Other people seem to have difficulty finding the ‘phase reversal’…”
This is pure distortion. This exchange is terminated. Do not address me in future.
Sincerely,
Paul Vaughan.
Paul Vaughan (20:49:13) :
This exchange is terminated. Do not address me in future.
That is one convenient way of avoiding to answer:
That paper is famous “AGW-road-kill”. I’ve seen you gunning at it more than once whenever some (poorly-informed) latecomer cites it in these forums.
Refresh my memory – I don’t recall/remember that famous paper.
Pretend you are that poorly-informed person and cite it. Or are we having yet another example [count stands at 3 now] of you not wanting to tell anybody…
Paul Vaughan (20:49:13) :
Leif Svalgaard (18:50:08) “Other people seem to have difficulty finding the ‘phase reversal’…”
This is pure distortion.
Show me the phase reversal in these plots then!
Chandler period filtered out:
http://img339.imageshack.us/img339/1050/chandlerwobbleyear.jpg
Year period filtered out:
http://img119.imageshack.us/img119/4125/chandlerwobblechandler.jpg
PS I am not impressed with you ability to communicate with other human beings in a civilised fashion.
Paul Vaughan (20:49:13) :
This exchange is terminated. Do not address me in future.
On another thread you suggested that all CO2 readings were false. I tested the theory with one station looking at weekly data and comparing to hourly. Basically I found an approx. 1 week delay in the houly data. There was nothing to show that the CO2 data was truly invalid as you suggested.
I have now checked out you (and your references) assertion that the wobble has a 180 phase shift in the 30’s. It is not present. I have checked another of your plots comparing wobble and rainfall. I cannot obtain the graph of wobble that you did.
Wavelet transforms are taking analysis away from the measured figures made on a 18.25 day schedule (this must mean the data is interpolated already) and adding in a mathematical interpolation between further analysis and reality. Chandler wobble may be a good candidate for this (it is unlikely (but not impossible) that the wobble sinusoid will vary wildly from a pure sinusoid. But this is only an assumption.
Here is what the real data looks like.
http://img265.imageshack.us/img265/1466/chandlerunfiltered.jpg
Difficult to see with all the “noise” – which of course may be signal – but still no phase change!
bill (02:50:10) “On another thread you suggested that all CO2 readings were false.”
This is not true. You have misunderstood (or worse).
I alerted people to the fact that rigid annual structure has been artificially imposed on some monthly CO2 time series and suggested that people use the NOAA time series.
Anyone with the necessary background will easily turn up the same results.
I pointed out the note at the bottom of the CDIAC “data” webpages alerting people of the adjustments. It appears you have not bothered to verify this.
The CDIAC “data” are actually statistics. There is a difference between data & statistics — statistics are summaries of data – i.e. based on calculations made from data.
bill (02:50:10) “[…] references) assertion that the wobble has a 180 phase shift in the 30’s. It is not present.”
You are claiming Jan Vondrak (Vice President International Astronomical Union), a leading authority on the Chandler wobble (& EOP more generally), is wrong about something really simple. It’s child’s play to show the phase reversal (if you know how).
I can spend a bit more time on this if you really want to make a solid effort to understand (something you never did when I patiently sacrificed my time addressing your questions about the CO2 ‘data’).
How are you estimating the period in this plot?
http://img339.imageshack.us/img339/8189/chandlerwobbleaveragepe.jpg
What you have done here?
http://img265.imageshack.us/img265/1466/chandlerunfiltered.jpg
bill (21:23:55) “PS I am not impressed with you ability to communicate with other human beings in a civilised fashion.”
Bold-faced obfuscation meets rejection. It’s simple – and it’s practical.
Reply: Ok everybody tone it down and I have to add the obligatory I don’t care who started it. ~ charles the moderator.
Paul Vaughan (12:56:58) :
bill (21:23:55) “PS I am not impressed with you ability to communicate with other human beings in a civilised fashion.”
Toned down: “by a show of hands, who out there disagrees with ‘bill’?
CO2
“The monthly values have been adjusted to the 15th of each month.” i.e. interpolated between actual measurement days. Not sure why it is done but it should not invalidate data. (hourly data compared to monthly data bears this out.
http://img13.imageshack.us/img13/2339/co2barrowhourvsmonthobs.jpg
The NOAA series is slightly different but not significantly so.
The wobble data is also not actual readings – taking readings 10/20 times per year at exact intervals may now be possible but is very unlikely to have been done in 1800s. Is this data therefore invalid?
Paul Vaughan (12:51:52) :
You are claiming Jan Vondrak … a leading authority on the Chandler wobble (& EOP more generally), is wrong about something really simple. It’s child’s play to show the phase reversal (if you know how).
Name and status do not matter to me. The data I obtained from your reference is shown in the many plots I have shown:
Yearly frequency removed:
http://img119.imageshack.us/img119/4125/chandlerwobblechandler.jpg
Chandler periods removed:
http://img339.imageshack.us/img339/1050/chandlerwobbleyear.jpg
There is no phase reversal shown. So obviously :
1. the data is wrong
2. or I am not displaying the phase Vondrak is measuring
3. or Excel is faulty
4. or The bandpass filter I am using is faulty (a possibility)
5. or Vondrak is wrong
6 or ????
The plot of chandler period (with no annual freq) does show the phase dropping to 15 deg at one of the low amplitude points but this quickly recovers to 90deg when amplitude is restored
(the low amplitude is caused by the two chandler periods shown in the FFT beating together giving a 82 year period (1.17 and 1.19 very APPROX)
How are you estimating the period in this plot?
http://img339.imageshack.us/img339/8189/chandlerwobbleaveragepe.jpg
This was done on zero crossings of y displacement then averaged over a 10 year period to try to get to your period vs rain plot:
http://www.sfu.ca/~plv/ChandlerPeriodAgassizBC,CanadaPrecipitationTimePlot.PNG
I have since changed the plotting to use positive peak to positive peak of y for time (this should be more defined than zero crossing)
and phase measured from
+ve peak y to +ve peak of x
-ve peak y to -ve peak of x
What you have done here?
http://img265.imageshack.us/img265/1466/chandlerunfiltered.jpg
This is the wobble with no filering of high frequency (short period) noise. bandpass filer bandwith is 0.05 to 250 years. It shows 1924 to 1929 noisy signal but the phase of x vs y is the same on entry to this period as on exit from it. The phase during the 1924 -1929 period may be grossly different but at 1923 and 1937 the phase is similar (or at 360 deg).
I can spend a bit more time on this if you really want to make a solid effort to understand (something you never did when I patiently sacrificed my time addressing your questions about the CO2 ‘data’).
You refused to state point blank the problem with the co2 data. I compared monthly and hourly co2 data to try to see what thew problem was:
http://img13.imageshack.us/img13/2339/co2barrowhourvsmonthobs.jpg
This showed no problem.
If you were to state what phase I am supposed to see with respect to what I will look.
There is no point continuing with the cryptic suggestions as my time is as important as yours. and I have no software for wavelet analysis.
Hello bill,
In order to diagnose the source of the misunderstandings, this may have to go back & forth a bit.
I have no doubt that these 2 matters can be sorted out to your satisfaction if you make a solid, patient effort to follow what I have written & what I write.
Let’s slow things down to whatever pace is necessary.
–
CO2
Please provide links to the exact webpages (plural) from which you are getting your data in this plot:
http://img13.imageshack.us/img13/2339/co2barrowhourvsmonthobs.jpg
Thank you.
This should help me localize the source of the misunderstanding. (My impression is that you are investigating something different from what I was commenting about.)
–
Polar Motion
bill (19:47:20) “Name and status do not matter to me.”
Name & status don’t guarantee scientific wins — I (& most here at WUWT I suspect) will whole-heartedly agree.
The more important part was:
“[…] is wrong about something really simple. It’s child’s play to show the phase reversal (if you know how).”
This is no exaggeration.
You need only 2 very simple things to demonstrate the phase reversal:
1) a stationary wave with a period of ~6.4 years.
2) a moving-estimate of the polar motion group-wave (envelope) period as a function of time.
I’ll assume you can handle #1.
There are many ways to obtain #2 (some of them dead-simple).
Suggestion:
Think of x & y as a 2-dimensional vector (instead of as 2 separate time series).
The task is not to compare the phase of x with the phase of y. Please acknowledge that you have understood this before we proceed. Thank you.
Also, before spending time doing a bunch of calculations (that may be heading down a path unrelated to the one we are trying to discuss here), please tell me one or 2 (or 3) ways you might like to go about pursuing item#2. (This will help me assess whether you are focused on the correct task. Thank you bill.)
Regards,
Paul.
bill (19:47:20) “You refused to state point blank the problem with the co2 data. “
I must object to this statement because it is false.
–
bill (19:47:20)
“I have no software for wavelet analysis.”
Do you have Excel?
That’s what I use.
I only resort to using SPlus (& SPSS, depending on the task) when I need higher-quality graphics.
Example of SPlus color-contour plot:
http://www.sfu.ca/~plv/ccLR1CRF.PNG
[featured: time-integrated cross-correlation of Log2(SunspotNumber+1) with cosmic ray flux]
Examples of Excel color-contour plots:
http://www.sfu.ca/~plv/1930sHarmonicPhaseDifference.PNG
http://www.sfu.ca/~plv/SunspotCyclePeriod.PNG
There are some substantial software-design problems with Excel-color-contour-plot-menus, but I’ve found solutions (&/or viable work-arounds) for all of them — feel welcome to enquire if you encounter obstacles.
Cheers,
Paul.
bill,
Here is some information about wavelet analysis and its use for tidal analysis and Chandler Wobble influence:
http://www.geo.uni-jena.de/geophysik/environ/pres_wg06/HU.ppt
bill,
A very useful reference work by Gross and Vondrak:
http://www.leif.org/EOS/1999GL900422.pdf
Of course, no hint of a phase shift.
bill,
And the famous Gross paper form 2000 explaining the excitation of the wobble: http://www.leif.org/EOS/2000GL011450.pdf
The last sentence in a publication is often telling:
“The wide distribution of these atmospheric and oceanic angular momentum estimates by the IERS Special Bureaus for the Atmosphere and Oceans enables the type of interdisciplinary research whose results are reported here.”
Keep in mind the Nasa PR machine (especially when results that leave new questions are publicized as final answers to age-old mysteries).
Keep in mind that SBA & SBO would like to survive & flourish.
Suggested:
Read papers by other authors that give a different treatment (bearing in mind the concept of shared-variance).
And this is telling:
In reviewing Gross’ work (including his 2007 overview in Treatise on Geophysics), pay scrutinizing attention to his treatment of r^2.
bill, I think you will find this a very distracting tangent [if you pursue it now] (but a very interesting one when you have time).
For now, I suggest wrapping up our misunderstanding expeditiously. It has nothing to do with Gross’ 2000 findings (which are limited by the short length of the employed series) and you can manage a basic conceptual understanding without learning wavelet methods – (that can come later, on your own time).
You need only 2 very simple things to demonstrate the phase reversal:
1) a stationary wave with a period of ~6.4 years.
2) a moving-estimate of the polar motion group-wave (envelope) period as a function of time.
Paul Vaughan.
Please provide links to the exact webpages (plural) from which you are getting your data in this plot:
ftp://ftp.cmdl.noaa.gov/ccg/co2/in-situ/brw/
http://cdiac.ornl.gov/ftp/trends/co2/barrsio.co2
OK 6.4 years ish is the beat frequency between the chandler wobble and the annual 365.2421897 day
However,there seem to be 2 chandler frequencies 1.15 and 1.19 years as shown in these two plots.
during the 30s the 1.15 slowly displaces the 1.19. I would therefore expect a phase change between the 6.4 fixed period (because that is what you have done) and the mixed chandler frequencies of 1.15+1.19.
however in physical terms all that happens is a slowing down of chandler period during the 30s. I was expecting a phase shift between x and y (i.e. reversal of direction).
Can you confirm that this is your “phase shift”
1.19ish period chandler wobble
http://img411.imageshack.us/img411/576/chandlerwobble119.jpg
1.15ish period chandler wobble
http://img151.imageshack.us/img151/5341/chandlerwobble115.jpg
Leif Thanks for those references!
It is interesting to note that the simple FFT so despised by Paul Vaughan, shows two distinct chandler frequencies. Using a bandpass filter pulls each frequency out of the mix 1 year, 1.15 years and 1.19 years. This seems to be an amazing band pass algorithm for excel. I will have to check it out on some other manufactured data and check for phase accuracy etc.
The same web site has a useful smoothing algorithm (hodrick prescott) which seems to produce a level of filering similar to a moving average with little phase/amplitude distortion compared to the moving average.
http://www.web-reg.de/
bill (10:48:59) “It is interesting to note that the simple FFT so despised by Paul Vaughan, shows two distinct chandler frequencies.
This suggests misunderstandings bill.
To probe them, I will ask 3 questions:
1) Do you think the 2 frequencies you mention are both continuously operating across the record?
2) How do you interpret the bulge around them (in your power spectrum plot)?
3) Have you ever used windowed-FFT?
– –
bill (07:37:27)
“however in physical terms all that happens is a slowing down of chandler period during the 30s.”
That’s part of it.
In order to see a phase reversal, one has to first decide, “relative to what?” If you look relative-to-a-stationary-wave, you will see (even without doing any calculations) that the polar motion group-wave (the envelope) is in ~anti-phase with a stationary wave with a period of ~6.4a before ~1931 and in-phase after (if you phase-align the latter part of the record).
This is equivalent to what Vondrak (& others) showed.
Figure 10 – top of top panel:
http://www.yspu.yar.ru/astronomy/lib/Rotation.pdf
It’s not complicated. I suppose if it is confusing (&/or has confused) people it might have something to do with the nature of the time series (2-dimensional vector with a beat-envelope – i.e. not the type of series (all) folks around these forums are normally used to handling – e.g. temperature time series, sunspot curves, etc.)
It is interesting to note that the (absolute) power falls during the ~20 year phase reversal interval. (This suggests other wavelet transforms – for example timescale-normalized. (The one I presented was time-normalized.)) …So at the time of the Chandler slow down / polar motion envelope phase-shift, the annual wobble played a (relatively) stronger role.
If you now go back through my earlier comments (in earlier threads) you will probably easily see why I took differences & used them to calculate a vector magnitude (makes things simpler). If you go through that exercise & plot the results on a grid with 6.4a (horizontal) spacing, the phase reversal is plain-as-day. [As I said upthread: I only (generally) bother with a wavelet transform if I can already envision that it will provide a concise summary of something I already see. However, unfortunately: Many of the academics I deal with dismiss the wavelet transforms on the grounds that they do not know enough about wavelet transforms to assess them. This certainly creates an “interesting” challenge.]
“slow down”
correction: “speed up”
(We are talking about frequencies & timescales in this exchange – & not always being careful.)
My emphasis added in bold:
“Values above are taken from a curve consisting of 4 harmonics plus a stiff spline and a linear gain factor, fit to monthly concentration values adjusted to represent 2400 hours on the 15th day of each month. Data used to derive this curve are shown in the accompanying graph. Units are parts per million by volume (ppmv) expressed in the 2003A SIO manometric mole fraction scale. The annual average” is the arithmetic mean of the twelve monthly values.”
http://cdiac.ornl.gov/ftp/trends/co2/barrsio.co2
This is the page you need to compare monthly values:
ftp://ftp.cmdl.noaa.gov/ccg/co2/in-situ/brw/brw_01C0_mm.co2
Difference both series and study the annual structure comparatively (across years & series). I look forward to hearing what you find.
Also, you are looking at Barrow, Alaska, USA. Recall that I was looking at Alert, Nunavut, Canada when I found the problem.
As previously indicated: There isn’t a problem if you are only interested in the undifferenced trend at super-annual timescales. (I want to make sure there are no misunderstandings.)
I will run the analysis for Barrow now (to make sure there are not further misunderstandings).
Feel welcome to ask any follow-up questions.
Re: bill (10:48:59)
I would be careful about the hazards of moving away from a boxcar kernel. My impression is that there are a lot of misunderstandings out there about moving-window time-integration (including smoothing). The “best” choice of kernel depends on the particular task. Boxcar kernels have some nice harmonic properties that few seem to appreciate (or even be aware of). It could be quite challenging to interpret time-integrated cross-correlation analyses based on kernels that introduce harmonic distortion.
Results of Barrow CO2‘ analysis (note the prime ‘ symbol, which indicates rate of change):
http://www.sfu.ca/~plv/BarrowNOAAprime.png
http://www.sfu.ca/~plv/BarrowCDIACprime.png
http://www.sfu.ca/~plv/BarrowNOAAprimeMinusCDIACprime.png
http://www.sfu.ca/~plv/BarrowCO2primeScatterplot.png
http://www.sfu.ca/~plv/BarrowCO2primeResiduals.png
Note the imposed annual structure for CDIAC. This is important for anyone modeling seasonal fluxes (such as ecosystem carbon modelers I know).
The results for Alert are even more dramatic (as has been discussed previously).
Paul Vaughan (12:03:35) :
I will ask 3 questions:
1) Do you think the 2 frequencies you mention are both continuously operating across the record?
The simple FFT obviously does not show this. I initially assumed that the peaks at 1.18 years were in reality just a bit of FM on the fundamental. However, the BP filter shows 2 discrete frequencies. Reducing the bw of the bp filter to just include the 1.15 year period shows an amplitude of 0.3 relative. the 1.19 year wobble shows an amplitude of 1.2 relative. The 365.25 period has an amplitude of 1.0 relative during the 1930s
The amplitudr of the 1.15 year wobble may be modulate with a 162 year wave.
2) How do you interpret the bulge around them (in your power spectrum plot)?
A with any plot like this more resolution could show individual frequencies however with the data available it shows as noise or perhaps occassional frequency excursions of the main wobbles (there are a few other discrete frequencies in this area.)
3) Have you ever used windowed-FFT?
The built in excel funcion does not have windowing function. However, I often have, as part ogf my work, used such functions on real-time FFTs on DSOs. I do understand that the window type will affect the shape of the spectrum (but not the frequency of the peaks).
In order to see a phase reversal, one has to first decide, “relative to what?” If you look relative-to-a-stationary-wave, you will see (even without doing any calculations) that the polar motion group-wave (the envelope) is in ~anti-phase with a stationary wave with a period of ~6.4a before ~1931 and in-phase after (if you phase-align the latter part of the record).
1. What is the physical manefestation of yourhyperthetical stationary wave vs group wave phase reversal?
2. If I chose 6 years then the phase is continuously changing. before and after the 30s the main wobble is 1.19 years during the 30s the main chandler wobble is 1.15 years. The chandler wobble beats with the 365.25 day annual wobble to create a 6.4y wave. It is obvious that the wave will be longer with 1.15 y (during the 1930s) and shorter (outside the 30s) This will cause a phase shift!
3.In one post to claim that artificial constraints have been applied to CO2 data from CDIAC on on other posts you impose an artificial FIXED period of 6.4 years to get your phase shift. This is inconsistent?
4. There are other frequencies that filtering picks up
~1.2years reasonably constant amplitude over the period of the data.
~1.225 years reasonably constant amplitude over the period of the data.
Missed the other high level wobble period and update on others
1.179 y period with an amplitude of 0.63 rel
1.192y period with an amplitude of 0.68 rel
1.0008y period with an amplitude of 0.601 rel
bill (19:43:50) “The chandler wobble beats with the 365.25 day annual wobble to create a 6.4y wave. It is obvious that the wave will be longer with 1.15 y (during the 1930s) and shorter (outside the 30s) This will cause a phase shift!”
The lights go on. Like I said: It’s simple.
Case closed.
Paul Vaughan (02:57:34) :
The lights go on. Like I said: It’s simple.
Case closed.
What on earth has this artificial, mathematically produced, phase change got to do with anything?
The phase shift is a methematical artefact.
It is not as shown in the references you gave which show a rapid phase change of 180 deg. – one figure before 1930 and 180 degrees offset after 1930, no hint that it is cyclical.
It is a smooth change in PERIOD from 1.17 to 1.19 year
There is no associated change in wobble direction
It is a natural effect of many driving frequencies on the wobble – can you explain the physical effects of this?
How can this effect climate?
Seems to me that this is the non-event of the earths history!
bill (06:23:54) “What on earth has this artificial, mathematically produced, phase change got to do with anything? The phase shift is a methematical artefact.”
A phase-reversal is a phase-shift of 180 degrees. The polar motion phase-reversal is not artificial; it is real. (It has been observed.) It is evidence of nonstationarity, a concept which you (seem to) repeatedly ignore despite cautions from John S. & I, which should alert you of the need to pursue other methods of power spectrum estimation (besides just basic FFT). [I’m not suggesting John S.’s comments were addressed specifically towards you; nonetheless, we can all benefit from heeding the wise advice he occasionally shares.]
–
bill (06:23:54) “It is not as shown in the references you gave which show a rapid phase change of 180 deg. – one figure before 1930 and 180 degrees offset after 1930”
You must be looking at figure 11 in Vondrak (1999) without reading the associated text. The empirical view is at the top of the top panel of figure 10 (as I’ve indicated above). (You will note that figure 11 relates to a simulation Dr. Vondrak ran. See Vondrak (2005) for more details, if interested.)
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bill (06:23:54) “no hint that it is cyclical.”
No claim has been made of cyclicity. (Note that only one phase-reversal occurs in the entire polar motion record (to-date).)
–
bill (06:23:54) “There is no associated change in wobble direction”
No claim has been made of a change in wobble direction. (Perhaps you misread “phase reversal” as “rotation reversal” and developed a very serious misunderstanding early-on?)
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bill (06:23:54) “How can this effect climate?”
It is well-established that things that happen in the oceans & atmosphere (& other parts of Earth) affect EOP.
My impression is that your impression of what is being claimed is largely imagination-driven.
I encourage you to:
a) read comments carefully, judiciously, & literally.
b) orient yourself relative to the EOP literature.
c) learn a method of power spectrum estimation that affords time-localization (so as to better cope with nonstationarity).
– – – –
Questions:
1) Do you now see that the monthly CDIAC CO2 stats differ from the monthly NOAA CO2 data?
– and –
2) Do you acknowledge that CDIAC fit the raw data to a curve? (as they have acknowledged publicly in writing via their webpages)
Regards,
Paul.