NEW An update to this has been made here:
Part II
By Basil Copeland and Anthony Watts
In Part I, we presented evidence of a noticeable periodicity in globally averaged temperatures when filtered with Hodrick-Prescott smoothing. Using a default value of lambda of 100, we saw a bidecadal pattern in the rate of change in the smoothed temperature series that appears closely related to 22 year Hale solar cycles. There was also evidence of a longer climate cycle of ~66 years, or three Hale solar cycles, corresponding to slightly higher peaks of cycles 11 to 17 and 17 to 23 shown in Figure 4B. But how much of this is attributable to value of lambda (λ). Here is where lambda (λ) is used in the Hodrick-Prescott filter equation:
The first term of the equation is the sum of the squared deviations dt = yt − τt which penalizes the cyclical component. The second term is a multiple λ of the sum of the squares of the trend component’s second differences. This second term penalizes variations in the growth rate of the trend component. The larger the value of λ, the higher is the penalty.
For the layman reader, this equation is much like a tunable bandpass filter used in radio communications, where lambda (λ) is the tuning knob used to determine the what band of frequencies are passed and which are excluded. The low frequency component of the HadCRUT surface data (the multidecadal trend) looks almost like a DC signal with a complex AC wave superimposed on it. Tuning the waves with a period we wish to see is the basis for use of this filter in this excercise.
Given an appropriately chosen, positive value of λ, the low frequency trend component will minimize. This can be seen in Figure 2 presented in part I, where the value of lambda was set to 100.
Figure 2 – click for a larger image
A lower value of lambda would result in much less smoothing. To test the sensitivity of the findings reported in Part I, we refiltered with a lambda of 7. The results are shown in Figures 3 and 4.
Figure 3 – click for a larger image
As expected, the smoothed trend line, represented by the blue line in the upper panel of Figure 3, is no longer as smooth as the trend in the upper panel of Figure 1 from Part I. And when we look at the first differences of the less smoothed trend line, shown in Figure 4, they too are no longer as smooth as in Figure 2 from Part I. Nevertheless, in Figure 4, the correlation to the 22 year Hale cycle peaks is still there, and we can now see the 11 year Schwabe cycle as well.
Figure 4 – click for a larger image
The strong degree of correspondence between the solar cycle peaks and the peak rate of change in the smoothed temperature trend from HadCRUT surface temperature data is seen in Figure 5.
Figure 5 – click for a larger image
The pattern in Figure 4, while not as eye-catching, perhaps, as the pattern in Figure 2 is still quite revealing. There is a notable tendency for amplitude of the peak rate of change to alternate between even and odd numbered solar cycles, being higher with the odd numbered solar cycles, and lower in even numbered cycles. This is consistent with a known feature of the Hale cycle in which the 22 year cycle is composed of alternating 11 year phases, referred to as parallel and antiparallel phases, with transitions occurring near solar peaks.
Even cycles lead to an open heliosphere where GCR reaches the earth more easily. Mavromichalaki, et. al. (1997), and Orgutsov, et al. (2003) contend that during solar cycles with positive polarity, the GCR flux is doubled. This strongly implicates Galactic Cosmic Ray (GCR) flux in modulating global temperature trends. The lower peak amplitudes for even solar cycles and the higher peak amplitudes for odd solar cycles shown in Figure 4 appears to directly confirm the kind of influence on terrestrial climate postulated by Svensmark in Influence of Cosmic Rays on Earth’s Climate (1998)From the pattern indicated in Figure 4, the implication is that the “warming” of the late 20th century was not so much warming as it was less cooling than in each preceding solar cycle, perhaps relating to the rise in geomagnetic activity.
It is thus notable that at the end of the chart, the rate of change after the peak associated with solar cycle 23 is already in the negative range, and is below the troughs of the preceding two solar cycles. Again, it is purely speculative at this point, but the implication is that the underlying rate of change in globally averaged temperature trends is moderating, and that the core rate of change has turned negative.It is important to understand that the smoothed series, and the implied rates of change from the first differences, in figures 2 and 4, even if they could be projected, are not indications of what the global temperature trend will be.
There is a cyclical component to the change in global temperature that will impose itself over the underlying trend. The cyclical component is probably dominated by terrestrial dynamics, while the smoothed series seems to be evidence of a solar connection. So it is possible for the underlying trend to be declining, or even negative, while actual global temperature increases because of positive cyclical factors. But by design, there is no trend in the cyclical component, so that over time, if the trends indicated in Figures 2 and 4 hold, global warming will moderate, and we may be entering a phase of global cooling.
Some are probably wondering which view of the historical correspondence between globally averaged temperatures and solar cycles is the “correct” one: Figure 2 or 4?
Such a question misconstrues the role of lambda in filtering the data. Here lambda is somewhat like the magnification factor “X” in a telescope or microscope. A low lambda (less smoothing) allows us to “focus in” on the data, and see something we might miss with a high lambda (more smoothing). A high lambda, precisely because it filters out more, is like a macroscopic view which by filtering out lower level patterns in the data, reveals larger, longer lived processes more clearly. Both approaches yield valuable insights. In Figure 2, we don’t see the influence of the Schwabe cycle, just the Hale cycle. In Figure 4, were it not for what we see in Figure 2, we’d probably miss some similarities between solar cycles 15, 16, and 17 and solar cycles 21, 22, and 23.In either case, we are seeing strong evidence of a solar imprint in the globally averaged temperature trend, when filtered to remove short term periodicities, and then differenced to reveal secular trends in the rate of change in the underlying long term tend in globally averaged temperatures.
At one level we see clear evidence of bidecadal oscillations associated with the Hale cycle, and which appear to corroborate the role of GCR’s in modulating terrestrial climate. At the other, in figure 4B, we see a longer periodicity on the order of 60 to 70 years, correspondingly closely to three bidecadal oscillations. If this longer pattern holds, we have just come out of the peak of the longer cycle, and can expect globally average temperature trends to moderate, and increased likelihood of a cooling phase similar that experienced during the mid 20th century.
In Lockwood and Fröhlich 2007 they state: “Our results show that the observed rapid rise in global mean temperatures seen after 1985 cannot be ascribed to solar variability, whichever of the mechanisms is invoked and no matter how much the solar variation is amplified.” . Yet, as Figure 5 demonstrates, there is a strong correlation between the solar cycle peaks and the peak rate of change in the smoothed surface temperature trend.
The periodicity revealed in the data, along with the strong correlation of solar cycles to HadCRUT surface data, suggests that the rapid increase in globally averaged temperatures in the second half of 20th century was not unusual, but part of a ~66 year climate cycle that has a long history of influencing terrestrial climate. While the longer cycle itself may be strongly influenced by long term oceanic oscillations, it is ultimately related to bidecadal oscillations that have an origin in impact of solar activity on terrestrial climate.
We are continuing to look at different methods of demonstrating a correlation. Please watch for future posts on the subject.
NEW An update to this has been made here:
References:
Demetrescu, C., and V. Dobrica (2008), Signature of Hale and Gleissberg solar cycles in the geomagnetic activity, Journal of Geophysical Research, 113, A02103, doi:10.1029/2007JA012570.
Hadley Climate Research Unit Temperature (HadCRUT) monthly averaged global temperature data set (description of columns here)
J. Javaraiah, Indian Institute of Astrophysics, 22 Year Periodicity in the Solar Differential Rotation, Journal of Astrophysics and Astronomy. (2000) 21, 167-170
Katsakina, et al., On periodicities in long term climatic variations near 68° N, 30° E, Advances in Geoscience, August 7, 2007
Kim, Hyeongwoo, Auburn University, “Hodrick-Prescott Filter” March 12, 2004
M. Lockwood and C. Fröhlich, Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature, Proceedings of the Royal Society of Astronomy doi:10.1098/rspa.2007.1880; 2007, 10th July
Mavromichalaki, et. al. 1997 Simulated effects at neutron monitor energies: evidence for a 22-year cosmic-ray variation, Astronomy and Astrophysics. 330, 764-772 (1998)
from Chile (AD 1587–1994)
, Planetary and Space Science 55 (2007) 158–164Svensmark, Henrik, Danish Metorological Institute, Influence of Cosmic Rays on Earth’s Climate, Physical Review Letters 15th Oct. 98
Wikipedia, Hodrick-Prescott Filter January 20, 2008
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
It looks pretty much like you picked a filter that a) eliminated the large positive trend between 1900 and 2008 and b) eliminated any frequency whose period was less than 22 years as can be seen from the bottom pane in Fig 3.
Figure 5 is not very informative. Better would be to graph the difference between the solar peak and the HadCRUT peak in years. That one jiggles all over the place
Anthony: “detrending” was part of the process, much like removing a DC or an extremely low frequencey component that is near DC from a complex AC signal. Pretty standard stuff in electronic signal processing. It was applied over the entire signal, not just a section.
Thank you for your suggestions on figure 5.
Well, the Earth does generate its own heat internally, molten
core and all that.
I think the earth’s own heat is ~.08 w/m^2.
As a relative beginner when it comes to understanding the math behind these kinds of posts I’m trying to come to grips with what is graphed above. In laymans terms it appears that you plotted the HadCRUT values against the smoothed HadCRUT as a zero baseline (figure 3 graph 2), used a filter to get 23 (or so) rate of change peaks (fig 4) and then plotted the peaks on a graph along with solar cycles but with no variables.
To me it appears that you’ve shown that the “noise” of the original data vs the smoothed data is correlated to sunspot cycles but does that have any bearing on the absolute value of the trend line itself? In other words, if the noise on the trendline was a sawtooth with the peaks aligned with max sunspot and the mins at min sunspot but the slope of the trendline was 2C/century would that correlation have any meaning?
Thanks. I wasn’t sure how much. Just wanted to illustrate that the sun isn’t the only heat source, just the vastly dominant one.
Nice work Basil and Anthony. Very interesting and well written. FYI – I duplicated your work and then tried a Gaussian smoothing on the HadCRU data and got virtually the same result.
http://i32.tinypic.com/x27320.jpg
This was done with a Gaussian smoothing routine with sigma = 3. An Excel add-in with this and other functions is available from SRS1 Software. It is shareware with a free 30 day trial period.
http://www.srs1software.com
I didn’t think it was the case, but this would seem to strengthen the argument that the cycle seen in the plots is not an artifact of the HP filtering.
REPLY: Jeff, thanks for the work on this. -Anthony
Pamela –
Speaking as a chemistry Professor, a Turkey freezes at exactly the same rate as it thaws when done at the same temperature. I think that you are assuming that it “freezes” soon after being placed in the freezer when in actuality it takes the same time. At the freezing point, q = mL (where L = 80cal/g) and at this temperature it is a reversible process. That is – any small increase in heat can EXACTLY be subtracted. By the way – most chemical reactions are irreversible, but phase changes are not.
Sorry for the OT post, but wanted to correct this “myth” (like hot water will freezes sooner than cold water placed in a freezer).
reminder,
flux density,
one month ago 0067.4
today 0079.3
Evan’s comment about a 60-year PDO cycle popped a random thought into my mind, and I offer this only as a curve-ball for others to bat… If you had *two* cycles from different sources, one of 60 and one of 66 years, IIRC they would ‘beat’ with a wavelength of LCM(60,66) = 660 years. The exact beat frequency is very sensitive to the exact periods of the two inputs (musicians, think about tuning a guitar).
Then consider the rough dates of the Medieval Warm Period, Little Ice Age and now…
Jeff C. good job. For me, the main/first complaint to answer was the use of a infrequently used filter in the climate environment.
I notice that the major ENSO events (1876-78, 1891, 1925-26, 1982-83, and 1997-98) have all occurred when the temperature Trends in Figure 2 are at, or very near, an upper peak.
Is it false to deduce that:
a) Because major ENSOs occurred near peak temp trends, see Fig 2
b) and temp trends correlate well with sunpost/solar cycles, as your paper indicates,
c) then El Ninos are mainly driven by sunspot/solar cycles?
We are always told that El Ninos cause global temps to increase, when if fact it’s probably the other way around. That is first the sunspots – then warming, and then the ENSO.
(Wikipedia says that the current cooling is caused by the current La Nina. How do we know its not the other way around?)
Anyone follow me?
The major ENSOs also line up well the sunspot cycles:
1876-78 – cycle 11
1891
Sorry – hit the wrong key!
1891 – cycle 13
ENSO 1925 – cycle16
ENSO 1980 – cycle 21
ENSO 1998 – cycle 23
I mean just recently a report came out saying the ocean temps have cooled a little over the last 5 years. Could this have led to the current El Nina?
Can I ask my question now? How do we use filtering to find the low stuff? I know how it is done for brainwaves. I would love to have a look at the minimums across the span: length, solar flares during minimums, last one out/first one in overlap, etc.
And one more question: I have noticed that solar flares seem to have a non-linear drop in amplitude, sort of like a switch that turns on and off when the sunspot gets to a certain size or overall number. Could this be a better predictive measure of solar effects on temperature, especially during the upswing and downturn? If the ramping up or down amplitudes leads temperature change, wouldn’t that be a possible strong case for cause-effect? Can we plot solar flare magnitude compared to temperature change? Does that data exist? The number of sunspots may have only a mild to moderate correlation to flares being produced. It seems logical to me that the heat of the flare (and all the stuff it ejects) is more important than the fact that it is counted.
Precisely, Pierre.
===========
Alan, we had three sunspots, now going away, and the flux is dropping. It is not unexpected to see last gasp last cycle sunspots. Flux will not rise consistently until we see new cycle sunspots with regularity, and surely not until they outnumber old cycle spots. Minimum may not be here, yet. Cherry Pie is delicious, though.
===========================================
Bill Illis – greenhouse gases take up a small % volume of the atmosphere, but they do lots of warming work. Most of the atmosphere is insensitive to IR. Look at any overview of the greenhouse effect (not GW per se, but just the basic effect) and you’ll see that at any given moment the Earth’s surface receives more warmth from the atmosphere’s backradiation than directly from the sun. Sounds strange, but true.
Certainly true at night, Ian. Some of what you call ‘back radiation’ started at the sun and directly warmed the atmosphere. It is not really back radiation.
=======================================
While my knowledge of the relevant maths is not sufficient to enable me to keep up with the article, it does seem to make sense. But on a different aspect of pattern recognition and cycles, last night, I was using an analytical device which has the most incredible way of recognising various cyclic events in a long data string. From a single varying voltage, my ears and brain were able to distinguish the various instruments playing in a symphony orchestra. If the temperature record, unsmoothed and unfiltered could be applied to an analogue converter of some sort to produce a voltage, then this could be played as a short track. Due to the woefully limited amount of data, you would probably only get a two or three second output, but it would be interesting to see whether the brain can “hear” different patterns, or “instruments”. Silly thought, but…who knows, you might just hear something, then again, you might just get a burst of noise, which might also give some insight into a lack of patterns.
Kim said:
and it heated the land and water. The stored heat is given back after the Sun drops. Mitigated by clouds to slow the heat radiation back into space. That Ole cloud effect, don’cha know.
Of course CO2 has its own impact, but…?
kim, yes, of course almost all of it came from the sun originally. And greenhouse gasses delay its return to space, warming the planet surface. Averaged over the planet, the surface is warmed more by the atmosphere than by _direct_ sunlight. Check any basic description/depiction of the greenhouse effect to confirm.
My point to Bill Illis was to avoid being misled by the scaling differences between TSI (normally expressed with a number over 1000) and CO2 concentration (expressed as a part per million), or to compare their change rates directly. (This is leaving aside the problems of comparing to the top-of-atmosphere TSI figure.) Bill, I was suggesting that your comparison doesn’t capture the extent to which IR, originally from the sun’s energy, is kept around by greenhouse gasses.
Paul’s comments caused me to look at fig 5 again. Did anyone notice that the sunspot is a straight line, but the surface data seems to show a very slight wave pattern ahead, then behind.
Note also that the pattern drifts a little after 1980. Could thissomehow be a reflection of exaggerated ground readings due to site violation?
Speaking of greenhouses, I have come across two observations that make one ponder
1) A garden green house ( or a closed car) does not work by trapping the heat because of the insulating and back radiation properties of the glass (or metal). It heats up because there are no convection currents within the green house( car). It is the enclosure that drives the heat up with respect to the outside temperatures. It is a misnomer to call the atmospheric effect “greenhouse” as there is plenty of convection in the atmosphere.
2) In http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.1161v3.pdf the position is taken by Gerhard Gerlich and Ralf D. Tscheuschner that :
“The atmospheric greenhouse effect, an idea that authors trace back to the traditional works of Fourier 1824, Tyndall 1861, and Arrhenius 1896, and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law
of thermodynamics such a planetary machine can never exist.”
It is a rambling paper, but this second of law thermodynamics would be serious trouble for the atmospheric greenhouse model . It is true that heat cannot be transfered from a lower temperature reservoir to a higher temperature reservoir ( the Clausius statement of the second law of thermodynamics) without work being done somehow. ( think of air conditioners ). As the temperature in the upper atmosphere ( outside a plane at 30000 feet) is lower than the temperature near the surface, what is doing the work?
Has anybody seen any discussion /have a link of the atmospheric greenhouse effect as a thermodynamic engine ,other than the above linked note which says it is a perpetual motion machine of the second kind?
Water vapour is by far the most important greenhouse gas, followed by the first 40 ppm of CO2, then by the next 80 ppm, then the next 160 and so on. The few ppms that we are now adding to the atmosphere are very minor in the overall greenhouse effect. The greenhouse effect of CO2 decays logarithmically as concentrations increase. Too many people falsely believe that it is a linear function. It is not.
Greenhouse gases do lots of warming work? Yes.
A few more ppms of CO2? No. They are insignificant!
Apparently, David Hathaway of NASA is becoming impatient and they are going to send a manned expedition, including Hathaway, to the Sun to see what is going on. In order to save costs and construction time, they are planning to make the trip at night so they won’t have to worry about the heat. It is hoped that they can get all their measuring devices planted and be far enough away from the sun before daybreak.
To Ian, yes I understood all that.
The impact of GHGs is often expressed in Watts/m2 as well which is variously quoted for a doubling of CO2 at 4.2 w/m2 (and we are only halfway there now.)
Changes in solar irradiance (divided by 4 for the Earth as a sphere and the lowest measured to the highest measured) have been as much as the current GHG forcings of approximately 2 W/m2.
How come solar has no impact while GHGs account for so much warming.
I also note that the 1878 temperatures (an El Nino year) from Hadley are virtually the same as today’s numbers (despite the 1878 temps being adjusted downward by Hadley.) Does that signal no warming for 130 years?