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
This is worth a reading, is clear and concise, good plots:
http://www.warwickhughes.com/agri/Solar_Arch_NY_Mar2_08.pdf
“Solar Cycle 24: Implications for the United States
David Archibald
International Conference on Climate Change”
“We have to be thankful to the anthropogenic global warming proponents for one thing. If it weren’t for them and their voodoo science, climate science wouldn’t have attracted the attention of non-climate scientists, and we would be sleepwalking into the rather disruptive cooling that is coming next decade. We have a few years to prepare for that in terms of agricultural production.”
As anna v. points out ‘back-radiative’ warming of the surface is nonsensical. CA had a AGW ‘radiative budget’ flow chart a couple of months back around the time Curry (GATech?) was posting.
The back-radiation AGW specifies approaches 25% of the original energy reaching the ground. This is impossible. There can be no net flow of heat between bodies at the same temperature, let alone a transfer from the cooler to the warmer.
The UAH MSU data demonstrates that the equatorial high troposphere is not warming.
In addition, the surface emissivity is more than two orders of magnitude greater than atmospheric CO2 and re-emits energy received faster than the CO2 can absorb.
The errors in the Greenhouse heuristic are legion and the G&T paper details the most basic of them well.
Pamela,
re: rate of rise versus rate of fall.
and
Drew
re: time constant of the ocean.
I have no idea if what you see is due to dynamics in the sun, or in the earth.
But, in my simpler world of cyclotron produced medical radioisotopes, the rate of change in amount of isotope is a function proportional to the beam current that hits the target minus the rate of decay times the amount of isotope created. Since the production rate goes to zero as the amount of isotope approaches saturation, it is not usually worth running for more than one half-life, and the rate of increase doesn’t change much from the rate of production.
So, for short term changes in my simple world the rate of rise is mostly based on the beam current and how it changes. But turn it off, and the rate of fall is solely due to the decay rate.
It may be possible that in the much more complex world and and the very complex sun and the ways they couple, that Anthony and Basil may have isolated a driver term and its coupling to a reservoir with a similar time scale , but are dealing with small perturbations from equilibrium instead of starting from absolute zero and trying to warm up the planet. Except, the the average temperature is a measurement of the atmosphere which is also driven by the sun TSI as gated by the GCR, amongst other effects, and the ocean time constant will be afunction of how it radiates, how it gives or takes heat from the atmosphere, and maybe many other things. But, if this math has filtered the data so that the rate of change seen in the atmosphere temperature is mostly due to the ocean and or the sun/gcr, and the rate of change in the ocean is mostly due to the sun/gcr and the coupling to the atmosphere, then for an initial perturbation from equilibrium the initial rate of rise in the atmosphere would have two components proportional to the sun/gcr driver term, and the rate of fall in the atmosphere would have a component based on the rate of fall in the ocean. (Sorry that sentance is so long.) So one could be seeing both time structure in the driver, and time structure inherent in the system.
I will leave it to others to come up with a real model and to see just what effect each part of the system has, which is what I tried to urge with my previous post. But it is worth remembering that a time constant much shorter than the time frame of changes in the driver will stay in equilibrium with changes in the driver, so one will see the longer time frame of the driver in that system. And a time constant much longer than the changes in the driver will not have enough time to react and the system will seem unperturbed by the changes in the driver. And time constants nearly the same as that of the driver will be more complex, and harder to tell apart.
And Drew, the total change, (integrated rate of change), should show the time lag. The current in an RC circuit is the rate of change of charge in C. The voltage on C lags the rate of change of the current.
The link between this work and the PDO has been mentioned a few times. Of particular interest is Paul Clark’s comment of beating between solar forcing and the PDO. From an oceanographic perspective the PDO involves the circulation of thermosteric anomalies around the Pacific Ocean. These derive from atmospheric/solar effects when the parcels of water at at the surface – Precipitation/evaporation balance effects salinity, amount of shortwave radiation reaching the ocean effects temperature anomalies = density changes. Clearly the GCRs implicated here will influence the salinity & temperature anomalies through influencing clouds.
The anomaly then circulates subsurface (ventilated thermocline theory) until it returns to the surface 50-70 years later. If the return is sufficiently in phase with solar cycles then the anomaly will be amplified, and if it is out of phase it will be attenuated.
We’ve been playing with wavelets to looks at oceanographic and coastal atmospheric processes related to the PDO and ENSO. There is clear evidence for interaction between the two, but we also are seeing a longer period pattern in paleoindices that suggests that there is something going on akin to beating.
The problem has been figuring why it is happening. The work summarised here is therefore intriguing.
Anna, with respect to part a) you have that a bit wrong, greenhouses work because the barrier (glass or whatever) cuts off convective flow from inside to outside, so the inside heats to the point where radiation and conduction from the surface match the incoming from the sun. There is plenty of convection inside the greenhouse.
As to part b) if you want the math rich version about why G&T are wrong take a look at Arthur Smith’s comment on Arxiv
A less mathematical, but longer version can be found at Rabett Run, which, as long as it is is but a fraction of the original on dot.earth.
REPLY: “…greenhouses work because the barrier (glass or whatever) cuts off convective flow from inside to outside, so the inside heats to the point where radiation and conduction from the surface match the incoming from the sun.” That is essentially correct, the term, “Greenhouse”, when used to describe atmospheric effects, is a popular misnomer. Notice that most greenhouses have fans/vents, hinged glass panels, and airflow control systems to help regulate temperature. -Anthony
Also, most commercial greenhouses have a machine in the corner pumping out CO2 to keep the level above 1000ppm. This is not to warm the atmosphere in the greenhouse, but to feed the plants. When the level of CO2 drops below 150ppm, (which it will do by mid-morning if not replenished), the plants will stop growing and if it drops below 90ppm then photosynthesis stops.
How about Miscolczi’s objection?
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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.
Rather than requiring readers to infer something about magnitude from the rate plot, why not point them to the trend plot in Fig. 3 from which it was derived? That tells you directly how much warming or cooling occurred.
I know very little about solar mechanics, or GCMs for that matter. But for what it’s worth, it does seem to me that you could be a bit more careful about implying things about the magnitude of potential effects from rate data — especially if it’s just peak rates. For example, I’m not sure it’s appropriate to imply anything about the magnitude of GCR flux as a temperature forcer based upon a measure of peak rate of change in temperature. If anything I would think that some kind of measure of the area under the curve for the period in question would be more appropriate — unless the fastest rate of change is more important than the overall magnitude of change. On that score, I can’t say. But if it is, I think your discussion could make that clearer. And also if it is, then more attention should be paid to a discussion of whether the measurement of those rates are appropriate.
And I still don’t understand why you picked the HP filter. It seems to me you’ve violated just about every theoretical assumption you could in that regard. But I’m not a good enough statistician to derive the filter’s response profiles on the one hand, and I sure as heck don’t know enough about solar dynamics on the other to mount a compelling argument. So I’m willing to take Paul Clark and other’s word on various other filtering results. And actually, I did spend some time putting the data through a variety of Butterworth and finite impulse response filters and was able to get similar results — assuming I was careful to pick the right cut-off frequencies and rolloff characteristics. I got some very pretty results, too! In fact, I got one that looked very similar to the graph in the Wikipedia article. Although I’m pretty sure the parameters I used made about as much sense as Jim B’s Batman logo, lol!
Sorry, still OT, but one more quick comment on greenhouses.
The place to see the earth’s ‘greenhouse effect’ at work is in a hot desert in summer.
Stand in the sun at 2pm and feel the heat pouring down on you. The temperature will be in the high 40s, maybe even 50 and the sweat will be pouring off you and quickly evaporating. Come back just before dawn and the temperature will be in the low single figures, maybe as low as zero. (You’ll also get a fantastic view of the stars.)
Move west along the same latitude until you cross the mountains and then stand in the sun at 2pm. The temperature will be in the high 30s or low 40s and the sweat will be pouring off you, but now it will not be evaporating. The glass from which you are drinking the cold beverage of you choice will seem to have developed a leak and be dripping on your leg. Come back just before dawn and the temperature will be in the high teens, maybe even low twenties and your glass will still be dripping.
The difference, of course, is the humidity, not the CO2 content of the atmosphere. Water vapour. THE greenhouse gas.
If, instead of spending millions, (billions?), on assesment reports, GIGO models and annual conferences in exotic locations, we had established a network of sensors measuring temperature, humidity and CO2 at hourly intervals, we would by now have maybe twenty years worth of empirical data to play with.
By searching for records where the humidty was the same and the CO2 was higher we could look at the slope of the night time temperature drop, as well as the maximum and minimum temperatures, and maybe find some experimental evidence for the effects of CO2. Anthony and the Steves would have loads of numbers to play with from known sites with known conditions, and if we’d spent a bit more on solar observations, the sun – climate link could have been teased out.
Experiments and reliable data? Nah, it’ll never catch on. Playing with supercomputers and having conferences is the way to do science.
Anna:
Re Gerhard Gerlich and Ralf D. Tscheuschner – Eli provided you with a link to Arthur Smith’s excellent paper refuting much of G&T. Admittedly, however, he doesn’t directly discuss the 2nd law issue.
So, to discuss that: Basically, the deal is that the greenhouse theory does not require the flow of energy from the upper atmosphere to the surface. The greenhouse gases in the atmosphere just reduce the amount of energy that escapes from the surface back into space. You can come up with radiative problems simple enough to give in a first-year physics course that demonstrate the same sort of effect. In fact, if I were a professor (rather than an industrial physicist), I would definitely give my students such a problem on a problem set or exam that would allow them to show that G&T are wrong!
Here is a sample problem that does this: A blackbody sphere S is held at a constant temperature T_S. Then put a blackbody spherical shell A around it. All of this in otherwise empty space. It is easy to calculate the temperature of the shell A due to the balance between the radiation it receives from S and what it radiates back out into empty space. If you then surround this shell A by another blackbody shell B, it is only slightly more difficult to calculate the temperature of both A and B. You will find that B (“the upper atmosphere” in this analogy) has a lower temperature than A (“the earth” in this analogy) and yet A has a higher temperature than it had in the absence of B!
Moral of the story: Conservation Laws (like the Laws of Thermodynamics) are very powerful tools but, like any powerful tool, they can also easily be misapplied.
NOTE: Over on the “Tamino” blog, there’s an application of “Rayleigh’s R” to Figure 5 demonstrating a result different from ours. We are currently looking into the application of Rayleigh’s R distribution to this issue.
Basil and I have discussed it and we agree, it is interesting and challenging at the same time. A central issue is how to correctly identify the peak of the solar cycle, and we are looking at that more closely.
There has been replication of the SSN to HadCRUT surface data link by at least three people, using different methods, including FFT, plus more traditional filters. We are currently exploring those replications along with additional statistical tests and correlations.
Rico,
Regarding filter selection, as several of us have demonstrated, very similar results can be obtained using a variety of filters. As you correctly point out, the selection of the high frequency cut-off is important as there seem to be numerous high-frequency waveforms modulated on the carrier that tend to mask the 22 year cycle if not removed.
Assuming the application of the filter is causing a spurious 22 year cycle to emerge, doesn’t it strike you as odd that this spurious signal happens to be in phase with the solar cycle? Not only that, there are actually two 22 year cycles, 180 degrees out of phase, of different amplitude. The larger amplitude 22 year cycle is in phase with the odd numbered solar cycles, the smaller amplitude 22 year cycle is in phase with the even numbered solar cycles. And , of course, the odd/even solar cycles have opposite polarity (i.e. are out of phase). That is an awful lot of coincidences for a spurious signal.
I don’t think anyone is saying this disproves AGW, just that there seems to be an interesting pattern in the temperature data related to the solar cycle. In fact, the need to plot the derivative of the filtered response to see the pattern would tend to argue against this relationship being the dominant trend in the data. Something else must be causing a significant portion of the positive linear slope over time or the pattern would be visible immediately after filtering without needing to plot dT/dt. That something else could be non-climactic (UHI, data adjustments, equipment changes, etc.) or it could be real (a longer unknown solar periodicity, PDO/AMO, Co2, etc.). Time will tell.
@Pierre Gosselin (aka AGWscoffer)
Re: ENSO and Solar Activity
Before his death in 2004, Dr Theodor Landscheidt made some uncanny predictions of El Nino and La Nina events (2-4 years in advance) based on predictions of solar activity.
The post Anthony refers to is here:
http://tamino.wordpress.com/2008/04/01/how-not-to-analyze-data-part-3/
I’m having trouble with figure 5. Obviously that the graph shows a roughly linear climbing line is of no interest – ascending numbers do that (wouldn’t an entirely different kind of graph be better at showing any correlation or lack there of without the misleading ascent). But aren’t solar cycles 11 year events or there abouts – and then, on the scale you’ve drawn (20 year intervals on the vertical axis), wouldn’t anything other than very closely or consistently aligned plots (the plot for your cycle 11 is in the wrong place by the way) result be needed to even begin to show any kind of correlating trend between the figures at all? As it is, (with even a cursory examination) it would seem as though peaks are variously hit and miss and quite random.
Infact, I’m surprised how uncorrelated the data appears to be.
RE: Jay, we recognize that we need to do a better job with figure 5. We are taking a new approach.
Kim, the Hungarian problem is mostly in assumption g) which simply is not true.
Anthony,
May I offer a hypothesis why the differential in Figure 4 doesn’t peak singularly for cycle 16. Until I give the answer, please be patient by following my line of thought. I have hunch that the influence of the solar cycle on earth’s climate is confounded with the amount of particulate matter (pm) in the stratosphere. I got this idea by looking at Atmoz’s pre-April Fool’s post where he showed the temperature series of the stratosphere and the troposphere. It shows that the stratosphere has cooled significantly in the last 30 years that, in my opinion, are due to less ash from volcanic eruptions and from less pm emitted by countries around the world, particularly the Former Soviet Union and China (the latter due to modernizaton). In other words, when pm reaches the stratosphere due to volcanism and man-made pollution, it heats the stratosphere (by absorption of energy) while at the same time cools the troposphere by shielding the sun. Now that I got your attention, look at the years where cycle 16 occurs – The Great Depression! A drop in worldwide industrial output (and pm pollution) coincided with the peak of cycle 16 to produce the highest temperatures in NA for the 20th century. Also, to answer a prior question regarding why the troughs in Figure 4 are rising for the past 4 cycles, it may be simply that the stratosphere has been progressively getting cleaner.
REPLY: Chris, this makes a lot of sense. Especially since the last total lunar eclipse was said to be “odd looking” due to the atmosphere being so clean.
See this article on the Feb 20th 2008 lunar eclipse:
http://environment.newscientist.com/channel/earth/climate-change/dn13376-lunar-eclipse-may-shed-light-on-climate-change.html
We have something similar in 1998, most of Pinatubo’s dust had settled by then, we had and El Nino, and a solar max coming on.
[snip]
Phil, I’m happy to post your comment, but please try again, perhaps with a “collegial” approach. Thank you for your consideration.
http://rabett.blogspot.com/
As for 1) you are right, I have expressed myself badly. Though “plenty of convection” in the garden greenhouse is true only while it starts heating up (no convection in a hot closed car).
Thank you for the references. I will look into them.
Joel Shore (16:55:44) : My last excursion into thermodynamic problems was back in 1959, I have to open textbooks from back then. I have though the clear summary in my head that thermodynamic laws are valid in all large scale systems. It is only in the microcosm that contradictions may arise, and those are resolved by statistical mechanics.
Now in your example with S, A and B, I have not done the problem, but assuming you are correct, work must be done to keep S into the steady temperature, no? , since it is radiating heat off. I am looking for that “work” in the system “surface heat reservoir”-“troposphere reservoir”, i.e. consistency with the laws of thermodynamics ( which I am sure nature obeys).
Kevin B (16:20:28) :
I am not disputing that H2O mainly is keeping our temperatures temperate, I just would want to see the right thermodynamic framework. Finding it might explain some data, for example why the upper troposphere is not heating up as the IPCC CO2 greenhouse signature demands.
Tony Edwards’ idea of using the best wave recognition system available, our ears, is quite brilliant! My interest in Fourier transforms on this data comes from some work in audio synthesis many years back, and I was joking about God playing sub-bass, but I hadn’t thought of taking it to the obvious conclusion… There’s something deeply romantic about listening to the Earth’s heartbeat (well, one of them, anyway).
But to return to practicalities: If we output the 1900-odd HADCRUT3 samples we’re using at 44.1KHz (CD sampling rate), it would only last about 43ms, so we’d have to loop it, but that’s probably OK as long as we detrend it so the ends match, to avoid a spike at 23Hz. The 11-year cycle would then show up as a 334Hz signal – somewhere around E4 (E above middle C), right where the human ear works best.
I’ll see what I can do…
REPLY: Why not use a lower sampling rate …if doesn’t matter to the data as long as all data is sampled equally. Music of the spheres.
An FFT of your Fig 4:
http://i25.tinypic.com/2884h00.jpg
REPLY: Thanks Bob. Could you elaborate a bit on how you reached this?
‘Also, most commercial greenhouses have a machine in the corner pumping out CO2 to keep the level above 1000ppm. This is not to warm the atmosphere in the greenhouse, but to feed the plants. When the level of CO2 drops below 150ppm, (which it will do by mid-morning if not replenished), the plants will stop growing and if it drops below 90ppm then photosynthesis stops.’~ Kevin B
Kevin, my wife is assistant grower at a local greenhouse (‘Assistant’ meaning, she does All the thinking and most of the work), and she knows whereof you speak!
It is also interesting how quickly a greenhouse can cool off when clouds or the energy screens are in effect. Even in the summer, it can get Cold inside.
Bravo Anthony and Basil!
You have shown a clear correlation between years in two consecutive time series. That’s fabulous! I hope you will publish this soon, hopefully in Nature or Science!
Keep up the good work, guys!
REPLY: Thanks but we need to rework figure 5. The correlation comes out different under other types of analysis.
I believe that correlation is a strong indicator of cause and effect but it is a poor indicator of which case is true. Leading indicators of later events are better for this purpose, especially if the correlation follows a mathematical predictive formula. In my brain research, I was able to say that the peaks I was looking at were mathematically connected to the onset of the pip tone and were frequency specific. I knew how fast these signals traveled from the earphone to the major synaptic junctions because I knew how fast signals traveled along the neural pathway from one junction to the next. Sure enough, all five peaks I found (peaks three through five were known, peaks one and two had not been measured yet or at least reported to have been measured in the literature) were predicted to be exactly in that spot along the time axis based on the onset of the pip and the mathematical calculation of where they should be.
What parts of these smoothed data strings show potential for that kind of predictive relationship between solar events and temperature change? It would seem to me that solar events would predict later temperature change in some kind of mathematical time lag.
Should we be looking at peaks, troughs or slopes for predictive value (thus cause and effect theory that passes the smell test)?