NEW An update to this has been made here:
NOTE: This essay represents a collaboration over a period of a week via email between myself and Basil Copeland. Basil did the statistical heavy lifting and the majority of writing, while I provided suggestions, reviews, some ideas, editing, and of course this forum. Basil deserves all our thanks for his labor. This is part one of a two part series. -Anthony
Evidence of a Significant Solar Imprint in Annual Globally Averaged Temperature TrendsBy Basil Copeland and Anthony Watts
It is very unlikely that the 20th-century warming can be explained by natural causes. The late 20th century has been unusually warm.
So begins the IPCC AR4 WG1 response to Frequently Asked Question 9.2 (Can the Warming of the 20th Century be Explained by Natural Variability?). Chapter 3 of the WG1 report begins:
Global mean surface temperatures have risen by 0.74°C ± 0.18°C when estimated by a linear trend over the last 100 years (1906-2005). The rate of warming over the last 50 years is almost double that over the last 100 years (0.13°C ± 0.03°C vs. 0.07°C ± 0.02°C per decade).
Was the warming of the late 20th century really that unusual? In recent posts Anthony has noted the substantial anecdotal evidence for a period of unusual warming in the earlier half of the 20th century. The representation by the IPCC of global trends over the past 100 years seems almost designed to hide the fact that during the early decades of the 20th century, well before the recent acceleration in anthropogenic CO2 emissions beginning in the middle of the 20th century, global temperature increased at rates comparable to the rate of increase at the end of the 20th century.
I recently began looking at the longer term globally averaged temperature series to see what they show with respect to how late 20th century warming compared to warming earlier in the 20th century. In what follows, I’m presenting just part of the current research I’m currently undertaking. At times, I may overlook details or a context, or skip some things, for the sake of brevity. For example, I’m looking at two long-term series of globally averaged annual temperature trends, HadCRUTv3 and GHCN-ERSSTv2. Most of what I present here will be based on HadCRUTv3, though the principal findings will hold true for GHCN-ERSSTv2.
I began by smoothing the data with a Hodrick-Prescott (HP) filter with lambda=100. (More on the value of lambda later.) The results are presented in Figure 1.
Figure 1 – click for a larger image
The figure shows the actual data time series, a cyclical pattern in the data that is removed by the HP filter, and a smoothed long term low frequency trend that results from filtering out the short term higher frequency cyclical component. Hodrick-Prescott is designed to distinguish short term cyclical activity from longer term processes.
For those with an electrical engineering background, you could think of it much like a bandpass filter which also has uses in meteorology:
Outside of electronics and signal processing, one example of the use of band-pass filters is in the atmospheric sciences. It is common to band-pass filter recent meteorological data with a period range of, for example, 3 to 10 days, so that only cyclones remain as fluctuations in the data fields.
(Note: For those that wish to try out the HP filter, a freeware Excel plugin exists for it which you can download here)
When applied to globally averaged temperature, it works to extract the longer term trend from variations in temperature that are of short term duration. It is somewhat like a filter that filters out “noise,” but in this case the short term cyclical variations in the data are not noise, but are themselves oscillations of a shorter term that may have a basis in physical processes.
For example, in Figure 1, in the cyclical component shown at the bottom of the figure, we can clearly see evidence of the 1998 Super El Niño. While not the current focus, I believe that analysis of the cyclical component may show significant correlations with known shorter term oscillations in globally averaged temperature, and that this may be a fruitful area for further research on the usefulness of Hodrick-Prescott filtering for the study of global or regional variations in temperature.
My original interest was in comparing rates of change between the smoothed series during the 1920’s and 1930’s with the rates of change during the 1980’s and 1990’s. Without getting into details (ask questions in comments if you have them), using HadCRUTv3 the rate of change during the early part of the 20th century was almost identical to the rate of change at the end of the century. Could there be some sense in which the warming at the end of the 20th century was a repeat of the pattern seen in the earlier part of the century? Since the rate of increase in greenhouse gas emissions was much lower in the earlier part of the century, what could possibly explain why temperatures increased for so long during that period at a rate comparable to that experienced during the recent warming?
As I examined the data in more detail, I was surprised by what I found. When working with a smoothed but non-linear “trend” like that shown in Figure 1, we compute the first differences of the series to calculate the average rate of change over any given period of time. A priori, there was no reason to anticipate a particular pattern in time (or “secular pattern”) to the differenced series. But I found one, and it was immediately obvious that I was looking at a secular pattern that had peaks closely matching the 22 year Hale solar cycle. The resulting pattern in the first differences is presented in Figure 2, with annotations showing how the peaks in the pattern correspond to peaks in the 22 year Hale cycle.
Besides the obvious correspondence in the peaks of the first differences in the smoothed series to peaks of the 22 year Hale solar cycle, there is a kind of “sinus rhythm” in the pattern that appears to correspond, roughly, to three Hale cycles, or 66 years. Beginning in 1876/1870, the rate of change begins a long decline from a peak of about +0.011 (since these are annual rates of change, a decadal equivalent would be 10 times this, or +0.11C/decade) into negative territory where it bottoms out about -0.013, before reversing and climbing back to the next peak in 1896/1893. A similar sinusoidal pattern, descending down into negative annual rates of change before climbing back to the next peak, is evident from 1896/1893 to 1914/1917. Then the pattern breaks, and in the third Hale cycle of the triplet, the trough between the 1914/1917 peak and the 1936/1937 peak is very shallow, with annual rates of change never falling below +0.012, let alone into the negative territory seen after the previous two peaks. This same basic pattern is repeated for the next three cycles: two sinusoidal cycles that descend into negative territory, followed by a third cycle with a shallow trough and rates of change that never descend below +0.012. The shallow troughs of the cycles from 1914/1917 to 1936/1937, and 1979/1979 to 1997/2000, correspond to the rapid warming of the 1920’s and 1930’s, and then again to the rapid warming of the 1980’s and 1990’s.
While not as well known as the 22 year Hale cycle, or the 11 year Schwabe cycle, there is support in the climate science literature for something on the order of a 66 year climate cycle. Schlesinger and Ramankutty (1994) found evidence of a 65-70 year climate cycle in a number of temperature records, which they attributed to a 50-88 year cycle in the NAO. Interestingly, they sought to infer from this that these oscillations were obscuring the effect of AGW. But that probably misconstrues the significance of the mid 20th century cooling phase. In any case, the evidence for a climate cycle on the order of 65-70 years extends well into the past. Kerr (2000) links the AMO to paleoclimate proxies indicating a periodicity on the order of 70 years. What I think they may be missing is that this longer term cycle shows evidence of being modulated by bidecadal rhythms. When the AMO is filtered using HP filtering, it shows major peaks in 1926 and 1997, a period of 71 years. But there are smaller peaks at 1951 and 1979, indicating that shorter periods of 25, 28, and 18 years, or roughly bidecadal oscillations. There is a growing body of literature pointing to bidecadal periodicity in climate records that point to a solar origin. See, for instance, Rasporov, et al, (2004). A 65-70 year climate cycle may simply be a terrestrial driven harmonic of bidecadal rhythms that are solar in origin.
In terms of the underlying rates of change, the warming of the late 20th century appears to be no more “unusual” than the warming during the 1920’s and 1930’s. Both appear to have their origin in a solar cycle phenomenon in which the sinusoidal pattern in the underlying smoothed trend is modulated so that annual rates of change remain strongly positive for the duration of the third cycle, with the source of this third cycle modulation perhaps related to long term trends in oceanic oscillations. It is purely speculative, of course, but if this 66 year pattern (3 Hale cycles) repeats itself, we should see a long descent into negative territory where the underlying smoothed trend has a negative rate of change, i.e. a period of cooling like that experienced in the late 1800’s and then again midway through the 20th century.
Figure 2 – click for a larger image
Figure 2 uses a default value of lambda (the parameter that determines how much smoothing results from Hodrick-Prescott filtering) that is 100 times the square of the data frequency, which for annual data would be 100. This is conventional, and is consistent with the lambda used for quarterly data in the seminal research on this technique by Hodrick and Prescott. I’m aware, though, of arguments for using a much lower lambda, which would result in much less smoothing.
In Part 2, we will look at the effect of filtering with a lower value of lambda. The results are interesting, and surprising.
Part 2 is now online here
NEW An update to this has been made here:
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DNorris,
Try:
http://www.leif.org/research/
http://www.leif.org/research/TSI-LEIF.pdf
The difference between the past and the presence can be attributed to CO2 – but this only amounts to 0.4 degC. This represents of CO2 sensitivity < 1 degC/doubling which is much smaller than the IPCC estimates.
Peter Hartley: Isn’t the hypothesis your describe is what Lindzen formulated and what he and Spencer have been discussing recently?
Was the warming of the late 20th century really that unusual?
I think we need to ask ourselves how much of the warming of the late 20th century was really that . . . real?
“Chapter 3 of the WG1 report begins:
Global mean surface temperatures have risen by 0.74°C ± 0.18°C when estimated by a linear trend over the last 100 years (1906-2005). The rate of warming over the last 50 years is almost double that over the last 100 years (0.13°C ± 0.03°C vs. 0.07°C ± 0.02°C per decade).”
Umm, that sounds like a convoluted way to say there was no warming in the first half of the century. 5 x 0.13 = 0.65, 10 x 0.07 = 0.70, so 0.05 for the first 50 years. Error ranges are left as an exercise for the reader. That clearly disagrees with the hadCRUT data below.
Anthony:
“I’m really beginning to see earth’s atmospheric processes more like that of an analog circuit with a variety of electrical components. There’s voltage, current, capacitance, reluctance and inductance in the irradiance-air-ocean systems.
I think an analog computer might very well model the earth’s atmosphere more accurately than a digital one. Digital signals do not exist in nature, but analog signals are abundant.”
Back in my EE systems class the instructor generally drew analogies to mechanical systems, e.g. springs, masses, dashpots. Digital computers replaced analog computers for very good reasons, but if you do make an analog analog, make it mechanical – far more photogenic and TV news media would be thrilled to air it. 🙂
Right after that semester the Club of Rome report came out with its two page system model. Then I read a SF book (Greybeard, by Brian Aldiss) that looked at England after an economic collapse. I was depressed for the rest of the month, but eventually figured out the Club’s predictive powers on resources and adaptations reflected at static world.
“Given that the temperature change has been about .7 rather than .3, I’ll wager it is a silicon rather than a germanium transistor.”
I got it, I got it! Boy, are you old. I might have a Germanium transistor or two in the basement….
I apologize for wandering OT, but following up on DNorris’ question:
In Dr. Svalgaard’s comments linked above, he states:
“Note, that Lean herself [with Wang, 2005] has published later reconstructions where the change since the MM was only 1 W/sqm and since 1900 only 0.5 W/sqm, effectively halving the increase you calculate.”
See the trace labeled as “Wang” in the plot. Although Dr. Svalgaard does not specifically state that this is the 2005 reconstruction, I’m pretty certain this is the implication. It much more closely matches those of the other solar scientists.
The AGW true believers will sieze on any error to discredit the arguments of skeptics so it is important we keep each other up to date. I appreciate your open mind in requesting futher information.
MattN,
On your question about why the cooling of the 1940’s to 1960’s didn’t take us back to where we were at the beginning of the 20th Century, wait for Part II. If you want to imagine what’s coming, ask yourself about what’s happened with solar activity during the 20th century. Figure 2 only shows part of the puzzle. None of what we are doing discounts the role of UHI, or crummy siting of surface stations, in possibly biasing the raw data we are working with so that the absolute values are higher than they would otherwise be at the end of the 20th century. But were focusing on something more fundamental.
I do hope people realize that what’s being plotted in Figure 2 are “rates of change” in temperature, not absolute values. Basically, Figure 2 plots the time derivatives, dx/dt, of the smoothed series from Figure 1. So Figure 2 is telling us that from one peak of a 22 year cycle to the next, dx/dt’s initially drop off, reach a nadir, and then begin to climb back up to the next peak. As to the “why” of that, again, wait for Part II.
Terry,
I’ve suggested the same thing — trying to get this published eventually in a peer reviewed journal. I’ve published in peer reviewed journals in the past, and have served as a referree — in economics, though, not climate science. Since we’re not in academia, there’s a certain bias that exists in the peer review process that we have to overcome. Given how politicized this issue has become, if it stands up to the kind of scrutiny we’re going to get from those who have stakes to protect, what we learn from that kind of scrutiny will help us to prepare something that is more likely to get published. We’ll just have to wait and see.
As to why we chose the particular filter we chose — that’s going to be part of the prejudice or bias we have to overcome, because it has its origins in economics. But time series are time series, and economics has learned a great deal about how to explore the properties of time series. When I started all of this, like some other economists, my first thought was to use some kind of ARMA (Box-Jenkins) analysis. But that would be treating temperature time series like a stock market trend where differencing is used to achieve stationarity and the data follows a random walk. That will not do here, because I think it is fundamentally wrong to believe that the processes we are investigating follow a random walk. It boils down to whether we expect dx/dt to be random or not. We don’t, not where “x” relates to physical processes like the influence of, say, the solar cycle on climate. The solar cycle shows a very well known pattern of variation in time. If it is influencing temperature, then it is going to show that influence through the dx/dt of temperature. HP filtering is an excellent tool for this. As to the role of lambda in HP filtering, we treat that in Part II.
Bob Tisdale,
I’m not sure of what you’ve done, but if you wait, then maybe you can put what you’ve done into a larger context. We’re just getting started. 🙂 I will tell you, though, that I don’t envisage anything in our Part II that might steal your thunder, whatever it is. We’ve already alluded to the role of terrestrial dynamics, where large scale, long lived oceanic oscillations seem to sit on top of Hale cycle periodicities, as it were, and modulate the influence of the solar cycle. I think the longer 65-70 year climate cycle is just that — the influence of terrestrial dynamics interacting with solar influences, to produce a complex system. Again, you’ll see more of where we are going with this in Part II, and then I’d be delighted to see what you’ve done with the PDO (and see how it compares to what we’ve done, but will not be specifically including in Part II).
Pamela Grey,
Why don’t you ask your question again, after we post Part II? You’ll should see something about how we would propose using HP smoothing to look for a relationship between temperature and sunspots.
Note to Anthony:
I’m talking about the chart I sent you this morning. While you work on finishing up the “science” part of Part II, I’m going to work on how to integrate that chart, and something else I’m thinking about, into Part II.
pablo an ex pat,
LOL!
Raven,
If I understand the science we’ll be presenting in Part II, it will not depend on the Sun’s radiative output, but how it gets modulated by something else. 🙂
As to your question about CO2, I don’t really question the science that says it should cause warming. As you intimate, the question is how much? I don’t think we are going to be able to show anything with an annual time series like we’re looking at here. To repeat what I said above, we’re basically exploring relationships in “dx/dt’s” There is a well known pattern to the dx/dt of CO2 emissions. But I wouldn’t be at all surprised that when we “drill down” and look at it this way, we will find the “dx/dt” of CO2 levels follows temperature, it doesn’t lead it. I’m pretty sure that’s already been explored. Look for studies dealing with “interannual” variations in CO2.
Basil
Jeff C. – Thanks… I will digest that tonight.
Raven – C02 Effect… Thanks. I am familiar with the work Lindzen and others on the decreasing effect of CO2 with increasing concentrations, but was actually looking for your Solar Output sources.
Onwards:
This post triggered a vague recall of a paper I read by Landscheidt. I finally found it at Still Waiting for Greenhouse.
SOLAR ACTIVITY:
A DOMINANT FACTOR IN CLIMATE DYNAMICS
RIP John and Theodor 🙁
Raven,
http://www.junkscience.com/Greenhouse/co2greenhouse-X2.png
I don’t think anyone can say exactly how little CO2 drove the temp. in the 20th century. Personally I don’t believe anyone who claims to.
Landscheidt made climate predictions based on solar activity, and some were right on the money (though he never told us about the ones that were wrong).
I have qualms about the direction this is all going. Like the CO2 kooks, we are trying to find one single, easy factor that drives the climate. I think it’s far more complex than that.
I will say, however, that the sun is at least 10 times a greater factor than CO2. Research dollars spent on solar research would certainly be a much wiser investment.
Using a cascading algorithm such as the one you used, it goes without saying that the results of the second step (Fig. 2) are very sensitive to the accuracy of the filter applied in the first step — i.e., how good it actually was at distinguishing the short-term “noise” from the actual trend. While that partially depends on the accuracy of the tau and lambda terms employed, it also depends upon two more assumptions which I think are far more critical: (a) there is only one trend, and (b) the “noise” (i.e., short term variations) is/are symmetric in their shape. To the extent that any of those things are in error, then the results of the second step will represent an accumulation of that error. And just an eye-ball examination of the first figure in your “The Solar to Global Warming Connection – A short essay” post suggests the assumption of symmetry is violated: the solar cycle variations are positively skewed (for laymen: the rising edge of each “hump” is steeper than the falling edge). Since you are attempting to imply something about solar cycles from temperature records, at the very least it seems to me encumbent upon you to demonstrate that the temerature records don’t violate those assumptions as well. If they do, then the HP filter is not the most appropriate one to use. A non-symmetric algorithm (e.g., a wavelet) is more appropriate.
Succeding in that, then there’s the even more critical assumption of a single trend. For that to be viable you’d have to assume solar irradiance is coupled with temperature through a single mechanism. In other words, you’d have to assume that land masses, oceans, and the atmosphere all react the same way, symmetrically, and on the same time scale — or at least that one of the three dominates to the extent that it obviates the others. IMO, that stretches credulity to the breaking point. Thus, I would argue that using an HP filter, combined with a cascading algorithm is not the way to go.
By the way, have you guys read Scafetta and West, 2007? It seems to me their approach is similar to yours (they take a heuristic approach), but vastly superior in a variety of ways.
REPLY: Rather than speculating on results you haven’t seen yet, may I suggest waiting for part 2 before claiming the methodology inferior? -Anthony
Paddy: Actually, I was talking about the Svensmark hypothesis — ie. that the sun’s magnetic field modulates the high energy cosmic ray flux reaching the lower atmosphere and hence the condensation nuclei for low level clouds over the oceans in particular. The Lindzen iris hypothesis as I understand it is a much shorter-term negative feedback mechanism. Essentially, storms in the tropics reduce the amount of water vapor in the stratosphere allowing more IR energy to escape and thus cooling the earth. The transistor analogy relates more to the Svensmark hypothesis as a mechanism for amplifying solar effects — the turning on and off of the cloud cover by fluctuations in the sun’s magnetic field strength modulates the flow of light from the sun like a small signal on a transistor gate modulates the much stronger current flow through the transistor.
“Research dollars spent on solar research would certainly be a much wiser investment.”
That’ll never do. We can’t sell solar offsets….
MattN: Here’s an illustration that may help. Solar is a pain unless you smooth it. While solar irradiance (TSI) leveled off and dropped a little mid-century, it didn’t fall back to the levels it was at in the early 1900s-late 1800s.
http://tinypic.com/fullsize.php?pic=5oa929&s=3&capwidth=false
Fascinating. Do you have a mechanism where by the solar cycles should drive the rate of change of global temperature? As far as I, maybe mistakenly, understand the cosmic ray theory is that the clouds they generate will modulate the equilibrium point of the earth’s energy balance, directly effecting the temperature, not its rate of change. But you show a good correlation with the rate of change.
Have you been able to isolate the components that are directly attributable to the small variations in TSI and the increase of CO2?
The results are interesting. I followed the procedure and made a spectral analysis of the differences time series (figure 2). There are two cycles, a low intensity one with a 14 year cycle and one with a 21 year cycle:
http://tinypic.com/view.php?pic=s2cxva&s=3
Two suggestions:
1. For the next post try to make a spectral analysis of the signal
2. Try to apply the same procedure for the temperature of the southern hemisphere
Rico,
Ditto what Anthony said. Yes, I’ve certainly read Scafetti and West. And it is an elegant piece of work. But it doesn’t show what we’re showing. For all their effort, the most they can say about the 20th century is:
“During the 20th century one continues to observe a significant correlation between the solar and temperature patterns: both records show an increase from 1900 to 1950, a decrease from 1950 to 1970, and again an increase from1970 to 2000.”
We’ve shown something entirely different, and potentially more significant: that the rate of change in a smoothed global temperature series follows a pattern that tracks with almost pinpoint accuracy the 22 year Hale cycle. They claim a broad correspondence to three periods in the 20th century. Figure 2 shows close correspondence to six Hale cycles over the past 130 years.
And if you think that is something — I certainly do — wait until Part II.
Basil
I think CO2 levels are a cyclic function of ocean absorption. The ocean is the biggest sponge of CO2. But it only acts as a sponge under certain conditions that appear to be tied to cycles. The CO2 that is absorbed than gets deposited in deep ocean bottom material. It does not cough it back up. Then, in the non-absorbing part of the cycle, it stops soaking up CO2, leaving it to rise into the upper stratum of the atmosphere to get measured by alarmists. When the time comes for the ocean to once again be receptive to CO2, the process begins all over again. We should be entering an ocean absorbing phase right about now, if it hasn’t already begun. This long cycle is just a theory since we haven’t been measuring CO2 long enough to discover a pattern. CO2 probably does serve to warm us up a bit but we should be considering the possibility that it is also cyclic in nature.
Anthony: Rather than speculating on results you haven’t seen yet, may I suggest waiting for part 2 before claiming the methodology inferior?
I didn’t speculate on much of anything. I commented on what you wrote, and on the logic contained in it. The assumptions I questioned were your own, and by extention those contained in your method. That’s not speculation or opinion, it’s logic.
I did, indicate that your assumption that solar irradiance is coupled with temperature through a single mechanism (which is what the assumption of a single trend requires) strains credulity. And I suppose that could be considered opinion. Nonetheless, the assumption itself does logically require that land masses, oceans, and the atmosphere all react the same way to irradiative forcings. And that would be an extraordinary claim. As such it requires extraordinary evidence. And you didn’t present any.
REPLY: “And you didn’t present any.” Well then, again I suggest kindly stay tuned for part 2.
RE: An historic and stable value for TSI and Svalgaard.
I have high regard for Dr. Svalgaard’s encyclopaedic grasp of all details solar, but I cannot condone regarding his opinions and theories as mainstream. Try his old collaborators, Schatten and Hoyt if orthodox belief is your central concern.
JM,
Interesting. What do you see spectral analysis telling us that we’re not seeing with the use of HP smoothing and first order differencing?
I have nothing against other tools and techniques. We often come at the same thing by different means. It doesn’t mean necessarily that one is better than the other. But unless you can tell me what spectral analysis will show me that I’m not already seeing, I already have a full plate of things to do.
The suggestion to look at the Southern continent is a good one. But don’t look for it in Part II. We are just breaking some ground here, and don’t expect these initial posts to be the final word. More like a quick introduction to a new way of looking at things.
But I do appreciate the feedback. I think the technique is one that has broad application in climate science, where we have historical time series data. It sounds like Bob Tisdale may be using it to look at the PDO.
Looking at the global temperature trend is just a start, and for very little effort, is producing some interesting results. Applying it to the SH is something to do, at some point.
Basil
REPLY: I agree that the southern hemispshere might be interesting to look at separately. I think what JM is getting at is that a spectral analysis would show which cycle or multiple thereof is the dominate peak. I certainly have nothing against the idea. Perhaps when we get a variety of feedbacks from this two part presentation, we can look further. – Anthony
Now that the global warming community has bullied Judith Lean into reconstructing her solar reconstructions at least three times now and the latest numbers show hardly any solar variation whatsoever, it is clear that the global warming community is going to re-write every historical record there is until only CO2 matters.
Effectively, solar irradiance is useless now for any kind of analysis since it hardly varies at all. All that can be used is “sunspot number” which obviously does not account for all the variation in solar output across the entire EM spectrum.
Its a good thing we have Roy Spencer and John Christy to keep the land-based temperature records honest going forward (not the historical ones however) but they could be silenced at any time as well.
Rico,
If I may, let me back up a bit ask something for clarification. You say:
“Succeding in that, then there’s the even more critical assumption of a single trend. For that to be viable you’d have to assume solar irradiance is coupled with temperature through a single mechanism.”
I do not follow you on this. Any single trend can be the result of multiple independent variables or influences. Personally, based on what we will present in Part II, I’m not sure that we should have brought solar irradiance into the discussion at all. Actually, I don’t think we have to show at all what the physical mechanism is that is involved in the connection between the Sun and globally averaged temperature to justify the title of this series. To the extent that we can shed any light on the physical mechanism involved, that’s serendipity. And that’s what has been saved for Part II.
For now, how has what we’ve done any different, say, than paleoclimate studies of tree rings that show through MTM or spectral analysis evidence of a 22 year periodicity in the data? When such studies are reported, don’t they just usually claim that this is indication of a solar influence? Would a referee reviewing such a paper reject it because it doesn’t contain a theory about the solar physics involved?
Basil
Anthony: “And you didn’t present any.” Well then, again I suggest kindly stay tuned for part 2.
Okay, I’ll wait for part 2. Until then I will simply speculate (lol!) that you will (a) better explain the values you used for tau and lambda, (b) provide a response profile of how the resulting filter applies to real life time scales (or at least provide the numbers that would allow someone else to do it), and (c) attempt to quantify the apparent forcing relationship between the Hale cycle and the temperature response (including the necessary logic to justify yourselves). It seems to me that if you don’t do that, then merely showing some sort of a qualitative relationship between the Hale cycle and temperature — even if “tight” — wouldn’t be exactly surprising.
Further, if you’re seriously contemplating submitting your findings to a real, honest to goodness peer reviewed journal, then it seems to me you are at the very least compelled to discuss them in light of Scafetta and West, along with others who have noted an apparent secular relationship between one or another (or more) frequency of TSI oscillation and surface temperature (e.g., Eddy, 1976; Lassen and Friis-Christensen, 1995; Lean et al., 1995; Crowley and Kim, 1996; Hoyt and Schatten, 1997; White et al., 1997, 2003). But I assume you already know that — assuming your intent is to seriously submit your study for peer review. If not, then I guess anything goes.
REPLY: See Basils response.
««Interesting. What do you see spectral analysis telling us that we’re not seeing with the use of HP smoothing and first order differencing?»»
Basil,
Spectral analysis is a more objective method to find cycles in the time series. It allows the detection of cycles with frequencies that may be obscured by other cycles.