Guest Post by Willis Eschenbach
I was pointed to a 2010 post by Dr. Roy Spencer over at his always interesting blog. In it, he says that he can show a relationship between total solar irradiance (TSI) and the HadCRUT3 global surface temperature anomalies. TSI is the strength of the sun’s energy at a specified distance from the sun (average earth distance). What Dr. Roy has done is to “composite” the variations in TSI. This means to stack them one on top of another … and here is where I ran into trouble.
I couldn’t figure out how he split up the TSI data to stack them, because the cycles have different lengths. So how would you make an 11-year composite stack when the cycles are longer and shorter than that? And unfortunately, the comments are closed. Yes, I know I could write and ask Dr. Roy, he’s a good guy and would answer me, but that’s sooo 20th century … this illustrates the importance of publishing your code along with your analysis. His analysis may indeed be 100% correct—but I can’t confirm that because I can’t figure out exactly how he did it.
Since I couldn’t confirm Dr. Roy’s interesting approach, I figured I’d take an independent look at the data to see for myself if there is a visible ~ 11 year solar signal in the various temperature records. I started by investigating the cycle in the solar variations themselves. The TSI data is here. Figure 1 shows the variations in TSI since 1880
Figure 1. Monthly reconstructed total solar irradiance in watts per square metre (W/m2). As with many such datasets this one has its detractors and adherents. I use it because Dr. Roy used it, and he used it for the same reason, because the study he was investigating used it. For the purposes of my analysis the differences between this and other variations are minimal. See the underlying Lean study (GRL 2000) for details. Note also that this is very similar to the sunspot cycle, from which it was reconstructed.
If I’m looking for a correlation with a periodic signal like the ~ 11-year variations in TSI, I often use what is called a “periodicity analysis“. While this is somewhat similar to a Fourier analysis, it has some advantages in certain situations, including this one.
One of the advantages of periodicity analysis is that the resolution is the same as the resolution of the data. If you have monthly data, you get monthly results. Another advantage is that periodicity analysis doesn’t decompose a signal into sine waves. It decomposes a signal into waves with the actual shape of the wave of that length in that particular dataset. Let me start with the periodicity analysis of the TSI, shown in Figure 2.
Figure 2. Periodicity analysis of the Lean total solar irradiance (TSI) data, looking at all cycles with periods from 2 months to 18 years. As mentioned above, there is a datapoint for every month-by-month length of cycle.
As you can see, there is a large peak in the data, showing the preponderance of the ~ 11 year cycle lengths. It has the greatest value at 127 months (10 years 7 month).However, the peak is quite broad, reflecting the variable nature of the length of the underlying sunspot cycles.
As I mentioned, with periodicity analysis we can look at the actual 127 month cycle. Note that this is most definitely NOT a sine wave. The build-up and decay of the sunspots/TSI occur at different speeds. Figure 3 shows the main cycle in the TSI data:
Figure 3. This is the shape of the main cycle for TSI, with a length of 10 years 7 months.
Let me stop here and make a comment. The average cyclical swing in TSI over the period of record is 0.6 W/m2. Note that to calculate the equivalent 24/7 average insolation on the earth’s surface you need to divide the W/m2 values by 4. This means that Dr. Roy and others are looking for a temperature signal from a fluctuation in downwelling solar of .15 W/m2 over a decade … and the signal-to-noise ratio on that is frankly depressing. This is the reason for all of the interest in “amplifying” mechanisms such as cosmic ray variations, since the change in TSI itself is too small to do much of anything.
There are some other interesting aspects to Figure 3. As has long been observed, the increase in TSI is faster than the decrease. This leads to the peak occurring early in the cycle. In addition we can see the somewhat flat-topped nature of the cycle, with a shoulder in the red curve occurring a few years after the peak.
Looking back to Figure 2, there is a secondary peak at 147 months (12 years 3 months). Here’s what that longer cycle looks:
Figure 4. The shape of the 147-month cycle (12 years 3 months) in the Lean TSI data
Here we can see an advantage of the periodicity analysis. We can investigate the difference between the average shapes of the 10+ and the 12+ year cycles. The longer cycles are not just stretched versions of the shorter cycles. Instead, they are double-peaked and have a fairly flat section at the bottom of the cycle.
Now, while that is interesting, my main point in doing the periodicity analysis is this—anything which is driven by variations in TSI will be expected to show a clear periodicity peak at around ten years seven months.
So let me continue by looking at the periodicity analysis of the HadCRUT4 temperature data. We have that temperature data in monthly form back to 1880. Figure 5 shows the periodicity analysis for the global average temperature:
Figure 5. Periodicity analysis, HadCRUT4 global mean surface air temperatures.
Bad news … there’s no peak at the 127 month period (10 year 7 month, heavy dashed red line) of the variation in solar irradiance. In fact, there’s very little in the way of significant periods at all, except one small peak at about 44 months … go figure.
Next, I thought maybe there would be a signal in the Berkeley Earth land temperature data. The land should be more responsive than the globe, because of the huge heat capacity of the ocean. However, here’s the periodicity analysis of the Berkeley Earth data.
Figure 6. Periodicity analysis, Berkeley Earth global land surface air temperatures. As above, heavy and light red lines show main and secondary TSI periods.
There’s no more of a signal there than there was in the HadCRUT4 data, and in fact they are very similar. Not only do we not see the 10 year 7 month TSI signal or something like it. There is no real cycle of any power at any frequency.
Well, how about the satellite temperatures? Back to the computer … hang on … OK, here’s the periodicity analysis of the global UAH MSU T2LT lower tropospheric temperatures:
Figure 7. Periodicity analysis, MSU satellite global lower troposphere temperature data, 1979-2013.
Now, at first glance it looks like there is a peak at about 10 years 7 months as in the TSI. However, there’s an oddity of the periodicity analysis. In addition to showing the cycles, periodicity analysis shows the harmonics of the cycles. In this example, it shows the fundamental cycle with a period of 44 months (3 years 8 months). Then it shows the first harmonic (two cycles) of a 44-month cycle as an 88 month cycle. It is lower and broader than the fundamental. It also shows the second harmonic, in this case with a period of 3 * 44 =132 months, and once again this third peak is lower and broader than the second peak. We can confirm the 132 month cycle shown above is an overtone composed of three 44-month cycles by taking a look at the actual shape of the 132 month cycle in the MSU data:
Figure 8. 132 month cycle in the MSU satellite global lower troposphere temperature data.
This pattern, of a series of three decreasing peaks, is diagnostic of a second overtone (three periods) in a periodicity analysis. As you can see, it is composed of three 44-month cycles of diminishing size.
So the 132-month peak in the T2LT lower troposphere temperature periodicity analysis is just an overtone of the 44 month cycle, and once again, I can’t find any signal at 10 years 7 months or anything like it. It does make me curious about the nature of the 44-month cycle in the lower tropospheric temperature … particularly since you can see the same 44-month cycle (at a much lower level) in the HadCRUT4 data. However, it’s not visible in the Berkeley Earth data … go figure. But I digress …
I’m sure you can see the problem in all of this. I’m just not finding anything at 10 years 7 months or anything like that in either surface or satellite lower troposphere temperatures.
I make no claims of exhausting the possibilities by using just these three analyses, of the HadCRUT4, the Berkeley Earth, and the UAH MSU T2LT temperatures. Instead, I use them to make a simple point.
If there is an approximately 11 year solar signal in the temperature records, it is so small that it does not rise above the noise.
My best wishes to everyone,
w.
PERIODICITY THEORY: The underlying IEEE Transactions paper “Periodicity Transforms” is here.
DATA: As listed in the text
CODE: All the code necessary for this is in a zipped folder here. At least, I think it’s all there …
USUAL REQUEST: If you disagree with something I said, and yes, hard as it is to believe it’s been known to happen … if so, please quote the exact words you disagree with. That way, everyone can understand your point of reference and your objections.
Leif, I cannot find the exact thread that I had in mind at the moment but here is something equivalent:
“Solar wind velocity is often high near solar minimum, where the absence of solar activity favors the creation of large coronal holes”
http://wattsupwiththat.com/2010/05/15/hey-dude-where%E2%80%99s-my-solar-ramp-up/#comment-392261
lsvalgaard says:
April 13, 2014 at 9:57 am
6378e3 * sqrt(9^2+17^2)/60*pi/180 = 35,687 meters
Yeah, that’s small.
Pamela Gray says:
April 13, 2014 at 10:12 am
Nice to see you brought along your sandals and gourds.
Ulric Lyons says:
April 13, 2014 at 10:12 am
“Solar wind velocity is often high near solar minimum, where the absence of solar activity favors the creation of large coronal holes”
Yes, you can see that in my plot http://www.leif.org/research/Climatological%20Solar%20Wind.png
where the green curve shows solar wind speed. Note that it peaks just before solar minimum
Bart says:
April 13, 2014 at 10:14 am
Yeah, that’s small.
completely irrelevant. There are three components of the nutation;
1) luni-solar tides
2) polar motion [wobble] due to changes of inertia
3) core nutation
(1) is large, the others are small.
You claim that the nutation moves the oceans around. “the sloshing of the oceans as forced by nutation of the Earth’s polar spin axis”. It is the other way around. /end-spoon-feeding
lsvalgaard says:
April 13, 2014 at 10:23 am
No, Leif. The Lunar/Solar induced nutation is due mostly to the fact that the Earth is an oblate spheroid. The Sun and the Moon tug on the Earth’s spin axis, due to the gravity gradient torque (see equation (6.17)). This is well-known and understood.
But, have it your way. It is moot. Either way, it has a strong periodicity of about 18.6 years, and the tilt with respect to the nominal spin axis has a period of half that, at 9.3 years. Combine it with the 11 year solar cycle, and you get 60 years and 5 years. Combine it with a more detailed model of solar activity, with harmonics at 10, 10.8, and 11.8 years, and you get a more complex waveform, which has periodicities in the range of ~60 years, and less than 5 years.
That is what is seen in the temperature records. It is a powerful influence – nothing like the infinitesimal influence of other planets.
“But, have it your way. It is moot.”
It is moot for the argument at hand. But, I hasten to add, it is in no-wise a concession. For the nutational dynamics in general, Leif is wrong. The forced nutation of the Earth’s spin axis is mostly from the oblate mass distribution of the Earth, and the oceans in their entirety form only a small portion of that mass.
Bart says:
April 13, 2014 at 10:39 am
It is moot
You avoided responding to the point which was your claim that the nutation moves the oceans around: “the sloshing of the oceans as forced by nutation of the Earth’s polar spin axis”.
That is your nonsense I pointed out.
That is what is seen in the temperature records.
The old saw ‘correlation is not causation’ applies here.
Bart says:
April 13, 2014 at 10:47 am
It is moot for the argument at hand. But, I hasten to add, it is in no-wise a concession. For the nutational dynamics in general, Leif is wrong.
OK, I should have said the lunar-solar torques. I guess ‘tides;’ slipped in because you said “The tides are not minute.” Strange how the mind can get trapped,
Anyway, you avoided responding to the point which was your claim that the nutation moves the oceans around: “the sloshing of the oceans as forced by nutation of the Earth’s polar spin axis”.
lsvalgaard says:
April 13, 2014 at 10:51 am
See above.
lsvalgaard says:
April 13, 2014 at 10:57 am
It is your belief that the movement of the Earth’s spin axis does not affect the tides?
Bart says:
April 13, 2014 at 10:57 am
See above.
Not responsive. Let me try this: Verify here that you said and mean “the sloshing of the oceans as forced by nutation of the Earth’s polar spin axis”
It should be obvious to any reasonable onlooker, other than perhaps Pamela in her cheerleader outfit, that the motion of the Earth’s spin axis affects the tides. The motion of the ocean affects the manner in which it stores radiant energy from the Sun. This creates a modulation of the solar cycle with the nutation of the Earth’s spin axis to affect the climate.
It is a powerful influence, and it is, at least at the top level, consistent with observations of temperature variations. That is the point I was trying to make, and I have made it. Since I do not stand a whelk’s chance in a supernova of influencing the hidebound opinions of Dr. Svalgaard, I am going to call it a day. Anything further he has to say on the topic, I refer you to Joe Pesci’s opening argument in the trial portrayed in My Cousin Vinny.
Bart says:
April 13, 2014 at 11:06 am
I am going to call it a day
Running away from responding to “the sloshing of the oceans as forced by nutation of the Earth’s polar spin axis”.
It should be obvious to any reasonable onlooker, other than perhaps Pamela in her cheerleader outfit, that the motion of the Earth’s spin axis affects the tides.
People that research this, e.g., http://www.leif.org/research/Thesis-Weiss-Ocean-Tides.png do not find this ‘obvious’, but perhaps you would not call them ‘reasonable’.
lsvalgaard says:
“Yes, you can see that in my plot http://www.leif.org/research/Climatological%20Solar%20Wind.png
where the green curve shows solar wind speed. Note that it peaks just before solar minimum”
What I can see *nearest* to the minima is the low in plasma speed, and the second lowest point is at the maxima, where the density/pressure is also at it’s lowest. So clearly with lows near sunspot minima AND maxima it does not follow the cycle, and I restate my original comment:
Well looking at the solar metric that has considerable variability, and that does relate at an event level to teleconnections such as ENSO and the AO/NAO, i.e. the solar wind, it does not simply follow the sunspot cycle. There is typically a reduced level just after the cycle minima, and again around the cycle maxima, with an interval of about a third of a cycle, 3.69yrs or 44.33 months for the average cycle. That period would likely be more consistent than the periods between cycle minima, and particularly [more consistent than the] the highly variable periods between cycle maxima.
Pamela Gray says:
April 13, 2014 at 10:12 am
I thought of Vuk and ……explaining their theories …
Hi Ms. Gray
I am flattered indeed, that you would think of me first, surely my minor persona is hardly worth of your esteemed attention, but that said, I thank you.
In my case, with respect and no reflection on efforts of the others, mentioned or implied, theory hardly, even hypothesis is an unattainable proposition, just an idle mind’s data manipulation.
Dear Ms Gray I wish you a pleasant and effortless progress in all of your endeavours.
m.v
Ulric Lyons says:
April 13, 2014 at 11:20 am
What I can see *nearest* to the minima is the low in plasma speed, and the second lowest point is at the maxima, where the density/pressure is also at it’s lowest. So clearly with lows near sunspot minima AND maxima it does not follow the cycle,
[You] are not being clear. If we see the same behavior in every cycle, then obviously the variable has a solar cycle variation. All the solar wind parameters have a solar cycle variation that is different from that of the SSN. In particular the solar wind speed has a maximum just before solar minimum. A typical example is for the year 2008. See slide 18 of http://www.leif.org/research/Historical%20Solar%20Cycle%20Context.pdf
Folks, I collect data all the time using research based valid and reliable tools, and am quite familiar with proper as well as improper use of statistics and analysis of statistical result. To the extent that I have put my job on the line for standing behind proper statistical methods. And have suffered for it. Would you be willing to lose your job over your awkward mechanism and statistical nightmare?
You may have fallen into this trap: Wriggle matching between two separate entities that have a variety of short and long term random walk oscillations combined with additional subcomponents and having many variables, can and often are forced to, match. That a match is found is predictable and can even be shown mathematically.
Thought experiment: Randomly generated signal data produced with separate signal generators (to the degree that they are made differently by two different and separate manufacturers, the signals on their face are clearly not the same, and one is on the Moon and the other on the Earth) thus described can be correlated, even highly correlated if analysed and tortured enough. That a plausible mechanism can be made that links the two signal generators is dubious but many will cough one up anyway.
I am bound to suggest that were I to give you guys a data series from the sounds of starlings and a data series from windshield wiper oscillations obtained from a school bus, and call them some kind of sciency sounding universe/galaxie/solar system/moon/Earth/Neptune signal, you would find a correlation and say that one is related to the other, with a plausible mechanism waiting to be found.
Until such a time as the climate trend null hypothesis (intrinsic variability, which DOES have a plausible mechanism) can be dismissed, I recommend this: Accept that you have nothing to show for your research into this or that solar system-related idea or pet theory that can be demonstrated to have superiority over the null condition.
That Leif puts his money where his mouth is, shares his raw data, stands in front of equals and better to present, has been peer reviewed/vetted at every stage, and has proposed reasonable mechanisms, gives him a large leg up compared to you guys. So yes, I readily admit to cheerleading good scientific work once I have vetted it for myself. And based on my reading, I don’t see any comparison at all between Leif’s work and what you all have proposed.
Willis Eschenbach says:
April 12, 2014 at 5:36 pm
..Thanks, Mario. I don’t think you quite get what I’ve done. I’ve looked, not for TSI, but for ANYTHING that moves in sync with sunspots. This includes UV, TSI, heliomagnetic field, and cosmic rays. If any of them through any mechanism were affecting the temperature, it would show up as an ~ 11 year signal in the temperature data … but to data, we find no such signal.
This negative result includes, as Beng says, ultraviolet, because UV varies on the same ~ 11 year cycle as the sunspots and the TSI and the cosmic rays.
w.
—————————————————
“””but for ANYTHING that moves “””” pssst don’t go hunting with Willis..lol
Well, I have something that moves, breathes and lives with solar cycle. GCR cosmic radiation messing up solar radiation.. perhaps.. But I’m skeptical of the TSI not varying enough..
This little study from Athens, incorporates the Cosmic Ray Induced Ionization CRII models (1+2) into their local model, giving a global view of GCR induced ionization in Earth’s atmosphere.
Even going so far as to say, that during a Maunder type minimum, the primary cause of ionization in Earth’s Atmosphere would come from GCR…
Calculation of the cosmic ray induced ionization for the region
of Athens
P Makrantoni1, H Mavromichalaki1, I Usoskin2, A Papaioannou1
Abstract. A complete study of ionization induced by cosmic rays, both solar and galactic, in
the atmosphere, is presented. For the computation of the cosmic ray induced ionization, the
CRII model was used [1] as well its new version [2] which is extended to the upper
atmosphere. In this work, this model has been applied to the entire atmosphere, i.e. from
atmospheric depth 0 g/cm2, which corresponds to the upper limit of the atmosphere, to 1025
g/cm2, which corresponds to the surface…
..2. The CRII model
The CRII model is a full numerical model, which computes the cosmic ray induced ionization in the
entire atmosphere, all over the Globe. The model computations reproduce actual measurements of the
atmospheric ionization in the full range of parameters, from Equatorial to Polar Regions and from the
solar minimum to solar maximum.
Roughly, the CRII rate expressed as the number of ion pairs produced in one gram of the ambient
air per second (ion pairs/gr. sec) at a given atmospheric depth x can be represented in as follows:
..3. Results
Using the CRII model [1], [2] a study of the distribution of ionization during the solar cycle 23 on a
monthly and yearly basis was performed. A gradual increase of the ionization rate from the solar
maximum to the solar minimum was observed.
The results at the solar maximum (year 2000) and minimum (year 2010), for a Polar region (Rc=0.1
GV), an Equatorial region (Rc=14.9 GV) and a middle latitude region (Athens, Rc=8.53 GV), as a
function of the atmospheric depth, are presented in Figure 1. It is obvious that during the solar
maximum (2000), the ionization has minimum values, while during the solar minimum (2010), the
ionization is maximum. This indicates that the ionization follows the behavior of the cosmic rays,
which is negatively correlated with the solar activity. It is important to mention that during the solar
maximum, the ionization is almost two times greater at the Poles than in Athens, while during the
solar minimum, it is almost three and a half times greater. In all cases, the ionization rate is maximum
at the atmospheric depth x=100 g/cm2, with a shift to lower atmospheric depths in the Polar regions.
..Furthermore, we compared
these distributions with the value of ionization in the case of zero solar activity, as it was during the
«Maunder Minimum», and found that the ionization in the atmosphere due to cosmic rays is constant
and greatest! This means that the contribution of galactic cosmic rays, even if the contribution of solar
cosmic radiation is negligible, it is essential to the creation of ions in the atmosphere and with the
maximum value of ionization. This may be associated with the Little Ice Age (1645-1715), during
which occurred the Maunder Minimum, i.e. zero solar activity (φ = 0).
http://iopscience.iop.org/1742-6596/409/1/012232/pdf/1742-6596_409_1_012232.pdf
Carla says:
April 13, 2014 at 3:08 pm
This may be associated with the Little Ice Age (1645-1715), during which occurred the Maunder Minimum, i.e. zero solar activity (φ = 0).
No cigar, Carla, the modulation parameter (φ) was not zero during the MM. In fact, solar modulation of cosmic rays was as strong back then as now.
lsvalgaard says:
“[You] are not being clear. If we see the same behavior in every cycle, then obviously the variable has a solar cycle variation.”
As there are two local minima in the solar wind through each cycle, one just after minimum and another around maximum, the periods between these minima are 3.69yrs, 7.38yrs, and of course both repeating every 11.07yrs on average. So it’s not a simple ~11yr signal. But due to the variation in cycle lengths, the 7.38 and 11.07 periods have more variation in length than the ~3.69yr min-to-max section of the cycles, so the 3.69yr periodicity should be stronger signal.
Ulric Lyons says:
April 13, 2014 at 3:45 pm
So it’s not a simple ~11yr signal.
Yes it is as the signal repeats every 11 years. It is not a sine-curve, but who said it was?
Ulric Lyons says:
April 13, 2014 at 3:45 pm
so the 3.69yr periodicity should be stronger signal.
You make the same mistake as Bart, believing that there is a physical signal of that length. There is not. The ‘signal’ comes about because there are different physical reasons for the various peaks.
lsvalgaard says:
April 13, 2014 at 3:30 pm
Carla says:
April 13, 2014 at 3:08 pm
This may be associated with the Little Ice Age (1645-1715), during which occurred the Maunder Minimum, i.e. zero solar activity (φ = 0).
No cigar, Carla, the modulation parameter (φ) was not zero during the MM. In fact, solar modulation of cosmic rays was as strong back then as now.
——————————————————
Yes, I know Dr. S.
Since NASA announced the Space Age High in GCR, you have mentioned it a gazillion times, bout the modulation during MM and so ..
Starting to get a phobia about the atmosphere lowering again, but this time a little lower than last time, which was already 38% lower than the time before that..
This GCR ionization doesn’t come with any up and out solar wind and eeeeeek…
Willis say:
“Thanks, Mario. I don’t think you quite get what I’ve done. I’ve looked, not for TSI, but for ANYTHING that moves in sync with sunspots. This includes UV, TSI, heliomagnetic field, and cosmic rays. If any of them through any mechanism were affecting the temperature, it would show up as an ~ 11 year signal in the temperature data … but to data, we find no such signal.”
++++++++++++
Thank you Willis. Is love how you look at data with an open mind, trying to find evidence to support and or debunk claims. This is good science – and why I call you a scientist. Your work can be followed. Makes me appreciate how much mental energy it takes for me to go back to what I’d done in my college years!
That said, I see that you have found that the correlations are not there in the same time domain. I, perhaps wishfully, believe that integrating the sun spot spot cycles with a baseline of about 40, above which accumulates energy and below which reduces energy to our system shows something different. Of course this presumes something magical about the number 40!
The integral of strength of the solar cycles shows a different story, which may or may not be correct. However, I do believe effects (changes in solar output –not just TSI) take time to show up in our temperature records. As the frequency make up of the energy changes there are hypothetically varying physical effects that change as well, which might lead to feedbacks. So Just looking at TSI and what happens in the same time domain won’t show anything obvious.
When we use PWM (pulse width modulation) to control temperature, there are tuning parameters called PID loops (Proportional Integral Derivative) that effects the timing of the input. Without looking into these, we will not necessarily see the signals.
Bart says:
April 13, 2014 at 8:48 am
I neither agree nor disagree. I don’t understand. When someone says the solar heating is “modulated by the sloshing of the oceans”, I’m lost. That’s just handwaving, that’s not a mechanism.
Then you make the claim that the “sloshing of the oceans is forced by nutation”. I fear you have the causation backwards. You are claiming that the nutation is forcing the ocean to slosh … but in fact the tides cause the nutation:
Bart, to move forwards, you need a testable result of your hypothesis. You’ve proposed that the 11-year solar cycle is somehow “modulated” into a ~ 5-year and a ~ 60-year cycle. That was good. That was testable … but unfortunately, it failed the test. There is no 5-year cycle in the data.
So right now, that’s all air, it’s not a mechanism of any kind. Your explanation boils down stating that the ocean sloshes around in the various basins (true), plus an incorrect claim that the sloshing is driven by nutation.
I agree that nutation can be important in some special situations like you mention. I can see that for satellites damping nutation would be essential, and for earthquakes as well. But most buildings on the planet pay no attention to nutation at all … and certainly not to the nutation of the earth itself.
But then, I didn’t say that nutation is no big deal in skyscrapers and satellites, did I? Because we were talking about the nutation of the earth.
Instead. I said that the nutation of the earth was tiny, so small it needs very specialized instruments to measure it. As a result, I doubted that it could modulate much of anything.
You still haven’t dealt with the fact that your whiz-bang theory failed its very first test, because there’s no 5-year signal in the data … but I hope you will. Otherwise, you’ll be stuck there forever.
w.