Guest Post by Willis Eschenbach
[UPDATE] In the comments, Nick Stokes pointed out that although I thought that Dr. Shaviv’s harmonic solar component was a 12.6 year sine wave with a standard deviation of 1.7 centimetres, it is actually a 12.6 year sine wave with a standard deviation of 1.7 millimetres (5 mm peak to peak) … I got 1.7 cm into my head and never questioned it because mm seemed way too small … but there it is. My thanks to Nick for pointing out my error.
So … in answer to the question, is a sine wave with a standard deviation of just under 2 mm detectable by Fourier analysis of the tidal station data … the answer is no. I’ve struck out the incorrect conclusions below.
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I got to thinking about whether the Fourier analysis I used in my most recent post was sensitive enough to reveal the putative “harmonic solar component” which Dr. Shaviv claims to have measured. He said that he’d found a sine wave signal with a standard deviation of 1.7 cm mm in the satellite sea level record. So I added a solar signal with a standard deviation of 1.7 cm to the same 199 long-term climate records. [Ten times the size of Dr. Shaviv’s signal.] Note that unlike Dr. Shaviv’s so-called “harmonic solar component”, which was actually just a sine wave, I have used the actual sunspot record, and I scaled it to give it the same standard deviation (signal strength) as Dr. Shaviv’s sine wave. Figure 1 shows the “before” graph of the 199 tide station records from my last post.
Figure 1. The average of the station by station periodograms of the tide station data without the solar signal. All stations detrended before periodogram is calculated.
Figure 1 shows the actual tide station data. Notice that there is no signal at around 11 years. And here’s what it looks like with an added solar (sunspot) signal with a standard deviation of 1.7 cm, a mere 3/4 of an inch, the size of Dr. Shaviv’s claimed signal.
Figure 2. Average of the periodograms of all tidal stations with records longer than 60 years, to each of which have been added a copy of the sunspot signal scaled to a standard deviation of 1.7 cm. This gives a signal (sunspot data) to noise (tidal data) ratio of one part signal, seven parts noise.
So in answer to the question, can my method detect a signal of the strength claimed by Dr. Shaviv mixed into the maelstrom of the individual tide station records, the answer is clearly yes, no problem. It is quite visible.
Ah, but Willis, I hear you say … surely all of these tide stations wouldn’t be affected by the solar changes at the same time. And that is true, there might be lags that differ on the order of months, seasons, or perhaps even years between the forcing change and the response in a given location. But that is the beauty of my method of averaging the periodograms. The periodogram finds the signal regardless of the phase. The phase of the signal doesn’t matter in the slightest—if the signal is there, the Fourier analysis will reveal it. As a result, the lag at any individual tidal station is immaterial.
Let’t push it further. Let’s see if we can do twice as well, say a signal to noise ratio of one part signal to fifteen parts of tidal noise. That would mean a tiny signal with a standard deviation of 0.8 cm … bear in mind what I’m doing. I’m adding a tiny duplicate of the solar signal to the monthly tide data, with a standard deviation of only eight freakin’ millimetres, less than half an inch. None of the tidal records cover exactly the same time span, and many have gaps. So each record gets a different chunk of the sunspot data. So the question is … can the periodogram find a solar signal at fifteen parts noise to one part signal?
OK, here’s that graph.
Figure 3. Average of the periodograms of all tidal stations with records longer than 60 years, to each of which have been added a copy of the sunspot signal scaled to a standard deviation of 0.78 cm.
Yes, I can still see the signal. It’s clearest at the lower edge of the black error bar lines behind the gold graph line. But I’d say we’ve reached the detection limit for this size of signal in this size of dataset … one part signal to 15 parts noise, a detectability limit of a signal strength of 0.8 cm. Not bad.
Conclusions? Well, I’d say that if there is a solar signal in the sea levels, it is vanishingly small. And I’d also say that Dr. Shaviv’s claimed signal with a 1.7 cm standard deviation is large enough to be found if it actually existed … see Figure 1 and 2 to decide if you think it exists.
And finally, I hope that this puts an end to the claim that Fourier analysis can’t find solar signals because they have different periods from nine to thirteen years. It not only can do so, it can do so in the face of stacks of noise and with the solar data covering different periods and often broken by gaps in individual tide station records. Consider that some of the records look like this …
Figure 4. Detrended monthly tidal data, Sheerness.
Despite the gaps, we can find a signal with a standard deviation of 8 mm in the midst of tidal data like that if we have enough tide stations … not bad.
Regards to all,
w.
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What signals are detectable in CruTem4:
http://www.vukcevic.talktalk.net/CT4-Spectrum.gif
4-5 years: ENSO
9.1 years: N. Atlantic SST (AMO)
21.5 years: Solar magnetic field (Hale cycle)
26.6 years: Asian monsoon
60.2 years: N. Atlantic SST (AMO), caution there are 164 years of data; 60 years is on the border of acceptable certainty.
Willis
You ask : “Is The Signal Detectable?”
Any answer to that question will depend upon the quality of the data that is being used. If you wanted to answer that question, you should first have carried out a quality audit of the data that you intended using. Poor quality data cannot produce a silk purse, one is left only with a sow’s ear. A quality audit of the data, would have quickly have led to the conclusion that the data cannot reveal anything of significance, because the real error bounds are larger than the signal being sought.
The reason why no one knows the sensitivity to CO2 is because of poor quality data. Nearly all the data sets in climate science are not fit for purpose such that no proper science can be carried out on these data sets.
There is probably only one data set that is acceptable and that is the Mauna Loa CO2 set. However, that does not clarify what the CO2 levels were prior to the start of the series, nor whether CO2 is a well mixed gas such that Mauna Loa data truly reflects global concentrations. The recent OCO 2 data (and the earlier Japanese satellite data) suggests that CO2 is not as well mixed as climate scientists would have one believe. Indeed, in essence the reason for rejecting the past chemical analysis of CO2 data (ie., the MBL estimation 1826- 1960 from directly measured data (Beck 2009)) rests upon CO2 not being well mixed.
Provided that the satellite temp data is properly and accurately calibrated against radiosonde balloon data, that data set is acceptable, but the duration is rather short. That said it is clear that there is no first order correlation between CO2 and temperature in that data set.
ARGO, has the potential to be good, but it is of too short a duration, and lacks spatial coverage such that the margins of error when assessing sea tem data globally is far larger than the 1/1000ths to which they claim that they can measure data.
The rest of the data sets, for want of a better word are garbage. This extends to sea level data.
The need for a proper quality audit of the data being used is the reason behind the surface station review. Unfortunately so many papers in climate science are being published on extrapolation and interpretations of p*ss poor data such that the conclusions of the paper are not worth a damn!
Here is the power spectrum for Honolulu tide guage as archived by UK’s PMSL service
http://www.psmsl.org/data/obtaining/
Data goes back to 1905
rate of change of sea level was used to remove the general upward trend and it should be noted that this attenuates the longer periods. A low-pass fitler was used to remove the annual and sub-annual signals.
Looks to be a fairly clear solar signal there. 5.36y is the first harmonic and 2.57y may also be the 2nd. These harmonics will be present since solar cycle is not a nice smooth sine wave, they are a result of it’s non symmetric shape.
It would seem that Dr Shaviv may have got a stronger result had he used the actual solar data instead of a simple sine wave approximation.
Willis,
I feel like throwing my hands up and screaming “aaaaagh!”
Your mini-series on this subject together with your last correction/update has now left a bunch of people with the entirely erroneous conclusion that a quasi 11-year cycle cannot be detected convincingly in tidal records.
Have a look again at the short series of posts from Mike August 20, 2015 at 9:53 am.
A low-pass filter applied to the level series renders the 11-year cycle visible in several of your chosen records..
Alternatively, generate the annual differences from the uncorrected monthly data and apply a Fourier analysis to the differentiated series. The 11-year cycle again becomes visible.
In fact, apply any reasonable filter to the high frequency (largely gravity-induced) annual variation any darn way you please and then tell us that the cycle is “not detectable by Fourier analysis”.
(Douglas 1997 “Global Sea-rise: a Redetermination” applied a more rigorous screening of tide-gauge data than just continuity. You might also consider testing his subset before declaring that the cycle is “not detectable by Fourier analysis”.)
Just to clarify my early comment on the 12mo diff as a filter, it is quite nice above 12mo, so suitable for what you suggested. It is basically the 1/f attenuation of the diff but falling to a zero at 12mo and with a max at 24 mo.
However, below 12mo there is also a zero at 6mo, 3mo, 1.5mo etc. That is the repetitive notch behaviour that I was recalling. I’d wouldn’t mind betting that every second lobe in that region is inverting the data. So it would probably be OK to remove a strong annual cycle prior to doing FT but would seriously corrupts the data if used as a time series filter.
Mike,
Agree with your comments, and thanks for posting the Honolulu results. I was offering Willis an adequate rather than a best methodology.
I just confirmed your Honolulu results, using a 12 month difference series followed by a 13 month box filter applied to the derivative series. Ran an FFT. A very crude 5 minute job, but out pops a cycle at 10.7 years, with an amplitude of 7.95mm/year.
This translates (by integration) into an amplitude of the level cycle of MSL of around 14mm if I have done my sums correctly – highly visible via a Fourier analysis.
Not all local records produce such a clear signal – because of latitude and geography dependence.
Thanks for the confirmation Paul. Good to have two different heads using different tools.
The Ijmuiden data from the same source has a strong 10.8y too. It’s on the dutch coast in the North Sea so makes a good alternative to Hawai’i
( pronounced : “Ay-mow-den” )
Paul_K “…. a cycle at 10.7 years, with an amplitude of 7.95mm/year.
This translates (by integration) into an amplitude of the level cycle of MSL of around 14mm if I have done my sums correctly ”
7.95*10.5 / ( 2* pi ) = 13.5 , looks right.
Anyone who knows –
Hitherto I had assumed at an increment of extra irradiance from sun to earth would cause ocean expansion or contraction almost immediately, as in instantaneous less any delay caused by slower progress through the atmosphere. My thought was that an alcohol thermometer seems to respond almost at once, given it takes time to change the temperature of the enclosing glass.
So, can we expect a change irradiance large enough to be detected to change ocean temperature at the surface immediately? As in soon enough to respond accurately to spectral analysis of frequencies as Willis has done here?
If the change is not instantaneous, where does the incoming energy reside in the lag period?
No Geoff, a change in radiative flux will cause rate of change of temperature. Then negative feedbacks in climate will eventually counteract it and a new settled level at a slightly higher ( lower ) temperature will result. It depends up on the thermal inertia of the system and how all the feedback interact as to how long that will take.
This is why the vast amount of climatology that tries to asses climate sensitivity is physically wrong they are regressing quantities that are out of phase. They say that climate takes decades to settle yet regress dRad and dTemp as though they were in-phase. This leads to all sorts of false negatives and false attribution problems.
The only thing that may just about work is a very slow and fairly constantly rising quantity like GHG forcing and all other factors are likely to be rejected and/or falsely contribute to AGW. If that’s what someone expects to see and they have little knowledge of the physical sciences, they will publish and become an expert on climate.
It’s a bit like the SST vs CO2 discussion. You need to look at d/dt(CO2) to see the correlation with SST. It is then in phase and can be correctly correlated.
whoops, I’d better close that strong tag or else every thing with follows will be bold 😕
This question was touched upon by Roy Spence ( Spencer & Baswell 2010 IIRC )
The temp record is a mix of in-phase and orthogonal data which makes assessing sensitivity to the driving radiation changes very difficult.
There is a detailed discussion about this here:https://climategrog.wordpress.com/2015/01/17/on-determination-of-tropical-feedbacks/
https://climategrog.wordpress.com/2015/01/17/on-determination-of-tropical-feedbacks/
PS, the phase information is lost when just plotting the magnitude of the FT which is what Willis, I and Paul_K are doing. So that is not relevant here.
Geoff,
Further to Mike’s comment, you need to distinguish clearly between energy and flux, which is energy per unit time.
If you turn the gas on a pan of water, then you have added to the heat flux (forcing). This causes the water to gain temperature in accordance with its calorific properties or heat capacity. As the water gains temperature, it also loses more heat to the atmosphere (temperature-dependent feedback). The net heat flux into the pan is the difference between the heat flux added by the gas and the heat flux lost by the water cooling to the atmosphere. The integral of the net heat flux over time gives you the total energy gained by the pan of water. If the calorific value of the water is Cw, expressed here in joules per degree centigrade, and we measure the change in temperature as T deg C, then the total energy gained by the water is then
E = Cw * T
If you differentiate this w.r.t. time, then you obtain the net heat flux going into the pan, hence:-
dE/dt = net heat flux = Cw* dT/dt. This is the rate of gain of heat energy of the water.
The heat flux into the pan from the gas is given by F, say. For small temperature changes, we can use a linear approximation for the cooling of the water:in the pan:- heat flux from the water = λT
The difference between the two must also equal the net heat flux going into the pan.
Hence,
The net heat flux going into the pan = F – λT
Equating the net heat fluxes, we obtain for our pan of water:-
Cw*dT/dt = F – λT
It is no coincidence that this equation looks identical to the single-body linear feedback equation much loved by many climate analysts. For the climate version, Cw represents the heat capacity of the oceans (or just the mixed layer), F represents a flux forcing and T represents global surface temperature (or just the sea-surface temperature). Please note that there is no missing energy implied by this system. If the energy arrived, then It is either in the form of heat in the water or it has been lost via cooling to space.
We can see immediately from this equation that we should not expect a simple relationship between forcing and temperature – Mike’s main point above.
If we apply an oscillatory forcing to this theoretical system, we also find (by solving the equation) that the temperature response is oscillatory and has the same periodicity as the input forcing. However, it is phase-shifted relative to the input forcing.
The net flux response is also oscillatory and is phase-shifted by exactly 90 degrees from the temperature response, (since dT/dt is phase shifted from T by 90 degrees). So, we find then that the peak in net flux leads the peak in forcing which leads the peak in temperature, with a phase shift between net flux and temperature of 90 degrees.
This theoretical system is however somewhat defective, because of (amongst other things) oversimplification of the ocean model. The sea surface temperature is responding to the mixed layer temperature. However, it is a reasonable assumption that the warmer the mixed layer, the faster its rate of heat loss to deeper ocean. If the simple mixed layer model is replaced by a more sophisticated ocean model, then the phase separation between net flux and temperature ceases to be 90 degrees. Instead, the phase separation has an upper bound of 90 degrees.
I hope this helps rather than confuses.
since the forcing is driving the flux, I’m not clear on how you see the flux changing first. Is this what you intended to write?
I’m inclined to defer to your expertise on this subject but wouldn’t the eddy diffusion also just represent a negative feedback and simple modify the value of lambda? Could you elaborate? Thanks.
Mike,
Although it may seem counterintuitive, yes the peak in net flux leads the peak in forcing for an assumed oscillatory forcing input for this model. The forcing in this instance is an unfettered independent input by assumption. It immediately induces a change in both temperature and in net flux. The forcing goes on to reach its first peak – unfettered – while the net flux finds itself increasingly constrained by the restorative cooling feedback. In this race, the net flux tails over before the forcing hits its peak. You can see this by solving the equation analytically for a sinusoidal forcing input, which can be done very simply with an integrating factor.
The loss of heat from the mixed layer is normally captured either as an upwelling diffusion term – with heat loss proportional to the temperature gradient – or, in a multiple body model, as something linearly proportional to the temperature difference between the mixed layer and the (next) deeper layer. In either event, this does not effect the feedback term – which is intended to reflect the radiative response from the surface upwards. In effect, for a two-body ocean model, the single-body governing equation which I described above would become :-
Cw *dTs/dt + K*(Ts-Td) = F – λTs
where the subscripts s and d refer to the surface and the deep ocean layer respectively.
You can see, I hope that this has not changed the radiative feedback term ( λTs) at all. Nor should it change the total net flux described by the RHS of this equation. What has happened is that the flux forcing F is now heating both the mixed layer and the assumed deeper layer.
The same thinking applies for an upwelling diffusion formulation or an n-body model where n>2 – they only affect the LHS of the energy (or actually flux) balance equation.
Thanks for the equation Paul, always helps to have some concrete to refer to. I’ll do some algebraic rearrangments:
Cw *d/dt(Ts) + K*(Ts-Td) = F – λTs
Cw *d/dt(Ts) = F – λTs- K*(Ts-Td)
Cw *d/dt(Ts) = F+ K*(Td) – Ts(λ+K)
So if Td is considered a quasi-constant deep ocean temperature we have a slightly modified forcing term and a new “effective” lambda. This is what I meant by it acting as an additional negative feedback.
Within the assumption that the temp of the bulk of the deep ocean does not change measurably, this equation seems to be essentially of the same form as the original, unless I’m missing something.
.
I think the substitution solution you are referring too is what you provided at Lucia’s for a sinusoidal forcing:
http://rankexploits.com/musings/2013/estimating-the-underlying-trend-in-recent-warming/#comment-116290
T = Asin(ωt) – Aωτcos(ωt) + Aωτexp(-t/τ)
where A = S/(1+(ωτ)^2)
The exp is a transient term that can be ignored in the settled response to a constant oscillation. Sketching out sin(ωt) – cos(ωt) it peaks between pi/2 and pi, after the forcing term of sin(ωt) and crosses zero ( max rate of change ) somewhere between 0 and pi/2 , ie. leading as you correctly said .If the time-const is small the cos term becomes less important and the phase of temperature is close to that of the forcing.
Cw *d/dt(Ts) is the flux term so it is the long time-constant ( small neg. feedback ) case where the flux is nearly in phase with the forcing.
Which all goes to show that the trivial linear regressions that are the main stay of attempts to assess climate sensitivity from observational data are fundamentally flawed and can be assured to give the wrong result.
The presence of both the in-phase and the orthogonal terms will dilute the regression slope. If dRad is used as the ordinate ( x-axis ), as is almost universal practice in climatology, the slope will be too low and the deduced climate sensitivity ( reciprocal of the slope ) will be too high.
Mike,
Your rearrangement is fine, but now to get an approximate solution for the two body problem, you can use the known solution of the first equation – the single body equation – with the deeper temperature fixed at a constant value and appropriate modification of the parameters, to solve for Ts and for dTs/dt. The net flux term however is not Cw*dTs/dt – which would be 90 deg out of phase with T, but is CwdT/dt + kT -kTd. This is a linear combination of a sin and cos function of the same phase plus an approximate constant, kTd. Hence net flux moves to being less than 90 deg out of phase with T. Alternatively we can say that 90 deg represents an upper bound on the phase difference.
This conversation about relative phasing of net flux, forcing and temperature response is very pertinent to Shaviv’s work – and why it was never appropriate to assume that the solar forcing should be in phase with MSL or with rate of change of MSL. The fact that MSL is also responding to additional changes (notably mass) adds a further complication, but overall, he was IMO perfectly correct to leave phase as a free variable – something that Willis seemed to think was wrong in some way.
Corrigendum: I wrote “This is a linear combination of a sin and cos function of the same phase …” when I should have written “This is a linear combination of a sin and cos function of the same periodicity…”
Sorry.
Thanks for the confirmation that this can still be treated as a simple linear feedback, with slightly modified parameters. You say that the eddy diffusion is usually treated as upwards +ve presumably following the same logic as +ve downwards for atmospheric fluxes. Thus K would be a negative constant.
This phase issue is a major problem for climatology and is at the heart of much of over-estimation of CS. As recently as Santer et al 2014 we find them still not getting it.
Original caption is “ENSO and volcanoes removed” yet we can see a major disturbance remains after Mt P. The initial dip shows that they are under-scaling volcanic effects and the following bump is the out of phase climate reaction.
Credit goes to Santer et al for clearly documenting this residual error in the paper, though it is a poor state of affairs that after 30 years of concentrated effort and resources they still have not got beyond high school level physics. This is first year undergraduate work in most hard sciences.
Marotzke & Forster 2015 make similar mistakes by repeatedly shunting the out of phase components into a “random error” term then applying regression as if the response was in phase with the forcing. These guys hold chair positions at major universities. Astounding.
Paul,
Thanks for the reply. My email is sherro1 at optusnet.com.au
In about 1972 I did some experiments with radon on the fringes of the Ranger (undeveloped then) ore bodies, looking at Radon movement.
A colleague who lived on site had a baby delivered by his wife and was up and down in the night. So, I asked him if he would duck out and take Rn and temperature measurements at various depths in the soil.
Here is a graph that seems to show peaks and troughs through the day rather where one would expect with a fast response system
http://www.geoffstuff.com/jabsoilt.jpg
There is the other observation that swimmers note that the top few cm of calm sea is warmer at noon than at midnight.
Could it be that you are modelling starting conditions while I’m observing near-equilibrium conditions?
The other problem I have is – if there is a lag as you note, 90 deg out of phase, where does the energy go while it awaits the right phase?
Why does an alcohol thermometer reswpond near instantaneously and the shallow sea not?
Cheers Geoff.
Sorry for the late reply – severe health problems in the family.
Willis
Re: Literature sea level periodograms showing 11-13 yr cycles vs Eschenbach
You said:
Further to my comment raising the periodogram of New York City by Scafetta (2013) showing an apparent solar cycle, see:
Kenigson, J. S., and W. Han (2014), Detecting and understanding the accelerated sea level rise along the east coast of the United States during recent decades, J. Geophys. Res. Oceans, 119, 8749–8766, doi:10.1002/2014JC010305
Note especially Fig. 1B .
These power periodograms clearly show an apparent solar cycle around 11 – 13 years for ten ports: Eastport, Portland (Maine), Boston, New York (The Battery), Philadelphia (Pier 9N), Atlantic City, Baltimore, Annapolis (Naval Academy), Sewells Point (Hampton Roads) and Charleston. These appear to have a similar order of magnitude to the multi-decadal oscillation of ~ 55-65 years. (Conversely I do not see the annual cycle shown in this figure).
So why do Kenigson & Han (2014) show 11-13 year cycles (solar cycle?) in 10 sea level periodograms, similar to Scafetta (2013) Fig. 3, yet you do not find such in your sea level periodogram analyses?
Scafetta, N. Common errors in analyzing sea level accelerations, solar trends and temperature records. Pattern Recognition in Physics 1, 37-58, doi:10.5194/prp-1-37-2013, 2013
PS Thanks for the correction in this post.
David,
I hope that Willis is still listening. Another reference which is worth looking at (also already mentioned in previous threads) is Jevrejeva 2008. Although his focus was on the quasi-60 year periodicity in the MSL dataset, his results based on tideguage data back to 1700 also clearly show evidence of something that looks remarkably like the solar cycle.
See Figure 2 from here:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.178.7972&rep=rep1&type=pdf
Yes, Willis seems to regard absence of a solar signal as proof of his tropical governor hypothesis and is a bit too invested in trying to prove a negative. I think he is basically correct that tropics are very insensitive to radiative change, however, this is less true for non tropical zones.
I have not seen him comment on this explicitly but I get the implied idea that he considers the topical ‘governor’ also means that other zones are insensitive too, which is less the case. Oceanic and atmospheric circulation ensure the tropics have a stabilising effect but mid latitudes are notably more sensitive to radiative forcing.
If there is some expansion in extra-tropical regions due to solar, the additional volume has plenty of time in 11 years to find its way around and be visible in all regions.
Reported average global temperatures fluctuate in a non-physical manner. Effective thermal capacitance prevents true energy level of the planet from changing so quickly. The effectively random fluctuation results because temperature distribution is not smooth, temperature measuring points are discreet and, for satellite based measurements, local weather causes variations.
Reported average global temperatures fluctuate in a non-physical manner because so-called scientists insist on averaging the temperature of two physically incompatible media: water and air, which have specific head capacities that differ by about three orders of magnitude.
The result is physically meaningless before you even work out what the numbers are.
But because air warms quicker it boosts the rate of “global warming” and that is the required result. Science be damned, this is politics.
What does any of that have to do with the impossibly rapid fluctuations in reported temperatures which are dominated by (approximately 71%) ocean surface temperature measurements?
I’ve been playing around with MODTRAN and the Ice Core Data and it is pretty hard to make the case that CO2 causes warming.
1) According to the Vostok data the ice age bottomed 18600 years ago, with CO2 at 185ppm, temps -8.73&Deg;C
2) Over the next 1,400 years CO2 remains basically unchanged, yet temperatures increased a full 1.26°C.
3)CO2 doesn’t start increasing until 1,200 years after temperatures began increasing.
4) CO2 bottomed at 182ppm, that puts the outgoing radiation at 292.993W/M^2 at its bottom. Assuming clear skys and 70m altitude.
5) Temperatures increase a full 9.34°C over the next 7400 years, and CO2 increased by 67ppm. That puts outgoing radiation at 291.455W/M^2. 1.5W/M^2 by CO2 corresponded with a 9.34°C increase.
6) Temperatures the drop from 0.616°C 11200 years ago, to -1.114°C 3000 year ago. CO2 went from 252 to 278, putting the outgoing radiation at 290.984W/^M2 . A 1.72°C drop corresponded with an increase in CO2 absorption of 0.5W/M^2
7) CO2 has then increased to 400ppm, resulting in 189.228W/M^2. A 1.7W/M^2 increase. Temperatures have increased 1.6°C.
8) The current temperatures are below the Holocene Max.
Bottom line, the change in temperatures seem to be unrelated to the changes in W/M^2 absorption by CO2.
That’s some interesting stuff you’ve been doing but I think you posted to the wrong thread. This is about solar and sea level, I think you were commenting on the thread on recent paper about “correcting” bolder dates to give the policially correct, required result.
Willis,
I have run a number of tests on various tide-gauges.
To render the cycle visible in the level series you need to do the following pre-processing
(a) remove the linear trend to stabilise the low frequency results
(b) run a 13 month box filter over the data (or better still a low pass filter)
(c) run a Fourier analysis
Alternatively, to render the cycle visible in the derivative series, you can:-
(a) convert the data to a 12 month difference series
(b) run a 13 month box filter (or better still a low pass filter)
(c) run a Fourier analysis
(d) convert the amplitude estimates from the derivative series (mm/yr) back to estimates for the level series in mm
These two approaches give me consistent estimates of amplitudes for the level series for the wavelengths of interest.
As a reference case, amongst other tests, I duplicated the New York results posted by Scafetta. This reveals an amplitude of about 10mm at a periodicity of 12 years, using data from 1906 forwards.
The fact that the average global amplitude of this cycle may be around 2.5mm does not imply that it is 2.5mm everywhere. If you wish to argue that the cycle is not visible in the tide records then – a la Feynman – you need to go to the tide records where it should be most visible and demonstrate that it is not present.