The average temperature was 0. 77C in July up by by 0.08C from June. Despite this small rise, 2021 is still on track to be the coldest year since 2014. After 7 months the average global temperature so far is 0.66C.
The Southern Hemisphere remains cooler than normal (1961-1990) in July whereas the Northern Hemisphere is in general much warmer.
La Nina is still evident with cooler temperatures across the SH.
The Northern Hemisphere is warm apart from cold spots in the Eastern United States and in Northern Siberia.
Northern Hemisphere temperatures.
Finally here is a plot of the 2021 average temperature after the first 7 months relative to a 1961-199o baseline.
You can download the monthly and annual data here and these are updated regularly.
Off topic a bit but still in the same hemisphere:
Any opinion on the documentary “Kiss the Ground”?
About 1/2 of .77 is tampering and UHI, based on my lukewarmer research.
I just read that July 21 by NOAA has been declared as the hottest since recorded history, in 142 years. Culd you please explain that? How is this possible?
July is the warmest month, explained here: https://spaceweather.com/glossary/perihelion.htm
So a record warm July would likely be the warmest month ever.
Quite right. Incoming solar energy peaks in July as the earth reaches its closest distance to the sun.
Counterintuitive, but the sun is actually closest in January.
Yes of course you’re right! That’s why the UV from the sun is so dangerous in Australia. It is warmer in July because there is twice as much land in the Northern Hemisphere.
Coldest since 2014 isn’t saying much. It is virtually certain that 2021 will go on to rank in the top 10 warmest years on record. And based on the year-to-date trend, it may end up ranking in the top 6, edging out 2018. The seven warmest Julys have all occurred since 2015. … https://climate.gov/news-features/understanding-climate/earths-hottest-month-was-record-hot-2021
Yes Global Warming is real
Both
July 2020 0.819722 C
and
July 2019 0.807386 C
were “warmer”
NOAA essentially show them the same so they are making silly claims. Also they don’t cover the poles properly.
Clive,
It has been a while since I have offered a comment on your website.
I decided it would be worth my time to offer a comment since you posted a link to your data. Herein, I furnish my results in analyzing the data you furnished.
Before I do that I wanted to offer some documentation for what I present that follows:
The following is from an article at NoTricksZone:
German Scientists Show Climate Driven By Natural Cycles – Global Temperature To Drop To 1870 Levels By 2100! http://notrickszone.com/2013/12/03/german-scientists-show-climate-driven-by-natural-cycles-global-temperature-to-drop-to-1870-levels-by-2100/
by Prof. H. Luedecke and C.O. Weiss (Original German version here).
I have for quite a while been analyzing various datasets for the presence of natural cycles in the datasets. Through my experience in the Naval Nuclear program, I am quite familiar with Fourier analysis of vibration data. A few years ago, I became familiar with the Optimal Fourier Transform (OFT) that was developed by Dr. David Evans. I use his spreadsheet to perform OFT analysis of the datasets. I then use those inputs for further analysis that reduces the Sum of the Squares Error (SSE).
Before we get to the analysis of your data let me acquaint you with where I am now with the HadCRUT4 (H4) data. I have analyzed the HadCRUT5 data too ;but I am going to avoid it until support of the H4 ends. I think the H5 data is contaminated with human adjustments to furnish warming.
H4 Data Analysis
The first thing I do when I get new data is that I presume as the climate models do that CO2 alone is responsible for the temperature change. Here are the results.
https://1drv.ms/u/s!AkPliAI0REKhhLs0OFTK1UaCL3y9Dw?e=W2hKOU
The climate models all champion higher values of ECS, which yield poor model performance. Dr. Spencer has shown this when he depicts all the models. There are models with a low value of ECS that enable a reasonable comparison with results. The problem is the importance of CO2 is so diminished there is no justification for the need for urgent climate action.
In my analysis of the dataset I do include a contribution from CO2. However it is greatly diminished since natural cycles dominate. That is shown in the figure below:
https://1drv.ms/u/s!AkPliAI0REKhhLs1YyMCJNtwXWE-Fw?e=Go90kx
There are several things worthy to note from this figure. I have heard both Dr. Lindzen and Dr. Curry note the temperature rise from 1910 to the 1940s. That is explained by the 67-yearcycle or the MDO. It also explains the decline in temperature in the 70s when we had the coming Ice Age scare.
The next figure is a closeup. It shows that we are presently in temperature decline and it shows there has been no global warming for over seven years.
https://1drv.ms/u/s!AkPliAI0REKhhLs2CQ2230KdElpyjg?e=YvHLHZ
The following figure furnishes a projection based upon the cyclical analysis.
https://1drv.ms/u/s!AkPliAI0REKhhLs3wVmvMr762QS27w?e=bj6hvm
The next figure reveals how the mean of CMIP5 and CMIP6 compare with the measurements. I do not understand CMIP6. It is worse than CMIP5. You would think that with time the models would perform better. This is just more fearmongering.
https://1drv.ms/u/s!AkPliAI0REKhhLs4v0qeAFzaAPTyzA?e=bEnPLm
I will add one more figure. It reveals model performance using the low, best, and worst-case ECS estimates.
https://1drv.ms/u/s!AkPliAI0REKhhLs5N9KCpVCVcg3f2A?e=hPjBlK
How could the worst-case model be championed? The measurements show the low case estimate for ECS is too high.
Clive Best’s Data
Things will be a little different here. I have not put this analysis into a spreadsheet ;so the graphs come from the analysis program I use TKSolver.
I will present the graphs in the same order as above.
https://1drv.ms/u/s!AkPliAI0REKhhLs8fh8aQmbh9-j3og?e=lV7bEL
I am sorry I did not change the title but this is Clive’s data.
https://1drv.ms/u/s!AkPliAI0REKhhLs9IJZzpmOfhEDn1w?e=DCSPjM
The close-up still shows the current declining trend and that there has been o warming for at least six years.
https://1drv.ms/u/s!AkPliAI0REKhhLs-TfDJfuZeG8Qgqw?e=DYxJ0D
The projection is similar to the H4 projection.
https://1drv.ms/u/s!AkPliAI0REKhhLs_CDr7Lw5MvTPKuQ?e=XgxWN7
The next chart is similar to the same one for the H4 data, I think it is worth noting that the old pause line that starts in 1997 is quite close to the overall slope. I think this is an indication of the heat that was added to this dataset.
https://1drv.ms/u/s!AkPliAI0REKhhLtAXVy4e-WHmwrKUA?e=ORKv3w
CMIP5 looks closer to the data than in H4 but they did add het in this dataset. Again, one must question the presence of CMIP6. I would like to think that models improve over time.
The performance of the models is just as dreadful as it was for H4.
https://1drv.ms/u/s!AkPliAI0REKhhLtBi-qcwjSZZGZOcA?e=VQqeih
Conclusions
I see no reason to change my conclusions. Until the climate models are able to include natural variations they are worthless. Once they do the importance of CO2 will drastically decline. Manmade climate change will auger itself into the ground.
We are wasting billions on remedial actions that are not needed. I expect manmade climate change propaganda to continue. I think many of the scientists are equivalent to prostitutes. They will keep the six figure checks coming in until the lie is exposed. Those that work on the models have to know they are not accurate or worthy for policy decisions.
Charles, You are still doing your signal analysis on temperature data – keep at it.
Yes I always suspected an underlying 60 year cycle.
https://clivebest.com/blog/?p=2353
Of course in the meantime the temperature data has been “updated” and the hiatus as reported in AR5 has disappeared. I also discovered this was not because of adding new station data to Hadcrut4. It was really due to adjustments made to the raw temperature data that made it vanish.
https://clivebest.com/blog/?p=8934
and following 2 posts.
Clive
Indeed, besides what you see here I do monthly updates of all four Nino regions and the UAH data. From time-to-time I also update the AMO and PDO.
The only dataset I trust now is the UAH. There data are untainted. There is a drawback to that. The limited time period fro their data limits the signal analysis.
Clive, I can remember some years ago that we agreed on the 60-year cycles.
Since last posting a comment my reach has increased. I send monthly reports to Dr. Evans, Dr. Page and Dr. Scafetta. BTW, Prof. Scafetta issued a paper not long ago that highlighted natural variation.
I no longer analyze the RSS data. I think it is totally corrupt. Years ago Monckton used the RSS data to document the pause that was getting close to 19 years as I recall. Dr. Mears took care of that.
I can document that change in the RSS data. In June of 2017 the pause existed. That same data was changed by the end of the month and its pivot point for rotation was 1997.
Although it has been a while. I still follow what you are doing, Clive.
Have you used ‘average temperature’ when you mean average temperature anomaly, twice?
(The inner pedant cries out!)
Yes it is always temperature anomalies. I note that climate scientists have dropped the “anomaly” bit. They say the Earth has warmed one degree or it is the hottest June ever. I am falling into the same trap !
Clive,
Today you get a bonus. A new data point was added to the SST database. I prefer the SST database. I think there is less noise in the data. The correlation coefficient of the cyclic analysis in this instance is 0.98.
I will try to be brief. If CO2 alone was responsible for the SST dataset the ECS would be 1.66. That reminds me of a value Lewis and Curry came up with a while ago.
https://1drv.ms/u/s!AkPliAI0REKhhLtKL739rIKqRbt2ow?e=dThy0A
The next figure is a close-up.
https://1drv.ms/u/s!AkPliAI0REKhhLtLefmg1SGFxAw1XQ?e=o0TfIR
You will note at the end the projection shows a downturn. However that is predicted from my analysis of the four Nino regions. That is shown in the figure below:
https://1drv.ms/u/s!AkPliAI0REKhhLtMmzEABf40qGWZZQ?e=Ws0sOc
My projection for SST is similar to HadCRUT4.
https://1drv.ms/u/s!AkPliAI0REKhhLtNIE1cboC8SI0AxA?e=9ZcTg5
I think the 67-year cycle really stands out. I think its presence can’t be challenged.
I can only conclude that the climate models are worthless until they find a way to introduce natural variability. Can the climate models tell you when the next El Nino or La Nina conditions will exist? I seem to have captured them. In fact, I will go this far, if the models can’t predict such events, it proves they are worthless.
Manmade climate change is a fiction of the virtue-signaling global elites. They are getting what they paid for. If they ever legitimately include natural variation in their models manmade climate change will auger into the ground.
I have not done anything here that I did not do for the 35 years I worked with FFTs.
Clive, I do have regard for what you do. I dropped out for a while, but I hope now to stay more involved.
” If CO2 alone was responsible for the SST dataset… ”
Why should CO2 alone be currently responsible for anything?
It is a contributor to Earth’s increasing energy imbalance, for sure.
But to claim it is currently the main one, that goes too far.
What scientists IMHO mean is rather that, all other things remaining equal, its permanent increase in the lower stratosphere might indeed create big problems in say 50 years.
J.-P. D.
It seems I have failed to communicate. The presumption of the models is that CO2 is responsible.
In the first figure look at the legend. There are two items with CO2 in them, There is the CO2 alone that has a value of 1.66. The second legend item is what CO2 contributes when it is combined with natural cycles. It has an ECS value less than 0.3,
In his work Dr. Evans has said the ECS value can’t be greater than 0.5.
What I am trying to show is that natural cycles drives the climate. CO2 has a diminished role.
.
“Within the trend, the Pacific Decadal Oscillation causes alternating global warming and cooling for 25 to 30 years at a go in each direction. We have just finished a warming phase, so expect mild global cooling for the next two decades.”
– Dr. Evans, 2011
https://financialpost.com/opinion/climate-models-go-cold
So, checking up on his prediction, I’m wondering what the trend has been for the period April, 2011 – July 2021, accorded to UAH?
In response to your comment, I decided to furnish some of my latest reports on my analysis work. It will save me some time and y’all will get the full reports.
UAH update
https://1drv.ms/b/s!AkPliAI0REKhhLtQBgJhVjGB3aHGwA?e=nByrVm
H4 update
https://1drv.ms/b/s!AkPliAI0REKhhLtR7px2mBs8XAKL0w?e=IhW2b7
Nino Regions update
https://1drv.ms/b/s!AkPliAI0REKhhLtSG9f1Wg245jS6fw?e=PoZTnW
This way you get to see it all together.
I would say that Charles May is providing some interesting time-series models of the natural variability but don’t see where the mechanism is coming from. Clive is usually keen on coming up with a physical mechanism behind the behavior. What we would like to see is something at least as detailed and calibrated to known physical processes as this analysis https://geoenergymath.files.wordpress.com/2021/04/supplementarydocument-egu-2021.pdf
I have a reply for this, and it comes from my present analysis.
When I started all this years ago all I analyzed was the yearly H4 data. The OFT was not available to me at that time. What I did was select frequencies identified in the McCracken paper. The cycles came from this picture.
https://1drv.ms/u/s!AkPliAI0REKhgZIHbNeO-Skn-p-tYQ?e=puLPFl
From my current analysis with only nine cycles being used I get the following results.
https://1drv.ms/u/s!AkPliAI0REKhhLtmY5le4OwDq6xFFg?e=784xX3
https://1drv.ms/u/s!AkPliAI0REKhhLtn1f_h_K4e4OhH3Q?e=stHoJE
The correlation coefficient that goes with the figure reflects the coefficient for all the cycles I use. However, you can see for yourself with only nine cycles I get a good fit.
Certainly, it can be seen that known solar cycles are part of the total picture. That certainly can’t be hard to believe. BTW, I might take the time to find it but NASA has found that solar cycles seem to have an influence on volcanic activity here on Earth. Seems reasonable. If the Jovian planets can influence solar activity, it would seem they can influence volcanic activity.
It appears that you are trying to associate this with a “Jovian planet grand alignement”.
Obviously this can’t impact the earth directly as Jupiter has an order of magnitude lower tidal gravitational influence than the moon or the sun has on the earth.
So your tenuous connection must be that Jupiter is somehow influencing the sun in how it generates its magnetic dynamo variations, and then this slight perturbation on the sun’s radiation level is somehow impacting the sloshing of the equatorial Pacific thermocline. Recall that you are the one that is generating the close fits to the ENSO cycles in your charts.
I think you are taking this too far. That figure comes from the MCracken paper. All I was trying to reveal is that cycles that are associated with solar activity are present in the temperature signal. That is all.
With the limits of the H4 data it is quite doubtful that a 2300 year cycle would be identified. However, for the other periods identified in the figure their influence is present in the temperature measurements. That is clear.
Whether those cycles that are present are also linked to the Jovian planets I do not know. Those signals are present in solar activity and that is enough.
“I think you are taking this too far. “
Taking what too far? Trying to validate a model? You were showing off a model that was matching the fine detail of an ENSO time series in Figure 10.
https://onedrive.live.com/?authkey=%21ABvX9VoNuOY0un8&cid=A14244340288E543&id=A14244340288E543%2173170&parId=A14244340288E543%2173139&o=OneUp
I am having some problems here. With my reply above I was only thing to point out that some of the cycles in the solar activity are present in the analysis of the H4 data. Solar cycles play a part in the H4 data.
In your comment below you switched to my analysis of the MEI data. That was independently analyzed for cycles using the OFT method I described earlier.
The MEI figure is given below:
https://1drv.ms/u/s!AkPliAI0REKhhLttVcTMk2deGEnQsg?e=q8Dc9t
The MEI seems to be full of periodicities and it is quite clear that the cyclical analysis might be different than what I had for the H4 data.
Each dataset I analyze is independently analyzed for its cyclical content. The only two datasets that I analyze that look very much the same are the SST and the H4.
It could certainly be me, but I don’t know why we jumped to the MEI dataset. I am failing to understand your point.
Charles,
Could you show us your ENSO predictions for, say, five years out, so we can see how they perform?
“The problem with curve fitting markets occurs on the right side of the curve, where models attempt to predict the future. This is easy to see by applying curve fitting algorithms to random data, where more complex models can easily find patterns and relationships between dependent and independent variables that don’t actually exist, and make predictions with high statistical confidence that are actually more prone to error.”
https://towardsdatascience.com/how-markets-fool-the-models-and-us-e9eb60279899
Snape
I am aware of what you refer to. You will note that I don’t make projections from the UAH data since it is of short duration. From only 40 years worth of data the long period cycles are not identified. With the UAH data I have tried to use some of the long period cycles manually to see if they work. They do but I think the results are too contrived and I won’t issue them.
The solution I use for the H4 data has remained stable I would say for a year now. When I look at that long period of projection I do not sense the errors are building up and giving me wild swings toward the end.. I have done one more thing with the H4 data. I took it back in time and nails the depth of the LIA at around 1700.
Take another look at the graphs for the Nino regions. I do identify earlier solutions so that people can see how they have changed with the addition of data. I may not be there where I would extend the projection out too far since things are still in flux.
I may look back at one of my early reports but last year the NOAA projections showed a strong predicted El Nino, They were wrong and my prediction held.
I will look at a longer extension tomorrow.
This is just a little bug with me but please don’t say that FFT analysis is curve fitting. As I indicated I worked with them on rotating equipment for 35 years and I can’t recall one false indication from an FFT. When something in the vibration signature that had a significant S/N it was my job to come up with the remedial design measures to drive it as close to background as I could get it.
Your request is reasonable. I hope to get to it tomorrow.
The devil did not make me do it. You did Snape.
Snape
I have changed the charts from the Nino regions out to 2025.
Nino Region 1.2
https://1drv.ms/u/s!AkPliAI0REKhhLtuue586yepLyIrkg?e=cYSUQq
I have remarked before that region 1.2 is the noisiest. You might think that El Nino in 2024 is outrageous but then look at what was measured in 2017. For the Nino regions I think the OFT is still learning. The projections from May show you that. Until I see a solution that holds steady from month-to-month I would be reluctant to make long-term projections.
Nino Region 3.0
https://1drv.ms/u/s!AkPliAI0REKhhLtvmgoNpGKwIQnpow?e=QcPrU3
This certainly looks reasonable, and it shares the two humps in Nino 1.2 in 2024 and 2023. BTW, the hump in 2017 show up but not at the magnitude in region 1.2.
Nino Region 3.4
https://1drv.ms/u/s!AkPliAI0REKhhLtwhusD-cs3FLfcRQ?e=zqAWqS
I think this looks reasonable as well. It has the hump in 2024 like the others and it looks like it was trying to happen in 2023. The hump in 2017 is present here also.
Nino Region 4.0
https://1drv.ms/u/s!AkPliAI0REKhhLtxWW1E2sDeeUtJqg?e=piVb8n
This region deviates from the others. It has a strong hump in 2023 and a minor one in 2024. We shall see. I can’t judge that it is not reasonable.
H4 data
I decided to include this projection to see if there is similar behavior.
https://1drv.ms/u/s!AkPliAI0REKhhLtygQssQBQtrq5LRQ?e=vs0oHG
I am glad I did this. Notice that although this was independently analyzed, it captures the humps in 2017, 2023, and 2024. I think this helps support the validity of my analysis. Can the climate models do this? The behaviors are similar. It would seem that the H4 cyclical analysis can project forthcoming Nino region events.
That’s not what you should be doing. Nobody here or elsewhere will care nor remember that you created predictions for 4 years ahead, and that will more than likely be wrong anyways. What needs to be done is various forms of cross-validation that trains to portions of the historical time-series and validates on other regions. I am certain that if you try that, the extrapolated fits will be wrong as well. That’s what happens if you apply a straight Fourier series approach to curve fitting without the benefit of a known calibrated forcing, just like what is done with tidal analysis.
Once again, like this: https://geoenergymath.files.wordpress.com/2021/04/supplementarydocument-egu-2021.pdf
BTW, Charles May is the same as “charplum” who posted the same “I’m an expert in FFTs on rotating equipment with 35 years experience” on this blog in 2015.
https://clivebest.com/?p=2353#comment-6950
Perhaps in the 6 years that had passed that you could have kept track of your model fits on your own blog? They are free in case you didn’t know that.
geoenergymath,
I don’t understand your objection to Charles presenting forecasts based on his work. If they end up being a close fit to observations, it will be a big deal and people will take notice.
If a very poor fit, which I think is more likely, then his work could serve as a cautionary tale to other like minded skeptics.
Snape, He did forecasts in 2015 as charplum, so why don’t you take a look at his graphs and see how they turned out? In the following comment from August 2015, he says he manipulated “89 sinusoids” to come up with an ENSO fit.
https://clivebest.com/?p=2353#comment-7633
I do it with a single lunisolar orbital path and a couple of nonlinear transfer functions derived from a solution to a Laplace’s Tidal Equations fluid dynamics formulation (i.e. a GCM). So who is doing the actual geophysics required to come to a understanding?
I can’t see his 2015 charts – keep getting redirected to a Microsoft advertisement.
He probably took them down. People like “CHARLES MAY” are just a smokescreen occluding better analyses approaches.
There is no need for the snide remarks. I can’t get to them either.
Do not make it personal. I could say more but I will let it drop.
The whole House of cards of manmade climate change will collapse as soon as natural cycles are introduced whether from me or someone else like Prof. Scafetta.
You have no intention of looking at anything but your own analysis. I looked at your stuff and stated my case. So not holding my breath that you will consider an actual geophysics-based model of the El Nino Southern Oscillation behavior
https://github.com/pukpr/GeoEnergyMath/wiki/Laplace's-Tidal-Equation-modeling
For completeness sake, I compared it against a naive Fourier series analysis (your approach) at the end of that page. The issue is essentially one of over-fitting caused by using too many factors in a model.
The laws of nature don’t pay attention to stern pronouncements.
Geoenergymath
You seem very confident in your conclusion. We will just have to agree to disagree. I don’t want to make this personal.
As I have mentioned I had 35 years of experience with FFTs. I can even remember the first desktop analyzer I saw. It was the Nicolet 444. It was a single channel analyzer.
I can remember only one time when the FFT fooled us. We had a single discreet peak surrounded by 3 or four lesser peaks on each side. Dr. Whitlow, who has reviewed what I have done and presented herein, and myself called it a “fingerprint” and if we could find something similar in the equipment then we had the source.
Well, it turns out we were both fooled. What the FFT was identifying with those nearby peaks was the wow and flutter in the analogue tape recorder. Digital recording changed everything.
Dr. Whitlow was responsible for doing the signal analysis on my equipment. It was my job to remedy signals with a high signal to noise. BTW, I have total buy-in from Dr. Whitlow in what I have documented.
That is it. The FFT never lied. All identified peak frequencies were real. They were all components of the total signal.
I will also remind you that I am not using FFT. I am using Dr. Evans OFT. I give you a link below and a brief description of what the OFT does differently.
https://jonova.s3.amazonaws.com/cfa/optimal-fourier-transform.pdf
The optimal Fourier transform (OFT) is a new development in Fourier analysis, with greater sensitivity and frequency resolution than the traditional discrete Fourier transform (DFT). It takes much longer to compute than the DFT but offers benefits in analyzing noisy datasets. In particular, the OFT is better than the DFT at estimating the exact frequencies of sinusoids in a time series.
Like the DFT, the OFT estimates the spectrum of a time series, describing its sinusoids with a series of coefficients of cosines and sines. Unlike the DFT, it can analyze irregular time series (data points not equally spaced), it considers all frequencies (rather than just a small set of equally-spaced frequencies like the DFT), it orders the spectral sinusoids by amplitude (so the lesser ones, more likely to be describing noise, can be discarded or never computed), it typically describes the spectrum in far fewer sinusoids than a DFT (it stops when the sum of the spectral sinusoids is close enough to the original time series), but it is not invertible (the orig inal time series cannot be exactly recovered from the OFT of the time series).
This paper includes examples of the OFT doing things that the DFT cannot do.
This paper also introduces the manual Fourier transform (MFT), which analyzes a time series into a spectrum of sinusoids at a given set of frequencies. The DFT is a special case of an MFT. The MFT is one of the key ingredients in the OFT. In turn the building blocks of the MFT are the four suprod functions, which are also introduced here.
The OFT, MFT, and suprods are original, as far as we know. They are unlikely to be completely original because the ideas are obvious, but we cannot find similar work elsewhere.
I will also remind you of a statement Dr. Judith Curry made some time ago. When said that under Obama only CO2 climate change would be funded. Our government never funded any skeptical science. That is why we are in the mess we are in. Science has been corrupted.
geoenergymath
You are one snarky dude. I have thick skin and comments from the likes of you don’t bother me.
I do consider geophysical models.
This seems to be a valid depiction of how geophysical models work. The figure below comes from March 2019.
https://1drv.ms/u/s!AkPliAI0REKhhLt9lvBnl6CHu4hqFw?e=xRAzpj
That sure looks like a an El Nino in July 2019. Let us see what happened.
Well, it did not take long to completely change. Look below.
https://1drv.ms/u/s!AkPliAI0REKhhLt-7zbz5E60eQXKbA?e=S11OQb
If NOAA was a subscription weather service, you might have canceled your subscription. Better to go with Weatherbell where they look at the models and the analogues.
Topological considerations of Laplace’s Tidal Equation simplifications of Navier-Stokes applied to the equatorial themocline — here’s an evolutionary understanding via presentations and publications over the last 6 years
“Nonlinear long-period tidal forcing with application to ENSO, QBO, and Chandler wobble”, EGU General Assembly Conference Abstracts, 2021, EGU21-10515
https://ui.adsabs.harvard.edu/abs/2021EGUGA..2310515P/abstract
“Nonlinear Differential Equations with External Forcing”,
ICLR 2020 Workshop DeepDiffEq https://openreview.net/forum?id=XqOseg0L9Q
“Mathematical geoenergy: discovery, depletion, and renewal”
John Wiley & Sons, 2019, chapter 12: “Wave Energy” https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch12
“Ephemeris calibration of Laplace’s tidal equation model for ENSO”
AGU Fall Meeting 2018, https://www.essoar.org/doi/abs/10.1002/essoar.10500568.1
“Biennial-Aligned Lunisolar-Forcing of ENSO: Implications for Simplified Climate Models”
AGU Fall Meeting 2017, https://www.essoar.org/doi/abs/10.1002/essoar.b1c62a3df907a1fa.b18572c23dc245c9.1
“Analytical Formulation of Equatorial Standing Wave Phenomena: Application to QBO and ENSO” , AGU Fall Meeting Abstracts 2016, OS11B-04, https://ui.adsabs.harvard.edu/abs/2016AGUFMOS11B..04P/abstract
This is not just some superposition of sinusoidal waves model, it’s deep partial differential equation analysis.
If you torture the data enough it will eventually give you the answers you want.