RJ Salvador: Predicting El Niño predicts the climate

Posted: June 30, 2016 by oldbrew in Analysis, climate, Dataset, ENSO

We’re pleased to say: Rick Salvador has been busy again.
[This graphic has been added by the Talkshop mainly for entertainment value]

Credit: Wikipedia

Credit: Wikipedia

RJS writes:
The following demonstrates that Metoffice Hadcrut4 is a restatement of the NOAA El Nino index. It’s based on the conjecture that not only do El Nino events have an immediate effect on world temperature but also the clustering of El Nino or La Nina events have a cumulative effect on the worlds temperature. Ian Wilson and Paul Vaughan have provide the frame work to show that El Nino events are governed by the interaction of the Sun and Moon coupled with the hemispherical asymmetry of the Earth’s surface properties. The climate variation is driven by the ratio in strength and frequency of El Nino to La Nina events.

El Nino data is available here:

The Hadcrut4 data is available here:

The Hadcrut4 data is processed by averaging the eleven temperature series for each month and then taking a rolling 12 month average of the monthly result to give a global smoothed temperature change. The result is shown below.

The data is fitted to a sixth power polynomial and the numerical value of the polynomial subtracted from Hadcrut4 to get a linear result.

This linear result is shown in the following two graphics compared to the El Nino index.
The modern data from 1950 to 2016 show excellent coherence. The Historical data from 1880 to 1949 coherence is good but as the data has less certainty there are discrepancies.

Based on the conjecture that the climate is driven by the cumulative effects of El Nino and La Nina events the following graphic compares the summation of the El Nino index to Hadcrut4 rotated so that it is reflective around the zero axis of El Nino. The coherence is again good.

The next step is to generate the Hadcrut4 from the El Nino data by correlating the cumulative El Nino index and The El Nino Index by month to Hadcrut4. The equation to do this is:

HD4=K1*(Sum of (El Nino index +K3) + K2*(El Nino index 12 month rolling average).
HD4=K1*(Sum of (El Nino index +K3) + K2*El Nino index.

K1= 0.00430122394
K2= 0.0488407259
K3= 0.0528349012

The zero of the Index is adjusted upwards by K3. This gives the slight warming trend. (The index itself may have been constructed to give a zero sum game.) The graphic is below and is an excellent fit considering the quality of historical data and the simplicity of the equation.

Predicting El Nino predicts the climate.

  1. oldbrew says:

    ‘There is no consensus on whether climate change will have any influence on the occurrence, strength or duration of El Niño events, as research supports El Niño events becoming stronger, longer, shorter and weaker.’

    Are they looking through the wrong end of the telescope here?

  2. 1) Correlation is not causation, and 2) the above graphs are not the proper way to show correlation, for they rely on a subjective judgment of the “goodness of fit”. Do a least-squares regression, with y=temp. and x=El Niño summation, and check the R-square value for the regression; that will tell you what fraction of the variations in temperature are explained by variations in the El Niño summation.

  3. Well, now I see the last illustration, with an R-square value (my internect is slow dialup). Still, I would only be impressed with an R-square above 0.9.

  4. graphicconception says:

    I tried something similar about 18 months ago. I found a PDO Index and, I think, HADCRUT4. It looked to me that if I integrated the PDO it might match the temperature.

    After some judicious factors were applied it produced quite a good fit, IMHO.
    Note, I am not claiming this is science – just me playing with Excel.


  5. […] Source: RJ Salvador: Predicting El Niño predicts the climate | Tallbloke’s Talkshop […]

  6. Paul Vaughan says:

    Harry, it’s not just about r^2. It’s also about whether no systematic pattern’s left in the residuals (as a function of other variables including time & space).

    Recall that RJ got a more impressive fit using sunspot numbers a few years ago. I think people had a hard time interpreting that result, which can be mathematically re-expressed (equivalently, but easing interpretation) in terms of solar cycle deceleration and sunspot integral.

    Exploration is good. Discouraging exploration isn’t good.

    We’ve already briefly discussed the above in Suggestions-19.

    RJ, one more step you (or someone else) could take is to include an ENSO volatility term. The climate system is non-linear (for example due to latent heat), so there’s seasonal polar aliasing of tropical volatility.

    Also, I gained a lot of insight by looking at empirical ensembles of alternative ENSO indices (which can be extracted from SST, wind, pressure, & other climate fields using a variety of methods).

    Thanks for sharing exploration. It gives occasion to reflect and sort thinking.

  7. Poly says:

    Well done on an clear and simple climate model.
    As you said above “Ian Wilson and Paul Vaughan have provided the frame work to show that El Nino events are governed by the interaction of the Sun and Moon coupled with the hemispherical asymmetry of the Earth’s surface properties. The climate variation is driven by the ratio in strength and frequency of El Nino to La Nina events”.
    The work of IW and PV can also be used to predict the future ratio in strength and frequency of El Nino to La Nina events.
    Please round off your presentation on your model by adding a medium (5 – 10 year) prediction graph.
    Many thanks,

  8. oldbrew says:

    Solar activity correlation with NAO and ENSO
    – Simeon Asenovski, Boian Kirov, Yana Asenovska

    Click to access Asikainen_03_2014.pdf

    The pdf is mainly graphics, with comments.

  9. Bitter& Twisted says:

    The 12 month moving average graphs show “cause and effect”. i.e temperature changes follow El Nino events.

    Something that CO2 and temperature have never shown:

    Changes in CO2 concentrations do not show such a relationship where changes in global atmospheric CO2 are lagging 11–12 months behind changes in global sea surface temperature. Also changes in global atmospheric CO2 are lagging 9.5–10 months behind changes in global (Humluma,Stordahlc, Solheimd (2013) The phase relation between atmospheric carbon dioxide and global temperature. Global and Planetary Change; Volume 100, Pages 51–69).

    Nether do changes in CO2 precede those of temperature on longer timescales e.g Pedro, J. B., Rasmussen, S. O., and van Ommen, T. D.: Tightened constraints on the time-lag between Antarctic temperature and CO2 during the last deglaciation, Clim. Past, 8, 1213-1221, doi:10.5194/cp-8-1213-2012, 2012.
    “Our analyses of ice cores from the ice sheet in Antarctica shows that the concentration of CO2 in the atmosphere follows the rise in Antarctic temperatures very closely and is staggered by a few hundred years at most,”

  10. Ian Wilson says:

    Great Presentation RJ – Bob Tisdale and I (amongst others) have proposed a link between the ratio of the El Nino to La Nina strength and world mean temperature. As PV rightly points out, the redistribution of heat away from the equator during periods dominated by El Nino events, warms the planet. The powers that be do not support this view, preferring instead to believe that the El Nino/ La Nina climate events magically cancel each other out over time.

    Here is a link to my paper

    Wilson, I.R.G., 2013, Are Global Mean Temperatures
    Significantly Affected by Long-Term Lunar Atmospheric
    Tides? Energy & Environment, Vol 24,
    No. 3 & 4, pp. 497 – 508


  11. RJ Salvador says:


    Please would you correct the formula in the post to;

    HD4=K1*(Sum of (El Nino index +K3) + K2*(El Nino index 12 month rolling average).

    Thanks RJ.


  12. RJ Salvador says:

    Thank you for the link to your paper. It’s an impressive work. I think the evidence for your conclusion that Lunar atmospheric tides influence the formation of El Nino/La Nina is overwhelming. As you have said in post on an other website “it is right in front of your collective noses – but you just don’t want to see it!”
    I couldn’t agree more.


  13. RJ Salvador says:


    Thanks for your comments. The discussion you and Ian had about in suggestion 18 about lunar long-term cycles and your graphic on El nino clustering got me to look at this.

    Concerning Harry’s comment on the R^2=0.75.
    Harry I can raise the R^2 to 0.886 by adding a 4th constant. Not the 0.9 you were looking for but close.
    I try to find the simplest form to make the case.

    If you are interested the equation is still basically the same with an addition of K4 to shift the Temperature curve calculation and presumably to account for what has gone on before the integration (summation) of the El Nino index has begun.

    HD4=K1*(Sum of (El Nino index +K3) + K2*(El Nino index 12 month rolling average)+K4

    k1 = 0.002383702
    k2 = 0.044040941
    k3 = 0.182901466
    k4 = -0.303885287



  14. RJ Salvador says:

    The graphic of the 4 parameter correlation looks like this

  15. oldbrew says:

    Dr Roy Spencer reports ‘a 2-month temperature fall of -0.37 deg. C, which is the second largest in the 37+ year satellite record…the largest was -0.43 deg. C in Feb. 1988.’


    Also: ‘In the tropics, there was a record fast 2-month cooling of -0.56 deg. C, just edging out -0.55 deg. C in June 1998 (also an El Nino weakening year)’

  16. Paul Vaughan says:

    There has been a serious misunderstanding.

    I regard ENSO as zero-sum.
    I agree with Bill Illis on that.

    This may come down to semantics.

    My operational definition of ENSO almost certainly differs on several technical points with the definitions being applied by other climate discussion commentators.

    Remember: I explore multivariate empirical ensembles.
    Administration-type “official” definitions are too unhinged from raw exploratory insights.

    This gets far too philosophical to sort out efficiently in writing. Even a 3 hour face-to-face discussion wouldn’t be enough to overcome something like this. It might take several or countless discussions, spaced out over time, affording opportunity to reflect in between.

    When complex human misunderstandings develop, it’s a formidably monstrous task to to even confront them, never mind overcome them. We’ll have to see what we can do moving forward.

    Meanwhile I’m sort of glad RJ provoked us with his latest line of exploration, as it clarifies exactly what some of the misunderstandings are.

    I’ll be thinking about this, you can be sure. I’m not going to try to blast through all of the misunderstandings in one shot, one comment, or one sitting. Rather I’ll try to be tactical, perhaps by strategically pointing out a variety of things to add perspective. They may not even look related.

    I regard the notion that ENSO drives climate as a misconception, misrepresentation, &/or misinterpretation.

    Ian: One specific misunderstanding I will address now:

    Volatility is not the integral.
    The integral is not volatility. (Similarly the mean is not the variance and the variance is not the mean.)

    When I talk about polar seasonal aliasing of ENSO volatility, I am NOT talking about the integral of ENSO. (I have repeated this clarification a number of times, so it concerns me that the same misinterpretation of my comments keeps arising.)

    The multidecadal pattern in EOF4 is NOT the centennial pattern in EOF23. They differ fundamentally. One’s related to an integral and the other’s related to asymmetrically aliased volatility.

    I’m going to suggest an exercise for RJ (or anyone):
    Run the 4 parameter model on an empirical ensemble of ENSO indices (say 2 dozen of them) and see what types of insight arise from the exercise. (Remember: This is territory I’ve covered in past explorations.) Please be sure to include ICOADS wind (available through KNMI Climate Explorer). ENSO indices can be isolated from fields using EOFs.

    Most of the obstacles to better mutual understanding are philosophical, not technical. I sense profound resistance to holistic proof.

  17. Paul Vaughan says:

    Serious Concern:

    I just searched
    for “volc”.

    Nothing found…

  18. oldbrew says:

    El Niño and Global Temperature
    John L. Daly

    Still worth a look after all this time.

  19. Paul Vaughan says:

    OB, the interannual component of global average T does not always correspond with ENSO.
    As I’ve pointed out before, it actually corresponds best with the interannual component of AMO.

    Some readers may recall that I went to considerable lengths exploring interannual spatiotemporal coupling-switching and variation back around something like 2009-2010.

    Just remember that (a) circulation is braided and 4-dimensional, (b) aggregates are over braids, and (c) there’s interannually-varying energy tied up underwater, melting ice, and in the sky as precipitable water (latent heat, ocean heat content).

    Another way to look at it: a balanced multi-axial differential, bounded in aggregate by a constraint of the form a+b+c+d+…=constant. The interannual variations just bounce around a conservation law.

    When we sample the surface temperature, we’re only aliasing the energy. Some of it’s tied up underwater, melting ice, and in the sky as precipitable water.

    The core spatiotemporal attractors — not the yo-yos bouncing on them — have my attention.

    What RJ has done here: RJ has fleeced out of EOF2 a blend of EOFs 1, 2, & 4. My interpretation of this remains the same as ever (including when I ran dozens of analogous explorations using dozens of different ENSO indices over recent years): EOFs 1 & 4 are low frequency climate modes that bias EOF2 (which is ENSO).

    Someone may ask the question: How do they get into EOF2 if it’s supposed to be orthogonal? It’s the same answer I’ve given before: Non-complex linear methods are blind to derivatives and volatility envelopes by design. Thus, if one is to rely on such methods they also need to rely on higher interpretive awareness and judgment. (That will save a lot of algorithm & software development time.)

    More advanced algorithms featuring complex spatiotemporal embeddings and factor rotations can be conceived to separate the variance more elegantly. Meanwhile higher awareness is the only substitute and it should always be kept in mind that without it sensible interpretation isn’t feasible anyway.

    A side-effect of this exchange:
    I’ve recognized a way to geometrically differentiate EOF3 from EOF4.

    …and that’s a big deal …and this has made my day …so thanks to those who gave occasion to reflectively sort thinking towards clarity.


  20. J Martin says:


    1. What would the r2 have been on the last graph if the start point had been 1918 or where it looks like good correlation starts.

    2. Can a number be derived for co2 sensitivity from the K3 number which gives the residual warming trend. If it can, presumably this is close to 1 °C

  21. RJ Salvador says:

    J Martin:
    I too wondered if a physical significance could be ascribed to K3. However as usual in differential climate science the data base “zero” points are arbitrary or assigned to be the average of the data set which in the case of the El Nino index produces a zero sum game. All we can say about K3 is that if the data set “zero” was slightly lower, K3 could be eliminated as a parameter.
    As for starting the correlation of the four parameter correlation in 1918 the R^2 would be 0.892

  22. Paul Vaughan says:

    The assumption that CO2 accounts for any residual linear trend should not be so automatic.

    CO2 appears as a factor in NONE of the EOFs.

  23. Paul Vaughan says:

    I would love to see someone try to model ENSO in such a way that they also model RJ’s 4 parameter result. I look forward (with zeal) to commenting about any such attempt. 100% related: If anyone needs help using KNMI Climate Explorer’s “Make EOFs”, I will be delighted to support such due attention to the spatial dimensions. Regards.

  24. Paul Vaughan says:

    Time to drag this one out for fun:

  25. Paul Vaughan says:

    RJ: Thanks again for providing occasion to reflect and sort insights. There may be a way to express the integral versus volatility conceptual difference in a more readily recognizable format, I’m beginning to suspect.

    I’ve noticed that “volatility” does not register at all with climate discussion participants. I’m sure people know what volatility is (e.g. in the context of financial markets), but the observed resistance of the climate discussion community to recognizing, quantifying, and acknowledging it’s role in climate has been mysterious. All focus in discussion is on the mean, as if asymmetry isn’t even on the community radar.

    I think I have an idea now about how to pursue correction of this (perhaps accidental) efficient-communication obstruction.

    Sharing exploration keeps the wheels turning.

    Thank you.

    Next: I need to find some time to quantitatively explore some dead-simple intuition about asymmetry that has dawned as result of this exchange… (time-frame: weeks to months probably)

    Meanwhile: I look forward to more stimulating contributions & links from other volunteers.

  26. Paul Vaughan says:

    2 notes — not criticisms of anything done here but rather technicalities for explorers to note, ponder, and learn from now or later:

    1. Neither the 3 nor 4 parameter models mimic the BDO (bidecadal oscillation). (This is a clue — to be discussed in future.)

    2. Look at the spatial pattern biting this when reviewing ERSST EOFs1-4:


    A) EOFs3&4 are both informing about sun-driven MOC (meridional overturning circulation).
    B) EOF4 is about multidecadal asymmetry of winter hemisphere equator-pole gradients defined by solar cycle length (elaboration in future as time/circumstances permit). (Note that this is a modification of how I’ve put it in the past — e.g. in Sun-Climate 101 versions 1 & 2).
    C) EOF3 is the sun (solar cycle) scrambled by the BDO = 1 / (J-S).

    C was previously a missing link in the puzzle. With it, now everything’s falling into place.

    These notes may make little sense as presented here at this time, but at least the notes are here for future reference …and contemplation can begin without delay.

  27. Paul Vaughan says:

    I’ve devised an index contrasting the effects of La Nina & El Nino on spatiotemporal pattern.
    MEIx (extended multivariate ENSO index) is split into 2 variables: 1 for El Nino & 1 for La Nina.
    An index of how they fight is then calculated and 3 nice results fall out:
    1. BDO
    2. 96
    3. coherence with explosive volcanism

    FYI this is the 1st time I’ve seen BDO visible to the naked eye in an ENSO index.

    That was easy.

    So to underscore what I’m trying to convey: It isn’t just about the integral of ENSO. It’s also about how El Nino & La Nina fight each other in a cumulative battle to shape spatiotemporal pattern.

    What RJ has shown pulls out the multidecadal wave (~66 years or whatever).
    To get the BDO & centennial wave demands only an analogous integration but with MEIx split into + & – (El Nino & La Nino) and then contrasted. This underscores the asymmetry in the variance & volatility structure. El Nino & La Nina aren’t just opposite ends of some linear sinusoidal quantitative continuum. They differ qualitatively.

    That may seem a little vague at this point, but it will be enough (for now) to get people thinking of El Nino & La Nina as being qualitatively different and wondering more intensely why the asymmetry gives BDO & 96.

    A bright person with the right combination of background knowledge could probably finish cracking this puzzle all the way to completion in one intense, focused sitting.

  28. oldbrew says:

    Anything relating to ENSO here?

    Monthly hemispheric sunspot numbers
    The North and South components of the monthly smoothed sunspot number for the last five cycles (13-month smoothed monthly values). Green fill color when the North number is higher than the South number, and red color when South is higher than North.

    The plot is based on data from the Uccle station (Royal Observatory of Belgium) up to 1991 and from the WDC-Sunspot Number network since January 1992.

  29. Paul Vaughan says:

    Yes, 9-11 96 year coherence (as we already knew).

  30. oldbrew says:

    Notice there’s very little red (‘when South is higher than North’) between 1950 and 1980.

    No sunspots at start of July. Current average barely above zero either.

  31. Paul Vaughan says:

    OB, a few years back we dug into the N-S asymmetry stuff.
    Imageshack links don’t work anymore, so all I illustrated back then is no longer linkable.
    …but here’s a little review:

    11.06964992 = 1/JEV
    9.007246722 = 1/SEV

    (11.06964992)*(9.007246722) / (11.06964992 – 9.007246722) = 48.34508981
    (11.06964992)*(9.007246722) / (11.06964992 + 9.007246722) = 4.966258966
    (11.06964992)*(9.007246722) / ( (11.06964992 + 9.007246722) / 2 ) = 9.932517933

    (22.13929985)*(18.01449344) / (22.13929985 – 18.01449344) = 96.69017963
    (22.13929985)*(18.01449344) / (22.13929985 + 18.01449344) = 9.932517933
    (22.13929985)*(18.01449344) / ( (22.13929985 + 18.01449344) / 2 ) = 19.86503587

    (29.447498)*(11.862615) / (29.447498 – 11.862615) = 19.86503587
    (19.86503587) / 2 = 9.932517933

    (11.06964992)*(9.932517933) / (11.06964992 – 9.932517933) = 96.69017963

    (11.862615)*(9.932517933) / (11.862615 – 9.932517933) = 61.04648218
    (11.862615)*(11.06964992) / (11.862615 – 11.06964992) = 165.5999728
    (165.5999728)*(61.04648218) / (165.5999728 – 61.04648218) = 96.69017963

    There are several ways to look at it.

    This is a solar cycle geometry attractor.

    practical efficient-communication concern noted here to start raising sharper awareness:
    People conflating the 61 year (Jupiter/Saturn geometry) cycle with the 66 year cycle (NOT THE SAME THING) will get themselves mightily confused. I know this is going to happen. I’ll have to mull over what (if anything) can be done to help avert the (unwelcome) impacts on communication efficiency.

    I have more faith that people will be able to get their heads around the Core Angular Momentum of 96, but I will note here that this is taking too long and we are now behind schedule…

  32. Paul Vaughan says:

    Centennial (96 year) El Nino – La Nina ASYMMETRY!!!

    To split MEIx into separate El Nino & La Nina indices, simply use 0 as a cut-off — i.e. El Nino index = MEIx except El Nino index = 0 whenever MEIx is negative; La Nina index = MEIx except La Nina index = 0 whenever MEIx is positive.

    The assumption of uniformity is TOTAL BS and the dark agents pushing it are long past due for correction.

    Folks, we are behind schedule and this is serious. Please redouble your efforts, being more serious than before. It’s ridiculous that the intransigence should continue — absolutely ridiculous.

  33. Paul Vaughan says:

    Geopolitical Asymmetry 101…
    I advise all sensible nations to give the leading European nation a favorable trade deal without any further delays. The realignment has to be in place before nature’s deadline.

  34. Poly says:

    Well done on your “Centennial (96 year) El Nino – La Nina ASYMMETRY” graphic.
    A very clear representation of long term movements and the assumption of El Nino – La Nina uniformity is strongly challenged!

  35. Paul Vaughan says:

    Thanks Poly.
    It’s actually quite simple.

    There are just 2 different sets of circulatory wheels
    (where 1 was falsely assumed):


    The mainstream isn’t being serious.
    They’re too caught up in politics.

    The corruption is epic.
    It will never go away on its own.

    It needs assertive help:
    Step #1: ERSSTv4 must be retracted.

    This is a trust issue.
    It’s non-negotiable.

  36. Paul Vaughan says:

    Centennial review (Georgieva, Tsanev, & Kirov) with 96-sharpened hindsight:
    https://tallbloke.wordpress.com/2013/03/02/bias-in-solar-activity-the-combination-of-hale-wolf-and-wolf-gliessberg-cycles/#comment-45336 (March 3, 2013 at 4:37 pm)

    (11.06964992)*(9.932517933) / (11.06964992 – 9.932517933) = 96.69017963
    (22.13929985)*(19.86503587) / (22.13929985 – 19.86503587) = 193.3803593
    (193.3803593) / 2 = 96.69017963

    (22.13929985)*(18.01449344) / (22.13929985 – 18.01449344) = 96.69017963
    (22.13929985)*(18.01449344) / (22.13929985 + 18.01449344) = 9.932517933
    (22.13929985)*(18.01449344) / ( (22.13929985 + 18.01449344) / 2 ) = 19.86503587

    (11.06964992)*(9.007246722) / (11.06964992 – 9.007246722) = 48.34508981
    (11.06964992)*(9.007246722) / (11.06964992 + 9.007246722) = 4.966258966
    (11.06964992)*(9.007246722) / ( (11.06964992 + 9.007246722) / 2 ) = 9.932517933

    That’s the core 48 year volcanic valve we were missing on polar aerosol contrast (~1917 – ~1965):

    Remember that SST BDO is J-S while CAM BDO is Hale, so the reconstructed historical PDO BDO needs a geometric spatiotemporal rethink. (I hope at least a few people are following…)

    The way the mainstream thinks about explosive volcanism, ENSO asymmetry, earth orientation parameters, & core angular momentum (CAM) is due for HOLISTIC adjustment.

    The methodological pendulum unnaturally (with a little political help from California & Mainland Europe) overshot western reductionism and now naturally swings holistically eastward.