Short term forecasting UAH lower troposphere

Posted: February 7, 2013 by tchannon in Analysis, Forecasting

On noticing Spencer has posted on WUWT about the latest UAH TLT global temperature, usually some days before gridded data is published, I did a very quick shufty, noting the new figure, then thought about updating the gridded I use here, then remembering not just yet.

However, I recall saying somewhere I expected a ramp up. Found the data directory, sorted by date, loaded a file to remind myself where I left things.

Image

As a reminder

Image

Left as is, transparent because I must have overlaid as a check.

Head figure shows two models, one where most recent data was withheld, the other using all, one of the things I do to give some idea on the sanity of extrapolation. (on checking, says to 2010, last data value December 2009)

Spencer’s report of .202, .206, .506 fits well enough with the model.

Why does this seem to work?

What I have noticed is how well sampled data of this kind has a pattern which has underlying structure. Any rapid deviation from this is hard. Really though I have no idea why. My assumption is it is the result of characteristic periods in some earth system interacting.

Biggest problem is when the dataset is changed, has happened many times, some without version number change.

Updated below

Very little change.

Image

Updated to Jan 2013. Filtered rises very slightly at the end.

Image

Updated to Jan 2013, filtered, model but not withheld version.

Future? Few points up there then down a bit, by then the extrapolation will know more data. Few months forecast is fine.

Yes you can hold me to this later. Better to show then always act safe.

h./t to WUWT

Post by Tim Channon

Comments
  1. tchannon says:

    Sorry if things are slow and non-controversial at the Talkshop. Rog is away and I’m not feeling too good again which doesn’t help brain engagement. (neither does the cold)

    Several people have suggested items but nothing I felt able to run with quickly. Lots here not ready.

  2. wayne says:

    “Sorry if things are slow and non-controversial at the Talkshop.”

    Slow? Non-controversial at the Talkshop? Tim, where are you? Try http://tallbloke.wordpress.com/2013/02/04/david-cosserat-atmospheric-thermal-enhancement-part-i-the-great-debate-begins/comment-page-1/#comment-43247 to get your mind of your cold. ;)

  3. From the Met Office

    “Our models cannot predict volcanic eruptions, the Mount Pinatubo eruption appears as a feature in the graph you refer to because these are retrospective forecasts, or hindcasts, which are used to assess the model performance. These should not be interpreted as actual forecasts. A hindcast is a way of testing a mathematical model. Known or closely estimated inputs for past events are entered into the model to see how well the output matches the known results. In retrospective forecasts volcanic forcing was specified, according to the CMIP5 protocol, such that eruptions occurring during the forecast were included even though they could not have been predicted at the time. “

  4. michael hart says:

    “Yes you can hold me to this later. Better to show then always act safe.”
    “Sorry if things are slow and non-controversial at the Talkshop.”

    Tim, I can think of plenty of places and people for whom predictions and statements they invite us to hold them to later would be outrageously controversial.

  5. michael hart says:

    I should add that clearly defining the perimeters and parameters of a serious prediction, at the time it is made, is critical. The consensus herd, like stock market gurus, know how to make elastic predictions that are difficult to nail-down when challenged later.

  6. Roger Andrews says:

    Interesting how the cooling following the 1984 El Chichón and 1991 Pinatubo eruptions fits the cyclic pattern. Volcanic eruptions aren’t supposed to behave like that.

  7. vukcevic says:

    R.A. Volcanic eruptions aren’t supposed to behave like that.
    Strange ? not a bit.
    High northern latitudes are very responsive to the old Sol

    http://www.vukcevic.talktalk.net/Ap-VI.htm

  8. steveta_uk says:

    Roger, I would have said that while the timing of the volcanos may happen to fit the downslopes, the cyclic pattern is very clearly disturbed downwards by those events.

    Two volcanic incidents that happen to fit within approx. 1/4 of a cyclic pattern is hardly beyond the bounds of chance events.

  9. tchannon says:

    RA, on seeing mention of volcanoes it crossed my mind there might be some on this data, perhaps illustrating how much I ignore them, no idea. Was going to look it up later.

    In my experience with minimal shape matching it is usually best to keep very simple, a trick is figuring out how far detail can go. In this case it is ridiculously minimal, with a very strong pattern.

    On actually thinking about it, goes left to right thump thump hole, thump thump hole … a meaningless pattern produced by a machine looking at the data. Begs questions though.

    Oddments trickling back into my brain, there was an excuse for the lack of the 1983 hot thing (never can remember the name) as a result of the volcanic eruption. The time delay between the eruption and the hole is long. Okay, fine.

    The second eruption is followed by a hole.

    The 1998 event is followed by a hole.

    2003 to 2006 is the peak of temperatures, now on the way back down. Aside: this co-incides with unusual solar/terrestrial magnetic conditions (and extensive ionospheric events), something I have been working on.

    We are currently at a second thump.

    It’s all horse manure, man seeing patterns. I’m uncomfortable doing this.

  10. Roger Andrews says:

    Vuk: Where did you get the “volcanic index” from? It shows a spike coinciding with Pinatubo but nothing coinciding with Agung in 1963 or Chichón in 1982 (not 1984, as I erroneously stated above).

    To me the question is how much of the cooling that followed these eruptions, in particular Pinatubo, was actually caused by the eruption. If a significant fraction of the Pinatubo cooling was a result of natural cycles, as Tim’s graphs suggest it was, then estimates of climate sensitivity based on the atmospheric response to the Pinatubo eruption are too high and the post-eruption cooling shown by climate models is overstated.

  11. vukcevic says:

    Hi Rodger
    I compiled it myself from the data for the northern latitudes where interaction between the Earth’s and solar magnetic fields is at its most evident. Eventually I will write some details.

  12. tchannon says:

    An aside although related, I was following up on something I knew a certain amount about, it seems though without newer revelations. An allegation which seems solidly suggested both by known fact and now a raft of released secret documentation is that the nuclear weapon scare was largely propaganda, in this case the nuclear winter idea has little foundation. Once such a widespread meme is inserted into a population it is never going to be removed.
    I knew some of it was nonsense.

    A telling snippet is that firestorms would not happen. The reason is about fuel density,rarely large enough, particularly given modern cities are not built of wood. In addition Russian work showed that severe blast destruction creates rubble which does no more than smoulder, same reason.

    Adding a little more, the two major problems for humans are first the tremendous thermal heat wave and then the blast wave. Radiation and contamination are much less of an issue. Injuries and death come from extreme heat burns and then supersonic shards of glass. There are descriptions of this such as from the individuals who survived both Japanese bomb drops. Take a train to Nagasaki and get caught again. Lived out normal lives.

    I’ve been shown private photos from that time by people who were there. Really strange stuff.

    Now, if the above is taken as the case it ought to come as no surprise that subconsciously supported 2+2=5 appear. Are these assumptions about volcanic eruptions based on belief?

    A possible additional instance of Armageddon announced was when oil facilities were set on fire during a Gulf war.

    I think the earth is far more stable than many assume. Natural variability is greater than certain sections accept in the face of strong evidence to the contrary.

    I’m going to largely vanish for a bit, is time to write a new article I’ve been meaning to do for some time, not that I can do more than scratch the surface. Been covered elsewhere but not on the Talkshop. This is critical to most of what we are doing.

  13. Doug Proctor says:

    Nice. A moderate view. Not to the extent that an Archibald would go with a Dalton-cum-Maunder around the corner.

    If the post-2000 “hiatus” is actually the top end of the warming, then I’d suggest we are going lower, maybe 0.4C. If the hiatus is where CO2/GHG warming equals a cooling, then what you have here looks reasonable. If you think that CO2 is only a portion of the previous warming, say 30%, then a quiet sun will have more of an effect, more of the -0.4C.

    Archbald refers to the north central US, the plains area in contact with Canada, the terrible place where all Americans know cold weather comes from. A 2C drop there is more like a 0.4C drop globally, telling a lot about thermal capacity and conductance rates of land vs sea water.

  14. Ninderthana says:

    Tim,

    The rough dates for the periodic twin peaks shown in your UAH TLT version 5.5 graph are:

    1980.7___1983.7
    1988.0___1991.0
    1995.3___1998.3
    2002.8___2005.8
    2010.1___2013.1

    # The separation of the peaks in each set of twin peaks is ~ 3.0 years.

    The time required for the perigee [line-of-apsides] of the lunar orbit to realign with the line-of-nodes of the Lunar orbit is 3.00 years.

    # The separation between each set of twin peaks is ~ 7.3 years.

    Multiples of half of the lunar synodic cycle (Msf) are almost exactly equal to whole multiples of a year, for 4.0 years, 4.0 + 4.0 = 8.0 years, 4.0 + 4.0 + 3.0 = 11.0 years, 4.0 + 4.0 + 3.0 + 4.0 = 15.0 years, and 4.0 + 4.0 + 3.0 + 4.0 + 4.0 = 19.0 years. Hence, spring tides that occur on roughly the same day of the year follow a 4:4:3:4:4 year spacing pattern (with an average spacing of (4 + 4 + 3 + 4 + 4)/5 = 3.8 years), with the pattern repeating itself after a period of almost exactly 19
    years. The 19.0 year period is known as the Metonic cycle. This cycle results from the fact that 235 Synodic months = 6939.688381 days = 19.000238 Tropical years.

    The line-of-apsides precesses once around the Earth with respect to the stars every 8.85 years.

    The beat period of this precession cycle with the time it takes the Spring tides to realign with the same day of the year is:

    (8.85 x 4) / (8.85 – 4) = 7.30 years

    Do you think that Moon has anything to do with these cycles [note: rhetorical question]?

  15. tchannon says:

    Can’t think of an obvious way the moon could change temperature.

    It must stay phase locked permanently.

    How can we test this? What actually does the moon do, I ask because whilst I am aware of theoretic ratios and other number stuff I don’t visualise at all.

  16. Roger Andrews says:

    Take out the volcanic eruptions and TLT is closely correlated with ENSO. It wouldn’t be surprising if there was a lunar/tidal component in ENSO.

  17. tchannon says:

    Sorry Ninderthana if I react cold, tend to do that, yes you have made a surprising observation.

  18. Roger Andrews says:

    Try this one on for size. Each of the three major volcanic eruptions of the second half of the 20th century was followed immediately by an EL Niño.

    Coincidence, or compensation?

  19. tchannon says:

    Coincidence, or compensation or conspiracy?

    How strange.

  20. Ninderthana says:

    Tim,

    I think what I am saying is that the cycle you have discovered (i.e the 7.3 year repetition of the twin peaks) in the recent world mean temperatures is possibly related to the time it takes for both the perigee of the lunar orbit and the phases of the Moon to realign with the seasons.

    Note also that 3 x 7.3 = 21.9 ~ 22 years – so it hints at a possible alignment of the Solar and lunar
    influences in the latter 20th century that may be responsible for some if not most of the warming.

    See: http://astroclimateconnection.blogspot.com.au/2011/11/el-ninos-and-extreme-proxigean-spring.html

    http://www.naturalclimatechange.info/?q=node/10

    and

    Possible forcing of global temperature by the oceanic tides
    Charles D. Keeling and Timothy P. Whorf

    http://www.pnas.org/content/94/16/8321.full

  21. Roger Andrews says:

    I like it. Back later with more. :-)

  22. Roger Andrews says:

    Ninderthana

    A year ago I wrote a post on how the sun might cause El Niños:

    http://tallbloke.wordpress.com/2012/03/16/roger-andrews-how-the-sun-caused-all-the-recent-global-warming/

    And you commented; “I hate to put a spanner (wrench) in the works, but I hope to publish a paper later this year that (I believe) will shows that the dominant triggering mechanism for the El Nino/La/Nina phenomenon are long-term lunar atmospheric tides.”

    Well, looks like you may have been right. But it would have been nice to have something other than a green ? coinciding with the 1997-98 “Superniño”. Maybe you might comment on how ? this event actually is.

    However, I still stand by my conclusion that all the recent warming was caused by ENSO-generated releases of stored heat from the ocean, similar to what Bob Tisdale theorizes but with a few twists.

    So if I’m right and you’re right, global warming was triggered by the moon (although with an assist from the sun, which put the stored heat in the oceans in the first place).

    The coincidence between lunar tides and the three volcanic eruptions is also intriguing. Do you get a similar coincidence with earlier eruptions, like Katmai, Santa Maria and Krakatoa?

  23. Ninderthana says:

    Rodger Andrews said:

    “However, I still stand by my conclusion that all the recent warming was caused by ENSO-generated releases of stored heat from the ocean, similar to what Bob Tisdale theorizes but with a few twists.”

    Yes, we both agree on the ENSO generated heat release of stored SOLAR heat from the oceans
    is most likely the dominant natural heating mechanism for the World’s mean temperatures.

    All I am saying is that between 1800 and 2013 there is an inordinate number of proxigean spring tides [these take place when A and N coincide on the plot that I posted at my blog site] that occur in the year prior to or the first year of an El Nino event. The number is so large that it cannot just happen by chance.

    It means that extreme proxigean spring tides must play a role in seting off El Nino events. It does not mean that all El Ninos can be explained by extreme proxigean spring tides by themselves (e.g. 1998). Other factors must also come into play.

    However, I believe that it is very likely that the Sun has some influence upon the inter-decadal changes tropical trade wind and mid-latitude westerly wind strength, mostly likely through
    the long term ~ 60 cycle (aka Nicola Scafetta’s papers). This could take place through a link between the Solar Inertial motion and changes in earth’s rotation rate:

    The Planetary Lunar Climate Connection

    http://www.gsjournal.net/h/papers_download.php?id=3811

    Are Changes in the Earth’s Rotation Rate Externally Driven and Do They Affect Climate?

    with possible reinforcement from syhronized lunar tidal effects.

    The Synchronization Between the Solar Inertial Motion and Lunar Orbit

    http://astroclimateconnection.blogspot.com.au/2010/03/synchronization-between-solar-inertial.html

  24. tchannon says:

    Do you have exact periods (earth time) for any of these lunar cycles?

    I can lock those in and see if anything fits.

  25. Ninderthana says:

    Tim,

    You will need to be a little more specific. What periods do you want?
    Many of the periods [stated to at least 6 decimal places] are available in this
    paper:

    http://www.benthamscience.com/open/toascj/articles/V006/49TOASCJ.pdf

  26. tchannon says:

    That’s fine thanks, can cherry pick, it’s just a thing to consider, I’m not expecting anything.

    Mass of stuff here on lunar paths http://xjubier.free.fr/en/index_en.html

  27. tchannon says:

    Initial attempts to force lunar met a strong “go away”, doesn’t want to know any which way. It very firmly insists ~7.6y is in there. (including put that as in addition to any trick I try on)

    First observation is this is roughly a major period in Hadcrut4, which is over a much longer timeframe. Is it the same? Not looked.

    What else could be the explanation for rejection?
    I am familiar with modulation causing an exact null, an actual factor is exactly missing.

    As I understand it we have a fiercely complex situation. We have a fast orbiting body around an ever faster spinning body. In this case with a single satellite trying to workaround aliasing, producing a part track, and that lot produces a sample point a month. And other stuff is going on.

    Goodnight.
    In theory given most of the parameters are closely known a huge simulation could be constructed which can run at very high time resolution and figure out what the satellite sees. If I was young, maybe.

  28. Greg Goodman says:

    tchannon says:

    Coincidence, or compensation or conspiracy?
    How strange.

    Willis Eschenbach has just been explaining a mechanism by which tropics can react on a daily timescale to compensate.

    http://wattsupwiththat.com/2013/02/08/slow-drift-in-thermoregulated-emergent-systems/

    I suggested that the reaction mechanism has limits and that it may take some time ot compensate for a major stratopheric eruption. I’ve been saying for a couple of years that volcanoes are long-term neutral because climate compensates. RogA’s Nino3.4 plot shows it very nicely.

    As usual climate scientists take the bit they want and ignore the rest.This is all part of the CO2 con-job. Without the volcanic cooling they would not need to be pumping up the CO2 effect with ficticious positive feedbacks.

  29. Greg Goodman says:

    Ninderthana says: It means that extreme proxigean spring tides must play a role in seting off El Nino events. It does not mean that all El Ninos can be explained by extreme proxigean spring tides by themselves (e.g. 1998). Other factors must also come into play.

    … must play a role in seting off El Nino ? I’d say more likely common cause of A and B rather than direct causality.

    You are very close to what I’m currently working on . Ill repost something I put in another thread here recently.

    53m =4.42a , I don’t need to spell out the rest. This appears to be a global wave. Probably what is commonly seen as circumpolar wave but I suspect is global.

    I’m finding a lot of 8.85 and harmonics in various basins using ICOADS v2.5 , I regard the Hadley datasets to be too heavily massaged to be of use in this kind of study.

    Tim, could you be more explicit about you “four term” model? What terms?

  30. Greg Goodman says:

    Tim , lunar orbit could easily affect climate if it is pulling large quantities of water in and out of tropics and polar waters.

    As inclination of lunar orbit is lowest, it will tend to draw water towards the equator, at the other extreme it would tend to spread it.

    Nino/Nina is about rising and lowering of the thermocline. Deep, colder, more saline (heavier) waters rise and fall. This is a basin wide phenomenon, like a huge oscillation of deep water.

    The accpeted explanation is winds cause warm water to pile up at one end and this pushes down. This seem both naive and improbable to me. It does not ring true.

    Cart before the horse I say.

    Should have something more definite on oscillations soon, but it’s time consuming. (At least the way I’m doing it)

  31. Greg Goodman says:

    Tim : First observation is this is roughly a major period in Hadcrut4

    Two points. Firstly Hadley is screwed. They have been mangling the data so much they have been inserting signals that are not there in ICOADS. They could me skilfully extracting some hidden underlying truth by my guess is they’re destroying structure of the data.

    As an exercise do the same precessing using ICOADS and see how the results compare.

    Also Hadcrut4 is a mix of HadSST3 and CRUT, that will muddy the waters even further.

    IMHO to detect cycles you need to get non-homogenised , non-pasteurised data , stick to SST and look basin by basin.

    As the graph I posted above shows, there is a global wave occurring but if you add all that together and take a global mean it will pretty much all average out.

    Not all basins are showing the same thing , though there are recurrent patterns. I have a fair amount to do on this but what I’m finding is far more of a harmonic nature than I expected.

    In fact I really did not expect to find these clear oscillations at all and I’m not doing some fourrier kind of exercise that assumes sinusoidal components.

  32. Greg Goodman says:

    Ninderthana says: (4 + 4 + 3 + 4 + 4)/5 = 3.8 years),

    could you explain this 44344 idea? I don’t follow. Is this different from a 3.8 year cycle rounded to the nearest year?

    45m was also a recurrent pattern I found and that is 3.75 years.

  33. Ninderthana says:

    Greg,

    I have a paper that will be published in the next month or so that shows that there are a number of hemispherical [and so possibly global] waves in SST and MSLP that are being driven
    by the 18.6/9.3 year draconic tides and the 20.3/10.1 year perigean spring tides. I am sorry but I cannot discuss the results of this paper until it gets into print.

  34. tchannon says:

    Bit pressed on time and energy at the moment Greg, handling the whole blog. Best bet is email me a time series, which includes operating on common data.

  35. Ninderthana says:

    Greg Goodman,

    It is important to note that many of the time intervals and
    orbital periods that are quoted are means or averages.
    The fact that they are averages allows us to quote them
    to the level of precision stated. However, in many cases
    there can be significant variation of these time intervals and
    orbital periods about the quoted value of the mean. Hence,
    the average values only become meaningful if we are
    considering time intervals that are long compared to the
    orbital period of the Moon.

    One Tropical year = 365.2421897 days ~ Seasonal year
    One Synodic month = 29.5305889 days
    1/2 Synodic month = 14.7652944 days = Msf

    Starting at a New Moon on January 1st at 00.00 hours U.T.
    you find the following differences after N tropical years.
    [Note: A New or Full Moon to occur up to 7.3826472 days
    before or after January 1st at 00:00 U.T.]

    N = 1.000 Tropical year = 365.2421897 days
    25.000 x Msf = 369.1323600 days
    Absolute Difference = 3.8901703 days
    [i.e. Full Moon will occur 3.8901703 days after end of 1st Tropical year]

    N = 4.000 Tropical years = 1460.9687588 days
    99.000 x Msf = 1461.7641456 days
    Absolute Difference = 0.7953868 days
    [i.e. Full Moon will occur 1.7953868 days after end of 4th Tropical year]

    N = 8.000 Tropical years = 2921.9375176 days
    198.000 x Msf = 2923.5282912 days
    Absolute Difference = 1.5907736 days
    [i.e. New Moon will occur 1.5907736 days after end of 8th Tropical year]

    N = 11.000 Tropical years = 4017.6640867 days
    272.000 x Msf = 4016.1600768 days
    Absolute Difference = 1.5040099 days
    [i.e. a New Moon will occur 1.5040099 days before the end of the 11th Tropical year]

    N= 15.000 Tropical years = 5478.6328455 days
    371.000 x Msf = 5477.9242224 days
    Absolute Difference = 0.7086231 days
    [i.e. A Full Moon will occur 0.7086231 days before the end of the 15th Tropical year]

    N = 19.000 Tropical years = 6939.6016043 days
    470.000 x Msf = 6939.688368 days
    Absolute Difference = 0.0867637 days = 2.08 hours!
    [i.e. A New Moon will occur 0.0867637 days after the end of the 19th Tropical year]

    Hence,

    4_____________ = 4.0 years
    4 + 4__________ = 8.0 years
    4 + 4 + 3_______ = 11.0 years
    4 + 4 + 3 + 4____ = 15.0 years
    4 + 4 + 3 + 4 + 4_ = 19.0 years

    represents the spacing at which the Synodic Lunar cycle realigns with the Tropical
    (i.e. seasonal ) year. The pattern is a result of the digitization of our calender into
    units of days. What you are seeing is a projection of a continuous (4+4+3+4+4) / 5
    = 3.8 year lunar cycle onto a digitized calender.

  36. Ninderthana says:

    Greg Goodman,

    Note the actual lunar spring tidal cycle is not exactly 3.8 tropical years but 3.796 tropical years. This is not that far off your 3.75 year value.

  37. Ninderthana says:

    Tim,

    We are all throwing ideas and unproven conjecture here. This is good as it is the nature of true scientific investigation. Have you noticed that:

    2 x 3.8 year = 7.6 years – may be this idea will fly?

    The 3.8 (= 19.00/5.0) year cycle is the one related to the realignment time
    between the seasonal (Tropical) year and the lunar Synodic cycle i.e. It’s roughly
    how long it takes the phases of the Moon (and hence the Spring Tides) to realign
    with the days of the month.

  38. Greg Goodman says:

    Ninderthana says:
    Greg,
    I have a paper that will be published in the next month or so that shows that there are a number of hemispherical [and so possibly global] waves in SST and MSLP that are being driven
    by the 18.6/9.3 year draconic tides and the 20.3/10.1 year perigean spring tides. I am sorry but I cannot discuss the results of this paper until it gets into print.

    OK, that brilliant. It will be interesting to see how our results compare, it looks pretty close. I guess you will be using a different method to that which I have developed so this should provide some useful corroboration for both of us.

    It is useful that you mention 10.1 years. I have been working in most detail on N. Atlantic and was expecting that when I manage to identify and remove the circa 9y what would remain woud be a clearer manifestation of the solar SSN signal.

    I was surprised to find that what was left looked like a much more a regular pattern close to 10.0 years.

  39. Greg Goodman says:

    “… lunar spring tidal cycle is not exactly 3.8 tropical years but 3.796 tropical years. ”

    the 45m I mentioned is the harmonic of 91m, to within the monthly resolution of the data, so 45.5 would probably be more accurate.

    91 / 12 / 2 = 3.792 years

    I would have to say 91 +/- 0.5m with this technique but it’s bang on target to be the cycle you indicated.

  40. Greg Goodman says:

    “What you are seeing is a projection of a continuous (4+4+3+4+4) / 5
    = 3.8 year lunar cycle onto a digitized calender.”

    OK, so there’s nothing irregular about it, it’s just that as the relative phase of the two cycles slides, at some point it will be nearer to 3 than 4.

    Thanks for the clarificaiton.

  41. Greg Goodman says:

    setting follow up notificaiton

  42. Greg Goodman says:

    yep, no surprises there. The “catastrophic accelerating melting” ended in 2007 !

  43. Greg Goodman says:

    oops. Too many people using wordpress, posted that to the wrong page. Sorry.

  44. Greg says:

    Tim : “On actually thinking about it, goes left to right thump thump hole, thump thump hole ”

    Look at the third panel in each of these. (Second diff of SST)

    In my simply correct ICOADS we see the trace of pairs of solar cycles. In the Met Office mangled version this structure has been lost.

    This is why I think the exercise of looking for cyclic signals is a waste of time on Hadley data. The frequency structure has been totally changed by their gridding process (which is quite a complex filtering / infilling / “climatology” process , not simply resampling).

  45. Greg says:

    I was splashing around in the Tropical S. Atl earlier and bumped by foot on this:

    You will recognise your bump-bump-trough, that I’d also pointed to in global ICOADS above.

    The “residual” here is because I was just fitting fund+2nd+3rd, that’s the bump-bump-trough. Now the residual was so obviously a heterodyne pattern and I quick saw it was 4th and 6th of the main 254month fundamental (21.17a) beating at 10.58

    So the bump-bump-trough is what you get when you filter heavily enough to remove 4th harmonic and above from 21 year pattern.

    These were the coeffs of the three terms in the bump-bump-trough:
    print a1,a2 ,a3
    0.0252947807800076 -0.0161982173181684 0.0113803631634106

    Now that is quite close to the taylor expansion of a triangular sawtooth.

    1/4 -1/6 + 1/9 x3 = -0.25 ( +1 -1/2 +1/3 …)

    http://www.intmath.com/fourier-series/1-overview.php

    All this is done in d/dt(SST) so the 0.25 is just a long term average rate of change, a vertical offset.

    So the “solar” pattern here is close to a 21 year ramp plus the blue chirp: a beats pattern of higher harmonics. Another feature of the Hale cycle is that there is often a double peak.

    The chirp also is close in form the the second derivative of the gaussian, The sombrero wavelet fn. Integrating back to the time series this would look like the guassian derivate: peak-trough.

    So it would seem that the bump-bump-trough is intimately related to Hale and Schwabe though was a bit disguised through over filtering.

  46. Greg says:

    Slight correction, though the window length I used was 254m, the fit latched onto a fundamental of 20.78 years, nearer to 252 months.

  47. Greg says:

    Fully fitted cycles for repetitive pattern in Tropical N. Atl.

    peak to peak = 12.828 K/century
    len=247; fitted = 246.081m = 20.507a

    print a1, a2 , a3, a4, a6
    0.0129543455615405
    -0.0163946964213131
    0.0198718372021518
    0.0304583435587401
    -0.010745097570464

    Even the small residual is crying out for the 7th harmonic.

    Note range is quite significant in size. The max excursion, ie the first bump, is about 0.65K/decade in amplitude, 1.2K/dec pk-pk.

  48. Ninderthana says:

    Greg,

    You might be interested in figure 3 in this article on my blog site:

    http://astroclimateconnection.blogspot.com.au/2012/06/singular-spectral-analysis-of-summer.html

    The spectrum displayed is reconstructed from the first 25 Principle Components of the Singular Spectral Analysis (SSA) of the median maximum daily temperatures in Adelaide between 1888 and 2011.

    If you use SSA to investigate the de-trended maximum temperature time series (see figure 2), you find that there are spectral peaks at all sub-multiples of the 22.3 year Hale (H) cycle from H/2 to H/10. The most prominent sub-harmonics are those at H/3, H/6, H/9 and H/10.

    This result strongly suggests that the long-term median summer time maximum temperatures in Adelaide are primarily being driven by factors that are associated with the 22.3 year Solar Hale Cycle.

    The presence of sub-harmonics in the temperature record is indicative of the fact that the ~ 22 year forcing term must have a broadened temporal structure that is triangular like in appearance.

    i speculated that the strength of northerly winds on the western side of high pressure systems might be controlled by a factor related to the Hale cycle. It is these winds that driving hot air off the central Australian deserts, producing heat waves in Adelaide summer. The strength of these winds would depend on the magnitude of the pressure gradients associated with the mid-latitude high pressure systems.

  49. Greg says:

    “The presence of sub-harmonics in the temperature record is indicative of the fact that the ~ 22 year forcing term must have a broadened temporal structure that is triangular like in appearance.”

    Thanks, that’a an interesting study though you’d have to go into a lot more detail before drawing the conclusion you state here. The plot shows magnitude but not sign. To suggest a triangle you’d need alternating signs in constantly decreasing magnitude ( 1/freq )

    I’m a bit distrustful of the whole principal component idea, I’ve seem some deceptive results produced that way. Another thing I don’t like is “NB first and fifth harmonics where used to detrend the data” . WTF? f +5th is not a “trend” . I don’t know what that’s about.

    However, the presence of all these higher harmonics is very interesting.

    I should add a note: the preivous plot I linked was tropical S.Atl , not North. I got my labels mixed. So this also relates to S.H. and shows similar extended harmonics present.

    Even the residual is clearly the 7th.

    I remains to be determined whether these harmonics are features of the solar cycle itself or the climate response to what is driving it.

  50. Greg says:

    One of repetitive patterns that came up actually looked surprisingly like the profile of a typical Hale cycle (though it was about 4.75 years)

    This illustrates that a the Hale cycle itself may just two harmonics, with the right phase delay:

    eg:
    hale(x)=a1*cos (2*pi*(x-z1)/p1) + a2*cos (2*pi*(x-z2)/(p1/2))

    chose a1 to give the length of Hale cycle and plot with following values:
    print a1/a1, a2/a1, z1, z2
    1.0 -0.2083
    0.6154 0.5589

    now there is a mathematical identity: sin(2x)=2.sin(x).cos(x)

    Considering that cos is the derivative of sine, this means that if a process and it’s derivative are inter-modulating, this will produce the second harmonic if they are in equal proportions.

    If they are unequal there will be the fundamental plus the harmonic. Further, if there is a delay between the initial effect and the manifestation of the derivative you have the small phase delay such as above.

    In the case of solar physics, if the surface activity dissipates some of the energy from whatever is causing it (which would seem at least likely) it would be simple to imagine a harmonic effect in the core with phase delayed derivative effect at the surface giving rise to the familiar form of the Hale cycle peaks.

    Just as an illustration: incoming radiative “forcings” produces _rate of change_ of temperature, they do not play on the temperature directly. On the ocean surface the temperature (not its derivative) will produce a second effect: in the sense of a negative feedback. Evaporative cooling and emissive radiation losses are a function of temperature. Evaporation , induced wind and Hadley cells, etc will take time to build up. There’s the phase delay.

    The resulting temp change would itself set up a similar chain of events so it is possible that at least some of this chain of harmonics is the result of the system response itself rather than the form of what is driving it.

    But working out the details is a job for someone else.

  51. Ninderthana says:

    Greg,

    Sorry, I have added to your confusion with my very poor explanation. You are correct to say that a little more detail is needed.

    Greg said:

    “Thanks, that’a an interesting study though you’d have to go into a lot more detail before drawing the conclusion you state here. The plot shows magnitude but not sign. To suggest a triangle you’d need alternating signs in constantly decreasing magnitude ( 1/freq )”

    The SSA method can be used to reconstruct a signal from a subset of the principal components. When you do this for the H/n (where H = 22.3 years) that are statistically significant (> 95 %), the reconstructed signal shows triangular-like pulses spaced at intervals of ~ 22 years.

    Greg said:

    “I’m a bit distrustful of the whole principal component idea, I’ve seen some deceptive results produced that way. Another thing I don’t like is “NB first and fifth harmonics where used to detrend the data” . WTF? f +5th is not a “trend” . I don’t know what that’s about.”

    I meant to say the 1st, 2nd and 4th,5th principal components (PCs). Those who are know the intricacies of SSA realize that the PCs come in pairs, that can be identified by their similarity in amplitude and [anti-]phase. The reconstructed signal from these four PCs produce a signal that accounts for most of the long term trends of the original times series. This reconstructed signal was used to remove this long-term trend from the time series.

    Note: The short length of the temperature record (~ 123 years from 1888 to 2011) means that it
    cannot be used to be used to investigate periodic cycles that are longer than ~ 1/5th of the time series length i.e. < or = 25 years.

  52. Greg says:

    ” The reconstructed signal from these four PCs produce a signal that accounts for most of the long term trends of the original times series. This reconstructed signal was used to remove this long-term trend from the time series.”

    Thanks,
    Perhaps we could avoid using the ill-defined and much abused term “trend(s)”. Since harmonics can only generate cyclically repetitive patterns, I assume you mean long term variations rather than “long term trends”.

    So what is the “long term trend” that you are removing ? Does your SSA also fit a linear rate of change that you are also removing.?