EMD Estimates of Natural Variation

Our approach so far has been to model natural climate variation of global temperature with sinusoidal curves, and potential AGW as increasing trends. A new algorithm called EMD (Empirical Mode Decomposition) promises to more robustly identify cyclical natural variation (NV), showing the contribution of NV and AGW to global temperature, and testing the IPCC claim that most of the recent warming is due to AGW.

Underestimation of natural variation (NV) is a crucial flaw in the IPCC’s logic, according to Dr Roy Spencer:

They ignore the effect of natural cloud variations when trying to diagnose feedback, which then leads to overestimates of climate sensitivity. … By ignoring natural variability, they can end up claiming that natural variability does not exist. Admittedly, their position is internally consistent. But then, so is all circular reasoning.

The relative contribution of AGW to temperature increase in the late 20th century underpins the IPCC global warming claims, according to the Wiki page on Scientific Opinion on Climate Change:

National and international science academies and scientific societies have assessed the current scientific opinion, in particular on recent global warming. These assessments have largely followed or endorsed the Intergovernmental Panel on Climate Change (IPCC) position of January 2001 that states:

An increasing body of observations gives a collective picture of a warming world and other changes in the climate system… There is new and stronger evidence that most of the warming observed over the last 50 years is attributable to human activities.[1]

Since 2007, no scientific body of national or international standing has maintained a dissenting opinion.

So estimating the relative proportion of natural variation vs. trend is very important. While widely used in other fields, EMD is relatively little used in climate science.

As an example, Lin and Wang (2004) used EMD for analysis of solar insolation. They claim that the solar eccentricity signal is much larger than previously estimated, more than 1% of solar irradiance, and adequate for controlling the formation and maintenance of quaternary ice sheets. This is a potential resolution of the 100,000 year problem, that has also been used to justify the necessity of CO2 feedback in producing ice ages.

Conventional spectral methods are strictly periodic — the period is constant in both frequency and amplitude. EMD relaxes these assumptions, allowing quasi-periodicity, which might explain why more variation is potentially explained. The EMD algorithm proceeds by first extracting out the highest frequency, called an intrinsic mode function (IMF) and leaving a residual. It does this to the next highest frequency, and so on, until only a trend is left.

While it is possible the residual is also part of a cycle — it is always possible to model a trend with a sinusoidal of long enough period — we treat this as AGW trend in order to estimate the maximum possible contribution of AGW to global warming.

Here are the results of applying EMD to the CRU global temperature series. Figure 1 below shows each of the 5 IMF’s and the residual, the remainder after subtracting out the periodics.

fig11

Each of the IMF’s is shown, with mean periods of 4.0, 6.6, 11.9, 23.4, and 55.1 years respectively. Most readers would be well aware of the similarity of these periods to major solar and oceanic cycles.

Below the CRU temperatures are plotting against the series, adding in each of the IMF’s sequentially to the residual, and we estimate the relative contribution of AGW and natural variation over a specific period from 1975 to 2000.

Here is the first IMF, showing the residual (solid red thin line), the largest IMF with a period of around 60 years (dashed thin red line), and the sum of the two (solid, thick red line) overlaid on the temperature in black.

fig111

The blue lines deliniate 1975 and 2000. The residual rises 0.157C during this time, but the first IMF rises 0.243C, giving a percentage contribution by the trend of only 39% of the overall rise during this period, suggesting most of the contribution is due to natural variation, and not anthropogenic factors.

Adding in the next IMF, the AGW is 0.157C, and the NV is 0.31 giving a contribution of only 33.8%.

fig12

Next is the residual plus 3 IMF’s. Here the AGW is 0.157C and the NV is 0.42C giving a contribution of only 27.1%.

fig13

You get the idea. Here is 4 and 5. AGW=0.157C, NV=0.49 is 24%, and AGW=0.157C NV=0.62 and 20%.

fig14

fig15

If we look at 1950 as the starting point, there is more time for the trend to increase, relative to the NV. Even so, the relative percentage contributions of the trend is 57%, 49%, 43%, 39%, and 34% for the IMF 1-5 respectively.

These results, based on the EMD algorithm at least, would seem to directly contradict the IPCC claim for which, since 2007, “no scientific body of national or international standing has maintained a dissenting opinion, that most of the warming observed over the last 50 years is attributable to human activities.”

Granted, we don’t know why natural variation could contribute almost 0.5C to global temperature over the space of 25 years, when solar insolation changes suggest a contribution of only as much as 0.1C from external forcing. I have a few ideas that I hope to pursue. However, its clear that strong claims about the contribution of AGW while NV is not understood is very premature, as according to Dr Roy Spencer:

In my experience, the public has the mistaken impression that a lot of climate research has gone into the search for alternative explanations for warming. They are astounded when I tell them that virtually no research has been performed into the possibility that warming is just part of a natural cycle generated within the climate system itself.

Turnkey R code for this analysis is here.

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63 thoughts on “EMD Estimates of Natural Variation

  1. When the magnitude of the Sun's magnetic field decreases (which results in a decrease in the number of sunspots), this allows penetration by intermediate energy cosmic rays which generate clouds around 6 km which results in cooling the Earth. Similarly, when the number and length of the cycle of sunspots increases, the solar wind picks up, the cosmic rays decrease, the clouds decrease and Earth heats. In short, it's the Sun and the Cosmos (hence the clouds) which drives the climate to first order – and local land use to second order. AGW is a pyramids of nonsense – even the term “greenhouse” is tragically misleading since on the Earth greenhouses heat because they lack turbulent cooling.

  2. When the magnitude of the Sun’s magnetic field decreases (which results in a decrease in the number of sunspots), this allows penetration by intermediate energy cosmic rays which generate clouds around 6 km which results in cooling the Earth. Similarly, when the number and length of the cycle of sunspots increases, the solar wind picks up, the cosmic rays decrease, the clouds decrease and Earth heats. In short, it’s the Sun and the Cosmos (hence the clouds) which drives the climate to first order – and local land use to second order. AGW is a pyramids of nonsense – even the term “greenhouse” is tragically misleading since on the Earth greenhouses heat because they lack turbulent cooling.

  3. This EMD looks like a good idea. The fastest cycling should be picked our first. This means the day-night cycle. People think they are being very clever by supposing that nature will average this out for them, but to rely on that is to throw away a very large part of the signal of interest, and to contaminate the rest of the analysis with effectively aliased unanalysed signal. And the many nearly periodic cycles are mostly not related by rational numbers.

  4. This EMD looks like a good idea. The fastest cycling should be picked our first. This means the day-night cycle. People think they are being very clever by supposing that nature will average this out for them, but to rely on that is to throw away a very large part of the signal of interest, and to contaminate the rest of the analysis with effectively aliased unanalysed signal. And the many nearly periodic cycles are mostly not related by rational numbers.

    • Indeed. Even though in the “mean” the minimum (early morning) temp is treated as equal in weight to the maximum (afternoon) temp, the two are obviously not radiatively equivalent, since radiation goes up by the fourth power of the temperature. For that reason ALONE but among several others, increases in maximum temperature are more important.

    • Yes there are a lot of interesting observations that I have not
      touched on. Eg, in analysis of the satellite record, the quasi-cycle
      is slightly longer that 12 months. Why? Similarly with day-night
      cycle, buffering could pump energy into longer period cycles.

  5. Indeed. Even though in the “mean” the minimum (early morning) temp is treated as equal in weight to the maximum (afternoon) temp, the two are obviously not radiatively equivalent, since radiation goes up by the fourth power of the temperature. For that reason ALONE but among several others, increases in maximum temperature are more important.

  6. Yes there are a lot of interesting observations that I have nottouched on. Eg, in analysis of the satellite record, the quasi-cycleis slightly longer that 12 months. Why? Similarly with day-nightcycle, buffering could pump energy into longer period cycles.

  7. By looking at ocean data only (UAH T2LT), there appears to be yearly cyclical patterns, particularly preceding, during and after El Nino events. I think the driver and indicator of global temps during this period (or any period for that matter) is in the tropical ocean and SOI seems to be tightly connected, which currently is reasonably similar to Oct/Nov 2006. During longer La Nina periods, the tropics dip quite a bit below global temps, then recovers to set up the next El Nino. I may be reading it wrong, but it seems the 97/98 El Nino left it's mark quite a bit longer after it waned, then over the next several years the cycles have become more predictable. Maybe the volcanoes Pinatubo and Crichton messed things up a bit. I think 2010 global temps will peak in Jan (most likely) or Feb, will be similar to 2007 in amplitude, and will be followed by another moderate to strong La Nina, perhaps more so than even 2008. Peak temps in 2010 will depend on the tropical ocean behavior in Nov/Dec. If it remains flat through the end of Dec, it is less likely Jan 2010 will be exceed .5C. Either way, it's the tropics to watch. El Nino persistence will also largely be dependent on the tropics IMO. I understand there are multiple ocean processes occurring and it is very complex, but for the past year I've used this simple method to fairly accurately forecast where it is now. While coolers were hopeful for continued drops in temps and warmers insist 2010/2011 will put global temps “back on track” with IPCC climate models, my take is OHC has remained somewhat constant since 2003 (although there is no definitive analysis), so if and until OHC makes a definite move up or down, we'll see this typical yearly pattern as seen in the following graphs, all the while producing a flat to increased cooling trend. Note the NoPol and/or SoPol are usually diverged from the rest of the oceans. Interestingly, since 2002, both the NoPol and SoPol are steadily trending downward which leads me to believe more cooling is in store. OTOH, I could be totally off my rocker on the whole thing! :)My question is, what drives the oceans? Black lines are global temps. http://tinyurl.com/ye3vzvzhttp://tinyurl.com/y85ry55http://tinyurl.com/yb8k5mhhttp://tinyurl.com/y8vlbpj

  8. I think you are thinking along the same lines. The EMD can be used topredict by predicting each cyclical component seperately andrecombining. If you think of the El Nino as one oscillation within alonger period oscillation it make more sense, and the intensity of itdue to phase locking of different cycles. What drives the oceans isthe forced oscillation from annual and decadal cycles interacting withnatural resonant periods.

  9. By looking at ocean data only (UAH T2LT), there appears to be yearly cyclical patterns, particularly preceding, during and after El Nino events. I think the driver and indicator of global temps during this period (or any period for that matter) is in the tropical ocean and SOI seems to be tightly connected, which currently is reasonably similar to Oct/Nov 2006. During longer La Nina periods, the tropics dip quite a bit below global temps, then recovers to set up the next El Nino.

    I may be reading it wrong, but it seems the 97/98 El Nino left it’s mark quite a bit longer after it waned, then over the next several years the cycles have become more predictable. Maybe the volcanoes Pinatubo and Crichton messed things up a bit.

    I think 2010 global temps will peak in Jan (most likely) or Feb, will be similar to 2007 in amplitude, and will be followed by another moderate to strong La Nina, perhaps more so than even 2008. Peak temps in 2010 will depend on the tropical ocean behavior in Nov/Dec. If it remains flat through the end of Dec, it is less likely Jan 2010 will be exceed .5C. Either way, it’s the tropics to watch.

    El Nino persistence will also largely be dependent on the tropics IMO. I understand there are multiple ocean processes occurring and it is very complex, but for the past year I’ve used this simple method to fairly accurately forecast where it is now. While coolers were hopeful for continued drops in temps and warmers insist 2010/2011 will put global temps “back on track” with IPCC climate models, my take is OHC has remained somewhat constant since 2003 (although there is no definitive analysis), so if and until OHC makes a definite move up or down, we’ll see this typical yearly pattern as seen in the following graphs, all the while producing a flat to increased cooling trend. Note the NoPol and/or SoPol are usually diverged from the rest of the oceans.

    Interestingly, since 2002, both the NoPol and SoPol are steadily trending downward which leads me to believe more cooling is in store. OTOH, I could be totally off my rocker on the whole thing! 🙂

    My question is, what drives the oceans?

    Black lines are global temps.
    http://tinyurl.com/ye3vzvz
    http://tinyurl.com/y85ry55
    http://tinyurl.com/yb8k5mh
    http://tinyurl.com/y8vlbpj

    • I think you are thinking along the same lines. The EMD can be used to
      predict by predicting each cyclical component seperately and
      recombining. If you think of the El Nino as one oscillation within a
      longer period oscillation it make more sense, and the intensity of it
      due to phase locking of different cycles. What drives the oceans is
      the forced oscillation from annual and decadal cycles interacting with
      natural resonant periods.

      • The signal is non-stationary and it’s non-linear.

        When you model a non-linear signal with a linear model, then model has no predictive power, i.e., it’s lagging indicator.

        And when you only look at a signal which is not stationary, i.e., when you’re only looking at part of the signal, then you’re setting yourself up to be fooled.

      • The purpose of the method is to extract out the stationary (ie cyclical) components of different period, leaving what EMD calls the residual. Now the residual could be a trend or could be a long period cycle. The debatable issues are over the nature of the residual, and the end point constraints. As you can see from the graphs, the residual in the period form 1975 to 2000 is almost linear anyway, even though it ultimately does appear cyclical, so makes little difference to the comparison of the amount of natural variation (ie stationary) vs trend over the period.

      • Since the signal is non-stationary, you only have a small piece of a non-linear signal of the signal to work with – hence you’re setting yourself up to be fooled.

      • In your rebuttal you might like to respond to this paper in PNAS.(http://rcada.ncu.edu.tw/reference008.pdf) with the identical analysis, except for stating that the relative proportion of NV exceeds the residue trend over the 19975-2000 period.

        “As discussed above, regression, moving mean, and filtering all are problematic in dealing with nonlinear nonstationary data.
        With these considerations, only the recently developed EMD method (1, 5–8) fits the requirements.”

      • Sorry you have to go, I would like for someone to prove that it is wrong to conclude that EMD shows natural variation exceeds the trend over the 1975-2000 period – which you have not done.

        The assumption that the residue is a all due to trend and not part of another cycle is designed to help AGW out maximally. As I said before, the residue could in fact be part of a longer cycle, but by assuming the trend is all due to AGW, it shows the maximum contribution that AGW could be making. And according to EMD, it is less than the contribution due to natural variation — therefore IPCC lies.

  10. The signal is non-stationary and it's non-linear. When you model a non-linear signal with a linear model, then model has no predictive power, i.e., it's lagging indicator.And when you only look at a signal which is not stationary, i.e., when you're only looking at part of the signal, then you're setting yourself up to be fooled.

  11. The purpose of the method is to extract out the stationary (iecyclical) components of different period, leaving what EMD calls theresidual. Now the residual could be a trend or could be a long periodcycle. The debatable issues are over the nature of the residual, andthe end point constraints. As you can see from the graphs, theresidual in the period form 1975 to 2000 is almost linear anyway, eventhough it ultimately does appear cyclical, so makes little differenceto the comparison of the amound of natural variation (ie stationary)vs trend over the period.

  12. In you rebuttal you might like to respond to this paper inPNAS.(http://rcada.ncu.edu.tw/reference008.pdf) with the identicalanalysis, except for stating that the relative proportion of NV exceedthe residue trend over the 19975-2000 period.”As discussed above, regression, moving mean, and filtering allare problematic in dealing with nonlinear nonstationary data.With these considerations, only the recently developed EMDmethod (1, 5–8) fits the requirements.”

  13. Since the signal is non-stationary, you only have a small piece of a non-linear signal of the signal to work with – hence you're setting yourself up to be fooled.

  14. Sorry you have to go, I would like for someone to prove that it is wrong to conclude that EMD shows natural variation exceeds the trend over the 1975-2000 period – which you have not done.The assumption that the residue is a all due to trend and not part of another cycle is designed to help AGW out maximally. As I said before, the residue could in fact be part of a longer cycle, but by assuming the trend is all due to AGW, it shows the maximum contribution that AGW could be making. And according to EMD, it is less than the contribution due to natural variation — therefore IPCC lies.

  15. The signal is non-stationary and it's non-linear. When you model a non-linear signal with a linear model, then model has no predictive power, i.e., it's lagging indicator.And when you only look at a signal which is not stationary, i.e., when you're only looking at part of the signal, then you're setting yourself up to be fooled.

  16. The purpose of the method is to extract out the stationary (ie cyclical) components of different period, leaving what EMD calls the residual. Now the residual could be a trend or could be a long period cycle. The debatable issues are over the nature of the residual, and the end point constraints. As you can see from the graphs, the residual in the period form 1975 to 2000 is almost linear anyway, even though it ultimately does appear cyclical, so makes little difference to the comparison of the amount of natural variation (ie stationary) vs trend over the period.

  17. In your rebuttal you might like to respond to this paper in PNAS.(http://rcada.ncu.edu.tw/reference008.pdf) with the identical analysis, except for stating that the relative proportion of NV exceeds the residue trend over the 19975-2000 period.”As discussed above, regression, moving mean, and filtering all are problematic in dealing with nonlinear nonstationary data.With these considerations, only the recently developed EMD method (1, 5–8) fits the requirements.”

  18. Since the signal is non-stationary, you only have a small piece of a non-linear signal of the signal to work with – hence you're setting yourself up to be fooled.

  19. Sorry you have to go, I would like for someone to prove that it is wrong to conclude that EMD shows natural variation exceeds the trend over the 1975-2000 period – which you have not done.The assumption that the residue is a all due to trend and not part of another cycle is designed to help AGW out maximally. As I said before, the residue could in fact be part of a longer cycle, but by assuming the trend is all due to AGW, it shows the maximum contribution that AGW could be making. And according to EMD, it is less than the contribution due to natural variation — therefore IPCC lies.

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