Inter-annual change in SOI and Carbon Dioxide

Ken Stewart, March 2012

Last April I demonstrated that changes in temperature precede changes in the concentration of atmospheric carbon dioxide.

Here I look at the increase in CO2 concentration more closely, and how it relates to atmospheric temperature and the Southern Oscillation Index (SOI).

There is no doubt that CO2 concentration has been rising, certainly since 1959, and that isotopic analysis shows this is largely due to fossil fuel burning.

But there’s more to the story.

This is a graph of CO2 concentration for the past 5 years, 2007-2011.


Some points to note:

The regular seasonal wave shows fluctuations.

There is a marked slowdown in February and March 2008 (following the temperature drop in the previous year), and another blip in March 2009 (resulting from the drop in energy consumption in late 2008.)

There is another slowdown in February, March, and April 2011.

The difference between consecutive peaks, and between troughs, varies each year.

These inter-annual differences interest me.

Here is a graph of the inter-annual monthly differences- the difference between the same months in consecutive years, e.g. January 2010 and January 2011.

Fig. 2

2010 was a very good year for CO2 increase.

Note the huge slump in the rate of increase in April 2008, and the even bigger and longer slump around April 2011.  In fact, April 2011 had the lowest inter-annual difference since July 2000.

The recent State of the Climate report claims that “Global CO2 concentrations in the atmosphere increased from 2009 to 2011 at 2 ppm per year” which is correct- the concentration in December of each year has risen by 2ppm. This was entirely due to 2010 however- by December 2011 the annual mean rise in concentration was down to 1.8ppm. 2011 was a below average year for CO2 increase. The BOM and CSIRO failed to mention this, I notice!

By comparison, here’s the same inter-annual rate of change for 1997 to 2001:

Fig. 3

There’s no comparison, is there?

Here’s a graph (2007- 2011 again) showing the relationship between rate of change of temperature and rate of change of CO2.  The temperature change has been doubled, and brought up to the same scale as CO2 change (2 is average).

Fig. 4

Notice once again that rapid temperature change precedes CO2 change by a couple of months. However, other factors may be involved.  Notice mid-2009.

Let’s zoom out and look at the 25 years from 1987 to 2011- actually, these plots show data up to February 2012.

Fig 5.  Temperature change vs CO2

I have marked in the eruption of Pinatubo, and the El Nino event of 1997-1998.  CO2 change can still be seen lagging temperature change.

Now compare temperature change with SOI change. Note that SOI values are inverted.

Fig. 6 Temperature change vs SOI change

Note: temperature change clearly lags SOI change by many months.

It has long been known that there is a link between ENSO events and CO2 concentration.  So can we see a relationship between inter-annual change in SOI and CO2?

Fig. 7 SOI change vs CO2 change

There is at least 10 months lag between SOI and CO2 change.

Now, smoothing with 12 month means:

Fig. 8: CO2, UAH, SOI changes

Applying 10 months lag to the SOI and 4 months lag to temperature:

Fig. 9: lagged SOI and UAH:

A pretty good match. El Ninos cause rapid CO2 increase. La Ninas and volcanoes are associated with slower CO2 increase.

Removing UAH shows the closer relationship between SOI and CO2.  Here the 12 month mean of SOI change has been advanced 10 months.

Fig. 10

Notice that in strong ENSO events the inter-annual change in CO2 can vary by more than 2 ppm per year.

Fig. 11

The 12 month mean of raw SOI (scaled: /20, +2) shows El Ninos occurring nearly a year before CO2 increase; La Ninas have a weaker match.

Here are graphs of SOI vs CO2 since 1959:  There are gaps in the CO2 mean because of missing months of data, after which 12 month means cannot be calculated.

Fig. 12

Notice the same pattern: CO2 change lags SOI change by nearly a year.

Fig. 13: SOI change advanced 10 months. ENSO events are shown as well.

Notice the very close match.

We can conclude that:

  • CO2 concentration is increasing, and the rate of increase has doubled from 1 to 2 ppm per year in the past 50 years
  • There is seasonal fluctuation in concentration
  • CO2 concentration responds not only to temperature change but also to changes in the La Nina- El Nino cycle, nearly a year later.

The ENSO cycles strongly influence changes in CO2 concentration- not enough to overwhelm it, but enough to double or halve the rate of increase. Much more study is needed.


Data used:

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6 Responses to “Inter-annual change in SOI and Carbon Dioxide”

  1. Jamal Munsh Says:

    Can you share the raw data with me?
    I would like to add to your analysis

  2. Geoff Sherrington Says:

    Hi Ken, I like simple, fun maths. For example, did you know that ‘Eleven plus two’ is an anagram for ‘Twelve plus one’?
    That said, I’ll have to read what you have written more closely, because of three possible concerns, a. Lags. It can be hard to distinguish a lead from a lag in this type of cyclic data – a few big anomalies are a help; b. Units; and c. Causation.
    At the end, we might find as usual that your maths and concepts are better than mine.
    a. Lags. Two similar aircraft can fly similar routes at different times, with one taking longer because of headwinds. It is lagged because of a mechanism that is known and can be measured separately, at least as to sense of direction. OTOH your Fig. 9, lagged SOI and UAH, involves some entities that are not so easy to measure separately.
    UAH is a mathematically manipulated microwave radiance of some gas species in certain layers of the atmosphere in various optional units, e.g. SI units W•sr−1•m−2•Hz−1 which in turn is converted to a temperature equivalent.
    From Wiki, ‘El Niño/La Niña-Southern Oscillation, or ENSO, is a quasiperiodic climate pattern that occurs across the tropical Pacific Ocean roughly every five years. The Southern Oscillation refers to variations in the temperature of the surface of the tropical eastern Pacific Ocean and in air surface pressure in the tropical western Pacific. The two variations are coupled: the warm oceanic phase, El Niño, accompanies high air surface pressure in the western Pacific, while the cold phase, La Niña, accompanies low air surface pressure in the western Pacific.’
    In a purer graph, you would be comparing temperature lagged against temperature, rather than an inferred temperature lagged against an SOI number that involves temperature and pressure. With a simple mind, one can drop out the temperatures either side of the equation and claim that the residual graph is a measure of air pressure. Even if this is an invalid move, the point remains that it is hard to devise a link analogous to the headwind in the aircraft example. This makes it harder to differentiate a 10 month lead from a 2 month lag with annual cycles.
    b. Units. These concern me because by your method of monthly subtraction you are performing a style of differentiation. The time differential of velocity is acceleration, and we can form a mind’s view of each of these. But, differentiate once more, which is valid mathematically, and you get another entity that it harder to envisage.
    When you show your figure 4 ‘Here’s a graph showing the relationship between rate of change of temperature and rate of change of CO2’, you are showing two entities that are harder to envisage than their origins. One has to ask the question ‘Is it part of your hypothesis that these entities must be linked in a physical way?’ to which I would have to answer ‘yes’. In other words, you are constructing a graph that assumes a dependence of rate of change of temperature on rate of change of CO2 or vice versa. This is the fundamental base of greenhouse warming theory, which is what all the argument is about. Only, in this case the magnitude of the relation between CO2 and T has not yet been derived by a clean experiment, so we have no analogy to the measurement of the headwind of those aircraft. Is it really correct to differentiate an entity like SOI which is more correctly a mixture of entities? What assures us that the same time scale rests below each of the sub-entities? I can readily agree that you show neat visual connections in your graphs that are suggestive of mathematical interrelationships. I’d be happier when the linking equations were solved, or as a minimum, shown to be free of killer conflicts.
    c. Causation. Within climate studies, various causations have been published. The IPCC was skewed from the beginning to show that globally, more atmospheric CO2 gives a higher temperature. There are many less grand relationships to examine and you have done so. Of course, these have value for predictive purposes, leading to amelioration and mitigation considerations, and so have importance in their own right.
    As to the main IPCC causation question, I have to agree with Pielke Snr –
    1) By virtue of the second law of Thermodynamics, heat cannot be transferred from a colder to a warmer body, and
    2) Since solar energy is the basic source of all energy on Earth, if we do not change the amount of solar energy absorbed, we cannot change the effective radiating temperature of the Earth.
    Both of the above statements are certainly true, but as we will show, the so-called Greenhouse Theory does not violate either of these two statements.
    Point 2 especially makes me think that your graphical work is a subset that is interesting in its own right, but hard to show in physics. If solar input is invariant (and I’m not saying it always is), then the temperature changes you are measuring are more from redistribution of energy within a closed construct than a reflection of global temperature changes in an open system. Analogy, more like measuring the variation of temperatures in a heating, stirred pot of water than measuring how much energy is coming from the gas jet below the pot and thinking about different implications from each process, when the aim is to discover how long it takes to boil. Some ways are harder than others, some ways give interesting supplementary information, some ways are prone to big errors.
    In the sense that you are chasing a way to predict future climate over a terms of some years at regional to country areas, it’s looking rather good. I’d be hesitant to extend it to the prediction of global temperature forecasting, because what with one thing and another, I don’t have confidence in any other reconstruction against which you could compare your success.
    I hope this helps. It’s not intended to hinder.

    • kenskingdom Says:

      Gday Geoff
      My response to your comments:
      a) Re SOI: straight from the BOM website, here’s how the SOI values I use (but invert) are calculated:-

      “There are a few different methods of how to calculate the SOI. The method used by the Australian Bureau of Meteorology is the Troup SOI which is the standardised anomaly of the Mean Sea Level Pressure difference between Tahiti and Darwin. It is calculated as follows:
      [ Pdiff - Pdiffav ]
      SOI = 10 ——————-
      Pdiff = (average Tahiti MSLP for the month) – (average Darwin MSLP for the month),
      Pdiffav = long term average of Pdiff for the month in question, and
      SD(Pdiff) = long term standard deviation of Pdiff for the month in question.”

      So my graphs are comparing rate of change of pressure difference with rate of change of CO2 concentration.

      b) The SOI is an index and doesn’t have units. Therefore my graphs don’t show units, although I suppose you could imagine Hectopascals per year vs parts per million CO2 per year. CO2 concentration is measured by partial pressure of CO2.

      c) Causation (which includes lags). The link between SOI and CO2 is well known, but the “lag” recognised varies from zero to 6 months, from what I have read. I am highlighting what I believe to be a lag of around about a year. The explanation given is the warming of water in the eastern Pacific in El Ninos followed by mid latitude drought and additional forest fires etc in SE Asia, apparently. See for example
      I think it would be courageous to posit the alternative, viz. a lead, implying that CO2 change causes ENSO events.
      I am not proposing a causal mechanism, but I suspect the oceans have something to do with it!


  3. kenskingdom Says:

    Thanks for your comments Geoff, I’ll have to spend a bit of time reading and thinking, and it’s the Qld election tomorrow so I’ll be a bit busy in the morning anyway. I’m confident I can justify re lags; units and causation are a bit tougher, though I’ve read a couple of papers that are (sort of) helpful. I’ll get back to you sometime!

  4. Geoff Sherrington Says:

    Sorry about the timing and length, Ken. It’s Sunday and the election results are out.
    I apologise for asking others to work through to a correct answer on Saturday, the same day that 70% of Queenslanders were preoccupied with doing the same. I am a Queensland lad myself.

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