Poles Apart

Satellite data from UAH (University of Alabama- Huntsville) are estimates of temperature in the Lower Troposphere, and thus a good indicator of whether greenhouse warming is occurring.  My next post about the length of The Pause in various regions will be ready in a few days’ time.  Meanwhile, I’ve been looking at the data in a different way.

In this post I will be examining how and when temperatures have changed in discrete regions of the globe, including over land and over oceans.  There are no startling revelations, but a different approach reinforces the need to understand climate variability in different regions.  The important regions of course are the Tropics and the Poles, and fortunately UAH data is available separately for just these three regions.

Firstly, Figure 1 shows the regions for which UAH has atmospheric data.

Fig. 1:  UAH Data Regions


The Northern and Southern Extra-Tropics include the Polar regions, so there are three discrete regions which do not overlap: Tropics, North Polar, and South Polar.  It would be very helpful if Dr Spencer provided data for the Extra Tropical regions excluding the Polar Regions.

For this analysis I use CuSum, which is a simple test of data useful for detecting linearity or otherwise, and identifying sudden changes in trend, or step changes.  It can be used for any data at all- bank balance, car accidents, rainfall, GDP, or temperature.  It is simple to use:  find the mean of the entire data, calculate differences for every data point from this mean, then calculate the running sum (Cumulative Sum) of the differences.  If done correctly, the final figure will be zero.  Plot the CuSum usually by time and identify points of any sudden change in direction.  A generally straight or smoothly curving line indicates linearity, but points of sudden change mean a change in trend or a step change.  (Further, data series with identical start and end points, exactly the same number of data points, and anomalies from the same period- such as UAH- should produce directly comparable CuSums.)  These points, and ranges between them, are then checked in the original data. The usefulness of CuSums will become obvious as we go, especially as they are compared.

The next figures show CuSum plots for various regions.

Fig. 2:  UAH CuSums for all regions


Points to note:

The brown line at the top is the South Polar region.  The line wobbles about zero, indicating little relative change in temperature from the mean.  Contrast this with the North Polar region (the blue line at the bottom.)  The Polar regions are conspicuously different from the other regions and from each other.

The spaghetti lines clustered in the middle are CuSums for (in order from top to bottom): Southern Extra-Tropics; Southern Hemisphere; Tropics; Globe; Northern Hemisphere; Northern Extra-Tropics.

The red arrows point to wobbles coinciding with major ENSO events.  These changes in direction indicate trend changes or step changes in the original data.  There are other changepoints, notably 2002-2003.

The vertical red line joins changepoints in all the CuSums in mid-1991 following the eruption of Mt Pinatubo.

Fig. 3: UAH CuSums for the Tropics, South Polar, and North Polar regions


Note there is little similarity between CuSums for the only regions with discrete data, and you have to look carefully to see North Polar CuSums changing some months after Tropics, but not always.

The next plots show the differing responses of Land and Ocean areas.

Fig. 4:   UAH CuSums for the Globe, Land and Ocean


Note that Land areas have greater relative temperature changes than the Oceans, and that the Global mean closely mirrors the Ocean CuSums (as the Globe is mostly Ocean).  The major turning point is in 1997-98.

Fig. 5:  UAH CuSums for the Tropics, Land and Ocean


Note once again the mean CuSums closely follow that of the Ocean as 20 degrees North to 20 degrees South is mostly water.  The changepoints are very distinct.

Fig. 6:  UAH CuSums for the North Polar region, Land and Ocean


Note that all CuSums are close, but after 1982 Ocean CuSum changes relatively more than Land- the blue line has switched to below the mean.  The main changepoints are 1991, 1993-94, 2002, 2009, and 2015.

Fig. 7:  UAH CuSums for the South Polar region, Land and Ocean


Now that is interesting.  Note all three CuSums have similar changepoints, but Land varies more than Ocean and after 1992 Land is largely negative, Ocean is largely positive.  The Land CuSum range is about half of the North Polar equivalent.

Remember CuSums in Figure 4 showed Land temperatures must vary more than Ocean (though not in the North Polar region).  The next figures show plots of UAH original data (not CuSums).

Fig. 8:  UAH original data for the Globe, Land and Ocean


I find a visual representation demonstrates greater relative variation in Land temperatures well.

Fig. 9:  UAH original data for the Tropics, Land and Ocean


Note much greater fluctuation with ENSO, and Land varying a little more that Ocean.

Fig. 10:  UAH original data for the North Polar region, Land and Ocean


Note the much greater variation, but Land is more often than not masked by Ocean.

Fig. 11:  UAH original data for the South Polar region, Land and Ocean


Note the much greater range in Land data, with large non-linear multi-year swings- calculate a linear trend for Land at your peril.

Having found changepoints, we can now analyse periods between them.  One way is to calculate means, and step changes between periods.

Fig. 12:  UAH original data for the Tropics based on CuSum changepoints


I deliberately ignored the 2001 changepoint- it made very little difference to means and appears to be a continuation of the series starting in 1997.  Note the step changes are very small, and the final step change is reliant on current data and will change.  While I have shown means and steps, the data are decidedly non-linear with sharp spikes and multi-year rises and falls.

Fig. 13:  UAH original data for the North Polar region based on CuSum changepoints


Note the large step change in the mid-1990s occurs before the 1997-98 El Nino.  The range is much greater than the Tropics.

As the Land data for the South Polar region looks more interesting, I decided to use Land instead of the mean.

Fig. 14:  UAH original data for the South Polar region (Land data) based on CuSum changepoints


Up and down like a toilet seat!


The data series are characterised by step changes and multi-year rises and falls.

The Polar regions are “poles apart” in their climate behaviours.  Explanations might include: different geography (an ocean almost surrounded by land but subject to warming and cooling currents vs a continent isolated from the rest of the world by a vast ocean); different snow and ice albedo responses; different cloud influences.

The Global mean combines data from regions with very different climatic behaviour.  Averaging hides what is really going on.  The Tropics are governed by ENSO events, and the Poles are completely different.

Please Dr Spencer can you provide separate data for 20-60 degrees North and South?

Comments and interpretations are most welcome.


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9 Responses to “Poles Apart”

  1. michaelspencer2 Says:

    Ken, you might be interested in a discovery made by a fried of mine into the true shape of a magnetic field, with the possible implications of what this might mean for understanding more logically the weather patterns and winds in different parts of the globe. We recorded a very simple little experiment (confirmed by Gaussmeter testing separately), and you will find the link on page 30 of this interactive PDF I’ve assembled about the weather: http://galileomovement.com.au/media/ShouldYouReallyBeAlarmed.pdf

    And, what a surprise; I think there just might be a link or two to your work included!


  2. robinedwards36 Says:

    As some of you will know I have been using cusum methods on climate-related series for many years (since 1992). I have produced thousands of graphics for my own amusement and instruction, and feel myself to be reasonably expert in their interpretation! Many different types of climate data and derivatives thereof are amenable to quite sensible analyses by this means, together with (occasionally multiple) linear regression when the cusums indicate that this is a reasonable model over a defined time region. I seem not to have the technology to post diagrams in blog replies – can someone send or post /full and simple/ instructions about how to do this.

    I like Ken’s brief description of some of the properties and interpretations of cusum plots very much, but as he is aware there is a great deal unsaid, with perhaps the simplest and most important concerning the overall general shape of the plot. This is often the most striking thing to a newcomer. Most of the plots here are in their most general interpretation of a V or U shape, not inverted V or U. (The U/V shape means that the original data exhibit an increasing trend, inverted symbols the opposite.) A linear fit to the data will have a positive and often (statistically) significant slope, but this does NOT mean that the linear fit is sensible. It is simply what climatologists think of as the “trend”. Incidentally, climate series are sometimes very long, The CET monthly means series is around 4700 items. This has, I believe, an interesting effect on the inferential statistics of the trend, in that the often cited Quenouille Correction for auto-correlation of residuals has effectively no effect because the t statistics of uncorrected and corrected residual degrees of freedom are almost identical. With some series, however, the correction is very important. My software produces all this stuff automatically!

    Cusums of this type can disguise some other features that could be read into the plot because their negative and positive slopes tend to camouflage other slope changes that might be important in a practical sense. One answer to this problem is to generate cusum plots of segments of the data that represent sections where the original cusum has a marked slope. I typically make several segmented plots of seemingly “linear” sections cusums, often revealing very interesting features that are not obvious in the overall cusum. It is also useful to create close-ups of the cusum, with data points individually visible, over regions of suspected step changes. This is especially useful if monthly data are available but because of gross seasonal effects are averaged to form annual values. I compensate for seasonal effects by subtracting the overall monthly means from their respective single month values. This simple operation can transform complex distributions to ones that are closely similar to the often desired normal distribution, which of course never occurs in the real world.

    A criticism of cusums that is sometimes advanced is that if they are applied to a non-stationary series (such as climate data almost invariably are) a U/V-type pattern tends to exaggerate the visible impression given by the plot, in particular creating the impression of a major change in roughly the centre of the series. De-trending – by fitting a linear model and calculating the residuals – produces a stationary series which gives a somewhat better impression of the behaviour of the original series, but one has to remember that there is already a slope built in to the residuals cusum. The residuals of course have a mean of zero, which might help in some calculations.

    An excellent example is found in the Central England Temperature series. Computing the linear residuals and their cusum results in a pattern that clearly matches in the simple cusum pattern but identifies the remarkable 1987 step change (that has gone unrecognised by climatologists) even better than the simple cusum. It is now seen to occur at December 1987. Since that date there has been no statistically significant change in the CET series. The Pause began in December 1987, 29 years ago!

    Ken doesn’t seem to mention, as far as I can remember, that the geometrical slope of the cusum plot at any given place represents the departure of the actual values at that place from the base value (often zero, as we’ve seen). This is rather obvious of course, but is useful to keep in mind. The change in the slopes of two adjacent “linear” segments is the size of the suspected step in the original data.

    There are other aspects of interpreting cusum patterns that I’ll not address here. It’s a fasciniating subject.

    • kenskingdom Says:

      Thank you Robin for your detailed reply. Where can I see your work? Please supply a link, I would love to read (and learn) more from someone more experienced than I am.

      • robinedwards36 Says:

        Hi there! Glad to see that you are interested in my cusum experience (of which I have a lot!).

        To get in touch with me you’ll have to use email, address which you know, and then we can correspond efficiently, and I can send diagrams.

        You can see a tiny example of the sorts of plots that I churn out by looking at Paul Homewood’s blog (Not a lot of people know that) for 22 Oct, regarding Greenland’s change in 1922- can’t remember the exact title. There’s an example that shows what happened in the autumn of 1922 in SW Greenland.

        Hope to hear from you! I have literally thousands of cusum plots, some of which are very interesting. Of particular interest to me is the CET series, and I’ve lots to say on that. Another interest is the European/Russian discontinuity of late 1987, or later for eastern sites. Very peculiar and intriguing, since I have no idea what might have caused it.

        Cheers, Robin

  3. MikeR Says:

    Hi Ken,

    Thanks again for your interesting material.

    I agree that it would be convenient if the UAH data include N ext and S ext regions for just 20-60 degrees latitude. However it is possible to estimate the temperatures for just this region by subtracting the polar temperatures with the appropriate weights.

    The surface area of each polar region (60 to 90 degrees) is about 6.7% percent of the earth’s surface. This is smaller by a factor of 3.91 than the surface area of the regions corresponding to 20-60 degrees which is 26.2% of the earth ‘s surface (for each hemisphere) .

    You can then calculate a realistic estimate by using a simple equation to relate the temperatures.

    The equation is,

    T (20 to 60 degrees) = 1.344 x Text ( 20 to 90 degrees) – 0.344 X T pole(60 to 90 degrees).

    This is a similar approach that the UAH uses to calculate TLT temperatures by combining AMSU channels that have different sensitivities to altitude, to reduce the impact of stratospheric cooling (see http://www.drroyspencer.com/2015/04/version-6-0-of-the-uah-temperature-dataset-released-new-lt-trend-0-11-cdecade/) .

    It would be interesting to see how these modifications would affect the trends. Logically you would expect the northern hemisphere trend to be smaller while the southern hemisphere trend to be larger than the reported values for N ext and S ext.

  4. kenskingdom Says:

    Thanks Mike for your contribution which is indeed helpful. It would then be interesting to see how closely the data (hopefully to be released in future) matches the calculation.

  5. Dig and Delve Part 1: Running Trends | kenskingdom Says:

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