Global Warming disproved: Bad posts, CET, Antarctic Ice and Fractal Noise

I was caught out this morning seeing a graph of Antarctic Ice (unlabelled) which I took to be a plot of the Central England Temperature series.

The fact I was confused is proof that that global warming is non-science.

So, I will now explain how this kind of mistake arises.

In my case, I was misled because I wrongly took the Antarctic ice level graph to be that of Central England Temperature series.

So I though it would be worth comparing the two.

Antarctic Ice levels

Central England Temperature

And yes! as I had thought, the two look remarkably similar particualarly in the right hand side which I highlight (Antarctic Ice 2005-1014, CET 1920-2010). Note there is no way they can be related as not only are they different physical entities, but very different time periods.

Indeed, I can see now how similar they look.

Fractal Noise

There is a reason why I was confused be this. That  reason is because all these climate signals are what I call “fractal noise”. That is, they are 1/f noise.

The reason I use the term “fractal noise” (and I’ve seen others use the same kind of idea), is that within any plot of 1/f noise you will find a sub section that looks like the overall data plot. And (assuming it is pure 1/f noise), within that subsection, there will be another subsection that looks the same.

Let us see how this applies to the Global Temperature. Below is the ubiquitous average of all global temperatures (a proxy for the real temperature)

Global Temperature

Now let us look at the global temperature graph and see if you can tell it from the fake:

gw1

Did you guess the right one?

If you guessed either was one was a fake global temperature, you are wrong! If, however, you guess either one is the global temperature graph, you are also wrong.

The reason is that both are a sub-section of the global temperature signal

Global Temperature showing sections in above graphs. Lef as is. Right: rotated 180edgere

Global Temperature showing sections in above graphs.
Lef as is. Right: rotated 180edgere

(Note: I’ve used a “detrended” version as this shows more high-frequency detail):

And just to show this happens in fractal noise:

A section of "Pink" fractal noise

A section of “Pink” fractal noise

And sure enough, it is easy to select out a section looking like the global temperature.

And sure enough, it is easy to select out a section looking like the global temperature.

(Note: I won’t highlight the section – as looking for the section will help you understand just how much such simple /\/ type patterns occur)

It is not a perfect fit, but there is no doubt that the subsections of the graph I’ve highlighted both for the global temperature and pink noise, bear a remarkable similarity to the overall global temperature plot. The reason for this is obvious (to me) in this graph:

Fig 1: Variability of observed global mean temperature as a function of time-scale (°C2 yr–1)  from figure 9.7 IPCC (2007)

Fig 1: Variability of observed global mean temperature as a function of time-scale (°C2 yr–1)
from figure 9.7 IPCC (2007)

This graph shows the scale of frequencies in the global temperature. It shows that the scale of change increases with the period over which we are looking at this change. This is clearly a complex idea (as climate academics still don’t understand it). But take it from me, that this is a signature of 1/f type noise which means that we would expect the global temperature to be 1/f or fractal noise. What this means is that for simple 1/f type noise, if we stretch the scale of the X so we only have half the graph showing and similarly stretch the scale of the Y axis, we will have noise that has the same general appearance. And if we scale by 3x, 4x, 10x, 100x, then for fractal noise we get back to a plot that whilst the individual features may differ, the general look remains the same. The only limits we have to this are when samples are averaged.

So, fundamentally, this is why I made such a balls up in the previous post. BECAUSE BOTH GLOBAL TEMPERATURE AND ANTARCTIC ICE ARE 1/F TYPE NOISE that is why they appear very similar to each other – despite being taken over very different time periods and representing very different physical properties.

Indeed, the only thing that is often required to make two lots of fractal noise look the same, is to scale them to the same size!

And this is why I have no doubt that most of what we see in the global temperature is just fractal noise. And here are some other important properties of fractal noise:

  1. Because of the dominance of low frequencies, the noise contains a rich ensemble of low-frequency components.
  2. This rich ensemble of low frequencies often produces long trends.
  3. This rich ensemble often produces a number of short-term trends. Added together these are easily confused with “cycles”.

How to distinguish “noise” from signal?

Trends

It is in fact very easy to see whether the overall pattern has an abnormal trend.

Remember: short sections of the graph look like longer sections, only scaled up. Therefore, if you can find short term sections that look like the total graph (only scaled up), then this strong evidence that the overall trend is just noise.

The overall trend must be larger than one would expect from the simple 1/f noise. Also if there is a significant trend this, being a low frequency, will tend to increase the low frequency components when the frequency profile is plotted.

As can be seen from the above frequency plot, if anything there is less low frequency than we would expect.

Cycles

Cycles are difficult. They tend to dominate in the longer periods. So, e.g. there is the classic ” /\/ ” shape of the 20th century graph which many have come to believe is just part of a 60 year cycle: “\/\/\/\/\/\”.

A much better example, existed around 2009 on the HADCRUT graph, sadly amended by later changes and no longer so obvious last time I looked. This used to show a pronounced 9-month cycle:

Global temperature with the ~9month cycle that appeared between 2001 and 2008

Global temperature with the ~9month cycle that appeared between 2001 and 2008

Note, that on the above graph we also get “two cycles” from 1992 to 2001 of a a 5.5 year cycle. Bearing in mind the sunspot cycle is twice this (11years), it would have been very easy for the analyst who is unfamiliar with the tricks of this type of noise and who only had data from 1992-2001 to have become excited by “sunspot harmonics”. Clearly (as the above graph shows) both the 9month and 5.5year cycle were just short term aberrations.

So, how can we tell the difference between what is real “signal” and what is signal-like noise? The honest answer is we cannot unless we have a longer time periods like the Central England Temperature record, but that is not always possible.

Instead, what engineers do, is that we use a rule of thumb. That varies, but one way it is put is that “it needs ten cycles to be an oscillation”.

Summary

In 1/f or fractal noise, low frequency or long periodic noise dominates. This noise is easily mistaken for a signal. The key features of /1f or fractal noise that we must be aware of and try to avoid mistaking noise for signal are:

Cycles in graph Appearance Effect
<1 cycle noise Overall Trend Usually present and so a rise or fall usually dominates dataset.
1-3 cycle noise Several turning points Gives graph its general shape
4 – 7 Appears as short bursts of cycles in short sections Usually present in some form.
8+ Appears as chaotic change Easily confused with “white noise”.When this happens, larger changes at lower frequencies will be falsely imagined as signal. Thus deluding the unskilled observer into imagining massive trends and cycles.

How does this prove global warming is non-science?

The fact that I embarrassed myself by confusing two very different plots – things that I have been looking at for years and should know better. Two plots which clearly are not related as they are entirely different time-scales, shows that the global warming signal is indistinguishable from the random variations of natural processes – is indistinguishable from natural variation – is indistinguishable from noise.

And if an expert like me (and I am an expert in this particular field as I used to deal with such temperature graphs day in day out), if I can’t tell them apart – then they are indistinguishable.

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8 Responses to Global Warming disproved: Bad posts, CET, Antarctic Ice and Fractal Noise

  1. Richard Mallett says:

    As a matter of interest, why do you use HadCRUT3 and not HadCRUT4 ?

    • There was only HADCRUT3 at the time I started the graph.

      I updated it every few months – but didn’t do any more after Climategate as I lost trust in the data from UEA.

      I just remember it because it was really weird watching the last one and a bit of those 9month cycles appearing. I had to remind myself that such cycles are to be expected.

  2. Pingback: Help needed! What’s difficult about fractal noise? | ScottishSceptic

  3. manicbeancounter says:

    Perhaps a reason for your lack of response is that people like to have reasons for what is happening. Fractal noise is accepting that no reasoned explanation of temperature change is possible – or at least within out lifetimes. That said, I have been drawn towards the concept of 60 years cycles. From your engineering background I would need to wait another 450 years to see if it was truly an oscillation. However, using a Popperian approach, I would give greater credibility to a simple theory that, on the basis of the cycles correctly forecast average temperatures in 2020 as being lower than today. Particularly in the context of a consensus predicting a resumption of warming.
    It could be that “fractal noise” might not be that large in the context of global surface temperatures. In January, a heatwave in Australia, with a mild winter in the Northern Hemisphere could result in a spike of 0.1 degrees globally upwards. Conversely a cold snap across much of North America and parts of Siberia could cause a spike downwards. But then that is a property of fractals. Drill down on temperature data in the dimensions of both time and space, and you get similar patterns.
    Whilst in reality we can get a lot of noise, it would be interesting to see if the amount of noise is affected by measuring and aggregation techniques. Do sea surface temperatures have more irregularities than land due to fewer data points, or less irregularities due to the moderating influence of water, or due to data smoothing? Do different data sets have similar levels of noise? Is there a divergence between satellite and surface temperatures? It is very easy to smooth that noise, or find reasons to impose patterns.

    On the subject of imposing patterns through our techniques I compared HADCRUT and GISTEMP data now with three years ago. Changes in the method of analysis, particularly with GISTEMP, tell a quite different story. If fractals are of relevance then the differing narratives are largely fictitious.
    http://manicbeancounter.com/2014/06/28/nasa-corrects-errors-in-the-gistemp-data/

    • That’s a very useful post. (Sorry for quality of response – it’s late)

      it hadn’t occurred to me that people might be put of if they felt: “that no reasoned explanation of temperature change is possible ”

      There’s also a huge difference between “reading errors” and “natural variability”. Reading errors do tend to be standard “white noise”, in contrast natural variation tends to be 1/f noise.

      The big difference is that averaging white noise over ever increasing periods, reduces error relative to signal. But averaging 1/f noise over larger periods increases error relative to signal. That is because as the period → infinity the noise → infinity.

      Re 450 years – unfortunately, we cannot change the laws of physics & statistics just because we are in a hurry. It’s not that “it’s a good idea to wait”, instead it is that “we do not know until we have waited”. There may be other ways to approach the issue such as working out precisely why the apparent cycle is taking place, and this may allow us to speed up the process, but we still would not know until we’ve been through a complete cycle (which means I will never know!!).

      It’s also worth baring in mind my article on how long it will take to improve the numerical forecast using a similar approach to the weather forecast. The answer is that it will be 2235AD till yearly forecast betters current monthly forecast.

      Again, this is just the best estimate for the time. I seem to recall using the same analysis, it would be something like 100,000 years before we can predict the century-long climate with the same accuracy as a short-term forecast. Of course, this is not something climate academics want to hear – but just because they would rather it was quicker, doesn’t mean either they or I can fundamentally change things (IF THEY CONTINUE USING THE SAME BASIC METHODOLOGY AS THEY USE FOR WEATHER FORECASTING)

      “It could be that “fractal noise” might not be that large in the context of global surface temperatures.” – if you’ve got the basic concept, then maybe I can move onto the more advanced stuff?

  4. Robertv says:

    If it doesn’t create panic it is useless for making money and/or changing the power structure. That’s why the sun has no role in today’s climate. Today we have no high priests who are able to control our star.

  5. Robertv says:

    I think life on Earth is all about ‘noise’

    Schumann’s Resonance

    Sun

    play them together.

    If you change the ‘noise’ you change the lifeforms. I think that big extinction moments occur when the ‘noise’ is changed. I think Dinosaurs probably would not survive in the current ‘noise’.

  6. Pingback: Mathematical requirement for fractals? Implications for 1/f noise and climate. | ScottishSceptic

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