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.
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.
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)
Now let us look at the global temperature graph and see if you can tell it from the fake:
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
(Note: I’ve used a “detrended” version as this shows more high-frequency detail):
And just to show this happens in fractal noise:
(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:
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:
- Because of the dominance of low frequencies, the noise contains a rich ensemble of low-frequency components.
- This rich ensemble of low frequencies often produces long trends.
- 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?
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 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:
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”.
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.