# “Nyquist doesn’t apply” !!!! ????

Those words as uttered by a respected Climate Scientist are indicative, not only of staggering lack of understanding of what is being done to his data, but also it applies to not only his work but apparently of the whole field.

Nyquist Sampling Theorem applies to every picture you take, every chart you draw, every calculation you make, every machine you build.

To say it doesn’t denies science.

The local thermal response to the solar input signal is first sampled as tMin/tMax over a day. That is the input frequency, modulated by orbital factors to provide the annual local cycle.

Nyquist also tells us that sampling hourly will get more accurate results than a simple tMin, tMax but we do not have that accuracy in most temperature series.

Nyquist is about the digitisation of an underlying signal, not the digitALisation. Applies to paper records as well as machine derivations.

We are trying to assess the local power transfer curve and its related usage to later compare to abstract, computer based, models of the same thing.

GIGO is not just a phrase, it is a real and living danger in all we do.

Each pixel in a photograph, each point you place on a chart, etc. have at their core Nyquist. It displays ignorance, not intelligence to make the claim that his work is irrelevant.

It also immediately labels all work that has that phrase attached that is has GIGO all over it.

For those who wish the academic view of Nyquist then https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem will provide some clues.

“A sufficient sample-rate is therefore 2B samples/second, or anything larger. Equivalently, for a given sample rate fs, perfect reconstruction is guaranteed possible for a bandlimit B < fs/2.

When the bandlimit is too high (or there is no bandlimit), the reconstruction exhibits imperfections known as aliasing. Modern statements of the theorem are sometimes careful to explicitly state that x(t) must contain no sinusoidal component at exactly frequency B, or that B must be strictly less than ½ the sample rate. The two thresholds, 2B and fs/2 are respectively called the Nyquist rate and Nyquist frequency. And respectively, they are attributes of x(t) and of the sampling equipment. The condition described by these inequalities is called the Nyquist criterion, or sometimes the Raabe condition. The theorem is also applicable to functions of other domains, such as space, in the case of a digitized image. The only change, in the case of other domains, is the units of measure applied to t, fs, and B.”

Notice space tucked in there? That means horizontal separation between point samples in Nyquist terminology.

And for the sake of this discussion a temperature map, however derived, is a ‘digital image’.

OK. So we are not going to proceed further in our thinking until we create an abstract experiment that will show Nyquist is present everywhere. This is abstract, not real, so please no distractions.

We are tasked with designing an experiment to prove the validity and accuracy of the work being done at a local site. Consider this a external, quality control, review step, to determine how best to spend our money.

There are 3 simple statements we are asked to consider.

1. Moving from tMin and tMax to an hourly sampled instrument will improve quality of the data. Yes or No.

2. Adding in extra instruments at 2m height (say 10 times the number we have now) across the sample area will improve the quality of the data. Yes or No.

3. Adding in extra instruments above and below the plane of the existing one(s) will improve the quality of the data. Yes or No.

Obviously we now see how Nyquist applies.

1. Is a statement of Nyquist in time.
2. Is a statement of Nyquist in in the horizontal plane.
3. Is a statement of Nyquist in in the vertical plane.

## 4 thoughts on ““Nyquist doesn’t apply” !!!! ????”

1. GarryD says:

Richard, your comments at Climate etc. along with Evan’s were most interesting and educational. I should also add your perspective on “Nyquist” is new to me. What do you consider the limitations of “Nyquist”? Why is this tool not mentioned more? The way you develop questions and implications begs the question, “why is Nyquist not being used more in climate research? I hope that you will continue to add your opinions to more climate analysis (it is a fresh and useful alternative). You, Leif Svalgaard and Robert G. Brown of Duke certainly certainly add some needed depth and perspective to science discussions. A lot fun! Your decorum is also to be admired. Please, let me know whenever you are commenting or writing. I have book marked this site.
Thank you,
Garry Dauron

• Hi Gary,

It is not the limitations of Nyquist that is the problem, it is the limitation of vision of people using Climate data without intellectually considering that Nyquist underpins all their work.

Nyquist applies in space and time regardless if they will admit it or not.

Under sampling in spatial terms means that the certainty which they quote is a thin veneer of ‘fool yourself’ drawn over the true meaning of what they see.

As a ‘Practicing Logician’ aka a Computer Geek, the precise definition of data, how it is collected and used, was part if my working life until I retired.

To hear said that ‘Nyquist does not apply’ astounds me. What planet do people think they are living on? How are they measuring it?

I have a very eclectic site if you have a look. All underpinned by rational logic.

2. “There are 3 simple statements we are asked to consider.

1. Moving from tMin and tMax to an hourly sampled instrument will improve quality of the data. Yes or No.
YES

2. Adding in extra instruments at 2m height (say 10 times the number we have now) across the sample area will improve the quality of the data. Yes or No.
YES

3. Adding in extra instruments above and below the plane of the existing one(s) will improve the quality of the data. Yes or No.
YES

Obviously we now see how Nyquist applies.
######################################
yes, Nyquist applies IF your goal is to capture the temperature signal with the best accuracy.
Nyquist applies IF your goal is designing a new system to capture temperature.

BUT
that is not our problem.
it is NOT the problem on the black board son.

The problem is this.

GIVEN that we only have tmin and tmax
GIVEN that we don’t have super dense spatial sampling
GIVEN that we dont have the data Nyquist would require…..
what is the best estimate.?

In other terms Nysquist tells us that our estimate will have error. DUH!!!

want to design a new system? please consult Nyquist
want to look at historical measurements?, his work doesnt apply, except to tell you your estimate
will have error. DUH

• That’s one of your problems, not mine