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.