I have moved most of the current stuff to dropbox
We have no idea how any straight ‘trend’ lines we may wish to draw on a time serias graph are to be constructed. They cover a range of the results of the current combination of a set of low frequency waves which we do not have the power to resolve accurately because the data sampling time window is too short and which itself cannot be extended backwards in time. We do not know how many, how big or in what phases anything low frequency that is present there combines to. 1 or 1000 combined together? A straight ‘trend’ line is a propaganda exercise (or fool ourselves anyway).
By definition on a time series graph we need an infinite lower bandwidth to draw a straight ‘trend’ line. A straight line is defined that way. Nyquist prevents us from achieving that certainty.
This is easliy demonstrated by the change from “it’s all going to be very cold” not too long back to “it’s all going to be very warm” now.
The flickerings up and down to be expected of any such ‘trend’ lines in the way I have suggested. We might be able to derive some grasp of any underlying, still to be discovered, frequencies by counting how many times that sort of change occurs in that or other records and at what periods it may be present.
I suppose that a valid treatment if you want straight ‘trend’ lines, is to increase the width of the line in some way to try and compensate as you go further back in time towards the start of the record. The fact the the ‘line’ may then become taller than the data it is covering may then prove awkward. Possibly a triangular, wedge shaped function to display more uncertancy as we go further back in time and as we reach closer to and beyond the lower Nyquist limit?
Taking a temperature reading of a thermometer and interpreting it requires the methodology used to honour Nyquist. It is a discrete, point or area/volume depending on the thermometer, sampling of an underlying continuous function. Every reading we take is a digitisation. Nyquist restated.
The differences between Global Satellite and Thermometer temperature data probably only displays the inevitable difference between any point sampled series with the required interpolation/extrapolation with ones which are area/volume based.
In computing we have developed methods that describe this rather abstract thing that is ‘data’ into an object that is usable in a computer system by a very rigid, precise, defined, format via RFC for collaberative work or in the market via API. A digitalisation rather than a digitisation. A bookkeeping task I suppose. But a very precise and clearly stated one. Based on principles laid down by Nyquist and others.