Since you are so fond if simple examples let me give you one. So your measuring inch worms with a yard stick and you get zero or 1 yard in your samples and you decided the mean was half a yard with high statistical confidence I would buy it. But if you said from all those measurements you could tell the inch worm grew 0.4 inches over the last year I would rightfully laugh in your face.

Give it up. You have proven to be less a genius and more challenged in reading comprehension. So you measured the variance in the noise!

BFD. You confuse a statistical number with a real world phenomena – they are not connected until you demonstrate the signal is outside the noise.

What you have failed to do is account for all the steps in the noise. The measurement itself has minor errors. The averaging over distance and time imparts enormous uncertainties on top of these which raise the noise level.

I mean do the math yourself! Take the daily measurements – then compute the uncertainty in coming up with a daily high and low for that 1 km circle. Then compute averages for a grid 500X500 km with proper decays in uncertainty. Then compute the additional uncertainties when you extrapolate from one grid with measurements to one without (half the grids on the planet are probably done this way).

Then come back and tell me the answer – if you dare!

What we find is a normal/natural day-2-day variation of temperature – taken at the exact same time of day – of +/- 8.85°F! That is a lot of natural variability. Can anyone prove a 0.8°C change in that range can be detected over 100 years and be deemed significant?

Uh, YES, because of the error on the mean, in effect. You can measure changes in the mean value of noisy data — except you have to fully understand statistics to understand whether or not what you have computed is statistically significant.

Why do you keep using these same ole incorrect arguments? Perhaps I can guess — because they sound totally obvious and totally plausible to those who have no knowledge of stats whatsoever. Also, gives such readers a nice warm feeling that they can spot something so totally obvious that those nasty academics only try to hide from us by wittering on about statistics and using alll those long words.

I won’t speculate further as to whether your understanding of statistics is really as bad as it seems to be, but add that if it isn’t, using such examples is grossly dishonest.

After reading your comment again I am still laughing. Especially this part:

Yes, very easy to say — wow, with a natural variation of umpteen degrees, how can anyone claim to measure differences which are a fraction of that natural variability. Except the whole basic statistical point about the distribution of single measurements versus the distribution of the mean of a sequence of measurements is what allows you to do that.

What is so funny is you confuse ‘measurement’ with ‘predicting’. 99.99+% of the temperatures used to ‘measure’ climate change are not measurements at all. They are predicted measurements based on unfounded extrapolation.

As I PROVED the certainty in any temperature MEASUREMENT decays rapidly over distance. Therefore you are not MEASURING the globe or region, you are predicting what nearby temperatures MAY be (with a lousy certainty, or massive error – take your pick).

You actually think running statistics on shoddy predictions is ‘measuring’ something? Too funny.

In the space business we don’t rely on trends in questionable estimates, predictions or guesstimates. We measure the decay of any measurement in any dimension to understand how much we can rely on it. If it decays too fast (uncertainty rises) we don’t use it because it leads to all sorts of wrong conclusions.

Maybe folks who use simple stats should learn more about things like Kalman filters and their proper application to complex physical systems – like climate and the atmosphere.

I was clear in what I was showing (back of the envelope – in case you missed it in the post). The natural variability is perfectly legitimate when claiming you can extrapolate temperatures thousands of kilometers without taking into account the uncertainty (and thus error in conclusions drawn from said extrapolation.

I must admit, you are pretty poor at this. I did not take one temperature. I took many temperatures and produced their population variability. The data is on a series of regional high temps, not one.

Go back and read it again and see if you can keep up. That was the population of temp ranges over 100 km. That is the most benign we will see in most places over those distances. Go back and do the compounding of uncertainty, and prove to us how you can produce a result of .8° as significant with an uncertainty of +/- 5° C? Is that your ‘professional’ claim?

ROFTLMAO!

Except you keep taking the uncertainty on this at the variation over time, whereas the error on the mean is less than this — a little something called error on the mean.

Yes, very easy to say — wow, with a natural variation of umpteen degrees, how can anyone claim to measure differences which are a fraction of that natural variability. Except the whole basic statistical point about the distribution of single measurements versus the distribution of the mean of a sequence of measurements is what allows you to do that.

Even if you do know this, your supposed initial example, which repeatedly presents plus or minus two degrees as the relevant uncertainty is profoundly misleading, since it creates the impression that natural variability is as accurate as you can get on anything, which is not the case.

To give a simple example that most people DO understand. I measure the heights of adult males across the UK. There is a large natural variability, yet if I take enough samples, I get a decent estimate of the mean height.

Let’s take adult males in another country. If all I took was one chap from each country, I can’t say much. Yet if I take a sample from each, I can meaningfully detect differences in the MEAN height of individuals that is far less than the natural variability in individual heights.

Hence what matters is NOT just natural variability, but natural variability divided by square root of the number of measurements — that is the appropriate error, and the figure that should be considered.

Hence we have the totally incorrect statement:

And even if there was a 0.8°C rise, is that really significant given the daily ranges temperatures can swing?

Yes, because I assume that decent scientists can do basic stats, and correctly compute errors on the mean.

Actually, no it is not wrong. The area I sampled is quite benign and very homogenous. It means that when you extrapolate 100′s of km’s your error bars grow (call it uncertainty if it helps, but it is the error in your extrapolated temp).

It means any claim to know a extrapolated temperature is +/- 2° because of the system being measured! The error comes from ignorance as to what the temperature really is 100 km’s away. And note I used STD DEV 1. I gather your brilliant mind can understand what happens to extrapolated temps if I want 95% confidence the number extrapolated is accurate??

What is sad to see is rank amateurs missing the point of basic mathematics. The GIS data map of the world, being 99.99+% extrapolated measurements is only valid to +/- 5° or so. Which means it cannot detect a change of 0.5°.

Duh. Maybe you should stick to speaking to animals.

* The average deviation was 2.00°F.

Therefore I claim that when you extrapolate a single station (or even 40 stations) out 160 km the best you could ever hope for is an uncertainty of +/- 2°F.

Which is nonsense – just because natural variability at one point of two dgerees does not mean that this is also the error on the mean temperature at that point. And if you don’t understand that, then you don’t understand even the most basic parts of statistical analysis — hence anything you have to say about the validity or otherwise of spatial sampling can be dismissed as meaningless.

Sad to see that so many posters seem to accept the whole of this article without comment, which suggests that they don’t understand even the most basic stats either……………………

BTW, anyone can determine the accuracy of these interpolations by comparing local temp measurements (the root data), averaged grid temps where data exists (the first introduction of error) and the estimates for grids without data (the 2nd introduction of error and the most unproven step in computing a global index) by comparing these to satellite measurements.

You will get a delta from the ground measurement and the sat measurement, you will get a delta from the averaged grid measurement with the SAME sat measurement, and you will get a delta from the grid with 100% guesstimated temp to the SAME sat measurement. These will not be equal and will grow in size as you move from the ground measurement outward.

If you do this over many days or years, you can determine with high precision the error in the extrapolation method to real temps.

If/when someone does this you will see how off the GISS, NCDC and CRU index is, and it will be on the order of degrees, not tenths of a degree as they claim.

And that will be the end of those theories.

You still have the same problem – you cannot extrapolate your measurements to represent the globe. Too few samples.

BTW, I am not the one who has to prove the sparse measurements over time are indicative of anything global. All I noted was the error bars on their measurements expand massively as they attempt to derive a global index, which makes their results garbage.

However we know from the temperature records that the sensors have moved. Both individual sensors have moved and a large percentage disappeared with the end of the cold war and for other reasons. My hypothetical sensors are better than the reality of the temperature sensors.

As for measuring only a tiny percentage of the globe, I don’t think you have shown why a long term delta can’t be measured in one part of the globe. You only showed that short term deltas are large, but that doesn’t prove that small long term deltas can’t be measured.