The ice pack at the poles provides proof enough that temperatures have risen. That isn't something that anyone can dispute.

What bothers me as an engineer is that I can't see how anything over a 150 year span at a global, hemispherical, continental, national or even regional level can be calculated to an actual accuracy of 0.1 degrees C and, even worse, enough precision to support conclusions with one digit after the decimal point.

For those who might not be clear in the difference between accuracy and precisions, here's what I hope is a simple explanation you can remember (works for me).

How close are you to the absolute correct number? "Absolute" starts with "A". This is accuracy. You are trying to cut a piece of aluminum to 1 unit in length. If every piece is about 1.2 units you are not very accurate. If every piece is about 0.95 units, you are far more accurate. You are closer to your target, absolute or real measurement.

Precision is related to grouping. I remember this by thinking "Group ends with P = Precision". Think of this in terms of how closely grouped your measurements might be.

Absolute > Accuracy
Group > Precision

Imagine you have to make an aluminum bar 1 unit in length. Here are various outcomes from making five bars and their accuracy/precision classification:

Accurate and Precise: [1.000, 1.005, 0.999, 1.002, 0.998]
Accurate and NOT Precise: [1.000, 1.050, 0.959, 1.022, 0.978]
NOT Accurate and Precise: [1.200, 1.205, 1.199, 1.202, 1.198]
NOT Accurate and NOT Precise: [1.220, 1.105, 1.127, 1.272, 1.298]

Sorry for the detour.

I read a number of documents [0] [1] (and more on that second link) describing the NOAA data used for most of these studies. I would not be honest if I didn't say that I can't help think there's a lot of stuff that feels less than correct.

I also revert to the simplest ideas (call it an Occam's razor impulse) that tells me that measuring temperatures over such long periods of time to these purported degrees of accuracy and precision is simply impossible. 0.5 degrees C over 150 years?

The only way this happens is if you takes averages of averages of averages, eliminate a bunch of readings and pretty much ignore some of the reality of such readings. And, BTW, you keep significant digits when, perhaps, you should not.

Here's a simple example in the spirit of Occam's razor thinking:

Take a look at this picture [2], source [3].

It is very easy to see that both where and when a temperature is measured can have a massive effect on the readings. Focusing on the peaks (both low and high), there's a roughly 3 degree C difference between the location with the lowest curve and the highest. Even if limited to temperatures from the same location, if your measurement is displaced by one hour the difference can is in the 1 to 2 degree range. If I measure the "Technical Services" location at 14:00 and "Music Hall" at 12:00 I get the same temperature. If I lump these measurements with measurements made at different location at different times, and average multiple times to aggregate across regions and time, well, there's no telling what the end result actually means. In this context, you'd be lucky to be able to claim results accurate within 1 degree and a precision of + or - 1 degree from there.

The evidence is clear, melting ice does not lie. However, these studies seem to be lacking something very fundamental. I can only put my finger on trying to extract accuracy and precision from data that cannot possibly support reporting at those levels. To make matters worse, most of these graphs plot deltas with respect to averages from what I will call hot periods.

What do I mean by this?

The graph in question does not plot a 150 year history with respect to the mean temperature spanning 150 years. They tend to use a contemporary average (I don't remember, let's say it is from 1980 to present day) as their baseline. Of course, with respect to this baseline everything before the reference period will look like an ice age (being dramatic). In my opinion, this makes for a more dramatic looking graph. Not necessarily a more truthful presentation, just more dramatic.

Someone mentioned in anther comment the idea of what you'd have to do to convince those skeptical about climate change. Well, for starters, the data and graphs presented has to be unimpeachable. Anyone can rightly ask "How could you possibly know the temperature in 1880 or 1910 to an accuracy of 0.1 C?". And they would be right to question such a claim. Not sure how to fix this. Just pointing out something that seems troublesome to me.

[0] https://www.st-andrews.ac.uk/~rjsw/papers/Jones-etal-1999.pd...

[1] https://www.ncdc.noaa.gov/monitoring-references/faq/anomalie...

[2] https://www.researchgate.net/publication/322719908/figure/fi...

[3] https://www.researchgate.net/figure/June-hourly-temperature-...