[sinh]

There is a qualitative difference which makes it beyond improbable that the changes we observe happen by chance.

Let's say your assumption is that the things we observe happen by chance. Now, we have, say 100 years of temperature records. If only the last year just happens to be the warmest year of all observations, there would be an 1:100 probability that this was by chance.

Now, Wikipedia says: "A 2013 article published in Geophysical Research Letters has shown that temperatures in the region haven't been as high as they currently are since at least 44,000 years ago and perhaps as long as 120,000 years ago. The authors conclude that "anthropogenic increases in greenhouse gases have led to unprecedented regional warmth."[12][13]"

So it is way more than one warm year in 100 years.

But to comprehend the unlikelihood that this happens by chance, consider another record. Look at this graph:

https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Gl...

It shows that the instrumental temperature record sind 1880 to today. You see that since 1980, every year was warmer than all the years before.

What is the probability of that for the hypothesis this happened by chance? From 1880 to 2017 are 137 years. The last 37 years have higher temperatures than all the years before. Assuming that no systematic change is happening, the probability is the same as putting the numbers from 1 to 137 into a box, drawing blindly 37 from them, and discovering that you have drawn the numbers 100, 101, 102, 103, 104, and so on, until 137. What is the probability of this?

It is given by the binominal coefficient:

https://en.wikipedia.org/wiki/Combination

with n = 137, k=37, 1 : n! / (k! (n - k)!).

Using Python:

    >>> def fak(n):
    ...     if n <= 1:
    ...         return 1
    ...     return n * fak(n-1)

    >>>def binom(n,k): 
    ... return fak(n) / (fak(k) * fak(n-k))
    
    >>> n=137
    >>> k=37
    >>> binom(n,k)
    3902541575254646835963436276286280L

So, the probability it happens by chance is

1 / 3902541575254646835963436276286280

Do you still think it happens by chance?

[posterboy]

I think OP was implying that your kind of reasoning is desperately needed, not just isolated evidence (although, I didn't read the article yet). Alas, your comment is preaching to the choir, not the audience OP might have had in mind. Although, the article is on an academic site -- so much for the audience.

xkcd had a nice illustration: https://xkcd.com/1732/