[tenthirtyam]

I think a 3.5-sigma event being a 1/1000 probability is only under the assumption of random data - a constant climate would deliver more-or-less random data around some mean.

The appearance of two 3.5-sigma events suggests that the data is no longer being randomly generated around that mean, but is instead drifting away from that mean.

More concretely, if all the data were within 2-sigma, then you could invoke the null-hypothesis and refute climate change. Beyond 2-sigma (and even worse two 3.5-sigma events) refuting climate change becomes (much) less reasonable.

[leereeves]

> The appearance of two 3.5-sigma events suggests that the data is no longer being randomly generated around that mean, but is instead drifting away from that mean.

Not if the two 3.5-sigma events are in opposite directions, as in this case.

[tenthirtyam]

> ... opposite directions ...

Yes, I'd forgotten that detail. Still, though, chaotic bifurcation could be present with Il Niño and La Niña driving high & low extremes. Same mean, maybe, but with a bimodal distribution?