Interestingly, if you have one-dimensional observations f(t) of a k-dimensional strange attractor, the lagged vector time series [f(t); f(t - tau); f(t - 2 * tau); ...; f(t - (k - 1) * tau)] maps onto the full k-dimensional attractor. Specifically (as I check Wikipedia) it's a diffeomorphism, an isomorphism of differentiable manifolds.

Presumably the earth system isn't at anything resembling an attractor right now, but I wouldn't be surprised if people are trying to use related techniques to try to detect qualitative changes in the system dynamics (like bifurcations).

Maybe someone more knowledgeable could chime in on whether/how measurements at a single point on the earth's surface might be used to do that?

https://en.wikipedia.org/wiki/Takens%27s_theorem