I read that the mathematical definition of bifurcation is that, at a critical value of a parameter that governs the dynamical system, the system changes to a topologically different system than the previous.
I recognize that the scope of this question is large, but still:
Why is this phenomenon relevant in atmospheric sciences?
One can say that since the topology of the systems orbit changed, so different, previously unaccounted for, phenomena will show up - but that is obvious.
Why, if at all, should a climatologist trying to predict a long term time series keep bifurcation in mind, given they can also compute the results numerically within the limits of precision, without explicitly worrying about bifurcation?