  It is often known, from modelling studies, that a certain mode of climate
tipping (of the oceanic thermohaline circulation, for example) is governed by
an underlying fold bifurcation. For such a case we present a scheme of analysis
that determines the best stochastic fit to the existing data. This provides the
evolution rate of the effective control parameter, the variation of the
stability coefficient, the path itself and its tipping point. By assessing the
actual effective level of noise in the available time series, we are then able
to make probability estimates of the time of tipping. This new technique is
applied, first, to the output of a computer simulation for the end of
greenhouse Earth about 34 million years ago when the climate tipped from a
tropical state into an icehouse state with ice caps. Second, we use the
algorithms to give probabilistic tipping estimates for the end of the most
recent glaciation of the Earth using actual archaeological ice-core data.
