  We apply two independent data analysis methodologies to locate stable climate
states in an intermediate complexity climate model and analyze their interplay.
First, drawing from the theory of quasipotentials, and viewing the state space
as an energy landscape with valleys and mountain ridges, we infer the relative
likelihood of the identified multistable climate states, and investigate the
most likely transition trajectories as well as the expected transition times
between them. Second, harnessing techniques from data science, specifically
manifold learning, we characterize the data landscape of the simulation output
to find climate states and basin boundaries within a fully agnostic and
unsupervised framework. Both approaches show remarkable agreement, and reveal,
apart from the well known warm and snowball earth states, a third intermediate
stable state in one of the two climate models we consider. The combination of
our approaches allows to identify how the negative feedback of ocean heat
transport and entropy production via the hydrological cycle drastically change
the topography of the dynamical landscape of Earth's climate.
