  The climate is a complex non-equilibrium dynamical system that relaxes toward
a steady state under the continuous input of solar radiation and dissipative
mechanisms. The steady state is not necessarily unique. A useful tool to
describe the possible steady states under different forcing is the bifurcation
diagram, that reveals the regions of multi-stability, the position of tipping
points, and the range of stability of each steady state. However, its
construction is highly time consuming in climate models with a dynamical deep
ocean, interactive ice sheets or carbon cycle, where the relaxation time
becomes larger than thousand years. Using a coupled setup of MITgcm, we test
two techniques with complementary advantages. The first is based on the
introduction of random fluctuations in the forcing and permits to explore a
wide part of phase space. The second reconstructs the stable branches and is
more precise in finding the position of tipping points.
