Description: We develop the theory of cyclic Markov chains and apply it to the El Niño-Southern Oscillation (ENSO) predictability problem. At the core of Markov chain modelling is a partition of the state space such that the transition rates between different state space cells can be computed and used most efficiently. We apply a partition technique, which divides the state space into multidimensional cells containing an equal number of data points. This partition leads to mathematical properties of the transition matrices which can be exploited further such as to establish connections with the dynamical theory of unstable periodic orbits. We introduce the concept of most and least predictable states. The data basis of our analysis consists of a multicentury-long data set obtained from an intermediate coupled atmosphere-ocean model of the tropical Pacific. This cyclostationary Markov chain approach captures the spring barrier in ENSO predictability and gives insight also into the dependence of ENSO predictability on the climatic state.

Description: It is widely accepted that orbital variations are responsible for the generation of glacial cycles during the late Pleistocene. However, the relative contributions of the orbital forcing compared to CO2 variations and other feedback mechanisms causing the waxing and waning of ice sheets have not been fully understood. Testing theories of ice ages beyond statistical inferences, requires numerical modeling experiments that capture key features of glacial transitions. Here, we focus on the glacial buildup from Marine Isotope Stage (MIS) 7 to 6 covering the period from 240 to 170 ka (ka: thousand years before present). This transition from interglacial to glacial conditions includes one of the fastest Pleistocene glaciation–deglaciation events, which occurred during MIS 7e–7d–7c (236–218 ka). Using a newly developed three-dimensional coupled atmosphere–ocean–vegetation–ice sheet model (LOVECLIP), we simulate the transient evolution of Northern Hemisphere and Southern Hemisphere ice sheets during the MIS 7–6 period in response to orbital and greenhouse gas forcing. For a range of model parameters, the simulations capture the evolution of global ice volume well within the range of reconstructions. Over the MIS 7–6 period, it is demonstrated that glacial inceptions are more sensitive to orbital variations, whereas terminations from deep glacial conditions need both orbital and greenhouse gas forcings to work in unison. For some parameter values, the coupled model also exhibits a critical North American ice sheet configuration, beyond which a stationary-wave–ice-sheet topography feedback can trigger an unabated and unrealistic ice sheet growth. The strong parameter sensitivity found in this study originates from the fact that delicate mass imbalances, as well as errors, are integrated during a transient simulation for thousands of years. This poses a general challenge for transient coupled climate–ice sheet modeling, with such coupled paleo-simulations providing opportunities to constrain such parameters.