Design and bifurcation analysis of implicit Earth System Models

The research presented in this thesis seeks to advance the exploration of feedbacks and transitions in the climate system. This aim motivates the development of fully implicit climate models that support a thorough exploration of equilibria through computational techniques that combine dynamical systems theory and numerical linear algebra. The core goal of this research is the development of a fully implicit Earth system model of intermediate complexity: the I-EMIC. With the I-EMIC, the construction of bifurcation diagrams for large-scale climate problems comes within reach. The model supports high dimensional fixed-point iterations that are fundamental to the numerical continuation techniques that construct branches of equilibria for complex problems. Moreover, stability properties, 'tipping points' and possible oscillatory behavior can be investigated through the solution of large-scale eigenvalue problems. We present the design and analysis of several implicit geophysical models, which are subjected to reformulations and eventually combined into a working implicit Earth system model. This demonstrates that it is possible to formulate climate models implicitly, combine them while maintaining differentiability, and that it is possible to solve the resulting linear systems and eigenvalue problems.