"Our society increasingly relies on numerical atmospheric models to predict extreme events such as intense storms or rare flow regime changes such as those leading to heat waves. Yet, how well these events can be reproduced with those models is currently unknown. In this project, we will make use of advances in the mathematics of stochastic differential equations to determine how the presence of delayed feedback influences the rates of rare transitions between flow regimesand the separation of nearby trajectories in geophysical fluid flows. Delayed feedbacks are an essential element of systems without a time scale separation, such as the atmosphere. This study is possible due to recent extensions of large deviation theory to systems with delay. We will also determine how approximations of dynamical systems influence the distributions of extreme events. Here we will use the theory of extreme values in dynamical systems that has been developed in the last few years and finite Markov approximation of the transfer operator. Together these results will greatly advance the understanding of how complex systems such as the Earth system can be simulated."