Stochastic methods are a crucial area in contemporary climate research and are
increasingly being used in comprehensive weather and climate prediction models as well as …

Klaus Hasselmann's revolutionary intuition in climate science was to use the stochasticity
associated with fast weather processes to probe the slow dynamics of the climate system …

The climate is a forced and dissipative nonlinear system featuring nontrivial dynamics on a
vast range of spatial and temporal scales. The understanding of the climate's structural and …

This paper has two interrelated foci:(i) obtaining stable and efficient data-driven closure
models by using a multivariate time series of partial observations from a large-dimensional …

We present methods for the reduction of the complexity of computational problems, both time-
dependent and stationary, together with connections to renormalization, scaling, and …

Determining the statistical properties of stochastic nonlinear systems is of major interest
across many disciplines. Currently, there are no general efficient methods to deal with this …

We develop a thorough mathematical analysis to deduce conditions for the accuracy and
convergence of different approximations of the memory integral in the Mori-Zwanzig (MZ) …

We develop new approximations of the Mori–Zwanzig equation based on operator series
expansions of the orthogonal dynamics propagator. In particular, we study the Faber …

We present a new method to approximate the Mori–Zwanzig (MZ) memory integral in
generalized Langevin equations describing the evolution of smooth observables in high …

This chapter considers the sub-seasonal to seasonal (S2S) prediction problem as
intrinsically more difficult than either short-range weather prediction or interannual-to …