The performance of three machine-learning methods for data-driven modeling of a multiscale chaotic Lorenz 96 system is examined. One of the methods is found to be able to predict the future evolution of the chaotic system well from just knowing the past observations of the large-scale component of the multiscale state vector. Potential applications to data-driven and data-assisted surrogate modeling of complex dynamical systems such as weather and climate are discussed.

The climate of Earth is governed by nonlinear processes of geophysics. This paper presents energy balance models (EBMs) embracing these nonlinear processes which lead to positive feedback, amplifying the effects of anthropogenic forcing and leading to bifurcations. We define bifurcation as a change in the topological equivalence class of the system. We initiate a bifurcation analysis of EBMs of Anthropocene climate, which shows that a catastrophic climate change may occur in the next century.

Most verification metrics for ensemble forecasts assess the representation of uncertainty at a particular location and time. We study a new diagnostic tool based on fractions of threshold exceedance (FTE) which evaluates an additional important attribute: the ability of ensemble forecast fields to reproduce the spatial structure of observed fields. The utility of this diagnostic tool is demonstrated through simulations and an application to ensemble precipitation forecasts.

The scientific questions posed by the climate sciences are central to socioeconomic concerns today. This paper revisits several crucial questions, starting with What can we predict beyond 1 week, for how long, and by what methods?, and ending with Can we achieve enlightened climate control of our planet by the end of the century? We review the progress in dealing with the nonlinearity and stochasticity of the Earth system and emphasize major strides in coupled climate–economy modeling.

Different dimension reduction methods may produce profoundly different low-dimensional representations of multiscale systems. We perform a set of case studies to investigate these differences. When a clear scale separation is present, similar bases are obtained using all methods, but when this is not the case some methods may produce representations that are poorly suited for describing features of interest, highlighting the importance of a careful choice of method when designing analyses.