Many different emission pathways exist that are compatible with the Paris climate agreement, and many more are possible that miss that target. While some of the most complex Earth System Models have simulated a small selection of Shared Socioeconomic Pathways, it is impractical to use these expensive models to fully explore the space of possibilities. Such explorations therefore mostly rely on one-dimensional impulse response models, or simple pattern scaling approaches to approximate the physical climate response to a given scenario. Here we present ClimateBench - a benchmarking framework based on a suite of CMIP, AerChemMIP and DAMIP simulations performed by a full complexity Earth System Model, and a set of baseline machine learning models that emulate its response to a variety of forcers. These emulators can predict annual mean global distributions of temperature, diurnal temperature range and precipitation (including extreme precipitation) given a wide range of emissions and concentrations of carbon dioxide, methane and aerosols, allowing them to efficiently probe previously unexplored scenarios. We discuss the accuracy and interpretability of these emulators and consider their robustness to physical constraints such as total energy conservation. Future opportunities incorporating such physical constraints directly in the machine learning models and using the emulators for detection and attribution studies are also discussed. This opens a wide range of opportunities to improve prediction, consistency and mathematical tractability. We hope that by laying out the principles of climate model emulation with clear examples and metrics we encourage others to tackle this important and demanding challenge.

Recent studies have documented that the Madden-Julian Oscillation (MJO) has impacts in extreme dry/wet conditions over tropical regions and in atmospheric state. They are based, however, in correlation analysis, and therefore do not consider non-linear interactions nor they establish cause-effect relationships.In this study we introduce a generalization of the non-linear Granger causality (GC) test to identify causal relations between MJO and hydrological extremes. The method is able to identify causal relations under noisy, nonlinear and non-stationary scenarios. A probabilistic extension is also introduced where the causal test operates directly on the marginal likelihood (also called evidence) of the observations, which is analytic. We apply our proposed method to MJO and satellite-based soil moisture (SM) data, and revisit the global teleconnection patterns induced by MJO events. Since El Ni\~no Southern Oscillation (ENSO) is a modulating factor that can result in abnormal SM global distributions, we also include it in the analysis as a potential driver of SM variability. Including ENSO allows us to differentiate the effect of the MJO and ENSO on the global SM anomalies and to learn the causal graph of their cause-effect relationships, and also the mutual relation between MJO and ENSO extreme events.