Emulators, or reduced complexity climate models, are surrogate Earth system models that produce projections of key climate quantities with minimal computational resources. Using time-series modelling or more advanced machine learning techniques, data-driven emulators have emerged as a promising avenue of research, producing spatially resolved climate responses that are visually indistinguishable from state-of-the-art Earth system models. Yet, their lack of physical interpretability limits their wider adoption. In this work, we introduce FaIRGP, a data-driven emulator that satisfies the physical temperature response equations of an energy balance model. The result is an emulator that (i) enjoys the flexibility of statistical machine learning models and can learn from observations, and (ii) has a robust physical grounding with interpretable parameters that can be used to make inference about the climate system. Further, our Bayesian approach allows a principled and mathematically tractable uncertainty quantification. Our model demonstrates skillful emulation of global mean surface temperature and spatial surface temperatures across realistic future scenarios. Its ability to learn from data allows it to outperform energy balance models, while its robust physical foundation safeguards against the pitfalls of purely data-driven models. We also illustrate how FaIRGP can be used to obtain estimates of top-of-atmosphere radiative forcing and discuss the benefits of its mathematical tractability for applications such as detection and attribution or precipitation emulation. We hope that this work will contribute to widening the adoption of data-driven methods in climate emulation.

A Perturbed Parameter Ensemble (PPE) with the Community Atmosphere Model version 6 (CAM6) is used to better understand the sensitivity of simulated clouds to both aerosol forcing and cloud feedbacks and the interactions between them. Aerosol forcing through aerosol-cloud interactions is mostly negative (a cooling) due to shortwave radiation, while feedbacks are positive or negative in different regions due to contrasting longwave and shortwave effects. Both forcing and feedbacks are related to the mean climate state. Higher magnitude cloud radiative effects generally mean larger net forcing and larger net feedback. Aerosol forcing is broadly related to the susceptibility of clouds to drop number. Feedbacks are less related to susceptibility, and in different regions. Aerosol forcing and cloud feedbacks are anti-correlated in the CAM6 PPE such that stronger negative forcing is associated with stronger positive feedbacks. Even the processes governing forcing and feedback sensitivity in the PPE are similar. These include the warm rain formation process, ice loss processes and deep convective intensity.

Neural Weather Models (NWM) are novel data-driven weather forecasting tools based on neural networks that have recently achieved comparable deterministic forecast skill to current operational approaches using significantly less real-time computational resources. The short inference times required by NWMs allow the generation of a large ensemble potentially providing benefits in quantifying the forecast uncertainty, particularly for extreme events, which is of critical importance for various socio-economic sectors. Here we propose a novel ensemble design for NWMs spanning two main sources of uncertainty: epistemic —or model uncertainty,— and aleatoric —or initial condition uncertainty. For the epistemic uncertainty, we propose an effective strategy for creating a diverse ensemble of NWMs that captures uncertainty in key model parameters. For the aleatoric, we explore the “breeding of growing modes” for the first time on NWMs, a technique traditionally used for operational numerical weather predictions as an estimate of the initial condition uncertainty. The combination of these two types of uncertainty produces an ensemble of NWM-based forecasts that is shown to improve upon benchmark probabilistic NWM and is competitive with the 51-member ensemble of the European Centre for Medium-Range Weather Forecasts based on the Integrated Forecasting System (IFS) —a gold standard in weather forecasting,— in terms of both error and calibration. In addition, we report better probabilistic skill than the IFS over land for two key variables: surface wind and air surface temperature.