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Emulators, or reduced complexity climate models, are surrogate Earth systemmodels that produce projections of key climate quantities with minimalcomputational resources. Using time-series modeling or more advanced machinelearning techniques, data-driven emulators have emerged as a promising avenueof research, producing spatially resolved climate responses that are visuallyindistinguishable from state-of-the-art Earth system models. Yet, their lack ofphysical interpretability limits their wider adoption. In this work, weintroduce FaIRGP, a data-driven emulator that satisfies the physicaltemperature response equations of an energy balance model. The result is anemulator that (i) enjoys the flexibility of statistical machine learning modelsand can learn from observations, and (ii) has a robust physical grounding withinterpretable parameters that can be used to make inference about the climatesystem. Further, our Bayesian approach allows a principled and mathematicallytractable uncertainty quantification. Our model demonstrates skillful emulationof global mean surface temperature and spatial surface temperatures acrossrealistic future scenarios. Its ability to learn from data allows it tooutperform energy balance models, while its robust physical foundationsafeguards against the pitfalls of purely data-driven models. We alsoillustrate how FaIRGP can be used to obtain estimates of top-of-atmosphereradiative forcing and discuss the benefits of its mathematical tractability forapplications such as detection and attribution or precipitation emulation. Wehope that this work will contribute to widening the adoption of data-drivenmethods in climate emulation.

FaIRGP: A Bayesian Energy Balance Model for Surface Temperatures Emulation