  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 \textit{(i)} enjoys the flexibility of statistical machine
learning models and can learn from data, and \textit{(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.
