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.

翻译：模拟器，或称降复杂度气候模型，是替代地球系统模型的代理工具，能以最小计算资源生成关键气候变量的预测。基于时间序列建模或更先进的机器学习技术，数据驱动型模拟器已成为一个前景广阔的研究方向，能够生成与先进地球系统模型在视觉上难以区分的空间解析气候响应。然而，其缺乏物理可解释性限制了更广泛的应用。本文提出FaIRGP，一种满足能量平衡模型物理温度响应方程的数据驱动型模拟器。该模拟器兼具以下特点：(i) 享有统计机器学习模型的灵活性，能够从数据中学习；(ii) 具有坚实的物理基础，其可解释参数可用于推断气候系统。此外，我们的贝叶斯方法提供了严谨且数学上可处理的量化不确定性评估。该模型在模拟未来真实情景下的全球平均地表温度及空间地表温度方面表现出色。其从数据中学习的能力使其优于能量平衡模型，而稳健的物理基础则防范了纯数据驱动模型的潜在缺陷。我们还展示了如何利用FaIRGP获得大气层顶辐射强迫的估计值，并讨论了其数学可处理性在检测归因或降水模拟等应用中的优势。希望本工作有助于推动数据驱动方法在气候模拟领域的更广泛应用。