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 modeling 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.

翻译：模拟器（或称降复杂度气候模型）是地球系统模型的代理，能以极少的计算资源生成关键气候变量的预估结果。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，其生成的空间解析气候响应在视觉上与最先进的地球系统模型难以区分。然而，这类模型缺乏物理可解释性，限制了其广泛应用。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模拟器。该模拟器兼具以下特性：（i）拥有统计机器学习模型的灵活性，能够从观测数据中学习；（ii）具备稳健的物理基础，其可解释参数可用于推断气候系统特征。此外，我们的贝叶斯方法能够实现原则性且数学上可处理的的不确定性量化。该模型在模拟全球平均地表温度及空间分布的地表温度方面展现出卓越性能，可覆盖多种现实未来情景。其数据学习能力使其优于传统能量平衡模型，而稳健的物理基础则规避了纯数据驱动模型的潜在缺陷。我们还展示了如何利用FaIRGP估算大气层顶辐射强迫，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。希望本研究能推动数据驱动方法在气候模拟领域的更广泛应用。