数据驱动的云量参数化方程发现
Data-Driven Equation Discovery of a Cloud Cover Parameterization
AI总结：
本文提出结合符号回归、顺序特征选择和物理约束的分层框架，从全球风暴解析模型数据中发现可解释且可迁移的云量诊断方程，其性能与神经网络相当且优于传统方案。
摘要：
一种改进气候模型中云表示并进而改进气候预估的有前景方法是利用全球风暴解析模型的输出来开发基于机器学习的参数化方案。虽然神经网络在其训练分布范围内可以达到最先进的性能，但在分布之外可能做出不可靠的预测。此外，神经网络通常需要事后工具进行解释。为了避免这些局限性，我们在一个分层建模框架中结合了符号回归、顺序特征选择和物理约束。该框架使我们能够从全球风暴解析模型模拟的粗粒度变量中发现诊断云量的新方程。这些解析方程在构造上即可解释，并且易于迁移到其他网格或气候模型。我们最优的方程在性能和复杂度之间取得了平衡，实现了与神经网络相当的性能（$R^2=0.94$），同时保持简单（仅含11个可训练参数）。在所有云类型中，它比Xu-Randall方案更准确地再现了云量分布（Hellinger距离$<0.09$），并且在富含凝结物的云类型中与神经网络表现相当。当将该方程应用于ERA5再分析数据并进行微调时，与所有其他最优云量方案相比，该方程对新数据表现出更优越的迁移能力。我们的研究结果表明，符号回归在发现可解释、物理一致且非线性的云量参数化方程方面是有效的。
英文摘要：
A promising method for improving the representation of clouds in climate models, and hence climate projections, is to develop machine learning-based parameterizations using output from global storm-resolving models. While neural networks can achieve state-of-the-art performance within their training distribution, they can make unreliable predictions outside of it. Additionally, they often require post-hoc tools for interpretation. To avoid these limitations, we combine symbolic regression, sequential feature selection, and physical constraints in a hierarchical modeling framework. This framework allows us to discover new equations diagnosing cloud cover from coarse-grained variables of global storm-resolving model simulations. These analytical equations are interpretable by construction and easily transferable to other grids or climate models. Our best equation balances performance and complexity, achieving a performance comparable to that of neural networks ($R^2=0.94$) while remaining simple (with only 11 trainable parameters). It reproduces cloud cover distributions more accurately than the Xu-Randall scheme across all cloud regimes (Hellinger distances $<0.09$), and matches neural networks in condensate-rich regimes. When applied and fine-tuned to the ERA5 reanalysis, the equation exhibits superior transferability to new data compared to all other optimal cloud cover schemes. Our findings demonstrate the effectiveness of symbolic regression in discovering interpretable, physically-consistent, and nonlinear equations to parameterize cloud cover.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
