The validation of global climate models plays a crucial role in ensuring the accuracy of climatological predictions. However, existing statistical methods for evaluating differences between climate fields often overlook time misalignment and therefore fail to distinguish between sources of variability. To more comprehensively measure differences between climate fields, we introduce a new vector-valued metric, the sliced elastic distance. This new metric simultaneously accounts for spatial and temporal variability while decomposing the total distance into shape differences (amplitude), timing variability (phase), and bias (translation). We compare the sliced elastic distance against a classical metric and a newly developed Wasserstein-based approach through a simulation study. Our results demonstrate that the sliced elastic distance outperforms previous methods by capturing a broader range of features. We then apply our metric to evaluate the historical model outputs of the Coupled Model Intercomparison Project (CMIP) members, focusing on monthly average surface temperatures and monthly total precipitation. By comparing these model outputs with quasi-observational ERA5 Reanalysis data products, we rank the CMIP models and assess their performance. Additionally, we investigate the progression from CMIP phase 5 to phase 6 and find modest improvements in the phase 6 models regarding their ability to produce realistic climate dynamics.

翻译：全球气候模型的验证对于确保气候预测的准确性至关重要。然而，现有的统计方法在评估气候场之间的差异时，常常忽略时间错位问题，因此无法区分变异来源。为更全面地衡量气候场之间的差异，我们引入了一种新的向量值度量——切片弹性距离。这一新度量能够同时考虑空间和时间变异性，并将总距离分解为形状差异（振幅）、时序变化（相位）和偏差（平移）。通过模拟研究，我们将切片弹性距离与经典度量及一种新开发的基于Wasserstein的方法进行了比较。结果表明，切片弹性距离通过捕捉更广泛的特征，优于先前的方法。随后，我们将该度量应用于评估耦合模型比对项目（CMIP）成员的历史模型输出，重点关注月平均地表温度和月总降水量。通过将这些模型输出与准观测的ERA5再分析数据产品进行比较，我们对CMIP模型进行了排序并评估了其性能。此外，我们研究了从CMIP第5阶段到第6阶段的进展，发现第6阶段模型在生成逼真的气候动力学能力方面有适度改进。