Evaluating Climate Models with Sliced Elastic Distance

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.