  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.
