Various ways of using empirical orthogonal functions for climate model evaluation

We present a framework for evaluating multi-model ensembles based on common empirical orthogonal functions (common EOFs) that emphasize salient features connected to spatio-temporal covariance structures embedded in large climate data volumes. This framework enables the extraction of the most pronounced spatial patterns of coherent variability within the joint dataset and provides a set of weights for each model in terms of the principal components which refer to exactly the same set of spatial patterns of covariance. In other words, common EOFs provide a means for extracting information from large volumes of data. Moreover, they can provide an objective basis for evaluation that can be used to accentuate ensembles more than traditional methods for evaluation, which tend to focus on individual models. Our demonstration of the capability of common EOFs reveals a statistically significant improvement of the sixth generation of the World Climate Research Programme (WCRP) Climate Model Intercomparison Project (CMIP6) simulations in comparison to the previous generation (CMIP5) in terms of their ability to reproduce the mean seasonal cycle in air surface temperature, precipitation, and mean sea level pressure over the Nordic countries. The leading common EOF principal component for annually or seasonally aggregated temperature, precipitation, and pressure statistics suggests that their simulated interannual variability is generally consistent with that seen in the ERA5 reanalysis. We also demonstrate how common EOFs can be used to analyse whether CMIP ensembles reproduce the observed historical trends over the historical period 1959-2021, and the results suggest that the trend statistics provided by both CMIP5 RCP4.5 and CMIP6 SSP245 are consistent with observed trends. An interesting finding is also that the leading common EOF principal component for annually or seasonally aggregated statistics seems to be approximately normally distributed, which is useful information about the multi-model ensemble data.