Kernel Taylor Diagram for Earth System Model Evaluation

Earth system model (ESM) intercomparison is essential for assessing model performance and identifying future challenges in climate modeling. The Taylor diagram [1] is one of the most widely used tools for this purpose, as it provides an intuitive summary of standard evaluation metrics — such as correlation, root-mean-square error, and standard deviation — by comparing multiple simulated datasets against a reference, typically observations or a ground truth, within a single plot.

However, in several relevant applications, including the development of new ESM parameterizations, the comparison of conceptual models, or the evaluation of simulated statistical distributions, classic linear correlation and RMSE metrics may be insufficient. Here, we propose a set of extensions to the Taylor diagram based on a generalization of cross-covariance using kernels, allowing both nonlinear relationships and distributional aspects of similarity to be taken into account. Nonlinear similarity is characterized through a kernel-space analogue of rotational alignment, while distributional similarity can be quantified using metrics such as maximum mean discrepancy, as originally introduced in [2], as well as alternative kernel-based measures. Using controlled synthetic experiments, we show that the proposed kernel Taylor diagrams can resolve differences in model skill that remain indistinguishable under the classical Taylor diagram. These results indicate that the kernel-based extensions provide complementary diagnostic information to standard metrics and can support more informative Earth system model evaluation and development.

[1] Taylor, K. E. (2001), Summarizing multiple aspects of model performance in a single diagram, J. Geophys. Res., 106(D7), 7183–7192, doi:10.1029/2000JD900719.

[2] Wickstrøm, K., Johnson, J. E., Løkse, S., Camps-Valls, G., Mikalsen, K. Ø., Kampffmeyer, M., & Jenssen, R. (2022). The Kernelized Taylor Diagram. doi:10.48550/arXiv.2205.08864