Common EOFs: a tool for multi-model comparison and evaluation

Abstract

With the increase in the volume of climate model simulations for past, present and future climate, from various institutions across the globe, there is a need for efficient and robust methods for model comparison and/or evaluation. This manuscript discusses common empirical orthogonal function analysis with a step-wise algorithm, which can be used for the above objective. The method looks for simultaneous diagonalisation of several covariance matrices in a step-wise fashion ensuring thus simultaneous monotonic decrease of the eigenvalues in all groups, and allowing therefore for dimension reduction. The method is applied to a number of tropospheric and stratospheric fields from the main four reanalysis products, and also to several historical climate model simulations from CMIP6, the Coupled Model Intercomparison Project (Phase 6). Monthly means as well as winter daily gridded data are considered over the Northern Hemisphere. The method shows consistency between mass fields as well as mid-tropospheric and stratospheric fields of the reanalyses, but also reveals significant differences in the 2 m surface-air temperature in terms of explained variance. CMIP6 models, on the other hand, show differences reflected in the percentage of explained variance of the leading common EOFs with inter-group variation ranging from 5–10% in the troposphere to about 25% in the stratosphere. Higher order statistics within the leading common modes of variability, in addition to further merits of the method are also discussed.

Various ways of using Empirical Orthogonal Functions for Climate Model evaluation

“…However, a general literature search with Google Scholar, the assessment reports of the Intergovernmental Panel on Climate Change (IPCC), and the documentation behind the ESMValTool (Eyring et al, 2020;Weigel et al, 2021) suggests that common EOFs are not widely used in the climate research community. The impression of a modest interest in common EOFs was also expressed in Benestad (2021) and is supported by a quote from Hannachi et al (2022): "To the best of our knowledge only two studies considered common EOFs, which go back more than two decades (Frankignoul et al, 1995;Sengupta and Boyle, 1998), which were based on the original Flury and Gautschi (1986) (FG86)'s algorithm". However, we also know of a few additional cases where common EOFs were employed, e.g.…”

“…Hannachi et al ( 2022) provide a description of the mathematics behind common EOFs which also is relevant for our analysis, but here we present a slightly different approach for applying them for the purpose of climate model evaluation and for assessing different model ensembles. Here we used singular vector decomposition (SVD) (Becker et al, 1988) on a joint data matrix rather than the step-wise algorithm for a set of covariance matrices described by Hannachi et al (2022). Hence, we obtained identical spatial maps and eigenvalues for all models in the joint data matrix, but different statistical properties (e.g.…”

“…However, we also know of a few additional cases where common EOFs were employed, e.g. those cited above, that were overlooked by Hannachi et al (2022). A Google Scholar search for "common principal component analysis" (1,680 hits, 2022-12-01) nevertheless suggests that common EOFs are discussed in scientific journals belonging to other scientific disciplines than climate science, such as statistics, biometrics, biology geology, and neuro-computing.…”

“…One of our objectives was to evaluate GCM data that are used as predictors for empirical-statistical downscaling (ESD) over Northern Europe, and we picked this as an example to demonstrate their utility and merit. While Hannachi et al (2022) used common EOFs to compare individual models, we present an approach where they were used to compare different ensembles, such as CMIP5 RCP4.5 and CMIP6 SSP245, and to assess if they provide a statistical representation that has a similar statistical population (Wilks, 2006, e.g. p.72) as the reanalysis.…”

Investigating the Effects of Sea Ice Melting on Oceanic Warming in the Arctic

“…This prompts the use of a Maximum Covariance Analysis (MCA) algorithm to determine the most prominent modes affecting these two variables. MCA uses singular value decomposition (SVD) techniques [14] to determine patterns that exhibit high fractions of covariance between the ocean temperature and sea ice spatial patterns. This allows for identifying modes that significantly contribute to correlated trends between sea ice and ocean temperature in the Arctic.…”