Science is naturally conservative and the scepticism to new ideas ensures high scientific quality. We have more confidence when different scholars arrive at the same conclusion independently of each other. But scientific research also brings about discoveries and innovations, and it typically takes time for such new understanding to receive acknowledgement and acceptance. In the meanwhile, it’s uncertain whether they really represent progress or if they are misconceived ideas. Sometimes we can shed more light on new ideas through scientific discussions.
I recently experienced the contrast between old knowledge and new ideas when my research group used a well-established mathematical concept in a new way. In this case, the mathematical concept is related to so-called eigenfunctions, but in climate research known as empirical orthogonal functions (EOFs) and discussed earlier in a post here (‘Why not use a clever mathematical trick?’). I decided to elaborate on this idea through a discussion paper in EGUsphere with an open review. It will hopefully lead to some scientific discussions that may tell me whether our new ideas represent a progress in terms of evaluating climate models.
A motivation for this discussion paper was that it came as a surprise to me that it’s rare that EOFs are applied to joint datasets, known as ‘common EOFs’. For instance, common EOFs are absent in the community-based ESMEvalTool (Eyring et al., 2020) despite their merits, something we discuss in our recent discussion paper (Benestad et al., 2023). Furthermore, text searches with “common EOFs”, “common principal component” and “common empirical orthogonal functions” through the full Working Group 1 report from the IPCC assessment report 6 (2409 pages) only gave one hit:
Predictor patterns that are common to observations and climate model data can be defined by common empirical orthogonal functions (Benestad, 2011).
On Google Scholar, the same search gave 116, 1680, 64 hits, and in this case, the higher number of hits for “common principal component” involved many more disciplines than climate research.
So why bother with common EOFs? Bernhard Flury wrote a book in 1986 with the title ‘Common principal components and related multivariate models’ (Flury, 1986), and a few other studies picked up the idea, such as a report from 1993 and in Sengupta and Boyle (1998). I think common EOFs are a clever concept and have used them as a framework for empirical-statistical downscaling since 2001 (Benestad, 2001). In 2017, a group of colleagues and I wrote a perspective on the use of statistical methods in climate research where we also discussed common EOFs (Benestad et al., 2017).
In the latest discussion paper, we highlighted several ways of using them to deal with large multi-model ensembles and huge data volumes, popularly known as “Big data”. They make use of the redundancy of information embedded within the data and boil it down to the most salient aspects. Also, common EOFs make it possible to take advantage of some attractive mathematical properties such as orthogonality. It is somewhat similar with Fourier series which too provide orthogonal components in addition to the ease to estimate any derivative and makes it simple to estimate the length of e.g. solar cycles (Benestad, 2005).
So far, I haven’t seen any arguments against the use of common EOFs. So why have common EOFs not been used more?
- V. Eyring, L. Bock, A. Lauer, M. Righi, M. Schlund, B. Andela, E. Arnone, O. Bellprat, B. Brötz, L. Caron, N. Carvalhais, I. Cionni, N. Cortesi, B. Crezee, E.L. Davin, P. Davini, K. Debeire, L. de Mora, C. Deser, D. Docquier, P. Earnshaw, C. Ehbrecht, B.K. Gier, N. Gonzalez-Reviriego, P. Goodman, S. Hagemann, S. Hardiman, B. Hassler, A. Hunter, C. Kadow, S. Kindermann, S. Koirala, N. Koldunov, Q. Lejeune, V. Lembo, T. Lovato, V. Lucarini, F. Massonnet, B. Müller, A. Pandde, N. Pérez-Zanón, A. Phillips, V. Predoi, J. Russell, A. Sellar, F. Serva, T. Stacke, R. Swaminathan, V. Torralba, J. Vegas-Regidor, J. von Hardenberg, K. Weigel, and K. Zimmermann, "Earth System Model Evaluation Tool (ESMValTool) v2.0 – an extended set of large-scale diagnostics for quasi-operational and comprehensive evaluation of Earth system models in CMIP", Geoscientific Model Development, vol. 13, pp. 3383-3438, 2020. http://dx.doi.org/10.5194/gmd-13-3383-2020
- R.E. Benestad, A. Mezghani, J. Lutz, A. Dobler, K.M. Parding, and O.A. Landgren, "Various ways of using Empirical Orthogonal Functions for Climate Model evaluation", 2023. http://dx.doi.org/10.5194/egusphere-2022-1385
- R.E. Benestad, "A comparison between two empirical downscaling strategies", International Journal of Climatology, vol. 21, pp. 1645-1668, 2001. http://dx.doi.org/10.1002/joc.703
- R. Benestad, J. Sillmann, T.L. Thorarinsdottir, P. Guttorp, M.D.S. Mesquita, M.R. Tye, P. Uotila, C.F. Maule, P. Thejll, M. Drews, and K.M. Parding, "New vigour involving statisticians to overcome ensemble fatigue", Nature Climate Change, vol. 7, pp. 697-703, 2017. http://dx.doi.org/10.1038/NCLIMATE3393
- R.E. Benestad, "A review of the solar cycle length estimates", Geophysical Research Letters, vol. 32, 2005. http://dx.doi.org/10.1029/2005GL023621