Multi-variate factorisation of numerical simulations

Daniel J. Lunt*, Deepak Chandan, Alan M. Haywood, George M. Lunt, Jonathan C. Rougier, Ulrich Salzmann, Gavin A. Schmidt, Paul J. Valdes

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)
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Factorisation (also known as "factor separation") is widely used in the analysis of numerical simulations. It allows changes in properties of a system to be attributed to changes in multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously proposed factorisations that have been applied in the field of climate modelling: the linear factorisation, the factorisation, and the factorisation. We show that, when more than two variables are being considered, none of these three methods possess all four properties of "uniqueness", "symmetry", "completeness", and "purity". Here, we extend each of these factorisations so that they do possess these properties for any number of variables, resulting in three factorisations - the "linear-sum"factorisation, the "shared-interaction"factorisation, and the "scaled-residual"factorisation. We show that the linear-sum factorisation and the shared-interaction factorisation reduce to be identical in the case of four or fewer variables, and we conjecture that this holds for any number of variables. We present the results of the factorisations in the context of three past studies that used the previously proposed factorisations.

Original languageEnglish
Pages (from-to)4307-4317
Number of pages11
JournalGeoscientific Model Development
Issue number7
Early online date8 Jul 2021
Publication statusPublished - 8 Jul 2021

Bibliographical note

Funding Information:
Financial support. This research has been supported by NERC (grant no. NE/P01903X/1).

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