Lunt, DJ, Chandan, D, Haywood, AM orcid.org/0000-0001-7008-0534 et al. (5 more authors) (2021) Multi-variate factorisation of numerical simulations. Geoscientific Model Development, 14 (7). pp. 4307-4317. ISSN 1991-959X
Abstract
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 Stein and Alpert (1993) factorisation, and the Lunt et al. (2012) 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds) > Inst for Climate & Atmos Science (ICAS) (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Jul 2021 09:52 |
Last Modified: | 26 Jul 2021 09:52 |
Status: | Published |
Publisher: | Copernicus Publications |
Identification Number: | 10.5194/gmd-14-4307-2021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:176043 |