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- Title
Multi-variate factorisation of numerical simulations.
- Authors
Lunt, Daniel J.; Chandan, Deepak; Haywood, Alan M.; Lunt, George M.; Rougier, Jonathan C.; Salzmann, Ulrich; Schmidt, Gavin A.; Valdes, Paul J.
- 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 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.
- Subjects
COMPUTER simulation; NUMERICAL analysis; ATMOSPHERIC models; FACTORIZATION
- Publication
Geoscientific Model Development, 2021, Vol 14, Issue 7, p4307
- ISSN
1991-959X
- Publication type
Article
- DOI
10.5194/gmd-14-4307-2021