Multi-variate factorisation of numerical simulations

Abstract. Factorisation (also known as “factor separation”) is widely used in the analysis of numerical simulations. It allows changes properties a system to be attributed multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously proposed factorisations have been applied field climate modelling: linear factorisation, Stein and Alpert (1993) Lunt et al. (2012) factorisation. We show that, when more than two being considered, none these methods possess all four “uniqueness”, “symmetry”, “completeness”, “purity”. Here, extend each so they do for any number variables, resulting – “linear-sum” “shared-interaction” “scaled-residual” linear-sum shared-interaction reduce identical case or fewer conjecture this holds variables. present results context past studies factorisations.