Submitted as: methods for assessment of models 05 Jun 2020

Submitted as: methods for assessment of models | 05 Jun 2020

Review status: a revised version of this preprint is currently under review for the journal GMD.

Multi-variate factorisation of numerical simulations

Daniel John Lunt1, Deepak Chandan2, Harry J. Dowsett3, Alan M. Haywood4, George M. Lunt5, Jonathan C. Rougier6, Ulrich Salzmann7, Gavin A. Schmidt8, and Paul J. Valdes1 Daniel John Lunt et al.
  • 1School of Geographical Sciences, University of Bristol, UK
  • 2Department of Physics, University of Toronto, Canada
  • 3U.S. Geological Survey, USA
  • 4School of Earth and Environment, University of Leeds, UK
  • 5AECOM, UK
  • 6School of Mathematics, University of Bristol, UK
  • 7Geography and Environmental Sciences, Northumbria University
  • 8NASA Goddard Institute for Space Studies, US

Abstract. Factorisation 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 three properties of uniqueness, symmetry, and completeness. 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-total factorisation. We show that the linear-sum factorisation and the shared-interaction factorisation reduce to be identical. We present the results of the factorisations in the context of studies that used the previously-proposed factorisations. This reveals that only the linear-sum/shared-interaction factorisation possesses a fourth property – boundedness, and as such we recommend the use of this factorisation in applications for which these properties are desirable.

Daniel John Lunt et al.

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Status: final response (author comments only)
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Daniel John Lunt et al.

Data sets

Pliocene surface temperature data for Multi-variate factorisation methods D. Chandan

Daniel John Lunt et al.


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Short summary
Often in science we carry out experiments with computers in which several factors are explored. For example, in the field of climate science, how the factors of greenhouse gases, ice, and vegetation affect temperature. We can explore the relative importance of these factors by "swapping in and out" different values of these factors, and can also carry out experiments with many different combinations of these factors. This paper discusses how best to analyse the results from such experiments.