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Results for “factorisation methods”

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NASA NTRS2021

Multi-Variate Factorisation of Numerical Simulations

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.

Numerical simulations↗
NASA NTRS2022

Multi-variate Factorisation of Numerical Simulations

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.

Numerican simulations↗
NASA NTRS2012

On the Causes of Mid-Pliocene Warmth and Polar Amplification

The mid-Pliocene (approximately 3 to 3.3 Ma ago), is a period of sustained global warmth in comparison to the late Quaternary (0 to approximately 1 Ma ago), and has potential to inform predictions of long-term future climate change. However, given that several processes potentially contributed, relatively little is understood about the reasons for the observed warmth, or the associated polar amplification. Here, using a modelling approach and a novel factorisation method, we assess the relative contributions to mid-Pliocene warmth from: elevated CO2, lowered orography, and vegetation and ice sheet changes. The results show that on a global scale, the largest contributor to mid-Pliocene warmth is elevated CO2. However, in terms of polar amplification, changes to ice sheets contribute significantly in the Southern Hemisphere, and orographic changes contribute significantly in the Northern Hemisphere. We also carry out an energy balance analysis which indicates that that on a global scale, surface albedo and atmospheric emmissivity changes dominate over cloud changes. We investigate the sensitivity of our results to uncertainties in the prescribed CO2 and orographic changes, to derive uncertainty ranges for the various contributing processes.

Lunt, Daniel J.↗