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Ensemble Averaging and Mean Squared Error

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  • 1 School of Mathematics, University of Bristol, Bristol, United Kingdom
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Abstract

In fields such as climate science, it is common to compile an ensemble of different simulators for the same underlying process. It is a striking observation that the ensemble mean often outperforms at least half of the ensemble members in mean squared error (measured with respect to observations). In fact, as demonstrated in the most recent IPCC report, the ensemble mean often outperforms all or almost all of the ensemble members across a range of climate variables. This paper shows that these could be mathematical results based on convexity and averaging but with implications for the properties of the current generation of climate simulators.

Corresponding author address: Jonathan Rougier, School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom. E-mail: j.c.rougier@bristol.ac.uk

Abstract

In fields such as climate science, it is common to compile an ensemble of different simulators for the same underlying process. It is a striking observation that the ensemble mean often outperforms at least half of the ensemble members in mean squared error (measured with respect to observations). In fact, as demonstrated in the most recent IPCC report, the ensemble mean often outperforms all or almost all of the ensemble members across a range of climate variables. This paper shows that these could be mathematical results based on convexity and averaging but with implications for the properties of the current generation of climate simulators.

Corresponding author address: Jonathan Rougier, School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom. E-mail: j.c.rougier@bristol.ac.uk
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