Predictability and the decay of information in mathematical and physical systems

Sienkiewicz, Ewelina (2017) Predictability and the decay of information in mathematical and physical systems. PhD thesis, London School of Economics and Political Science.

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Abstract

This thesis explores the predictability of nonlinear systems, both mathematical systems (as realised on a digital computer) and geophysical systems (the El Ni˜no Phenomena, and climate prediction via downscaling). How far into the future does a forecast system provide information beyond that available purely from the past? How does information in a probabilistic forecast decay with time? Is it true that, no matter how good the simulation model used for prediction is, there will be a point where predictability is lost? That is, that there is always a time horizon beyond which any forecast fails to yield useful information. The two main limits to predictability are identified and discussed. Sensitivity to initial condition complicates the forecasting of chaotic dynamical systems, even when the model is perfect. Structural model error (model inadequacy) is a distinct cause of the decay of predictability, a decay that may often be mistakenly interpreted as resulting from chaos. These features are distinguished and demonstrated both in low-dimensional mathematical systems and weather and climate models. Model inadequacy is shown to be important in real-world forecasting, with reference to Columbia University's C-Z model for El Ni˜no predictions and climate models used in the North American Regional Climate Change Assessment Program (NARCCAP). Repercussions for forecast performance are discussed. In short, (i) NARCCAP regional simulations are quickly inconsistent with the global simulations used to drive them, (ii) the C-Z model allows experiments into the decay of predictability when one model version is employed as the system, and a second, structurally distinct model version is used as the model. The decay of predictability is studied from the view point of information theory. Information theoretic tools are allied both to mathematical system-model pairs and to physical system-model pairs. A flaw in formulating one such tool, proposed by Du and Smith (2012, PRE) is exposed and alternative normalisations are explored in various experiments. A quantity called the information deficit, introduced in that same paper, is considered in several settings. New properties of the information deficit are discovered, and it is demonstrated that the information deficit can be a useful tool in identifying (and correcting) shortcomings of a forecasting system.

Item Type:	Thesis (PhD)
Additional Information:	© 2017 Ewelina Sienkiewicz
Library of Congress subject classification:	H Social Sciences > HA Statistics
Sets:	Departments > Statistics
Supervisor:	Smith, Leonard A.
URI:	http://etheses.lse.ac.uk/id/eprint/3716

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