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The Linear Model in 4D-Var

Tim Payne

May 21st 2009

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Introduction

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Best linear approximation for functions

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Data assimilation cycle

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Issue 1 – Is the conditional mode what we want?

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Posterior pdf

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4D-Var strategies

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Reg-A: Optimising linear model for analysis

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Reg-A: Optimising linear model for analysis

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Solution to Reg-A

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Reg-A’: optimising linear model for conditional mean

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Solution to Reg-A’

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Reg-A applied to Vis op

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Issue 2: Will improving analysis improve forecasts?

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Short forecast error

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Schematic of why improving analysis may not improve short forecast

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Reg-B: Optimising linear model for short forecast

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Reg-B applied to logistic map

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More Issues

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Reg-M revisited

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TL versus Reg-M applied to modified logistic map

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TL versus Reg-M with many outer loops

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Summary