DOUBLE PENDULUM "1+1"D VAR ALGORITHM

Ross Bannister, Data Assimilation Research Centre

Read-in the initial guess,

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Set-up the background state, ( for first run, from last forecast for later runs)

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Set-up the linearization state

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Work out perturbation of the background from the linearization state,

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Do a forecast to the end of the current cycle, starting from

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Calculate the gradient of w.r.t. model observations

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Linearize the forward model,

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Calculate the Hessian in model space,

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Diagonalize the Hessian, eigenvectors , eigenvalues

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Calculate the components of the -transform,

(this makes the Hessian in transformed space identity, )

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Calculate the gradient of w.r.t. the transformed variables,

(the analysis increment in transformed space is )

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Calculate the analysis increment in model space,

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Calculate a new linearization state,

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¬ If , go to , otherwise is the analysis: perform an integration from and go to