1 / 43

The Construction and Use of Linear Models in Large-scale Data Assimilation

Tim Payne Large-Scale Inverse Problems and Applications in the Earth Sciences October 24th 2011. The Construction and Use of Linear Models in Large-scale Data Assimilation. Part I. The Construction of Linear Models

varana
Download Presentation

The Construction and Use of Linear Models in Large-scale Data Assimilation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Tim Payne Large-Scale Inverse Problems and Applications in the Earth Sciences October 24th 2011 The Construction and Use of Linear Models in Large-scale Data Assimilation

  2. Part I. The Construction of Linear Models in Data Assimilation

  3. Notation

  4. Update-Prediction Cycle

  5. First Strategy – exact evolution of covariances

  6. Second strategy – EKF using tangent-linear

  7. Third strategy – EKF using best linear approximation

  8. Explicit formula for best linear approximation

  9. Basic properties of best linear approximation

  10. Cloud function

  11. Smith Cloud Scheme with ‘ad hoc’ Regularisation

  12. Smith Cloud Scheme with ‘Optimal’ Regularisation

  13. Incremental 4D-Var

  14. Options for linearisation step required for incremental 4D-Var

  15. Gain matrix implied by each option

  16. Advantage of BLA over TL in incremental 4D-Var

  17. Pseudo Chain-rule for best linear approximation

  18. Use of best linear approximation in EKF

  19. The prior covariance implied by different approximations

  20. Prior covariance using best linear estimate

  21. Prior covariance using the best linear estimate always underestimates the true prior

  22. The Duffing Map

  23. 100,000 iterates of Duffing Map

  24. Reminder of EKF algorithm

  25. Prior covariance for Duffing Map

  26. Mean square analysis error in Duffing map: TL and best linear estimate compared

  27. Part II. The Use of Linear Models in Data Assimilation

  28. Linearisation error in 4D-Var as used in real numerical weather prediction models

  29. Linear model for evolution of increments

  30. Linearisation error as a stochastic error

  31. Issues in forming EKF

  32. Signal model for system with time correlated linearisation error

  33. EKF with time correlated linearisation error

  34. Parameters for filter including linearistion error

  35. Example: L95, nearly perfect full model, persistence for linear model

  36. Example: L95, nearly perfect full model, persistence for linear model, results

  37. Variational version: weak constraint 4D-Var allowing for time correlated linearisation error

  38. Remarks on variational form

  39. Long window weak constraint 4D-Var allowing for linearisation error, same example

  40. Summary to Part I

  41. Summary to Part II

  42. The End

More Related