Download
slide1 n.
Skip this Video
Loading SlideShow in 5 Seconds..
Weak and Strong Constraint 4D variational data assimilation: Methods and Applications PowerPoint Presentation
Download Presentation
Weak and Strong Constraint 4D variational data assimilation: Methods and Applications

Weak and Strong Constraint 4D variational data assimilation: Methods and Applications

117 Views Download Presentation
Download Presentation

Weak and Strong Constraint 4D variational data assimilation: Methods and Applications

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Weak and Strong Constraint 4D variational data assimilation:Methods and Applications Di Lorenzo, E. Georgia Institute of Technology Arango, H. Rutgers University Moore, A. and B. Powell UC Santa Cruz Cornuelle, B and A.J. Miller Scripps Institution of Oceanography Bennet A. and B. Chua Oregon State University

  2. Short review of 4DVAR theory (an alternative derivation of the representer method and comparison between different 4DVAR approaches) • Overview of Current applications • Things we struggle with

  3. ASSIMILATION Goal Initial Guess Best Model Estimate (consistent with observations) (A) (B) WEAK Constraint STRONG Constraint …we want to find the correctionse

  4. Best Model Estimate Corrections Initial Guess ASSIMILATION Goal (A) (B) WEAK Constraint STRONG Constraint …we want to find the correctionse

  5. Best Model Estimate Corrections Initial Guess ASSIMILATION Goal

  6. Best Model Estimate Corrections Initial Guess ASSIMILATION Goal

  7. Best Model Estimate Corrections Initial Guess ASSIMILATION Goal

  8. Best Model Estimate Corrections Initial Guess ASSIMILATION Goal Tangent Linear Dynamics

  9. ASSIMILATION Goal Best Model Estimate Corrections Initial Guess Integral Solution Tangent Linear Propagator

  10. ASSIMILATION Goal Best Model Estimate Corrections Initial Guess

  11. ASSIMILATION Goal Best Model Estimate Corrections Initial Guess The Observations

  12. ASSIMILATION Goal Best Model Estimate Corrections Initial Guess Data misfit from initial guess

  13. ASSIMILATION Goal is a mapping matrix of dimensions observations X model space def: Data misfit from initial guess

  14. ASSIMILATION Goal is a mapping matrix of dimensions observations X model space def: Data misfit from initial guess

  15. Quadratic Linear Cost Function for residuals is a mapping matrix of dimensions observations X model space

  16. Quadratic Linear Cost Function for residuals 2) corrections should not exceed our assumptions about the errors in model initial condition. 1) corrections should reduce misfit within observational error is a mapping matrix of dimensions observations X model space

  17. Minimize Linear Cost Function

  18. def: 4DVAR inversion Hessian Matrix

  19. def: 4DVAR inversion Hessian Matrix Representer-based inversion

  20. def: 4DVAR inversion Hessian Matrix Representer-based inversion Representer Coefficients Stabilized Representer Matrix Representer Matrix

  21. def: 4DVAR inversion Hessian Matrix Representer-based inversion Representer Coefficients Stabilized Representer Matrix Representer Matrix

  22. An example of Representer Functionsfor the Upwelling System Computed using the TL-ROMS and AD-ROMS

  23. An example of Representer Functionsfor the Upwelling System Computed using the TL-ROMS and AD-ROMS

  24. Applications of the ROMS inverse machinery: • Baroclinic coastal upwelling: synthetic model experiment to test the development • CalCOFI Reanalysis: produce ocean estimates for the CalCOFI cruises from 1984-2006. Di Lorenzo, Miller, Cornuelle and Moisan • Intra-Americas Seas Real-Time DAPowell, Moore, Arango, Di Lorenzo, Milliff et al.

  25. Coastal Baroclinic Upwelling System Model Setup and Sampling Array section

  26. Applications of inverse ROMS: • Baroclinic coastal upwelling: synthetic model experiment to test inverse machinery 1) The representer system is able to initialize the forecast extracting dynamical information from the observations. 2) Forecast skill beats persistence 10 day assimilation window 10 day forecast

  27. SKILL of assimilation solution in Coastal UpwellingComparison with independent observations Weak SKILL Strong Climatology Persistence Assimilation Forecast  DAYS Di Lorenzo et al. 2007; Ocean Modeling

  28. Day=0 Day=2 Day=6 Day=10

  29. Assimilation solutions Day=0 Day=2 Day=6 Day=10

  30. Day=14 Day=18 Day=22 Day=26

  31. Day=14 Day=18 Day=22 Day=26

  32. Forecast Day=14 Day=14 Day=18 Day=18 Day=22 Day=22 Day=26 Day=26

  33. Intra-Americas Seas Real-Time DAPowell, Moore, Arango, Di Lorenzo, Milliff et al. www.myroms.org/ias April 3, 2007

  34. CalCOFI Reanlysis: produce ocean estimates for the CalCOFI cruises from 1984-2006. Di Lorenzo, Miller, Cornuelle and Moisan

  35. …careful

  36. …careful Data Assimilation is NOT a black box

  37. …careful Data Assimilation is NOT a black box • Typically we do not have sufficient data to constraint the models (e.g. underdetermined systems  fitting vs. assimilating data)

  38. …careful Data Assimilation is NOT a black box • Typically we do not have sufficient data to constraint the models (e.g. underdetermined systems  fitting vs. assimilating data) • Linear sensitivity are not always great! (e.g. Instability of Tangent linear dynamics)

  39. …careful Data Assimilation is NOT a black box • Typically we do not have sufficient data to constraint the models (e.g. underdetermined systems  fitting vs. assimilating data) • Linear sensitivity are not always great! (e.g. Instability of Tangent linear dynamics) • Coastal data assimilation is STILL a science question (e.g. model biases and Gaussian statistics assumption, inadequate error covariances)

  40. …careful Data Assimilation is NOT a black box • Typically we do not have sufficient data to constraint the models (e.g. underdetermined systems  fitting vs. assimilating data) • Linear sensitivity are not always great! (e.g. Instability of Tangent linear dynamics) • Coastal data assimilation is STILL a science question (e.g. model biases and Gaussian statistics assumption, inadequate error covariances)

  41. Assimilation of SSTa True Initial Condition True

  42. Assimilation of SSTa True Initial Condition Which model has correct dynamics? Model 1 Model 2 True

  43. Wrong Model Good Model True Initial Condition Model 1 Model 2 True

  44. Time Evolution of solutions after assimilation Wrong Model DAY 0 Good Model

  45. Time Evolution of solutions after assimilation Wrong Model DAY 1 Good Model

  46. Time Evolution of solutions after assimilation Wrong Model DAY 2 Good Model

  47. Time Evolution of solutions after assimilation Wrong Model DAY 3 Good Model

  48. Time Evolution of solutions after assimilation Wrong Model DAY 4 Good Model

  49. What if we apply more background constraints? Wrong Model Good Model True Initial Condition True Model 1 Model 2

  50. Assimilation of data at time True Initial Condition True Model 1 Model 2