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Hernan G. Arango IMCS, Rutgers

Predictability of Mesoscale Variability in the East Australia Current given Strong Constraint Data Assimilation. Hernan G. Arango IMCS, Rutgers. John L. Wilkin IMCS, Rutgers. Javier Zavala-Garay IMCS, Rutgers. Outline. E ast A ustralia C urrent ( EAC ), and ROMS EAC application

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Hernan G. Arango IMCS, Rutgers

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  1. Predictability of Mesoscale Variability in the East Australia Current given Strong Constraint Data Assimilation Hernan G. Arango IMCS, Rutgers John L. Wilkin IMCS, Rutgers Javier Zavala-Garay IMCS, Rutgers

  2. Outline • East Australia Current (EAC), and ROMS EAC application • Incremental, Strong-constraint 4- Dimensional Variational (IS4DVAR) data assimilation • Two applications of IS4DVAR • Reanalysis (assimilation window) • Prediction (forecast window) • Predictability of mesoscale variability in EAC given IS4DVAR • Final remarks • Future work

  3. EAC

  4. -24 -28 -32 -36 -40 -44 -48 165 155 150 160 145 East Australia Current Application Configuration

  5. IS4DVAR

  6. Forward model

  7. Forward model

  8. Forward model

  9. Forward model

  10. IS4DVAR • Given a first guess (a forward trajectory)

  11. IS4DVAR • Given a first guess (a forward trajectory)… • And given the available data…

  12. IS4DVAR • Given a first guess (a forward trajectory)… • And given the available data… • What are the changes (or increment) to the IC so that the forward model fits the observations?

  13. The best fit becomes the reanalysis assimilation window

  14. The final state becomes the IC for the forecast window assimilation window forecast

  15. The final state becomes the IC for the forecast window assimilation window forecast verification

  16. How IS4DVAR operates * • IS4DVAR tries to minimize a cost function that measures the misfit between model and observations • The is4dvar tries o find the best road from first guess * to a better initial guess * • The road might not be very nice because of nonlinearity. * state variable * state variable

  17. Predictability in EAC given IS4DVAR

  18. 4DVar Observations and Experiments XBTs 7-Day IS4DVAR Experiments E1:SSH, SST E2:SSH, SST,XBT SSH 7-Day Averaged AVISO SST Daily CSIRO HRPT Days since January 1st 2001, 00:00:00

  19. EAC Incremental 4DVar: Surface Versus Sub-surface Observations

  20. EAC Incremental 4DVar: Surface Versus Sub-surface Observations First Guess SSH/SST

  21. EAC Incremental 4DVar: Surface Versus Sub-surface Observations Observations SSH/SST First Guess SSH/SST

  22. EAC Incremental 4DVar: Surface Versus Sub-surface Observations Observations ROMS IS4DVAR: SSH/SST SSH/SST SSH/SST First Guess ROMS IS4DVAR: XBT Only SSH/SST SSH/SST

  23. EAC Incremental 4DVar (IS4DVAR) Temperature along XBT line Temperature along XBT line SSH SSH E1 Observations Temperature along XBT line SSH E2 7-Day 4DVar Assimilation cycle E1: SSH, SST Observations E2: SSH, SST, XBT Observations Temperature along XBT line SSH E1 – E2

  24. Quantifying the IS4DVAR fit and forecast skill • Correlation: Close to 1 if the patterns of variability in ROMS are very similar to the patterns of variability in observations. • Root Mean Square (rms): small if the fit is very good. • Good fit or forecast skill if correlation are close to 1 and rms close to 0.

  25. 2001 EAC 4DVar Sequential Assimilation: E2 SSH Lag Pattern Correlation Lag Forecast Time (weeks) 0.6 Days since January 1st 2001, 00:00:00 SSH Lag Pattern RMS Lag Forecast Time (weeks) Days since January 1st 2001, 00:00:00

  26. 2001 EAC 4DVar Sequential Assimilation: E2 SSH Correlations Between Observations and Forecast lag = -1 week lag = 0 lag = 1 week lag = 2 weeks lag = 3 weeks lag = 4 weeks SSH RMS Between Observations and Forecast lag = -1 week lag = 0 lag = 1 week lag = 2 weeks lag = 3 weeks lag = 4 weeks

  27. rms error normalized by the expected variance in SSH lag = 0 week lag = 1 week lag = 1 week lag = 2 weeks lag = 3 weeks lag = -1 week

  28. Ensemble prediction • Assimilation of SSH+SST and SSH+SST+XBT gives similar rms and decorrelation maps of SSH when compared with observations • So does assimilation of XBT help to better predict the SSH? • Yes, the resulting analysis is less sensible to errors in the IC • We computed the optimal perturbations at day 85 from from the two reanalysis E1 and E2 • Produced an ensemble (10 members) by perturbing the corresponding IC with the leading optimal perturbations (scaled to represent realistic errors) E1 OP E2 OP

  29. Ensemble Prediction: E1 1-day forecast 8-days forecast 15-days forecast

  30. Ensemble Prediction: E2 1-day forecast 8-days forecast 15-days forecast

  31. Remarks on assimilation of surface (SSH and SST) versus subsurface (XBT) information • Assimilation of subsurface information (XBT) improves predictability • Assimilation of subsurface information can help to determine surface information (SSH) • In practice it is impossible to observe the subsurface at all model domain, at all times. • It will be nice to infer the subsurface from surface observations • Synthetic XBT (proxies for subsurface temperature and salinity given SSH and SST; provided by Griffin)

  32. Example of synthetic XBT

  33. Comparison between ROMS fit and observed temperature from all XBTs. Note: actual XBT-data was not assimilated, it is used here to evaluate the quality of the reanalysis. SSH+SST

  34. Comparison between ROMS fit and observed temperature from all XBTs. Note: actual XBT-data was not assimilated, it is used here to evaluate the quality of the reanalysis. SSH+SST SSH+SST+SynXBT

  35. Comparison between ROMS prediction and observed temperature from all XBTs.

  36. Comparison between ROMS prediction and observed temperature from all XBTs.

  37. Comparison between ROMS prediction and observed temperature from all XBTs.

  38. Comparison between ROMS prediction and observed temperature from all XBTs.

  39. Comparison between ROMS prediction and observed temperature from all XBTs.

  40. Final Remarks • Good ocean state predictions for up to 2 weeks in advance • Assimilation of just surface information is not enough • Assimilation of subsurface information help by • improving estimate of the subsurface • making more stable the system to errors in IC • Proxies for subsurface information can be obtained based on surface information, but need lots of subsurface data to construct a robust empirical relationship • The fact that an empirical (linear) relationship exist suggest that there could be a simple dynamical relationships linking the surface with the subsurface variability • The idea is actually not new (Weaver et al 2006: “multivariate balance operator”)

  41. Future work • Include balance terms in the IS4DVAR • Improve boundary forcing • Better global forecast and/or boundary conditions • Determine the optimal boundary forcing via “weak constraint” data-assimilation (WS4DVAR) • Use of along track SSH data instead of reanalysis • Use of is4dvar and w4dvar to downscale GCMs climate change projections

  42. Thanks to… • David Griffin (CSIRO) for the XBT • David Robertson (IMCS) for the editing of nice figures • John Evans (IMCS) for XBT observation files

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