Observations and Ocean State Estimation: Impact, Sensitivity and Predictability

1. Observations and Ocean State Estimation: Impact, Sensitivity and Predictability Andy Moore University of California Santa Cruz Hernan Arango Rutgers University

2. Outline • State estimation • Observation impact • Information content • Observation sensitivity • Forecast error and predictability • Examples from the California Current

3. may include ocean dynamics as in 4D-Var Ocean State Estimation and Data Assimilation Ocean state vector: From Bayes’ Theorem: Posterior Prior Gain Innovation Obs Obs operator Kalman gain: Obs error cov Prior error cov TL obs operator

4. identified iteratively using 4D-Var Practicalities of 4D-Var Typically done using conjugate gradients (CG) Practical Gain Matrix Alternatively, view CG and 4D-Var as a function: 4D-Var

5. Two Views of 4D-Var OR Posterior Prior Innovation

6. The Role of Observations Q: What is the influence of the observations on the analysis? Observation impact: Observation sensitivity: Predictability:

7. Observation Impact Q: How does each obs contribute to the analysis? Consider a function of the circulation:

8. Observation Impact

9. Observation Sensitivity Q: How does the analysis change if the observations change? Consider again the function Let

10. Observation Sensitivity

11. Observation Sensitivity

12. Observations and Predictability Q: How does each obs contribute to the forecast predictability? Consider now an ensemble of forecast function values for obtained by perturbing priors and obs. Expected forecast error variance: Forecast error covariance

13. Observations and Predictability Forecast error covariance Tangent linear model Control priors where: Posterior error covariance Tangent Linear 4D-Var Adjoint Linear 4D-Var

14. 37N 500m Mesoscale eddies The California Current

15. fb(t), Bf bb(t), Bb xb(0), Bx Previous assimilation cycle The California Current The Regional Ocean Modeling System (ROMS) COAMPS forcing ECCO open boundary conditions 30km, 10 km & 3 km grids, 30- 42 levels Veneziani et al (2009) Broquet et al (2009) Moore et al (2010)

16. Observations (y) CalCOFI & GLOBEC ~90% SST & SSH EN3 Ingleby and Huddleston (2007) TOPP Elephant Seals (APB) ~10% ARGO Data from Dan Costa

17. Sequential Data Assimilation: July 2002-Dec2004 Observations Observations Observations prior prior prior Data Assimilation Data Assimilation Data Assimilation Posterior Posterior Posterior 7 days Forecast Forecast Forecast

18. XBT CTD All in situ data: July 2002 – Dec 2004 ARGO TOPP

19. Observation Impact Q: How does each obs contribute to the analysis?

20. Observation Impacts on Transport 7day average transport 10km ROMS Transport increment = (Posterior-Prior)

21. Example: 37N Transport CUC CC No assim JAS time mean alongshore Flow (10km, 42 lev) CC = California Current CUC = California Under Current CC CUC With Data Assimilation

22. Poleward Equatorward Offshore Onshore Prior alongshore transport (CC+CUC+CJ) Prior cross-shore transport

23. rms Analysis Cycle – Observation Impacts 10km ROMS Poleward Alongshore transport Equatorward Cross-shore transport Offshore Onshore (Moore et al, 2011c)

24. IGW Adjoint CTW (GT) IGW CTW (G) IGW Gyre Circulation Alongshore Transport Impacts Sv (10-5) SSH

25. Degrees of Freedom (dof) y y Observation vector Observation vector x x “Perfect World” dof ~ Nobs Redundancy dof < Nobs

26. Information Content of Obs Degrees of freedom of obs (dof): Cardinali et al, 2004; Desroziers et al., 2009 Bennett & McIntosh, 1982 Tr{KH}/Nobs vs assimilation cycle upper & lower bounds 30km Only ~10% of obs contain independent info (Moore et al, 2011b)

27. Observation Sensitivity Q: How does the analysis change if the observations change? Q: How does the analysis change if the observation array changes?

28. Impact vs Sensitivity Single 4D-Var cycle obs Impact on 37N transport Sensitivity of 37N transport to removing observations

29. Observation Sensitivity: An OSSE 4D-Var change in 37N transport when all SSH removed Change in 37N transport predicted by obs sensitivity Change in 37N transport predicted by obs impact

30. Sequential Data Assimilation: July 2002-Dec2004 Observations Observations Observations prior prior prior Data Assimilation Data Assimilation Data Assimilation Posterior Posterior Posterior 7 days Forecast Forecast Forecast

31. Observations and Predictability Q: How does each obs contribute to the forecast predictability?

32. Forecast Ensembles Expected uncertainty of analysis Small spread Predictable Large spread Unpredictable

33. Predictability Forecast ensemble t0 t0-7d t0+14d t0+7d Analysis cycle ending t0 Forecast cycle ending t0+14 Analysis cycle ending t0+7d Forecast cycle ending t0+14

34. Predictability positive impact of obs on predictability Alongshore transport Cross-shore transport

35. Summary • In situ observations have a large impact on • circulation estimates, despite small number. • Adjoint operators provide considerable utility • for quantifying the impact and value of ocean • observations. • Routine monitoring of adjoint-based • diagnostics → real-time monitoring of • observing array. • Quantification of the true value of observations.