Analysis and Prediction of a Noisy Nonlinear Ocean

1. Analysis and Prediction of a Noisy Nonlinear Ocean With: L. Ehret, M. Maltrud, J. McClean, and G. Vernieres

2. Modeling and Analysis • Ocean models predict the evolution of the ocean from approximate initial conditions according to incompletely resolved dynamics forced by approximate inputs. • We treat noise according to the formalism of random processes. • Data assimilation is our best hope for resolving physical questions in terms of models and data • Most data assimilation schemes are based on linearized theory

3. TheDynamicalSystems Approach • Linear systems are characterized by their steady solutions and stability characteristics... • But the ocean is nonlinear, and nonlinear systems may have multiple stable solutions • Stable solutions may not be steady • Stability characteristics tell you about essential local behavior.

4. Example: The Kuroshio • The Kuroshio exhibits multiple states. Is it • A system with multiple equilibria? • A complex nonlinear oscillator? • Both? Neither? • Many plausible models give output that resembles the observations. • We show results from a QG model and a 1/10 degree PE model (J. McClean, M. Maltrud) • Use a variational method to assimilate satellite data (G. Vernieres) • Dynamical systems techniques and data assimilation will help us decide among models

5. Fine Resolution Model • 1/10o North Pacific model • Courtesy J. McClean & M. Maltrud

6. Model-Data Comparison

7. Model-Data Comparison

8. 2-Level QG Model • 2-layer QG model on curvilinear grid • Assimilate SSH data at one point at three times • Strong constraint: adjust initial condition only • First guess contains a transition • Use representer method

9. Typical steady states of the Kuroshio (adapted from Kawabe, 1995)

10. Typical steady states of the Kuroshio (adapted from Kawabe, 1995) nNLM: nearshore non large meander ssh [cm] and geostrophic velocities [m/s] (AVISO merged TOPEX/POSEIDON products)

11. Typical steady states of the Kuroshio (adapted from Kawabe, 1995) oNLM: offshore non large meander

12. Typical steady states of the Kuroshio (adapted from Kawabe, 1995) tLM: typical large meander ssh [cm] and geostrophic velocities [m/s] (AVISO merged TOPEX/POSEIDON products)

13. Contours of ssh nNLM LM nNLM tLM

14. Contours of ssh nNLM LM Unstable nNLM tLM

15. Contours of ssh nNLM LM Stable nNLM tLM

16. Qualitative comparison with satellite data

17. Qualitative comparison with satellite data ~4.0km/day

18. Qualitative comparison with satellite data ~4.0km/day ~4.0 km/day

19. Qualitative comparison with satellite data ~800km

20. Qualitative comparison with satellite data ~ 800km ~ 800 km

21. 3 data points for the assimilation!

22. Data / Forward model We want to assimilate ssh data that spans the last transition from the nNLM to the tLM state

23. Summary • Model nonlinear systems can behave as real world noisy nonlinear systems • Simplified systems share enough with detailed models, and both resemble observations sufficiently to make comparisons useful • Consequences of applying linearized techniques to intrinsically nonlinear systems are yet to be explored