Eddy-Mean Flow and Eddy-Eddy Interaction: Insights from Satellite Altimetry Measurements

1. Eddy-Mean Flow and Eddy-Eddy Interaction: Insights from Satellite Altimetry Measurements Bo Qiu Dept of Oceanography University of Hawaii Contributors: D. Chelton, S. Chen, R. Scott “A Workshop on Mesoscale and Submesoscale Oceanic Processes: Explorations with Wide-Swath Interferometry Radar Altimetry” 28-30 April 2008 Scripps Institution of Oceanography

2. Charges • What have we learned from existing altimetry data and what are the limitations and challenges? • What new dynamics can we study with an O(10) km resolution SSH dataset?

3. Trajectories of cyclonic vs anticyclonic eddies with lifetimes > 4weeks nonlinearity = u/c Kuroshio Extension South Pacific Subtropical Countercurrent Chelton et al. (2007, GRL)

4. Schematic of NW Pacific Ocean Circulation Chelton et al. (2007, GRL)

5. Semi-monthly Kuroshio Extension paths (1.7m SSH contours) Stable yrs: 1993-94, 2002-04 Unstable yrs: 1996-2001, 2006-07

6. (a) Upstream KE path length (141-153°E) (b) Eddy kinetic energy (141-153°E, 32-38°N) Stable yrs: 1993-94, 2002-04 Unstable yrs: 1996-2001, 2006-07

7. PDO index EKE level Mesoscale EKE level in the KE region lags the PDO index by ~ 4 yrs

8. Pacific Decadal Oscillations(Mantua et al. 1997) • Center of action of wind forcing is in the eastern half of the N Pacific basin • Positive (negative) phase of PDO generates – (+) local SSH through Ekman divergence (convergence)

9. Yearly SSH anomaly field in the North Pacific Ocean + + -

10. EKE level SSH field SSHA along 34°N PDO index L H L center of PDO forcing 135E 145E 155E 165E

11. SSHA along 34°N from wind-driven Rossby wave model SSHA along 34°N PDO index L H L center of PDO forcing

12. EKE modulations on interannual and longer timescales atmosphere wind stresses WBC mean flow mesoscale eddies stability properties feedback ?

13. Feedback of eddies to the modulating time-mean flow: • Surface ocean vorticity equation: eddy-driven mean flow modulation • Evaluate: mechanical feedback of eddies onto the time-varying SSH field (e.g. Hoskins et al. 1983, JAS) • Introduce the Kuroshio Extension index = loading of the 1st EOF mode of the zonally-averaged SSHA field: low eddy variability high eddy variability

14. Eddy-forced S(x,y,T) field regressed to the – KE index • +: anticyclonic forcing vs . –: cyclonic forcing • In the upstream KE region, enhanced eddy variability (when KE index <0) works to increase the intensity of the northern/southern recirculating sub-gyres.

15. Are the eddy vorticity fluxes properly resolved? SSH snapshot from the NLOM model for 04/10/2006 Right: from the original 1/32°-resolution output Left: reduced to 1/3°-resolution (observable by current nadir-looking satellite altimeters) (NLOM data provided by IPRC-APDRC)

16. SSH vs vorticity snapshot from the NLOM model for 04/10/2006 reduced 1/3°-resolution original 1/32°-resolution

17. PDF of modeled vorticity as a function of intensity anti-cyclonic cyclonic Ratio = anticyclonic/cyclonic anticyclone-dominant cyclone-dominant original 1/32°-res. reduced 1/3°-res.

18. PDF of modeled and observed vorticity as a function of intensity anti-cyclonic cyclonic original 1/32°-res. reduced 1/3°-res. AVISO SSHA-derived

19. Chelton et al. (2007, GRL)

20. Statistics of eddy tracking in the South Pacific STCC band • maximum # of eddies in October • maximum average eddy amplitude in January • maximum eddy diameters in March (courtesy of D. Chelton)

21. Chelton et al. (2007, GRL)

22. Statistics of eddy tracking in the North Pacific STCC band • maximum # of eddies in April • maximum average eddy amplitude in August • maximum eddy diameters in September (courtesy of D. Chelton)

23. Chelton et al. (2007, GRL) STCC band September T(y,z) along 170°E Eastward-flowing STCC overlying westward-flowing SEC

24. STCC-SEC shear ΔU vs regional EKE annual cycle September T(y,z) along 170°E Eastward-flowing STCC overlying westward-flowing SEC

25. Instability analysis for the 21/2-layer S Pacific STCC/SEC system • Stability condition depends on seasonally-varying STCC/SEC shear and upper ocean N2. • Maximum Aug/Sept growth rate: ~50 days • Unstable wavelengths: 200~370 km; most unstable: 250 km (scaled well by f2|dU/dz|/βN2).

26. Quantifying eddy-eddy interaction • Consider 2-d momentum eqs: • Take discrete Fourier transform and form kinetic energy PSD eq: where spectral energy transfer term PE to KE conversion term dissipation term • In a slowing-evolving eddy field: Qiu, Scott and Chen (2008, JPO)

27. Spectral energy transfer T(kx, ky) in the S Pacific STCC region +: energy sink _ : energy source • In a slowing-evolving eddy field:

28. Spectral energy transfer T(kx, ky) in the S Pacific STCC region • Baroclinic instability provides the energy source for the eddy-eddy interaction. • At wavelengths > 370km, nonlinear triad interactions serve as an EKE sink.

29. Bimonthly spectral energy transfers in the S Pacific STCC region

30. In the quasi-equilibrium state, the spectral energy transfer is related to the convergence of spectral energy fluxes: where signifies spectral energy flux from k<K to k>K through eddy-eddy interactions k K Scott and Wang (2005, JPO)

31. Spectral energy flux ΠK in the S Pacific STCC region +: forward cascade _ : inverse cascade • Inverse energy cascade is seen in signals with wavelengths > 230km • There exists little preference in the x-y direction of the inverse energy cascade

32. Explaining Chelton’s eddy statistics in the S Pacific STCC band • maximum baroclinic shear of STCC-SEC in August; baroclinic instability occurs, but with a weak growth rate: O(months) • maximum # of eddies in October resulting from baroclinic instability • maximum average eddy amplitude in January; slow growth to reach full amplitude • maximum eddy diameters in March; due to inverse energy cascade from eddy-eddy interaction

33. Is that all there is? NLOM original 1/32°-res. vorticity NLOM reduced 1/3°-res. vorticity

34. Spectral energy transfer T(kx, ky) in the S Pacific STCC region: NLOM result +: energy sink _ : energy source

35. Spectral energy transfer T(kx, ky) in the S Pacific STCC region: NLOM result primary baroclinic instability of STCC-SEC shear secondary frontal instability of STCC (?) (what determines its growth and scales?) +: energy sink _ : energy source

36. Spectral energy transfer T(kx, ky) in the S Pacific STCC region: NLOM result +: forward cascade Spectral energy flux ΠK _ : inverse cascade

37. In addition to being a better tool for monitoring the global SSH signals, wide-swath satellite altimetry will help us discover new features of the turbulent ocean operating on different space/time scales. With enhanced coverage and accuracy, wide-swath altimeter data can be used to test dynamic hypotheses, leading to improved understanding of the ocean and climate system. Comments

38. Longitude-time plot of EKE along 21-29°S OFES 1/10°-res. climatological run result

39. Longitude-time plot of EKE along 21-29°S

41. High-quality SSH data of the past 15 yrs allows us to quantify changes in the mean circulation brought about by the basin-wide wind forcing. It further helps us explore the extent to which the mean circulation changes leads to the modulation in the mesoscale EKE field. Although there is evidence that time-modulating mesoscale eddies modify the mean circulation field, the presently available SSH data is insufficient to accurately evaluate the feedback processes (e.g., eddy vorticity flux divergence). Comments

42. Energy flow in a 2-layer baroclinic turbulent ocean Rhines (1977) Vallis (2006)

43. NLOM field: original 1/32°-res. reduced 1/3°-res. (note the different color scale)

44. NLOM field of S original 1/32°-res. reduced 1/3°-res. +: anticyclonic forcing –: cyclonic forcing

45. Yearly-mean sea surface height field

46. Baroclinic instability growth ratebased on upper ocean f/Ri1/2 Figure courtesy of D. Chelton