Measuring the Properties of Rossby Waves from Space

2. Measuring the Properties of Rossby Waves from Space Peter Challenor, Paolo Cipollini & the Laboratory for Satellite Oceanography Southampton Oceanography Centre, U.K.

3. Outline • Observations of planetary waves with satellite altimetry • Speed estimation techniques • Observed propagation speed vs theoretical speed • Observations of planetary waves in other datasets • SST • Ocean Colour • Possible mechanisms • Looking for the single wave events

4. Some relevant properties of Planetary waves • Amplitude of surface manifestation: 1-20cm • Propagation speeds: a few cm s-1 • They take months or years to cross the oceans • Speeds depends on latitude: faster for waves closer to the equator • Speed is an important issue as it sets the ‘response time’ of the oceans to perturbations and climatic anomalies

5. Sea surface height anomaly from Topex/Poseidon altimeter; 10 day cycles

7. North Atlantic, 34°N

9. “Classic” techniques to study RWs • Fourier Transform of longitude/time plots (Tokmakian and Challenor, 1993) • Peaks correspond to single sinusoidal components of the propagating signal • Radon Transform (2D-RT): projected sum of the diagram at an angle theta (Chelton and Schlax, 1996) • Then we look for the value of thetawhich maximises the energy of the RT - good objective estimate of propagation speed.

10. Schematic of the 2-D Radon Transform

12. Global speed results by Fu and Chelton (2001) after Chelton & Schlax (1996) Ratio to standard theory Ratio to extended theory

14. Going 3-D….. • We want to detect and study the possible deviations of RW propagation from pure Westward • Need to add a N-S dimension (latitude) • The dataset is then a full 3-D cuboid (long x lat x time) • We have developed a 3-D extension of the Radon Transform (3D-RT) and implemented it with MATLAB and FORTRAN

15. The 3-D cuboid of data

16. The 3-D Radon Transform Challenor et al., JAOT, 2001

17. Example of 3D-RT analysis

19. Rossby waves in other datasets • SST (both IR and microwave) • A signature could be expected as SST and SSH have some degree of correlation • Ocean colour ??

20. Rossby waves detected in the SST anomaly field Ref: Hill et al, JGR, 2000

21. Speeds from T/P SSH Speeds from ATSR SST Ref: Hill et al, JGR, 2000

24. Ratio to standard theory Ratio to extended theory

25. Why do we see Rossby waves in Ocean colour? Two main hypotheses: • Horizontal displacement • Vertical processes

26. Note: phase difference between SSH and OC will depend on the time the tracer (chl) anomaly takes to go back to equilibrium (relaxation time) This can be modelled (Killworth & Blundell)….

28. MODEL Pure H advection Chl v SSH phase  = 60 d DATA Observed Chl v SSH phase

29. 1st conclusion: horizontal advection is important • But does it explain all the signal we see in the colour field? • Need to focus on those regions where observations and predictions do not match well.. • …and on those regions where the meridional gradient of chl is weak

30. Possible vertical mechanisms • Real pumping effect (vertical advection of nutrients into the euphotic zone! ) - ‘rototiller effect’ • This can be modelled and computed but it is currently a puzzle - modelled signal is small but at the equator and phase does not seem to match the observations • However modelling of this effect suffers from very poor nutrients climatology! • Vertical advection of phytoplankton • Shoaling of DCM and its ‘erosion’ into the mixed layer (suggested by Kawamiya and Oschlies, 2001)

31. Need further investigations….. • … vertical mechanisms could still be playing a significant role in some places - and they would phase-shift the SSH/SST/OC relationship • They would also be very important for the biology • Let’s see an example in the Indian Ocean…

33. A different methodological approach….. • Techniques like FFTs, RTs and Crosscorrelations on satellite data have yielded ‘mean’ properties. • We want to look at the single wave events. Identify them and study how their characteristics change as they propagate across the ocean basins • This can be done with a model-fitting approach - Gaussian ‘crests’ and ‘troughs’

34. Four parameters each: • Amplitude • horizontal scale • Slope of track • intercept of track

36. Gaussian model fitting • First of all, we split the longitude/time plots into ‘narrow’ partially overlapping sub-windows

38. Results: a table of wave parameters for each sub-window Gaussian model fitting • First of all, we split the longitude/time plots into ‘narrow’ partially overlapping sub-windows • In any sub-window, we fit and remove the strongest Gaussian, then we fit and remove the next strongest, etc. • Finally, we “compact” the results, reconstructing the trajectories of the single events.

40. Some pre-processing • filter out annual cycle and any non-Westward signals • taper both the longitude/time plot and the fitting function with a Hanning window in longitude • increases ‘localization’ of information • improves amplitude retrieval

41. Original sub-window Fitted elementary waves Residuals + 0.2 m 0 - 0.2m

42. 34N Original data (filtered + tapered) Fitted elementary waves

43. Move 1 subw to the W  couple (wave, wave to the E) compute COSTFUNCTION (fc) (it’s a matrix whose elements depend on squared errors on amp., slope, intercept, width) min(fc)< ? label all remaining waves as ‘new’ no yes Move 1 subw to the W etc… - Join the two waves - write off row and column in fc Joining waves label all waves in Emost sub-window as ‘new’

44. 34N wave NA34_0097

45. The story of a single wave… MAR

48. Planetary wave forecast strategy • Find ‘most similar wave’ (to the one to be propagated) in parameter space • Propagate wave in accordance to behaviour of ‘most similar wave’

49. Example of hindcast

50. Std deviation of reference data RMS error with simple ‘persistence’ of wave properties RMSE - hindcast 1 RMSE - hindcast 2