Tyson Hilmer Advisors: Mark Merrifield, Pierre Flament, Doug Luther

1. Radar sensing of surface waves Tyson Hilmer Advisors:Mark Merrifield, Pierre Flament, Doug Luther

2. Kaena Koko Head Ko’olina

3. Outline • Motivation: explaining and correcting waveheight estimates • Low-bias at large Hs • Spatial variations

4. Significant waveheight (Hs):Waimea Buoy & WERA radar Correlation r = 0.93RMS error = 0.43 mRSE error = 16 %

5. Comparison studies of radars to buoys WERA 9.4 1- 4 0.93 16 %

6. Hs spatial variation • Spatial field of Hs estimates showed large variations in space and time. • O(5) m differences within 25 km and 1 hour • Variations are non-physical; and their magnitude precludes further physical analysis

7. Outline • Motivation: explaining and correcting waveheight estimates • Low-bias at large Hs • Spatial variations • Theory • First order measurement • Second order measurement • Energy bias • Noise characteristics and corrections • Signal-to-Noise filtering • Model-based approach • Complex EOF filtering • Conclusions

8. Wellen Radar (WERA): • 16 MHz transmit frequency • 100 km nominal range • 7.2 deg angular resolution • 1.5 km range resolution Bragg scattering ocean waves: • 9.38 m wavelength • 2.45 s period • 0.41 Hz frequency 17-Oct to 06-Nov 2002, 21 days

9. Land Shadowing Blocking land-shadowed angles from the directional spectrum increases Hs error, primarily at lower waveheights. This is because short wavelength, wind seas should not be negated. The energetic long wavelengths (swell) are not shadowed.

10. Significant waveheight (Hs) equation Using theory derived from electromagnetic and hydrodynamic first principles,the radar is capable of measuring Hs as a ratio of integrated first order (linear) to second order (non-linear) energies. Information encoded primarily in amplitude

11. First Order Bragg Scattering First order scattering is a simple proportional relationship between the EM and ocean waves. To any order, coherent signal will only occur from surface features with the Bragg wavelength

12. Second Order Scattering Again, second order signal can only occur for coherent scattering off features with the Bragg wavelength. These are nonlinear ocean waves, and EM double-scattering Perturbation expansion of nonlinear equations for free water surface and the EM fields yields second-order terms.Represented as coupling coefficient Gamma.

13. Coupling Coefficient, i.e. Second-Order Weighting Function The geometry for both second order effects is identical The two physical interactions are unique and independent Electromagnetic Hydrodynamic

14. The second order integral relationship is a convoluted mapping of the ocean wave directional spectrum to the radar spectrum. Each radar frequency is an integration over a closed wavevector contour.

15. Waveheight bias

16. Waveheight bias Scattering theory predicts the frequency separation between first and second order peaks will decrease as the ocean swell moves to lower frequencies.As the energy of the peaks is convolved, the first order energy is overestimated, i.e. the Hs is biased low.

17. Hs spatial variation • Spatial field of Hs estimates showed large variations in space and time. • O(5) m differences within 25 km and 1 hour • Variations are non-physical; and their magnitude precludes further physical analysis

18. Noise contamination • Range-independence is characteristic of external interference, not systematic Spectra from the same time, but steered: Directly towards noiseDirectly away from noise Noise is sufficiently large to modify second order energy

19. Noise level: fcn(time,angle) • Both sites have strong interference at 200 deg incident • Headings agree to within 1 degree. • Strong diurnal cycling -> solar / anthropogenic

20. Radio Frequency Interference (RFI) • Coincidentally,the Jindalee Operational Radar Network (JORN) coincides with the heading of the primary noise source. • Australian Department of Defence, 5-30 MHz at 560 kW (WERA = 30 W) • Philippines and Russia are secondary sources • Ionospheric propagation ( > 6,000 km)

21. Signal-To-Noise Ratio (SNR) • Mean SNR of 50 dB to ~ 70 km • Second order energy mostly degraded First order Second order

22. SNR Filtering • Small improvement to accuracy: • + 0.05 r, - 3% normalized error • Maximum accuracy occurred at intersection of center-beams; attributed to optimal beamforming • 80% reduction is usable data • Spatial accuracy is not significantly improved 60 degrees 0 degrees

23. Model-based noise reduction RFI has linear phase signature Only effective when phase and amplitude are accurately estimated. Ocean signal has random phase

24. Complex Eigenfunction Filtering Eigen-decomposition methods are often based on the assumption that signal (or noise) can be represented by only a few independent modes Energetic noise and signal modes are not independent. High-pass filtered, i.e. noise only All data

25. Eigenfunction filtering is only accurate when the signal and noise modes are independent

26. Conclusions • Spatial averaging yields good Hs timeseries estimates from the radar • Hs bias at large waveheights is due to merging of first and second order energies. The effect is due to spectral width; i.e. statistical properties of the measurement and/or sampling resolution, not a theoretical limitation. • Hs accuracy of ~20% normalized standard deviation is possible; cannot "guarantee" the spatial field unless noise sources are removed • Stricter SNR requirements do not significantly improve the estimate, and greatly decrease available data (~80%) • Thus, the primary goal for improving Hs accuracy is the removal of external interference. Model and eigen-based methods show promise providing the noise can be accurately estimated.

27. Acknowledgments I would like to thank my advisors for their generous support, guidance, and patience;Mark Merrifield, Pierre Flament, and Doug Luther. I would like to thank Cedric Chavanne and Jerome Aucan for assisting me with the radar and buoy data. A big mahalo to Derek Young for his help and teachings. To my classmates and peers for their enlightening discussions and support.

30. Surface currents derived from First Order scatter Chavanne, 2007 Current information is carried in the frequency content of the signal, not amplitude Difference from known frequency is due to surface currents (and Stokes Drift)

31. SNR Filtering: before and after • Spatial accuracy is not significantly improved

32. Beamforming = spectral filtering, except in spatial (antenna) domain instead of temporal.Shape depends on chosen filter, and becomes progressively worse with increasing angle. 60 degrees 0 degrees 45 degrees

33. The second order integral relationship is a convoluted mapping of the ocean wave directional spectrum to the radar spectrum. Each radar frequency is an integration over a closed wavevector contour.

34. The coupling coefficient, and consequently Hs, varies with “look” direction. • Assumption of a mean coefficient allows for calculation of Hs

35. Nearshore modeling Engineering projects, ship navigation, vessel traffic control Mitigation of oil spills, ocean pollutants Shoreline protection, beach erosion Real-time sea state conditions for the tourism industry Physical Processes Applications Data Products • Current measurements cover broad band of motions:subinertial (<48 h), tidal, inertial (29 h), high frequency (5 h) and residual currentsTides, eddies, internal wave surface expression • Current-Waveinteractions:current-induced shoaling, refraction • Wind-Wave energy exchange • Currents • Significant wave height • Wind direction • Wave direction