1. cBathy on Open Beaches Rob Holman SECNAV/CNO Chair in Oceanography Update since 2011 Shoreline problems Storm performance Camera seam problem Phase-locked harmonics Outliers Doppler Process error?

2. Updates Since 2011 Has been a game changer for nearshore remote sensing Published in JGR, 2013 Toolbox implemented with docs and debug tools Disseminated to Netherlands, England, Australia Applied to radar by Honegger and Haller at OSU Being exercised in wide range of locations and conditions

3. Oregon State University Phase 1 - Wavenumber Analysis Steps 1.Compute normalized Fourier Transform, G = FT(I)/|FT(I)| 2.Compute the cross-spectral matrix, for a number of f-bands 3. Compute the first complex EOF, expressed as phase and amplitude maps 4.Model the EOF phase of C as 4.Compute weighted cost function, where weighting w ij is product of EOF magnitude and spatial Hanning filter 5.Use nonlinear least-squares to find k x, k y (or k-alpha) that minimize J.

4. Oregon State University Phase I - Wavenumber Analysis Steps : (Tile-based phase and magnitude example)

5. Oregon State University Analysis Steps – Add Phase 2 1.Compute normalized Fourier Transform, G = FT(I)/|FT(I)| 2.Compute the cross-spectral matrix, for a number of f-bands 3.Model the phase of C as 4.Compute weighted cost function, where w ij is the coherence 5.Use nonlinear least-squares to find k x, k y that minimize J. 6.From resulting [f, k x, k y ], estimate depth using linear dispersion (or better alternate) using N most coherent f-bands wavenumber bathymetry

6. Oregon State University Bad Example Raw Bathy Estimate Estimated depth Estimated error January 13, 2010, early morning with sun glare

7. Oregon State University Kalman Filtering P- estimate error Q- process error R- measurement error K- time step ĥ- estimated depth - - prior value h, cBathy est., filtered

8. Oregon State University Process Error, Q Variance of prior estimates degrades with time and wave energy. Based Q on SandyDuck daily survey variance (mean square abs dev.) Dependent on H and cross-shore location

9. Oregon State University cBathy - Comparison With Ground Truth 2-year test 16 surveys 1000 x 500 m Turn-key (no tuning)

10. Oregon State University

23. Global bias 0.19 m Global rmse 0.51 m

24. Oregon State University Ground Truth Tests, Egmond, The Netherlands Leo SembiringTU Delft - Shore

25. Oregon State University Ground Truth Tests, RIVET

26. Oregon State University Shoreline Issues! Large errors common at shoreline Thought it was issue of merging phase content from waves and sand in single tile Appears to be more problem of runup appearing progressive Unclear fix

27. cBathy Performance During High Wave Conditions (10/17/11 – 11/08/11; Becca Aiken, CIL) ~ y=925 transect Survey 1 10/17/11 Survey 2 11/16/11 Mini-survey 11/07/11

28. cBathy Performance During High Wave Conditions

29. Oregon State University Time Variations of Hourly Returns Hs = 1.4 m

30. Oregon State University Wave Height Dependency

31. Oregon State University Wave Height Dependency Good performance limited to low wave conditions. Scientific interest focused on storms Fix unclear (to me).

32. Oregon State University Camera Seam Problems! Depth anomalies along camera seams (at times) Originally assumed geometry problem Recently discovered camera timing problems (one cam off by ½ s, etc) Requires cam timing pre- processing (easy!)

33. Oregon State University Phase-locked Harmonics Narrow-banded nonlinear swell (like cnoidal waves) have fundamental and phase-locked harmonics Harmonics travel as same speed as fundamental, NOT like independent linear components Best estimate depth pulled too deep by these fast harmonics Issue with radar (nonlinear imaging physics) Unclear fix. Massaguacu, Brazil

34. Oregon State University Shallow Anomalies Occasion estimates that are clearly wrong but appear good (Max examples) Usually low signal areas, can be boat passage Dominate Kalman result until next good signal Unclear fix (Max?)

35. cBathy At Tidal Inlet Environments – Doppler!!! RIVET 2013 – Columbia River, OR SELFE Model, Baptista

36. cBathy Variations With Tidal Currents Tide-level corrected flood ebb

37. Histogram of Non-Doppler cBathy Depths, MCR survey cBathy mean

38. Ground Truth Tests, RIVET flood ebb

39. RMSE: 56 cm Bias: 14 cm G.V. ESTIMATES: Depth Channel structure recovered Estimate accuracy & precision deteriorates to the south Honegger and Haller, X-band radar.

40. Oregon State University Process Error, Q Process error represents expected decay of faith in estimate with time Standard cBathy formulation based on one set of daily CRAB surveys at Duck. Should vary with location, wave regime, bar configuration, etc. May have to bootstrap better estimates (assume form, do cBathy, use estimates to constrain bathy change, repeat until converged).

41. Oregon State University Summary cBathy seems to be a game-changer Fabulous under small waves, unusable for storms. For VERY small signals sensitive to non-waves (boats??) Some technical issues with seams and shorelines More to be done on nonlinear waves (esp harmonics) and process error.

42. Oregon State University Questions?