RADAR SENSING OF OCEAN WAVE HEIGHTS A THESIS SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HAWAI‘I IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN OCEANOGRAPHY DECEMBER 2010 By Tyson Hilmer Thesis Committee: Mark Merrifield, Chairperson Pierre Flament Douglas Luther This work is dedicated to my beautiful wife Susanne for her unequivocal patience ii Figure 0.1 iii Acknowledgements I would like to thank my advisor, Pierre Flament, and the other members of my M.S. committee, Mark Merrifield, and Doug Luther for all their feedback. I am thankful to Jerome Aucan for his assistance with the CDIP buoy data, and to Jim Potemra for assistance with archived IPRC data. Special thanks to my friends and family for encouragement and support throughout this project. Radar data were furnished by the Radio Oceanography Laboratory, Department of Oceanog- raphy, University of Hawaii at Manoa. Buoy data were furnished by the Coastal Data Informa- tion Program (CDIP), Integrative Oceanography Division, operated by the Scripps Institution of Oceanography, under the sponsorship of the U.S. Army Corps of Engineers and the California Department of Boating and Waterways. Multi-Spectral Model (MSM) wind model output were furnished by Yi-Leng Chen, Department of Meteorology, University of Hawaii. iv ABSTRACT This thesis focuses on explaining and improving the estimation of ocean wave heights from high-frequency oceanographic radar. Three months of data from a WERA HF radar is com- pared to a Datawell MarkIII directional waverider buoy, under a wide range of sea states. Large spatial and temporal variation in the radar-derived waveheight, significantly greater than previously reported, are explained in terms of various error sources. Averaging and filtering methods for im- proving the significant waveheight are evaluated, and the dominant error source is shown to be external radio frequency interference. Eigen-analysis and model-based methods are evaluated for the removal of interference. A comprehensive summary of the second order radar-ocean scattering equations is given, with evaluation of its terms. v Contents Acknowledgements iv Abstract v List of Tables viii List of Figures ix 1 Introduction1 1.1 Applications......................................2 1.2 Operational Description of Oceanographic Radars..................2 1.3 Development History.................................7 1.4 Electromagnetic Scattering Theory..........................7 1.5 Previous Research................................... 19 1.5.1 Currents.................................... 19 1.5.2 Winds..................................... 20 1.5.3 Waves..................................... 25 2 Methods 32 2.1 WERA radar and directional wave buoy....................... 32 2.2 Processing....................................... 37 3 Results 43 3.1 Winds......................................... 43 3.2 Significant Waveheight................................ 47 3.3 Noise Error...................................... 56 3.3.1 Introduction.................................. 56 3.3.2 Observations................................. 57 3.3.3 Noise Estimation............................... 64 3.3.4 Noise Removal................................ 73 3.4 Significant Waveheight Regression Analysis..................... 80 3.5 Electromagnetic Scattering: Second Order Integral................. 83 3.6 Spectral Averaging.................................. 88 vi 4 Discussion 93 4.1 Wind Estimates.................................... 93 4.2 Significant Waveheight Estimates........................... 94 5 Conclusion 99 Appendices 100 A Electromagnetic Scattering Derivations 101 A.1 Ground Wave Propagation.............................. 101 A.2 Ground Wave Scatter................................. 103 A.3 Far Field Scatter.................................... 106 A.4 Average Scattered Signal Spectrum.......................... 107 A.5 First Order Spectrum................................. 109 A.6 Second Order Spectrum................................ 110 B WERA Significant Waveheight Algorithm 114 C Beamforming 117 D Vector Correlation 120 vii List of Tables 1.1 Comparison studies of radar to buoys......................... 31 3.1 Hs error analysis................................... 52 viii List of Figures 1.1 Radar Doppler Spectrum...............................3 1.2 Vector current estimate from two radial components.................4 1.3 Geographic Dilution of Precision...........................5 1.4 Bragg scattering diagram...............................8 1.5 Electromagnetic scattering diagram......................... 10 1.6 Hydrodynamic scattering diagram.......................... 11 1.7 Hydrodynamic scattering diagram: closeup..................... 12 1.8 EM scattering geometry................................ 13 1.9 Bistatic radar geometry................................ 15 1.10 Bragg ratio diagram.................................. 22 1.11 Bragg ratio vs Angle for a variety of different spreading models.......... 23 1.12 Bragg ratio vs. in-situ wind directions........................ 25 1.13 Radar to Buoy wind estimate comparison...................... 26 1.14 Linearized form of Hs ................................. 28 2.1 Example CDIP buoy energy spectrum........................ 33 2.2 Example CDIP buoy directional spectrum...................... 34 2.3 Radar sampling geometry............................... 35 2.4 Temporal coverage and study period......................... 36 2.5 Buoy significant wave height Hm0 timeseries..................... 36 2.6 Example Doppler spectra............................... 38 2.7 Hs errors due to difference search algorithm..................... 39 2.8 Bragg centroid frequency............................... 40 2.9 Bragg frequency; comparison of centroid vs. peak method............. 41 2.10 Distribution of difference in Bragg frequency methods............... 42 3.1 Multi-Spectral Model grid.............................. 44 3.2 QuickSCAT winds for the Hawaiian Islands..................... 44 3.3 Example radar-derived wind field........................... 45 3.4 Radar wind field compared to MSM output..................... 45 3.5 Radar wind field compared to QuickSCAT...................... 46 3.6 Hs timeseries for CDIP buoy and radar........................ 47 3.7 Spatial and temporal variation in radar Hs field................... 48 3.8 Hs linear regression between CDIP buoy and radar................. 48 3.9 Hs linear regression between CDIP buoy and radar timeseries............ 49 ix 3.10 Hs power law regression............................... 50 3.11 Hs power law regression; spatial average....................... 51 3.12 Radar and buoy Hs distributions........................... 52 3.13 Hsdirectional dependence algorithm comparison................... 53 3.14 Theoretical and observed Hs spatial correlation................... 54 3.15 Hs mean; 1 day.................................... 55 3.16 Hs 21 day median................................... 55 3.17 Example low and high noise antenna spectra..................... 58 3.18 Radio interference in second order region...................... 59 3.19 A well-resolved Doppler spectrum.......................... 60 3.20 A poorly-resolved Doppler spectrum......................... 61 3.21 Example low and high noise fields.......................... 62 3.22 Noise CDF estimates................................. 65 3.23 Spectral histogram of noise levels.......................... 66 3.24 Noise distribution for Kaena and Koolina...................... 67 3.25 Cumulative Signal-to-Noise Ratio.......................... 68 3.26 201◦ noise source, world map............................. 69 3.27 Sampling field of the JORN radar.......................... 69 3.28 Noise level as a function of angle and time...................... 70 3.29 Noise level as a function of range and time...................... 70 3.30 Functional noise model................................ 71 3.31 Noise model: NI (θ; t) term.............................. 72 3.32 MUSIC algorithm results............................... 75 3.33 Noise as a function of beam-steered direction.................... 76 3.34 Range eigenfunctions................................. 76 3.35 Range eigenfunctions; noise only........................... 77 3.36 RFI phase difference................................. 78 3.37 RFI removal results.................................. 78 3.38 RFI removal; effect of incorrect phase........................ 79 3.39 Hs linear regression coefficients........................... 81 3.40 Hs linear regression; coefficient of determination.................. 82 3.41 Hs linear regression; RMS error........................... 82 3.42 Second order Doppler-Wavevector relation...................... 84 3.43 Hydrodynamic and Electromagnetic Coupling Coefficients............. 85 3.44 S2 integral product.................................. 86 3.45 Doppler frequency-averaged Coupling Coefficient.................. 87 3.46 Example of spectral averaging............................ 88 3.47 Spectrogram normalized by S1............................ 89 3.48 Close-up of normalized spectrogram......................... 90 3.49 Mean spectrum with outliers removed........................ 91 3.50 Comparison of Hs timeseries from spectral averaging................ 91 3.51 Spectral time-evolution................................ 92 4.1 Merging of first and second order peaks....................... 95 x A.1 Effect of surface roughness on impedance...................... 102 A.2 EM transmission loss over the ocean........................