Tyson Hilmer

Advisors:Mark Merrifield, Pierre Flament,

Doug Luther

Radar sensing of surface waves

Kaena

Ko’olina

Koko Head

Outline

Motivation: explaining and correcting waveheight estimates

1. Low-bias at large Hs

2. Spatial variations

Significant waveheight (Hs):Waimea Buoy & WERA radar

Correlation r = 0.93RMS error = 0.43 mRSE error = 16 %

Comparison studies of radars to buoys

WERA 9.4 1- 4 0.93 16 %

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

Outline

1. Motivation: explaining and correcting waveheight estimates

1. Low-bias at large Hs

2. Spatial variations

2. Theory

1. First order measurement

2. Second order measurement

3. Energy bias

3. Noise characteristics and corrections

1. Signal-to-Noise filtering

2. Model-based approach

3. Complex EOF filtering

4. Conclusions

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

Land ShadowingBlocking 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.

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

First Order Bragg Scattering

To any order, coherent signal will only occur from surface features with the Bragg wavelength

First order scattering is a simple proportional relationship between the EM and ocean waves.

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.

Coupling Coefficient, i.e. Second-Order Weighting

Function

Hydrodynamic Electromagnetic

The geometry for both second order effects is identical

The two physical interactions are unique and independent

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.

Waveheight bias

Waveheight biasScattering 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.

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

Range-independence is characteristic of external interference, not systematic

Spectra from the same time, but steered:

Directly towards noise

Directly away from noise

Noise contamination

Noise is sufficiently large to modify second order energy

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

•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)

Radio Frequency Interference (RFI)

Signal-To-Noise Ratio (SNR)

Mean SNR of 50 dB to ~ 70 km

Second order energy mostly degraded

First order

Second order

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

0 degrees 60 degrees

Model-based noise reduction

Only effective when phase and amplitude are accurately estimated.

RFI has linear phase signature

Ocean signal has random phase

Complex Eigenfunction Filtering

All data High-pass filtered, i.e. noise only

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.

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

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.

Acknowledgments

I would like to thank my advisors for their generous support, guidance, and patience;Mark Merrifield, Pierre Flament, and Doug Luther.

A big mahalo to Derek Young for his help and teachings.

I would like to thank Cedric Chavanne and Jerome Aucan for assisting me with the radar and buoy data.

To my classmates and peers for their enlightening discussions and support.

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)

SNR Filtering: before and after

• Spatial accuracy is not significantly improved

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

0 degrees

45 degrees

60 degrees

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.

The coupling coefficient, and consequently Hs, varies with “look” direction.

Assumption of a mean coefficient allows for calculation of Hs

Data Products

Currents

Significant wave height

Wind direction

Wave direction

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

Current measurements cover broad band of motions:

subinertial (<48 h), tidal, inertial (29 h), high frequency (5 h) and residual currents

Tides, eddies, internal wave surface expression

Current-Wave interactions:

current-induced shoaling, refraction

Wind-Wave energy exchange

ApplicationsPhysical

Processes