Radar sensing of surface waves
Tyson Hilmer
Advisors:
Mark Merrifield, Pierre Flament,
Doug Luther
Kaena
Koko Head
Ko’olina
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 = 0.93
RMS error = 0.43 m
RSE 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.
2.
3.
4.
Motivation: explaining and correcting waveheight estimates
1.
Low-bias at large Hs
2.
Spatial variations
Theory
1.
First order measurement
2.
Second order measurement
3.
Energy bias
Noise characteristics and corrections
1.
Signal-to-Noise filtering
2.
Model-based approach
3.
Complex EOF filtering
Conclusions
17-Oct to 06-Nov 2002, 21 days
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
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.
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
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
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 doublescattering
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
The geometry for both
second order effects is
identical
The two physical interactions
are unique and independent
Hydrodynamic
Electromagnetic
Each radar frequency is
an integration over a
closed wavevector
contour.
The second order integral
relationship is a
convoluted mapping of the
ocean wave directional
spectrum to the radar
spectrum.
Waveheight bias
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.
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
Noise contamination
Range-independence is characteristic of external
interference, not systematic
Spectra from
the same time,
but steered:
Directly towards
noise
Directly away
from noise
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

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)
Signal-To-Noise
Ratio (SNR)
First
order
 Mean SNR of 50 dB to ~ 70
km
Second
order
 Second order energy mostly
degraded
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
RFI has linear phase
signature
Only effective when
phase and
amplitude are
accurately
estimated.
Ocean signal has
random phase
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.
All data
High-pass filtered, i.e. noise only
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.
To my classmates and
peers for their
enlightening discussions
and support.
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.
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.
60 degrees
0 degrees
45 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
Physical
Applications
Processes

Currents

Significant wave height
 Current measurements
cover broad band of
motions:

Wind direction

Wave direction
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





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