A study of sea surface height retrieval using
Doppler measurements from numerically
simulated low grazing angle backscatter data
IGARSS 2011 Vancouver
Jul 26th, 2011
Chun-Sik Chae and Joel T. Johnson
ElectroScience Laboratory
Department of Electrical and Computer Engineering
The Ohio State University
ElectroScience Lab
Motivation
•
Recent interest in attempting to retrieve the deterministic sea surface profile
from low grazing angle, range-resolved radar measurements
•
Demonstrations to date have used measured datasets, error assessment is
difficult due to problems in measuring the true sea surface.
•
Simulations are of interest in order to compare true and retrieved profiles and
study errors and signals
•
A numerical study using the MOM (Johnson et al, TGRS 2009) and Doppler
retrievals shows good correlation between real and retrieved heights in both
visible and shadowed regions
•
Having seen the feasibility, detailed information of Doppler vs. range and the
degree of influence of multi-path and shadowing to the retrieval performance
are of interest
•
It is desirable to compare observed performance to that expected from standard
signal model
ElectroScience Lab
Outline
•
Review :
- Doppler radar
- Numerical simulation
- Retrieval procedure
•
Doppler spectra vs. horizontal distance from numerical simulation (MOM)
•
Physical Optics approach for the retrieval (no multi-path, shadowed regions)
•
Comparison of retrievals bet. MOM and PO
•
Monte Carlo simulation result using a simple signal model
•
Retrieval error study of the use of the model
ElectroScience Lab
Overview of Low grazing
Angle Doppler Radar
14 m
524 m
1200 m
•
Radar uses one antenna that transmits multiple pulses and records
received fields coherently as surface evolves in time
•
FFT over time at each range produce Doppler spectra versus range
- Doppler shift vs. range is obtained from centroids of Doppler spectrum
•
Changes in Doppler shift vs. range assumed to correspond to long wave
orbital velocity
- allows retrieval of surface profile
ElectroScience Lab
Numerical simulation & geometry
•
1-D MOM for impedance surfaces (Johnson et al, TGRS 2009)
- frequency : 2975 ~ 3026.1 MHz (512 frequencies, ~ 3.4 m range resolution)
- antenna height : 14 m
- mean grazing angle : 1 degree
•
Captures shadowing and multipath effects ; note no thermal noise
•
Scattered fields computed for a single realization time-evolved over 256 time-steps of
5 ms each
- Pierson-Moskowitz spectrum with weakly non-linear effects (Creamer model)
- wind speed :15 m/s
1st
256th
- RMS height : 1.17 m
ElectroScience Lab
Doppler computation
• Fields versus range are obtained from 512 frequencies at each time step
Fields vs. range
Fields vs. frequency
ElectroScience Lab
Doppler spectra vs. range
Retrieval example using Doppler spectra
• Doppler centroids
• Orbital velocity(i.e.,
(using speed
Doppler frequency
c
multiplied
by
where c is
of light)
2f
speed of light and f is
Orbital velocities
electromagnetic frequency)
(gravitational
is converted
to height by
usingconstant
linear model
(i.e.,
and FFT)
FFT of Orbital velocity 
 Surface
divided
by gkprofile
where g is
heights constant and k
gravitational
is wave number from
frequency in FFT 
inverse FFT)
ElectroScience Lab
Real
More on Doppler spectrum
HH
•
Less
dispersion
of Doppler
spectrum
with VV
case in
shadowed
region.
• Discrete
behavior of
Doppler
spectra
both in HH
polarization
and VV
polarization
cases.
ElectroScience Lab
VV
More on Doppler spectrum
HH
ElectroScience Lab
Broadening of the width of Doppler spectrum
• Broadening of the width of spectra is clearly observed with the use of 256 pulses
• Comparisons with profile statistics obtained directly from the surface profiles showing that the
dependence of the width of Doppler spectra on the number of computed pulses arises from
deviation of orbital velocity within the measurement time
Spectrum with 128 pulses (128*0.005ms)
Spectrum with 256 pulses (256*0.005ms)
Histogram of Orbital velocity with 128 profiles
Histogram of Orbital velocity with 256 profiles
• Surface height
profiles  Fourier
transformed,
multiplied by where
g is the gravitational
constant and k is a
given Fourier compone
nt’s wave number,
and then inverse
Fourier-transformed).
 Oribital velocity vers
us horizontal distance
 Histogram of
Orbital velocity vs. hori
zontal distance
ElectroScience Lab
Direct reflection : Physical Optics Approxiation
(with 2.5 GHz frequency bandwidth)
Doppler Spectra vs distance
Mean Doppler freq. vs distance
• Good correlation (0.99) bet. Doppler centroids (blue line) from spectrum and mean Doppler freq. (red
line) from the profiles.  see (a)
• The average of the differences is 5.8Hz corresponding to 28.9 cm/s. This value is very close to the Bra
gg phase velocity which is 27.9 cm/s (Doppler frequency 5.6 Hz).
• The correlation between the width of Doppler spectra of PO and the width of the distribution of the
inversed Doppler frequency from the profiles is examined.  Correlation of 0.79 is obtained, see (c)
ElectroScience Lab
Direct reflection : Physical Optics Approxiation
(with 50 MHz frequency bandwidth)
Doppler Spectra vs distance
Histogram of Orbital velocity
Mean Doppler freq. vs distance
• The bandwidth of 50 MHz is more feasible for current radar systems and also this dataset was able to b
e used to be compared with the MOM dataset which also is obtained with the same bandwidth.
• Similar results to the case of 2.5 GHz bandwidth.
• An additional procedure which is weighted averaging with adjacent profiles heights is performed to
take into account the effect of range resolution to the mean Doppler frequency vs. horizontal
distance.
ElectroScience Lab
Comparison bet. MOM and PO signals
Doppler freq. vs distance
•
Very high correlation (0.98) bet. Doppler centroids of PO and MOM in visible (a) regions. High
correlation (0.62) bet. Doppler widths in visible regions.  effect of multi-path propagation to the retrieval
is not significant.
• High correlation (0.61) bet. Doppler centroids in shadowed regions shows that Doppler centroids
still holds quite good information about the mean orbital velocity in shadowed regions.
ElectroScience Lab
Comparison bet. MOM and PO signals
Doppler spectrum at two visible locations
•
Similar Doppler spectra in visible points
•
No significant multi-path effects in visible regions
ElectroScience Lab
Modeling expected performance
•
Assumes scattered fields are complex Gaussian random process
- Describes correlated speckle noise signal at the antenna
- Real & imaginary parts of fields are Gaussian random variables, correlated over
multiple time steps
•
For simplicity, model correlation function as
C(t)  exp(i2ft)  exp( 2k 22t 2 )
Results in “Doppler broadening”
where f is the mean Doppler frequency, k is the center frequency wave number,
and  2 is the variance of the Doppler frequency obtained from PO results
•
Can perform a separate Monte Carlo simulation of Doppler frequency estimation to
obtain expected error caused by speckle
ElectroScience Lab
Examination of the error in retrieved frequency
Received fields are separated into
visible and shadowed regions
Calculate the centroid of Doppler
frequency from MOM result
 fMOM
Calculate mean and variance from Doppler
spectra vs. distance of PO results
 f & 2
Use the signal model at each range using
f and  to determine expected error SIM in
Doppler frequency estimation
fMOM  f
SIM
ElectroScience Lab
Deviation from Signal model
• lower plot show that large normalized deviations from the simple model expectations are common in
the shadowed regions, likely due to the fact that such points do not experience direct free space propaga
tion between the surface and the radar antenna, as well as the complex Doppler spectra in such regions
that are not well modeled by the Gaussian form.
•The top plot for visible regions shows more reasonable results, indicating the performance is
approaching that predicted by the signal model.
ElectroScience Lab
Conclusions
•
Numerical studies performed of the use of Doppler spectra for retrieving surface profile
information
•
A “discrete” behavior of Doppler spectra versus range is observed.
- Similar “discrete” behaviors observed in orbital velocity statistics computed from surface profiles
•
Less dispersion of Doppler spectra is observed in VV-polarization than in HH-polarization is
observed.
•
To impose direct reflection from the radar to the point of interest and no shadowing effects are
involved, Doppler spectra vs. horizontal distance obtained by using the PO approach is studied.
•
The results of PO study revealed that Doppler centroid has frequency shift arisen from long wave
orbital velocity and Bragg phase velocity with weakly nonlinear sea surface profiles used in this
study.
•
The distribution of orbital velocities at a distance point is one of that sources that determine the
width of Doppler spectra of scattered signals of the point.
•
Comparison between the MOM and the PO results shows that the influence of multi-path
propagation to Doppler spectra vs. distance is not significant in visible regions.
•
High correlation in Doppler centroids in shadowed region shows that even though the shadowing
effects make the Doppler spectra dispersed, the Doppler centroids still hold quite good information
about the mean orbital velocity.
ElectroScience Lab