IGARSS 2011 Vancouver Jul 26th , 2011 Chun-Sik Chae and Joel T. Johnson ElectroScience Laboratory

1. 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

2. 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

3. 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

4. Overview of Low grazing Angle Doppler Radar 14 m 1200 m 524 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

5. 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 • - RMS height : 1.17 m 1st 256th

6. Doppler computation • Fields versus range are obtained from 512 frequencies at each time step Fields vs. range Fields vs. frequency Doppler spectra vs. range

7. Retrieval example using Doppler spectra • Orbital velocity(i.e., Doppler frequency multiplied by where c is speed of light and f is electromagnetic frequency) is converted to height by using linear model (i.e., FFT of Orbital velocity  divided by where g is gravitational constant and k is wave number from frequency in FFT  inverse FFT) • Doppler centroids (using speed of light) Orbital velocities (gravitational constant and FFT)  Surface profile heights Real

8. More on Doppler spectrum HH VV • Less dispersion of Doppler spectrum with VV case in shadowed region. • Discrete behavior of Doppler spectra both in HH polarization and VV polarization cases.

9. More on Doppler spectrum HH

10. 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 256 pulses (256*0.005ms) Spectrum with 128 pulses (128*0.005ms) • Surface height profiles  Fourier transformed, multiplied by where g is the gravitational • constant and k is a • given Fourier component’s wave number, • and then inverse • Fourier-transformed). •  Oribitalvelocity versus horizontal distance  Histogram of • Orbital velocity vs. horizontal distance Histogram of Orbital velocity with 128 profiles Histogram of Orbital velocity with 256 profiles

11. 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 Bragg 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)

12. 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 be 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.

13. 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.

14. 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

15. 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 where is the mean Doppler frequency, is the center frequency wave number, and 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 Results in “Doppler broadening”

16. 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  Calculate mean and variance from Doppler spectra vs. distance of PO results  & Use the signal model at each range using and to determine expected error in Doppler frequency estimation

17. 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 propagation 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.

18. 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.