A Study of the Electromagnetic Bias in GNSS-R Altimetry

1. TH2.09 - GNSS+R Remote Sensing II A Study of the Electromagnetic Biasin GNSS-R Altimetry Jeonghwan Park1, Joel T. Johnson1, and Stephen T. Lowe2 1The Ohio State University, Columbus, OH, USA 2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

2. Outline • Overview • Electromagnetic Bias • Monte Carlo Approach • Hydrodynamic Models • Choppy Wave Models for Nonlinear Surfaces • EM Bias from Pulse Returns • Short Wave Effects on the EM Bias • Summary

3. GNSS-R for Ocean Altimetry • GNSS-R (Global Navigation Satellite System – Reflectometry) • Using reflected GNSS signal from the Earth’s surface for geophysical remote sensing • Altimetry : sea surface height • Scatterometry : wind speed, wind direction, soil moisture, etc. • Bistatic radar configuration • GNSS-R Missions • Extensive ground and air-borne research reported • limited number of existing satellite demonstrations (e.g. UK-DMC) • Multiple satellite missions (PARIS, GEROS, CYGNSS) in the planning phases GNSS-R Geometry

4. Electromagnetic Bias • Sea surface height accuracy requirements are very high considering applications such as monitoring global sea level rise. • Sources of errors in altimetry measurements include measurement noise, orbit determination, atmospheric propagation, and the electromagnetic bias. • EM bias is a small term compared to other GNSS-R altimetry errors, but may become important in the future. • The EM bias results from the non-symmetric property of sea waves • Wave crests are narrow while the troughs are wide • More electromagnetic energy is reflected from wave troughs • Thus, the estimated sea surface height is lower than the actual sea level Wide troughs Narrow crests EM Bias

5. Review Past EM Bias Studies • Conventional EM Bias methods • Many past studies of nadir cases • Airborne and satellite altimetry • S (3.2 GHz), C(5.3 GHz), and Ku (13.6 GHz) Band • Method used here similar to Naenna et al.’s [Naenna 2010] • Differences about GNSS-R EM bias • Bistaticangle • Passive mode : using GPS signal • L-band (1.575 GHz) • Questions : Influence of angle on bias Influence of L-band frequency [Naenna 2010] P. Naenna and J. T. Johnson, “A Monte Carlo Study of Altimeter Pulse Returns and the Electromagnetic Bias,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 8, pp. 3218–3224, 2010.

6. Electromagnetic Bias • The EM bias results from the offset between the means of the true surface height and the specular surface height • The EM bias for backscattering is defined as difference between the normalized first moments of the linear pulse return and nonlinear pulse returns [Naenna 2010] • For backscattered pulse return, Jackson (1979) defined the EM bias • Is this result still applicable for bistatic case? , where

7. Monte Carlo Approach Generate a set of linear and nonlinear sea surfaces Compute forward scattering over a range of freqs. Pulse returns Transform forward scattered fields versus frequency into the time domain Average pulse return power over realizations Linear Nonlinear Estimate EM bias by comparing linear and nonlinear pulse returns Surface profiles [Naenna 2010] P. Naenna and J. T. Johnson, “A Monte Carlo Study of Altimeter Pulse Returns and the Electromagnetic Bias,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 8, pp. 3218–3224, 2010.

8. Geometry • Monte Carlo physical optics : L-band (1.575 GHz) with 32 MHz BW • Assumed 1-D perfectly conducting flat surface • 85 km long sampled into 2048K points  resolve short waves down to 5 cm • GPS transmitter (20541 km) with LEO receiver (690 km) • 60000 realizations for good convergence  Parallel computing is utilized • 60000 realizations in 3 hours on 100 processes • Wind speed : 20 m/s, Receiver antenna gain : 23.12 dB • Bias can be modeled analytically but studying Monte Carlo to simplify

9. Hydrodynamic Models • Linear • Linear Gaussian random process surfaces are generated as realizations of the Pierson-Moskowitz spectrum • Nonlinear • Naennaet al. used Creamer et al.’s method; computationally expensive • Nonlinear surfaces are generated by “Choppy Wave Model” [Guérin 2009] which is based on horizontal rather than vertical local displacement of a linear surface • Choppy transformation : • Choppy Wave Method does not capture all non-linear effects of Creamer et al. but much less CPU intensive Linear Nonlinear : Hilbert transform : Spatial Fourier Transform of surface elevation [Guérin2009] F. Nouguier C. Guérin, and B. Chapron, ““Choppy wave” model for nonlinear gravity waves”, Journal of Geophysical Research, vol 114, C09012, 2009

10. Nonlinear Surface Realization • Sharper crests • flatter troughs

11. Choppy Wave Model (CWM) • Comparison of the distribution of elevations for the CWM and Gaussian distribution • Choppy Wave Model underestimates nonlinearity !! Def. of skewness :

12. Pulse Returns • Pulse return power for θ=33.9 degree • θ : Incident angle at specular point • Nonlinear pulse return is shifted !!

13. Pulse Returns • Pulse return power with various bistatic angles • θ : Incident angle at specular point With same peak values • As angle increases, return power decreases due to increased range • Nonlinear pulse returns are shifted for all bistatic angles

14. EM Bias form Pulse Returns • EM Bias with various bistatic angles • Comparison with Jackson’s theory for 0 degree case • As angle increases, EM Bias decrease • Looks similar to Cosine function

15. Bistatic EM Bias with Cosine function • Relationship between EM Bias and small height changes (Δ) in bistatic configuration Path traveled : : Time delay Bistatic EM Bias : EM Bias for nadir looking • Cosine function acts major role in bistatic EM Bias

16. Short Wave Effects on the EM Bias • EM bias with various high cut-off frequencies • Short wave effects are examined by varying the range of surface length scales included in the surface profiles. L-band More short waves • EM Bias increases when more short waves are included • Saturation appears for shorter waves than EM wavelength

17. Conclusions • Studies of EM bias with bistatic configuration using Monte Carlo simulation have been performed. • Nonlinear surface was obtained using the Choppy Wave Model • The EM bias decreases as bistatic angle increases. • Short waves play an significant role for the electromagnetic bias • 1-D bistatic approach could be expanded to 2-D case. • Analytical formulation in progress