### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Position of the Problem
- 3. Extended Kirchhoff Model for the Normalized Radar Cross Section
- 4. Results and Discussion
- 5. Conclusion
- Appendix A:: NRCS Expression of Existing in the Case of Gaussian Statistics
- Acknowledgments
- References

[1] Asymptotic models (small perturbation and small slope approximation at first-order, Kirchhoff approximation or two-scale model) used to predict the normalized radar cross section of the sea surface generally fail to reproduce in detail backscatter radar measurements. In particular, the predicted polarization ratio versus incidence and azimuth angles is not in agreement with experimental data. This denotes the inability of these standard models to fully take into account the roughness properties with respect to the sensor's configuration of measurement (frequency, incidence, and polarization). On the basis of particular assumptions, to decompose the scattered electromagnetic field between zones covered with freely propagating waves and others where roughness and slopes are enhanced, recent works were able to match observations. In this paper, we do not assume such a decomposition but study the latest improvements obtained in the field of approximate scattering theories of random rough surfaces using the local and resonant curvature approximations. These models are based on an extension of the Kirchhoff Approximation up to first order to relate explicitly the curvature properties of the sea surface to the polarization strength of the scattered electromagnetic field. Consistency with previous approaches is discussed. As shown, dynamically taking into account the sea surface curvature properties of the surface is crucial to better interpret normalized radar cross-section and polarization ratio sensitivities to both sensor characteristics and geophysical environment conditions. The proposed developments, termed the Resonant Curvature Approximation (RCA), are found to reproduce experimental data versus incidence angle and azimuth direction. The polarization sensitivity to the wind direction and incidence angle is largely improved. Finally, Gaussian statistical assumption adopted to derive the analytical expression of the normalized radar cross section is also discussed. In particular, the third-order cumulant function is shown to better reproduce the second-order up-/down-wind azimuth modulation. The proposed developments appear very promising for improvement of our understanding and analysis of both sea surface radar backscatter and Doppler signals.