Code Record


[DOI: 10.21982/M8S62C] Asymptotic methods for microwave scattering
Nouguier, Frederic; Chapron, Bertrand; Mouche, Alexis
Asymptotic Methods for backscattered Normalized Radar Cross Section (NRCS) and geophysical Doppler shifts (GDS) from random linear sea surfaces in the microwave regime. Available asymptotics methods are:
* KA : Kirchhoff Approximation
* SSA : Small Slope Approximation
* GO2 : Geometrical Optics
* WCA : Weighted Curvature Approximation
Input parameters:
* Electromagnetic frequency/wavelength
* Permittivity
* incidence and azimuth for ongoing EM wave
* incidence and azimuth for outgoing EM wave (in bistatic case only)
* Ocean spectrum
* wind speed
* wind direction
Output parameters:

There are two main difficulties in running accurate simulations:
1) The evaluation of the correlation functions has to be derived on a spatial grid adapted to the electromagnetic wavelength/geophysical conditions. I coded an "autolim" mode that automatically provides adapted standards parameters. However, the user can manually force values for the two critical parameters (Nr and rmax). The provided example is an example of the "autolim" mode usage. Details of this mode can be found in a typical ipython environment : >>PolarOceanCorrelation?
2) A unified numerical code evaluating nrcs and doppler shift for all possible frequency / incidence / azimuth / polarization / wind speed / waves conditions is very complex. I did many tests on this code and here are my conclusions:
The difficulty increases when:
- Microwave frequency decrease (S and L band)
- Incidence angles increase (>50 deg)
- wind speed decrease
- in cross-wind compared to up/down wind

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Appears in: [1] T. Elfouhaily, S. Guignard, R. Awadallah, and D.R. Thompson, Local and non-local curvature approximation: a new asymptotic theory for wave scattering, Waves Random Complex Media 13 (2003), pp. 321–337.

[2] Voronovich, A.G., 1994, Small Slope Approximation for electromagnetic wave at a rough interface of two dielectric half-spaces, Waves in Random Media,, 4, 337-367.

[3] Nouguier F., Guerin C-A., Soriano G. (2011). Analytical Techniques for the Doppler Signature of Sea Surfaces in the Microwave Regime-I: Linear Surfaces . Ieee Transactions On Geoscience And Remote Sensing , 49(12), 4856-4864 .

[4] Mouche A., Chapron B., Reul N., Collard F (2008). 'Predicted Doppler shifts induced by ocean surface wave displacements using asymptotic electromagnetic wave scattering theories . Waves in Random and Complex Media , 18(1), 185-196 .

[5] Guérin, C-A , Soriano, G. and Chapron, B. (2010) 'The weighted curvature approximation in scattering from sea surfaces', Waves in Random and Complex Media, 20: 3, 364 — 384

Code Languages: Python

To compile code: Requires standard Python libraries (numpy, scipy, ...) as well as the parallel Python library (

Sensor Categories: Microwave Radiometer, Microwave Spectrometer, SAR, Scatterometer

Geophysical Model: Direct

Geophysical Categories: Ocean: Surface Winds, Ocean: Salinity, Ocean: Currents, Ocean: Surface Temperature, Ocean: Other

Keywords: Asymptotic Methods, Normalized Radar Cross Section (NRCS), geophysical Doppler shift, sea surface, microwaves, Kirchhoff Approximation, Small Slope Approximation, Weighted Curvature Approximation, Geometrical Optics