## Code Record

**2017-09-18**

[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:

* NRCS

* GDS

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

**Code Access Instructions: **Accessing to code repository can be
obtained by emailing: frederic.nouguier@ifremer.fr

**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 (http://www.parallelpython.com/).**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