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Among the different available wind sources, i.e. in situ measurements, numeric weather models, the retrieval of wind speed from Synthetic Aperture Radar (SAR) data is one of the most widely used methods, since it can give high wind resolution cells. For this purpose, one can find two principal approaches: via electromagnetic (EM) models and empirical (EP) models. In both approaches, the Geophysical Model Functions (GMFs) are used to describe the relation of radar scattering, wind speed, and the geometry of observations. By knowing radar scattering and geometric parameters, it is possible to invert the GMFs to retrieve wind speed. It is very interesting to compare wind speed estimated by the EM models, general descriptions of radar scattering from sea surface, to the one estimated by the EP models, specific descriptions for the inverse problem. Based on the comparisons, some ideas are proposed to improve the performance of the EM models for wind speed retrieval.

The exploitations of Synthetic Aperture Radar (SAR) images to retrieve oceanic parameters have been widely studied in the literature, due to many advantages of SAR systems: stable operations in most meteorological conditions, revisit period, high resolution. Among the important oceanic parameters, sea surface wind plays a crucial role for the studies of the other parameters, i.e. waves, currents, marine meteorology, and the coupling of oceanic and atmospheric systems. As well as, surface wind speed is an important parameter in the studies of many oceanic applications, i.e. oil slick observation [

The common point of both EP and EM models is the use of the geophysical model functions (GMFs) to describe the dependency of normalized radar cross section (NRCS) on wind speed and the geometry of observations. Therefore, by knowing NRCS and geometric parameters, it is possible to invert the GMFs to estimate wind speed. For the EP models (also known as scatterometry-based approaches), the GMFs are constructed and validated by the series of satellite scattero meter missions. For instance, the C-band GMFs, known as CMOD.4 [

In both EM and EP models, wind direction is a crucial parameter for wind speed estimation. It can be obtained from different available wind sources, i.e. in situ measurements, numeric weather models, retrieval from SAR data, etc. The last approach is the most widely used in the literature, since it can give (almost) immediately the information of wind directions with high resolution. The methods to retrieve wind directions can be divided into two categories: one is in the spectral domain, and the other is in the spatial domain. The most well-known method in the spectral domain is the Fourier Fast Transform (FFT) [

The outline of this paper is as follows. In Section 2, the descriptions of the SPM and CMOD.5 are presented in detail. It also includes the analyses of validity domain, and the impact of different variables on the relation between radar backscattering and sea surface. Section 3 presents the data used for the studied models to retrieve wind speed. Section 4mentions the retrieval of wind directions from SAR images. Section 5 presents the estimation of wind speed by using the SPM and CMOD.5. The obtained results are compared to in situ measurements to evaluate. Section 6 discusses the advantages and limits of the SPM for wind speed estimation. Section 7 summarizes the main points of this paper, and proposes the perspectives to improve the performance of the EM models for wind speed retrieval.

The SPM, also known as Bragg resonance, was first identified as an important mechanism of radar backscattering from the water surface a long time ago. It was then developed for radar backscattering from the short-scale waves in the ocean by Wright (1966, 1968) [

where

number; k_{x}, k_{y} are the x- and y-axis components of k, respectively; θ indicates the radar incident angle (and also backscattering angle in monostatic case); α_{pp} denotes the Bragg coefficients in VV-or HH-pol; σ and W represent the standard deviation and normalized roughness spectrum of sea surface waves, respectively.

The Bragg coefficients in VV- and HH-pol, α_{VV} and α_{HH}, are described as a function of sea water permittivity ε_{r} and incident angle θ, as given by (2) and (3).

The calculations of sea water permittivity have been shown in many references [_{r}, as given by (4).

where

relaxation time; ε_{0} is the permittivity of free space (ε_{0} = 8.854 × 10-12 F/m); σ is the ionic conductivity. The temperature T and salinity S of the sea water of the Iroise Coast (France) are collected via www.previmer.org, from Oct. 2014 to Apr. 2015. The temperature T varies between 4˚C (Feb. 2015) and 18˚C (Oct. 2014), while S is quite stable around 32 - 35 ppt. By using (4), we note that the permittivity of sea water varies slightly from ε_{r} = 62.54 + j39.82 (Feb 2015) to ε_{r} = 66.81 + j34.93 (Oct 2014). It signifies that temperature and salinity do not have significant effects on the calculation of radar backscattering as in (1).

In contrast to temperature and salinity, the roughness spectrum of sea surface is an important parameter for the NRCS calculations. In fact, it concerns a lot of parameters, particularly wind vector which is the favorite one in this paper. For a simple description, σ and W in (1) are replaced by the directional surface wave spectrum S(K, ), with wave propagation referenced to wind direction. The spectrum S(K,Φ) is generally described by the two parts as given by (5).

where S(K,0) is the omnidirectional spectrum, and f(K,Φ) is the angular spreading function. In general, S(K,0) is influenced by wind speed, while both wind speed and wind direction affect in the description of f(K, Φ). By knowing S(K,Φ) and Φ, it is possible to estimate wind speed. One should note that K in (5) is the wavenumber of ocean waves. For the SPM (or Bragg resonance), K relates to the radar wavenumber k in (1) as K = 2k × sinθ, where θ is always the radar incident angle.

The theoretical modelling of sea surface roughness spectrum has a history as long as the investigation of radar backscattering from the ocean surface. The initial studies were proposed by Cox and Munk (1954) [

The validity condition of the SPM has been discussed in [

where U_{10} is the wind speed at the 10 m height. Equation (6) is only validated under the wind condition: 1 m/s < U_{10} < 13 m/s. By combining (6), the conditions of mss < 0.09, and 1 m/s < U_{10} < 13 m/s,we realize that the validity domain of SPM limits for wind speed below 13 m/s. According to the Beaufort scale, for this level of wind speed, there are only wavelets, sometimes short-scale waves on the sea surface. It signifies that the SPM should be used under the condition of slightly rough sea surface, without the presence of intermediate- or/and long- scale waves. In comparison to the other EM models, which can describe sea surface roughness more generally (i.e. TSM, SSA), the SPM works well for moderate incident angles from 32.5˚ to 45˚.

A general form of the GMFs described in the EP models is defined as in (7) [

where Φ is the wind direction relative to the radar look direction, A, B, b_{1}, b_{2} are the functions of U_{10} and θ. Thus, by determining _{10} can be estimated by inverting (7). As indicated, we select the CMOD.5 for the estimation of wind speed, since it can work well for most wind regimes. As well as the SPM, the validity domain of the CMOD.5 is limited under some conditions. The CMOD.5 can work well for the incident angles of 20˚ - 50˚, and for wind speed below 25 - 30 m/s [

Since the EP GMFs are only defined for VV-pol, a polarization ratio, PR, should be used for the SAR images in HH-pol. The calculations of PR have been studied in many references [

where α is an adjustable parameter. It is calibrated via the in situ measurements. In fact, one can find some values of α: α = 0.6 in [

where A_{Φ}, B_{Φ}, and C_{Φ} are the parameters determined by the in situ measurements and SAR images, with regard to the impact of wind directions. Based on the study of Mouche, some studies [_{Φ}, B_{Φ}, and C_{Φ} to better agree with the different C-band SAR data and in situ measurements. In this paper, we use the model proposed by Liu et al. [

_{10} = 13 m/s and θ = 30˚ - 45˚ which correspond to the validity domain of the SPM. At θ = 30˚, for both up-wind (

The results obtained in

SAR images studied in this paper are acquired by the C-band Sentinel-1 satellite. It was launched in April 2014 by the European Space Agency (ESA), with the aim of providing an independent operational capability for continuous radar mapping of the Earth. The acquisition modes of the Sentinel-1 include: Stripmap (SM), Interferometric Wide Swath (IWS), Extra Wide Swath (EWS), and Wave Model (WM). The images can be acquired in single polarization (VV/HH), or in dual-polarization (VV+VH / HH+HV). In this study, we use the Level-1 images acquired with SM mode in HH-pol, and with IWS mode in VV-pol. They are downloaded via https://scihub.esa.int. The acquired date are the type of GRD (Ground Range, Multi-Look, Detected), with high resolution (HR). This type allows reducing speckle noise, but it also decreases the spatial resolution of the image. For instance, the spatial resolution of the studied image in SM mode is reduced to 23 m × 23 m, instead of 3.6 m × 4.9 m. As well, the image in IWS mode has a spatial resolution of 20 m × 22 m, instead of 3.5 m × 22 m.

The in situ measurements used in this paper are collected at the meteorological stations of Météo France along the Iroise Coast (

where u_{2} stands for the wind speed at height z_{2} and u_{1} and z_{1} are the known wind speed and height, respectively.

For both SPM and CMOD.5, wind direction is a crucial parameter for wind speed estimation, in particular for high wind speed. However, its impact is not the same for the two models. In fact, for the SPM the effect of wind direction is noted in the angular spreading function of sea roughness spectrum (as in (5)), while it is represented by the cosΦ and cos2Φ parameters in the CMOD.5 (as in (7)). As shown in

The wind direction data can be obtained via many ways, i.e. from: a) in situ measurements, b) numeric weather models, or c) extraction from SAR images. Among them, the retrieval of wind directions from SAR data is the most widely used, since it can give high wind resolution. In addition, it can be one of the rare choices to have wind direction information in the areas where the fixed meteorological buoys are not installed. As indicated, the LG method is preferred to the FFT one since it can give wind directions with smaller resolution cells (even 1 km × 1 km in some cases [

1) First, the filtered images should be reduced dimension sizes to enhance wind streaks, and divided into the sub-images according to expected spatial resolution.

2) Then, for each defined sub-image, the histogram of LG directions must be weighted and smoothed.

3) After that, the main LG direction of each sub-image is estimated, and the orthogonal of the most frequent gradient direction is assigned as the most available wind direction.

4) Finally, the 180˚ ambiguity of wind direction can be solved either by in situ measurements, or via the Continuous Wavelet Transform (CWT) method.

The first step is a crucial task to obtain good extractions in respect to spatial resolution. The spatial resolution of extracted wind directions depends on the acquisition model of SAR images. It can be 1 km × 1 km if the quality of SAR image is good enough. For the images used in this paper (SM and IWS modes), a wind direction cell of 3 km × 3 km seems to be enough for the SPM and CMOD.5 to have good spatial resolution of wind speed . The importance of the second step can be verified in

One of the most important constraints of the LG method is the 180˚ ambiguity of the extracted wind directions. It can be solved by in situ measurements or numerical weather models. However, the measured data are not always available for all cases. Recently, the CWT method has been developed to solve this problem. Nevertheless, it seems to be complicated to apply. There is another way to solve the 180˚ ambiguity of extracted wind direction, if wind streaks on SAR images are visible enough to observe. As shown in

Wind speed estimation on a VV-pol Sentinel-1 image by using the SPM and CMOD.5 is presented in

so noted for θ = 35˚ - 40˚, but the deviation is less significant (only about 1 - 2 m/s). For θ = 40˚ - 45˚, the SPM and CMOD.5 give (quite) similar wind speed estimation. They are also very close to the measured data (the same range of 5 - 7 m/s). Compared to the SPM, the CMOD.5 seems to give higher spatial resolution of wind speed, especially for the range of 1 - 5 m/s. Indeed, the noted minimum value of the SPM wind speed is about 4 - 5 m/s, while it is 0 - 1 m/s for the CMOD.5 wind speed.

For the Sentinel-1 data in VV-pol, wind speed estimated by the SPM is quite similar to the one offered by the CMOD.5 for the range of θ = 32.5˚ to 45˚. The deviation of 2 - 3 m/s is tolerable in some applications (e.g. weather forecasting). Certainly, this conclusion is only validated in the wind speed range of 1 - 12 m/s, corresponding to the validity domain of the SPM. Nevertheless, from our study, the SPM still gives (quite) similar wind speed estimation to the CMOD.5 for wind speed above 12 m/s. This result is only acceptable under the point of view of mathematics. It has not any physical significance. However, if the SPM is corrected to widen the validity domain of wind speed and incident angle, it can be used to estimate wind speed from SAR images as the EP models. Indeed, the TSM is a good successive model of the SPM to study radar backscattering with higher wind speed and different ranges of incident angles [

For the images in HH-pol, the SPM overestimates wind speed in most cases of incident angle and wind direction. This result can be explained by some facts. First, the polarizations of radar backscattering respond to sea

surface roughness and wave breaking differently. In fact, as shown in many studies [

This paper has discussed about the application of the EM models to estimate wind speed from SAR data. Under the point of view of the inverse problem, the SPM has been selected due to its flexibility of inversion. Nevertheless, it can only work well for wind speed below 13 m/s, and for moderate incident angles of 32.5˚ - 45˚. The wind speed estimated by the SPM is specifically compared to the one offered by the CMOD.5. The CMOD.5 is a widely used empirical model in the literature to estimate wind speed from SAR data. In both studied models, wind direction plays an important role to estimate accurately wind speed. In the indicated validity domain (wind speed below 13 m/s and incident angles of 32.5˚ - 45˚), the SPM gives quite similar wind speed estimation to the CMOD.5 in VV-pol. However, the resolution of wind speed obtained by the SPM is lower than that of the CMOD.5. In HH-pol, the SPM overestimates wind speed in most cases of incident angle and wind direction. This result can be explained by some facts which concern the different behavior of radar backscattering to polarization, and the difference between the standard wave spectrum used in the SPM and the practical one at the moment of SAR image acquisition.

In the next steps, in order to improve the validity domain of the SPM, the other EM models like TSM or SSA should be used. They are expected to possibly estimate wind speed above 13 m/s, and for different ranges of incident angles, notably for θ = 20˚ - 30˚. In particular, to improve wind speed estimation in HH-pol, together with the other EM models, a study of sea surface roughness spectrum should be done.

This work is supported by the French General Directorate for Armament (DGA) in the frame of Project SIMUSO. TheSentine-1 images are provided by the European Space Agency (ESA) via https://scihub.esa.int/. The in situ measurements are collected via http://www.infoclimat.fr/.

Tran Vu La,Ali Khenchaf,Fabrice Comblet,Carole Nahum,Helmi Ghanmi, (2016) Exploitation of Electromagnetic Models for Sea Wind Speed Estimation from C-Band Sentinel-1 Images. Journal of Electromagnetic Analysis and Applications,08,42-55. doi: 10.4236/jemaa.2016.83005