Exploitation of Electromagnetic Models for Sea Wind Speed Estimation from C-Band Sentinel-1 Images ()
Received 26 January 2016; accepted 26 March 2016; published 30 March 2016
1. Introduction
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 [1] , and ship detection [2] . The retrieval of wind fields has been carried out from different SAR data via different approaches [3] - [8] . In such studies, the resolutions of the estimated wind vectors are significantly dependent on the signal-to-noise ratio (SNR) of each SAR system. In practice, one can obtain a 1 km × 1 km wind cell in cases where the speckle noise level is quite low. In spite of the diverse approaches, the retrieval of wind vectors by using the physical models is particularly preferred, due to their generality. For this approach, one can find two principal methods: via empirical (EP) models, and electromagnetic (EM) models.
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) [24] , while the Local Gradient (LG) [25] is the most widely used one in the spatial domain. Generally, wind directions retrieved by the LG have (much) higher resolution than the ones given by the FFT. In fact, the LG can offer a wind cell of 3 km × 3 km, even 1 km × 1 km in some conditions [25] , instead of a cell of 20 km × 20 km given by the FFT. The common issue of both the LG and FFT is the 180˚ directional ambiguity of the retrieved wind directions. It can be removed only if wind shadow is present and visible enough in the lee of coastlines, or if there are additional wind source data, i.e. in situ measurements, SCAT wind data, etc.
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.
2. Methodology
2.1. Small Perturbation Method (SPM)
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) [26] , Valenzuela (1978) [27] , and Plant (1990) [28] . Depending on different approaches, the descriptions of the SPM in terms of equation, parameters, and validity domain are diverse. In this paper, for the monostatic case of radar scattering, we use the definition presented in [23] as shown by (1).
(1)
where 
denotes the radar backscattering (or NRCS) from sea surface in VV- or HH-pol; k is the radar wave
number; kx, ky are the x- and y-axis components of k, respectively; θ indicates the radar incident angle (and also backscattering angle in monostatic case); αpp 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, αVV and αHH, are described as a function of sea water permittivity εr and incident angle θ, as given by (2) and (3).
(2)
(3)
(4)
where 
and 
are the static and high-frequency dielectric constants, respectively; τ is the
relaxation time; ε0 is the permittivity of free space (ε0 = 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 εr = 62.54 + j39.82 (Feb 2015) to εr = 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).
(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 validity condition of the SPM has been discussed in [23] [44] , but it seems to be difficult to give the obvious conclusions in terms of wind speed and incident angle, since this condition concerns the mean square slope (mss) of sea wave spectrum used in the SPM. Generally, as indicated in [44] the SPM works well for the root mean square slope (rmss) < 0.3, or mean square slope (mss) < 0.09. The relation of mss and wind speed has been studied and validated in many studies as discussed in [38] . Among them, the most successful measurements were proposed by Cox and Munk (1954) [33] . For a clean sea surface, the mss is defined as in (6).
(6)
where U10 is the wind speed at the 10 m height. Equation (6) is only validated under the wind condition: 1 m/s < U10 < 13 m/s. By combining (6), the conditions of mss < 0.09, and 1 m/s < U10 < 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˚.
2.2. Comparison of SPM and CMOD5
A general form of the GMFs described in the EP models is defined as in (7) [9] - [12] .
(7)
where Φ is the wind direction relative to the radar look direction, A, B, b1, b2 are the functions of U10 and θ. Thus, by determining 
and θ from the SAR data, and Φ, wind speed U10 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 [11] . One should know that the range of 20˚ - 50˚ is widely used to acquire images for most SAR systems, and wind speed is rarely beyond 25 - 30 m/s. This signifies that the CMOD.5 is generally a good empirical model to estimate wind speed from SAR data.
(8)
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 [13] , α = 1.0 in [14] , and α = 1.2 in [15] . Contrary to the Thompson model, in 16], Mouche et al. concluded that the PR depends not only on radar incident angle, but also on wind direction. Hence, they proposed a new model for PR calculation as given by (9).
(9)
where AΦ, BΦ, and CΦ 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 [17] [18] have re-calculated AΦ, BΦ, and CΦ 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. [18] for wind speed retrieval in HH-pol.
Figure 1 presents the comparison of the NRCS calculated by the SPM with the Elfouhaily wave model (SPM- Elf) and CMOD.5 in VV-poland HH-pol. The studied values of wind speed and incident angle limit at u10 = 13 m/s and θ = 30˚ - 45˚ which correspond to the validity domain of the SPM. At θ = 30˚, for both up-wind (Figure 1(a)) and cross-wind directions (Figure 1(b)), the NRCS in VV-pol calculated by the SPM-Elf is (about) 2 - 4 dB lower than that offered by the CMOD.5. At θ = 45˚, the two models give quite similar NRCS level for up- wind direction. Meanwhile, for cross-wind direction the level calculated by the SPM-Elf is (about) 2 - 3 dB higher than that of the CMOD.5. In HH-pol, in most cases of incident angle and wind direction, the SPM-Elf underestimates NRCS level in respect with wind speed (about 5 - 7 dB).
The results obtained in Figure 1 show that in VV-pol, the SPM-Elf can offer similar wind speed estimation to the CMOD.5for up-wind direction, and a little more for cross-wind direction. This conclusion is noted for moderate incident angles (32.5˚ - 45˚). On the contrary, in HH-pol for most cases of incident angle and wind direction, wind speed obtained by the SPM-Elf is overestimated in comparison to the one given by the CMOD5. This is particularly noted for quite low incident angles (30˚ - 32.5˚).
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(a)![]()
(i) (b) (ii)
Figure 1. Comparisons of NRCS calculated by SPM with Elfouhaily spectrum (SPM-Elf) and CMOD.5 for θ = 30˚ and θ = 45˚. (i) VV-pol. (ii) HH-pol. (a) Up-wind direction. (b) Cross-wind direction.
3. Data Preparation
3.1. Sentinel-1 Images
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.
3.2. In Situ Measurements
The in situ measurements used in this paper are collected at the meteorological stations of Météo France along the Iroise Coast (Figure 2), since there are not any fixed meteorological buoys in this area. These stations (red points) are located very close to the open sea. This allows reducing as possible the difference between the measured data along the coast and on the open sea. Since wind speed is measured at different heights, it needs to be corrected to the reference level of 10 m height for comparisons with estimated results. The correction methods of wind speed can be found in [45] [46] . However, the obtained results with the studied models are not much different. In this study, we use a simple power-law varying wind profile as given by (10) [45] .
![]()
(10)
where u2 stands for the wind speed at height z2 and u1 and z1 are the known wind speed and height, respectively.
![]()
Figure 2. Meteorological stations (red points) of Météo France along the Iroise Coast (France).
4. Wind Direction Extraction
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 Figure 1, the NRCS for up-wind direction is higher than the one in cross-wind direction, and this result is noted for both polarizations. Meanwhile, as shown in Figure 3, the difference of NRCS in respect to wind direction calculated by the CMOD.5 is more significant than the one calculated by the SPM, in particular between up- and cross-wind directions, and for high wind speed.
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 Figure 4. Due to being weighted and smoothed, the extracted wind directions are very close to the measured data (red arrows). As shown in the right, the difference between the not-smoothed wind direction and measured data is up to 35˚, while it is reduced to 5˚ for the smoothed wind direction.
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Figure 3. NRCS in respect to wind direction and wind speed studied by the SPM and CMOD.5.
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Figure 4. Extraction of wind direction by LG method on a Sentinel-1 image (SM mode), acquired on 27th Dec. 2014 from 06:23:46 UTC to 06:24:15 UTC. (Left) Smoothed vs. measured (red arrows) wind directions. (Right) Main LG direction of a sub-image before and after smoothing, compared to measured wind direction.
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 Figure 5, after reducing the dimension sizes of the SAR image presented in Figure 4, the wind streaks are much more visible to be noted. Based on this observation, the 180˚ ambiguity of extracted wind directions can be easily solved. The efficiency of this method depends on the visibility of wind streaks which depends on wind regimes and speckle noise level. For low wind regimes (below 5 m/s), it is generally difficult to determine wind streaks. This is the same in the case where speckle noise is significant.
5. Wind Speed Estimation
Figure 6 describes the indispensable steps to retrieve wind speed from SAR images. The Level-1 Sentinel-1 images are processed by the toolbox for data calibration, land masking, and sub-image division. Thanks to this step, the NRCS of the image is determined. Then, by using the LG method described above, wind directions with different spatial resolutions can be determined. They are compared to the measured data to verify. Finally, the NRCS and wind directions extracted from SAR images are applied in the SPM and CMOD.5 to retrieve wind speed with different spatial resolutions. To evaluate, the estimated wind speed will be compared to the measured data collected at the stations in Figure 2.
5.1. VV-Pol Image
Wind speed estimation on a VV-pol Sentinel-1 image by using the SPM and CMOD.5 is presented in Figure 7. This image is acquired in IWS mode with radar incident angles from 32.5˚ to 45˚. The spatial resolution of wind direction and wind speed in this case is 3 km × 3 km. As discussed in Section 4, for this level of spatial resolution, the different wind speed areas may be well visualized. As expected from Figure 1, for the range of θ = 32.5˚ - 35˚, the wind speed estimated by the SPM is 2 - 3 m/s higher than that given by the CMOD.5. This is al-
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Figure 5. Enhancement of wind streaks on the SAR image presented in Figure 4 to obtain exact wind direction.
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Figure 6. Diagram of wind speed retrieval carried out by the SPM and CMOD.5, from Level-1 Sentinel-1 images in VV- and HH-pol.
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(a)![]()
(b)
Figure 7. Map of wind speed estimated by the SPM (a) and CMOD.5 (b) from a VV-pol Sentinel-1 image in IWS mode acquired on 15th Apr 2015, from 18:12:46 UTC to 18:13:15 UTC.
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.
5.2. HH-Pol Image
Figure 8 shows the wind speed estimations on a HH-pol Sentinel-1 image by using the SPM and CMOD.5. This image is acquired in SM mode with radar incident angles from 42˚ to 46˚. As well as in the previous case, the spatial resolution of wind direction and wind speed in this case is 3 km × 3 km. As expected from Figure 1, SPM overestimates wind speed in most cases of incident angle and wind direction. That can be verified in this case. While the wind speed estimated by the CMOD.5 is only in the range of 10 m/s - 15 m/s, that of the SPM is 10 - 15 m/s higher. This is confirmed by the comparisons with the measured data which are only in the range of 10 - 16 m/s. As well as in Figure 7, the 3 km × 3 km spatial resolution gives the good distinction of wind speed areas. In particular, in contrast to the previous case, the wind streaks can be well noted in this case. This is an important sign to solve the 180˚ ambiguity of extracted wind direction, as discussed in Figure 4 and Figure 5.
6. Discussion and Validation
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 [23] . In Figure 7, the wind speed estimated by the SPM has lower spatial resolution than that of the CMOD.5. This is probably from the sea surface roughness spectrum studied in this paper, or from the SPM. Therefore, to well understand, the other wave spectrum models should be taken into account in the next paper.
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
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(a) (b)
Figure 8. Map of wind speed estimated by the SPM (a) and CMOD.5 (b) from a HH-pol Sentinel-1 image in SM mode acquired on 27th Dec 2014, from 18:12:46 UTC to 18:13:15 UTC.
surface roughness and wave breaking differently. In fact, as shown in many studies [26] - [28] , VV-pol is dominated by Bragg resonance scattering, while non-Bragg scattering mechanisms is more appropriate for HH-pol (maybe VH-pol). In other words, the SPM can describe well radar backscattering in VV-pol, while for HH-pol the other EM models (i.e. TSM, SSA) should be used. Second, long wind waves are not aligned with local wind, and there may be waves, i.e. swell, not related to the local wind. Furthermore, the sea can be partially developed, and this makes the wave spectrum different from the standard reference ones (i.e. Elfouhaily). In other words, while the standard models assume that the roughness statistics are homogenous, in practice, they vary nonlinearly. This constraint for HH-pol is more sensitive than for VV-pol because NRCS in HH-pol is normally several dBs lower than NRCS in VV-pol. Therefore, a non-linear spectral description of sea surface roughness should be used to improve wind speed estimation.
7. Conclusions and Perspectives
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.
Acknowledgements
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/.