Investigation of EM Backscattering from Slick-Free and Slick-Covered Sea Surfaces Using the SSA-2 and SAR Images

This paper is devoted to investigating the electromagnetic (EM) backscattering from slick-free and slick-covered sea surfaces at various bands (L-band, C-band, X-band, and Ku-band) by using the second-order small slope approximation (SSA-2) and the measured synthetic aperture radar (SAR) data. It is known that the impact of slick on sea surface is mainly caused by two factors: the Marangoni damping effect and the reduction of friction velocity. In this work, the influences induced by these two factors on the sea curvature spectrum, the root mean square (RMS) height, the RMS slope, and the autocorrelation function of sea surfaces are studied in detail. Then, the slick-free and slick-covered sea surface profiles are simulated using the Elfouhaily spectrum and the Monte-Carlo model. The SSA-2 with the tapered incident wave is employed to simulate the normalized radar cross-sections (NRCSs) of sea surfaces. Furthermore, for slick-free sea surfaces, the NRCSs simulated with the SSA-2 at various bands are compared with those obtained by the first-order small slope approximation (SSA-1), the classic two-scale model (TSM), and the geophysical model functions (GMFs) at various bands, respectively. For slick-covered sea surfaces, the SSA-2-simulated NRCSs are compared with those obtained from C-band Radarsat-2 images and L-band uninhabited aerial vehicle synthetic aperture radar (UAVSAR) images, respectively. The numerical simulations illustrate that the SSA-2 can be used to study the EM backscattering from slick-free and slick-covered sea surfaces, and it has more advantages than the SSA-1 and the TSM. The works presented in this paper are helpful for understanding the EM scattering from the sea surface covered with slick, in theory.


Introduction
Oil spill pollution on the sea surface is harmful to marine ecosystems, fisheries, wildlife, and other societal interests.Scientists and researchers have made a great effort to monitor oil spills on the sea surface.Many scientific papers covering a wide range of topics have written about the used means of monitoring of oil spills, e.g., Salberg et al. [1], Skunes et al. [2], Lupidi et al. [3], etc.It is well-known that the synthetic aperture radar (SAR) is almost independent of atmospheric conditions, and can provide high-resolution measurements at both day and night [4].It has been proven that SAR is a useful tool for ocean remote sensing, especially for oil spill detection and monitoring.In previous literature, the problem of oil spill monitoring has been studied mainly from two aspects.The first one focuses

The Damping Model
The influences of the slick can mainly induce by two effects, i.e., the damping effect for small-scale sea waves, and the reduction of friction velocity.In general, the damping effect caused by slick is modeled by the Marangoni theory [13,21].The damping ratio induced by slick can be expressed as: where τ, X, and Y are given as: In Equation (1), k w is the wavenumber of sea waves, ω is the angular frequency of sea waves, ν is dynamic viscosity, and ρ is the density of seawater, respectively.E 0 denotes the elasticity modulus, and ω D is a characteristic pulsation.In this work, we investigate two kinds of slicks, which are denoted as Remote Sens. 2018, 10,1931 3 of 19 slick-a (E 0 = 9 mN/s, ω D = 6 rad/s) and slick-b (E 0 = 25 mN/s, ω D = 11 rad/s), and correspond to organic films measured in two cases.These values were retrieved from field experiments, and have been used in previous works for studying the impacts of slicks on EM scattering field from sea surface [12,13].It should be noted that this model does not involve the thickness of slick.
Besides, given that the slick film may be partially dispersed by the winds and the sea waves, a fractional filling factor F is introduced to modify the damping ratio.Finally, the damping ratio can be written as [13]: Obviously, the damping model is homogeneous, which implies that the damping effect is not associated with wind direction.
As the small-scale waves of the slick-covered surface are damped, the roughness of the surface is reduced.As a consequence, the energy transferred from the wind to sea waves, which is related to the friction velocity, is reduced.This phenomenon has been observed in field experiments: the friction velocity of the slick-covered surface is smaller than the slick-free surface.The friction velocity of a slick-covered surface u * c can be calculated empirically with [22]: where β < 1.In this work, the value of β suggested by Gade et al. is adopted [23]; i.e., β = 0.7.Thus, the spectrum of sea surface covered by slick is related to the clean sea surface spectrum by: where S s (k w , u * c ) denotes the spectrum covered by slick, and S w (k w , u * c ) denotes the clean sea surface spectrum.

The Second-Order Small Slope Approximation (SSA-2)
According to the theory of small slope approximation, the scattering amplitude of the second order can be written as [19,20]: (q 0 +q) √ P inc dr (2π) 2 G(r, h) exp −j k e − k e 0 • r + j(q 0 + q)h(r) × B(k e , k e 0 ) − j 4 M k e , k e 0 ; ξ h(ξ) exp(jξ • r)dξ The incoherent scattering amplitude can be calculated with ∆S k e , k e 0 = S k e , k e 0 − S k e , k e 0 .The incoherent scattering coefficient can be calculated with the incoherent scattering amplitude by: σ 0 = 16π 3 q 0 q∆S(k e , k e 0 )[∆S(k e , k e 0 )] * .
The meanings of the parameters in the equations above can be found in the Appendix A. As shown in Equation (6), the calculation of scattering amplitude of the SSA-2 is rather complex, as it requires the calculation of a fourfold integral.This involves a large amount of computation, and it takes a long time to perform the numerical simulation, which is the main drawback of the SSA-2.For more details about the numerical simulations mentioned above, please refer to Appendix A.
Additionally, to model the seawater dielectric constant, the Debye model is employed in all simulations, where the temperature equals 20 • C, and the salinity equals 35 ppt.For microwave scattering, the dielectric constant of the oil is much smaller than seawater; the oil layer can be regarded as a "transparent" layer.That is to say, the EM scattering energy is mainly contributed by the seawater under oil.Besides, the thickness of a surface film (either a monomolecular slick or a thin oil spill) is small compared with the penetration depth of microwaves into the water.Thus, in numerical simulation, the impact induced by the dielectric constant of slick has been neglected [23].

Impacts of Slick on the Sea Surface
The EM scattering field is highly dependent on the characteristics of the rough surface.To study the EM scattering from the slick-covered sea surface, it is necessary to make how the slick influences the sea surface clear.Therefore, in this part, the impacts of slicks on a clean sea surface are simulated and discussed from several aspects, including the sea curvature spectrum, the RMS height, RMS slope, and the autocorrelation function.

The Damping Ratio for Various Bands
According to Section 2, the damping ratio can be calculated with Equation (3). Figure 1 displays the damping ratios of two kinds of slicks.

Impacts of Slick on the Sea Surface
The EM scattering field is highly dependent on the characteristics of the rough surface.To study the EM scattering from the slick-covered sea surface, it is necessary to make how the slick influences the sea surface clear.Therefore, in this part, the impacts of slicks on a clean sea surface are simulated and discussed from several aspects, including the sea curvature spectrum, the RMS height, RMS slope, and the autocorrelation function.

The Damping Ratio for Various Bands
According to Section 2, the damping ratio can be calculated with Equation (3). Figure 1 displays the damping ratios of two kinds of slicks.In Figure 1, it is observed that the damping ratios first increase, and then decrease with sea wavenumber.There exist peak values for both kinds of slicks.For about k <100 rad/m, slick-b has a larger damping ratio, while for about k >100 rad/m, slick-a has a larger damping ratio.The damping effect becomes more significant with a larger fractional filling parameter F. According to Bragg scattering theory, the Bragg wavenumber of sea surface can be written as: where k e is the electromagnetic wavenumber, and θi is the incident angle.
Figure 2 shows the Bragg wavenumber ranges corresponding to L-band, C-band, X-band, and Ku-band electromagnetic waves, respectively.The damping ratios that correspond to F = 1 and F = 0.6 of two kinds of slicks for four bands are plotted as functions of the incident angles in Figure 2. In Figure 2a,c, it can be noted that the damping ratios for the X-band and Ku-band monotonically decrease with incident angle.While for the C-band, the damping ratio first increases and then decreases.For the L-band, the damping ratio monotonically increases with incident angle.In Figure 2b,d, it can be noted that the damping ratios for the C-band, X-band, and Ku-band decrease with incident angle.While for the L-band, the damping ratio increases with incident angle.The C-band has a larger damping ratio than the other three bands.Comparing Figure 2a with Figure 2c, and Figure 2b with Figure 2d, F makes significant influences on the damping ratios at four bands, which correspond to Figure 1.According to equations ( 3) and ( 8), we know that the Bragg wavenumbers that correspond to different bands are different, and the damping ratios for different Bragg wavenumbers are also different.As a consequence, the damping effects caused by slicks on the L-band, C-band, X-band, and Ku-band are different.In Figure 1, it is observed that the damping ratios first increase, and then decrease with sea wavenumber.There exist peak values for both kinds of slicks.For about k <100 rad/m, slick-b has a larger damping ratio, while for about k >100 rad/m, slick-a has a larger damping ratio.The damping effect becomes more significant with a larger fractional filling parameter F. According to Bragg scattering theory, the Bragg wavenumber of sea surface can be written as: where k e is the electromagnetic wavenumber, and θ i is the incident angle.
Figure 2 shows the Bragg wavenumber ranges corresponding to L-band, C-band, X-band, and Ku-band electromagnetic waves, respectively.The damping ratios that correspond to F = 1 and F = 0.6 of two kinds of slicks for four bands are plotted as functions of the incident angles in Figure 2. In Figure 2a,c, it can be noted that the damping ratios for the X-band and Ku-band monotonically decrease with incident angle.While for the C-band, the damping ratio first increases and then decreases.For the L-band, the damping ratio monotonically increases with incident angle.In Figure 2b,d, it can be noted that the damping ratios for the C-band, X-band, and Ku-band decrease with incident angle.While for the L-band, the damping ratio increases with incident angle.The C-band has a larger damping ratio than the other three bands.Comparing Figure 2a with Figure 2c, and Figure 2b with Figure 2d, F makes significant influences on the damping ratios at four bands, which correspond to Figure 1.According to equations (3) and ( 8), we know that the Bragg wavenumbers that correspond to different bands are different, and the damping ratios for different Bragg wavenumbers are also different.As a consequence, the damping effects caused by slicks on the L-band, C-band, X-band, and Ku-band are different.

Impacts of Slick on the Curvature Spectrum
A sea spectrum describes the distribution of each harmonic component of the sea surface as functions of the spatial wavenumber and wind direction.Usually, it can be expressed as:  is the angle between the observation angle and upwind direction.In the literature, various sea spectral models have been proposed; among these models, the Elfouhaily spectrum is one of the most widely used sea spectra in ocean remote sensing [24,25].In this work, the Elfouhaily spectrum is employed to describe sea waves.Figure 3 shows the impacts of the Marangoni damping effect (denoted as D), the reduction of friction velocity (denoted as R), and F on the curvature spectrum () w Bk , where ( ) The wind speed at 10-m height (U10) is set as 7 m/s.In Figure 3a, we can note that the short-gravity and capillary waves are damped significantly due to the Marangoni effect.In fact, the Marangoni effect mainly influences the small-scale waves, and it makes no influences on the large-scale waves.Moreover, slick-b has a heavier damping effect than slick-a when k <100 rad/m, while slick-a has a heavier damping effect when k >100 rad/m.Besides, the reduction of friction velocity mainly influences the large-scale waves and makes slight influences on the small-scale waves.The reduction of friction velocity is not associated with the properties of slicks.As illustrated in Figure 3b, the fractional filling factor F only influences the short-gravity and capillary waves.The differences between the two kinds of slicks become smaller when the value of F gets smaller.

Impacts of Slick on the Curvature Spectrum
A sea spectrum describes the distribution of each harmonic component of the sea surface as functions of the spatial wavenumber and wind direction.Usually, it can be expressed as: where S 0 (k w ) represents the omnidirectional part and f (k w , ϕ) represents the spreading function.ϕ is the angle between the observation angle and upwind direction.In the literature, various sea spectral models have been proposed; among these models, the Elfouhaily spectrum is one of the most widely used sea spectra in ocean remote sensing [24,25].In this work, the Elfouhaily spectrum is employed to describe sea waves.Figure 3 shows the impacts of the Marangoni damping effect (denoted as D), the reduction of friction velocity (denoted as R), and F on the curvature spectrum B(k w ), where B(k w ) = k 3 w S(k w ), and S(k w ) = π −π S(k w , ϕ)dϕ.The wind speed at 10-m height (U 10 ) is set as 7 m/s.In Figure 3a, we can note that the short-gravity and capillary waves are damped significantly due to the Marangoni effect.In fact, the Marangoni effect mainly influences the small-scale waves, and it makes no influences on the large-scale waves.Moreover, slick-b has a heavier damping effect than slick-a when k <100 rad/m, while slick-a has a heavier damping effect when k >100 rad/m.Besides, the reduction of friction velocity mainly influences the large-scale waves and makes slight influences on the small-scale waves.The reduction of friction velocity is not associated with the properties of slicks.As illustrated in Figure 3b, the fractional filling factor F only influences the short-gravity and capillary waves.The differences between the two kinds of slicks become smaller when the value of F gets smaller.

Impacts of Slick on the RMS Height and the RMS Slope
The profile of the sea spectrum changes when an oil slick presents on the sea surface, which results in changes in the slope variances and height variances.Figure 4 presents the RMS heights of the sea surfaces under different conditions.It can be observed in Figure 4 that the influences of the Marangoni effect and F on the RMS height are quite small.In addition, the curves of the two kinds of slicks are similar, and the reduction of friction velocity is the main reason for the reduction of the RMS height.Figure 5 shows the RMS slopes of sea surfaces plotted as functions of wind speed.In fact, the RMS height mainly depends on the large-scale waves, while the RMS slope depends both on the large-scale and the small-scale waves.Thus, unlike the RMS height, the influence of the reduction of the friction velocity on the RMS slope cannot be neglected.The influence caused by the Marangoni effect seems more obvious than the reduction of friction velocity.For Figure 5b, the value of F has a significant influence on the RMS slope.The RMS slope is also modulated by the physical property of different kinds of slicks.

Impacts of Slick on the RMS Height and the RMS Slope
The profile of the sea spectrum changes when an oil slick presents on the sea surface, which results in changes in the slope variances and height variances.Figure 4 presents the RMS heights of the sea surfaces under different conditions.It can be observed in Figure 4 that the influences of the Marangoni effect and F on the RMS height are quite small.In addition, the curves of the two kinds of slicks are similar, and the reduction of friction velocity is the main reason for the reduction of the RMS height.

Impacts of Slick on the RMS Height and the RMS Slope
The profile of the sea spectrum changes when an oil slick presents on the sea surface, which results in changes in the slope variances and height variances.Figure 4 presents the RMS heights of the sea surfaces under different conditions.It can be observed in Figure 4 that the influences of the Marangoni effect and F on the RMS height are quite small.In addition, the curves of the two kinds of slicks are similar, and the reduction of friction velocity is the main reason for the reduction of the RMS height.Figure 5 shows the RMS slopes of sea surfaces plotted as functions of wind speed.In fact, the RMS height mainly depends on the large-scale waves, while the RMS slope depends both on the large-scale and the small-scale waves.Thus, unlike the RMS height, the influence of the reduction of the friction velocity on the RMS slope cannot be neglected.The influence caused by the Marangoni effect seems more obvious than the reduction of friction velocity.For Figure 5b, the value of F has a significant influence on the RMS slope.The RMS slope is also modulated by the physical property of different kinds of slicks.Figure 5 shows the RMS slopes of sea surfaces plotted as functions of wind speed.In fact, the RMS height mainly depends on the large-scale waves, while the RMS slope depends both on the large-scale and the small-scale waves.Thus, unlike the RMS height, the influence of the reduction of the friction velocity on the RMS slope cannot be neglected.The influence caused by the Marangoni effect seems more obvious than the reduction of friction velocity.For Figure 5b, the value of F has a significant influence on the RMS slope.The RMS slope is also modulated by the physical property of different kinds of slicks.

Impacts of Slick on the Autocorrelation Function
The autocorrelation of the displacement field of the sea surface profile corresponds to the inverse Fourier transform of the sea spectrum.It describes the correlations between two arbitrary points on the rough surface.In the numerical simulation by the SSA-2, the scattering coefficient is related to the autocorrelation function.As limited by the length of the paper, we cannot provide a detailed discussion here; for more discussions about the autocorrelation function, please refer to Voronovich et al. [20].It is interesting to compare the autocorrelation functions of slick-free and slick-covered sea surfaces, since the correlation length and the autocorrelation function shape are also closely related to the roughness of the rough surface.
Figure 6 shows the autocorrelation functions normalized by the height variances of the sea surfaces.In Figure 6a, the impacts of slicks on the autocorrelation function are similar to the RMS height.The reduction of friction velocity is very influential upon the autocorrelation function.In contrast, the Marangoni effect changes the autocorrelation function slightly.In Figure 6b, the value of F also makes negligible influences on the autocorrelation function.Through Figure 6, it can be noted that the reduction of friction speed makes a shorter correlation length, and the two kinds of slicks produce similar impacts on the shape of autocorrelation functions.

NRCS of Slick-Free and Slick-Covered Sea Surfaces
In this part, the normalized radar cross-sections (NRCS) of slick-free and slick-covered sea surfaces are estimated according to Section 2. For slick-free sea surface, the NRCSs simulated by the SSA-2 are compared with those obtained using the geophysical model functions (GMFs), the classic

Impacts of Slick on the Autocorrelation Function
The autocorrelation of the displacement field of the sea surface profile corresponds to the inverse Fourier transform of the sea spectrum.It describes the correlations between two arbitrary points on the rough surface.In the numerical simulation by the SSA-2, the scattering coefficient is related to the autocorrelation function.As limited by the length of the paper, we cannot provide a detailed discussion here; for more discussions about the autocorrelation function, please refer to Voronovich et al. [20].It is interesting to compare the autocorrelation functions of slick-free and slick-covered sea surfaces, since the correlation length and the autocorrelation function shape are also closely related to the roughness of the rough surface.
Figure 6 shows the autocorrelation functions normalized by the height variances of the sea surfaces.In Figure 6a, the impacts of slicks on the autocorrelation function are similar to the RMS height.The reduction of friction velocity is very influential upon the autocorrelation function.In contrast, the Marangoni effect changes the autocorrelation function slightly.In Figure 6b, the value of F also makes negligible influences on the autocorrelation function.Through Figure 6, it can be noted that the reduction of friction speed makes a shorter correlation length, and the two kinds of slicks produce similar impacts on the shape of autocorrelation functions.

Impacts of Slick on the Autocorrelation Function
The autocorrelation of the displacement field of the sea surface profile corresponds to the inverse Fourier transform of the sea spectrum.It describes the correlations between two arbitrary points on the rough surface.In the numerical simulation by the SSA-2, the scattering coefficient is related to the autocorrelation function.As limited by the length of the paper, we cannot provide a detailed discussion here; for more discussions about the autocorrelation function, please refer to Voronovich et al. [20].It is interesting to compare the autocorrelation functions of slick-free and slick-covered sea surfaces, since the correlation length and the autocorrelation function shape are also closely related to the roughness of the rough surface.
Figure 6 shows the autocorrelation functions normalized by the height variances of the sea surfaces.In Figure 6a, the impacts of slicks on the autocorrelation function are similar to the RMS height.The reduction of friction velocity is very influential upon the autocorrelation function.In contrast, the Marangoni effect changes the autocorrelation function slightly.In Figure 6b, the value of F also makes negligible influences on the autocorrelation function.Through Figure 6, it can be noted that the reduction of friction speed makes a shorter correlation length, and the two kinds of slicks produce similar impacts on the shape of autocorrelation functions.

NRCS of Slick-Free and Slick-Covered Sea Surfaces
In this part, the normalized radar cross-sections (NRCS) of slick-free and slick-covered sea surfaces are estimated according to Section 2. For slick-free sea surface, the NRCSs simulated by the SSA-2 are compared with those obtained using the geophysical model functions (GMFs), the classic

NRCS of Slick-Free and Slick-Covered Sea Surfaces
In this part, the normalized radar cross-sections (NRCS) of slick-free and slick-covered sea surfaces are estimated according to Section 2. For slick-free sea surface, the NRCSs simulated by the SSA-2 are compared with those obtained using the geophysical model functions (GMFs), the classic TSM, and the SSA-1, respectively.For slick-covered sea surface, the simulated NRCSs of the SSA-2 are compared with the SAR data acquired by the C-band Radarsat-2 and the L-band uninhabited aerial vehicle synthetic aperture radar (UAVSAR).

NRCS of Slick-Free Sea Surfaces
GMFs are empirical models that are related to the incident angle, wind speed, and wind direction.The GMFs are often applied for wind field retrieval.It has been proven that GMFs could provide accurate predictions in practical applications.Thus, the NRCS estimated with GMFs can be regarded as reliable references.To evaluate the effectiveness of the SSA-2 for sea surface NRCSs estimation, in this part, the NRCSs calculated with the SSA-2 are compared with those obtained from L-band GMF [26], C-band CMOD7 [27], C-band CSARMOD [28], X-band XMOD2 [29], and Ku-band NSCAT4 [30], respectively.Besides, the SSA-2 is also compared with the classic TSM and the SSA-1.
Figure 7 shows the NRCSs computed using the SSA-1, the SSA-2, the TSM, and the GMFs.It should be noted that the L-band GMF can be employed only for HH polarization, the CMOD7 is valid for VV polarization, the CSARMOD is valid for both HH and VV polarizations, the XMOD2 is valid for VV polarization, and the NSCAT4 is valid for both HH and VV polarizations (where 'V' denotes the vertical polarization, and 'H' denotes the horizontal polarization).Firstly, in Figure 7, it can be noted that the difference between the SSA-1 and the SSA-2 is quite small both for HH and VV polarization.Compared with TSM, it is quite similar for incident angles larger than 30 • for all four bands.While the incident angle is smaller than 30 • , there exist larger differences among the C-band, X-band, and Ku-band.With respect to the SSA-2, the scattering coefficient is influenced by surface sample intervals and surface length.The discrepancies between the SSA-2 and TSM for incident angles smaller than 30 • at the C-band, X-band, and Ku-band may be introduced by the surface length.For an HV-polarized channel, the curves of the SSA-2 and the TSM are similar to each other.Through Figure 7a-d, compared with GMFs at different bands, the VV polarized scattering coefficient with the SSA-2 agrees well with the GMFs.While for HH-polarized channels at the C-band and Ku-band, there exist quite larger differences between the SSA-2 and the NSCAT4.That is to say, the SSA-2 simulates VV-polarized NRCS more accurately than HH polarization.
Remote Sens. 2018, 10, x FOR PEER REVIEW 8 of 20 TSM, and the SSA-1, respectively.For slick-covered sea surface, the simulated NRCSs of the SSA-2 are compared with the SAR data acquired by the C-band Radarsat-2 and the L-band uninhabited aerial vehicle synthetic aperture radar (UAVSAR).

NRCS of Slick-Free Sea Surfaces
GMFs are empirical models that are related to the incident angle, wind speed, and wind direction.The GMFs are often applied for wind field retrieval.It has been proven that GMFs could provide accurate predictions in practical applications.Thus, the NRCS estimated with GMFs can be regarded as reliable references.To evaluate the effectiveness of the SSA-2 for sea surface NRCSs estimation, in this part, the NRCSs calculated with the SSA-2 are compared with those obtained from L-band GMF [26], C-band CMOD7 [27], C-band CSARMOD [28], X-band XMOD2 [29], and Ku-band NSCAT4 [30], respectively.Besides, the SSA-2 is also compared with the classic TSM and the SSA-1.
Figure 7 shows the NRCSs computed using the SSA-1, the SSA-2, the TSM, and the GMFs.It should be noted that the L-band GMF can be employed only for HH polarization, the CMOD7 is valid for VV polarization, the CSARMOD is valid for both HH and VV polarizations, the XMOD2 is valid for VV polarization, and the NSCAT4 is valid for both HH and VV polarizations (where 'V' denotes the vertical polarization, and 'H' denotes the horizontal polarization).Firstly, in Figure 7, it can be noted that the difference between the SSA-1 and the SSA-2 is quite small both for HH and VV polarization.Compared with TSM, it is quite similar for incident angles larger than 30° for all four bands.While the incident angle is smaller than 30°, there exist larger differences among the C-band, X-band, and Ku-band.With respect to the SSA-2, the scattering coefficient is influenced by surface sample intervals and surface length.The discrepancies between the SSA-2 and TSM for incident angles smaller than 30° at the C-band, X-band, and Ku-band may be introduced by the surface length.For an HV-polarized channel, the curves of the SSA-2 and the TSM are similar to each other.Through Figure 7a-d, compared with GMFs at different bands, the VV polarized scattering coefficient with the SSA-2 agrees well with the GMFs.While for HH-polarized channels at the C-band and Ku-band, there exist quite larger differences between the SSA-2 and the NSCAT4.That is to say, the SSA-2 simulates VV-polarized NRCS more accurately than HH polarization.In Figure 8, we can note that the NRCSs of the SSA-1 are almost the same with the SSA-2.Combing the results presented in Figure 7, we can know that the NRCS estimated by the SSA-1 is precise enough in most cases.However, the drawback of the SSA-1 is that it cannot provide the estimation of cross-polarized NRCS in a backscattered direction.In Figure 8a, for the SSA-2 and the TSM, it is hard to say which method is better.These two methods have similar accuracies, with small overestimation or underestimation of the NRCSs for the small or large wind speed.In Figure 8b-d, for VV-polarized NRCS estimation, the SSA-2 seems better than the TSM.In fact, the differences between the SSA-2 and the TSM are not large.That is to say, the TSM is also an effective method in EM scattering computations.Meanwhile, the main disadvantage of the TSM is that it involves an arbitrary parameter, i.e., the scale-dividing parameter (k d , in this paper, k d = k i /3) separating the small-and large-scale components of the roughness.With respect to HH-polarized channels at the C-band and Ku-band, the curves of the SSA-2 are quite different from those of the GMFs.Assuming that the GMFs are precise enough, through the comparisons presented in Figure 8, we can know that the SSA-2 provides better results for a VV-polarized channel than an HH-polarized channel.The SSA-2 performs better than TSM at the C-band, X-band, and Ku-band.In Figure 8, we can note that the NRCSs of the SSA-1 are almost the same with the SSA-2.Combing the results presented in Figure 7, we can know that the NRCS estimated by the SSA-1 is precise enough in most cases.However, the drawback of the SSA-1 is that it cannot provide the estimation of cross-polarized NRCS in a backscattered direction.In Figure 8a, for the SSA-2 and the TSM, it is hard to say which method is better.These two methods have similar accuracies, with small overestimation or underestimation of the NRCSs for the small or large wind speed.In Figure 8b-d, for VV-polarized NRCS estimation, the SSA-2 seems better than the TSM.In fact, the differences between the SSA-2 and the TSM are not large.That is to say, the TSM is also an effective method in EM scattering computations.Meanwhile, the main disadvantage of the TSM is that it involves an arbitrary parameter, i.e., the scale-dividing parameter (kd, in this paper, kd = ki/3) separating the smalland large-scale components of the roughness.With respect to HH-polarized channels at the C-band and Ku-band, the curves of the SSA-2 are quite different from those of the GMFs.Assuming that the GMFs are precise enough, through the comparisons presented in Figure 8, we can know that the SSA-2 provides better results for a VV-polarized channel than an HH-polarized channel.The SSA-2 performs better than TSM at the C-band, X-band, and Ku-band.

NRCS of Slick-Covered Sea Surfaces at the C-Band
The RADARSAT-2 data acquired at the C-band has been employed to study oil spill on sea surfaces [31].The radarsat-2 data used in this part was acquired during the oil spill experiment

NRCS of Slick-Covered Sea Surfaces at the C-Band
The RADARSAT-2 data acquired at the C-band has been employed to study oil spill on sea surfaces [31].The radarsat-2 data used in this part was acquired during the oil spill experiment conducted by the Norway Clean Seas Association for Operating Companies (NOFO) in the North Sea [32].The acquisition time is 17:27 (UTC), 8 June 2011.The resolution in the range and azimuth directions are 5.2 m and 7.6 m, respectively.The incident angle is about 34.5~36.1 • .The dark area in Figure 9 is biogenetical slick.The wind speed is 1.6~3.3m/s.conducted by the Norway Clean Seas Association for Operating Companies (NOFO) in the North Sea [32].The acquisition time is 17:27 (UTC), 8 June 2011.The resolution in the range and azimuth directions are 5.2 m and 7.6 m, respectively.The incident angle is about 34.5~36.1°.The dark area in Figure 9 is biogenetical slick.The wind speed is 1.6~3.3m/s.In Figure 10, the NRCSs in VV, HH, and HV-polarized channels are presented, respectively.In the numerical simulation, the wind speed U10 is set as 3.3 m/s.The NRCSs of RADARSAT-2 data are extracted along the white line in Figure 9.As shown in Figure 10, for clean sea surface, the VV-polarized and HH-polarized NRCSs of the SSA-2 agree better with the RADARSAT-2 data than HV-polarized channel.For the slick-covered surface, the VV-polarized NRCS estimated with the SSA-2 is consistent with the RADARSAT-2 data when F = 0.7.It is well-known that the VV polarization channel is preferred because of its larger radar cross-section from the sea surface, which yields larger differences between the sea surfaces covered with and without oil slicks [33].Combining the results exhibited in Figure 10, we can note that the VV-polarized NRCS with the SSA-2 is more suitable to study the EM scattering than the HH and HV-polarizations.

NRCS of Slick-Covered Sea Surfaces at the L-Band
The L-band SAR images used in this part are acquired by uninhabited aerial vehicle synthetic aperture radar (UAVSAR) during the Deepwater Horizon (DWH) oil spill accident in the Gulf of Mexico in 2010 [34,35].UAVSAR is a fully polarimetric L-band SAR.The center frequency of the incident wave is 1.2575 GHz.Two multi-look (three and 12 looks in the range and azimuth directions, respectively) UAVSAR images with a 5-m slant range resolution and 7.In Figure 10, the NRCSs in VV, HH, and HV-polarized channels are presented, respectively.In the numerical simulation, the wind speed U 10 is set as 3.3 m/s.The NRCSs of RADARSAT-2 data are extracted along the white line in Figure 9.As shown in Figure 10, for clean sea surface, the VV-polarized and HH-polarized NRCSs of the SSA-2 agree better with the RADARSAT-2 data than HV-polarized channel.For the slick-covered surface, the VV-polarized NRCS estimated with the SSA-2 is consistent with the RADARSAT-2 data when F = 0.7.
conducted by the Norway Clean Seas Association for Operating Companies (NOFO) in the North Sea [32].The acquisition time is 17:27 (UTC), 8 June 2011.The resolution in the range and azimuth directions are 5.2 m and 7.6 m, respectively.The incident angle is about 34.5~36.1°.The dark area in Figure 9 is biogenetical slick.The wind speed is 1.6~3.3m/s.In Figure 10, the NRCSs in VV, HH, and HV-polarized channels are presented, respectively.In the numerical simulation, the wind speed U10 is set as 3.3 m/s.The NRCSs of RADARSAT-2 data are extracted along the white line in Figure 9.As shown in Figure 10, for clean sea surface, the VV-polarized and HH-polarized NRCSs of the SSA-2 agree better with the RADARSAT-2 data than HV-polarized channel.For the slick-covered surface, the VV-polarized NRCS estimated with the SSA-2 is consistent with the RADARSAT-2 data when F = 0.7.It is well-known that the VV polarization channel is preferred because of its larger radar cross-section from the sea surface, which yields larger differences between the sea surfaces covered with and without oil slicks [33].Combining the results exhibited in Figure 10, we can note that the VV-polarized NRCS with the SSA-2 is more suitable to study the EM scattering than the HH and HV-polarizations.

NRCS of Slick-Covered Sea Surfaces at the L-Band
The L-band SAR images used in this part are acquired by uninhabited aerial vehicle synthetic aperture radar (UAVSAR) during the Deepwater Horizon (DWH) oil spill accident in the Gulf of Mexico in 2010 [34,35].UAVSAR is a fully polarimetric L-band SAR.The center frequency of the incident wave is 1.2575 GHz.Two multi-look (three and 12 looks in the range and azimuth directions, respectively) UAVSAR images with a 5-m slant range resolution and 7.It is well-known that the VV polarization channel is preferred because of its larger radar cross-section from the sea surface, which yields larger differences between the sea surfaces covered with and without oil slicks [33].Combining the results exhibited in Figure 10, we can note that the VV-polarized NRCS with the SSA-2 is more suitable to study the EM scattering than the HH and HV-polarizations.

NRCS of Slick-Covered Sea Surfaces at the L-Band
The L-band SAR images used in this part are acquired by uninhabited aerial vehicle synthetic aperture radar (UAVSAR) during the Deepwater Horizon (DWH) oil spill accident in the Gulf of Mexico in 2010 [34,35].UAVSAR is a fully polarimetric L-band SAR.The center frequency of the incident wave is 1.2575 GHz.Two multi-look (three and 12 looks in the range and azimuth directions, respectively) UAVSAR images with a 5-m slant range resolution and 7.2-m azimuth resolution are employed in this part.The SAR images used in this work were acquired from two adjacent, overlapping flight tracks that covered the main oil spills in the Gulf of Mexico.The two flight lines are gulfco_14010_10054_100_100623 (hereafter denoted as Case (a)) and gulfco_32010_10054_101_100623 (hereafter denoted as Case (b)), respectively.More information about the data are summarized in Table 1 [33].The UAVSAR images are presented in Figure 11, where the dark areas indicate the oil spills.To compare the simulated results with the UAVSAR data, transects related to oil-free (red lines in Figure 11) as well as oil-covered sea surface (white lines in Figure 11) are extracted from SAR images and compared with the SSA-2 predictions.In order to compare the simulated results with measured data, the UAVSAR data are processed as follows.Firstly, a 100 × 3300 matrix is obtained by extracting 100 rows of pixels along the red and white lines in Figure 11.Then, a 1 × 3300 array can be obtained by computing the mean value of each column.Finally, the mean values are calculated in each 1 The UAVSAR images are presented in Figure 11, where the dark areas indicate the oil spills.To compare the simulated results with the UAVSAR data, transects related to oil-free (red lines in Figure 11) as well as oil-covered sea surface (white lines in Figure 11) are extracted from SAR images and compared with the SSA-2 predictions.In order to compare the simulated results with measured data, the UAVSAR data are processed as follows.Firstly, a 100 × 3300 matrix is obtained by extracting 100 rows of pixels along the red and white lines in Figure 11.Then, a 1 × 3300 array can be obtained by computing the mean value of each column.Finally, the mean values are calculated in each 1° incident angle range.Figure 12 presents the comparisons between the results simulated by the SSA-2 and UAVSAR data for sea surfaces without and with slicks, respectively.In Figure 12a, for slick-free sea surface, one can see that the VV-polarized NRCS simulated by the SSA-2 agrees well with the measured UAVSAR data.For HH polarization, the SSA-2 cannot provide a prediction as well as VV polarization.This conclusion is similar to the case of TSM presented by Wright et al. [36].For the cross-polarized NRCS, the differences between the SSA-2 and UAVSAR are quite large.Additionally, there exist small differences between two UAVSAR images.This may be attributed to the differences of the thickness or the filling proportion between the two images.With respect to sea surface covered with slicks, the NRCSs of slick-covered sea surface with F = 1 and F = 0.9 are plotted in Figure 12b, 12c, and 12d, respectively.In Figure 12b, the fractional filling factor F affects slick-b heavier than slick-a.The NRCS extracted from Case (a) agrees well with the results obtained based on slick-a for F = 1 and slick-b for F = 0.9.The NRCS extracted from Case (b) agrees well with the results obtained based on slick-a for F = 0.9.In fact, as the actual values of the physical parameters and the fractional filling factor for the oil spills in Figure 11 cannot be known, it is hard to compare the numerical results with measured data in detail.Figure 12 presents the comparisons between the results simulated by the SSA-2 and UAVSAR data for sea surfaces without and with slicks, respectively.In Figure 12a, for slick-free sea surface, one can see that the VV-polarized NRCS simulated by the SSA-2 agrees well with the measured UAVSAR data.For HH polarization, the SSA-2 cannot provide a prediction as well as VV polarization.This conclusion is similar to the case of TSM presented by Wright et al. [36].For the cross-polarized NRCS, the differences between the SSA-2 and UAVSAR are quite large.Additionally, there exist small differences between two UAVSAR images.This may be attributed to the differences of the thickness or the filling proportion between the two images.With respect to sea surface covered with slicks, the NRCSs of slick-covered sea surface with F = 1 and F = 0.9 are plotted in Figure 12b, 12c, and 12d, respectively.In Figure 12b, the fractional filling factor F affects slick-b heavier than slick-a.The NRCS extracted from Case (a) agrees well with the results obtained based on slick-a for F = 1 and slick-b for F = 0.9.The NRCS extracted from Case (b) agrees well with the results obtained based on slick-a for F = 0.9.In fact, as the actual values of the physical parameters and the fractional filling factor for the oil spills in Figure 11 cannot be known, it is hard to compare the numerical results with measured data in detail.For HH-polarized NRCS, as exhibited in Figure 12c, the numerical results match well with the UAVSAR data for incident angles from 25° to 55°.In Figure 12d, there exist large differences between the simulated results and measured data for cross-polarized NRCS.

Distinguishing Ability of Different Bands
In previous sections, both for slick-free and slick-covered sea surfaces, it has shown that the SSA-2 could provide an accurate prediction for VV-polarized NRCS.In order to study the capacities of different bands for oil distinguish further, the slick-to-water contrasts at different bands are studied based on VV polarization.A slick-to-water contrast can be defined as [11]: where 0  c is the NRCS of the slick-covered sea surface, and 0  f is the NRCS of the slick-free sea surface.A larger value of C indicates that slick makes a more significant influence on NRCS.As a consequence, it can be more easily separated from sea backgrounds.Thus, the slick-to-water contrast can be taken as a measurement of distinguishability for different bands to separate slicks from sea backgrounds.
Figure 13 shows the slick-to-water contrasts evaluated with the SSA-2 as functions of incident angles.A common scatterometer typically operates at a moderate incident angle between about 20-60°.Thus, the incident angle is limited from 20° to 60°.Both for slick-a and slick-b, it seems that the value of C is larger for the smaller incident angle.The distinguishing abilities of four bands change with incident angle.For slick-a, it seems that the X-band has a larger C-value than other three bands for incident angles smaller than about 35°.For incident angles between 35-60°, the C-band is preferred to distinguish slick-a.For slick-b, it seems that the C-band has a larger C-value than the For HH-polarized NRCS, as exhibited in Figure 12c, the numerical results match well with the UAVSAR data for incident angles from 25 • to 55 • .In Figure 12d, there exist large differences between the simulated results and measured data for cross-polarized NRCS.

Distinguishing Ability of Different Bands
In previous sections, both for slick-free and slick-covered sea surfaces, it has shown that the SSA-2 could provide an accurate prediction for VV-polarized NRCS.In order to study the capacities of different bands for oil distinguish further, the slick-to-water contrasts at different bands are studied based on VV polarization.A slick-to-water contrast can be defined as [11]: where σ c 0 is the NRCS of the slick-covered sea surface, and σ f 0 is the NRCS of the slick-free sea surface.A larger value of C indicates that slick makes a more significant influence on NRCS.As a consequence, it can be more easily separated from sea backgrounds.Thus, the slick-to-water contrast can be taken as a measurement of distinguishability for different bands to separate slicks from sea backgrounds.
Figure 13 shows the slick-to-water contrasts evaluated with the SSA-2 as functions of incident angles.A common scatterometer typically operates at a moderate incident angle between about 20-60 • .Thus, the incident angle is limited from 20 • to 60 • .Both for slick-a and slick-b, it seems that the value of C is larger for the smaller incident angle.The distinguishing abilities of four bands change with incident angle.For slick-a, it seems that the X-band has a larger C-value than other three bands for

A.2. The Second Order Small Slope Approximation
The EM scattering configuration is plotted in Figure A2.Assuming the EM wave incidents on the two-dimension sea surface z = h(r).The two-dimension sea surface height can be generated with the Monte-Carlo model.The incident wave vector denoted as k e i and the scattering wave vector denoted as k e s .θi, φi, θs, φs denote the incident angle, incident azimuth angle, scattering angle and scattering azimuth angle, respectively.

Appendix A.2 The Second Order Small Slope Approximation
The EM scattering configuration is plotted in Figure A2.Assuming the EM wave incidents on the two-dimension sea surface z = h(r).The two-dimension sea surface height can be generated with the Monte-Carlo model.The incident wave vector denoted as k e i and the scattering wave vector denoted as k e s .θ i , φ i , θ s , φ s denote the incident angle, incident azimuth angle, scattering angle and scattering azimuth angle, respectively.

A.2. The Second Order Small Slope Approximation
The EM scattering configuration is plotted in Figure A2.Assuming the EM wave incidents on the two-dimension sea surface z = h(r).The two-dimension sea surface height can be generated with the Monte-Carlo model.The incident wave vector denoted as k e i and the scattering wave vector denoted as k e s .θi, φi, θs, φs denote the incident angle, incident azimuth angle, scattering angle and scattering azimuth angle, respectively.

Figure 1 .
Figure 1.The damping ratios of different slicks and fractional filling factors (F).

6 Figure 1 .
Figure 1.The damping ratios of different slicks and fractional filling factors (F).

Figure 3 .
Figure 3.The curvature spectra, U10 = 7 m/s.(a) Influenced by the Marangoni effect and reduction of friction velocity, F = 1.(b) Influenced by F with D and R.

Figure 4 .
Figure 4.The RMS heights, U10 = 7 m/s.(a) Influenced by the Marangoni effect and the reduction of friction velocity, F = 1.(b) Influenced by F with D and R.

Figure 3 .
Figure 3.The curvature spectra, U 10 = 7 m/s.(a) Influenced by the Marangoni effect and reduction of friction velocity, F = 1.(b) Influenced by F with D and R.

Figure 3 .
Figure 3.The curvature spectra, U10 = 7 m/s.(a) Influenced by the Marangoni effect and reduction of friction velocity, F = 1.(b) Influenced by F with D and R.

Figure 4 .
Figure 4.The RMS heights, U10 = 7 m/s.(a) Influenced by the Marangoni effect and the reduction of friction velocity, F = 1.(b) Influenced by F with D and R.

Figure 4 .
Figure 4.The RMS heights, U 10 = 7 m/s.(a) Influenced by the Marangoni effect and the reduction of friction velocity, F = 1.(b) Influenced by F with D and R.

Figure 5 .
Figure 5.The root mean square (RMS) slopes of sea surfaces, U10 = 7 m/s.(a) Influenced by the Marangoni effect and reduction of friction velocity.(b) Influenced by F with D and R.

Figure 6 .
Figure 6.The autocorrelation functions, U10 = 7 m/s.(a) Influenced by the Marangoni effect and reduction of friction velocity.(b) Influenced by F with D and R.

6 Figure 5 .
Figure 5.The root mean square (RMS) slopes of sea surfaces, U 10 = 7 m/s.(a) Influenced by the Marangoni effect and reduction of friction velocity.(b) Influenced by F with D and R.

Figure 5 .
Figure 5.The root mean square (RMS) slopes of sea surfaces, U10 = 7 m/s.(a) Influenced by the Marangoni effect and reduction of friction velocity.(b) Influenced by F with D and R.

Figure 6 .
Figure 6.The autocorrelation functions, U10 = 7 m/s.(a) Influenced by the Marangoni effect and reduction of friction velocity.(b) Influenced by F with D and R.

Figure 6 .
Figure 6.The autocorrelation functions, U 10 = 7 m/s.(a) Influenced by the Marangoni effect and reduction of friction velocity.(b) Influenced by F with D and R.

Figure 8
Figure 8 illustrates the NRCSs estimated with different methods under different wind speeds.In Figure8, we can note that the NRCSs of the SSA-1 are almost the same with the SSA-2.Combing the results presented in Figure7, we can know that the NRCS estimated by the SSA-1 is precise enough in most cases.However, the drawback of the SSA-1 is that it cannot provide the estimation of cross-polarized NRCS in a backscattered direction.In Figure8a, for the SSA-2 and the TSM, it is hard to say which method is better.These two methods have similar accuracies, with small overestimation or underestimation of the NRCSs for the small or large wind speed.In Figure8b-d, for VV-polarized NRCS estimation, the SSA-2 seems better than the TSM.In fact, the differences between the SSA-2 and the TSM are not large.That is to say, the TSM is also an effective method in EM scattering computations.Meanwhile, the main disadvantage of the TSM is that it involves an arbitrary parameter, i.e., the scale-dividing parameter (k d , in this paper, k d = k i /3) separating the small-and large-scale components of the roughness.With respect to HH-polarized channels at the C-band and Ku-band, the curves of the SSA-2 are quite different from those of the GMFs.Assuming that the GMFs are precise enough, through the comparisons presented in Figure8, we can know that the SSA-2 provides better results for a VV-polarized channel than an HH-polarized channel.The SSA-2 performs better than TSM at the C-band, X-band, and Ku-band.

Figure 8
Figure 8 illustrates the NRCSs estimated with different methods under different wind speeds.In Figure8, we can note that the NRCSs of the SSA-1 are almost the same with the SSA-2.Combing the results presented in Figure7, we can know that the NRCS estimated by the SSA-1 is precise enough in most cases.However, the drawback of the SSA-1 is that it cannot provide the estimation of cross-polarized NRCS in a backscattered direction.In Figure8a, for the SSA-2 and the TSM, it is hard to say which method is better.These two methods have similar accuracies, with small overestimation or underestimation of the NRCSs for the small or large wind speed.In Figure8b-d, for VV-polarized NRCS estimation, the SSA-2 seems better than the TSM.In fact, the differences between the SSA-2 and the TSM are not large.That is to say, the TSM is also an effective method in EM scattering computations.Meanwhile, the main disadvantage of the TSM is that it involves an arbitrary parameter, i.e., the scale-dividing parameter (kd, in this paper, kd = ki/3) separating the smalland large-scale components of the roughness.With respect to HH-polarized channels at the C-band and Ku-band, the curves of the SSA-2 are quite different from those of the GMFs.Assuming that the GMFs are precise enough, through the comparisons presented in Figure8, we can know that the SSA-2 provides better results for a VV-polarized channel than an HH-polarized channel.The SSA-2 performs better than TSM at the C-band, X-band, and Ku-band.

Figure 12 .
Figure 12.Comparison between the estimations of the SSA-2 and UAVSAR data.(a) Slick-free sea surface.(b) Slick-covered sea surface for VV polarization.(c) Slick-covered sea surface for HH polarization.(d) Slick-covered sea surface for HV polarization.

Figure 12 .
Figure 12.Comparison between the estimations of the SSA-2 and UAVSAR data.(a) Slick-free sea surface.(b) Slick-covered sea surface for VV polarization.(c) Slick-covered sea surface for HH polarization.(d) Slick-covered sea surface for HV polarization.

Figure A2 .
Figure A2.Configuration of EM scattering from sea surface.

Figure A2 .
Figure A2.Configuration of EM scattering from sea surface.Figure A2.Configuration of EM scattering from sea surface.

Figure A2 .
Figure A2.Configuration of EM scattering from sea surface.Figure A2.Configuration of EM scattering from sea surface.