Dual-Polarized L-Band SAR Imagery for Temporal Monitoring of Marine Oil Slick Concentration

SAR sensors are usually used in the offshore domain to detect marine oil slicks which allows the authorities to guide cleanup operations or prosecute polluters. As radar imagery can be used any time of day or year and in almost any weather conditions, the use and programming of such remote sensing data is usually favored over optical imagery. Nevertheless, images collected in the optical domain provide access to key information not accessible today by SAR instruments, such as the thickness or the amount of pollutant. To address this knowledge gap, a methodology based on the joint use of a scattering model (U-WCA) and remote sensing data collected by a low frequency (e.g., L-band) imaging radar over controlled release of mineral oil spill is reported in this paper. The proposed method allows estimation of the concentration of pollutant within an oil-in-water mixture as well as the temporal variation of this quantity due to weathering processes.


Introduction
The authorities and petroleum companies usually use airborne and spaceborne SAR (Synthetic Aperture Radar) images to detect and monitor marine slicks [1,2]. In an operational context, radar images are favored over optical ones because radar can be used any time and in almost any weather conditions [3][4][5]. In the microwave regime, the ocean surface is modelled as a set of slightly rough tilted facets that contributes to the backscattering of the Electromagnetic (EM) wave. Each facet has superimposed small-scale surface roughness that creates a Bragg scatterer when the wind-driven roughness scale is commensurate with the radar wavelength [6]. When oil is released in the marine environment, these scales of roughness, namely the capillary and short gravity waves, are damped, and slick-covered surface appears as a low backscattering area in the SAR image [7].
While remote sensing instruments operating in the microwave domain are of great interest for detecting and monitoring maritime pollution, some issues remain unresolved when using SAR images only, such as the characterization and the quantification of the detected substance [2,7]. Characterization aims at distinguishing between anthropic and biogenic oil slicks. Quantification is the estimation of the amount of pollutant within the spilled area and is investigated in this paper.
The EM frequency is of primary importance when imaging the ocean surface and particularly for remotely sensed slick-covered area [8][9][10]. High-frequency imaging radars (e.g., X-or C-band) are preferable to those operating at lower frequency (e.g., L-band) for mineral oil slick detection [8]. SAR data collected at L-band allows definition of the characteristics of a marine slick along a level ranging from thin surface films to oil-in-water emulsion [10,11]. In any case, the instrument noise is a Remote Sens. 2018, 10, 1012 3 of 17

Bragg Scattering Theory
In the microwave regime, the ocean surface, when imaged by a remote sensing system with incidence angles ranging from around 30 to 60 • , is considered to be a rough surface for which the dominant scattering mechanism is Bragg scattering [6]. In that case, the EM signal backscattered by the sea depends strongly on the polarization state of the transmitted wave [24]. The dual-co-polarized radar backscattered power is proportional to the normalized radar cross-section (NRCS), which is defined in the Bragg scattering theory [6] as where the subscript p denotes either H (horizontal) or V (vertical) polarization; k EM = 2π/λ EM is the EM wavenumber corresponding to the radar wavelength, λ EM ; Γ pp is the reflectivity; W(k B ) is the spectral density of the ocean surface roughness evaluated at the so-called Bragg wavenumber, k B ; and θ i is the radar local incidence angle. In the Bragg scattering theory, the backscatter power is higher in vertical polarization than in horizontal, ensuring a polarization ratio (PR) smaller than unity.
Although dominant, Bragg scattering is not the only scattering mechanism which contributes to the total backscattered energy from the ocean surface. Non-resonant mechanisms generally associated with large-scale events (e.g., breaking waves, whitecaps . . . ) contribute to the signal backscattered by the sea surface. Those events are frequency-dependent and explain the deviation commonly observed between experimental observations and model estimations [18,19], mainly in high-frequency imaging radar (e.g., X-and C-band). At lower frequency (e.g., L-band), it has been reported that the relative impact of those non-Bragg mechanisms with respect to the total power scattered from the ocean surface is negligible [20].
Thus, at L-band the EM signal backscattered by the ocean surface is well modeled by the Bragg theory and it comes from (1)-(3) that the polarization ratio depends mainly on the local incidence angle and the dielectric properties of the sea surface [6,11,21].

Impact of Oil on the Sea Surface
When oil is released in the marine environment, it can behave in two different ways: it can either manifest as a film on the top of the sea surface or mix with the seawater within the water column. In the first case (film or sheen), the product surface layer will damp the gravity-capillary waves, which are the main contributors to backscattered EM signal, thereby attenuating the radar backscattered power. As discussed above, this attenuation of the surface roughness should not have significant impact on the polarization ratio at L-band (see [12] Figure 13d). Moreover, as the film thickness usually encountered (µm to mm [5]) is small compared to the penetration depth [12], the EM wave is not attenuated and penetrates the film to scatter from the seawater underneath. Therefore, the effective dielectric constant remains that of seawater and is not changed by the different dielectric constant of the oil film. As a result, at low EM frequency, the measured polarization ratio over film-covered sea surface is close to that measured over the surrounding uncovered sea surface.
In the second case (oil-in-water emulsion), the mixture between oil and seawater modifies the dielectric properties of the remotely sensed surface, thus impacting the reflection coefficients of the scattering process as well as the value of the polarization ratio with respect to the surrounding clean-sea surface.
Please note that an oil layer at sea is quickly spread and mixed within the water column by weathering processes such as natural wind stress and waves motion. At the resolution cell scale, an emulsion and a partially covered surface have a similar impact on the Polarization Ratio. In this paper, it is assumed that the slick is homogeneous at the pixel scale (metric in this experiment) and the distinction between covered, partially covered and uncovered surface can be done using a detection method based on, for example, the Polarization Difference [10,14] which is mostly impacted by the sea surface roughness.
The polarization ratio of low-frequency imaging radars allows measurement of the dielectric properties of both seawater and oil-in-water mixture. For slick-free or slick-covered area, those properties are described by the complex relative dielectric constant, ε, defined as The dielectric constant is material-dependent. Typical values are given in Table 1, taken from [25] for seawater and from [26,27] for mineral oil. Values for mineral oil are nearly constant in the range 1-10 GHz, with a loss factor (imaginary component) close to zero, suggesting a non-negligible penetration of the EM wave through this medium. A linear mixing model is often employed [11,12] between mineral oil and seawater (5) to estimate the effective dielectric constant of an oil-in-water mixture, ε eff . However, a more relevant approach from the Effective Medium Theory [28] advocates the use of the Bruggeman formula (6) to estimate the effective complex dielectric constant of such a mixture [21]: where υ, ranging from 0 to 1, is the oil content (in volume) of the oil-water mixture, and ε w and ε oil are the relative dielectric constant of seawater and oil, respectively ( Table 1). The real and imaginary parts of the effective dielectric constant of an oil-in-water emulsion are displayed in Figure 1 as a function of the oil content (in percentage) for both linear (blue curve) and Bruggeman's model (red curve). One can observe a strong overestimation of both real and imaginary parts of the effective dielectric constant with the linear model compared to the Bruggeman formula. This overestimation is more pronounced at high concentration of oil (oil content~60-80%). In the following, the Bruggeman formula will be adopted to estimate the effective dielectric constant of an oil-in-water emulsion.
of the effective dielectric constant of an oil-in-water emulsion are displayed in Figure 1 as a function of the oil content (in percentage) for both linear (blue curve) and Bruggeman's model (red curve). One can observe a strong overestimation of both real and imaginary parts of the effective dielectric constant with the linear model compared to the Bruggeman formula. This overestimation is more pronounced at high concentration of oil (oil content~60-80%). In the following, the Bruggeman formula will be adopted to estimate the effective dielectric constant of an oil-in-water emulsion.

NOFO'2015 Oil-on-Water Exercise
In June 2015, the NOFO (Norwegian Clean Seas Association for Operating Companies) has managed controlled releases of mineral oil at sea to test mechanical recovery systems. The oil spill cleanup exercise was carried out in the North Sea between the Norway and the United Kingdom within 10 Nautical Miles of position 59 • 59'N, 02 • 27'E. In the following we will focus on the 9 June exercises, during which the MOS Sweeper [29] and DESMI Boom [30] systems were tested at sea ( Figure 2). For both experiments, hydrocarbons were released by a floating pump at the sea surface towed by a leading vessel (Stril Mariner) and recovered by a second vessel (Stril Luna), at only a few hundred meters. Figure 3 shows an illustration of the offshore spill area taken from a balloon during the MOS Sweeper experiment.

NOFO'2015 Oil-on-Water Exercise
In June 2015, the NOFO (Norwegian Clean Seas Association for Operating Companies) has managed controlled releases of mineral oil at sea to test mechanical recovery systems. The oil spill cleanup exercise was carried out in the North Sea between the Norway and the United Kingdom within 10 Nautical Miles of position 59°59'N, 02°27'E. In the following we will focus on the 9 June exercises, during which the MOS Sweeper [29] and DESMI Boom [30] systems were tested at sea ( Figure 2). For both experiments, hydrocarbons were released by a floating pump at the sea surface towed by a leading vessel (Stril Mariner) and recovered by a second vessel (Stril Luna), at only a few hundred meters. Figure 3 shows an illustration of the offshore spill area taken from a balloon during the MOS Sweeper experiment.   Trials with MOS Sweeper and DESMI Boom were conducted, respectively, in the morning (from 06:00 until 10:30 UTC) and in the afternoon (from 12:30 until 15:00 UTC) of June 9, using 45 m 3 of mineral oil for MOS Sweeper and 35 m 3 for DESMI Boom. The released product is an emulsion of mineral oil-in-water, with a water content of 60%. It consists of a mixture of seawater, Oseberg crude oil and a small addition of IFO 380 (Intermediate Fuel Oil or marine diesel oil, with viscosity of 380 mm 2 ·s −1 ). The emulsion was prepared onshore by the NOFO several weeks before the exercises at sea. The stability and the exact constitution of the spilled product at the time of the exercise is therefore not precisely known. Trials with MOS Sweeper and DESMI Boom were conducted, respectively, in the morning (from 06:00 until 10:30 UTC) and in the afternoon (from 12:30 until 15:00 UTC) of June 9, using 45 m 3 of mineral oil for MOS Sweeper and 35 m 3 for DESMI Boom. The released product is an emulsion of mineral oil-in-water, with a water content of 60%. It consists of a mixture of seawater, Oseberg crude oil and a small addition of IFO 380 (Intermediate Fuel Oil or marine diesel oil, with viscosity of 380 mm 2 ·s −1 ). The emulsion was prepared onshore by the NOFO several weeks before the exercises at sea. The stability and the exact constitution of the spilled product at the time of the exercise is therefore not precisely known.
Wind and waves information during the oil spill cleanup exercises was obtained from the Norwegian Meteorological Institute and is given in Table 2.

Airborne SAR Acquisitions
Polarimetric SAR (POLSAR) images were recorded during the oil-in-water exercise by SETHI, the airborne remote sensing system developed by ONERA [23]. POLSAR data in linear basis (HH, HV, VH, VV) were collected at L-band (EM frequency of 1.325 GHz) with a transmitted bandwidth equal to 150 MHz (range resolution of 1 m) and processed with an azimuth resolution of 1 m. The imaged area is 9.5 km in azimuth and 1.5 km in range, with incidence angles from 34 • to 52 • . SETHI is a high-resolution imaging radar characterized by a low instrument noise floor, see Figure 4 reproduced from [12], allowing a sufficiently high SNR over marine slick for efficient surface properties estimation.
The SETHI remote sensing system flew over the oil spill area during the two cleanup exercises and collected SAR images throughout the 9 of June. In the following, four SAR scenes are investigated: three collected during the MOS Sweeper experiment at 09:37, 10:02 and 10:27 UTC and one at 13:30 UTC during the DESMI Boom exercise, cf. Table 3. The last one (run 4) was acquired 3 h after the last image of the MOS Sweeper exercise (run 3). Nevertheless, this image still contains part of the spill released during the morning experiment, MOS Sweeper, cf. HV, VH, VV) were collected at L-band (EM frequency of 1.325 GHz) with a transmitted bandwidth equal to 150 MHz (range resolution of 1 m) and processed with an azimuth resolution of 1 m. The imaged area is 9.5 km in azimuth and 1.5 km in range, with incidence angles from 34° to 52°. SETHI is a high-resolution imaging radar characterized by a low instrument noise floor, see Figure 4 reproduced from [12], allowing a sufficiently high SNR over marine slick for efficient surface properties estimation. The SETHI remote sensing system flew over the oil spill area during the two cleanup exercises and collected SAR images throughout the 9 of June. In the following, four SAR scenes are investigated: three collected during the MOS Sweeper experiment at 09:37, 10:02 and 10:27 UTC and one at 13:30 UTC during the DESMI Boom exercise, cf. Table 3. The last one (run 4) was acquired 3 h after the last image of the MOS Sweeper exercise (run 3). Nevertheless, this image still contains part of the spill released during the morning experiment, MOS Sweeper, cf. Figure 5-red box. A 4-h temporal monitoring of this spill is then possible, between 09:37 UTC and 13:30 UTC.  . SETHI instrument noise floor (NESZ) plotted by increasing incidence angle-reproduced from [12].  The four SAR scenes investigated in this paper have been projected from the slant range to the ground range geometry ( Figure 6). The spilled area has been automatically detected using the polarization difference (in linear unit) between VV and HH channels [10,12,14,31] and the temporal evolution of the detected area is pictured on Figure 7 in a false color representation: drifting of the MOS Sweeper spill for one hour (from 09:37 to 10:27 UTC) in the morning of 9 June ( Figure 7a) and drifting of the spill for four hours (from 09:37 to 13:30 UTC), Figure 7b. The spilled product during the MOS Sweeper exercise has drifted in the North-East direction, under the influence of wind (coming from 250°, cf. Table 2). The distance traveled by the spill between the first (09:37) and the last acquisition (13:30) is about 1.8 km in 4 h, which corresponds to a drift speed of about 0.125 m·s −1 . The four SAR scenes investigated in this paper have been projected from the slant range to the ground range geometry ( Figure 6). The spilled area has been automatically detected using the polarization difference (in linear unit) between VV and HH channels [10,12,14,31] and the temporal evolution of the detected area is pictured on Figure 7 Table 2). The distance traveled by the spill between the first (09:37) and the last acquisition (13:30) is about 1.8 km in 4 h, which corresponds to a drift speed of about 0.125 m·s −1 . evolution of the detected area is pictured on Figure 7 in a false color representation: drifting of the MOS Sweeper spill for one hour (from 09:37 to 10:27 UTC) in the morning of 9 June (Figure 7a) and drifting of the spill for four hours (from 09:37 to 13:30 UTC), Figure 7b. The spilled product during the MOS Sweeper exercise has drifted in the North-East direction, under the influence of wind (coming from 250°, cf. Table 2). The distance traveled by the spill between the first (09:37) and the last acquisition (13:30) is about 1.8 km in 4 h, which corresponds to a drift speed of about 0.125 m·s −1 .

Estimation of Oil Concentration in an Oil-in-Water Slick Emulsion
As discussed in Paragraph 2, the ratio between the two dual-co-polarized channels (3), at low frequency (e.g., L-band), is a useful quantity for measuring the concentration of oil within a marine slick [21]. The approach presented in this paper is based on the comparison between the polarization ratio measured by a radar operating at L-band and the values estimated by an analytical scattering model, namely the Universal Weighted Curvature Approximation (U-WCA), [22].

The Universal Weighted Curvature Approximation Scattering Model
With a remote sensing imaging radar collecting data at L-band, PR is only slightly impacted by changes in surface roughness but is mainly varying with the local incidence angle and the dielectric properties of the surface [11,12,21]. The proposed methodology for estimating the proportion of oil in an oil-in-water mixture is based on the comparison between the experimental value of PR with a scattering model, the Universal Weighted Curvature Approximation.
The U-WCA scattering model [22] belongs to the family of so-called "unified models" [32], such as the Two Scale Models (TSM) [6,33] or the Small-Slope Approximation [34], that is models which

Estimation of Oil Concentration in an Oil-in-Water Slick Emulsion
As discussed in Paragraph 2, the ratio between the two dual-co-polarized channels (3), at low frequency (e.g., L-band), is a useful quantity for measuring the concentration of oil within a marine slick [21]. The approach presented in this paper is based on the comparison between the polarization ratio measured by a radar operating at L-band and the values estimated by an analytical scattering model, namely the Universal Weighted Curvature Approximation (U-WCA), [22].

The Universal Weighted Curvature Approximation Scattering Model
With a remote sensing imaging radar collecting data at L-band, PR is only slightly impacted by changes in surface roughness but is mainly varying with the local incidence angle and the dielectric properties of the surface [11,12,21]. The proposed methodology for estimating the proportion of oil in an oil-in-water mixture is based on the comparison between the experimental value of PR with a scattering model, the Universal Weighted Curvature Approximation.
The U-WCA scattering model [22] belongs to the family of so-called "unified models" [32], such as the Two Scale Models (TSM) [6,33] or the Small-Slope Approximation [34], that is models which are able to cope with both large scales and small ripples at the sea surface. The U-WCA model leads to non-trivial roughness-dependent PR but has the considerable advantage of a simple formulation involving the nominal incidence angle only and requiring no facet decomposition. The expression of the co-polarized NRCS given by the U-WCA model is as follows where Is is proportional to the classical Kirchhoff integral and Bpp and K are the Bragg and the Kirchhoff kernels [32], respectively. In the Two Scale approach, ocean surfaces are usually modelled as a composition of slightly rough tilted facets, each of which has superimposed small-scale surface roughness that creates a Bragg scattering [6]. Small-scale roughness is randomly distributed on the scattering surface and responds to the strength of local wind, i.e., gravity-capillary waves. The tilt of the facet is caused by larger-scale waves on the ocean surface that changes the local orientation, or tilt, of the short waves [35]. The orientation of the facet changes the value of the local incidence angle of the EM wave interacting with the surface and therefore the levels of the backscattered signal and the polarization ratio. In general, a precise knowledge of the local incidence angle is not available; an approximation from SAR data can be obtained from an uncovered area close to the oil slick assuming homogeneous large-scale phenomena over the entire imaged area [11]. To overcome this strong limitation, the use of the U-WCA scattering model allows estimation of the polarization ratio without requiring the knowledge of the locale incidence angle [21,22], resulting from the local tilt of the facets composing the sea surface. In this paper, the polarization ratio measured by a radar sensor is compared to those estimated by the U-WCA model, the difference over slick covered area being linked to the modification of the effective dielectric constant compared to the surrounding clean sea surface.
PR values estimated with the U-WCA scattering model at 1.325 GHz are shown Figure 8. The simulation has been carried out in the upwind direction with the U-WCA scattering model using the classical Elfouhaily [36] sea surface directional spectrum. As expected, we observe strong variations of PR with the incidence angle but few variations with the sea surface roughness (Figure 8a). On the contrary, for a given value of incidence angle, PR values are strongly varying with the oil content into the oil-in-water mixture, especially for high oil concentration rates (Figure 8b). One can also note the strong difference between the Bragg theory (Figure 8a-black dotted line) and the U-WCA model (Figure 8a-colored full line). By construction, the U-WCA model, which is a weighted summation of Bragg and Kirchhoff kernels (see Equation (7)), produces higher PR than the pure Bragg model (recall that the Kirchhoff PR is one). This explains the discrepancy between the PR values computed using the Bragg theory (Equations (1)-(3)) and the U-WCA scattering model (Equation (3) with the HH and VV NRCS given by Equation (7)). also note the strong difference between the Bragg theory (Figure 8a-black dotted line) and the U-WCA model (Figure 8a-colored full line). By construction, the U-WCA model, which is a weighted summation of Bragg and Kirchhoff kernels (see Equation (7)), produces higher PR than the pure Bragg model (recall that the Kirchhoff PR is one). This explains the discrepancy between the PR values computed using the Bragg theory (Equations (1)-(3)) and the U-WCA scattering model (Equation (3) with the HH and VV NRCS given by Equation (7)).

Comparison with L-Band Remote Sensing Data
A comparison between experimental and theoretical values of the polarization ratio at L-band is of primary importance and is displayed in Figure 9 with environmental conditions given in Table 2.  (Table 3, run 2). We found a very good agreement between the PR values estimated by U-WCA (Figure 9a-black dotted line) and those measured by the SAR sensor over uncovered sea surface (Figure 9a-blue line). This confirms that at low EM frequency (e.g., L-band) the relative contribution of the non-polarized component with respect to the total power scattered from the ocean surface is negligible and hence that the scattering model can be used as a reference. The impact of mineral oil on the PR values is obvious, with a marked difference between histograms computed over free sea surface (Figure 9b-blue line) and covered area (Figure 9b-red line). This difference is due to the variation of the dielectric properties between the mineral oil slick and the surrounding clean sea surface. The quantitative estimation of the proportion of oil in an oil-in-water emulsion is made possible by comparing the PR measured by the remote sensing SAR data at L-band and the values estimated by the U-WCA scattering model, using a previously calculated data sheet (Figure 10a) allowing quick oil concentration estimation to meet operational constraints. For a given value of incidence angle, the unicity of the estimate is ensured by the monotonic variation of PR with the oil concentration (Figure 10a).

Comparison with L-Band Remote Sensing Data
A comparison between experimental and theoretical values of the polarization ratio at L-band is of primary importance and is displayed in Figure 9 with environmental conditions given in Table 2.  (Table 3, run 2). We found a very good agreement between the PR values estimated by U-WCA (Figure 9a-black dotted line) and those measured by the SAR sensor over uncovered sea surface (Figure 9a-blue line). This confirms that at low EM frequency (e.g., L-band) the relative contribution of the non-polarized component with respect to the total power scattered from the ocean surface is negligible and hence that the scattering model can be used as a reference. The impact of mineral oil on the PR values is obvious, with a marked difference between histograms computed over free sea surface (Figure 9b-blue line) and covered area (Figure 9b-red line). This difference is due to the variation of the dielectric properties between the mineral oil slick and the surrounding clean sea surface. The quantitative estimation of the proportion of oil in an oil-in-water emulsion is made possible by comparing the PR measured by the remote sensing SAR data at L-band and the values estimated by the U-WCA scattering model, using a previously calculated data sheet (Figure 10a) allowing quick oil concentration estimation to meet operational constraints. For a given value of incidence angle, the unicity of the estimate is ensured by the monotonic variation of PR with the oil concentration ( Figure 10a).
The data sheet of PR values estimated at L-band with the Bragg theory is displayed in Figure 10b. Compared to the U-WCA reference map (Figure 10a), the use of the Bragg model results in a strong overestimation of the oil concentration of a marine slick: an incidence angle of 45 • and an actual value of PR value of 0.3 lead to an oil concentration estimate of 65% and 77% using the U-WCA (Figure 10a) and the Bragg model (Figure 10b The data sheet of PR values estimated at L-band with the Bragg theory is displayed in Figure  10b. Compared to the U-WCA reference map (Figure 10a), the use of the Bragg model results in a strong overestimation of the oil concentration of a marine slick: an incidence angle of 45° and an actual value of PR value of 0.3 lead to an oil concentration estimate of 65% and 77% using the U-WCA (Figure 10a) and the Bragg model (Figure 10b), respectively.

Quantifying the Concentration of Oil within a Marine Slick with Real Airborne SAR Data
The methodology described in section 4 has been first applied to L-band SAR data collected by SETHI at 10:02 during the MOS Sweeper oil spill exercise (Table 3, run 2). A VV polarized image is displayed in Figure 11 together with the experimental PR and the estimated oil concentration maps. A detection mask has first been applied, based on the thresholding of the polarization difference [10,12,14,31]. The ranges of variation of PR values and oil concentrations have been reduced to 0.15-0.35 and 20-80%, respectively, to enhance the visualization.
On the PR map (Figure 11b), one can observe strong variations of the PR values in the range direction due to the incidence angle changes across the swath. The second-order variation is due to the modification of the dielectric properties of the surface related to the oil content within the oil-in-water mixture. The oil concentration is estimated by firstly, selecting, for each pixel, the closest value between the actual PR and those given by the U-WCA data sheet (Figure 10a) and then by The data sheet of PR values estimated at L-band with the Bragg theory is displayed in Figure  10b. Compared to the U-WCA reference map (Figure 10a), the use of the Bragg model results in a strong overestimation of the oil concentration of a marine slick: an incidence angle of 45° and an actual value of PR value of 0.3 lead to an oil concentration estimate of 65% and 77% using the U-WCA (Figure 10a) and the Bragg model (Figure 10b), respectively.

Quantifying the Concentration of Oil within a Marine Slick with Real Airborne SAR Data
The methodology described in section 4 has been first applied to L-band SAR data collected by SETHI at 10:02 during the MOS Sweeper oil spill exercise (Table 3, run 2). A VV polarized image is displayed in Figure 11 together with the experimental PR and the estimated oil concentration maps. A detection mask has first been applied, based on the thresholding of the polarization difference [10,12,14,31]. The ranges of variation of PR values and oil concentrations have been reduced to 0.15-0.35 and 20-80%, respectively, to enhance the visualization.
On the PR map (Figure 11b), one can observe strong variations of the PR values in the range direction due to the incidence angle changes across the swath. The second-order variation is due to the modification of the dielectric properties of the surface related to the oil content within the oil-in-water mixture. The oil concentration is estimated by firstly, selecting, for each pixel, the closest value between the actual PR and those given by the U-WCA data sheet (Figure 10a) and then by

Quantifying the Concentration of Oil within a Marine Slick with Real Airborne SAR Data
The methodology described in Section 4 has been first applied to L-band SAR data collected by SETHI at 10:02 during the MOS Sweeper oil spill exercise (Table 3, run 2). A VV polarized image is displayed in Figure 11 together with the experimental PR and the estimated oil concentration maps. A detection mask has first been applied, based on the thresholding of the polarization difference [10,12,14,31]. The ranges of variation of PR values and oil concentrations have been reduced to 0.15-0.35 and 20-80%, respectively, to enhance the visualization.
On the PR map (Figure 11b), one can observe strong variations of the PR values in the range direction due to the incidence angle changes across the swath. The second-order variation is due to the modification of the dielectric properties of the surface related to the oil content within the oil-in-water mixture. The oil concentration is estimated by firstly, selecting, for each pixel, the closest value between the actual PR and those given by the U-WCA data sheet (Figure 10a) and then by finding the concentration rate corresponding to the modelled PR value. The result is displayed in Figure 11c. The mean value of oil content within the emulsion is equal to 52% and more than 80% of the pixels within the slick have a concentration between 40 and 65%. Usually, the water content of marine oil slick lies between 50 and 75% [37], that is oil concentration between 50 and 25%. The values obtained in this experiment are slightly higher, which could be due to the relative short time lag between the release of oil by NOFO at sea and the scene acquisition by the radar sensor.
Remote Sens. 2018, 10, x FOR PEER REVIEW 11 of 16 finding the concentration rate corresponding to the modelled PR value. The result is displayed in Figure 11c. The mean value of oil content within the emulsion is equal to 52% and more than 80% of the pixels within the slick have a concentration between 40 and 65%. Usually, the water content of marine oil slick lies between 50 and 75% [37], that is oil concentration between 50 and 25%. The values obtained in this experiment are slightly higher, which could be due to the relative short time lag between the release of oil by NOFO at sea and the scene acquisition by the radar sensor. The same methodology has been applied to the other SAR scenes collected during the NOFO'2015 experiment and investigated in this paper (Table 3). All oil concentration maps have been projected in the ground geometry and are displayed in Figure 12 as well as the corresponding normalized histograms in Figure 13. The oil concentration underwent little change between 09:37 and 10:27 UTC (only 50 min) and no significant variation can be seen between the three histograms ( Figure 13-blue, red and green curves). The average value of the oil concentration is 52%, 52% and 49% for the acquisitions of 09:37, 10:02 and 10:27 UTC, respectively. Compared to the first three histograms, the last histogram (acquisition at 13:30 UTC, 3-h later) is shifted to the lower values of oil The same methodology has been applied to the other SAR scenes collected during the NOFO'2015 experiment and investigated in this paper (Table 3). All oil concentration maps have been projected in the ground geometry and are displayed in Figure 12 as well as the corresponding normalized histograms in Figure 13. The oil concentration underwent little change between 09:37 and 10:27 UTC (only 50 min) and no significant variation can be seen between the three histograms ( Figure 13-blue, red and green curves). The average value of the oil concentration is 52%, 52% and 49% for the acquisitions of 09:37, 10:02 and 10:27 UTC, respectively. Compared to the first three histograms, the last histogram (acquisition at 13:30 UTC, 3-h later) is shifted to the lower values of oil content ( Figure 13-black curve), with an average value of oil concentration of 43%. This decrease of oil concentration is due to weathering processes (wind, waves, evaporation . . . ) whose impact is clearly highlighted on the oil concentration histograms.
Remote Sens. 2018, 10, x FOR PEER REVIEW 12 of 16 content ( Figure 13-black curve), with an average value of oil concentration of 43%. This decrease of oil concentration is due to weathering processes (wind, waves, evaporation …) whose impact is clearly highlighted on the oil concentration histograms.

Confidence in Oil Concentration Estimate
The quantification method proposed in this paper is based on the U-WCA scattering model and the Bruggeman formula for estimating the oil concentration from the effective dielectric constant of the oil-in-water mixture. Usually, a simple linear mixing between mineral oil and seawater is employed [11,12]. This important simplification leads to a significant error in the estimate of the oil concentration within an oil slick. The Figure 14 below shows two histograms of the oil concentration (run 2-10:02 UTC) obtained using a linear (blue curve) and the Bruggeman model (red curve). With a linear mixing, the histogram is shifted to the higher values of oil concentration, resulting in a  (Figure 13-black curve), with an average value of oil concentration of 43%. This decrease of oil concentration is due to weathering processes (wind, waves, evaporation …) whose impact is clearly highlighted on the oil concentration histograms.

Confidence in Oil Concentration Estimate
The quantification method proposed in this paper is based on the U-WCA scattering model and the Bruggeman formula for estimating the oil concentration from the effective dielectric constant of the oil-in-water mixture. Usually, a simple linear mixing between mineral oil and seawater is employed [11,12]. This important simplification leads to a significant error in the estimate of the oil concentration within an oil slick. The Figure 14 below shows two histograms of the oil concentration (run 2-10:02 UTC) obtained using a linear (blue curve) and the Bruggeman model (red curve). With a linear mixing, the histogram is shifted to the higher values of oil concentration, resulting in a

Confidence in Oil Concentration Estimate
The quantification method proposed in this paper is based on the U-WCA scattering model and the Bruggeman formula for estimating the oil concentration from the effective dielectric constant of the oil-in-water mixture. Usually, a simple linear mixing between mineral oil and seawater is employed [11,12]. This important simplification leads to a significant error in the estimate of the oil concentration within an oil slick. The Figure 14 below shows two histograms of the oil concentration (run 2-10:02 UTC) obtained using a linear (blue curve) and the Bruggeman model (red curve). With a linear mixing, the histogram is shifted to the higher values of oil concentration, resulting in a strong overestimation of the average oil concentration (75% against 52%). These results show that the selection of the dielectric mixing model is a key aspect. The Bruggeman model has proven [28] to accurately reproduce the effective dielectric constant of an emulsion-type mixture and is highly recommended against the linear one when investigating the surface properties of marine slick from SAR imagery.
Remote Sens. 2018, 10, x FOR PEER REVIEW 13 of 16 strong overestimation of the average oil concentration (75% against 52%). These results show that the selection of the dielectric mixing model is a key aspect. The Bruggeman model has proven [28] to accurately reproduce the effective dielectric constant of an emulsion-type mixture and is highly recommended against the linear one when investigating the surface properties of marine slick from SAR imagery. The second source of errors comes from the wind information which is one of the inputs of the U-WCA scattering model. This information usually comes from large-scale forecast models, which cannot describe local variations. According to the Norwegian Meteorological Institute, the wind speed (U10) was 5 m/s during SAR data acquisition at 10:02 UTC (run 2). The oil concentration has been estimated in a wind speed interval of +/− 2 m/s around the reported value. Histograms of oil concentration estimated from dual-pol SAR data collected at 10:02 UTC and for an input wind speed of 3, 5 and 7 m/s are shown in Figure 15. As discussed in Paragraph 4.1, at low EM frequency the polarization ratio has a weak dependence on surface roughness and therefore modelling with the U-WCA scattering model varies only slightly with wind speed. Hence, wind speed uncertainties induce little errors on the estimate of the oil content into the oil-in-water mixing. For the investigated SAR data collected at 10:02 UTC, the mean oil concentration is estimated to be 51.9%, 52.4% and 50.8% for a wind speed of 3, 5 and 7 m/s, respectively.  The second source of errors comes from the wind information which is one of the inputs of the U-WCA scattering model. This information usually comes from large-scale forecast models, which cannot describe local variations. According to the Norwegian Meteorological Institute, the wind speed (U 10 ) was 5 m/s during SAR data acquisition at 10:02 UTC (run 2). The oil concentration has been estimated in a wind speed interval of +/− 2 m/s around the reported value. Histograms of oil concentration estimated from dual-pol SAR data collected at 10:02 UTC and for an input wind speed of 3, 5 and 7 m/s are shown in Figure 15. As discussed in Paragraph 4.1, at low EM frequency the polarization ratio has a weak dependence on surface roughness and therefore modelling with the U-WCA scattering model varies only slightly with wind speed. Hence, wind speed uncertainties induce little errors on the estimate of the oil content into the oil-in-water mixing. For the investigated SAR data collected at 10:02 UTC, the mean oil concentration is estimated to be 51.9%, 52.4% and 50.8% for a wind speed of 3, 5 and 7 m/s, respectively.
Since the remote sensing dataset explored in this study was not collected with validation data, no comparison between oil concentration estimate and in situ sampling within the spill areas can be performed. Even if the method reported in this paper is based on physical justifications, it cannot be formally validated. However, all the results presented herein are consistent with the expected behavior of an oil slick imaged area. First, the values of the oil concentration estimate are close to the concentration usually observed [37]. Then, we observe no trend of the estimation in the range direction, which suggests that the incidence angle variation across the swath as well been considered. Moreover, SAR data collected with a small time gap (09:37, 10:02 and 10:27 UTC) give similar oil content maps, despite the polluted area is differently positioned in the swath between the images, which ensures the robustness of the proposed methodology. Finally, the estimated maps covering the evolving spill over a 4-h period indicates a decrease of the average oil concentration, which can be attributed to weathering processes. of 3, 5 and 7 m/s are shown in Figure 15. As discussed in Paragraph 4.1, at low EM frequency the polarization ratio has a weak dependence on surface roughness and therefore modelling with the U-WCA scattering model varies only slightly with wind speed. Hence, wind speed uncertainties induce little errors on the estimate of the oil content into the oil-in-water mixing. For the investigated SAR data collected at 10:02 UTC, the mean oil concentration is estimated to be 51.9%, 52.4% and 50.8% for a wind speed of 3, 5 and 7 m/s, respectively.

Conclusions
A methodology to estimate the proportion of oil within an oil-in-water marine slick mixture has been reported in this paper as well as its application to the temporal monitoring of the oil concentration.
The key aspects of this study rely on three elements: the use of a rigorous surface scattering model to estimate the polarization ratio; the estimation of the volume fraction of oil from the Bruggemann formula; and the uniqueness of the dataset collected from controlled releases of mineral oil by an airborne SAR sensor operating at L-band, characterized by an instrument noise floor that is much lower than is currently available from spaceborne SARs.
At low frequency imaging radar (e.g., L-band), the relative contribution of non-resonant scattering with respect to the total backscattered energy from the ocean surface is negligible. For this reason, the polarization ratio measured by a radar sensor can be well approximated by a simple analytical scattering model such as U-WCA (see Figure 9a), which provides a non-trivial PR but depends only on the incidence angle of the incident radiation. Another advantage of using low frequency SAR images is that the ratio between the two co-polarized channels is only slightly dependent on the sea surface roughness but strongly affected by the dielectric properties of the imaged surface. This is not the case for higher frequency remote sensing radar, operating at C-or X-band. The volume fraction of oil within an oil-in-water mixture can then be retrieved from an Effective Medium Theory using the Bruggeman formula, by comparing the actual and the modelled polarization ratio at L-band.
The proposed methodology has been applied to an original set of L-band SAR scenes collected in June 2015 during an oil spill cleanup exercise carried out in the North Sea by the NOFO. Polarimetric SAR images have been acquired over controlled releases of mineral oil at sea by an airborne sensor characterized by a low instrument noise floor allowing a sufficiently high SNR over both slick-free and slick-covered areas for valid analysis of surface properties. Over freshly spilled mineral oil emulsion, the average oil concentration has been estimated to be above 50% with values ranging mainly from 40 to 65%. SAR data collected 4-h later permit to monitor the temporal behavior of the oil content and a decrease from around 50% to less than 45%, due to weathering processes, has been highlighted.
As shown in this paper, a combined utilization of an analytical scattering model and L-band SAR images collected with a sufficiently high SNR allows efficient estimation the concentration of oil within a marine oil slick (mixture between seawater and mineral oil). This estimation is shown to be robust to the uncertainties related to the sea state. Although no in situ measurements were collected with the remote sensing data, all the results presented herein are consistent with the expected behavior of an oil slick imaged area.