An alternative approach to determine critical angle of contrast reversal and surface roughness of oil slicks under sunglint

ABSTRACT

The critical angle is the angle at which the contrast of oil slicks reverse their contrasts against the surrounding oil-free seawater under sunglint. Accurate determination of the critical angle can help estimate surface roughness and refractive index of the oil slicks. Although it’s difficult to determine a certain critical angle, the potential critical angle range help to improve the estimation accuracy. In this study, the angle between the viewing direction and the direction of mirror reflection is used as an indicator for quantifying the critical angle and could be calculated from the solar/viewing geometry from observations of the Moderate Resolution Imaging Spectroradiometer (MODIS). The natural seep oil slicks in the Gulf of Mexico were first delineated using a customized segmentation approach to remove noise and apply a morphological filter. On the basis of the histograms of the brightness values of the delineated oil slicks, the potential range of the critical angle was determined, and then an optimal critical angle between oil slicks and seawater was then determined from statistical and regression analyses in this range. This critical angle corresponds to the best fitting between the modeled and observed surface roughness of seep oil slicks and seawater.

KEYWORDS:

• Sunglint
• critical angle
• natural seep oil slicks
• surface roughness
• MODIS

1. Introduction

Natural hydrocarbon seepages and marine oil spill can form the oil slicks on top of ocean surface (Macdonald et al. 1993; Howari 2004; Zhong and You 2011; Charnotskii et al. 2016), which can be detected by different remote sensors (Brekke and Solberg 2005; Chust and Sagarminaga 2007; Leifer et al. 2012; Lu, Li, et al. 2013; Lu, Tian, et al. 2013; Lu, Zhan, and Hu 2016; Sun, Hu, and Tunnel Jr 2015; Sun and Hu 2016; Sun et al. 2016). The spilled oils show darker than the oil-free seawater in Synthetic Aperture Radar (SAR) data, are due to the modulation on surface roughness reduces Bragg scattering (Migliaccio, Gambardella, and Tranfaglia 2007; Li et al. 2014; Zhang et al. 2012, 2017). Although the classification and quantification of various spilled oils mainly depend on the different reflectance spectra of them, the surface sunglint reflection helps detection and presents challenges on classification and quantification. Oil slicks can modulate seawater surface roughness and appear both darker (negative contrast) and brighter (positive contrast) than the surrounding oil-free seawater under sunglint in optical imagery (Hu et al. 2009; Jackson and Alpers 2010; Lu, Sun et al. 2016; Sun and Hu 2016; Lu et al. 2017).

The idealized critical angle is the intersection point between the normalized sunglint radiance (L_gn) of oil slicks and seawater changing from dark to bright area (Hu et al. 2009; Jackson and Alpers 2010), and the core idea of simulation of L_gn of oil slicks or seawater is from Cox-Munk Model (Cox and Munk 1954). The space-borne optical sensors can measure sunglint reflectance (L_g, L_gn= πL_g) of oil slicks or seawater by using near-infrared bands (i.e. 859 nm band of Moderate Resolution Imaging Spectroradiometer, MODIS) (Zhang and Wang 2010; Jackson and Alpers 2010; Lu, Sun et al. 2016). Usually, if the refractive indices of seep oil slicks and seawater have been given, and the seawater (seep oil slicks) leaving radiance have been ignored in some near-infrared bands under sunglint, their surface roughness could be estimated using statistical analyses between modeled and MODIS-derived L_gn (Lu, Sun et al. 2016). The oils have different refractive indices (Ghandoor et al. 2003; Carolis, Adamo, and Pasquarisllo 2014) and the background ocean environment (i.e. wind speed, wind direction, and depth of seawater) is very complex, making it difficult to point out the precise location of critical angle using space-borne sensors’ imageries. On the other hand, this means that the preliminary estimation of potential critical angle range (an important boundary condition) can help to improve the determination of seep oil slicks surface roughness or refractive index.

The aim of this study is to estimate the oil slicks surface roughness using normalized sunglint reflectance (L_gn) image and spatial distribution information of seep oil slicks. The θ_m was used by Hu et al. (2009) to describe the angle difference between the viewing direction and the direction of mirror reflection, is recommended to be an indicator of critical angle range in this study. When the seep oil slicks covered the main satellite tracks uniformly, the image pixels show no or negligible contrast between oil slicks and oil-free seawater under sunglint in a certain angle and implies it is the critical angle. Due to the ocean circulation, the dark and bright seep oil slicks have the specific morphological characteristics, and then, they can be extracted from background seawater based on the Gaussian filter and oil slicks morphology feature detection (Wang and Hu 2015) and helps to figure out the potential critical angle range. This angle range and modeled L_gn of seawater determined reasonable L_gn values of oil slicks, which corresponds to an appropriate surface roughness range of oil slicks. By comparing to image-derived L_gn values, a couple of optimum surface roughness of oil slick and seawater was selected, and the intersection of them provided a more precise critical angle range. Nevertheless, this study shows an alternative approach to determine the critical angle and seep oil slicks surface roughness from optical remotely sensed imagery in the future.

2. Study area and imagery

The study area is located in the northern Gulf of Mexico (GoM) which is one of the famous oil and gas fields (Macdonald et al. 1993). The light hydrocarbon seepage floating to seawater surface forms seep oil slicks which appear both darker (negative contrast) or brighter (positive contrast) than the surrounding oil-free seawater under sunglint in some optical imagery (Hu et al. 2009; Jackson and Alpers 2010; Lu, Sun et al. 2016). The water depth in the study area arranges is from 50 to 2500 m. The wind speed varies very little and is not more than 4 m/s (Jackson and Alpers 2010). MODIS level-0 data covering the study area on 2 June 2005 at 16:55 UTC was obtained from the NASA Goddard Space Flight Center (GSFC). The NASA software package SeaDAS (version 7.0) has been used to convert the level-0 data to level-1 data (L_t, calibrated total radiance after ozone correction). L_gn of seep oil slicks and seawater can be estimated from MODIS band at 859 nm with the assumption that water-leaving radiance is negligible over seawater (Figure 1(a)). Meanwhile, the modeled L_gn of seep oil slicks and seawater had been calculated using the viewing angle imageries (the solar zenith angle θ₀, sensor zenith angle θ, and relative azimuth angle Φ) (Figure 1(b–d)).

Figure 1. (a) MODIS/Terra RGB image of 2 June 2005 (16:55 GMT) covering the GoM (inset), the main study was cut from the band of 859 nm, the white solid line indicated the satellite track, and the white dotted line indicated MODIS scan lines direction, (b) the Solar zenith angel θ₀, (c) the Sensor zenith angel θ, and (d) the relative azimuth angle Φ.

3. Methods

3.1. Extraction of seep oil slicks

The morphology of the seep oil slicks in this imagery show distinct characteristics as a result of the ocean circulation and has been used as an important descriptor to discriminate seep oil slicks from false alarms in the previous studies (Wang and Hu 2015; Lehr and Simecek-Beatty 2000). Therefore, the dark and bright seep oil slicks under sunglint show obviously morphological characteristics and can be extracted according to the following steps. (1) Correct the large scale image gradient due to glint contamination using the average pixel value from a local window and remove the salient speckles; (2) Apply a 3×3 Gaussian filter to reduce random noise and obtain coherent features; (3) Adopt histogram equalization using appropriate cut-off values to intensify the oil features. For negative slicks, the cut-off value of bright pixels can be set as a 50% of the maximum pixels value; (4) Apply a threshold filter with adjusted parameters and segment the potential features, OTSU thresholds can be used as a reference (Otsu 1979); (5) Connect the ‘broken’ features through a directional search operator and use roundness and area to exclude features that are neither too round nor too small to be real oil pixels. Roundness of the extracted feature (R_factor) is calculated as Equation (1), where S is the area of the feature and C is the circumference (Wang and Hu 2015; Lehr and Simecek-Beatty 2000; Otsu 1979).(1)

3.2. Modeled L_gn using Cox-Munk Model

The Cox-Munk model has been developed for interpreting the statistics of the sunglint on the sea surface (Cox and Munk 1954), and was used to model the L_gn of seep oil slicks and sea surface according to Equations (2–4) (Jackson and Alpers 2010; Lu, Sun et al. 2016):(2) (3) (4) where β is wave surface tilt, σ² is the surface roughness of oil slicks or oil-free seawater, ρ(ω) is the Fresnel reflection coefficient of oil slicks or oil-free seawater which could be calculated according to Snell Law and the viewing angles. P (θ₀, θ, Φ, σ²) is the probability density function of Cox-Munk model. In this study, the refractive indices of seawater, oil slicks, and air were set to 1.34, 1.38, and 1.0, respectively. Three viewing angles can be collected from space-borne sensors. According to the above equations, if the surface roughness of oil slicks or oil-free seawater can be given, the L_gn will be calculated using viewing angles, and there will be a critical angle of L_gn contrast reversal between oil slicks and seawater. In other words, if the potential critical angle and the viewing angles have been given, the surface roughness of them can be estimated using space-borne sensors derived L_gn.

3.3. MODIS-derived L_gn

The sunglint imagery covering the GoM on 2 June 2005 was collected from MODIS 859 nm band (level-0 data). Thus, the SeaDAS (version 7.0) was used to process the MODIS level-0 data to get the ozone calibrated radiance L_t, which can be expressed as Equation (5) in the absence of whitecaps (Wang and Bailey 2001; Hu, Carder, and Muller-Karger 2000; Zhang and Wang 2010).(5) where F₀ is the extraterrestrial solar irradiance, λ represents the wavelength, and 859 nm is chosen here to ignore the impact of water-leaving radiance L_w (L_w is negligible at band 859 nm). L_r is calculated using the lookup tables for Rayleigh scattering in SeaDAS. L_a is derived from the nearby pixel free of sunglint. T and T₀ are the beam transmittance of pixel-to-satellite and sun-to-pixel respectively, whereas the t is pixel-to-satellite diffuse transmittance, and they can all be derived from Rayleigh optical thickness, aerosol optical thickness, solar zenith angel, and sensor zenith angel. On the basis of the atmosphere correction, the MODIS-derived L_g (sr⁻¹) of seep oil slicks and seawater multiply by π equal to the modeled L_gn (L_gn= πL_g).

4. Results and discussions

4.1. Determining potential critical angle range

The angle (θ_m, cosθ_m=cosθ₀cosθ-sinθ₀sinθcosΦ) can be calculated using viewing angles (θ₀, θ, and Φ) for quantization of the critical angle range. Figure 2(a) shows that the range of θ_m is from 5.99° to 19.39° in this case. The same angle (θ_m) also means that the same surface has the same normalized sunglint reflectance. Based on the method in Section 3.1, the seep oil slicks could be figured out and marked with red signs (Figure 2(b)). Moreover, the potential critical angle range between dark and bright seep oil slicks (θ_m is from 12.12° ∼ 12.92°) has been deduced which is an important boundary condition for the approach of seep oil slicks surface roughness. Figure 2(c) shows the statistic features of MODIS-derived L_gn image, such as the average L_gn of seawater changed from dark to bright area (Figure 2(c)), and the minimum or maximum L_gn of seep oil slicks in negative contrast (dark seep oil slicks) or positive contrast (bright seep oil slicks) from the background seawater depends on the same angle (θ_m).

Figure 2. (a) The angle (θ_m) between the viewing direction and the direction of mirror reflectance, (b) Seep oil slicks extraction from MODIS image and the potential critical angle range, and (c) The statistical values of seep oil slicks and seawater collected from MODIS imagery.

4.2. Simulation of the critical angle

Based on the test refractive indices of seep oil slicks, air and seawater, the modeled L_gn of seep oil slicks and seawater can be figured out using Cox-Munk model (Hu et al. 2009; Jackson and Alpers 2010; Lu, Sun et al. 2016). Due to the surface wind speed varies little and is lower than 4 m/s on the day of MODIS imaging (Hu et al. 2009), the modeled L_gn of seawater for five different seawater roughness (0.013, 0.016, 0.018, 0.021, and 0.023, corresponding to surface wind speed of 2.0, 2.5, 3.0, 3.5, and 4.0 m/s) were used to match the MODIS-derived L_gn of seawater. At the same time, the 7 curves of modeled L_gn of seep oil slicks which roughness changed from 0.004 to 0.010 were figured out (Figure 3(a)). In the potential critical angle range (θ_m is 12.12° ∼ 12.92°), six intersection points between the modeled L_gn of seep oil slicks and seawater could be pointed out (Figure 3(b)). Furthermore, these different intersection points implied the surface roughness combination between seep oil slicks and seawater (Figure 3(b)).

Figure 3. (a) Modeled L_gn of seep oil slicks and oil-free seawater which viewing angles corresponding to the MODIS imagery. There are six intersection angles in the potential critical angle range (12.12° ∼ 12.92°), (b) six surface roughness combinations of seep oil slicks and seawater could be pointed out in this range.

In the modeled results, the variation range of seep oil slicks surface roughness is from 0.006 to 0.007, and the seawater surface roughness varies from 0.013 to 0.023. Therefore, the regression analysis between modeled and MODIS-derived L_gn help to promote these preliminary results.

4.3. Approaching surface roughness

According to six intersection points in potential critical angle range (Figure 3(b)), the numerical relationship between modeled L_gn and MODIS-derived L_gn of seep oil slicks and seawater depending on the same angle (θ_m) of them were figured out as follow (Figure 4). Although these potential critical angle ranges are reasonable, the optimal statistical regression between modeled and MODIS-derived L_gn of them will promote the more accurate result of approximation of surface roughness.

Figure 4. MODIS-derived and modeled L_gn of six potential critical angles with seep oil slicks and seawater roughness corresponding to Figure 3.

The statistical relationships between the modeled and MODIS-derived L_gn of them showed in Figure 5. The linear relationships are all satisfactory due to the change trend of L_gn is consistent from dark to bright area corresponding to the angle (θ_m) changed from small to large. Although the multiple correlation coefficient (R²) increases with the increase of the roughness, the root mean square deviation (RMSE) of them is not monotonic changing. The minimum RMSE of them are 0.026095 (seep oil slicks) and 0.006803 (seawater) corresponding to σ² _oil (0.007) and σ² _water (0.016) (Figure 5). Therefore, the surface roughness of seep oil slicks and seawater were recommended around 0.007 and 0.016 corresponding to the surface wind speed of about 2.5 m/s.

Figure 5. Statistical relationships between modeled and MODIS-derived L_gn of seep oil slicks and seawater (potential critical angle range is from 12.12° to 12.92°).

5. Conclusions

Seep oil slicks is a kind of very thin oil film floating on the ocean surface, and the leaving radiance can be ignored in near-infrared wavelength. They could appear both brighter and darker than the surrounding water under sunglint on the sides of the critical angle in the optical remotely sensed imagery. This is due to different refractive index and surface roughness of them. Although it’s difficult to figure out the accurate critical angle, determining potential critical angle range helps to improve estimation of seep oil slicks and seawater surface roughness. The angle (θ_m) between the viewing direction and the direction of mirror reflection is recommended as an accurate position indicator for quantifying the critical angle and can be calculated from solar/viewing geometry of remotely sensed data. Based on the extraction of dark and bright seep oil slicks from MODIS imagery, a potential critical angle range can be figured out for the suggestion of preliminary surface roughness of them. In this range, the optimal fitting results between MODIS-derived and modeled L_gn of them further indicate the surface roughness and refractive index. Nevertheless, surface sunglint reflectance contains some information which help to derive more details and require more attention.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yingcheng Lu http://orcid.org/0000-0002-9528-053X

Yongxue Liu http://orcid.org/0000-0002-6837-5015

Additional information

Funding

This work was supported by Natural Science Foundation of Jiangsu Province [Grant no. BK20160023] National Natural Science Foundation of China [Grant Nos. 41771376, 41371014, 61675099], and the National Key Research and Development Program of China [Grant no. 2016YFC1400901].