# Investigation of Electromagnetic Scattering Mechanisms from Dynamic Oil Spill–Covered Sea Surface

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## Abstract

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## 1. Introduction

## 2. The 3D Geometric Model of Oil Spill–Covered Sea Surface Area

#### 2.1. Sea Spectrum

_{clean}is the oil–free sea spectrum. In this manuscript, the Elfouhaily [6,19] spectrum is adopted to generate the clean sea. y

_{s}is the attenuation coefficient, which describes the attenuation effect of sea waves affected by oil film. Viscous damping is the most direct and important influencing factor of oil spills on sea waves. When a certain amount of oil spill covers the sea surface, the oil spill, and sea surface can be regarded as a bilayer fluid model. In this case, the viscous damping of the oil spill should consider oil film thickness, the surface tension, elasticity, viscosity, and other parameters of sea water and oil spill. The relative attenuation coefficient y

_{L}of the Jenkins and Jacobs model [8] can be expressed as:

_{s}(k) = y

_{L}(k), it represents the oil film coverage of the whole observed sea surface in this situation.

_{cut}refers to the cut-off wavenumber. The wavenumbers between K

_{min}and K

_{cut}indicate that these wave numbers generate large scale waves, K

_{Bragg}means Bragg wavenumber, the capillary wave is reduced to cosine wave generated by Bragg wavelength.

_{0}= 0.7 U

_{w}(U

_{w}is the friction velocity of the clean wind-driven sea surface, w is water, and o is oil) is often used to calculate the friction velocity of the sea surface covered by the oil spill [35]. Under the same conditions of an oil spill, the spectra peak moves to the low-frequency region as the wind speed increases. The effect of small–scale waves affected by oil film at high wind speeds is weaker than that at low wind speed; the main reason is that small–scale waves affected by oil film are weaker than the interaction between sea waves.

#### 2.2. Oil/Water Mixture

_{mix}is for the mixture of oil and water, ε

_{w}is for water (in [38], w is water), ε

_{oil}= 2 + j0.01, P

_{oil}is the oil proportion, and P

_{w}is the water proportion P

_{w}= (1 − P

_{oil}).

#### 2.3. Oil Spill Diffusion

_{w}is the density of sea water; and P

_{o}is the density of the oil spill (o is oil). The other parameters are given by [41].

#### 2.4. Sea Surface

**K**= Kcosφ

**e**

_{x}+ Ksinφ

**e**

_{y}; φ is the wind direction; S(K

_{x}, K

_{y}) is the sea spectrum; ω(K

_{x}, K

_{y}) is the angular velocity, which is related to the wavenumber K; ω

^{2}= gK(1 + K

^{2}/K

_{m}

^{2}); and k

_{m}= 363 rad/m. IFFT2 is a two–dimensional inverse Fourier transform.

_{i}= 30°, φ = 10°, and U

_{10}= 5 m/s. The truncated size of sea surface is 300 m × 300 m.

_{10}= 5 m/s. The solid black line represents the clean sea surface; the dashed blue line represents the initial oil spill, which covers 2% of the surface area; and the oil spill thickness is set to 5 mm. The dashed red line shows the stable state of the oil spill, which covers 100% of the surface area (the values are referred to in Refs. [36,39]).

## 3. EM Scattering Model

#### 3.1. The EM Scattering of Clean Sea

**x**,

**y**,

**z**) and (

**x**′,

**y**′,

**z**′). In the global coordinate, θ

_{s}and θ

_{i}show the scattering and incident angle. Correspondingly, θ

_{s}′ and θ

_{i}′ are the scattering and incidence angles in local coordinates. k

_{i}and k

_{s}show the incident and scattered wave vector.

_{mn}

^{(n′)}(2Ksinθ

_{i}′, 0) corresponds to the Bragg scattering component, Δx and Δy are sampling intervals along the x and y directions, and R is the straight–line distance between the radar and center of inclined facet element. The specific other parameters are referred to in [15,20].

#### 3.2. The EM Scattering of Oil Spill-Covered Sea

_{upper}is the scattering of upper surface; σ

_{volpp}is the contribution of second part scattering, which is from the oil spill layer; σ

_{bspp}is the scattering of bottom surface; and σ

_{inpp}is the contribution of forth part scattering, which comes from the interaction among the upper surface, oil spill layer, and bottom surface. Relevant expressions of the specific parameters are referred to in [20].

## 4. Results and Discussion

#### 4.1. Comparison of Experimental Data and Simulation Results

_{10}= 4 m/s. Equation (6) shows that the relative dielectric parameters of the oil spill is ε

_{oil}= (2.96, 0.04) (mixture of 80% oil and 20% water), the seawater is ε

_{sea}= (72.6, 69), and φ

_{w}= 120° expresses the wind direction. The calculation size of the sea surface is 300 m × 300 m, and the interval sample is 1 m × 1 m.

_{10}= 9.26 m/s, ε

_{oil}= (2.93, 0.06) (mixture of 80% oil and 20% water), ε

_{sea}= (48, 38.8), and φ

_{w}= 120°. The calculation size of the sea surface is 300 m × 300 m, and the interval sample is 1 m × 1 m. Figure 7 illustrates the simulation results are the statistical average results of 100 samples under the conditions of VV polarization.

#### 4.2. Comparison of Hydrodynamic and Tilt Modulation

_{10}= 3 m/s. The small facet size is 1 m × 1 m, θ

_{n}is the tilt of the small facet, and φ

_{n}is the azimuth angle. Based on the dynamic oil spill process, the oil spill changes from heavy oil to thin oil, and the oil spill thickness is considered to be reduced from 5 mm to 0.1 mm in the simulation. When the small facet is covered with an oil spill, the damping effect will lead to a smaller θ

_{n}and a smaller RMS height of small-scale waves. The damping effect will be stronger with the increase of the oil spill thickness. This is consistent with [46].

_{n}for the scattering coefficient of the small facet at different oil spill thicknesses for VV and HH, where φ

_{n}= 190°. Figure 8c displays the influence of φ

_{n}on the backscattering coefficient, where θ

_{n}= 30°. The simulation results of Figure 8 can draw the following conclusions: (1) Both hydrodynamic and tilt modulations contribute to EM scattering of the oil spill-covered facet. (2) As φ

_{n}= 190°, NRCS decreases steadily when θ

_{n}increases. The larger the oil spill thickness, the greater the damping effect on small-scale waves, and the smaller the NRCS of the small facet caused by an oil spill. (3) When θ

_{n}= 30°, the scattering intensity is distributed in cosine with the increase of φ

_{n}. (4) The scattering intensity of the small facet for VV is higher than for HH, which can more clearly reflect the changes brought about by the existence of an oil spill. (5) Compared with the hydrodynamic effect in the small facet, the tilt modulation is the main factor. As time goes by, the dynamic oil changes and the scattering coefficient of the small facet increases. The EM scattering of the whole observed sea surface is actually the comprehensive effect of the oil spill layer and the oil spill-covered surface area.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The 3D geometric model of oil spill-covered sea surface (the black part shows the oil spill-covered sea area). (

**a**) Clean sea; (

**b**) Oil spill covers 2% of the surface area; (

**c**) Oil spill covers 20% of the surface area; (

**d**) Oil spill covers 50% of the surface area.

**Figure 3.**The geometric characteristics of oil spill-covered sea. (

**a**) Features of sea surface profile along the x direction; (

**b**) Slope of sea surface profile along the x direction; (

**c**) Slope of sea surface profile along the y direction; (

**d**) The RMS height of sea surface; (

**e**) The RMS slope of sea surface.

**Figure 5.**The demonstration diagram of EM scattering from oil spill-covered sea; (1), (2), (3), and (4) represent the four part contributions of an oil spill layer.

**Figure 6.**(

**a**) The UAVSAR measured data, the comparison of the simulated NRCS, the SSA-2 results simulated by Zheng et al. [26], and the measured result; (

**b**) Clean sea, VV, and HH; (

**c**) Oil spill-covered sea and VV; (

**d**) oil spill-covered sea and HH.

**Figure 7.**(

**a**) The NASA/MSC photograph of the oil–covered sea surface area and clean sea; (

**b**) Comparison of experimental data and simulation results; (

**c**) Comparison of experimental data and simulation results for different wind speeds.

**Figure 8.**(

**a**) The EM scattering simulation of grid elements in clean sea and oil spill–covered sea surface; (

**b**) Influence of θ

_{n}on backscattering coefficient; (

**c**) Influence of φ

_{n}on backscattering coefficient.

**Table 1.**Relevant parameters of oil spill (see [8]).

Physical Parameters | Values |
---|---|

Water density (ρ) | 1023 kg · m^{−3} |

Oil density (ρ_{+}) | 900 kg · m^{−3} |

Surface viscosity (υ_{s+}) | 0 |

Interfacial viscosity (υ_{s}_{−}) | 0 |

Kinematic viscosity of water(υ) | 10^{−6} m^{2} · S^{−1} |

Kinematic viscosity of oil (υ_{+}) | 10^{−4} m^{2} · S^{−1} |

Surface elasticity (χ+) | 15 mN · m^{−1} |

Interfacial elasticity (χ−) | 10 mN · m^{−1} |

Surface tension (γ+) | 25 mN · m^{−1} |

Interfacial tension (γ−) | 15 mN · m^{−1} |

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**MDPI and ACS Style**

Li, D.; Zhao, Z.; Ma, W.; Xue, Y. Investigation of Electromagnetic Scattering Mechanisms from Dynamic Oil Spill–Covered Sea Surface. *Remote Sens.* **2023**, *15*, 1777.
https://doi.org/10.3390/rs15071777

**AMA Style**

Li D, Zhao Z, Ma W, Xue Y. Investigation of Electromagnetic Scattering Mechanisms from Dynamic Oil Spill–Covered Sea Surface. *Remote Sensing*. 2023; 15(7):1777.
https://doi.org/10.3390/rs15071777

**Chicago/Turabian Style**

Li, Dongfang, Zhiqin Zhao, Wenying Ma, and Yajuan Xue. 2023. "Investigation of Electromagnetic Scattering Mechanisms from Dynamic Oil Spill–Covered Sea Surface" *Remote Sensing* 15, no. 7: 1777.
https://doi.org/10.3390/rs15071777