**3. Drone-based radar approach**

In this section, we describe in detail the proposed approach for oil spill monitoring for oil spill detection, estimation, and classification.

#### **3.1 System model**

## *3.1.1 Reflection coefficient for multi-layer structure*

To physically model the oil slicks on top of the sea surface, we consider a multilayer structure: air, oil, and seawater. We study the reflection of the electromagnetic waves from the sea layer covered by an oil layer, which is modeled as a thick slick with a thickness of up to 10 mm [13]. **Figure 1** shows such a simulated oil spill. When the ocean is calm and the wind speed is low, such a thick layer significantly reduces the surface roughness [37, 62], dampens capillary and short gravity waves, and calms the smaller waves on the sea [63]. As a result, within the radar cross section, the incident electromagnetic waves are reflected along the specular component due to the smooth surface. By operating the radar on a nadir-looking system, the reflected power is fully reflected for normal incident waves, without losses due to off-nadir backscattering.

*Recent Advances in Oil-Spill Monitoring Using Drone-Based Radar Remote Sensing DOI: http://dx.doi.org/10.5772/intechopen.106942*


#### **Table 1.**

*Non-satellite-based state-of-the-art techniques for oil spill monitoring.*

**Figure 1.** *Simulated oil spill with thickness range from 0 to 10 mm.*

We define the electrical properties (relative dielectric constants) for the air, oil, and seawater to be respectively ε1, ε2, and ε3. The different media are assumed to be nonmagnetic. If radar reflections from the seafloor are neglected, we can calculate the field reflection coefficients for the layers at the boundaries where interaction with electromagnetic waves occurs. They are denoted for the first interface (between air and oil) and the second interface (between oil and water) by *ρ*<sup>12</sup> and *ρ*23, respectively. Hence, the power reflection coefficient for the three-layer structure, also denoted by the reflectivity *R*, is derived using the Transfer Matrix Approach [64, 65] as:

$$\mathbf{R} = \left| \frac{\rho\_{12}\mathbf{e}^{\mathrm{j}8} + \rho\_{23}\mathbf{e}^{-\mathrm{j}8}}{\mathbf{e}^{\mathrm{j}8} + \rho\_{12}\rho\_{23}\mathbf{e}^{-\mathrm{j}8}} \right|^2 \tag{1}$$

*δ* is the propagation constant that is dependent on the oil's relative permittivity (ε2Þ, the frequency of the electromagnetic wave (the wavelength λ), and the thickness of the oil layer (d). It is given by:

$$
\delta = \frac{2\pi\sqrt{\varepsilon\_2}\,d}{\lambda} \tag{2}
$$

#### *3.1.2 Smooth and rough surfaces*

Several statistical attributes can be calculated for a random surface [66]. The surface height measurements may be described using standard statistical parameters, namely:


Based on the surface statistics with respect to the electromagnetic wavelength, we can differentiate between two types of surfaces: a perfectly *smooth* (flat) or *rough* surface. If the correlation length of the ocean waves is large and the rms-height of capillary waves is very small, as it is for calm ocean conditions, then the surface is considered smooth. In this case, radar reflections are along the specular direction and can be calculated according to Eq. (1). Otherwise, a non-coherent component is introduced in the scattering pattern along all directions other than the specular, whenever the surface is rough. For this, with *θ* denoting the incident angle of the electromagnetic waves to the interfaces, the reflectivity in the specular direction is called the coherent reflectivity *Rcoherent*, and it is given by:

$$R\_{coherent} = R\,\mathcal{e}^{-4\left(\frac{2\pi\,\nu\,\text{con}(\theta)}{\lambda}\right)^2} \tag{3}$$

#### *3.1.3 Reflectivity behavior*

For our approach, we suggest the incorporation of multiple bands using remote sensing nadir-looking wide-band radar sensors. Since frequencies from the L-band (1–2 GHz) will not change the reflectivity value over the 1–10 mm thickness range by more than 1 dB, they are not considered to be relevant for the proposed approach. Instead, we will use frequencies from the C-band (4–8 GHz) and X-band (8–12 GHz).

### *Recent Advances in Oil-Spill Monitoring Using Drone-Based Radar Remote Sensing DOI: http://dx.doi.org/10.5772/intechopen.106942*

To better understand the reflectivity behavior at each wave frequency, **Figure 2** shows the reflectivity value defined in Eq. (1) versus the oil thickness, which is varied from 1 mm to 10 mm where different subplots correspond to different scanning frequencies at increments of 1 GHz from 4 to 12 GHz [67]. The relative dielectric constant of the air and thick oil is 1 and 3, respectively. We neglect the imaginary part of the relative permittivity of the oil, which is of order 0.01 [68]. The relative dielectric constant of seawater depends on the water temperature (assumed to be 20 degrees), the water salinity (assumed to be 35 ppt), and the frequency of the radar signal [66]. For ease of reference, we also mark the mean reflectivity value in the case of no oil spill as a constant straight line per subplot.

For instance, at 4 GHz, the curve of the reflectivity is monotonically decreasing slowly with the thickness. It has a very small slope at small thickness values (0–3 mm), but this slope increases with the increase of the oil slick thickness (3–7 mm). At some thicknesses, any error in the power reflectivity measurements at 4 GHz would mislead the oil detection due to the very small variation from the water reflectivities. In addition, for small thickness values, the difference between reflectivity values is very small, so the estimation could go easily wrong. A different pattern is observed at higher frequencies (7–12 GHz). The reflectivity curve admits a steeper slope for small values of thicknesses, which improves the detection of oil slick thickness. However, due to the appearing cyclic behavior, many thickness values give the same reflectivity value leading to false interpretations for detection or estimation. Therefore, it is important to use more than one frequency to improve the detection or estimation. To see the effect of the relative permittivity of the oil on the reflectivity, **Figure 3** studies the variation of this parameter evaluated at two frequencies: 4 and 12 GHz [69]. For the same frequency, the effect of the variation in the relative permittivity on the reflectivity value is dependent on the oil thickness. Also, by

**Figure 2.** *Reflectivity (in dB) versus oil slick thickness (in mm) at different scanning frequencies. Retrieved from [67].*

**Figure 3.** *Reflectivity R (in dB) versus oil thickness (in mm) at different frequencies (4 GHz, and 12 GHz) and different oil dielectric constants. Retrieved from [69].*

looking at the reflectivity plots at the same frequency, they look very similar over the full thickness range even if the relative permittivity of the oil slick is changing. However, the reflectivity behavior varies a lot from one frequency to another.

### **3.2 Detection**

To perform the detection functionality of the monitoring system, we are proposing in this section different detection algorithms that use the statistical characterization of the reflectivity values and their distribution under different oil thicknesses to obtain a final decision on whether oil exists or not. Any previous knowledge about the existence or absence of oil in the surface scanned should be taken into consideration to weigh the probability of the decision in the detector block. Nevertheless, without any previous knowledge about the spill situation, the detector decision will be totally based on the statistics of the measured power reflection coefficients ratio [69].

Let "o, w" be the events indicating the presence of the oil slick and the water, respectively. Let R be the event representing the measurement of the reflectivity value (s). R could represent one or more reflectivity values that are measured at the same or at different frequencies. The reflectivity values are assumed to be independent events, i.e., they are uncorrelated in the time domain at multiple observations, and in the frequency domain at multiple frequency measurements. After some derivation steps shown in [69], the detector algorithm evaluates the following ratio:

$$\frac{\Pr(\mathbf{o}|\mathbf{R})}{\Pr(\mathbf{w}|\mathbf{R})} = \frac{\Pr(\mathbf{R}|\mathbf{o})}{\Pr(\mathbf{R}|\mathbf{w})} \overset{>}{\underset{<}{\times}} \mathbf{1} \tag{4}$$

With this ratio, the detector compares the probability of getting an oil or water event given that radar reflectivities are measured. If the ratio gives a result greater
