## 2 Seawater Channel Modelling Elements
### Scattering Phase Function Formats  
Generally speaking, all elastic and inelastic scattering occurs from interactions between photons and molecules or atoms at the most elementary, microscopic level. The elastic scattering means that there will be a change to the light wavelength \(\lambda\), while the inelastic scattering does not. The following discussions consider the elastic scattering only; otherwise, an inelastic scattering scenario will be indicated. However, scattering in clear waters is conveniently viewed as being caused by small-scale (i.e., <<\(\lambda\)) density fluctuations attributable to random molecular motions, by the large (i.e., >>\(\lambda\)) abundant organic and inorganic particles and by large-scale (i.e., >>\(\lambda\)) turbulence-induced fluctuations in the absolute index of refraction. The scattering categorisation here is based on relevant mathematical assumptions that describe scattering in the various size domains. The scattering properties of seawater are substantially influenced by the particulate matter that is always present. Against such a background, the research community divided seawater into four types, as shown in Table 3.  
SPF is a critical factor in determining scattering in ocean water. Numerous researchers have conducted VSF studies. Thus, this section also explains the SPF observed by Petzold and five mathematical formulas for modelling SPF. [PERSON] et al. [74] calculated Petzold's average particle phase function by averaging some phase functions evaluated using observed VSF measurements via Petzold in 1972 at a wavelength of 530 nm for different kinds of water [49]. The particle backscattering ratio is BP = 0.0183 when this phase function is numerically integrated throughout backward angles between \(90^{\circ}\) and \(180^{\circ}\). The backscattering ratio is the proportion of the scattered light scattered in the backward direction. The magnitude of the scattered intensity \(I_{s}(\theta,\lambda)\) typically increases by five or six orders of magnitude in going from \(\theta=90^{\circ}\) to \(\theta=0.1^{\circ}\) for a given seawater volume,  
Figure 5: HG-SPF, anisotropy parameter (\(g\)) set {0.0, 0.5, 0.9}. and scattering at a given angle \(\theta\) can vary by two orders of magnitude among water volumes [73]. Small-scale scattering by water molecules determines the minimum values for the scattering properties. The wide dynamic range of \(I_{s}(\theta,\lambda)\) causes the rapid change in \(\beta(\theta,\lambda)\) over a small \(\theta\) range (Figure 5), which requires attention when implementing an RTE numerical solution. Also, enhanced backscatter has been reported in suspensions of latex spheres; a factor-of-two increase in \(I_{s}(\theta,\lambda)\) between \(\theta=179.5^{\circ}\) and \(180.0^{\circ}\) is typical [75]. However, unlike FSO channels, photons would hit a significantly greater number of particles in an underwater environment. Hence, many scattering events play a big part in obtaining optical power compared to optical wireless communication channels [66]. Few measurements are available, with some originating from Petzold, due to the difficulty in distinguishing the scattered photons from the incident ones across small forward angles and the wide range of scattering amplitudes throughout the possible range of scattering angles (\(\theta\)s). The accurate computation of \(\beta(\theta,\lambda)\) over a small \(\theta\) range is crucial to the determination of \(b(\lambda)\) by integration since, predictably, one-half of all scattering occurs at \(\theta\) values of less than a few degrees. Scattering at small \(\theta\)s is essential in the UOWC system. The behaviour of \(\beta(\theta,\lambda)\) extremely near \(\theta=180^{\circ}\) is vital in laser remote sensing applications. The SPF has several formats depending on the scattering limits' assumption and seawater type.