## 2 Seawater Channel Modelling Elements
### Water Channel Impairments  
When a photon with energy, \(E=h. (v/\lambda)\), where \(h\) is the Planck's constant (6.6256 \(\times\) 10\({}^{-34}\) J.s), \(v\) (m/s) is the speed of light, and \(\lambda\) (m) is the vacuum light wavelength, is travelling in a water channel, there are abstractly two potential channel impairments that manipulate the arrival of the photon under observation from reaching the receiver photodiode surface at the other end of the channel (Figure 3A). Many physical phenomena produced by light-matter interaction occur in UOWC. A beam from the source to the receiver and a collection of random rays are formed to obtain the channel model. A PDF generates the polar angle \(\theta\) of the emitted rays, which is then processed while considering several factors. For example, a ray travelling underwater can collide with some particles depending on the particles' density and size. Also, when a rayimpacts the seawater surface, it will be reflected (or not) at various angles depending on the surface condition and governed by [PERSON]'s law [59; 60; 61]. Absorption is one of them, which causes the elimination of the photon due to the transformation of its energy E converted into another form, such as a heat or chemical form. This optical defect is described by the absorption coefficient \(a(\lambda)\), which is \(\lambda\)-dependent. The second potential impairment is scattering, which leads to a change in the photon's propagation direction. The scattering coefficient \(b(\lambda)\) expresses the optical scattering. These two impairments/events attenuate the transmitted optical irradiance while the photons travel through the channel. The overall attenuation loss coefficient \(c(\lambda)\) in m\({}^{-1}\) can be conveyed as follows [32; 62]:  
\[c(\lambda)=a(\lambda)+b(\lambda) \tag{1}\]  
From Equation (1), another IOP commonly used in developing a solution for RTE is the spectral single-scattering albedo \(w_{0}(\lambda)\), which is defined as follows:  
\[w_{0}(\lambda)=\frac{b(\lambda)}{c(\lambda)} \tag{2}\]  
In waters, the beam attenuation is due primarily to scattering; \(w_{0}\) is near one. In waters where the beam attenuation is due primarily to absorption, \(w_{0}\) is near zero. It is worth mentioning that the single-scattering albedo can be considered as the probability that a photon will be scattered in any given interaction event. Hence, \(w_{0}(\lambda)\) is also known as the probability of photon survival (Table 3). Equation (1) is a simple, abstract, and inclusive equation. The inclusivity is rooted in the fact that any optical impairment or event, e.g., scintillation and turbulence, can be modelled as absorption, which means that the photons involved in scintillation and turbulence will be discounted. This approach is very simplistic but not realistic. Such photons can come back and join the travelling photons later, eventually distorting the received optical pulse shape \(h_{opt}(t)\) and causing an elongation in the received optical pulse, which eventually contributes to overlapping between the received optical pulses. Hence, it is more factual to model scintillation and turbulence as contributing components to the overall elastic scattering. Regarding inelastic scattering, some of the light at a given wavelength \(\lambda\) is removed and re-emitted at a longer wavelength, i.e., lower frequency. In such a scenario, we must focus on Raman scattering in water. Accordingly, the difference in the incident and scattered light frequencies is defined as the Raman shift \(\Delta f\)[10; 63; 64; 65], which we can write in terms of wavelength \(\Delta\lambda_{r}=\lambda_{s}+\lambda_{i}\). The wavelength shift \(\Delta\lambda_{r}\) is represented by Raman scattering coefficient \(b_{rs}\) (in m\({}^{-1}\)). The coefficient \(b_{rs}\) quantifies the impact of Raman scattering. Hence, the coefficient \(b_{rs}\) is defined as the ratio of scattered quanta per second at \(f_{s}\) to the incident quanta per second at \(f_{i}\). This coefficient is one of the members in the IOP set.