## 4 Monte Carlo Simulation  
One of the main objectives for many MCS studies in the field of UOWC is to conclude the seawater propagation channel profile \(h_{c}(t)\)[27; 28; 113; 114; 115; 116] or the PL [12; 12; 103; 117; 118; 119; 120; 121; 122], which are reviewed in Section 5. The RTE expression in Equation (43) shows the potential energy flow between the emission, absorption, and scattering streams. Similarly, the MCSmathematical construct is a probabilistic-statistical approach that tracks many photons to simulate underwater light transmission degradations via absorption and scattering. Hence, any additional propagation impairments, e.g., scintillation and turbulence, should be modelled along one or two flow streams of energy. In this manner, the dynamics of the proposed solution follow the RTE energy flows. It solves the problem by simultaneously delivering individual photons over specific and computationally monitored probable channel paths. This is repeated over randomly selected points, including just one photon or a group of photons distributed across the optical source's profile.  
Depending on the underlying solution approach, the source profile can be described in terms of the spatial and temporal distribution of the transmitted optical pulse \(h_{p}(t)\). Also, many reported MCS studies assumed a point optical source, which implies that all the tracked photons share the same initial position. This assumption implies that \(h_{p}(t)=constant=I_{0}\), where \(I_{0}\) is uniformly distributed irradiance that can be defined by the total number of photons from the Tx optical source. The probability of occurrence of absorption, scattering, and any additional modelled impairments/events under consideration within the underwater channel defines the randomness of each simulated photon path. It is based on understanding the IOP and VSF/SPF depending on media type and link configuration. Such a procedure can be used to construct the framework of the MCS model. The main factors that influence the MCS method complexity are computational run time [90], the light source profile \(h_{p}(t)\), the impairment events' dominance for a given water type, and the scope of the FOV, which is related to the link regime (LOS or NLOS).  
The MCS approach has the advantages of simple programming, consistent solution elements, and great flexibility. Nevertheless, it might have inherent random statistical error margins, particularly when the assumption limits the scope of randomness. This might prevent the underlying MCS scheme from satisfying the CLT.  
The RTE model solutions discussed in Section 3 can be used as a benchmark to measure the reliability and validity of MCS results. The benchmark could be one or two of the following: BLL in Equation (44), SSA in Equation (48), TSA in Equation (49), SSA in Equation (50), DOM in Equation (54), the invariant-imbedding method, and the stochastic model in Equation (55). Also, it is a good exercise to use DGF curve fitting to support the consistency of MCS output.  
The MSC Implementation Notes subsection demonstrates the claim's validity that the MCS approach is a simple numerical solution. This subsection explains the steps for the why, the what, and the how to construct the architecture, design, and implementation (using Python) to produce a working object-oriented MCS programme using less than 700 lines of Python code.