The development of numerical methods for solving the integro-differential radiation transfer equation remains a relevant task. Among them, we can highlight the Monte Carlo method, which is in demand in various niches of modern ocean optics. The purpose of this work is a clear and concise presentation of the basics of the forward Monte Carlo method of light fields modeling in seawater, accompanied by a detailed description of its software implementation. The basics of the method are described, the procedures for choosing the type of interaction, the mean free path and the direction of photon motion are described. A simple case is considered, corresponding to an infinitely distant point source of unpolarized light, the absence of atmospheric influence, a smooth air-seawater interface, and the absence of stratification of inherent optical properties. In this case, realistic values of the absorption and scattering coefficients were used, calculated in accordance with the Case 1 model for a chlorophyll concentration of 1 μg/L, and a strongly elongated Henyey-Greenstein phase function with the parameter g = 0.95. The Fresnel reflection of light from the air-seawater interface was taken into account. The relative errors in the values of the diffuse attenuation coefficient for downward irradiance K d and the diffuse reflectance R, calculated in the spectral range of 400–700 nm using 106 photons, in comparison with the HydroLight results were 1.5 % and 0.4 %, respectively. Spectral calculation on one core of a 2017 Intel Core i5-8250U mobile processor in MATLAB takes 6 minutes. An assessment of the choice of the optimal number of photons required to obtain the desired quantities with a given accuracy was made. The implemented method is useful for becoming familiar with the basic principles used to numerically solve the radiative transfer equation in seawater using statistical methods and is used in the “Ocean Optics” course, taught by the author to 4th year students of the Department of Thermohydromechanics of the Ocean at MIPT.
