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The objective of this paper is to derive a model for the irradiance distribution of underwater optical waves propagation in the combined presence of turbulence and air bubbles. The proposed distribution is based on modelling the medium index of refraction as a shot noise process and using the Rytov solution to the stochastic wave equation. Since the oceanic turbulence spectrum is different than the atmospheric spectrum, recent studies show that the well-known probability density functions poorly describe optical wave propagation underwater in the combined presence of air bubbles and turbulence, and that a mixture of distributions is generally needed. This conclusion, however, does not follow from theoretical investigations. Moreover, the physical aspects of the phenomena, such as the bubble size distribution, are not included in these models, and as such may limit their applicability. The approach introduced in this paper allows for including the environment physical properties directly in to the medium index of refraction. In this paper, intensity distribution model is derived based on Rytov theory of propagation through weak turbulence. The physical processes in effect are directly included by assuming a shot noise index of refraction model. Using the beam propagation method combined with the random phase screen method, the derived distribution is validated by simulation over a large range of turbulence levels and shows excellent agreement with the simulation data. In particular, the qualitative aspect of two peak distribution is modelled by the proposed distribution. • A proposed approach for the intensity pdf of optical waves through random mediums. • The proposed approach incorporates the physical characteristics of the mediums. • Underwater optical waves in presence of turbulence and air bubbles is considered. • The model is verified through simulation of underwater turbulent environment. [ABSTRACT FROM AUTHOR]