In underwater optical wireless communications (UOWC), scattering of the propagating light beam results in both intensity and phase variations, which limit the transmission link range and channel bandwidth, respectively. Scattering of photons while propagating through the channel is a random process, which results in the channel-dependent scattering noise. In this work, we introduce for the first time an analytical model for this noise and investigate its effect on the bit error rate performance of the UOWC system for three types of waters and a range of transmission link spans. We show that, for a short range of un-clear water or a longer range of clear water, the number of photons experiencing scattering is high, thus leading to the increased scattering noise.