Recently, compared with acoustic and radio methods, underwater optical wireless communications has been considered as a high-speed and high-bandwidth transmitting method at a lower cost. Absorption, scattering, and optical turbulence are three destructive phenomena that affect the performance of underwater optical communication systems. In this work, we use computer simulations to mimic the statistical behavior of underwater media employing the Monte Carlo method. Our simulation results for optical turbulence are in good agreement with the lognormal probability density function, which describes weak turbulence well, and they deviate as the turbulence moves away from weak. By considering the combined effect of absorption, scattering, and turbulence (AST) phenomena, we obtain the underwater channel's impulse response (IR). We demonstrate that there is no noticeable difference between the mean of ensemble IRs of the AST channel and the IR of the channel when turbulence is not taken into account. Moreover, our results predict that tripling the coastal link length from 10 to 30 m increases the average variance of sample IRs of the AST channel from their ensemble average by more than five times.