In this paper, we perform the statistical modeling for turbulence-induced intensity fluctuations with optical waves propagating in turbulent ocean vertically. To accurately model the turbulence-induced optical wavefront distortion in vertical direction, we construct the wave optics simulation (WOS). In WOS procedure, we use the general oceanic turbulence spatial power-law spectrum and Argo experimental data to produce depth-dependent random phase screens. We specify the number and interval of phase screens based on Fourier optics theory so that we can determine the placement depth of phase screens reasonably. By fitting the WOS statistical results under various typical sea areas and system configurations, we propose the mixture Weibull-generalized Gamma (WGG) distribution to model oceanic turbulence-induced intensity fading. We then develop the analytical expression of the outage probability (OP) and average bit-error rate (BER) for vertical underwater wireless optical communication (UWOC) systems by use of the WGG distribution. The analytical results demonstrate the non-negligible effects of water depths on the performance of vertical UWOC systems.