In this paper, we investigate the performance of vertical underwater visible light communication (VLC) links. In vertical links, water properties such as temperature and salinity change with the depth. This leads to changes in the refractive index eventually affecting the variance of turbulence-induced fading. Considering such variations with respect to depth, we first model the vertical underwater link as the concatenation of multiple layers and develop a statistical turbulence channel model based on the cascaded structure of fading coefficients. Then, we use this expression to formulate a closed form expression for bit error rate performance. We confirm the analytical derivations through simulations.