  In this paper, we model the multi-layer vertical underwater link as a
cascaded channel and unify the performance analysis for the underwater optical
communication (UWOC) system using generalized Gamma (GG), exponential GG (EGG),
exponentiated Weibull (EW), and Gamma-Gamma ({\Gamma}{\Gamma}) oceanic
turbulence models. We derive unified analytical expressions for probability
density function (PDF) and cumulative distribution function (CDF) for the
signal-to-noise ratios (SNR) considering independent and non-identical
(i.ni.d.) turbulent models and zero bore-sight model for pointing errors. We
develop performance metrics of the considered UWOC system using outage
probability, average bit error rate (BER), and ergodic capacity with asymptotic
expressions for outage probability and average BER. We develop the diversity
order of the proposed system to provide a better insight into the system
performance at a high SNR. We also integrate a terrestrial OWC (TOWC) subjected
to the combined effect of generalized Malaga atmospheric turbulence,
fog-induced random path gain, and pointing errors to communicate with the UWOC
link using the fixed-gain amplify-and-forward (AF) relaying. We analyze the
performance of the mixed TWOC and multi-layer UWOC system by deriving PDF, CDF,
outage probability, and average BER using the bivariate Fox H-function. We use
Monte-Carlo simulation results to validate our exact and asymptotic expressions
and demonstrate the performance of the considered underwater UWOC system using
measurement-based parametric data available for turbulent oceanic channels.
