Statistical Characterization of Wind-Induced Beam Refraction in Water-to-Air Optical Channels

Direct water-to-air (W2A) optical communications experience strong beam refraction at the dynamic sea surface. This letter proposes a novel and tractable statistical channel model for a vertical W2A link between an underwater node and an unmanned aerial vehicle under varying wind speeds, modeling wind-induced pointing errors with a Beta mixture fitted via the Expectation-Maximization algorithm. By accounting for link interruptions due to total internal reflection (TIR) and receiver field-of-view limitations, we derive closed-form expressions for the channel distribution and link outage probability. Our analysis reveals a fundamental TIR-induced outage floor limiting link reliability and providing insight for robust W2A system design.