A Simple Model of Sea Spray

Abstract

We propose a stochastic model of sea spray as a shot noise process attached to a homogeneous Poisson process whose intensity measure is the sea spray generation function, that is to say the average number of droplets of a given radius ejected into the atmosphere per unit area per unit time. We assume the impulse response function defining the shot noise is determined by the trajectory of the center of a spherical droplet whose radius may change with time. We also assume the droplet trajectory is vertical and droplets don't interact with one another. Under these assumptions we show the total mass of airborne sea spray droplets is a stationary stochastic process whose mean and covariance can be written explicitly as functions of the physical parameters. We illustrate the model through examples of increasing physical relevance the most general of which includes gravity, Stokes drag forces, and Langmuir's D-squared law of evaporation. A consequence of this particular example is an estimate of the height of the marine boundary layer at sufficiently large wind speeds.