Approximation formulas for the microphysical properties of saline droplets

Abstract

Microphysical theory has proven essential for explaining sea spray's role in transferring heat and moisture across the air-sea interface. But large-scale models of air-sea interaction, among other applications, cannot afford full microphysical modules for computing spray droplet evolution and, thus, how rapidly these droplets exchange heat and moisture with their environment. Fortunately, because the temperature and radius of saline droplets evolve almost exponentially when properly scaled, it is possible to approximate a droplet's evolution with just four microphysical endpoints: its equilibrium temperature, Teq; the e-folding time to reach that temperature, τT; its equilibrium radius, req; and the e-folding time to reach that radius, τr. Starting with microphysical theory, this paper derives quick approximation formulas for these microphysical quantities. These approximations are capable of treating saline droplets with initial radii between 0.5 and 500 μm that evolve under the following ambient conditions: initial droplet temperatures and air temperatures between 0 and 40 °C, ambient relative humidities between 75% and 99.5%, and initial droplet salinities between 1 and 40 psu. Estimating Teq, τT, and τr requires only one-step calculations; finding req is done recursively using Newton's method. The approximations for Teq and τT are quite good when compared to similar quantities derived from a full microphysical model; Teq is accurate to within 0.02 °C, and τT is typically accurate to within 5%. The estimate for equilibrium radius req is also usually within 5% of the radius simulated with the full microphysical model. Finally, the estimate of radius e-folding time τr is accurate to within about 10% for typical oceanic conditions.