Open AccessA model for the probability density function of downwelling irradiance under ocean waves
Author(s) -
Max Shen,
Zao Xu,
Dick K. P. Yue
Publication year - 2011
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.19.017528
Subject(s) - downwelling , probability density function , monte carlo method , statistical physics , optics , exponential function , gaussian , physics , irradiance , geology , mathematics , statistics , mathematical analysis , quantum mechanics , oceanography , upwelling
We present a statistical model that analytically quantifies the probability density function (PDF) of the downwelling light irradiance under random ocean waves modeling the surface as independent and identically distributed flat facets. The model can incorporate the separate effects of surface short waves and volume light scattering. The theoretical model captures the characteristics of the PDF, from skewed to near-Gaussian shape as the depth increases from shallow to deep water. The model obtains a closed-form asymptotic for the probability that diminishes at a rate between exponential and Gaussian with increasing extreme values. The model is validated by comparisons with existing field measurements and Monte Carlo simulation.