A model for the probability density function of downwelling irradiance under ocean waves

Area of Science:

• Ocean Optics
• Statistical Modeling
• Radiative Transfer

Background:

• Accurate quantification of underwater light irradiance is crucial for understanding marine ecosystems and optical remote sensing.
• Existing models often simplify ocean surface wave effects or light scattering, limiting their predictive accuracy in diverse conditions.

Purpose of the Study:

• To develop a novel statistical model for analytically quantifying the probability density function (PDF) of downwelling light irradiance.
• To incorporate the distinct influences of surface short waves and volume light scattering on light distribution.
• To capture the PDF's shape evolution from skewed in shallow water to near-Gaussian in deep water.

Main Methods:

• Modeled the ocean surface as independent and identically distributed flat facets.
• Developed a theoretical framework to analytically derive the PDF of downwelling light irradiance.
• Derived a closed-form asymptotic for the probability of extreme values.

Main Results:

• The statistical model successfully quantifies the PDF of downwelling light irradiance under random ocean waves.
• The model demonstrates that the PDF shape transitions from skewed to near-Gaussian with increasing water depth.
• An asymptotic form was derived, showing extreme value probabilities diminish at a rate between exponential and Gaussian.

Conclusions:

• The presented statistical model provides an accurate and versatile tool for predicting underwater light irradiance.
• The model's ability to incorporate wave and scattering effects enhances its applicability across various oceanic environments.
• Validation against field measurements and Monte Carlo simulations confirms the model's reliability.