Modeling variation coefficient of wave-induced underwater irradiance for clear ocean and its application to find the optimal detector size.

In measuring the coefficient of variation (CV) of underwater wave-induced sunlight irradiance, the spatial integration of irradiance signals due to the finite aperture size of an irradiance detector usually causes underestimation of the measured variance. Because this spatial integration effect is strongly coupled with ocean wave features, inherent optical properties (IOPs) of water, and atmospheric radiance conditions, direct deconvolution techniques from measured irradiance signals can lead to serious signal-to-noise degradation in a noisy upper ocean. On the other hand, choosing a small detector to guarantee CV accuracy is expensive. We address the intrinsic dependence of the CV on the detector size and choice of optimal detector size for measuring irradiance variability in a turbid ocean environment. We present a new theoretical model to directly obtain the form of the CV of the wave-induced scalar irradiance as the function of the detector size, ocean surface wave parameters, and IOPs of ocean water. The model is derived under the small-angle scattering approximation and the first-order assumption of Snell's law and Fresnel transmission coefficient. We demonstrate the validity and efficacy of the model for weakly roughened Gaussian ocean surface conditions, by comparison with Monte Carlo radiative transfer simulations. The model shows that the CV of wave-induced irradiance reaches an asymptotic with decreasing the detector size, thereby providing an optimal or maximum detector size for given IOP and environmental conditions.