Reflection of Spectral Sky Irradiance on the Surface of the Sea and Related Properties

Observed angular distributions of spectral sky radiance clearly demonstrate the anisotropic nature of the radiance and lead to significant deviations from the isotropic case when the optical quantities resulting from these distributions are calculated. The ratio of diffuse downward irradiance and zenith radiance is determined at seven wavelengths from 370 nm to 650 nm, varying between 1.8 and 5.1 at 370 nm for the solar zenith angle range θs=17°–67°, and between 1.2 and 8.5 at 650 nm for the range θs=16°–76°. A consequence of these observations is that the frequently applied assumption of isotropic sky radiance may lead to errors of up to 170% for the contribution to nadir radiance from zenith radiance reflected on the surface of the sea. The surface reflectance of diffuse irradiance obtains values between 0.053 and 0.088 at 370 nm θs=12°–67° and between 0.048 and 0.124 at 650 nm θs=13°–76°. The assumption of isotropic sky radiance may in this case lead to errors of up to 85% for the reflectance. The values for the average cosine of downward sky radiance lie in the range 0.43–0.60 at 370 nm θs=12°–67° and in 0.31–0.62 at 650 nm θs=13°–76°, which again are significant deviations from the value 0.50 for the average cosine of the isotropic radiance distribution. Beneath the surface of the sea the transmitted sky radiance produces an average cosine that only varies between 0.82 and 0.89 at 370 nm θs=12°–67° and between 0.78 and 0.89 at 650 nm θs=13°–76°. Linear relations approximating the ratio of diffuse irradiance and zenith radiance, the diffuse reflectance, and the average cosines as functions of the solar zenith angle are presented. The determining factors in predictions of the mentioned optical quantities become the diffuse downward irradiance, the ratio of diffuse and total irradiance, and the solar zenith angle.