Estimates of radiance reflected towards the zenith at the surface of the sea

Remote sensing of water colour by ship-mounted sensors represents an important tool for the validation of satellite products and the monitoring of water quality. The recorded radiance from the sea has to be corrected for the surface-reflected radiance from sun and sky in order to obtain the water-leaving radiance. Here the simple case of radiance reflected towards the zenith is studied. A set of observed sky radiance and solar irradiance data from Oslo has been used together with a Gaussian slope distribution for the sea surface in order to estimate the reflected radiance. The spectral range studied is 405-650 nm, the solar zenith angles are in the range 37 degrees-76 degrees, and the wind speeds are up to 10 ms(-1). The analysis of the results show that the reflected radiance has to be separated into three contributions: sky radiance and sun rays reflected at the foam-free surface and irradiance reflected by whitecaps and foam. It is then demonstrated that by using four input values, namely the downward irradiance, the sky radiance from the zenith, the solar zenith angle and the wind speed, it is possible to obtain by simple expressions estimates of the reflected radiance that only differ from the former calculated values by relative errors of less than 5%. The analysis also indicates that for the spectral range studied neither the water-leaving radiance nor the surface-reflected radiance can be disregarded relative to the other one in the Case 2 waters of the Oslofjord-Skagerrak area. The results form a first step towards the study of reflected radiance in viewing angles differing from the nadir direction.