A model based on a matrix-operator theory capable of simulating underwater daylight in the ocean is presented. The main focus is on gelbstoff and chlorophyll fluorescence as well as water Raman scattering as sources of inelastic scattering and their effect on underwater daylight and relevance for the remote sensing of ocean color. Any combination of inelastic sources can be investigated, including differences in simulated underwater daylight in the absence and the presence of these sources. To our knowledge, it is the first matrix-operator model to include all these inelastic sources. The model allows simulations for case 1 and case 2 waters. Calculations can be done with highly anisotropic phase functions as they are observed in the ocean, and every order of multiple scattering is considered. A detailed mathematical description of inelastic sources is given, and a special treatment of the depth dependency of these sources is presented. The model is validated by comparison with depth-dependent and spectrally resolved measurements of downward irradiance in the open ocean. The differences between measured and simulated data are within the error of the radiometric measurements. Water Raman scattering has been found to contribute significantly to water-leaving radiance. The inelastic fraction depends on the water Raman scattering coefficient, on the ratio of the total attenuation coefficient at excitation and emission wavelengths, and on the spectral course of the irradiance incident on the ocean. For clear ocean waters the inelastic fraction can reach values of more than 17% [C = 0.03 mg m-3, ay (440 nm) = 0.01 m-1] at wavelengths relevant for the remote sensing of ocean color. The inelastic fraction of gelbstoff fluorescence can reach or even exceed the relevance of water Raman scattering at short wavelengths. In the water column, depending on optically active substances and on actual depth, water Raman scattering can provide 100% of the light field at wavelengths greater than 580 nm. The effect of gelbstoff fluorescence on depth-dependent irradiances is less significant than the effect of water Raman scattering in all cases considered, except for near surface levels and high gelbstoff concentrations.
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