Relationship of the Quanta-to-Energy Ratio of Photosynthetically Active Radiation with Chlorophyll-a in Case I Seawater

A predetermined quanta-to-energy ratio is often used in many ecosystem models to transform photosynthetically radiant flux density into photosynthetic photon flux density when light penetrates seawater. The calculation formula of the ratio is reduced in this study as the product of a constant and the defined principal wavelength. The principal wavelength is discussed in this paper and may be expressed as an exponential function using theoretical reasoning. The deviation of the principal wavelength is defined as the difference between two natural logarithms of the observed principal wavelength in real seawater and the simulated principal wavelengths of pure seawater under the same surface solar radiation. The deviation has a quasi-linear relationship with the non-water diffuse attenuation coefficient at 490 nm, which is related to the chlorophyll-a concentration. A semi-empirical formula between the deviation and chlorophyll-a concentration is established with a determination coefficient of more than 84%. In pure seawater, an empirical formula for the principal wavelength profile is also constructed. The parameterization formula for the quanta-to-energy ratio is provided as a function of the chlorophyll-a concentration and the surface principal wavelength. When applied to in situ observations, the statistical relative inaccuracy is found to be less than 10%. The parameterization formula can be applied to the ecosystem models to realize the transformation between photos and energy in the PAR waveband.