A simple analytical formula to compute clear sky total and photosynthetically available solar irradiance at the ocean surface

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Abstract
A simple yet accurate analytical formula is proposed to compute total and photosynthetically available solar irradiance at the ocean surface under clear skies. The formula takes into account the most important processes occurring within the atmosphere, namely, scattering by molecules and aerosols and absorption by water vapor, ozone, and aerosols. These processes are parameterized as a function of solar zenith angle, aerosol type, atmospheric visibility, and vertically integrated water vapor and ozone amounts. When compared with the radiative transfer model of Tanré et al. (1979), the formula shows excellent agreement (to within 1%) under most atmospheric conditions and solar zenith angles. There is also good agreement with formulas developed by other investigators to estimate total solar irradiance. Comparisons of calculated and measured total and photosynthetically available solar irradiances for several experiments in both tropical and mid‐latitude oceanic regions show 39 and 14 Wm−2 rms errors (6.5 and 4.7% of the average measured values) on an hourly time scale, respectively. The proposed formula is unique in its ability to predict surface solar irradiance in the photosynthetically active spectral interval. Furthermore, it may also be used for converting total irradiance measurements into photosynthetically available irradiance estimates. Combining the clear sky irradiance formula with satellite techniques to retrieve cloud effect on solar irradiance, pigment concentration, and sea surface temperature would provide useful primary productivity estimates over large oceanic areas and eventually the global oceans.