An arc tangent model of irradiance in the sea

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Abstract
The solar energy flux as a function of depth (the irradiance profile) in the ocean is an important function. It influences the dynamics of the mixed layer via the heat budget as well as the biology of the euphotic zone. The following three‐parameter model can take into account the very rapid decrease near the surface due to absorption of long‐wavelength radiation by water as well as the eventual exponential decrease at great depths. , where E(z) is the irradiance at depth z and K1, K2, and K3 are constants that depend on the optical properties of the water. The constants are determined for Jerlov's water types. The constants can readily be calculated from any irradiance profile.

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