Self‐shading of in‐water optical instruments

Abstract
The self‐shading of in‐water optical radiometers for measuring upwelling (Lu) and irradiance (Eu) is estimated from Monte Carlo simulations of the light field in the presence and absence of the instrument. It is found that the error (ε) induced by the presence of the radiometer is a function of its size and the absorption coefficient (a) of the medium, i.e. when ε 15–20% the error is independent of the scattering coefficient (b). Direct measurement of Lu or Eu with ε ≤ 5% places severe limitations on the instrument size, e.g. in the case of a cylindrical housing and small solar zenith angles (the worst case) the diameter of the instrument must be ≲ 1/30a for Eu and ≲ 1/100a for Lu. A correction method based on a simple model of ε is proposed and it is shown that when used these constraints on the diameter are reduced to 1/6a and 1/30a, respectively, for an after‐correction error of 5%. The self‐shading error is estimated across the spectrum as a function of the pigment concentration of case 1 waters, and it is found that it can be large for typical radiometers, especially at high pigment concentrations or wavelengths >600 nm.