The total radiant energy, and the average depth of all the photons, in the water column

John T. O. Kirk

Limnol. Oceanogr., 58(1), 2013, 93-98 | DOI: 10.4319/lo.2013.58.1.0093

ABSTRACT: Using radiative transfer theory I show that for a given waveband, the total radiant energy, Q_t, present within the water column (per square meter of surface) is proportional to the scalar irradiance just below the surface [E₀(0)] and inversely proportional to the irradiance-weighted vertical attenuation coefficient for scalar irradiance (^wK_0,av), in accordance with[eqn] where c_w is the speed of light in the water. Further, Qt = E(0)/c_wa where E(0)is the net downward irradiance just below the surface, and a is the absorption coefficient of the water for the waveband in question. The average depth, z_p, of all the photons in the water column in a given waveband is equal to [^wK_E,av]^-1, the reciprocal of the irradiance-weighted vertical attenuation coefficient for net downward irradiance. This conclusion, at which we arrive on theoretical grounds, is confirmed by numerical modeling of the underwater light field.