Vertical attenuation coefficient for the downward irradiance in the spectral range (lambda, lambda + delta lambda) can be defined as follow:
Vertical attenuation coefficient for the upward irradiance in the spectral range (lambda, lambda + delta lambda) can be defined:
The vertical attenuation coefficients are the apparent properties of sea water. They depend on the concentration and composition of the suspended and dissolved matter, the position, the depth, the orientation, the wavelength, the solar elevation, the cloud cover, the state of the sea, the depth to the bottom and the albedo of the bottom.
In homogeneous sea waters they are almost independent from the surface light conditions (solar elevation) and the depth, i.e. they display quasi-inherent properties. For inhomogeneous sea waters normally horizontally stratified within the relevant length scales, they vary only slightly with respect to the solar elevation.
The vertical attenuation coefficients attain always positive values in both absorbing and passive (no internal radiating sources) media, like sea water. In some rare cases with high concentrations of plankton pigments near the surface the sea water can not be considered passive around lambda=685 nm due to intense pigment fluorescence. So, in this spectral region and at shallow depths even negative K (lambda=685 nm) can be observed.
Højerslev N. K., 1986, Optical properties of sea water, [In:] Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Vol. 3 Oceanography, J. Sündermann, (Ed.), Springer-Verlag, Berlin etc...