## Optical depth

As we have already noted, but will discuss more fully later, the downward irradiance diminishes in an approximately exponential manner with depth. This may be expressed by the equation

where Ed (z) and Ed(0) are the values of downward irradiance at z m depth, and just below the surface, respectively, and Kd is the average value of the vertical attenuation coefficient over the depth interval 0 to z m. We shall now define the optical depth, Z, by the eqn

It can be seen that a specified optical depth will correspond to different physical depths but to the same overall diminution of irradiance, in waters of differing optical properties. Thus in a coloured turbid water with a high Kd, a given optical depth will correspond to a much smaller actual depth than in a clear colourless water with a low Kd. Optical depth, Z, as defined here is distinct from attenuation length, t (sometimes also called optical depth or optical distance), which is the geometrical length of a path multiplied by the beam attenuation coefficient (c) associated with the path.

Optical depths of particular interest in the context of primary production are those corresponding to attenuation of downward irradiance to 10% and 1% of the subsurface values: these are Z = 2.3 and Z = 4.6, respectively. These optical depths correspond to the mid-point and the lower limit of the euphotic zone, within which significant photosynthesis occurs.

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