Critical Depth and Marine Primary Production

The concept of critical depth, as formulated by Sverdrup (J. Cim. perm. int. Explor. Mer. 18, 287 (1953)) to explain the onset of the spring bloom of phytoplankton, is discussed. Simplifying assumptions (use of a linear photosynthesis-light curve, use of daily averaged irradiance), adopted by Sverdrup in his computation of the growth term, are removed. An exact expression is found for the critical depth in terms of a generalized, biomass-specific, loss term. The loss term is calculated as the sum of contributions from algal respiration and excretion, grazing by micro- and macro-zooplankton, and sedimentation. Critical depth is then estimated using figures typical of the North Atlantic, and a sensitivity analysis is done. The respiratory costs of algal growth and metabolism dominate the generalized loss term. It is pointed out that the Sverdrup critical depth criterion is a necessary, but not sufficient, condition for the initiation of phytoplankton blooms. As a diagnostic tool, its value is therefore limited. It tells only whether net growth is possible: it tells nothing about how rapidly the phytoplankton will increase. But from the information used to calculate critical depth, it is possible to deduce the rate of increase in algal biomass (or, equivalently, the net production) for the mixed layer. As long as the growth rate is positive, the Sverdrup criterion is respected. This leads to a characteristic timescale for the development of a bloom. When the timescale is short relative to the time between mixing by storms, a bloom can be expected to occur.