Residence time and exposure time of sinking phytoplankton in the euphotic layer

The residence time of a sinking particle in the euphotic layer is usually defined as the time taken by this particle to reach for the first time the bottom of the euphotic layer. According to this definition, the concept of residence time does not take into account the fact that many cells leaving the euphotic layer at some time can re-enter the euphotic layer at a later time. Therefore, the exposure time in the surface layer, i.e. the total time spent by the particles in the euphotic layer irrespective of their possible excursions outside the surface layer, is a more relevant concept to diagnose the effect of diffusion on the survival of phytoplankton cells sinking through the water column.While increasing the diffusion coefficient can induce both a decrease or an increase of the residence time, the exposure time in the euphotic layer increases monotonically with the diffusion coefficient, at least when the settling velocity does not increase with depth. Turbulence is therefore shown to increase the total time spent by phytoplankton cells in the euphotic layer.The generalization of the concept of exposure time to take into account the variations of the light intensity with depth or the functional response of phytoplankton cells to irradiance leads to the definition of the concepts of light exposure and effective light exposure. The former provides a measure of the total light energy received by the cells during their cycling through the water column while the latter diagnose the potential growth rate.The exposure time, the light exposure and the effective light exposure can all be computed as the solution of a differential problem that generalizes the adjoint approach introduced by Delhez et al. (2004) for the residence time. A general analytical solution of the 1D steady-state version of this equation is derived from which the properties of the different diagnostic tools can be obtained.