A Lagrangian photoresponse model coupled with 2nd-order turbulence closure

Vertical mixing can transport nutrients from deep layer to euphotic zone. Therefore, it plays a very important role for biological productivity. Also, it can transport phytoplankton vertically and varies light exposure history of individual phytoplankton. When phytoplankton_fs response to the ambient light intensity is slow compare to the time scale of vertical mixing, production averaged in space can be varied caused by vertical mixing. In the past, such effects of vertical mixing on the photoresponse of phytoplankton have been considered with constant eddy diffusivity. However, vertical mixing is not independent of time, and variable vertical mixing in time should be examined for the Lagrangian photoresponse. In present study, a 2nd-order turbulence closure approach was coupled with a Lagrangian phytoplankton model, in order to examine the effect of time-dependent vertical eddy diffusion on the photoresponse of phytoplankton in a wind-driven upper mixing layer. In general, stronger wind mixing in a lower-transparency water column contributes to greater phytoplankton production. According to our study, vertical mixing is insignificant for photoinhibition in relatively clear open ocean water, while it can be more important in relatively turbid coastal water. A simple Ekman layer model provided surprisingly similar production to that observed with the 2nd-order closure scheme when the starting distribution of the phytoplankton cells was normalized. Two factors involved in the process are the change in the background stratification and the time dependence of the diffusivity coefficient. The influences of these 2 factors cancel each other to reduce the apparent difference between the total production estimated by the Ekman model compared to that estimated by the 2nd-order closure scheme.