Vertical advection of phytoplankton and productivity estimates: a dimensional analysis

Standard incubation procedures may underestimate phytoplankton productivity by maintaining the organisms at fixed light intensities or depths. Conditions under which bias could occur are quantified in terms of 2 dimensionless groups. The first is a dimensionless time, t' = k2Yt, where k = diffuse attenuation coefficient for light, K, = coefficient of vertical eddy diffusivity, t = incubation time. It represents the duration of the incubation scaled to the time required for a freely-circulating ensemble of phytoplankton to diffuse 1 optical attenuation length. The second is a photoinhibition index, (Ib')-' = I&,. where I . = surface incident irradiance, I, is a parameter characterizing the photoinhibition region of the light saturation curve of photosynthesis; photoinhibition at surface intensities is 0 when (Ita)-' = 0, and increases as (Itm)-l increases. Published data on the effects of vertical motion on phytoplankton photosynthesis indicate that (Ib')-' must exceed a critical value for negative bias to occur in productivity estimates. In general, the critical value is a function of t', but certain boundaries can be identified. A minimum critical value of (Itm)-' = 0.25 (i.e. low susceptibility to photoinhibition), below which there is no bias, occurs at t' = 10. For (I,')-' > 1.5 (high susceptibility to photoinhibition), some bias occurs for all values of t' Values of (Ib')-' are examlned in 4 regions to infer the degree to which previous data sets may have been biased.