One-dimensional numerical simulation of primary production: Lagrangian and Eulerian formulations
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It has been argued (Wolf and Woods, in Toward a Theory On Biological-Physical Interactions in the World Ocean, Rothschild, (ed.), 1988) (WW88) that phytoplankton growth models are sensitive to Lagrangian effects because populations at a given depth and time contain a wide distribution of photoadaptive properties. On the other hand, Lande and Lewis (Deep-Sea Research, 36, 1161-1175, 1989) (LL89) have claimed that for a different photosynthetic model, this distribution of properties can be adequately represented by a mean value in a much simpler and more efficient Eulerian formulation. This study compares Lagrangian and Eulerian integrations of these two different models of photosynthesis under two mixing regimes. For relatively weak mixing, the growth rate predicted by the different formulations of the two models is small (less than or equal to 5%). In vigorously mixed conditions, Lagrangian effects cause a significant (similar to 20%) reduction in the mean growth rate of the WW88 model, while the differences in the two integrations of the LL89 model differ only slightly (similar to 3%). The apparent discrepancy in the comparisons between Lagrangian and Eulerian integrations of the two different photosynthesis models is a result of different parameterizations of photoadaptive reaction kinetics.