Description: Understanding the plankton ecosystem in the ocean requires detailed demographic analysis. It is impossible to sample the ocean adequately for such analysis, but progress can be made by analysing data sets generated by mathematical models provided they realistically simulate the ecosystem. The Lagrangian Ensemble method is well suited to demographic studies because it generates large data sets containing complete information on all the families living in the simulated ecosystem. It provides audit trails of individual families for unambiguous analysis of mechanisms responsible for the simulated changes in community and environment. Recent papers based on the Lagrangian Ensemble method are reviewed.

Description: According to Sverdrup's (1953) model of the spring bloom, phytoplankton biomass decreases in winter when the mixed layer depth exceeds the critical depth. We have used a one-dimensional mathematical model integrated by the Lagrangian Ensemble method to simulate a population of diatoms during the winter between two growing seasons off the Azores. The model allows us to diagnose the demographic changes in the simulated diatom population from a variety of perspectives. The total population falls to a minimum of 70 million diatoms m-2 at the end of February. The vertical distribution of the population dynamics is first analysed in terms of daily Eulerian averages over 1 m depth intervals. Growth starts in February when the diurnal thermocline becomes shallower than 50 m, but while the mixed layer is still 200 m deep. The natural mortality has a minimum in winter because it is reduced (in the model) with temperature and population density. Eulerian analysis suggests that in winter, diatoms have a life expectancy of more than 3 months, so a significant number will survive the months of December, January and February when there is very little growth. Losses to grazing are negligible in winter. Lagrangian analysis shows how an individual diatom responds to its changing ambient environment caused by variation in depth (due to turbulent mixing) and the diurnal and seasonal changes in the photosynthetically active radiance. The different trajectories followed by the thousands of plankton particles simulated by the model produce diversity in growth rate ranging over several orders of magnitude, so care has to be taken in statistical analysis. The paper ends with a re-assessment of the value of the critical depth and compensation depth as predictors for onset of the spring bloom. The compensation depth was computed by Eulerian averaging over 1 m depth inter-vals each day. For 1 month after the vernal equinox the compensation depth follows the ascent of the mixed layer as it rises from a depth of 100 m to 40 m. Lagrangian analysis reveals that this is due to the photo-adaptation better matching the ambient irradiance experienced by diatoms in the mixed layer compared with those at the same depth in the seasonal thermo-cline. By mid-April the spring bloom has already ad-vanced so far that self shading influences the compensation depth, which then rises into the mixed layer. We conclude that Sverdrup's criterion is not useful for predicting changes in the diatom population simulated by our model.

Description: The plankton multiplier is a positive feedback mechanism linking the greenhouse effect and biological pump (Woods.J.D., Royal Commission on Environmental Pollution, 1990). As pollution increases the atmospheric concentration of carbon dioxide, the enhanced greenhouse effect induces radiative forcing of the ocean, which diminishes the depth of winter convection, reducing the annual resupply of nutrients to the euphotic zone and therefore the annual primary production. That weakens the biological pump, which contributes to oceanic uptake of CO2,. As the ocean takes up less CO2, more remains in the atmosphere, accelerating the rise in radiative forcing. We have used a mathematical model of the upper ocean ecosystem, based on the Lagrangian Ensemble method, to estimate the sensitivity of the biological pump to radiative forcing, which lies at the heart of the plankton multiplier. We conclude that increasing radiative forcing by 5 W m− (equivalent to doubling atmospheric CO2) reduces the deep flux of paniculate carbon by 10%. That sensitivity is sufficient to produce significant positive feedback in the greenhouse. It means that the plankton multiplier will increase the rate of climate change in the 21st century. It also suggests that the plankton multiplier is the mechanism linking the Milankovich effect to the enhanced greenhouse effect that produces global warming at the end of ice ages.

Description: The current status of the Sverdrup theory for the initiation of plankton blooms is examined. A prescription is given for the computation of the Sverdrup critical depth, using recently-published algorithms for mixed-layer primary production and a generalised loss term. Using no further information, the intrinsic rate of increase of phytoplankton biomass in the mixed layer can also be found. This rate, compared against the local frequency of storm occurrence, provides an alternative criterion for the initiation of blooms. The Eulerian (bulk property) methods used to derive these results are contrasted with the Lagrangian Ensemble method. The Lagrangian approach provides one avenue to the elaboration of the Sverdrup criterion to include the effect of processes with characteristic timescales small compared to one day. The incidence of blooms in the apparent absence of vertical stratification is reviewed: it is concluded that these observations do not undermine the basic logic of the Sverdrup theory. However, they do provoke interest in a re-examination of the feedbacks between the physical and biological dynamics in the mixed layer: an example is given. Finally, suggestions are made for further work in this subject area.