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: One of the most striking features of the upper North Atlantic Ocean is an extensive layer of water with temperature close to 18°C and salinity close to 36.5‰, (ref. 1). This 18°C water is formed by winter convection in the Sargasso sea2,3, but aspects of the annual rate of 18°C water formation remain obscure4. We have simulated this water mass formation by integrating a one-dimensional model along a 4-yr trajectory of a water column circulating around the Sargasso Sea. Winter convection is deep (≥200 m) in regions where the ocean suffers a net annual heat loss to the atmosphere, and shallow (≤lOOm) where the ocean gains heat each year. The origin of the thermostad (nearly isothermal layer) is a thick layer of nearly homogeneous water subducted beneath the seasonal boundary layer in the year that the water column passes through the line dividing annual cooling from annual heating. We estimate the annual production of 18°C water to be 446,000 km3 yr−1. Downstream, more stratified central water is formed each year at a rate that depends more on Ekman pumping (wind-forced convergence) than on the decreasing depth of winter convection