Description: Solar heating is an important factor in modelling the upper boundary layer of the ocean. It influences not only the temperature, but also the depth of the mixed layer and must be taken into account in circulation dynamics. The study reported in this paper was designed to reveal the principal features of the global climatology of solar heating in the ocean, with such applications in mind. The meridional, seasonal and diurnal variations of the vertical distribution of solar heating inside the ocean, expressed in terms of I(z), the rate of heat accumulation below depth z, and †(z) = (1/c). dzI(z), the rate of temperature rise, are calculated for given values of cloud cover and seawater turbidity (expressed in terms of Jerlov's water types) using a model that incorporates a new parametrization of I(z)/I(0), which is shown to be more accurate than previous versions. At present there exist no reliable global climatologies of cloud cover and seawater turbidity, so the values of the corresponding parameters are held constant in each computation, which is then repeated using parameter sets covering the full ranges from clear to overcast sky, clear to turbid ocean water. It is found that uncertainty in cloud cover is more important in the mixed layer, and uncertainty in seawater turbidity is more important below. The results presented in this paper are mainly concerned with solar heating below the mixed layer. It is calculated that the annual temperature rise can exceed 1 K and the annual heat accumulation can exceed 100 MJ/m2 below the mixed layer in the tropics. At higher latitudes solar heating produces similar heating rates in summer, but the stored heat is extracted locally in winter when the mixed layer depth exceeds the maximum depth of solar heating, defined here by a daily temperature rise of 1 mK or a heat flux of 86.4 KJ/m2d (=1 W/m2). The sensitivity of the seasonal and meridional variations of the maximum depth of solar heating to cloud cover and seawater turbidity is investigated. The actual change of temperature due to solar heating in the seasonal thermocline at Ocean Weather Station ‘C’ is calculated using Bunker's monthly mean cloud cover and Jerlov's seawater turbidity. Extension of such calculations to the whole of the World Ocean must await the publication of global climatologies of cloud cover and seawater turbidity, which are expected to be derived from satellite observations during the next decade. A solar heating climatology is a prerequisite for computation of the thermal response of the ocean to CO2 pollution of the atmosphere. The implications of the results obtained from the present study are discussed. An early rise in tropical sea surface temperature seems likely, but exact prediction will be hindered by uncertainty in the turbidity of the tropical ocean.

Description: The results of two earlier papers on convection in the mixed layer and on the solar heating profile are here introduced into a one-dimensional model in order to investigate the following consequences of the daily cycle of solar heating in the upper ocean: 1. the daytime convection depth becomes less than the turbocline depth; 2. the convective power supply to turbulence in the mixed layer is reduced; 3. the mixed layer below the convection layer becomes stably stratified; 4. the depth of the turbocline is reduced, leaving a diurnal thermocline between it and the top of the seasonal thermocline; 5. the heat content and potential energy of the diurnal and seasonal thermoclines are increased, slowing down the subsequent nocturnal descent of the turbocline. These diurnal changes are illustrated by integrating a one-dimensional model forced by the astronomical cycle of solar heating and seasonal variation of surface meteorology derived from Bunker's climatology. The model is integrated for 18 months to show the seasonal modulation of the diurnal cycle. Nocturnal convection plays a dominant role. The convection depth closely follows the thermal compensation depth during the day when they are less than the turbocline depth. Integrating the model with a 24-hour time step leads to large errors in the seasonal variation of mixed layer temperature and depth, and in the source term of isopycnic potential vorticity. The errors are reduced by using two time steps per day, one for the daytime when convection is quenched, the other for the night when it is active. A novel parametrization based on tuning the daily equivalent solar elevation to surface temperature further reduces the error. This parametrization is used to investigate the sensitivity of the seasonal cycles of mixed layer depth and temperature to: (1) seasonality in the surface fluxes; (2) systematic changes in the net annual solar heating; (3) random changes in the seasonal cycles of solar heating induced (i) monthly and (ii) daily. The sensitivity to uncertainty in seawater turbidity is investigated in the same way. The profile of isopycnic potential vorticity subducted into the thermocline depends on the vernal correlation of mixed layer depth and density, so gyre circulation is sensitive to solar heating in spring.

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: This paper establishes the predictability of a one-dimensional virtual plankton ecosystem created by Lagrangian Ensemble integration of an individual-based model. It is based on numerical experiments for a scenario, in which the surface fluxes have stationary annual cycles, and the annual surface heat budget is in balance, i.e. solar heating equals cooling to the atmosphere. Under these conditions, the virtual ecosystem also followed a stationary annual cycle. We investigate the stability of this ecosystem by studying the statistics of multi-year simulations of the ecosystem in a virtual mesocosm moored off the Azores. The integrations were initialised by a first guess at the state of the ecosystem at the end of the cooling season, when the mixed layer was approaching the annual maximum depth. The virtual ecosystem quickly adjusted to a stable attractor, in which the inter-annual variation was only a few percent of the multi-year mean. This inter-annual variation was due to random displacement of individual plankters by turbulence in the mixed layer. The inter-annual variance is nearly, but not exactly ergodic; the deviation is due to inheritance of zooplankton weight through lineages. The virtual ecosystem is independent of initial conditions: that is the proof of stability. The legacy of initialisation error decays within three years. The form of the attractor depends on three factors: the specification of the ecosystem model, the resource level (nutrients), and the annual cycle of external forcing. Sensitivity studies spanning the full range of model parameters and resource levels demonstrate that the virtual ecosystem is globally stable. In extreme cases the zooplankton becomes extinct during the simulation; the attractor adjusts gracefully to this new regime, without the emergence of vacillation or a strange attractor that would signal instability. At high resource levels, some of the zooplankton produce two generations per year (as was observed by Marshall and Orr [Marshall, S. M., and Orr, A. P. (1955). The biology of a marine copepod. Edinburgh: Oliver and Boyd. 188 pp.]; again the attractor adjusts gracefully to the new regime. Ocean circulation does not disrupt the stability of the virtual ecosystem. This is demonstrated by a numerical experiment in which the virtual ecosystem drifts with the mean circulation on a five-year cycle, following a track in the Sargasso Sea that penetrates deep into the zones of annual heating and cooling. The legacy of initialisation error decays within three cycles of the external forcing. Thereafter the ecosystem lies on a five-year geographically/lagrangian attractor. The stability of virtual ecosystems offers useful predictability with a good sign-to-noise ratio. (c) 2005 Elsevier Ltd. All rights reserved.

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 profile generated by a steady wind stress is disturbed by the diurnal variation of mixed layer depth forced by solar heating. Momentum diffused deep at night is abandoned to rotate inertially during the day when the mixed layer is shallow and then re-entrained next night when it deepens. The resulting variation of current profile has been calculated with a one-dimensional model in which power supply to turbulence determines the profile of eddy viscosity. The resulting variations of current velocity at fixed depths are so complicated that it is not surprising that current meter measurements have seldom yielded the classical Ekman solution. However, the progressive vector diagrams do exhibit an Ekman-like response (albeit with superimposed inertial disturbances) suggesting that the model might be tested by tracking drifters designed to follow the flow at fixed depths. The inertial rotation of the current in the diurnal thermocline leads to a diurnal jet, the dynamical equivalent of the nocturnal jet in the atmospheric boundary layer over land. The role of inertial currents in deepening the mixed layer is clarified, leading to proposals for improving the turbulence parametrizations used in models of the upper ocean. The model predicts that the diurnal thermocline contains two layers of persistent vigorous turbulence separated by a thicker band of patchy turbulence in otherwise laminar flow.