Geoffrey T. Evans

A Model of Annual Plankton Cycles

AbstractA model is presented that exhibits a spring phytoplankton bloom as one feature of a steadily repeating annual cycle of plankton populations. Populations respond to seasonal changes in light (which are gradual) and in mixed layer depth (which may be rapid). The occurrence of a bloom does not require a shallowing of the mixed layer; it does require a low rate of primary production in winter. The lack of phytoplankton blooms in the subarctic Pacific can be explained in terms of this model.Analysis of a simplified version of the model shows that a bloom is a deviation from quasi-equilibrium behavior and explains why this will occur when winter production rates are low.

Towards a model of ocean biogeochemical processes

Themes in modelling ocean biogeochemical processes.- Global extrapolation.- Fluctuations: a task package for the physicists.- Trophic resolution.- Modelling growth and light absorption in the marine diatom Skeletonema costatum.- Carbon: a phycocentric view.- Towards a general description of phytoplankton growth for biogeochemical models.- Modelling zooplankton.- Microbial processes and the biological carbon pump.- Dissolved organic matter in biogeochemical models of the ocean.- Modelling particle fluxes.- The significance of interannual variability.- Some parametric and structural simulations with a three-dimensional ecosystem model of nitrogen cycling in the North Atlantic euphotic zone.- Data assimilation for biogeochemical models.- An annotated bibliography of marine biological models.- List of participants.

Representing phytoplankton aggregates in biogeochemical models

We show how to represent changes in the distribution of size and sinking speed of marine particles by a two-parameter model. In contrast to fully size-resolved models, this representation holds promise for constructing ocean biogeochemical models with detailed spatial resolution and seasonally varying sinking speed. We treat the mass and number of particles as separate state variables, each obeying its own conservation law. Average size and sinking speed of particles change as particles aggregate or the largest particles sink out. The distribution of particle sizes is assumed to follow a power law, whose exponent changes as a function of average particle size. Compared to biogeochemical models with constant particle sinking speed, our approach imposes a modest increase in computational cost and produces important effects like more rapid sinking immediately following a phytoplankton bloom. Compared to models that use hundreds of size classes to represent the detailed evolution of particle size distribution, our approach offers a major reduction in computational cost, while maintaining realistic behaviour like the sudden onset of significant aggregation when particles are sufficiently abundant.

The role of local models and data sets in the Joint Global Ocean Flux Study

Abstract The purpose of local studies within the Joint Global Ocean Flux Study (JGOFS) is to determine something, typically a model with parameter values, that is useful for making regional or global estimates of fluxes. An iterative process of improvement should lead towards a model that fits available local data well, and local data that constrain the range of possible models well, so that the extrapolation from local to global can be made with confidence. This paper addresses issues in evaluating the fit of models and the constraining power of data. For illustrative purposes it treats the data and the form of the model as fixed, so that improvement is confined to the parameter values of the model. The plankton model of Fasham et al.(1990) (Journal of Marine Research, 48, 591–639) fits the data of the JGOFS North Atlantic Bloom Experiment of 1989 reasonably well, and that data set constrains the parameters of that model reasonably well. Studying their interplay suggests directions for improvement in both.

Defining misfit between biogeochemical models and data sets

Abstract Marine biogeochemistry deals with diverse variables, many of them (especially biological rates) difficult to measure. For parameter estimation and data assimilation, differences between predicted and measured values of these variables must be summarized by a single misfit number. A ‘correct’ measure of misfit incorporates choices about issues that include (1) the relative importance of deviations from a small and a large predicted value; (2) the relative importance of small and large deviations from a predicted value; (3) the relative importance of deviations above and below a predicted value; (4) comparing discrepancies measured in intrinsically different units, like concentrations and rates. Recent papers on estimating ecological parameters represent a variety of different choices. This paper uses a data set and model for the subtropical North Atlantic to demonstrate that the choices made for defining misfit can have a large influence on the ‘best’ estimate of biogeochemically important fluxes and concentrations.

A vertically resolved model for phytoplankton aggregation

This work presents models of the vertical distribution and flux of phytoplankton aggregates, including changes with time in the distribution of aggregate sizes and sinking speeds. The distribution of sizes is described by two parameters, the mass and number of aggregates, which greatly reduces the computational cost of the models. Simple experiments demonstrate the effects of aggregation on the timing and depth distribution of primary production and export. A more detailed ecological model is applied to sites in the Arabian Sea; it demonstrates that aggregation can be important for deep sedimentation even when its effect on surface concentrations is small, and it presents the difference in timing between settlement of aggregates and fecal pellets.

Functional Response and Stability

R. bulbosus L., and R. acris L. I. Population flux and survivorship. J. Ecol. 61: 675-716. Shetler, S. G., and H. R. Meadow. 1972. A provisional checklist of species for Flora North America. FNA Report 64. Department of Botany, Smithsonian Institution, Washington, D.C. 648 pp. Smith, H. B. 1927. Annual versus biennial growth habit and its inheritance in Melilotus alba. Amer. J. Bot. 14:129-146. Stevens, 0. A. 1932. The number and weight of seeds produced by weeds. Amer. J. Bot. 19: 784-794. Struik, G. J. 1965. Growth patterns of some native annual and perennial herbs in southern Wisconsin. Ecology 46:401-420. Werner, P. A. 1975. Predictions of fate from rosette size in teasel (Dipsacus fullonum L.). Oecologia 20:197-201. Whittaker, R. H., and G. M. Woodwell. 1968. Dimensions and production relations of trees and shrubs in the Brookhaven forest, New York. J. Ecol. 56:1-25.

Themes in Modelling Ocean Biogeochemical Processes

This book is about how to write mechanistic models of marine ecology that describe and predict how concentrations and fluxes of biologically important elements (especially carbon) vary in space and time, throughout the ocean over many years, in response to physical forcing. Such models are needed because of widespread interest in the global carbon cycle and the ocean’s place in it. The chances of achieving them are improving because computers are getting better, because satellite remote sensing offers much more information, and because many scientists worldwide are cooperating, through the Joint Global Ocean Flux Study (JGOFS), to collect relevant data and understand relevant processes. As different research groups undertake modelling projects, comparisons between them can become as much of an issue as comparisons with observations. It will help the whole modelling community if common approaches are used where possible, and if divergent approaches arise from clearly understood reasons instead of by accident. In the first week of May 1992, a NATO Advanced Research Workshop (with additional funding from the Scientific Committee on Oceanic Research) “Towards a Model of Ocean Biogeochemical Processes” was held at the Chateau de Bonas in Gascony, France. It brought together 45 scientists from 16 countries to discuss the issues and to explore the extent to which a common approach is possible, emphasizing the model-building process rather than the results of particular models. This book is the record of invited lectures and working group discussions of that meeting.

Non-diffusive aspects of the amplified climbing-sine map

Abstract The amplified climbing-sine model that generates some of the properties of turbulent diffusion also induces a net flow toward the origin, creates spatial patterns in an initially uniform distribution, and cannot be regarded as a fully satisfactory model of turbulence.