Formulation and Validation of a Mathematical Model of Phytoplankton Growth

Collins, Carol D.

doi:10.2307/1937430

Cited by 25 publications

(5 citation statements)

References 46 publications

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“…It can be regarded in the narrow formal sense defined above, as a quantitative method of evaluating an identified model. There have been few such analyses [Thomann et al, 1974;Jorgensen et al, 1978;Collins, 1980 ;Najarian et al, 1984], and they can largely be subsumed under what has been discussed here as the checks and balances of section 6. Validation might otherwise be regarded in a much broader philosophical vein, almost as a vague concept (albeit intuitively understandable) that in practice is most useful in specifying procedures and protocols for model building [Cale et al, 1983a;Caswell, 1976;Holling, 1978;Mankin et al, 1977;Lewandowski, 1982;Loehle, 1983].…”

Section: Prediction Error Propagationmentioning

confidence: 99%

Water quality modeling: A review of the analysis of uncertainty

Beck¹

1987

Water Resources Research

863

431

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This paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction. More specifically, four problem areas are examined in detail: uncertainty about model structure, uncertainty in the estimated model parameter values, the propagation of prediction errors, and the design of experiments in order to reduce the critical uncertainties associated with a model. The review is rather lengthy, and it has therefore been prepared in effect as two papers. There is a shorter, largely nontechnical version, which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling. Enclosed by this shorter discussion is the main body of the review dealing in turn with (1) identifiability and experimental design, (2) the generation of preliminary model hypotheses under conditions of sparse, grossly uncertain field data, (3) the selection and evaluation of model structure, (4) parameter estimation (model calibration), (5) checks and balances on the identified model, i.e., model “verification” and model discrimination, and (6) prediction error propagation. Much time is spent in discussing the algorithms of system identification, in particular, the methods of recursive estimation, and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first‐order error analysis. There are two obvious omissions from the review. It is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty, although clearly some reference must be made to these topics. In brief, the review concludes (not surprisingly) that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality, and much remains to be done. A lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior, and there is ample evidence to show that the “larger,” more “comprehensive” models are easily capable of generating highly uncertain predictions of future behavior. For the future of the subject, it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification, a need for new questions to be posed in the problem of prediction, and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence.

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Section: Prediction Error Propagationmentioning

confidence: 99%

Water quality modeling: A review of the analysis of uncertainty

Beck¹

1987

Water Resources Research

863

431

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“…The pelagic ecosystem model, SWACOM, permits us to investigate system behavior that might be expected as a result of synergistic and antagonistic effects. Although the model performed well in tests against independent data [5,6], it is still an imperfect representation of the real system. Therefore, we should not expect the model to duplicate all the responses of the ecosystem [7].…”

Section: Introductionmentioning

confidence: 99%

Patterns of toxicological effects in ecosystems: A modeling study

O’Neill

Bartell

Gardner

1983

Enviro Toxic and Chemistry

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Differences in patterns of response in a pelagic ecosystem due to seasonal exposure and differential sensitivities of populations and trophic levels to chemical stress were examined with a simulation model. Simulations of constant 7‐d exposures initiated at different times of year demonstrated that stresses imposed during the spring reduced average producer and consumer biomass. Stresses imposed later in the year reduced grazer biomass and permitted increased phytoplankton production. Simulated exposures to phenol, naphthalene and four heavy metals predicted different effects when toxic sensitivities of populations and trophic levels were ignored. Risks of increased blue‐green algae production or decreased game fish production were estimated from repeated simulations that extrapolated uncertainties associated with individual toxic effects parameters. Estimates of risk that included population‐specific toxicities were two or three times greater than risks estimated from trophic level toxicities alone.

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“…Nutrient uptake depends hyperbolically on the nutrient concentration external to the cell (Zonneveld, 1996) using Monod uptake kinetics (Monod, 1950), whereas growth depends only on the intracellular quotas of nutrients (Droop, 1973). The concept of quota models is considered more realistic because if there are no more nutrients in the environment, growth can continue with nutrients previously accumulated in the cells (Collins, 1980;Haney and Jackson, 1996). This can explain the discrepancies between the maximum measured and simulated photosynthetic rates in summer.…”

Section: Results Obtained For P Bmentioning

confidence: 99%