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Interpretation of optimization algorithms applied to biogeochemical models
de Brauwere, A. (2003). Interpretation of optimization algorithms applied to biogeochemical models. MSc Thesis. Vrije Universiteit Brussel. Faculteit Wetenschappen. Onderzoeksgroep ANHC: Brussel. 84 pp.

Thesis info:
    Vrije Universiteit Brussel; Faculteit Wetenschappen & Bio-ingenieurswetenschappen (WE), more

Available in Author 
    VLIZ: Non-open access 97817
Document type: Dissertation

Keywords
    Algorithms; Biogeochemical cycle; Ecosystems; Isotopes; Models; Tracer techniques; Marine

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  • de Brauwere, A., more

Abstract
    In the framework of aquatic ecosystems studies, the determination of exchange rates between different nutrient reservoirs is of crucial importance for the understanding of biogeochemical cycles. Quantification of the exchange rates based on stable isotope tracer experiments is considered in this study. In order to extract values for the flux rates from these measurements, it is necessary to postulate a model and, if required, to choose an appropriate optimization method. The numerical values will
    argely depend upon the criterion and method used to match model and measurements. The aim of this work is to make a rigorous contribution to the estimation of flux rates, allowing to issue statements about the result uncertainty for both random and systematic errors. A series of models is considered, describing both the silicon and nitrogen cycling in aquatic systems. Besides, different optimization and estimation methods are explained and validated.

    In order to get familiar with the estimation concepts, two classical criteria for the goodness of fit (Least Squares and Weighted Least Squares cost functions) are described in detail. The optimal flux rates correspond to a minimal cost function, and thus highly depend on the chosen cost function and on the used minimization technique. Both aforementioned methods are applied on the same data, to facilitate an illustration of the differences. Since experimental uncertainties are known, the Weighted Least Squ
    res method is preferred: (i) it provides a more reliable estimation, and (ii) the residual cost function value can be interpreted, thus providing additional information concerning the significance of the difference between model and measurements. For instance, the examined experiment has been identified as an outlier, although it was not yet compared to any other measurement. When the method is applied to the whole data set of 53 experiments, two other outliers are unmasked. Moreover, an overall statistical
    analysis reveals that the experimental uncertainties, provided by the experimentalist, are overestimations of the real ones.

    In the second part, in order to assimilate the gathered knowledge, the Weighted Least Squares procedure and its underlying assumptions are validated on simulations. Some weaknesses of the Weighted Least Squares estimator are illustrated. An improvement is proposed, based on taking both input and output experimental uncertainties into account. This procedure appears to offer better results, especially to quantify the overall uncertainty on the final estimation results.

    Finally, a new optimization method is presented, based on Interval Analysis. Whereas all previous methods used local optimizations, this approach is able to guarantee that the parameters found correspond to the global minimum, of the cost function. In addition, it assures to find all global minimizers, within the chosen parameter space. These features allow a unique reliability of the solutions. The interval-based optimization is first tested regarding its applicability. Although the method has his limitati
    ns, it could be applied to several nitrogen models in order to determine whether the solution loci associated with the model are uni- or multi-modal.

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