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  • 1
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    Copernicus Publications (EGU)
    In:  Geoscientific Model Development, 11 (3). pp. 1181-1198.
    Publication Date: 2019-02-01
    Description: Biogeochemical models, capturing the major feedbacks of the pelagic ecosystem of the world ocean, are today often embedded into Earth system models which are increasingly used for decision making regarding climate policies. These models contain poorly constrained parameters (e.g., maximum phytoplankton growth rate), which are typically adjusted until the model shows reasonable behavior. Systematic approaches determine these parameters by minimizing the misfit between the model and observational data. In most common model approaches, however, the underlying functions mimicking the biogeochemical processes are nonlinear and non-convex. Thus, systematic optimization algorithms are likely to get trapped in local minima and might lead to non-optimal results. To judge the quality of an obtained parameter estimate, we propose determining a preferably large lower bound for the global optimum that is relatively easy to obtain and that will help to assess the quality of an optimum, generated by an optimization algorithm. Due to the unavoidable noise component in all observations, such a lower bound is typically larger than zero. We suggest deriving such lower bounds based on typical properties of biogeochemical models (e.g., a limited number of extremes and a bounded time derivative). We illustrate the applicability of the method with two real-world examples. The first example uses real-world observations of the Baltic Sea in a box model setup. The second example considers a three-dimensional coupled ocean circulation model in combination with satellite chlorophyll a.
    Type: Article , PeerReviewed
    Format: text
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  • 2
    Publication Date: 2018-06-01
    Description: Mastermind is a two players zero sum game of imperfect information. Starting with Erdos and Rényi (1963), its combinatorics have been studied to date by several authors, e.g., Knuth (1977), Chvátal (1983), Goodrich (2009). The first player, called 'codemaker', chooses a secret code and the second player, called 'codebreaker', tries to break the secret code by making as few guesses as possible, exploiting information that is given by the codemaker after each guess. For variants that allow color repetition, Doerr et al. (2016) showed optimal results. In this paper, we consider the so called Black-Peg variant of Mastermind, where the only information concerning a guess is the number of positions in which the guess coincides with the secret code. More precisely, we deal with a special version of the Black-Peg game with n holes and k=n k=n colors where no repetition of colors is allowed. We present upper and lower bounds on the number of guesses necessary to break the secret code. For the case k=n k=n , the secret code can be algorithmically identified within less than (n-3)log 2 n+52 n-1 (n-3)log2n+52n-1 queries. This result improves the result of Ker-I Ko and Shia-Chung Teng (1985) by almost a factor of 2. For the case k〉n k〉n , we prove an upper bound of (n-2)log 2 n+k+1 (n-2)logn?+k+1 . Furthermore, we prove a new lower bound of n for the case k=n k=n , which improves the recent n-loglog(n) n-loglog(n) bound of Berger et al. (2016). We then generalize this lower bound to k queries for the case k=n k=n .
    Keywords: ddc:330 ; Mastermind ; combinatorial problem ; permutation ; algorithm ; complexity
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
    Type: doc-type:article
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  • 3
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    Copernicus Publications (EGU)
    In:  Geoscientific Model Development, 10 . pp. 127-154.
    Publication Date: 2019-09-23
    Description: Global biogeochemical ocean models contain a variety of different biogeochemical components and often much simplified representations of complex dynamical interactions, which are described by many (≈10–≈100) parameters. The values of many of these parameters are empirically difficult to constrain, due to the fact that in the models they represent processes for a range of different groups of organisms at the same time, while even for single species parameter values are often difficult to determine in situ. Therefore, these models are subject to a high level of parametric uncertainty. This may be of consequence for their skill with respect to accurately describing the relevant features of the present ocean, as well as their sensitivity to possible environmental changes. We here present a framework for the calibration of global biogeochemical ocean models on short and long time scales. The framework combines an offline approach for transport of biogeochemical tracers with an Estimation of Distribution Algorithm (Covariance Matrix Adaption Evolution Strategy, CMAES). We explore the performance and capability of this framework by five different optimizations of six biogeochemical parameters of a global biogeochemical model. First, a twin experiment explores the feasibility of this approach. Four optimizations against a climatology of observations of annual mean dissolved nutrients and oxygen determine the extent, to which different setups of the optimization influence model's fit and parameter estimates. Because the misfit function applied focuses on the large-scale distribution of inorganic biogeochemical tracers, parameters that act on large spatial and temporal scales are determined earliest, and with the least spread. Parameters more closely tied to surface biology, which act on shorter time scales, are more difficult to determine. In particular the search for optimum zooplankton parameters can benefit from a sound knowledge of maximum and minimum parameter values, leading to a more efficient optimization. It is encouraging that, although the misfit function does not contain any direct information about biogeochemical turnover, the optimized models nevertheless provide a better fit to observed global biogeochemical fluxes.
    Type: Article , PeerReviewed
    Format: text
    Format: archive
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  • 4
    Publication Date: 2019-09-24
    Description: Global biogeochemical ocean models rely on many parameters, which govern the interaction between individual components, and their response to the physical environment. They are often assessed/calibrated against quasi-synoptic data sets of dissolved inorganic tracers. However, a good fit to one observation might not necessarily imply a good match to another. We investigate whether two different metrics—the root-mean-square error to nutrients and oxygen and a metric measuring the overlap between simulated and observed oxygen minimum zones (OMZs)—help to constrain a global biogeochemical model in different aspects of performance. Three global model optimizations are carried out. Two single-objective optimizations target the root-mean-square metric and a sum of both metrics, respectively. We then present and explore multiobjective optimization, which results in a set of compromise solutions. Our results suggest that optimal parameters for denitrification and nitrogen fixation differ when applying different metrics. Optimization against observed OMZs leads to parameters that enhance fixed nitrogen cycling; this causes too low nitrate concentrations and a too high global pelagic denitrification rate. Optimization against nutrient and oxygen concentrations leads to different parameters and a lower global fixed nitrogen turnover; this results in a worse fit to OMZs. Multiobjective optimization resolves this antagonistic effect and provides an ensemble of parameter sets, which help to address different research questions. We finally discuss how systematic model calibration can help to improve models used for projecting climate change and its effect on fisheries and climate gas emissions.
    Type: Article , PeerReviewed
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  • 5
    Publication Date: 2017-01-09
    Description: Global biogeochemical ocean models contain a variety of different biogeochemical components and often much simplified representations of complex dynamical interactions, which are described by many ( ≈ 10 to  ≈ 100) parameters. The values of many of these parameters are empirically difficult to constrain, due to the fact that in the models they represent processes for a range of different groups of organisms at the same time, while even for single species parameter values are often difficult to determine in situ. Therefore, these models are subject to a high level of parametric uncertainty. This may be of consequence for their skill with respect to accurately describing the relevant features of the present ocean, as well as their sensitivity to possible environmental changes. We here present a framework for the calibration of global biogeochemical ocean models on short and long timescales. The framework combines an offline approach for transport of biogeochemical tracers with an estimation of distribution algorithm (Covariance Matrix Adaption Evolution Strategy, CMA-ES). We explore the performance and capability of this framework by five different optimizations of six biogeochemical parameters of a global biogeochemical model, simulated over 3000 years. First, a twin experiment explores the feasibility of this approach. Four optimizations against a climatology of observations of annual mean dissolved nutrients and oxygen determine the extent to which different setups of the optimization influence model fit and parameter estimates. Because the misfit function applied focuses on the large-scale distribution of inorganic biogeochemical tracers, parameters that act on large spatial and temporal scales are determined earliest, and with the least spread. Parameters more closely tied to surface biology, which act on shorter timescales, are more difficult to determine. In particular, the search for optimum zooplankton parameters can benefit from a sound knowledge of maximum and minimum parameter values, leading to a more efficient optimization. It is encouraging that, although the misfit function does not contain any direct information about biogeochemical turnover, the optimized models nevertheless provide a better fit to observed global biogeochemical fluxes.
    Print ISSN: 1991-959X
    Electronic ISSN: 1991-9603
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union (EGU).
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  • 6
    Publication Date: 2018-03-29
    Description: Biogeochemical models, capturing the major feedbacks of the pelagic ecosystem of the world ocean, are today often embedded into Earth system models which are increasingly used for decision making regarding climate policies. These models contain poorly constrained parameters (e.g., maximum phytoplankton growth rate), which are typically adjusted until the model shows reasonable behavior. Systematic approaches determine these parameters by minimizing the misfit between the model and observational data. In most common model approaches, however, the underlying functions mimicking the biogeochemical processes are nonlinear and non-convex. Thus, systematic optimization algorithms are likely to get trapped in local minima and might lead to non-optimal results. To judge the quality of an obtained parameter estimate, we propose determining a preferably large lower bound for the global optimum that is relatively easy to obtain and that will help to assess the quality of an optimum, generated by an optimization algorithm. Due to the unavoidable noise component in all observations, such a lower bound is typically larger than zero. We suggest deriving such lower bounds based on typical properties of biogeochemical models (e.g., a limited number of extremes and a bounded time derivative). We illustrate the applicability of the method with two real-world examples. The first example uses real-world observations of the Baltic Sea in a box model setup. The second example considers a three-dimensional coupled ocean circulation model in combination with satellite chlorophyll a.
    Print ISSN: 1991-959X
    Electronic ISSN: 1991-9603
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union (EGU).
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  • 7
    Publication Date: 2017-06-20
    Description: Biogeochemical models, capturing the major feedbacks of the pelagic ecosystem of the world ocean, are today often embedded into Earth System models which are increasingly used for decision making regarding climate policies. These models contain poorly constrained parameters (e.g., maximum phytoplankton growth rate) which are typically adjusted until the model shows a reasonable behavior. Systematic approaches determine these parameters by minimizing the misfit between the model and observational data. In most common model approaches, however, the underlying functions mimicking the biogeochemical processes are non-linear and non-convex. Thus, systematic optimization algorithms are likely to get trapped in a local minimum and might lead to non-optimal results. To judge the quality of an obtained parameter estimate, we propose to determine a preferably large lower bound for the global optimum, that is relatively easy to obtain and that will help to assess the quality of an optimum, generated by an optimization algorithm. Due to the unavoidable noise component in all observations, such a lower bound is typically larger than zero. We suggest to derive such lower bounds based on typical properties of biogeochemical models (e.g., a limited number of extremes and a bounded time-derivative). We evaluate this approach with synthetic observations and demonstrate a real-world example, consisting of phytoplankton observations in the Baltic Sea.
    Print ISSN: 1991-9611
    Electronic ISSN: 1991-962X
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union (EGU).
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  • 8
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