Surrogate-Based Optimization for Marine Ecosystem Models

Marine ecosystem models are of great importance for understanding the oceanic uptake of carbon dioxide and for projections of the marine ecosystem’s responses to climate change. The applicability of a marine ecosystem model for prognostic simulations crucially depends on its ability to resemble the actually observed physical and biogeochemical processes. An assessment of the quality of a given model is typically based on its calibration against observed quantities. This calibration or optimization process is intrinsically linked to an adjustment of typically poorly known model parameters. Straightforward calibration attempts by direct adjustment of the model parameters using conventional optimization algorithms are often tedious or even beyond the capabilities of modern computer power as they normally require a large number of simulations. This typically results in prohibitively high computational cost, particularly if already a single model evaluation involves time-consuming computer simulations. The optimization of coupled hydrodynamical marine ecosystem models simulating biogeochemical processes in the ocean is here a representative example. Computing times of hours up to several days already for a single model evaluation are not uncommon. A computationally efficient optimization of expensive simulation models can be realized using for example surrogate-based optimization. Therein, the optimization of the expensive, so-called high-fidelity (or fine) model is carried out by means of a surrogate – a fine model’s fast but yet reasonably accurate representation. This work comprises an investigation and application of surrogate-based optimization methodologies employing physics-based low-fidelity (or coarse) models. Seeking a computationally efficient calibration of marine ecosystem models serves as the fundamental aim. As a case study, two illustrative marine ecosystem models are considered. Here, coarse models obtained by a coarser temporal resolution and by a truncated model spin-up are investigated. The accuracy of these computationally cheaper coarse models is typically not sufficient to directly exploit them in the optimization loop in lieu of the fine model. I investigate suitable correction techniques to ensure that the corrected coarse model (the surrogate) provides a reliable prediction of the fine model optimum. Firstly, I focus on Aggressive Space Mapping as one of the original Space Mapping approaches. It will be shown that this optimization method allows to achieve a reasonable reduction in the optimization costs, provided that the considered coarse and fine model are sufficiently “similar”. A multiplicative response correction approach, subsequently investigated, turned out to be very suitable for the considered marine ecosystem models. A reliable surrogate can be obtained. Exploiting the latter in a surrogate-based optimization algorithm, a computationally cheap but yet accurate solution is achieved. The optimization costs can be significantly reduced compared to what is achieved by the Aggressive Space Mapping algorithm. The proposed methodologies, particularly the multiplicative response correction approach, serve as initial parts of a set of tools for a computationally efficient calibration of marine ecosystem models. The investigation of further enhancements of the presented algorithms as well as other promising approaches in the framework of surrogate-based optimization will be highly valuable

A Fast and Robust Optimization Methodology for a Marine Ecosystem Model Using Surrogates

Model calibration in climate science plays a key role for simulations and predictions of the earth's climate system. Straightforward attempts by employing the high-fidelity (or fine) model under consideration directly in an optimization loop using conventional optimization algorithms are often tedious or even infeasible, since typically a large number of computationally expensive fine model evaluations are required. The development of faster methods becomes critical, where the optimization of coupled marine ecosystem models, which simulate biogeochemical processes in the ocean, are a representative example. In this paper, we introduce a surrogate-based optimization (SBO) methodology where the expensive fine model is replaced by its fast and yet reasonably accurate surrogate. As a case study, we consider a representative of the class of one-dimensional marine ecosystem models. The surrogate is obtained from a temporarily coarser discretized physics-based low-fidelity (or coarse) model. and a multiplicative response correction technique. In our previous work, a basic formulation of this surrogate was sufficient to create a reliable approximation, yielding a remarkably accurate solution at low computational costs. This was verified by model generated, attainable data. The application on real data is covered in this paper. Enhancements of the basic formulation by utilizing additionally fine and coarse model sensitivity information as well as trust-region convergence safeguards allow us to further improve the robustness of the algorithm and the accuracy of the solution. The trade-offs between the solution accuracy and the extra computational overhead related to sensitivity calculation will be addressed. We demonstrate that SBO is able to yield a very accurate solution at still low computational costs. The optimization process - when compared to the direct fine model optimization - is significantly speed up to about 85 \%

Surrogat-Basierte Optimierung für Marine Ökosystem-Modelle

Marine ecosystem models are of great importance for understanding the oceanic uptake of carbon dioxide and for projections of the marine ecosystem’s responses to climate change. The applicability of a marine ecosystem model for prognostic simulations crucially depends on its ability to resemble the actually observed physical and biogeochemical processes. An assessment of the quality of a given model is typically based on its calibration against observed quantities. This calibration or optimization process is intrinsically linked to an adjustment of typically poorly known model parameters. Straightforward calibration attempts by direct adjustment of the model parameters using conventional optimization algorithms are often tedious or even beyond the capabilities of modern computer power as they normally require a large number of simulations. This typically results in prohibitively high computational cost, particularly if already a single model evaluation involves time-consuming computer simulations. The optimization of coupled hydrodynamical marine ecosystem models simulating biogeochemical processes in the ocean is here a representative example. Computing times of hours up to several days already for a single model evaluation are not uncommon. A computationally efficient optimization of expensive simulation models can be realized using for example surrogate-based optimization. Therein, the optimization of the expensive, so-called high-fidelity (or fine) model is carried out by means of a surrogate – a fine model’s fast but yet reasonably accurate representation. This work comprises an investigation and application of surrogate-based optimization methodologies employing physics-based low-fidelity (or coarse) models. Seeking a computationally efficient calibration of marine ecosystem models serves as the fundamental aim. As a case study, two illustrative marine ecosystem models are considered. Here, coarse models obtained by a coarser temporal resolution and by a truncated model spin-up are investigated. The accuracy of these computationally cheaper coarse models is typically not sufficient to directly exploit them in the optimization loop in lieu of the fine model. I investigate suitable correction techniques to ensure that the corrected coarse model (the surrogate) provides a reliable prediction of the fine model optimum. Firstly, I focus on Aggressive Space Mapping as one of the original Space Mapping approaches. It will be shown that this optimization method allows to achieve a reasonable reduction in the optimization costs, provided that the considered coarse and fine model are sufficiently “similar”. A multiplicative response correction approach, subsequently investigated, turned out to be very suitable for the considered marine ecosystem models. A reliable surrogate can be obtained. Exploiting the latter in a surrogate-based optimization algorithm, a computationally cheap but yet accurate solution is achieved. The optimization costs can be significantly reduced compared to what is achieved by the Aggressive Space Mapping algorithm. The proposed methodologies, particularly the multiplicative response correction approach, serve as initial parts of a set of tools for a computationally efficient calibration of marine ecosystem models. The investigation of further enhancements of the presented algorithms as well as other promising approaches in the framework of surrogate-based optimization will be highly valuable.Marine Ökosystem-Modelle sind von großer Bedeutung, um die ozeanische Aufnahme von Kohlendioxid zu verstehen sowie Vorhersagen über die Reaktionen des marinen Ökosystems auf den Klimawandel treffen zu können. Die Anwendbarkeit eines marinen Ökosystem-Modells für prognostische Simulationen hängt entscheidend von seiner Fähigkeit ab, die tatsächlich beobachteten physikalischen und biogeochemischen Prozesse wiederzugeben. Um die Qualität von verschiedenen Modellen zu validieren, werden diese typischerweise an vorhandene Beobachtungsdaten angeglichen. Diese Validierung (oder Parameter- Identifikation) erfordert die Anpassungen von in der Regel wenig bekannten Modellparametern. Die direkte Kalibrierung des Modells mit Hilfe konventioneller Optimierungsalgorithmen ist üblicherweise ein langwieriger Prozess, der gegebenenfalls sogar jenseits verfügbarer Rechenressourcen liegt. Ein Grund dafür ist die meist große Zahl erforderlicher Modellsimulationen. Dies führt insbesondere dann zu einem erheblichen Rechenaufwand, wenn bereits eine einzelne Modellauswertung teure Computersimulationen notwendig macht. Ein Beispiel hierfür ist die Kalibrierung gekoppelter mariner Ökosystem-Modelle. Rechenzeiten von Stunden bis hin zu mehreren Tagen für eine einzelne Modellauswertung sind nicht unüblich. Eine effiziente Optimierung von teuren Computermodellen lässt sich beispielsweise mit Hilfe von surrogat-basierten Optimierungsverfahren realisieren. Ein Surrogat – eine schnelle aber dennoch ausreichend genaue Approximation des sogenannten feinen Modells – ermöglicht hierbei dessen Optimierung. Diese Arbeit umfasst die Untersuchung und Anwendung von Verfahren im Rahmen surrogat-basierter Optimierungsalgorithmen, bei denen die Surrogate auf sogenannten physikalischen groben Modellen beruhen. Übergreifendes Ziel ist eine effiziente und schnelle Kalibrierung von marinen Ökosystem-Modellen. Es werden zwei illustrative Modelle betrachtet. Die dazugehörigen groben Modelle werden beispielhaft durch grobe zeitliche Diskretisierung sowie durch einen verkürzten Modell-Spin-Up gewonnen. In der Regel sind solche groben Modelle nicht genau genug, um sie in der Optimierung direkt als Ersatz der feinen Modelle zu verwenden. Mit Hilfe geeigneter Techniken zur Korrektur der groben Modelle konstruiere ich daher ausreichend genaue Surrogate. Zuerst nutze ich hierfür Aggressive Space Mapping, einen der ursprünglichen Space Mapping-Algorithmen. Es wird gezeigt, dass dieses Optimierungsverfahren eine hinreichende Reduktion der Optimierungskosten erzielen kann, vorausgesetzt, das grobe und feine Modell stimmen ausreichend überein. Anschließend betrachte ich eine multiplikative Korrektur. Wie gezeigt wird, ist dieser Ansatz für die betrachteten Modelle gut geeignet. Zusätzlich ist die Optimierung der damit konstruierten Surrogate kostengünstig, erzielt aber dennoch eine ausreichend präzise Lösung. Die Optimierungskosten lassen sich hierbei deutlich gegenüber dem Aggressive Space Mapping-Algorithmus senken. Die vorgestellten Verfahren, insbesondere die multiplikative Korrektur, stellen erste Teile einer Sammlung von Tools für eine effiziente Kalibrierung mariner Ökosystem-Modelle dar. Die Untersuchung weiterer Verbesserungen der betrachteten Methoden sowie anderer möglicher Ansätze im Rahmen surrogat-basierter Optimierung ist vielversprechend

Numerische Methoden für marine biogeochemische Modelle

Marine ecosystem models are an indispensable component in the forecast of climate change. CO2 is the major anthropogenic greenhouse gas which substantially determines global warming. As an essential component of the global carbon cycle, the marine ecosystem absorbs atmospheric CO2 and, hence, slows down global warming. More specifically, the marine ecosystem stores the CO2 over a long time period, for example by fixing it through biogeochemical conversion processes. Marine ecosystem models facilitate the simulation of the marine ecosystem and, thus, the research of different processes in this ecosystem and a forecast of the evolution of the marine ecosystem. Owing to a high computational effort, the simulation of marine ecosystem models is limited by the available computing power, even on high-performance computers. To reduce the computational effort for the computation of a steady annual cycle for a marine ecosystem model, this thesis comprises the investigation of the reduction of the computational effort by using larger time steps and by predicting the steady annual cycle by means of an artificial neural network. To apply the time step always as large as possible without relying on any manual selection, two methods based on the automatic time step adjustment during the simulation are presented. The prediction of an artificial neural network served as an initial concentration for an additional simulation because the accuracy of the prediction was insufficient. These approaches, in particular, lowered the computational effort with a tolerable loss of accuracy. By the use of the surrogate-based optimization, the approaches to reduce the computational effort were applied for a parameter identification which optimizes the model parameters to adapt the marine ecosystem model output to observational data. This optimization yielded parameters close to the target ones and lowered the computational effort clearly.Marine Ökosystemmodelle sind ein unverzichtbarer Bestandteil zur Vorhersage des Klimawandels. Die globale Erwärmung wird im Wesentlichen durch Emissionen des bedeutendsten anthropogenen Treibhausgases Kohlenstoffdioxid (CO2) bestimmt. Als eine zentrale Komponente des globalen Kohlenstoffkreislaufs absorbiert das marine Ökosystem atmosphärisches CO2 und verlangsamt so die globale Erwärmung. Marine Ökosystemmodelle ermöglichen die Simulation und somit die Erforschung verschiedener Prozesse innerhalb des marinen Ökosystems sowie eine Vorhersage der zu erwartenden Entwicklung. Allerdings erfordert eine solche Simulation einen immensen Rechenaufwand und unterliegt selbst auf Hochleistungsrechnern durch die begrenzte Rechenleistung erheblichen Einschränkungen. Für die Berechnung einer jährlich periodischen Lösung des marinen Ökosystemmodells zeigt diese Arbeit Wege zur Reduktion des Rechenaufwands durch die Verwendung größerer Zeitschritte und durch die Vorhersage eines neuronalen Netzes auf. Es werden zwei Methoden vorgestellt, die auf der automatischen Anpassung des Zeitschritts während der Simulation basieren, um ohne manuelle Wahl immer den größtmöglichen Zeitschritt zu verwenden. Die Vorhersage der periodischen Lösung mit Hilfe eines neuronalen Netzes diente als Anfangskonzentration für eine zusätzliche Simulation, da die Genauigkeit der Vorhersage unzureichend war. Beide Ansätze verringerten den Rechenaufwand bei einem tolerierbaren Genauigkeitsverlust. Die Konzepte zur Reduktion des Rechenaufwands wurden für eine Parameteroptimierung mit der surrogat-basierten Optimierung verwendet, die die Modellparameter zur Anpassung des marinen Ökosystemmodells an Beobachtungsdaten optimiert. Diese Optimierung lieferte nahezu die anvisierten Parameter und verringerte den Rechenaufwand

Advancing coastal ocean modelling, analysis, and prediction for the US Integrated Ocean Observing System

Author Posting. © The Author(s), 2017. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Journal of Operational Oceanography 10 (2017): 115-126, doi:10.1080/1755876X.2017.1322026.This paper outlines strategies that would advance coastal ocean modeling, analysis and prediction as a complement to the observing and data management activities of the coastal components of the U.S. Integrated Ocean Observing System (IOOS®) and the Global Ocean Observing System (GOOS). The views presented are the consensus of a group of U.S. based researchers with a cross-section of coastal oceanography and ocean modeling expertise and community representation drawn from Regional and U.S. Federal partners in IOOS. Priorities for research and development are suggested that would enhance the value of IOOS observations through model-based synthesis, deliver better model-based information products, and assist the design, evaluation and operation of the observing system itself. The proposed priorities are: model coupling, data assimilation, nearshore processes, cyberinfrastructure and model skill assessment, modeling for observing system design, evaluation and operation, ensemble prediction, and fast predictors. Approaches are suggested to accomplish substantial progress in a 3-8 year timeframe. In addition, the group proposes steps to promote collaboration between research and operations groups in Regional Associations, U.S. Federal Agencies, and the international ocean research community in general that would foster coordination on scientific and technical issues, and strengthen federal-academic partnerships benefiting IOOS stakeholders and end users.2018-05-2

The assimilation of satellite-derived data into a one-dimensional lower trophic level marine ecosystem model

Lower trophic level marine ecosystem models are highly dependent on the parameter values given to key rate processes, however many of these are either unknown or difficult to measure. One solution to this problem is to apply data assimilation techniques that optimize key parameter values, however in many cases in situ ecosystem data are unavailable on the temporal and spatial scales of interest. Although multiple types of satellite-derived data are now available with high temporal and spatial resolution, the relative advantages of assimilating different satellite data types are not well known. Here these issues are examined by implementing a lower trophic level model in a one-dimensional data assimilative (variational adjoint) model testbed. A combination of experiments assimilating synthetic and actual satellite-derived data, including total chlorophyll, size-fractionated chlorophyll and particulate organic carbon (POC), reveal that this is an effective tool for improving simulated surface and subsurface distributions both for assimilated and unassimilated variables. Model-data misfits were lowest when parameters were optimized individually at specific sites; however, this resulted in unrealistic overtuned parameter values that deteriorated model skill at times and depths when data were not available for assimilation, highlighting the importance of assimilating data from multiple sites simultaneously. Finally, when chlorophyll data were assimilated without POC, POC simulations still improved, however the reverse was not true. For this two-phytoplankton size class model, optimal results were obtained when satellite-derived size-differentiated chlorophyll and POC were both assimilated simultaneously. Key Points Used an ecosystem model in a 1-D data assimilative framework Assimilation of satellite-derived size-differentiated chlorophyll and POC Assimilating satellite data at multiple sites constrained ecosystem parameter

Autotrophic Stoichiometry Emerging from Optimality and Variable Co-limitation

Autotrophic organisms reveal an astounding flexibility in their elemental stoichiometry, with potentially major implications on biogeochemical cycles and ecological functioning. Notwithstanding, stoichiometric regulation, and co-limitation by multiple resources in autotrophs were in the past often described by heuristic formulations. In this study, we present a mechanistic model of autotroph growth, which features two major improvements over the existing schemes. First, we introduce the concept of metabolic network independence that defines the degree of phase-locking between accessory machines. Network independence is in particular suggested to be proportional to protein synthesis capability as quantified by variable intracellular N:C. Consequently, the degree of co-limitation becomes variable, contrasting with the dichotomous debate on the use of Liebig's law or the product rule, standing for constantly low and high co-limitation, respectively. Second, we resolve dynamic protein partitioning to light harvesting, carboxylation processes, and to an arbitrary number of nutrient acquisition machineries, as well as instantaneous activity regulation of nutrient uptake. For all regulatory processes we assume growth rate optimality, here extended by an explicit consideration of indirect feed-back effects. The combination of network independence and optimal regulation displays unprecedented skill in reproducing rich stoichiometric patterns collected from a large number of published chemostat experiments. This high skill indicates (1) that the current paradigm of fixed co-limitation is a critical short-coming of conventional models, and (2) that stoichiometric flexibility in autotrophs possibly reflects an optimality strategy. Numerical experiments furthermore show that regulatory mechanisms homogenize the effect of multiple stressors. Extended optimality alleviates the effect of the most limiting resource(s) while down-regulating machineries for the less limiting ones, which induces an ubiquitous response surface of growth rate over ambient resource levels. Our approach constitutes a basis for improved mechanistic understanding and modeling of acclimative processes in autotrophic organisms. It hence may serve future experimental and theoretical investigations on the role of those processes in aquatic and terrestrial ecosystems