Surrogate-Based Optimization of Climate Model Parameters Using Response Correction

We present a computationally efficient methodology for the optimization of climate model parameters applied to a (one-dimensional) representative of a class of marine ecosystem models. We use a response correction technique to create a surrogate from a temporarily coarser discretized physics-based low-fidelity model. We demonstrate that replacing the direct parameter optimization of the high-fidelity ecosystem model by iteratively updating and re-optimizing the surrogate leads to a very satisfactory solution while yielding significant cost saving - about 84\% when compared to the direct high-fidelity model optimization

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 \%

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