Description: We have already shown in a previous methodological work that the surrogate-based optimization (SBO) approach can be successful and computationally very efficient when reconstructing parameters in a typical nonlinear, time-dependent marine ecosystem model, where a one-dimensional application has been considered to test the method's functionality in a first step. The application on real (measurement) data is covered in this paper. Essential here are a special model data treatment and further methodological enhancements which allow us to improve the robustness of the algorithm and the accuracy of the solution. By numerical experiments, we demonstrate that SBO is able to yield a solution close to the original model's optimum while time savings are again up to 85% when compared to a conventional direct optimization of the original model.

Description: We present the application of the Surrogate-based Optimization (SBO) method on a parameter identification problem for a 3-D biogeochemical model. SBO is a method for acceleration of optimization processes when the underlying model itself is of very high computational complexity. In these cases, coupled simulation runs require large amounts of computer time, where optimization runs may become unfeasible even with high-performance hardware. As a consequence, the key idea of SBO is to replace the original and computationally expensive (high-fidelity) model by a so-called surrogate, which is created from a less accurate but computationally cheaper (low-fidelity) model and a suitable correction approach to increase its accuracy. To date, the SBO approach has been widely and successfully used in engineering applications and also for parameter identification in a 1-D marine ecosystem model of NPZD type. In this paper, we apply the approach onto a two-component biogeochemical model. The model is spun-up into a steady seasonal cycle via the Transport Matrix Approach. The low-fidelity model we use consists of a reduced number of spin-up iterations (several decades instead of millennia used for the original model). A multiplicative correction operator is further exploited to extrapolate the rather inaccurate low-fidelity model onto the original one. This corrected model builds our surrogate. We validate this SBO method by twin-experiments that use synthetic observations generated by the original model. We motivate our choice of the low-fidelity model and the multiplicative correction and discuss the computational advantage of SBO in comparison to an expensive parameter optimization in the context of the high-fidelity model. The proposed SBO technique is shown to yield a solution close to the target at a significant gain of computational efficiency. Without further regularization techniques, the method is able to identify most model parameters. The method is simple to implement and presents a promising and pragmatic tool to calibrate biogeochemical models in a global three-dimensional setting

Description: Methods and results for parameter optimization and uncertainty analysis for a one-dimensional marine biogeochemical model of NPZD type are presented. The model, developed by Schartau and Oschlies, simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column and is driven by ocean circulation data. Our aim is to identify parameters and fit the model output to given observational data. For this model, it has been shown that a satisfactory fit could not be obtained, and that parameters with comparable fits can vary significantly. Since these results were obtained by evolutionary algorithms (EA), we used a wider range of optimization methods: A special type of EA (called quantum-EA) with coordinate line search and a quasi-Newton SQP method, where exact gradients were generated by Automatic/Algorithmic Differentiation. Both methods are parallelized and can be viewed as instances of a hybrid, mixed evolutionary and deterministic optimization algorithm that we present in detail. This algorithm provides a flexible and robust tool for parameter identification and model validation. We show how the obtained parameters depend on data sparsity and given data error. We present an uncertainty analysis of the optimized parameters w.r.t. Gaussian perturbed data. We show that the model is well suited for parameter identification if the data are attainable. On the other hand, the result that it cannot be fitted to the real observational data without extension or modification, is confirmed. (C) 2010 Elsevier Ltd. All rights reserved.

Description: We present the application of a micro/macro parareal algorithm for a 1-D energy balance climate model with discontinuous and non-monotone coefficients and forcing terms. The micro/macro parareal method uses a coarse propagator, based on a (macroscopic) 0-D approximation of the underlying (microscopic) 1-D model. We compare the performance of the method using different versions of the macro model, as well as different numerical schemes for the micro propagator, namely an explicit Euler method with constant stepsize and an adaptive library routine. We study convergence of the method and the theoretical gain in computational time in a realization on parallel processors. We show that, in this example and for all settings, the micro/macro parareal method converges in fewer iterations than the number of used parareal subintervals, and that a theoretical gain in performance of up to 10 is possible.