Marine Ecosystem Model Calibration through Enhanced Surrogate-Based Optimization - Simulation and Modeling Methodologies, Technologies and Application - page 197

Ta b l e 1 . Solutions u c , u f , u s 1 and u s 2 of an illustrative coarse, fine model optimization and of
a SBO run, exploiting the original and the improved correction scheme. Solutions u s 1 and u s 2
correspond to points 1 and 2 in Figure 4.

iterate u 1

u 2 ... u 12

SBO (original and improved scheme)

u s 1 0.705 0.626 0.044 0.015 0.060 0.937 1.908 0.016 0.147 0.020 0.629 4.237

u s 2

0.738 0.604 0.028 0.010 0.036 1.024 1.678 0.010 0.206 0.020 0.541 4.318

Coarse model optimization

u c

0.300 1.066 0.036 0.065 0.064 0.025 0.040 0.065 0.010 0.012 0.730 3.448
Fine model optimization

u f 0.747 0.596 0.025 0.010 0.030 0.999 2.046 0.010 0.203 0.020 0.493 4.310

u d 0.750 0.600 0.025 0.010 0.030 1.000 2.000 0.010 0.205 0.020 0.500 4.320

u s 2
(point 2 in Figure 4) with a significantly higher accuracy - again both in terms of pa-
rameter match and optimal fit of the target data - can be obtained (cf. Figure 5 and
Table 1) at the same cost as were required for the original one

On the other hand, when exploiting the improved correction scheme, a solution

u s 1

, i.e., 60 equivalent

fine model evaluations.
It should be emphasized that the surrogate model utilized in this work only satisfies
zero-order consistency with the fine model. Still, as demonstrated in this section, the
performance of our surrogate-based optimization process is satisfactory, particularly in
terms of obtaining a good match between the model response and a given target output.
Improved matching between the optimized model parameters and those corresponding
to the target output could be obtained by executing larger number of SBO iterations
(cf. Figure 4), which is mostly because of low sensitivity of the model with respect
to some of the parameters. Also, the use of derivative information together with the
trust-region convergence safeguards [4,8] would bring further improvement in terms of
matching accuracy. Clearly, the trade-offs between the accuracy of the solution and the
extra computational overhead related to sensitivity calculation has to be investigated.
The aforementioned issues will be the subject of future research.

6 Conclusions

Parameter identification in climate models can be computationally very expensive or
even beyond the capabilities of modern computer power. Before a transient simulation
of a model (e.g., used for predictions) is possible, the latter has to be calibrated, i.e.,
relevant parameters have to be identified using measurement data. This is the point
where large-scale optimization methods become crucial for a climate system forecast.
Using the high-fidelity (or fine) model under consideration in conventional opti-
mization algorithms that require large number of model evaluations is often infeasible.
Therefore, the development of faster methods that aim at reducing the optimization cost,