Marine Ecosystem Model Calibration through Enhanced Surrogate-Based Optimization - Simulation and Modeling Methodologies, Technologies and Application - page 185

There are processes in the climate system where where even without much simplifi-
cation (through e.g. “parametrizations” to reduce the system size, see for example [12])
several quantities or parameters are unknown or very difficult to measure. This is for
example the case for growth and dying rates in marine ecosystem models [5,17], one of
which our work in this paper is based on. 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 (sometimes also known as data assimila-
tion). For this purpose, large-scale optimization methods become crucial for a climate
system forecast.
The aim of parameter optimization is to adjust or identify the model parameters such
that the model response fits given measurement data. The mathematical task thus can
be classified as a least-squares type optimization or inverse problem [2,3,21]. This opti-
mization (or calibration) process requires a substantial number of function and option-
ally sensitivity or even Hessian matrix evaluations. Evaluation times for the high-fidelity
model of several hours, days or even weeks are not uncommon. As a consequence, opti-
mization and control problems are often still beyond the capability of modern numerical
algorithms and computer power. For such problems, where the optimization of coupled
marine ecosystem models is a representative example, development of faster methods
that would reduce the number of expensive simulations necessary to yield a satisfactory
solution becomes critical.
Computationally efficient optimization of expensive simulation models ( high-fidelity
or fine models) can be realized using surrogate-based optimization (SBO), see for ex-
ample [1,6,9,15]. The idea of SBO is to exploit a surrogate, a computationally cheap
and yet reasonably accurate representation of the high-fidelity model. The surrogate
replaces the original high-fidelity model in the optimization process in the sense of pro-
viding predictions of the model optimum. Also, it is updated using the high-fidelity
model data accumulated during the process. The prediction-updating scheme is nor-
mally iterated in order to refine the search and to locate the high-fidelity model opti-
mum as precisely as possible. One of possible ways of creating the surrogate, our work
in this paper is based on, is to utilize a physics-based low-fidelity (or coarse) model. The
development and use of low-fidelity models obtained by, e.g., coarser discretizations (in
time and/or space) or by parametrizations is common in climate research [12], whereas
their applications for surrogate-based parameter optimization in this area is new.
In [14], a surrogate-based methodology has been developed for the optimization of
climate model parameters. As a case study, a selected representative of the class of
one-dimensional marine ecosystem models was considered. Since biochemistry mainly
happens locally in space and since the complexity of the biogeochemical processes
included in this specific model is high, this model serves as a good test example for the
applicability of surrogate-based optimization approaches. The technique described in
[14] is based on a multiplicative response correction of a temporally coarser discretized
physics-based low-fidelity model. It has been successfully applied and demonstrated to
yield substantial computational cost savings of the optimization process when compared
to a direct optimization of the high-fidelity model.
In this paper, we demonstrate that by employing simple modifications of the original
response correction scheme, one can improve the surrogate's accuracy, as well as further