Marine Ecosystem Model Calibration through Enhanced Surrogate-Based Optimization - Simulation and Modeling Methodologies, Technologies and Application - page 186

reduce the computational cost of the optimization process. We verify our approach by
using synthetic target data and by comparing the results of SBO with the improved
surrogate to those obtained with the original one. The optimization cost is reduced three
times when compared to previous results, i.e., from about 15% to only 5% of the cost of
the direct high-fidelity ecosystem model optimization (used as a benchmark method).
The corresponding time savings are increased to from 84% to 95%.
It should be emphasized that the proposed approach does not rely on high-fidelity
model sensitivity data. As a consequence, the first-order consistency condition between
the surrogate and the high-fidelity model (i.e., agreement of their derivatives) is not
fully satisfied. Nevertheless, the combination of the knowledge about the marine system
under consideration embedded in the low-fidelity model and the response correction is
sufficient to obtain a quality solution in terms of good model calibration, i.e., its match
with the target output.
The paper is organized as follows. The high-fidelity ecosystem model, considered
here as a test problem, as well as the low-fidelity counterpart that we use as a basis to
construct the surrogate model, are described in Section 2. The optimization problem
under consideration is formulated in Section 3. The original and improved response
correction schemes and the comparison of the corresponding surrogate model qualities
are discussed in Section 4. Numerical results for an illustrative SBO run are provided
in Section 5. Section 6 concludes the paper.

2 Model Description

The considered example for the class of one-dimensional marine ecosystem models
simulates the interaction of dissolved inorganic nitrogen, phytoplankton, zooplankton
and detritus (dead material), thus is of so-called NPZD type [13]. The model uses pre-
computed ocean circulation and temperature data from an ocean model (in a sometimes
called off-line mode ), i.e., no feedback by the biogeochemistry on the circulation and
temperature is modeled, see again [13]. The original high-fidelity (fine) model and its
low-fidelity (coarse) counterpart which we use as a basis to construct a surrogate for
further use in the optimization process are briefly described below.

2.1 The High-Fidelity Model

The NPZD model simulates one water column at a given horizontal position. This
is motivated by the fact that there have been special time series studies at fixed loca-
tions. Clearly, the computational effort in a one-dimensional simulation is significantly
smaller than in the three-dimensional case. However, as pointed out in the introduction,
the model - from point of view of the complexity of the included processes - serves as
a good test example for the applicability of SBO approaches.
In the NPZD model, the concentrations (in mmol N m − 3 ) of dissolved inorganic
nitrogen N , phytoplankton P , zooplankton Z , and detritus (i.e., dead material) D are
summarized in the vector y =( y ( l ) ) l = N,P,Z,D and described by the following coupled
PDE system