Marine Ecosystem Model Calibration through Enhanced Surrogate-Based Optimization - Simulation and Modeling Methodologies, Technologies and Application - page 191

Fig. 1. Surrogate's, fine (down-sampled, smoothed) and coarse (smoothed) model responses

β
f and y c for the tracer detritus at the uppermost depth layer at two points u k and corre-
sponding perturbation u k , illustrating the generalization capability of the surrogate

s k , y

By definition, the surrogate model is zero-order consistent with the (down-sampled and
smoothed) fine model in the point u k ,i.e.,

β
f ( u k ) .

s k ( u k )= y (12)

As we do not use sensitivity information from the fine model, the first-order consistency
condition cannot be satisfied exactly. Nevertheless, as was shown in [14], this surrogate
model exhibits quite good generalization capability, which means that the surrogate
provides a reasonable approximation of the fine one in the neighborhood of u k .

Figure 1 shows the surrogate's, fine (down-sampled) and coarse model responses
s k , y

β
f

u k and u k . The surrogate model is established at
u k and, therefore, its response is perfectly aligned with the one of the fine model at

and y c at two different points,

u k ,

whereas its prediction is still reasonably accurate at u k .
Note that only the selected tracers for a chosen section in the whole time interval
and at one selected depth layer are shown. The total dimension of the model response
is too large to present a full response here. We emphasize that shown responses are
representative for the overall qualitative behavior the other tracers, time sections and
depth layers.

4.2 Difficulties of Basic Surrogate Formulation

Occasionally, when using the surrogate given in (10), there might occur a situation
where the coarse model response is close to zero (and maybe even negative due to
approximation errors) and a few magnitudes smaller than the fine one, which leads to