Geoscience Reference
In-Depth Information
4.2 Monte Carlo Simulations: Evaluation of Response Surfaces
The Monte Carlo (MC) simulations were applied to prepare response surfaces in
order to assess whether the unique optimal parameter values exist. First, 100,000
parameter sets composed of four parameters (
K
x
,
A
,
A
s,
and
) were created. Each
parameter was drawn from a uniform distribution over the following intervals:
K
x
[1; 17],
A
[5; 12],
A
s
[0.01; 0.5],
a
[0.03; 3].
For each parameter set a simulation was computed, and a value of the least
square objective function (the same as during calibration) was determined. Next,
the response surfaces were created. An example of the response surface planes is
shown in Fig.
4
. Analysis of the response surfaces shows that it is possible to
identify minimum values of objective function in the case of two parameters:
K
x
and
A
. On the other hand, unique parameter values do not exist for the objective
function when it comes to
A
s
and
a
.
The dead zone model seems to be a case of the equifinality, since many sets of
parameters exist that give equally good predictions. In this case, unique choice of
parameters is not possible either by means of applied optimization method or by
Monte Carlo simulations. The Monte Carlo simulations show that the choice of
optimal parameter values is very uncertain.
a
Fig. 4 Comparison between results of deterministic calibration and results of Monte Carlo
(MC) simulations for sub-reach 1-2, flow rate
Q
3, on the basis of least square objective func-
tion
F
