Stochastic versus Deterministic Approaches - Environmental Modelling: Finding Simplicity in Complexity - page 139

Log 10 elec. resist ( Ω m)

N

OB-11

1.70
1.50
1.30
1.10
0.90
0.70
0.50
0.30
0.01

OB-5

OB-13

OB-4

OB-10

OB-3

OB-19

OB-18

OB-2
OB-7

SEA-2

OB-12

OB-1

OB-16

OB-17

OB-9

OB-20

OB-6

OB-15

OB-8

SEA-1

BW-1

OB-14

BW-2

BW-3

BW-7

BW-4

BW-8

BW-9

New plant

Well with datalogger

BAROM

Barometer

Old plant

Well without datalogger
Current production well
100 m

Figure 8.5 Map displaying the location of the observation boreholes (OB) and current production beach wells (BW). The hydraulic
head at observation wells depicted by black dots was continuously monitored. Two sensors (SEA-1 and SEA-2) were located at the
sea-shore for measuring the sea level fluctuation. A barometer (depicted by a star) was located at the old desalination plant. The
background image depicts the estimated electrical resistivity arising from a preliminary geophysical campaign (Reproduced with
permission from Alcolea et al . (2009). Alcolea, A, Renard, P., Mariethoz, G. and Bertone, F. (2009) Reducing the impact of a
desalination plant using stochastic modelling and optimization techniques. Journal of Hydrology , 365 (3-4), 275-88).

amenable to be solved in a stochastic framework. This
inverse problem can be solved using different techniques
in the framework of multi-Gaussian fields (de Marsily
et al ., 1999; Carrera et al ., 2005; Hendricks Franssen et al .,
2009). Here, the regularized pilot-points method (Alcolea
et al ., 2006) was used to obtain 200 Monte Carlo simula-
tions of the hydraulic conductivity and storativity fields
(not displayed here) constrained by all available data.
Four of these simulations are depicted in Figure 8.7.
The goodness of these characterizations is evaluated
in terms of fits to available head data (Figure 8.6) and
physical plausibility of the inverted hydraulic conduc-
tivity and storativity fields, which are evaluated visually
(Figure 8.7). All the aforementioned simulations present
highly conductive channels (possibly karstic conduits),
well connected to the sea. This result corresponds to the
initial guess (karstification caused by dissolution). It also
reveals zones with very low hydraulic conductivity close

to the seashore, which can be explained by the deposition
of fine, less permeable, materials along the coast line. Fits
to available head data are displayed in Figure 8.6. They
are in all cases satisfactory.
The hydraulic conductivity fields were then used to
define the optimal locations and corresponding produc-
tion rates of the pumping wells. To that end, we made
use of a genetic algorithm minimizing a penalty function
accounting for the operational and maintenance costs.
One particular aspect of the optimization when deal-
ing with stochastic models is that many different and
equiprobable descriptions of the reality are considered.
For each description, a different pumping network config-
uration is optimal. But only one single pumping scheme
will be implemented in the field. Therefore the optimum
solution must be defined over the ensemble of the possible
Monte Carlo simulations using a criterion of robustness:
the optimal design should be efficient for all of them. It