3. Methodology
Two major objectives were addressed in this study. The first objective
was to identify the maximum pumping rates of the wells by considering
the R-A exchanges component. This also includes examining the impact of
different types of model domains on the output of R-A exchanges and to
find the best model domain and boundary conditions. Whereas the second
objective was to compare the Pareto front developed by different coupled
simulation-optimization models. Different groundwater model domains were
taken by using the different boundary conditions and the impact of each
domain on R-A exchanges and correspondingly the water budgeting of the
aquifer was examined. Figure 2 shows the flow chart of the methodology.
Total four optimization techniques were compared i.e. Multi-objective
Genetic Algorithm (MoGA), Multi-objective Particle Swarm Optimization
(MOPSO), Pareto Search (PS), and Multi-Objective Evolutionary Algorithm
based on Decomposition (MOEA/D). To deal with a large number of wells,
the wells in the domain were grouped based on the municipal zones and
distance of the wells from the river. If any well in the municipal zone
had a distance from the river less than a threshold of 1 km, then it was
classified as a new well zone.
In the objective functions, maximum pumping rates in the well zones and
maximum groundwater inflow into the river were considered. Conceptual
models in GMS-MODFLOW (Groundwater Modelling System, Aquaveo) were
developed to simulate the river-aquifer exchanges for the lower part of
the River Ain, France and these were coupled with optimization models
available in the MATLAB platform. To implement the coupling between the
two systems, MATLAB scripts were developed which carried out the
following tasks, (i) run the optimization model with Modflow as cost
function, (ii) read and write the decision variables from the ‘.h5’
input file for Modflow, (iii) run the simulation model, extract and
post-process the output of simulation model to calculate a cost for
optimization model.
Additionally, the sets of optimized costs (Pareto fronts) were compared
using various criteria (convergence, diversity, and uniformity) and
metrics (hypervolume, spread, and IGD). Decision variables corresponding
to these Pareto fronts were also compared in terms of spatial and
quantitative distribution in different model domains.
3.1 Groundwater Model Development :
The groundwater flow modeling was performed using MODFLOW. GMS 10.4
based on conceptual model approach was adopted to create different
geospatial data-based input layers for defining the surface recharge,
boundary conditions, discharge wells, observation wells, and hydraulic
conductivity of the area and to build the groundwater model. The
piezometric surface of groundwater was created using hydrograph data of
280 wells in the study area.
The topography, top, and bottom of the study area, was found in the
range of 240 m to 550 m where SRTM data was used to get the surface
elevation of the area. The bottom surface was prepared with the help of
well log data obtained by BRGM. The two-layered model was developed for
the underlying sediments where each layer was assumed to be horizontal,
homogeneous, and isotropic. The mean thickness of the layer was taken as
25 m. The initial values of hydraulic conductivity were taken from
0.0018 m/s for the older sediment and 0.003 m/s for the younger
sediment. The horizontal hydraulic conductivity was estimated from the
pumping well test data and the literature data obtained by BRGM. Thus,
the obtained data have been used as initial distributions that were
subsequently modified during calibration of the numerical model to
achieve the best fit between the simulated and the observed data.
Specific yield (Ss) values for the alluvial deposits were found in the
range from 1 to 17%.
Boundary Conditions: The model was developed by defining two
types of external model boundaries i.e. constant head and constant flow
boundaries. Figure-3 shows the different types of domains that were
considered to perform the groundwater modeling. The figure shows that in
the Domain-1, eastern & western sides of the model domain were defined
based on watershed divide line i.e. no-flow boundary respectively,
whereas in Domain-2 alluvium plain of the Ain river were considered and
the eastern & western side of the model domain was defined based on
constant flow boundaries. The constant flow values were referred to from
the published report of BRGM (Ref.). Whereas, the model Domain-3 was
chosen the same as Domain-1 with one modification in the lower eastern
part. The Rhone river was introduced in the model domain through the
constant head boundary. This modification helped to find the impact of
incorporating the Rhone river in the modeling area.
Piezometer and River water level data: In this study, a total of
15 piezometers were available, where a few piezometers had data for the
period of 2008 to 2010 and the remaining piezometers covered the data
from 2002 to 2015. The data thus collected, showed that the piezometer
doesn’t show very high fluctuation in values. This variation ranged from
3.7m to 1.2m, which showed that the groundwater table, and
correspondingly groundwater scenario, is very stable in the region.
Further, the river water level data, which was measured at 5 locations
of the study area, was obtained from Banque Hydro France. The data from
2002 to 2015 was also examined to understand the trend of data. This
analysis showed a fluctuation range of 2.54 m at Chezy and 1.67m at
point de’Ain on the river Ain. Data of other tributaries such as
Albarine also showed a maximum fluctuation of 1.36m.
Recharge & Evapotranspiration: Rainfall was considered as the
source of groundwater recharge. Rainfall data from the Météo France
database was used to calculate the recharge input values and applied
uniformly over the polygons constructed in the model domain. The
different recharge polygons were developed based on a land-use map
created from satellite imageries (Figure 6). Six categories were taken
for classification purposes such as water body, agriculture, fallow
land, built-up, forest/vegetation, sand. Supervised classification was
performed to create the land-use map where the fusion of Satellite
imageries of Sentinel 1 and Landsat 8 was used. In Sentinel-1 bands, VV
and VH were used whereas in Landsat 8 bands 1 to 7 were used for
classification purposes. Random Forest model was used as classifier and
training accuracy, test accuracy, and kappa coefficient were 99.98%
98.45%, and 97.77% respectively. The initial value of recharge was
taken as 10%, 50%, 50%, 80%, and 60% for built-up, agriculture,
vegetation, sand, and fellow land of total precipitation i.e. 1650
mm/year. Estimated evapotranspiration was taken as 638 mm/year with an
extinction depth of 2 m. The potential evapotranspiration was considered
uniformly distributed over the study area. For the future forecast, 10
years’ monthly average of rainfall were taken and corresponding recharge
values were used.
Water Demand and Supply: Water consumption in the study area is
mainly done by agriculture, the rest is used for domestic purposes and
some for industrial usage. The discharge details about the wells were
computed on the basis of agricultural and domestic demands of the area.
The field survey was carried out to collect the information of water
demand as per the cropping pattern and domestic water consumption. The
total agriculture water demand was identified through the classification
of satellite imagery data for three seasons. The groundwater abstraction
varies seasonally as well as yearly due to variable demands for
irrigation. The quantitative data, available from 2002, are obtained
from three sources - the Rhône-Méditerranée-Corse Water Agency (AERMC),
the Directorate Department of Agriculture and Forestry (DDAF), and the
Association Syndicale of Ain Irrigation (ASIA). The groundwater
abstraction is divided into three uses (Table 1). Thus, the total
catchments identified are 372, representing a total annual volume of
40,130,104 m3. which varies up to 27
Mm3 in some conditions. The total water requirement
computed by this method is found to be 106.78 mcm, which is 5% more
than the value available by administrative authority i.e., 101.43 mcm.
Calibration and Validation: A regional groundwater flow model was
constructed and calibrated to the transient-state condition with a
stress period of four months. In the calibration of the model, the value
of recharge and boundary inflow was taken. Calibration of the model was
performed based on computed and observed values of groundwater head at
20 evenly distributed points in the study area. Based on the
availability of data, the model was calibrated from 2008 to 2010 based
on all piezometers and further from 2010 to 2012 on the basis of
remaining wells. The further model was validated based on data from 2012
to 2015. In the calibration processes, the groundwater head values which
were computed by the model and observed at the observation wells were
analyzed at 95% confidence level (Figure 4) at four different
locations. The mean square error was computed for the calibration
process. The differences between observed and computed values were found
less in the middle part of the valley whereas on the boundary of the
model domain they were not found within the range of the 95% confidence
level due to inaccuracy for defining the head flux boundaries.
Therefore, head flux boundary values were modified within the range of
10%, and the effect on the error was observed. Initially, the constant
flow boundary was calibrated in the study state condition to incorporate
the groundwater in-flow from the adjacent aquifer. The recharge rate was
calibrated with the help of PEST (a popular parameter estimation
program) in the MODFLOW package. Final outputs of the model were
obtained as water table contour maps and directions of groundwater
movement together with mass water balances for the model domain, and
river-aquifer exchanges. Further, river-aquifer exchanges were
calculated with the help of a calibrated model.