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.