Groundwaters in the Auvergne-Rhône-Alpes Region, France: Grouping Homogeneous Groundwater Bodies for Optimized Monitoring and Protection
Abstract
:1. Introduction
2. Materials and Methods
2.1. Auvergne-Rhône-Alpes Region
2.2. The French Groundwater Reference System
2.3. Sise-Eaux Database
2.4. Analytical Procedure
- Consistent with previous studies [10], the data underwent a logarithmic transformation (decimal logarithm) using the formula y = log10(x + DL), where x and DL, respectively, represent the measurement of the physico-chemical or bacteriological parameter X and its detection limit [15]. Only the pH, which already corresponds to the logarithmic transformation of the chemical activity of H3O+, was retained without conditioning. The goal was to align the distributions of each parameter with a normal distribution, but more importantly, to limit the influence of extreme values that could mask certain processes responsible for the variability in water quality within the dataset [11,12].
- Each water sample was then assigned to a groundwater body (GWB) based on its geographical coordinates and depth. At this stage, GWBs with too few analyses (less than 10 water samples collected) were excluded from the analysis.
- Principal component analysis (PCA) was subsequently performed on the log-transformed data to reduce the dimensionality of the data space and identify and classify sources of variability within the dataset [27]. PCA is based on the correlation matrix and thus considers standardized variables, allowing the integration of parameters of diverse nature and units (bacteriology, chemistry, etc.). Moreover, it was conducted by diagonalizing the correlation matrix. Under these conditions, the obtained factorial axes are orthogonal to each other in the hyperspace of the data, thus associated with independent processes responsible for water quality variability. The results of this principal component analysis were presented in a previous study [14]. The first six factorial axes, representing 85% of the total variance, were retained for further analysis. The last factorial axes, explaining a small percentage of the variance, were eliminated, considering them to represent background geochemical noise in the dataset [28].
- For each of the selected factorial axes, the average value of the groundwater body (GWB) on the factorial axis was calculated. At this stage, each GWB is characterized by a 6-dimensional vector, with 6 factorial axes being retained.
- Unsupervised hierarchical agglomerative clustering (HAC) was performed on all remaining GWBs, assigning equal weight to each of the 6 factorial axes [29,30]. The aim of this clustering was to group GWBs based on a similarity criterion, considering all parameters. The number of groups chosen was guided by the presence of a break in slope in the relationship between the percentage of explained variance and the number of groups, thus maximizing intra-group homogeneity and inter-group heterogeneity. The results were iteratively compiled to produce a dendrogram and presented in map form [31]. For each group, the mean of the parameters was calculated for group comparisons.
- Ascending hierarchical classification was conducted on all parameters based on their mean values on the first 6 factorial axes of the PCA to detect redundancies in information and behavior among the parameters.
- For each parameter, the information loss induced by aggregating sampling points into GWBs and then into GWB groups was estimated based on the explained variance (R2) using an analysis of variance (ANOVA) [32,33]. Since the analyses were conducted on multiple dates at various sampling points, the total dataset variance includes both temporal variabilities, reflected in different values at the same sampling point, and spatial variability, reflected in different means between sampling points. The R2 calculated on the “sampling point” criterion as an explanatory variable corresponds to spatial variability at this scale. The complement to 1 of R2, i.e., the fraction of unexplained variance, reflects temporal variance if we neglect a small portion of variance related to analytical imprecision. The same calculation conducted at the GWB and GWB group scales allows quantifying the amount of information contained at these different spatial scales and thus tracking the information loss during grouping [15].
- Linear discriminant analysis (LDA) was conducted to test the possibility of assigning each sample to a sampling point, a groundwater body (GWB), or a group of GWBs based on its chemical and bacteriological composition [34,35]. The GWB groups are established from the mean value of each GWB on the factorial axes. As mentioned earlier, this average includes spatial variability within the GWBs and temporal variability since samples were not collected on the same date. This variability may pose challenges for discriminating each GWB group. LDA serves as an indirect way to assess if differentiation is significant at the sample level. It independently verifies, post hoc, the need to apply the proposed method for determining GWB groups.
- Finally, a principal component analysis (PCA) and discriminant analysis (LDA) were conducted on two of the obtained groups as an illustrative application to identify the main mechanisms occurring in each group, with the goal of establishing a roadmap for water resource monitoring.
3. Results
3.1. GWB Groups
3.2. Discriminant Analysis
3.3. ANOVA, Clustering, and Information Loss
3.4. Detailed Analysis of Groups 6 and 7
4. Discussion
4.1. Criteria for Group Discrimination
4.2. A Minimal Loss of Information
4.3. Method Applicability
4.4. Examples of Roadmaps for Monitoring Groups 6 and 7
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Rhone Basin | Loire Basin | Garonne Basin | |
---|---|---|---|
Number of sampling points (Full matrix) | 1204 | 481 | 264 |
Number of groundwater bodies (GWBs) | 60 | 21 | 8 |
Group | Ent. | E. coli | E.C. | pH | K | Na | Ca | Mg | Cl | SO4 | HCO3 | Fe | NO3 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.291 | 0.309 | 2.583 | 7.624 | −1.345 | −0.029 | 1.865 | 0.303 | 0.355 | 0.832 | 2.350 | 0.538 | 0.162 |
2 | 0.204 | 0.240 | 2.700 | 7.484 | −1.125 | 0.356 | 1.994 | 0.556 | 0.568 | 1.197 | 2.476 | 0.417 | 0.129 |
3 | 0.410 | 0.501 | 2.585 | 7.545 | −0.260 | 0.356 | 1.837 | 0.556 | 0.484 | 0.828 | 2.308 | 1.096 | 0.430 |
4 | 0.075 | 0.085 | 2.765 | 7.419 | −0.281 | 0.752 | 1.995 | 0.897 | 0.911 | 1.301 | 2.499 | 0.509 | 1.038 |
5 | 0.125 | 0.126 | 2.693 | 7.452 | −0.058 | 0.669 | 1.953 | 0.629 | 0.924 | 0.978 | 2.362 | 1.169 | 1.044 |
6 | 0.078 | 0.078 | 2.734 | 7.378 | 0.174 | 0.990 | 1.971 | 0.764 | 1.244 | 1.436 | 2.393 | 1.112 | 1.072 |
7 | 1.056 | 1.255 | 2.384 | 7.120 | 0.538 | 1.072 | 1.379 | 0.770 | 1.179 | 1.201 | 1.949 | 1.898 | 0.874 |
8 | 1.592 | 1.853 | 2.127 | 7.268 | 0.412 | 0.900 | 1.060 | 0.488 | 1.021 | 0.962 | 1.637 | 2.314 | 0.643 |
9 | 0.514 | 0.580 | 2.132 | 7.191 | 0.067 | 0.584 | 1.122 | 0.609 | 0.478 | 0.606 | 1.796 | 1.185 | 0.502 |
10 | 0.382 | 0.395 | 1.945 | 6.862 | 0.116 | 0.536 | 0.874 | 0.520 | 0.393 | 0.161 | 1.613 | 0.856 | 0.597 |
11 | 0.863 | 0.962 | 1.903 | 6.463 | 0.138 | 0.689 | 0.682 | 0.276 | 0.785 | 0.391 | 1.256 | 1.393 | 0.831 |
12 | 0.539 | 0.593 | 1.790 | 6.524 | −0.195 | 0.621 | 0.636 | 0.064 | 0.449 | 0.472 | 1.317 | 1.039 | 0.388 |
from\to | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | Total | % Correct |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 44 | 52 | 40 | 7 | 5 | 1 | 0 | 0 | 0 | 5 | 2 | 0 | 156 | 28.21 |
2 | 24 | 100 | 40 | 20 | 11 | 5 | 1 | 0 | 1 | 0 | 0 | 0 | 202 | 49.50 |
3 | 10 | 15 | 577 | 32 | 165 | 23 | 7 | 2 | 36 | 7 | 8 | 9 | 891 | 64.76 |
4 | 1 | 22 | 69 | 293 | 67 | 51 | 0 | 0 | 5 | 1 | 1 | 0 | 510 | 57.45 |
5 | 3 | 8 | 88 | 92 | 757 | 25 | 1 | 0 | 13 | 11 | 0 | 2 | 1000 | 75.70 |
6 | 0 | 3 | 5 | 35 | 110 | 335 | 3 | 0 | 10 | 1 | 1 | 3 | 506 | 66.21 |
7 | 0 | 0 | 0 | 0 | 8 | 62 | 356 | 159 | 4 | 0 | 12 | 14 | 615 | 57.89 |
8 | 0 | 0 | 0 | 0 | 0 | 0 | 50 | 204 | 0 | 0 | 13 | 1 | 268 | 76.12 |
9 | 2 | 6 | 85 | 9 | 23 | 2 | 16 | 13 | 351 | 233 | 86 | 46 | 872 | 40.25 |
10 | 0 | 0 | 3 | 0 | 2 | 0 | 8 | 1 | 117 | 851 | 39 | 76 | 1097 | 77.58 |
11 | 0 | 0 | 12 | 0 | 18 | 3 | 25 | 59 | 30 | 64 | 723 | 93 | 1027 | 70.40 |
12 | 1 | 0 | 0 | 0 | 1 | 1 | 9 | 19 | 71 | 94 | 117 | 618 | 931 | 66.38 |
Total | 85 | 206 | 919 | 488 | 1167 | 508 | 476 | 457 | 638 | 1267 | 1002 | 862 | 8075 | 64.51 |
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Ayach, M.; Lazar, H.; Lamat, C.; Bousouis, A.; Touzani, M.; El Jarjini, Y.; Kacimi, I.; Valles, V.; Barbiero, L.; Morarech, M. Groundwaters in the Auvergne-Rhône-Alpes Region, France: Grouping Homogeneous Groundwater Bodies for Optimized Monitoring and Protection. Water 2024, 16, 869. https://doi.org/10.3390/w16060869
Ayach M, Lazar H, Lamat C, Bousouis A, Touzani M, El Jarjini Y, Kacimi I, Valles V, Barbiero L, Morarech M. Groundwaters in the Auvergne-Rhône-Alpes Region, France: Grouping Homogeneous Groundwater Bodies for Optimized Monitoring and Protection. Water. 2024; 16(6):869. https://doi.org/10.3390/w16060869
Chicago/Turabian StyleAyach, Meryem, Hajar Lazar, Christel Lamat, Abderrahim Bousouis, Meryem Touzani, Youssouf El Jarjini, Ilias Kacimi, Vincent Valles, Laurent Barbiero, and Moad Morarech. 2024. "Groundwaters in the Auvergne-Rhône-Alpes Region, France: Grouping Homogeneous Groundwater Bodies for Optimized Monitoring and Protection" Water 16, no. 6: 869. https://doi.org/10.3390/w16060869
APA StyleAyach, M., Lazar, H., Lamat, C., Bousouis, A., Touzani, M., El Jarjini, Y., Kacimi, I., Valles, V., Barbiero, L., & Morarech, M. (2024). Groundwaters in the Auvergne-Rhône-Alpes Region, France: Grouping Homogeneous Groundwater Bodies for Optimized Monitoring and Protection. Water, 16(6), 869. https://doi.org/10.3390/w16060869