Accurate prediction of salinity in Chott Djerid shallow aquifers, southern Tunisia: Machine learning model development

Figures & data

Figure 1. Simplified geological map of southern Tunisia showing the study area (a), sampling points (b) and a bloc diagram (c) of the Chott Djerid aquifer system.

Table 1. Summarized metrics used for model validation.

Metric	Formula	Description
RMSE	$\sqrt{MSE}$	Measures the average distance between the predicted and the actual values.	Eq. (1)Eq. (1) $Xn=2\ast \frac{X-Xmin}{Xmax-Xmin}-1$Eq. (1)
MSE	$\frac{\stackrel{n}{\sum _{i=1}}{(y_i-{\hat{y}}_i)}^2}{n}$	Average of the squared errors between the predicted and the actual values.	Eq. (2)Eq. (2) $RSME=\sqrt{\frac{\stackrel{n}{\sum _{i=1}}{(y_i-{\hat{y}}_i)}^2}{n}}$Eq. (2)
SSE	$\stackrel{n}{\sum _{i=1}}(y_i-{\hat{y}}_i{)}^2$	The sum of the squared errors between the predicted and the actual values.	Eq. (3)
R^2	$1-\frac{\sum _{i=1}^n{(y_i-{\hat{y}}_i)}^2}{\sum {(y_i-{\bar{y}}_i)}^2}$	Measures how well the model explains the variance in the data.	Eq. (4)
SD	$\frac{\stackrel{n}{\sum _{i=1}}{(y_i-{\bar{y}}_i)}^2}{n-1}$	Measures the spread of the data.	Eq. (5)

Figure 2. (a) architecture of the ANN model used in this study and (b) the proposed predictive BP neural network model (modification after Bashar et al., 2023).

Table 2. Statistical indexes of the studied water physical-chemical properties.

Var.	N	Mean	SD	Median	Min	Max	Range	Skew	Kurtosis	SE
Depth (m)	51	14.76	12.86	8.4	4.6	50	45.4	1.64	1.47	1.8
EC (µS/cm)	51	7052.2	3441.06	7810	535	13330	12795	−0.47	−0.75	481.84
Temp. (°C)	51	20.89	2.28	20.8	16	26.3	10.3	0.39	−0.08	0.32
pH	51	7.23	0.67	7.49	6.21	8.16	1.95	−0.37	−1.51	0.09
Cl (mg/L)	51	1495.83	986.75	1511.28	26.35	4179.7	4153.35	0.37	−0.2	138.17
NO3 (g/L)	51	40.93	98.31	6	0	558	558	4	16.5	13.77
SO4 (mg/L)	51	2021.31	959.95	2272.85	91.9	3482.8	3390.9	−0.82	−0.51	134.42
CO3 (mg/L)	51	3.54	9.4	0	0	42	42	2.68	6.44	1.32
HCO3 (mg/L)	51	273.78	175.18	268.4	25.62	895.48	869.86	1.34	2.57	24.53
Na (mg/L)	51	859.58	549.59	833.2	22.51	2277.6	2255.09	0.34	−0.32	76.96
K (mg/L)	51	49.16	51.39	49.9	0	253.04	253.04	1.92	4.78	7.2
Mg(mg/L)	51	243.27	141.46	256.2	16.39	494.2	477.81	−0.03	−1.1	19.81
Ca (mg/L)	51	613.38	264.67	697.65	41.07	1078.8	1037.73	−0.96	−0.07	37.06
Sr (mg/L)	51	4.8	3.74	4.61	0	10.88	10.88	0.1	−1.36	0.52
TDS (mg/L)	51	5775.02	2893.59	6260	360	11010	10650	−0.47	−0.73	405.18

Figure 3. Hierarchical cluster analysis of water samples from the Chott Djerid shallow aquifer.

Figure 4. Boxplots for the studied geochemical parameters based on clusters.

Figure 4. (Continued).

Figure 5. Pairs panels for the studied geochemical parameters.

Figure 6. PCA variable factor map.

Table 3. Matrix of the main principal components and percentage of variance after variomax-rotation (n = 51).

Component
Parameter	1	2	3	4	5
EC	0.972	0.128	0.095	−0.118	0.037
Cl	0.902	0.126	0.159	−0.323	0.044
NO3	−0.194	0.787	−0.234	0.291	0.445
SO4	0.946	0.022	0.058	0.202	−0.022
CO3	−0.144	−0.126	0.844	0.481	0.051
HCO3	0.562	−0.59	−0.3	0.319	0.204
Na	0.92	0.195	0.086	−0.215	−0.012
K	0.548	0.55	−0.129	0.388	−0.454
Mg	0.938	−0.119	0.007	0.003	0.024
Ca	0.873	0.007	0.177	−0.025	0.179
TDS	0.989	0.074	0.072	−0.05	0.045
Sr	0.731	−0.327	−0.393	0.293	−0.053
Eigenvalue	7.327	1.483	1.11	0.863	0.49
Variance %	61.062	12.36	9.251	7.194	4.083
Cumulative %	61.062	73.422	82.674	89.868	93.951

Figure 7. Structure of the BPNN adopted in this study.

Figure 8. Fitting the predicted values from BPNN and experimental values.

Table 4. Cross validation criteria for the proposed BPNN model.

Accuracy	Sensitivity	Specificity	Kappa	RMSE	MSE	SSE	R^2	Adj R^2	SD
1.0000	1.0000	1.0000	1.0000	0.0402	0.0016	0.0146	0.9721	0.9790	0.1240

Bashar, A. M., Nozari, H., Marofi, S., Mohamadi, M., & Ahadiiman, A. (2023). Investigation of factors affecting rural drinking water consumption using intelligent hybrid models. Water Science & Engineering, 16(2), 175–183. doi:10.1016/J.WSE.2022.12.002

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Data availability statement

Data are available upon request.