Prediction of the sodium absorption ratio using data-driven models: a case study in Iran

Figures & data

Figure 1. Details of the SVM.

Table 1. Characteristics of the dataset used in this study.

Variables	Minimum	Maximum	Mean	Standard error	Standard deviation	Kurtosis	Skewness	Sample variance
Training dataset
TDS (mg/l)	112	484	240.164	3.108	68.721	−0.453	0.334	4722.604
Ec	178	745	373.204	4.827	106.751	−0.478	0.363	11,395.794
PH	5.2	8.44	7.830	0.018	0.404	4.605	−1.701	0.163
CO3 (meq/l)	0	0.6	0.050	0.005	0.103	5.752	2.318	0.011
HCO3 (meq/l)	0.9	5	3.072	0.038	0.839	−0.883	−0.040	0.704
Cl (meq/l)	0.08	2.6	0.345	0.008	0.180	51.180	4.657	0.032
SO4 (meq/l)	0.01	2.25	0.351	0.014	0.299	6.431	2.094	0.089
Ca (meq/l)	0.9	4.1	2.442	0.036	0.791	−1.197	−0.058	0.625
mg (meq/l)	0.09	4	1.106	0.025	0.562	4.723	1.727	0.315
na (meq/l)	0.03	2	0.224	0.007	0.164	34.076	4.318	0.027
K (meq/l)	0	3.05	0.036	0.007	0.146	370.268	18.125	0.021
SAR	0.029	1.754	0.246	0.008	0.169	18.823	3.159	0.029
Testing dataset
TDS (mg/l)	40	663	362.688	5.885	99.346	0.449	0.547	9869.645
Ec	260	1020	564.484	8.835	149.144	0.381	0.685	22,243.997
PH	6	8.69	7.727	0.030	0.498	0.512	−0.912	0.248
CO3 (meq/l)	0	1.4	0.064	0.009	0.156	20.820	3.684	0.024
HCO3 (meq/l)	1.25	6.6	3.981	0.064	1.085	−0.583	−0.069	1.178
Cl (meq/l)	0.1	3.3	1.109	0.022	0.380	3.759	0.905	0.144
SO4 (meq/l)	0	2.77	0.565	0.027	0.458	3.145	1.489	0.210
Ca (meq/l)	0.95	5.6	2.982	0.056	0.949	−0.566	−0.155	0.901
mg (meq/l)	0.6	5.7	1.840	0.041	0.697	3.393	1.339	0.486
na (meq/l)	0.06	2.8	0.841	0.025	0.419	0.548	0.352	0.175
K (meq/l)	0	1.13	0.080	0.009	0.144	34.504	5.227	0.021
SAR	0.059	2.44	0.80	0.025	0.418	0.203	0.279	0.175
Total dataset
TDS (mg/l)	40	663	285.279	3.613	100.520	0.823	0.805	10,104.362
Ec	178	1020	443.637	5.556	154.562	0.803	0.809	23,889.259
PH	5.2	8.69	7.792	0.016	0.444	2.415	−1.354	0.197
CO3 (meq/l)	0	1.4	0.055	0.004	0.125	20.824	3.477	0.016
HCO3 (meq/l)	0.9	6.6	3.407	0.037	1.034	−0.341	0.271	1.069
Cl (meq/l)	0.08	3.3	0.626	0.016	0.457	1.811	1.277	0.209
SO4 (meq/l)	0	2.77	0.431	0.014	0.380	5.345	1.937	0.144
Ca (meq/l)	0.9	5.6	2.641	0.032	0.891	−0.703	0.066	0.794
mg (meq/l)	0.09	5.7	1.376	0.025	0.709	2.811	1.317	0.503
na (meq/l)	0.03	2.80	0.451	0.015	0.412	1.669	1.424	0.170
K (meq/l)	0	3.05	0.052	0.005	0.147	237.489	13.102	0.022
SAR	0.02	1.725	0.318	0.010	0.278	1.574	1.395	0.077

Figure 2. Locations of the study area.

Table 2. Details of the user-defined functions for GP.

Kernel function	User-defined functions
RBF kernel	Gaussian noise = 1, $\gamma$ = 0.8
PUK kernel	Gaussian noise = 1, $\omega$ = 0.8, $\sigma$ = 6.8

Table 3. Performance of GP.

	Training dataset				Testing dataset
Approaches	CC	RMSE	NSC	MARE	CC	RMSE	NSC	MARE
GP_RBF	0.9761	0.0379	0.8993	0.1806	0.8931	0.1870	0.5988	0.2385
GP_PUK	0.9340	0.0723	0.6338	0.4511	0.9570	0.2982	0.8288	0.3705

Bold values provide the most precise values of the performance evaluation parameters

Figure 3. Performance of the GP model.

Table 4. Details of the user-defined functions for SVM.

Kernel function	User-defined functions
RBF kernel	C = 3, $\gamma$ = 0.8
PUK kernel	C = 3, $\omega$ = 0.8, $\sigma$ = 6.8

Table 5. Performance of SVM.

	Training dataset				Testing dataset
Approaches	CC	RMSE	NSC	MARE	CC	RMSE	NSC	MARE
SVM_RBF	0.9995	0.0038	0.9989	0.0163	0.9509	0.0992	0.8873	0.1328
SVM_PUK	0.9993	0.0047	0.9984	0.0190	0.9948	0.0365	0.9847	0.063

Bold values provide the most precise values of the performance evaluation parameters

Figure 4. Performance of the SVM model.

Table 6. Performance of ANN and best-selected kernel of SVM and GP.

	Training dataset				Testing dataset
Approaches	CC	RMSE	NSC	MARE	CC	RMSE	NSC	MARE
ANN	0.9999	0.0015	0.9998	0.0098	0.9966	0.0286	0.9906	0.0194
GP_PUK	0.9340	0.0723	0.6338	0.4511	0.9570	0.2982	0.8288	0.3705
SVM_PUK	0.9993	0.0047	0.9984	0.0190	0.9948	0.0365	0.9847	0.063

Bold values provide the most precise values of the performance evaluation parameters

Figure 5. Performance of the ANN model and best-selected kernel of GP and SVM model.

Figure 6. Performance of Seilsepour and Rashidi model to predict the SAR.