Calculation of the irrigation indices
Based on the results obtained from Table 1 and according to Table 2, the water quality classification indices for irrigation were calculated from major groundwater ions (Fig. 6) and listed in Table 3. As shown in Table 3, the quality of indices for agriculture purposes was classified as excellent in the following indices: MR (except w6 in the dry season), SAR, Na% (just w16 and w18 in dry and w7, w15, and w19 in wet seasons), RSC, pH, KR (except w4 and w13 in the dry season), and CR (just w16 and w18 in dry and w7, w15, and w18 in wet seasons). Accordingly, w18 has the best, and w4 and w13 have the worst quality for irrigation purposes among other sample wells in dry and wet seasons, respectively.
Table 3
The important parameters and indices which determine the IW quality of the study area in wet and dry seasons
DRY SEASON
|
Sample
|
RSC
|
Na%
|
MR
|
KR
|
PS
|
SAR
|
CR
|
EC
|
pH
|
W1
|
-1.30
|
33.29
|
31.83
|
0.48
|
3.45
|
1.59
|
1.24
|
829
|
7.08
|
W2
|
-2.91
|
42.05
|
32.35
|
0.72
|
6.86
|
2.70
|
2.48
|
1234
|
6.92
|
W3
|
-2.67
|
37.78
|
34.53
|
0.59
|
5.45
|
2.07
|
2.40
|
983
|
7.97
|
W4
|
-0.61
|
55
|
48.07
|
1.20
|
6.03
|
3.57
|
2.25
|
983
|
7.47
|
W5
|
-3.11
|
42.34
|
33.74
|
0.72
|
6.02
|
2.44
|
3.53
|
994
|
7.96
|
W6
|
-0.76
|
46.39
|
62.88
|
0.85
|
4.05
|
2.48
|
1.69
|
784
|
7.45
|
W7
|
-0.61
|
41.93
|
29.75
|
0.71
|
4.20
|
2.26
|
1.34
|
896
|
8.02
|
W8
|
-2.92
|
38.7
|
40.71
|
0.62
|
6.28
|
2.19
|
2.82
|
1050
|
7.70
|
W9
|
-2.70
|
37.74
|
42.48
|
0.59
|
5.32
|
2.06
|
2.36
|
975
|
7.48
|
W10
|
-1.47
|
38.29
|
42.59
|
0.61
|
3.80
|
1.80
|
1.95
|
706
|
7.53
|
W11
|
-1.51
|
42.98
|
31.73
|
0.74
|
4.62
|
2.40
|
1.90
|
911
|
7.98
|
W12
|
-1.26
|
40.55
|
40.22
|
0.68
|
3.88
|
2.03
|
1.78
|
764
|
8.01
|
W13
|
-2.44
|
53.4
|
27.03
|
1.13
|
7.80
|
3.76
|
3.77
|
1211
|
7.88
|
W14
|
-3.73
|
43
|
15.56
|
0.75
|
8.38
|
3.00
|
2.91
|
1430
|
7.81
|
W15
|
-3.69
|
47.42
|
29.31
|
0.90
|
7.69
|
3.16
|
4.70
|
1198
|
7.61
|
W16
|
-0.50
|
19.94
|
13.62
|
0.25
|
0.92
|
0.56
|
0.71
|
326
|
7.69
|
W17
|
-3.69
|
41.42
|
40.98
|
0.70
|
7.11
|
2.59
|
3.32
|
1173
|
7.53
|
W18
|
0.09
|
19.69
|
18.63
|
0.24
|
0.51
|
0.58
|
0.25
|
375
|
7.55
|
W19
|
-0.36
|
36.68
|
23.81
|
0.57
|
1.76
|
1.27
|
1.20
|
405
|
7.17
|
WET SEASON
|
Sample
|
RSC
|
Na%
|
MR
|
KR
|
PS
|
SAR
|
CR
|
EC
|
pH
|
W1
|
0.51
|
42.23
|
18.55
|
0.72
|
3.13
|
2.36
|
0.78
|
936
|
7.57
|
W2
|
-3.36
|
32.74
|
13.38
|
0.48
|
6.31
|
2.04
|
1.70
|
1360
|
7.28
|
W3
|
-2.90
|
30.33
|
18.59
|
0.42
|
5.61
|
1.74
|
1.49
|
1239
|
7.44
|
W4
|
-1.07
|
41.27
|
19.67
|
0.69
|
6.04
|
2.65
|
1.36
|
1256
|
7.25
|
W5
|
-2.97
|
32.01
|
15.34
|
0.46
|
6.12
|
2.01
|
1.45
|
1382
|
7.43
|
W6
|
-0.63
|
36.75
|
28.57
|
0.57
|
3.78
|
2.03
|
1.00
|
988
|
7.33
|
W7
|
-1.09
|
14.66
|
13.21
|
0.11
|
1.84
|
0.45
|
0.45
|
877
|
7.45
|
W8
|
-3.15
|
30.77
|
18.58
|
0.44
|
6.59
|
2.00
|
1.37
|
1517
|
7.10
|
W9
|
-2.97
|
27.62
|
35.19
|
0.37
|
5.35
|
1.64
|
1.24
|
1335
|
7.15
|
W10
|
-3.24
|
39.03
|
16.61
|
0.61
|
6.90
|
2.61
|
1.89
|
1480
|
7.34
|
W11
|
-3.47
|
29.91
|
23.32
|
0.42
|
6.59
|
1.96
|
1.38
|
1531
|
7.26
|
W12
|
-2.34
|
31.08
|
13.46
|
0.44
|
5.25
|
1.91
|
1.16
|
1355
|
7.45
|
W13
|
-3.13
|
34.29
|
16.97
|
0.51
|
6.67
|
2.22
|
1.63
|
1433
|
7.43
|
W14
|
-2.34
|
31.91
|
18.18
|
0.46
|
5.47
|
2.05
|
1.15
|
1469
|
7.25
|
W15
|
-0.18
|
12.97
|
13.92
|
0.11
|
0.74
|
0.41
|
0.19
|
805
|
7.43
|
W16
|
-1.33
|
34.17
|
14.29
|
0.44
|
3.40
|
1.57
|
1.11
|
945
|
7.28
|
W17
|
-3.29
|
38.07
|
27.10
|
0.60
|
6.63
|
2.41
|
2.22
|
1279
|
7.41
|
W18
|
-0.18
|
30.89
|
37.21
|
0.17
|
1.09
|
0.48
|
0.54
|
550
|
7.40
|
W19
|
-4.14
|
15.70
|
33.13
|
0.18
|
5.41
|
0.82
|
1.36
|
1200
|
7.50
|
Interpolation of calculated irrigation indices
Figure 7 shows the prepared maps of the irrigation indices by interpolation. Accordingly, medium to high anomalies was revealed in the center to north parts in most indices. It can be related to the groundwater flow's direction (south to north) and leaching of the main ions from the sediment structures upstream of groundwater streams. Furthermore, it might have been caused due to the higher density of urban areas and agricultural lands in the center to northern parts of the plain. As can be seen, the trend of index changes in the wet and dry seasons is different for some indices. This case is well visible in the central and northern regions. As can be seen, in the dry season, the maximum rates of CR, EC, KR, Na%, PS, and SAR are observed in the northeastern regions. However, in the wet season, precisely the opposite of the dry season, these indices' minimum rate is observed in described areas. It can be related to changes in the leaching rates and groundwater flow rates and ion exchanges between ions in the dry and wet seasons.
Indices standardization
Figures 8 and 9 show the fuzzy standardized IW indices according to fuzzy memberships. Because the RSC parameter has negative values, and the "Fuzzy Small" function cannot calculate these type values, the "Linear" function was used for this parameter. Considering that in the CR, KR, MR, EC, SAR, and PS indices, low values are more suitable in irrigation, the "Small" function was used to fuzzy standardize. Due to the suitability values between 6.5 to 8.5 as the appropriate range in the pH parameter, the "Gaussian" function was used. In this regard, value 7.5 was selected as the midpoint. Based on Table 2, classification values of Na% ranked linearly, and the distance of each quality class to the next class is fixed. For this reason, the "Linear" function was used for this parameter. Furthermore, because the smaller values are better suited to this index, this function's decreased form was used to fuzzy standardize.
Aggregation indices
As shown in Fig. 10, in the "SUM" and the "OR" overly operations, the highest values of membership were selected that indicates they are expander operations. On the contrary, in the "PRODUCT" and the "AND" overly operations, the lowest membership’s values were selected. This means they are restrictive operations. However, the "PRODUCT" is more restrictive than the "AND" function because the multiplication of the standardized indices less than one has lower values than the value of the standardized parameters (Lewis et al. 2014).
Figure 11 showed that in the "GAMMA" overlay operation, an increase in "γ" value caused the higher accuracy. In contrast to our results, some authors (Araya-Muñoz et al. 2017) believe that "γ" values above 0.7 cause to decline in the accuracy. However, our results were confirmed by the research of Lewis et al. (2014), Mohebbi Tafreshi et al. (2018), Mohebbi Tafreshi et al. (2021b), Mortazavi Chamchali and Ghazifard (2019), and Mortazavi Chamchali and Ghazifard (2020). These researches were indicated that "GAMMA 0.8" and "GAMMA 0.9" are more accurate than other overlay operations.
Identify the most accurate operation
To specify the most accurate overlay operation, the correlations between the fuzzy membership and operation maps were used. For this purpose, the "Band collection statistics" tool in ArcGIS software was used.
Despite the relatively good correlation of most membership functions with overlapping operators, the lowest correlation is F-pH and F-MR in both dry and wet seasons (Table 4). However, contrary to the better trend of correlations in the dry season, for these two parameters, the correlation values are higher in the wet season.
Table 4
The correlation between the "Fuzzy membership" and "Fuzzy overlay" raster maps. In this table, the "Fuzzy Na%", the "Fuzzy SAR", the "Fuzzy PS", the "Fuzzy pH", the "Fuzzy RSC", the "Fuzzy EC", the "Fuzzy KR", the "Fuzzy MR" and the "Fuzzy CR" are fuzzy membership raster form of the indices and the "SUM", AND", OR, PRODUCT", the "GAMMA 0.1", the "GAMMA 0.2", the "GAMMA 0.3", the "GAMMA 0.4", the "GAMMA 0.5", the "GAMMA 0.6", the "GAMMA 0.7", the "GAMMA 0.8", the "GAMMA 0.9", the "GAMMA 0.95" and the "GAMMA 0.99" are fuzzy overlay raster form. The values are the correlation between the "Fuzzy membership" and "Fuzzy overlay" raster maps, and the values that have been marked with an underline, are the highest value amount in each category.
DRY SEASON
|
Overlay vs. membership
|
F-CR
|
F-EC
|
F-KR
|
F-MR
|
F-Na%
|
F-pH
|
F-PS
|
F-RSC
|
F-SAR
|
SAVC
|
AND
|
0.580
|
0.570
|
0.113
|
0.111
|
0.323
|
0.042
|
0.892
|
-0.177
|
0.079
|
2.888
|
OR
|
0.301
|
0.228
|
0.696
|
-0.067
|
0.643
|
0.113
|
0.053
|
-0.488
|
0.812
|
3.401
|
PRODUCT
|
0.374
|
0.387
|
0.066
|
0.065
|
0.203
|
0.028
|
0.989
|
-0.109
|
0.045
|
2.268
|
SUM
|
0.003
|
0.003
|
0.042
|
0.016
|
0.027
|
-0.001
|
0.001
|
-0.014
|
0.036
|
0.143
|
GAMMA 0.1
|
0.413
|
0.435
|
0.075
|
0.073
|
0.227
|
0.030
|
0.988
|
-0.120
|
0.051
|
2.411
|
GAMMA 0.2
|
0.459
|
0.491
|
0.085
|
0.083
|
0.255
|
0.032
|
0.979
|
-0.134
|
0.058
|
2.576
|
GAMMA 0.3
|
0.515
|
0.556
|
0.098
|
0.097
|
0.290
|
0.034
|
0.960
|
-0.152
|
0.067
|
2.770
|
GAMMA 0.4
|
0.582
|
0.631
|
0.116
|
0.114
|
0.334
|
0.037
|
0.928
|
-0.176
|
0.080
|
2.998
|
GAMMA 0.5
|
0.663
|
0.716
|
0.140
|
0.139
|
0.391
|
0.041
|
0.878
|
-0.209
|
0.099
|
3.276
|
GAMMA 0.6
|
0.759
|
0.806
|
0.178
|
0.175
|
0.466
|
0.048
|
0.804
|
-0.261
|
0.130
|
3.628
|
GAMMA 0.7
|
0.865
|
0.891
|
0.240
|
0.226
|
0.568
|
0.059
|
0.700
|
-0.348
|
0.187
|
4.083
|
GAMMA 0.8
|
0.948
|
0.931
|
0.338
|
0.277
|
0.692
|
0.074
|
0.557
|
-0.492
|
0.292
|
4.601
|
GAMMA 0.9
|
0.936
|
0.860
|
0.464
|
0.277
|
0.793
|
0.083
|
0.383
|
-0.681
|
0.456
|
4.934
|
GAMMA 0.95
|
0.876
|
0.777
|
0.520
|
0.241
|
0.811
|
0.081
|
0.300
|
-0.766
|
0.546
|
4.919
|
GAMMA 0.99
|
0.809
|
0.695
|
0.556
|
0.196
|
0.807
|
0.077
|
0.241
|
-0.817
|
0.611
|
4.807
|
WET SEASON
|
Overlay vs. membership
|
F-CR
|
F-EC
|
F-KR
|
F-MR
|
F-Na%
|
F-pH
|
F-PS
|
F-RSC
|
F-SAR
|
SAVC
|
AND
|
0.586
|
0.835
|
0.215
|
-0.067
|
0.493
|
0.154
|
0.527
|
-0.388
|
0.298
|
3.563
|
OR
|
0.578
|
0.388
|
0.507
|
-0.205
|
0.653
|
0.236
|
0.156
|
-0.234
|
0.815
|
3.771
|
PRODUCT
|
0.305
|
0.420
|
0.113
|
0.013
|
0.319
|
0.086
|
0.984
|
-0.222
|
0.151
|
2.611
|
SUM
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
0.000
|
-0.000
|
0.000
|
0.000
|
GAMMA 0.1
|
0.330
|
0.447
|
0.122
|
0.013
|
0.341
|
0.092
|
0.984
|
-0.238
|
0.164
|
2.733
|
GAMMA 0.2
|
0.362
|
0.479
|
0.134
|
0.014
|
0.369
|
0.101
|
0.980
|
-0.259
|
0.181
|
2.878
|
GAMMA 0.3
|
0.403
|
0.515
|
0.149
|
0.015
|
0.403
|
0.111
|
0.970
|
-0.285
|
0.202
|
3.054
|
GAMMA 0.4
|
0.457
|
0.556
|
0.168
|
0.018
|
0.446
|
0.126
|
0.951
|
-0.318
|
0.230
|
3.270
|
GAMMA a 0.5
|
0.527
|
0.604
|
0.191
|
0.023
|
0.497
|
0.145
|
0.919
|
-0.364
|
0.266
|
3.536
|
GAMMA 0.6
|
0.617
|
0.655
|
0.216
|
0.032
|
0.555
|
0.172
|
0.868
|
-0.425
|
0.314
|
3.856
|
GAMMA 0.7
|
0.727
|
0.706
|
0.238
|
0.045
|
0.613
|
0.210
|
0.790
|
-0.507
|
0.372
|
4.209
|
GAMMA 0.8
|
0.840
|
0.742
|
0.248
|
0.061
|
0.652
|
0.260
|
0.684
|
-0.607
|
0.433
|
4.526
|
GAMMA 0.9
|
0.927
|
0.747
|
0.234
|
0.075
|
0.651
|
0.314
|
0.556
|
-0.706
|
0.482
|
4.692
|
GAMMA 0.95
|
0.951
|
0.736
|
0.218
|
0.080
|
0.632
|
0.339
|
0.491
|
-0.748
|
0.497
|
4.692
|
GAMMA 0.99
|
0.960
|
0.720
|
0.202
|
0.082
|
0.610
|
0.358
|
0.442
|
-0.775
|
0.504
|
4.653
|
After calculating the correlations, the SAVC of each overlay method was obtained. Accordingly, a higher SAVC amount shows the more accurate "overlay operation".
Based on the result shown in Table 4, the "GAMMA 0.9" and "GAMMA 0.95" methods with the highest SAVC are the best overlay operation in dry and wet seasons, respectively. In the following, the "GAMMA 0.95" and the "GAMMA 0.99 in the dry season, and the "GAMMA 0.9" and the "GAMMA 0.99 in the wet season are next ranking, respectively. Comparing the results obtained in dry and wet seasons shows that the rate of adaptation of operators in the dry season is higher than in the wet season.