Q- Q plot (Zn)
4.5 Geostatistical Analysis
4.5.2 Deterministic Methods
4.5.3.1 Ordinary Kriging
119 4.5.3 Geostatistical Methods
Geostatistical techniques assume that at least some of the variation observed in natural phenomena can be modeled by random processes with spatial autocorrelation and require that the spatial autocorrelation be explicitly modeled. Geostatistical techniques can be used to describe and model spatial patterns (variography), predicts values at unmeasured locations (kriging), and assess the uncertainity associated with a predicted value at the unmeasured locations (kriging). The geostatistical wizard offers several types of kriging, which are suitable for different types of data and have different underlying assumption of Ordinary, Simple, Universal, Indicator, Probability, Disjunctive, Areal interpolation etc..
These mean standardized prediction error (MSPE), root mean square standard prediction error (RMSSPE) and average standard prediction error (ASPE) was used to select the best fitted models.
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Table 4.19: Cross validation results of ordinary kriging for different models of Cd in soil
Models aMPE bRMSPE cASPE dMSPE eRMSSPE
Circular 0.0244 1.2724 1.4398 0.0081 0.9097
Spherical 0.0361 1.2590 1.4399 0.0161 0.8994
Tetraspherical 0.0436 1.2520 1.4348 0.0199 0.8986
Pentaspherical 0.0442 1.2475 1.4141 0.0200 0.9148
Exponential 0.0597 1.2521 1.4073 0.0245 0.9244
Gaussian 0.0295 1.2638 1.4375 0.0107 0.9102
Rational quadratic 0.0959 1.2498 1.3924 0.0358 1.0139
Hole Effect 0.0524 1.2634 1.4322 0.0310 0.9219
K-Bessel 0.0550 1.2359 1.4111 0.0231 0.9043
J-Bessel 0.0220 1.2359 1.4284 0.0087 0.8980
Stable 0.0630 1.2322 1.4074 0.0275 0.9036
Table 4.20: Cross validation results of ordinary kriging for different models of Ni in soil
Models aMPE bRMSPE cASPE dMSPE eRMSSPE
Circular 0.0730 1.2542 1.4066 0.0295 0.9257
Spherical 0.0883 1.2427 1.4049 0.0392 0.9180
Tetraspherical 0.0967 1.2424 1.4034 0.0442 0.9170
Pentaspherical 0.0978 1.2380 1.4023 0.0445 0.9152
Exponential 0.1151 1.2264 1.4036 0.0519 0.9001
Gaussian 0.0622 1.2659 1.4332 0.0261 0.9234
Rational quadratic 0.1468 1.2260 1.4029 0.0696 0.9516
Hole Effect 0.0938 1.3416 1.4173 0.0484 0.9768
K-Bessel 0.1160 1.2229 1.3948 0.0523 0.9116
J-Bessel 0.0732 1.2664 1.4220 0.0329 0.9255
Stable 0.1186 1.2283 1.3929 0.0541 0.9145
aMPE= Mean Prediction Error, bRMSPE= Root Mean Square Prediction Error, cMSPE= Mean Standardized Prediction Error, dRMSSPE=
Root Mean Square Standard Prediction Error, eASPE= Average Standard Prediction Error
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Cd Ni Pb Zn
Explanation of Cd
Larger green region was visible with a small yellow region.
Noticeable red region with ocher, orange and orange red color region were found.
Most contaminated spot was found near the center of the waste disposal site with high intensity Cd concentration.
Explanation of Ni
Considerable orange red region near the center of the study area.
Similar orange and ocher color pattern were also noticeable.
Considerable green region was also detected.
Most contaminated spot was also found near the center of disposal site with high Ni concentration.
Explanation of Pb
No red or orange red region was visible.
Small ocher region with large yellow region was observed.
Considerable green region was also detected.
Contamination of soil of waste disposal site is comparatively less.
Explanation of Zn
Larger green region was visible with a small yellow region.
Noticeable red region with ocher, orange and orange red color region were found.
Most contaminated spot was found near the center of the waste disposal site with high intensity Zn concentration.
Color variation and
visual contamination
level from spatial distribution
Figure 4.26: Spatial distribution of Cd, Ni, Pb and Zn in soil using ordinary kriging for best fitted model.
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The prediction surface produced by rational quadratic model represented larger greenish and yellow region indicated the level of contamination of soil was low. Fom Figure 4.26, the contamination hotspots were found near the center of the waste disposal site.
Cross Validation of Nickel, Lead and Zinc
Among the cross validation results of eleven distinct models for Ni, it was observed that the values of MSPE ranges from 0.0261 to 0.0696 and RMSSPE from 0.9001 to 0.976793.
The value of MSPE (0.0484) was found to be closest to zero, RMSSPE (0.9768) closest to 1 as well as ASPE (1.4173) closed to RMSPE with 1.3416 for the model of hole effect (Table 4.20). So, based on this configuration, hole effect model was selected for metal element Ni. The spatial distribution of Ni for this best fitted model shown in Figure. 4.26 and this figure repepresented larger greenish and yellow region indicated the low level of contamination in soil. Figure 4.26 also showed the contamination hotspots for Pb and Zn near the center of the waste disposal site.
Similarly, the best fitted models were seleced through cross validation of eleven distinct models using ordinary kriging interpoltaion for other metal elements following the same procedure based on the statement of MSPE, RMSSPE, ASPE and RMSPE stated earlier.
Cross validation results revealed that the best fitted model for Pb and Zn was same as hole effect (Table 4.21 and Table 4.22). Results reveals in produced prediction surface, greenish color region represented the level of less contamination and redish color area represented the level of highly contaminated soil for both the metal elements of Pb and Zn.
In addition, the cross validation of eleven distinct models using ordinary kriging was performed for the metal elements of Al, As, Ba, Ca, Co, Cr, Cu, Fe, Hg, K, Mn, Na, Sb, Sc, Sr, Ti, and V in soil and the results are provided in Table F.1 to Table F.17 as well as the spatial distribution for these metal elements is depicted in Figure F. 1 to Figure F.17 in the Annex-F. Result reveals that in produced prediction surface for all these metal elements,, greenish color region represented the level of less contamination and redish color area represented the level of highly contaminated soil.
In addition, the best fitted model from cross validation results of eleven distinct models using ordinary kriging interpolation for the studied metal elements of Al, As, Ba, Ca, Cd, Co, Cr, Cu, Fe, Hg, K, Mn, Na, Ni, Pb, Sb, Sc, Sr, Ti, V and Zn in soil is provided in Table 4.23.
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Table 4.21: Cross validation results of ordinary kriging for different models of Pb in soil
Models aMPE bRMSPE cASPE dMSPE eRMSSPE
Circular 0.0998 12.1487 17.6798 -0.0008 0.7172
Spherical -0.2039 12.1431 17.5225 -0.0183 0.7173
Tetraspherical -0.2009 12.1397 17.4972 -0.0186 0.7199
Pentaspherical -0.2148 12.1331 17.4802 -0.0195 0.7202
Exponential -0.0502 12.2256 17.5881 -0.0101 0.7242
Gaussian -0.1240 12.1179 17.5628 -0.0141 0.7174
Rational quadratic 0.0842 12.1877 17.5603 -0.0031 0.7257
Hole Effect -0.5162 12.1974 17.4139 -0.0338 0.7204
K-Bessel -0.1292 12.1086 17.5570 -0.0145 0.7168
J-Bessel -0.3339 12.1375 17.3920 -0.0259 0.7232
Stable -0.1234 12.0964 17.5665 -0.0141 0.7158
Table 4.22: Cross validation results of ordinary kriging for different models of Zn in soil
Models aMPE bRMSPE cASPE dMSPE eRMSSPE
Circular 0.2522 8.0045 10.3394 0.0017 0.7936
Spherical 0.1441 7.9873 10.2595 -0.0074 0.7829
Tetraspherical 0.1452 8.0009 10.2872 -0.0076 0.7814
Pentaspherical 0.1489 8.0015 10.3103 -0.0072 0.7789
Exponential 0.1497 8.0794 10.5987 -0.0032 0.7682
Gaussian 0.5291 7.9571 10.1408 0.0374 0.9158
Rational quadratic 0.2064 8.0041 10.3895 -0.0009 0.7678
Hole Effect -0.0197 8.0749 9.1687 -0.0402 0.9258
K-Bessel 0.4592 7.8992 10.1817 0.0262 0.8399
J-Bessel 0.1210 7.6625 9.7297 -0.0117 0.8264
Stable 0.4636 7.9276 10.1875 0.0245 0.8386
aMPE= Mean Prediction Error, bRMSPE= Root Mean Square Prediction Error, cMSPE= Mean Standardized Prediction Error, dRMSSPE=
Root Mean Square Standard Prediction Error, eASPE= Average Standard Prediction Error
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Table 4.23: Fitted parameters of the theoretical variogram model for heavy metal parameter
Metal
elements Models Predicted errors
aMPE bRMSPE cASPE dMSPE eRMSSPE Al Hole Effect 10.844 145.577 170.976 0.05278 0.8876
As J-Bessel 0.0701 1.4997 1.8929 0.0269 0.8365
Ba J-Bessel 0.5681 14.5981 17.296 0.02793 0.8887
Ca Hole Effect 6.5894 48.8408 48.068 0.0529 1.5581
Cd Rational quadratic 0.0958 1.2498 1.39247 0.03582 1.0139
Co K-Bessel 0.0469 1.3034 1.2201 0.01969 1.1676
Cr Circular -0.0038 2.081 2.217 -0.0045 0.965
Cu Hole Effect 0.1637 2.5916 3.5444 0.04146 0.7525
Fe J-Bessel 17.891 496.523 482.812 0.00085 1.0234
Hg J-Bessel 0.2565 2.0116 1.8865 0.1207 1.7894
K Exponential 6.7203 80.83 86.4309 0.04847 0.9687
Mn J-Bessel 0.0597 5.627 6.737 -0.0032 0.88
Na Rational quadratic 0.6671 24.2788 24.1802 0.0147 1.0495
Ni Hole Effect 0.0938 1.3416 1.4173 0.0484 0.9767
Pb Hole Effect -0.516 12.1973 17.4139 -0.03381 0.7203
Sb J-Bessel 0.0132 1.54348 1.78 0.00981 0.9004
Sc J-Bessel 0.0203 2.4072 2.62 0.00956 0.9546
Sr J-Bessel 0.267 6.185 7.3186 0.033 0.8779
Ti Rational quadratic 12.739 280.391 296.743 0.02302 1.0204
V Hole Effect 0.7895 12.1697 14.4548 0.0451 0.8677
Zn Hole Effect -0.0196 8.0749 9.1687 -0.0402 0.9258
aMPE= Mean Prediction Error, bRMSPE= Root Mean Square Prediction Error, cMSPE=
Mean Standardized Prediction Error, dRMSSPE= Root Mean Square Standard Prediction Error, eASPE= Average Standard Prediction Error