# Water Quality Index Estimations Using Machine Learning Algorithms: A Case Study of Yazd-Ardakan Plain, Iran

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Water Quality Index

#### 2.3. Wilcox and Schoeller Diagrams

Index | Standard Range in Water | Equation | Reference |
---|---|---|---|

Ec | 0–3000 (µmohs cm ^{−1}) | - | [29] |

Ps | (mmol L^{−1}) | $\mathrm{PS}={\mathrm{Cl}}^{-}+\frac{1}{2}{\mathrm{SO}}_{4}^{2-}$ | [30] |

SAR | 0–15 (meq L ^{−1}) 0.5 | $\mathrm{SAR}=\frac{{\mathrm{Na}}^{+}}{\sqrt{\frac{\mathrm{Ca}\hspace{0.17em}+\hspace{0.17em}\mathrm{Mg}}{2}}}$ | [31] |

MAR | <50 | $\mathrm{MAR}=\frac{\mathrm{Mg}}{\mathrm{Ca}\hspace{0.17em}+\hspace{0.17em}\mathrm{Mg}}\times 100$ | [32] |

SSP | <40 (meq L ^{−1}) | $\mathrm{SSP}=\frac{\mathrm{Na}+\mathrm{K}}{\mathrm{Ca}\hspace{0.17em}+\hspace{0.17em}\mathrm{Mg}\hspace{0.17em}+\hspace{0.17em}\mathrm{Na}}\times 100$ | [29] |

PI | 0.19–7.15 | $\mathrm{PI}=\frac{\left(\left(\mathrm{Na}+\mathrm{K}\right)+\sqrt{{\mathrm{Hco}}_{3}}\right)\times 100}{\mathrm{Ca}\hspace{0.17em}+\hspace{0.17em}\mathrm{Mg}\hspace{0.17em}+\hspace{0.17em}\mathrm{Na}\hspace{0.17em}+\hspace{0.17em}\mathrm{K}}$ | [33] |

KR | 0–1 | $\mathrm{KR}=\frac{{\mathrm{Na}}^{+}}{\mathrm{Ca}\hspace{0.17em}+\hspace{0.17em}\mathrm{Mg}}$ | [34] |

#### 2.4. Modified Water Quality Index

#### 2.5. Artificial Intelligence Models

#### 2.5.1. Gene Expression Programming (GEP)

#### 2.5.2. Model Tree

#### 2.5.3. Multivariate Adaptive Regression Splines (MARS)

#### 2.6. Statistical Metrics

## 3. Results and Discussion

#### 3.1. WQI and FAHP-WQI

#### 3.2. Chemical Indicators

_{3}, Ca, Na, and SO

_{4}, were all located within the normal and standard ranges, but the parameters, EC, TDS, mg, and Ca, were above the allowable standard upper bounds. Despite the average of some samples being in the standard range, the maximum values of all parameters showed that there were areas in the study area that are not suitable for irrigation purposes. The high values of EC and TDS in this plain are due to the existence of salt formations, the amount of water input to the aquifer and the amount of water harvested from it. The electrical conductivity of irrigation water or soil saturation extractives are indicators of the amount of minerals dissolved in the soil environment, and, as such, determine the quality and classification of water and soil in terms of salinity. Therefore, EC must be measured in all studies and research regarding the salinity of water and soil [50]. The electrical conductivity of groundwater in the region under study was in the range of 375–19,960 μmho/cm, and the average EC value was equal to 4878.21. The total dissolved solid in the study area was also in the range of 240–12,000 mg/L, and the average TDS was equal to 3017.78. As shown in Figure 4a, the results of constructing a zoning map of the parameters under investigation indicated that, for parameters EC and TDS, the quality of water was not suitable for agriculture in most areas of Yazd-Ardakan plain. In fact, 47.36% of the wells in this plain were in poor condition, according to the EC indicator. Moreover, regarding the parameter TDS, 45.26% of the wells were in poor conditions The salinity in Yazd-Ardakan plain followed a decreasing trend from east to west. There was also a decreasing trend from north to south. The satisfactory water quality in the central and western regions is mainly due to the existence of rocks formed in these regions, because these parts have Eocene-aged rocks of andesite, latite, ignimbrite, and basalt, for which the existing waters are mainly fresh water.

**Table 6.**Statistical characteristics of well water used, along with their standards [53].

SO_{4} | Cl^{−} | Na^{+} | Mg^{2+} | Ca^{2+} | HCO_{3} | TDS | pH | Ec | Parameter |
---|---|---|---|---|---|---|---|---|---|

meq∙L^{−1} | mg∙L^{−1} | - | mmoh cm^{−1} | ||||||

45.8 | 208.68 | 173.99 | 41.82 | 46.31 | 10.96 | 12,000 | 8.75 | 19,960 | Maximum |

0.42 | 0.79 | 0.22 | 1.03 | 1.2 | 1.52 | 240 | 7 | 375 | Minimum |

12.08 | 38.39 | 31.81 | 11.88 | 10.27 | 4.09 | 3017.78 | 7.82 | 4878.21 | Average |

10.91 | 45.37 | 37.52 | 10.74 | 9.33 | 1.77 | 2918.01 | 0.31 | 4740.49 | Standard deviation |

0–20 | 0–30 | 0–40 | 0–5 | 0–20 | 0–10 | 0–2000 | 6.5–8 | 0–3000 | Standard domain |

_{3}) and bicarbonate (HCO

_{3}) are in equilibrium within ground waters. However, carbonate is released from under the ground immediately after water outflow. Examinations of the data obtained from the wells under study showed that the minimum, maximum and average values were equal to 1.52, 10.96, and 4.09 for bicarbonate, 0.42, 45.8, and 12.08 mEq/L for sulfate, respectively. Equivalence maps of bicarbonate and sulfate values for the Yazd-Ardakan plain were plotted using the ordinary Kriging method and are presented in Figure 4c.

#### 3.3. Wilcox and Schoeller Diagrams

#### 3.4. Assessment of AL Models in WQI Prediction

_{4}, Cl, HCO

_{3}, pH, TDS, TH, EC, K, Na, Mg and Ca, were used to develop GEP, M5P and MARS.

#### 3.4.1. GEP Model

#### 3.4.2. M5P Tree Model

_{4}, Cl, HCO

_{3}, pH, K, and Na parameters were selected as the best input combination. Since the results of this model are in the form of regression relationships, the regression model is presented according to Equation (19).

#### 3.4.3. MARS Model

_{3}, SO

_{4}, Cl, and TH parameters. Leading and trailing phases were used for prediction. In this research, the number of basic functions (NBF) equaled 14 functions, introduced with the symbol λ. In the implementation of this model, GCV equal to 0.1375 was obtained. The basic functions of this model are calculated in Table 7, and the general relation extracted from the mentioned model for estimation is also obtained according to Equation (20):

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Table 1.**Permissible limit for each parameter [23].

Chemical Parameters | K+ | Na+ | pH | Ca^{2+} | ${\mathrm{SO}}_{4}^{2-}$ | Cl^{−} | ${\mathrm{HCO}}_{3}^{-}$ | EC | TH | TDS | Mg^{2+} |
---|---|---|---|---|---|---|---|---|---|---|---|

Sn | 12 | 200 | 8.5 | 200 | 250 | 600 | 120 | 1500 | 500 | 1500 | 150 |

**Table 2.**Water quality classification based on WQI definition [25].

Class | WQI Value | Water Quality Status |
---|---|---|

A | <50 | Excellent |

B | 51–100 | Good |

C | 101–200 | Poor Water |

D | 201–300 | Very Poor Water |

E | >300 | Water Unsuitable for Drinking |

Linguistic Scale for Importance | Triangular | Triangular Fuzzy Reciprocal Scale |
---|---|---|

Just equal | (1, 1, 1) | (1, 1, 1) |

Equally important | (1/2, 1, 3/2) | (2/3, 1, 2) |

Weakly more important | (1, 3/2, 2) | (1/2, 2/3, 1) |

More important | (3/2,2,5/2) | (2/5, 1/2, 2/3) |

Strongly more important | (2, 5/2, 3) | (1/3, 2/5, 1/2) |

Absolutely more important | (5/2, 3, 7/2) | (2/7, 1/3, 2/5) |

Description of Parameters | Setting of Parameters |
---|---|

Function set | $+.-.\times .\xf7$ |

Linking function | Addition |

Mutation rate | 0.00138 |

Inversion rate | 0.00546 |

One-point and two-point recombination rates | 0.00277 |

Fitness function | RMSE |

Permutation | 0.00546 |

Head size | 7 |

Number of Genes | 3 |

Number of chromosomes | 30 |

Fixed Coefficients | Basis Functions | ||
---|---|---|---|

C1 | 0.00065043 | ${\lambda}_{1}$ | max (0, Ec—2950) |

C2 | −0.00068293 | ${\lambda}_{2}$ | max (0, 2950—Ec) |

C3 | 33.358 | ${\lambda}_{3}$ | max (0, pH—7.8) |

C4 | −33.391 | ${\lambda}_{4}$ | max (0, 7.8—pH) |

C5 | 116.88 | ${\lambda}_{5}$ | max (0, K—0.05) |

C6 | −113.52 | ${\lambda}_{6}$ | max (0, 0.05—K) |

C7 | 1.9707 | ${\lambda}_{7}$ | max (0, HCO_{3}—2.96) |

C8 | −1.8072 | ${\lambda}_{8}$ | max (0, 2.96—HCO_{3}) |

C9 | 0.54801 | ${\lambda}_{9}$ | max (0, SO_{4}—20.82) |

C10 | −0.52785 | ${\lambda}_{10}$ | max (0, 20.82—SO_{4}) |

C11 | 0.24887 | ${\lambda}_{11}$ | max (0, Cl—65.99) |

C12 | −0.24965 | ${\lambda}_{12}$ | max (0, 65.99—Cl) |

C13 | 0.0011579 | ${\lambda}_{13}$ | max (0, TH—2659) |

C14 | −0.0014433 | ${\lambda}_{14}$ | max (0, 2659—TH) |

R | RMSE | MAE | NSE | Ia | ||
---|---|---|---|---|---|---|

GEP | Training | 0.986 | 4.366 | 2.884 | 0.971 | 0.993 |

Testing | 0.980 | 5.557 | 3.973 | 0.920 | 0.975 | |

M5p | Training | 0.999 | 0.286 | 0.196 | 0.999 | 1.000 |

Testing | 1.000 | 0.225 | 0.175 | 0.999 | 1.000 | |

MARS | Training | 1.000 | 0.172 | 0.127 | 1.000 | 1.000 |

Testing | 0.999 | 0.212 | 0.167 | 0.999 | 1.000 |

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**MDPI and ACS Style**

Goodarzi, M.R.; Niknam, A.R.R.; Barzkar, A.; Niazkar, M.; Zare Mehrjerdi, Y.; Abedi, M.J.; Heydari Pour, M.
Water Quality Index Estimations Using Machine Learning Algorithms: A Case Study of Yazd-Ardakan Plain, Iran. *Water* **2023**, *15*, 1876.
https://doi.org/10.3390/w15101876

**AMA Style**

Goodarzi MR, Niknam ARR, Barzkar A, Niazkar M, Zare Mehrjerdi Y, Abedi MJ, Heydari Pour M.
Water Quality Index Estimations Using Machine Learning Algorithms: A Case Study of Yazd-Ardakan Plain, Iran. *Water*. 2023; 15(10):1876.
https://doi.org/10.3390/w15101876

**Chicago/Turabian Style**

Goodarzi, Mohammad Reza, Amir Reza R. Niknam, Ali Barzkar, Majid Niazkar, Yahia Zare Mehrjerdi, Mohammad Javad Abedi, and Mahnaz Heydari Pour.
2023. "Water Quality Index Estimations Using Machine Learning Algorithms: A Case Study of Yazd-Ardakan Plain, Iran" *Water* 15, no. 10: 1876.
https://doi.org/10.3390/w15101876