# Estimation of Global Water Quality in Four Municipal Wastewater Treatment Plants over Time Based on Statistical Methods

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{5}, COD, TSS, temperature, pH and ammonia in the case of WWQI. Consequently, the MLR method is used in many environmental studies [19].

- (1)
- Reduction of dimensionality of the data. This can be useful when the initial data contain a large number of variables and are therefore difficult to visualize or analyze.
- (2)
- Derivation/extraction of new features or elements from the original data that are more insightful or understandable than the original ones.
- (3)
- Visualization of high-dimensional data in two or three dimensions that may not have been visible in the initial high-dimensional space.
- (4)
- Reduction of the impact of noise or measurement errors on data.
- (5)
- Reduction of the impact of multicollinearity in the analysis by identifying the most important characteristics or components.

- (1)
- Difficulty in interpreting the resulting principal components, which are not always easy to understand or describe in terms of the original characteristics.
- (2)
- Loss of information when choosing a subset of the most crucial features or components to reduce the dimensionality of the data.
- (3)
- Difficulty in identifying the most crucial features due to distortion of the covariance matrix by outliers.
- (4)
- Difficulty in scaling: although PCA assumes that the data are scaled and centralized, some resulting principal components may not correctly represent the underlying patterns in the data if the data are not correctly scaled.
- (5)

## 2. Materials and Methods

#### 2.1. Study Area Sites

#### 2.2. Parameters Monitored

_{5}) and dissolved organic carbon (DOC) content in both influent and effluent. Furthermore, a wastewater quality index (WWQI) has been developed to estimate the overall quality status of the raw and treated waters.

#### 2.3. Descriptive Statistics

#### 2.4. Correlation Analysis

#### 2.5. Wastewater Quality Index Calculations

_{1}), frequency (F

_{2}) and amplitude (F

_{3}) being calculated based on the quality limitations [44,45]. WWQI of the influent and effluent flows is calculated from the wastewater monitoring results using Equations (1) to (6):

_{1}is the percentage of measured variables that do not meet limit at least once during the time period; F

_{2}is the percentage of individual tests that do not meet limit; F

_{3}is the amount by which failed test values do not meet limit; Excursion is the number of times by which an individual test is greater than limit; nse is the collective amount by which individual tests are out of compliance.

## 3. Results

#### 3.1. Temporal Evolution of Influent and Effluent Qualities

_{5}and DOC measurements of influent and effluent with the same trend in all WWTPs during March 2019 to January 2021. The most remarkable aspect is that the parameters BOD

_{5}, TSS, nitrogen and phosphorus in the influent can be described by a linear expression, while dissolved organic carbon can be described by a 2nd degree polynomial expression. This opposite trend indicates that as the amount of available dissolved organic carbon increases, the level of pollutants in the influent wastewater decreases. Regarding the effluent quality parameters, it was observed that the variation of organic matter throughout the treatment process had a considerable impact on the concentration of other quality parameters, especially TSS, TP and TN. An increase in the amount of DOC, COD and BOD

_{5}led to a decrease in the concentration of TSS in the effluent and an increase in the level of BOD

_{5}. After treatment, it is possible to reduce suspended particulate matter and achieve a significant reduction in BOD

_{5}and COD, which allows compliance with discharge regulations for most wastewaters. In fact, obtaining all wastewater data makes decision making by operators still challenging due to the complex interrelationships of parameters.

#### 3.2. Multivariate Statistical Analysis Approach

_{5}and COD, followed by TN, TSS and TP. Rather, the effluent was dominated by TN, TSS and COD. These parameters characterize the organic and inorganic compounds present in municipal wastewater; PC2 was affected by COD. PC3 was affected mainly by BOD

_{5}and COD; PC4 was affected by pH; and PC5 was affected by TP and COD. In the case of the MO-WWTP, the first component of influent values presents high pH and moderate effluent load. The second component presents high TSS, TN, BOD

_{5}and TP values, which is attributed to the massive input of organic waste due to increased biological activities. PC3 presents high EC loadings in both influent and effluent and high COD loadings, a common parameter used to characterize the total content of organic and inorganic compounds in the effluent. The fourth component has high pH and TP loadings, and PC5 was affected mainly by BOD

_{5}. In the case of LZ-WWTP, PC1 presents high negative loads with EC in both influent and effluent and positive loads with DOC in influent and also TP, TN and COD in effluent. PC2 exhibits high nitrate, phosphate and also BOD

_{5}and COD loads, mainly due to nutrients that have passed through the aerobic part of an activation tank. PC3 was affected mainly by pH. PC4 was affected by BOD

_{5}and TSS. PC5 of the influent values was heavily loaded with TSS and DOC. Concerning the SP-WWTP, the first component has a high pH load for both influent and effluent. PC2 was saturated mainly in the influent by BOD

_{5}, COD, TN, TSS and TP. The third component has high EC loadings in the influent and also TSS. PC4 has high negative loadings with BOD

_{5}in the effluent and positive loadings with TP and COD. Finally, PC5 has positive loadings with DOC in both influent and effluent and also with TSS in effluent, which were of low concentrations and therefore contributed to the less important PCs.

_{5}, TSS and nutrient pollution) with the aim of extracting further information for process optimization [48].

#### 3.3. Approach to Statistical Modeling

_{5}concentrations of influent and effluent. A total of 10 numerical expressions derived from the influent and effluent quality parameters considered above were used to identify the WWQIs described in Table 4.

#### 3.4. Assessment and Verification of Model Quality

^{2}) and the root mean square error of prediction of the concentrations (RMSE), which was calculated based on the Equation (7). These standard metrics were used to assess the quality of each model by indicating the concentration of the data around the line of best fit between the measured concentrations of the training data and the precision with which the test data were estimated.

- Predicted
_{i}= values of predicted parameter - Calculated
_{i}= values of measured parameter - N = Total number of samples

## 4. Conclusions

_{5}using empirical expressions could be used as a first approximation for the modeling of a wastewater treatment process at any WWTP, which will certainly help to minimize the negative impact generated by the reuse of these water resources in agricultural areas with water scarcity. Similarly, these methodological tools can contribute to restore, as far as possible, the quantity and quality of groundwater in overexploited and degraded coastal aquifers.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Flow Rate in Million Gallons Day (mgd) | |||||
---|---|---|---|---|---|

WWTP ^{(}*^{)} | Population Served | Design Flow | Flow Treated | Effluent Uses | Technology Used ^{(}**^{)} |

AL | 41,966 | 3 | 1.5 | Irrigation | CAS + DS + C + F + SF + UV |

MO | 69,785 | 6 | 4 | Irrigation & Public domain | CAS + EA + C + F + SF + UV |

LZ | 16,891 | 5 | 1.5 | Irrigation | CAS + EA + C + F + SF + UV |

SP | 26,152 | 4.4 | 2 | Public domain | CAS + MBR + UV |

WWQI | ||||
---|---|---|---|---|

Excellent | Good | Fair | Marginal | Poor |

95–100 | 80–94 | 65–79 | 45–64 | 0–44 |

Very close to natural or pristine levels | Rarely depart from natural or desirable levels | Sometimes depart from natural or desirable levels | Often depart from natural or desirable levels | Quality is almost always threatened or impaired |

WWTP | Influent | Effluent | ||

Score | Category | Score | Category | |

AL | 45–60 | Marginal | 95–100 | Excellent |

MO | 44–60 | Marginal | 96–100 | Excellent |

LZ | 45–60 | Marginal | 97–100 | Excellent |

SP | 45–60 | Marginal | 98–100 | Excellent |

AL | Principal Component ^{a} | MO | Principal Component ^{b} | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

PC1 | PC2 | PC3 | PC4 | PC5 | PC1 | PC2 | PC3 | PC4 | PC5 | ||

pHi | −0.56 | 0.45 | 0.79 | ||||||||

ECi | −0.78 | 0.84 | |||||||||

TSSi | 0.69 | 0.90 | |||||||||

CODi | 0.92 | 0.86 | |||||||||

TNi | 0.88 | 0.89 | |||||||||

TPi | 0.69 | 0.83 | |||||||||

BODi | 0.91 | 0.85 | |||||||||

DOCi | 0.88 | 0.68 | |||||||||

pHe | -0.85 | 0.77 | 0.47 | ||||||||

ECe | −0.44 | 0.49 | −0.45 | −0.44 | −0.44 | 0.81 | |||||

TSSe | 0.50 | −0.76 | |||||||||

CODe | 0.42 | 0.71 | 0.78 | ||||||||

TNe | 0.73 | −0.76 | |||||||||

TPe | 0.55 | 0.70 | |||||||||

BODe | 0.90 | 0.53 | |||||||||

DOCe | 0.68 | 0.42 | 0.48 | ||||||||

Eigenv | 6.18 | 2.37 | 1.73 | 1.50 | 1.27 | 5.19 | 2.87 | 2.29 | 1.76 | 1.43 | |

Var (%) | 34.32 | 13.17 | 9.61 | 8.32 | 7.03 | 28.82 | 15.93 | 12.73 | 9.79 | 7.93 | |

Cum (%) | 34.32 | 47.49 | 57.10 | 65.41 | 72.44 | 28.82 | 44.75 | 57.48 | 67.27 | 75.20 | |

LZ | Principal Component ^{c} | SP | Principal Component ^{d} | ||||||||

PC1 | PC2 | PC3 | PC4 | PC5 | PC1 | PC2 | PC3 | PC4 | PC5 | ||

pHi | 0.90 | 0.90 | |||||||||

ECi | −0.66 | 0.94 | |||||||||

TSSi | 0.86 | 0.56 | 0.56 | ||||||||

CODi | 0.77 | 0.86 | |||||||||

TNi | 0.63 | 0.68 | 0.76 | ||||||||

TPi | 0.74 | −0.45 | 0.78 | ||||||||

BODi | 0.91 | 0.61 | |||||||||

DOCi | 0.65 | 0.64 | −0.57 | 0.54 | |||||||

pHe | 0.95 | 0.86 | |||||||||

ECe | −0.83 | 0.93 | |||||||||

TSSe | 0.86 | 0.59 | |||||||||

CODe | 0.68 | −0.69 | 0.48 | ||||||||

TNe | 0.55 | −0.60 | −0.68 | ||||||||

TPe | 0.70 | 0.60 | |||||||||

BODe | 0.83 | −0.65 | |||||||||

DOCe | −0.77 | 0.68 | |||||||||

Eigenv | 6.62 | 3.17 | 1.82 | 1.69 | 1.31 | 3.85 | 3.17 | 2.31 | 2.09 | 1.42 | |

Var (%) | 36.79 | 17.58 | 10.13 | 9.36 | 7.29 | 21.39 | 17.62 | 12.82 | 11.61 | 7.87 | |

Cum (%) | 36.79 | 54.37 | 64.50 | 73.86 | 81.15 | 21.39 | 39.01 | 51.83 | 63.44 | 71.31 |

^{a}Rotation converged in 9 iterations;

^{b}Rotation converged in 8 iterations.

^{c}Rotation converged in 7 iterations;

^{d}Rotation converged in 7 iterations.

WWTP | Numerical Expression | R^{2} | RMSE | |
---|---|---|---|---|

Data | ||||

Train | Train | Test | ||

AL | $WWQ{I}_{i}=70.06-0.06TS{S}_{i}-0.8T{N}_{i}+3.6\times {10}^{-5}BO{D}_{I}^{2}+4.2\times {10}^{-5}TS{S}_{i}^{2}+0.012T{N}_{i}^{2}-0.001BO{D}_{i}\times T{N}_{i}+0.001T{N}_{i}\times TS{S}_{i}-0.001T{P}_{i}\times BO{D}_{i}$ | 0.903 | 2.15 | 7.06 |

$WWQ{I}_{e}=72.96-0.09TS{S}_{e}+0.99T{N}_{e}+0.36BO{D}_{e}^{2}+0.31TS{S}_{e}^{2}+0.025T{N}_{e}^{2}-0.001BO{D}_{e}\times T{N}_{e}+0.001T{N}_{e}\times TS{S}_{e}-0.001T{P}_{e}\times BO{D}_{e}$ | 0.907 | 1.20 | 1.36 | |

MO | $WWQ{I}_{i}=60.9-0.04TS{S}_{i}-0.9T{N}_{i}+{10}^{-5}BO{D}_{I}^{2}+2.6\times {10}^{-5}TS{S}_{i}^{2}+0.02T{N}_{i}^{2}-0.0011BO{D}_{i}\times T{N}_{i}+0.0011T{N}_{i}\times TS{S}_{i}-0.0011T{P}_{i}\times BO{D}_{i}$ | 0.952 | 0.67 | 2.20 |

$WWQ{I}_{e}=92.15-0.1TS{S}_{e}-0.1T{N}_{e}+0.1BO{D}_{e}^{2}+{10}^{-5}TS{S}_{e}^{2}+0.08T{N}_{e}^{2}-0.001BO{D}_{e}\times T{N}_{e}+0.001T{N}_{e}\times TS{S}_{e}-0.001T{P}_{e}\times BO{D}_{e}$ | 0.927 | 0.04 | 0.17 | |

LZ | $WWQ{I}_{i}=58.2-0.05TS{S}_{i}-0.7T{N}_{i}+4.1\times {10}^{-5}BO{D}_{I}^{2}+3.8\times {10}^{-5}TS{S}_{i}^{2}+0.015T{N}_{i}^{2}-0.0011BO{D}_{i}\times T{N}_{i}+0.0011T{N}_{i}\times TS{S}_{i}-0.003T{P}_{i}\times BO{D}_{i}$ | 0.782 | 0.24 | 3.29 |

$WWQ{I}_{e}=122.1-9TS{S}_{e}-0.3T{N}_{e}+{10}^{-5}BO{D}_{e}^{2}+0.9TS{S}_{e}^{2}+0.03T{N}_{e}^{2}-{10}^{-5}BO{D}_{e}\times T{N}_{e}+0.002T{N}_{e}\times TS{S}_{e}-0.2T{P}_{e}\times BO{D}_{e}$ | 0.909 | 0.05 | 0.29 | |

SP | $WWQ{I}_{i}=66.9-0.05TS{S}_{i}-0.8T{N}_{i}+3.7\times {10}^{-5}BO{D}_{I}^{2}+4.2\times {10}^{-5}TS{S}_{i}^{2}+0.013T{N}_{i}^{2}-0.0011BO{D}_{i}\times T{N}_{i}+0.0011T{N}_{i}\times TS{S}_{i}-0.0011T{P}_{i}\times BO{D}_{i}$ | 0.816 | 0.20 | 0.68 |

$WWQ{I}_{e}=93.04-0.3TS{S}_{e}+0.3T{N}_{e}+0.1BO{D}_{e}^{2}+0.03TS{S}_{e}^{2}+0.1T{N}_{e}^{2}-0.2BO{D}_{e}\times T{N}_{e}+0.2T{N}_{e}\times TS{S}_{e}+0.2T{P}_{e}\times BO{D}_{e}$ | 0.979 | 0.01 | 0.02 | |

GL * | $WWQ{I}_{i}=76.01-0.06TS{S}_{i}-0.8T{N}_{i}+3.6\times {10}^{-5}BO{D}_{I}^{2}+4.2\times {10}^{-5}TS{S}_{i}^{2}+0.012T{N}_{i}^{2}-0.001BO{D}_{i}\times T{N}_{i}+0.001T{N}_{i}\times TS{S}_{i}-0.001T{P}_{i}\times BO{D}_{i}$ | 0.810 | 0.84 | 1.51 |

$WWQ{I}_{e}=58.82-0.1TS{S}_{e}+0.1T{N}_{e}+0.1BO{D}_{e}^{2}+0.02TS{S}_{e}^{2}+0.22T{N}_{e}^{2}-0.1BO{D}_{e}\times T{N}_{e}+0.1T{N}_{e}\times TS{S}_{e}+0.1T{P}_{e}\times BO{D}_{e}$ | 0.743 | 0.08 | 0.10 |

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**MDPI and ACS Style**

El Aatik, A.; Navarro, J.M.; Martínez, R.; Vela, N.
Estimation of Global Water Quality in Four Municipal Wastewater Treatment Plants over Time Based on Statistical Methods. *Water* **2023**, *15*, 1520.
https://doi.org/10.3390/w15081520

**AMA Style**

El Aatik A, Navarro JM, Martínez R, Vela N.
Estimation of Global Water Quality in Four Municipal Wastewater Treatment Plants over Time Based on Statistical Methods. *Water*. 2023; 15(8):1520.
https://doi.org/10.3390/w15081520

**Chicago/Turabian Style**

El Aatik, Abderrazak, Juan Miguel Navarro, Ramón Martínez, and Nuria Vela.
2023. "Estimation of Global Water Quality in Four Municipal Wastewater Treatment Plants over Time Based on Statistical Methods" *Water* 15, no. 8: 1520.
https://doi.org/10.3390/w15081520