# Determination of Pollution Loads in Spillways of the Combined Sewage Network of the City of Cuenca, Ecuador

^{1}

^{2}

^{*}

## Abstract

**:**

_{5}, COD, fecal and total coliforms, nitrates, nitrites, ammoniacal nitrogen, dissolved orthophosphate and total phosphorus. The results show that CSOs contribute to the deterioration of the water quality of the Tomebamba River during the rainy season. The analysis of the dynamics of the pollutants determined that the maximum conductivity values occur at the beginning of the discharge, and the maximum turbidity is located near the peak discharge flow. The relationship between rain and the characteristics of the CSO was also analyzed through a canonical correlation analysis and partial least squares regression, obtaining a prediction model of pollutants based on the precipitation parameters. These results can be used for the implementation of integrated ecological models that enable a complete analysis of the city’s sanitation systems, their impact on the receiving bodies and their restoration.

## 1. Introduction

_{5}), chemical oxygen demand (COD), conductivity, pH, ammonium, nitrates and nitrites [8,16,17,18]. Microbiological parameters are also analyzed to determine the quality of the water during CSO [2,5,7,8].

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The annual average temperature changes, according to the altitude, from 9 to 16.3 °C [28,29]. The rainy season runs from the middle of February until the beginning of July and from the second half of September until the first two weeks of November, while the rest of the year constitutes the dry season [24]. The average rainfall is approximately 879 mm per year [30].

^{3}/s [32] and has been in operation since November 1999 [33]. About 80% of the wastewater in the City of Cuenca is treated before its return to the water bodies [22].

#### 2.2. Discharge Flow Measurement

#### 2.3. Sample Collection

_{min}= 2.5 cm (Figure 2).

_{min}level exceed the set threshold (Figure 2), the ISCO 6712 begins collecting samples with a time interval of 3 min [8,20]. The samples are stored at the bottom of the device in 24 one-liter plastic bottles. Therefore, due to the capacity of the ISCO 6712, the sampling span is a maximum time of 72 min (24 bottles multiplied by 3 min) for each CSO event. If the wastewater pour extends beyond 72 min, the entire discharge process cannot be sampled. Of the 18 events recorded, 11 of them had a pour time of less than 72 min and only three lasted a little over 100 min. The water quality parameters considered for the investigation were conductivity, turbidity, five-day biochemical oxygen demand (BOD

_{5}), chemical oxygen demand (COD), fecal coliforms (FC), total coliforms (TC), nitrates (NO

_{3}-N), nitrites (NO

_{2}-N), ammoniacal nitrogen (NH

_{3}-N), dissolved orthophosphate (PO

_{4}-P) and total phosphorus (P). The conductivity and turbidity were recorded for all 24 samples from each test. Subsequently, considering the maximum conductivity value, five samples were selected to perform the COD analysis. The COD was obtained from the sample with the highest conductivity value. Moreover, two samples prior to this and two subsequent samples were also analyzed, skipping one sample, until completing the five records. BOD

_{5}, total coliforms, and fecal coliforms were obtained in most cases, but only for the sample with the highest conductivity value. In the last two samplings corresponding to the El Vado CSO, additional parameters were measured, NO

_{3}-N, NO

_{2}-N, NH

_{3}-N, PO

_{4}-P and P, for five of the 24 samples in each test (Table A2). Conductivity was recorded through a YSI-probe 600R multiparameter probe (By YSI—a Xylem brand based in Yellow Springs, OH, USA), while a Turb 555 turbidimeter (By WTW—a Xylem brand, Weilheim, Germany) was used to measure turbidity. These two tests were performed in the hydrophysics laboratory of the Water and Soil Management Program, PROMAS, University of Cuenca. The parameters BOD

_{5}, COD, FC, TC, NO

_{3}-N, NO

_{2}-N, NH

_{3}-N, PO

_{4}-P and P were analyzed in the water laboratory of the Faculty of Chemical Sciences of the University of Cuenca using standardized methodologies [8,10,11].

#### 2.4. Dynamics of Pollutants during CSO

- (i)
- The first event had and BOD
_{5}and COD values close to the median; - (ii)
- The second selected event had maximum BOD
_{5}and COD values.

#### 2.5. Relationship between Rain and CSO Characteristics

_{d}), the maximum rainfall intensity at five minutes (I

_{max}), the mean rainfall intensity (I

_{mean}), the duration of the rainstorm event (D) and the dry weather duration before the rainfall event (D

_{d}) [3,13,14,20,27]. The maximum intensity values (I

_{max}) strongly depend on the time steps in which they are determined. Sandoval et al. [14] considered a duration of 30 min to determine the maximum rainfall intensity. This interval was defined considering the response time of the catchment. According to Sandoval et al. [14], the correlations between rainfall and CSO parameters did not vary for other maximum intensities defined in intervals of 5 and 15 min. In this sense, considering that the concentration time of the contribution catchment is relatively short (10–15 min), the maximum intensity of a rainfall event in a period of 5 min was taken to define the parameter I

_{max}[20].

_{max}), the mean conductivity (C

_{mean}), the mean turbidity (Tur

_{mean}) and the average chemical oxygen demand (COD

_{mean}) [3,13,14,20].

#### 2.5.1. Canonical Correlation Analysis

#### 2.5.2. Partial Least Squares Regression

## 3. Results and Discussion

#### 3.1. Characterization of the Pollutant Load

_{5}registered values were between 7 and 528 mg/L; the COD remained between 40 and 1450 mg/L (Figure 3). The Coliseo CSO presented higher values of turbidity, COD and BOD

_{5}compared to those found in the El Vado and Multifamiliares CSOs (Figure 3b,d). This suggests a higher degree of pollution related to suspended material, microorganisms and organic matter from the Coliseo CSO.

^{3}/s (average of 17.50 m

^{3}/s) between the Coliseo and Multifamiliares CSOs during the rainy season.

_{5}values for the El Vado, Multifamiliares and Coliseo CSOs were 92.7, 134.1 and 170.0 mg/L, respectively (Figure 3d). On the other hand, Jerves-Cobo et al. [24] determined the BOD

_{5}values for the section of the Tomebamba River between the Coliseo and Multifamiliares CSOs to be below 2.5 mg/L during the wet season. The above shows a significant contribution of organic matter from the CSOs to the Tomebamba River during high rainfall events. For conductivity (Figure 3a), the values obtained in the three discharges were mostly between 120 μS/cm and 240 μS/cm. However, the Multifamiliares and El Vado CSOs presented more dispersed data than the Coliseo CSO. Jerves-Cobo et al. [24] obtained conductivity values between 92 and 95 μS/cm in the study section in the Tomebamba River during the rainy season. The average conductivity of the wastewater discharged by the CSOs is higher than the conductivity found in the Tomebamba River. The average turbidity at the El Vado, Multifamiliares and Coliseo resulted in 130.6, 96.2 and 216.3 NTU, respectively (Figure 3b). Jerves-Cobo et al. [24] recorded turbidity values in the range of 4.4 to 8.7 NTU in the study section in the Tomebamba River during the wet season. Regarding the microbiological parameters, the three CSOs registered fecal coliform values in the range of 1.6 × 10

^{6}to 1.9 × 10

^{10}MPN/100 mL (Figure 3e) and total coliforms from 4.8 × 10

^{6}to 4.1 × 10

^{10}MPN/100 mL (Figure 3f). Jerves-Cobo et al. [24] determined that the fecal coliform and total coliform values in the stretch of river spanning the three CSOs were in the order of 1.1 × 10

^{5}to 2.4 × 10

^{5}MPN/100 mL and 1.4 × 10

^{5}to 9.2 × 10

^{5}MPN/100 mL, respectively. These records correspond to the wet season, with flows measured in the Tomebamba River between 11.12 to 19.79 m

^{3}/s. The difference between the values of the parameters registered in the three CSOs and those recorded in the receiving body are large. This means that the waters of the CSOs present a high degree of contamination compared to the waters of the Tomebamba River. The combined sewer overflows that pour into the Tomebamba River during its passage through the city contribute to the deterioration of the river’s water quality during the rainy period.

_{3}-N, nitrites NO

_{2}-N, ammoniacal nitrogen (NH

_{3}-N), dissolved orthophosphate PO

_{4}-P and total phosphorus (P), which were carried out during the last two CSO events in the El Vado (Table A2). The samplings registered values for nitrate between 0.12 to 0.53 mg/L (Figure 4a). Jerves-Cobo et al. [24] determined NO

_{3}-N values between 0.2 to 0.3 mg/L for the stretch of river between the three CSOs during the wet season. The nitrite concentration in the El Vado CSO was in the order of 3.74 to 66.27 μg/L (Figure 4b). According to Jerves-Cobo et al. [24], the NO

_{2}-N values measured in the corresponding section of the Tomebamba River varied between 3.3 and 8.2 μg/L in the rainy season. Based on the parameters NO

_{3}-N and NO

_{2}-N, it is evident that the El Vado CSO contributes to the deterioration of the waters of the Tomebamba River during CSO events. The dissolved orthophosphate values were in the range of 0.13 to 1.03 mg/L, with a mean value of 0.49 mg/L (Figure 4d). Ammoniacal nitrogen ranged from 0.49 to 2.54 mg/L, with a mean value of 1.34 mg/L (Figure 4c). Finally, the total phosphorus values were between 2.47 to 5.65 mg/L, with an average value of 3.77 mg/L (Figure 4e). Ecuadorian regulations establish a maximum daily mean value of 30 mg/L for ammoniacal nitrogen and 10 mg/L for total phosphorus [26], for the discharge of effluents into a body of fresh water. The concentrations of these two parameters in CSO El Vado are below their respective limits.

#### BOD_{5}/COD Ratio

_{5}/COD) for all the samples analyzed was in the range of 0.04 to 0.92. This result evidences a high variation in the carbon sources of wastewater, showing a wide range from small to large amounts of biodegradable matter in wastewaters [22]. Table 2 shows that the Multifamiliares and El Vado CSOs display a greater range of variability, presenting a larger range in the type of pollutants.

_{5}and COD variables by means of a logarithmic regression with an R

^{2}of 0.62. In this study, it was determined that the data fit better with a quadratic relationship, in which R

^{2}was 0.73 (Appendix A—Figure A1). These results can be used for the prediction of in discharges from the values.

#### 3.2. Environmental Legislation

_{5}, only one sample was analyzed for each CSO event. Therefore, it was not possible to establish a characteristic mean value for the discharge event. However, for the purposes of comparison with the regulations, it is assumed that the point value obtained represents the average concentration of the CSO event. Thus, in the discharge data for Multifamiliares, 67% of the samples comply with the limits established by the legislation for the parameter For BOD

_{5}(≤100 mg/L). In the El Vado CSO, 56% of the samples comply with the regulations and in the Coliseo CSO, none of the samples meet the limits of BOD

_{5}. For the microbiological parameters, the regulations establish a limit of 2000 MPN/100 mL for the daily average value of fecal coliforms [26]. Although the mean total coliform values were not obtained for each CSO event, all the samples analyzed recorded values above this limit (between 800 and 1.0 × 10

^{7}times higher).

#### 3.3. Dynamics of Pollutants during CSO

#### 3.4. Relationship between Rain and the CSO Characteristics

_{mean}), has an influence on the maximum discharge flow (Q

_{max}), for this correlations a p value less than 0.05 was obtained (Table A3 and Table A4). It is considered a significant correlation. Furthermore, in the El Vado CSO the maximum intensity of precipitation (I

_{max}) is related to the maximum flow Q

_{max}(p value < 0.05). This same relationship is obtained in the Multifamiliares CSO, but with p value of 0.10. Sandoval et al. [14], in their research on the main CSO in Berlin, found that the maximum and average intensity of precipitation is related to the volume of water discharged, as well as the maximum flow and the average discharge flow. At CSO El Vado, a significant relationship was also found between total precipitation R

_{d}and maximum flow Q

_{max}.

_{max}and I

_{mean}respectively also seem to influence the values of the average turbidity (Tur

_{mean}) (Figure 6 and Figure A4). In the same way, these correlations obtained a p value less than 0.05. According to Murillo [57], turbidity helps determine the amount of suspended material, where the higher the intensity of rain is, the greater the drag of suspended solids will be. Likewise, Sandoval et al. [14] found a relationship between I

_{max}and I

_{mean}with the value of total suspended solids.

_{mean}is related to the duration of the dry period prior to a rainfall event (D

_{d}) with a statistical significance related to a p value less than 0.05. In this CSO, it was also found that the COD

_{mean}is related to the average intensity of precipitation (I

_{mean}) with a p value of 0.12. D

_{d}and I

_{mean}, which can influence the amount of drag material due to the runoff and resuspension of material deposited in the drainage ducts that cause higher pollution loads [2,14,20].

_{max}, I

_{mean}, Q

_{max}and Tur

_{mean}.

#### 3.4.1. Canonical Correlation Analysis

_{max}), the average intensity (I

_{mean}) and the total rainfall depth (R

_{d}) seem to have influence on the variables Q

_{max}and Tur

_{mean}. These relationships agree with those obtained from the analysis of the correlation matrices. From the analysis of L(3), it was determined that the duration of the rain (D) and the total rainfall depth (R

_{d}) (to a lesser degree) are related to the mean turbidity values (Tur

_{mean}).

#### 3.4.2. Partial Least Squares Regression (PLSR)

_{mean}at the El Vado CSO. In the same way, the PLSR prediction models were determined for the other dependent variables, C

_{mean}, COD

_{mean}, and Q

_{max}, for all CSOs.

_{mean}as a function of the number of components used in the construction of the model. Table 4 shows the percentage of variability explained by each of the components of the model. Considering the reduction of the RMSEP and the levels of variability explained, two components were determined for the construction of the PLS model to predict Tur

_{mean}for the El Vado CSO (Figure A7).

_{mean}, C

_{mean}, Tur

_{mean}, Q

_{max}) based on the input rainfall characteristics (R

_{d}, I

_{max}, I

_{mean}, D and D

_{d}). The structure of the PLSR is reported in Equation (1).

_{1}, C

_{2}, C

_{3}, C

_{4}, C

_{5}and C

_{6}) of the PLSR models for the prediction of the CSO variables in the El Vado CSO are presented in Table 5. The results of the PLSR for the Multifamiliares and Coliseo CSOs are presented in Table A5 and Table A6, respectively.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Summary of the collected physical, chemical and microbiological data based on the registration of 18 CSO events in the Coliseo, El Vado and Multifamiliares CSOs in 2017 and 2018.

CSO | Parameter | Units | Mean Value | Standard Deviation | Min Value | Max Value | Median Value | |
---|---|---|---|---|---|---|---|---|

Coliseo | Conductivity | µS/cm | 155 | ± | 56 | 68 | 295 | 133 |

Turbidity | NTU | 216 | ± | 106 | 68 | 378 | 171 | |

Five-day biochemical oxygen demand | mg/L | 170 | ± | 33 | 140 | 206 | 164 | |

Chemical oxygen demand | mg/L | 420 | ± | 327 | 90 | 1450 | 380 | |

Fecal coliforms | NMP/100 mL | ${4.7\times 10}^{9}$ | ± | ${5.5\times 10}^{9}$ | ${1.0\times 10}^{9}$ | ${1.4\times 10}^{10}$ | ${1.1\times 10}^{9}$ | |

Total coliforms | NMP/100 mL | ${9.0\times 10}^{9}$ | ± | ${5.5\times 10}^{9}$ | ${1.1\times 10}^{9}$ | ${2.0\times 10}^{10}$ | ${1.0\times 10}^{10}$ | |

El Vado | Conductivity | µS/cm | 195 | ± | 114 | 59 | 616 | 154 |

Turbidity | NTU | 131 | ± | 62 | 47 | 319 | 117 | |

Five-day biochemical oxygen demand | mg/L | 93 | ± | 116 | 7 | 361 | 45 | |

Chemical oxygen demand | mg/L | 249 | ± | 149 | 46 | 670 | 240 | |

Fecal coliforms | NMP/100 mL | ${3.6\times 10}^{9}$ | ± | ${6.0\times 10}^{9}$ | ${1.6\times 10}^{6}$ | ${1.9\times 10}^{10}$ | ${3.9\times 10}^{8}$ | |

Total coliforms | NMP/100 mL | ${6.2\times 10}^{9}$ | ± | ${6.0\times 10}^{9}$ | ${9.8\times 10}^{6}$ | ${4.1\times 10}^{10}$ | ${1.6\times 10}^{9}$ | |

Nitrate-N | mg/L | 0.26 | ± | 0.16 | 0.12 | 0.53 | 0.22 | |

Nitrite-N | µg/L | 34.7 | ± | 29.1 | 3.7 | 66.3 | 39.3 | |

Ammoniacal nitrogen—N | mg/L | 1.34 | ± | 0.74 | 0.49 | 2.54 | 1.25 | |

Dissolved orthophosphate—P | mg/L | 0.49 | ± | 0.30 | 0.13 | 1.03 | 0.52 | |

Total phosphorus | mg/L | 3.77 | ± | 1.21 | 2.47 | 5.65 | 3.32 | |

Multifamiliares | Conductivity | µS/cm | 198 | ± | 112 | 50 | 664 | 183 |

Turbidity | NTU | 96 | ± | 76 | 9 | 345 | 66 | |

Five-day biochemical oxygen demand | mg/L | 134 | ± | 187 | 8 | 528 | 46 | |

Chemical oxygen demand | mg/L | 262 | ± | 296 | 40 | 1410 | 140 | |

Fecal coliforms | NMP/100 mL | ${3.3\times 10}^{9}$ | ± | ${3.7\times 10}^{9}$ | ${3.5\times 10}^{6}$ | ${1.0\times 10}^{10}$ | ${2.5\times 10}^{9}$ | |

Total coliforms | NMP/100 mL | ${1.7\times 10}^{10}$ | ± | ${3.7\times 10}^{9}$ | ${4.8\times 10}^{6}$ | ${4.0\times 10}^{10}$ | ${1.1\times 10}^{10}$ |

**Table A2.**Number of samples analyzed for each water quality parameter in the three CSOs: El Vado, Multifamiliares and Coliseo.

CSO | Test Name | Date | C | Tur | ${\mathbf{BOD}}_{\mathbf{5}}$ | $\mathbf{COD}$ | $\mathbf{FC}$ | $\mathbf{TC}$ | NO_{3}-N | NO_{2}-N | NH_{3}-N | PO_{4}-P | P |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Coliseo | CO-5 | 8 Apr 2017 | 6 | 7 | 1 | 5 | 2 | 2 | |||||

CO-6 | 12 Apr 2017 | 9 | 15 | 1 | 5 | 1 | 1 | ||||||

CO-12 | 18 Apr 2017 | 23 | 24 | 1 | 4 | 4 | 4 | ||||||

El Vado | VA-2 | 29 Mar 2017 | 22 | 22 | 2 | 5 | |||||||

VA-3 | 30 Mar 2017 | 19 | 19 | 2 | 4 | ||||||||

VA-7 | 12 Apr 2017 | 24 | 24 | 1 | 5 | 2 | 2 | ||||||

VA-10 | 14 Apr 2017 | 13 | 15 | 1 | 5 | 1 | 1 | ||||||

VA-11 | 18 Apr 2017 | 24 | 24 | 1 | 5 | 4 | 4 | ||||||

VA-13 | 20 Apr 2017 | 24 | 24 | 1 | 5 | 2 | 2 | ||||||

VA-15 | 14 Nov 2017 | 23 | 23 | 5 | 5 | ||||||||

VA-16 | 4 Apr 2018 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | ||

VA-17 | 9 May 2018 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | ||

Multifamiliares | MU-1 | 21 Mar 2017 | 21 | 1 | 5 | ||||||||

MU-2 | 29 Mar 2017 | 18 | 18 | 2 | 4 | ||||||||

MU-4 | 8 Apr 2017 | 13 | 13 | 1 | 5 | 2 | 2 | ||||||

MU-8 | 12 Apr 2017 | 23 | 24 | 1 | 5 | 1 | 1 | ||||||

MU-9 | 14 April 2017 | 24 | 24 | 1 | 5 | 1 | 1 | ||||||

MU-14 | 20 April 2017 | 24 | 24 | 1 | 5 | 2 | 2 |

_{3}-N (nitrates); NO

_{2}-N (nitrites); NH

_{3}-N (ammoniacal nitrogen); PO

_{4}-P (dissolved orthophosphate) and P (total phosphorus).

**Table A3.**Statistical significance (p values) of the correlations between the variables of rainfall and CSO in the El Vado CSO.

${\mathbf{R}}_{\mathbf{d}}$ | ${\mathbf{I}}_{\mathbf{max}}$ | ${\mathbf{I}}_{\mathbf{mean}}$ | $\mathbf{D}$ | ${\mathbf{D}}_{\mathbf{d}}$ | |
---|---|---|---|---|---|

${\mathrm{Q}}_{\mathrm{max}}$ | 0.01 | ${7.0\times 10}^{-4}$ | 0.02 | 0.75 | 0.85 |

${\mathrm{C}}_{\mathrm{mean}}$ | 0.18 | 0.39 | 0.33 | 0.35 | 0.74 |

${\mathrm{Tur}}_{\mathrm{mean}}$ | 0.22 | 0.04 | 0.08 | 0.16 | 0.84 |

${\mathrm{COD}}_{\mathrm{mean}}$ | 0.65 | 0.72 | 0.46 | 0.26 | 0.23 |

**Table A4.**Statistical significance (p values) of the correlations between the variables of rainfall and CSO in the Multifamiliares CSO.

${\mathbf{R}}_{\mathbf{d}}$ | ${\mathbf{I}}_{\mathbf{max}}$ | ${\mathbf{I}}_{\mathbf{mean}}$ | $\mathbf{D}$ | ${\mathbf{D}}_{\mathbf{d}}$ | |
---|---|---|---|---|---|

${\mathrm{Q}}_{\mathrm{max}}$ | 0.60 | 0.10 | 0.04 | 0.51 | 0.89 |

${\mathrm{C}}_{\mathrm{mean}}$ | 0.34 | 0.63 | 0.56 | 0.68 | 0.14 |

${\mathrm{Tur}}_{\mathrm{mean}}$ | 0.91 | 0.25 | 0.04 | 0.33 | 0.01 |

${\mathrm{COD}}_{\mathrm{mean}}$ | 0.96 | 0.48 | 0.12 | 0.44 | 0.36 |

**Figure A2.**Variation of water quality parameters over time for the Multifamiliares CSO. Criterion (

**i**) event with BOD

_{5}and COD values close to the mean. Criterion (

**ii**) event with high BOD

_{5}and COD values. (

**a**) conductivity, (

**b**) turbidity and (

**c**) COD.

**Figure A3.**Variation of water quality parameters over time for the Coliseo CSO. Criterion (

**i**) event with BOD

_{5}and COD values close to the mean. Criterion (

**ii**) event with high BOD

_{5}and COD values. (

**a**) conductivity, (

**b**) turbidity and (

**c**) COD.

**Figure A4.**Correlation between rainfall and the CSO variables in the Multifamiliares CSO. The range of colors indicates the degree of correlation according to the graphic’s scale. The colors close to brown represent a strong positive correlation between the variables, while shades of dark blue instead represent a negative correlation. Cyan, green and yellow show low or no correlation between the variables.

**Figure A5.**Correlation between rainfall and the CSO variables in the Coliseo CSO. The range of colors indicates the degree of correlation according to the graphic’s scale. The colors close to brown represent a strong positive correlation between the variables, while shades of dark blue instead represent a negative correlation. Cyan, green and yellow show low or no correlation between the variables.

**Figure A6.**Root mean squared error of Prediction (RMSEP) as a function of the number of components of the prediction PLSR model for the variable Tur

_{mean}in the El Vado CSO.

**CV**: the ordinary CV estimate;

**adjCV**: the bias-corrected CV estimate [44].

**Figure A7.**Cross-validated predictions with two components versus the measured values for the mean turbidity for the El Vado CSO. The dots represent the mean turbidity values measured and predicted by the PLSR model. The line corresponds to the target line with a ratio of 1 (predicted = measured).

**Table A5.**Regression coefficients for the prediction equations of the CSO variables as a function of the rainfall parameters for the Multifamiliares CSO. R

^{2}is the coefficient of determination of the PLSR.-N is the number of components used to build the PLSR model and X is the percentage of variability explained by the model.

CSO Variable | Regression Coefficients (PLSR) | N | X (%) | R^{2} | |||||
---|---|---|---|---|---|---|---|---|---|

${\mathbf{C}}_{\mathbf{1}}$ | ${\mathbf{C}}_{\mathbf{2}}$ | ${\mathbf{C}}_{\mathbf{3}}$ | ${\mathbf{C}}_{\mathbf{4}}$ | ${\mathbf{C}}_{\mathbf{5}}$ | ${\mathbf{C}}_{\mathbf{6}}$ | ||||

${\mathrm{Q}}_{\mathrm{max}}$ | 3.638 | 20.553 | 2.152 | −1.919 | −9.809 | 314.896 | 2 | 96.1 | 0.57 |

${\mathrm{C}}_{\mathrm{mean}}$ | −0.394 | −1.568 | −0.653 | 0.017 | 4.311 | 138.720 | 2 | 97.5 | 0.57 |

${\mathrm{Tur}}_{\mathrm{mean}}$ | 0.965 | 4.469 | 1.745 | −0.423 | 6.720 | 26.148 | 2 | 99.0 | 0.91 |

${\mathrm{COD}}_{\mathrm{mean}}$ | 1.898 | 10.873 | 9.220 | −0.834 | 8.214 | 44.239 | 3 | 99.9 | 0.37 |

**Table A6.**Regression coefficients for the prediction equations of the CSO variables as a function of the rainfall parameters for the Coliseo CSO. R

_{2}is the coefficient of determination of the PLSR.-N is the number of components used to build the PLSR model and X is the percentage of variability explained by the model.

CSO Variable | Regression Coefficients (PLSR) | N | X (%) | R_{2} | |||||
---|---|---|---|---|---|---|---|---|---|

${\mathbf{C}}_{\mathbf{1}}$ | ${\mathbf{C}}_{\mathbf{2}}$ | ${\mathbf{C}}_{\mathbf{3}}$ | ${\mathbf{C}}_{\mathbf{4}}$ | ${\mathbf{C}}_{\mathbf{5}}$ | ${\mathbf{C}}_{\mathbf{6}}$ | ||||

${\mathrm{Q}}_{\mathrm{max}}$ | 0.592 | 1.093 | −0.058 | 5.594 | 4.266 | −95.744 | 1 | 96.6 | 0.84 |

${\mathrm{C}}_{\mathrm{mean}}$ | −0.114 | −0.167 | 0.025 | −1.114 | −0.768 | 256.847 | 1 | 96.6 | 0.65 |

${\mathrm{Tur}}_{\mathrm{mean}}$ | −0.199 | −0.331 | 0.031 | −1.909 | −1.389 | 345.263 | 1 | 96.6 | 0.75 |

${\mathrm{COD}}_{\mathrm{mean}}$ | −0.240 | 0.217 | 0.230 | −2.835 | −0.924 | 586.029 | 1 | 95.7 | 0.18 |

**Figure A8.**Triplot that represents the cases, the response variables and the predictor variables of the PLS model of the Multifamiliares CSO in the same graph.

**Figure A9.**Triplot that represents the cases, the response variables and the predictor variables of the PLS model of the Coliseo CSO in the same graph.

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**Figure 1.**Map of the CSOs location, including the combined sewer overflow (CSO) contribution areas. Georeferenced UTM-WGS 84.

**Figure 3.**Analysis of the samples collected in the three CSOs throughout the study period of 2017–2018. (

**a**) Conductivity; (

**b**) turbidity; (

**c**) chemical oxygen demand; (

**d**) five-day biochemical oxygen demand; (

**e**) fecal coliforms; (

**f**) total coliforms. The blue dot and dash line represent the values recorder in the Tomebamba River in the rainy season [24].

**Figure 4.**Analysis of the samples collected in the El Vado CSO for (

**a**) nitrate, (

**b**) nitrite, (

**c**) ammoniacal nitrogen, (

**d**) dissolved orthophosphate and (

**e**) total phosphorus. Two CSO events were recorded: 4 April 2018 and 9 May 2018. The blue dot and dash line represent the values recorder in the Tomebamba River in the rainy season [24].

**Figure 5.**Variation of water quality parameters over time in the El Vado CSO. Criterion (

**i**) event with BOD

_{5}and COD values close to the mean. Criterion (

**ii**) event with high BOD

_{5}and COD values. (

**a**) conductivity, (

**b**) turbidity and (

**c**) COD.

**Figure 6.**Correlation between rainfall and CSO variables in the El Vado CSO. The range of colors indicates the degree of correlation according to the graphic’s scale. The colors close to brown represent a strong positive correlation between the variables, while shades of dark blue instead represent a negative correlation. Cyan, green and yellow show low or no correlation between the variables.

**Figure 7.**Triplot that represents the cases, the response variables and the predictor variables of the PLS model of the El Vado CSO in the same graph.

**Table 1.**Definition of the dependent variables (CSO characteristics) and independent variables (rainfall characteristics) for the canonical correlation analysis (CCA) and the partial least squares regression model (PLSR).

Independent Variables (Rainfall Characteristic) | Dependent Variables (CSO Characteristic) | ||||
---|---|---|---|---|---|

Characteristic | Name | Unit | Characteristic | Name | Unit |

R_{d} | Total rainfall depth | Mm | Q_{max} | Maximum flow | L/s |

I_{max} | Maximum rainfall intensity | mm/h | C_{measn} | Mean conductivity | μS/cm |

I_{measn} | Mean rainfall intensity | mm/h | Tur_{measn} | Mean turbidity | NTU |

D | Rainfall duration | Min | COD_{measn} | Mean COD | mg/L |

D_{d} | Dry weather duration | hours |

**Table 2.**The BOD

_{5}/COD ratio for the samples recorded throughout the study period of March 2017 to May 2018.

CSO | BOD_{5}/COD | Standard Deviation | ||
---|---|---|---|---|

Max | Min | Mean | ||

El Vado | 0.81 | 0.04 | 0.38 | 0.24 |

Multifamiliares | 0.92 | 0.17 | 0.52 | 0.33 |

Coliseo | 0.63 | 0.34 | 0.44 | 0.16 |

**Table 3.**Canonical loads (ρ) between (a) the explanatory rain variables and (b) response variables, with the significant canonical variables L(1) and L(3) for the El Vado CSO. Values that represent the possible influence of rainfall variables on CSO are highlighted in gray.

(a) | (b) | ||||
---|---|---|---|---|---|

L(1) | L(3) | L(1) | L(3) | ||

R_{d} | 0.582 | −0.573 | Q_{max} | 0.992 | 0.03 |

I_{max} | 0.948 | 3 × 10−4 | C_{mean} | −0.441 | 0.252 |

I_{mean} | 0.626 | 0.219 | Tur_{mean} | 0.809 | 0.503 |

D | 0.026 | −0.832 | COD_{mean} | −0.238 | 0.123 |

D_{d} | 0.263 | −0.392 |

**Table 4.**Percentages of variance explained according to the number of components of the PLS model for prediction of the variable Tur

_{mean}in the El Vado CSO.

1 Comp | 2 Comp | 3 Comp | 4 Comp | 5 Comp | |
---|---|---|---|---|---|

Explained variance (%) | 77.17 | 92.23 | 99.06 | 99.98 | 100 |

**Table 5.**Regression coefficients for the prediction equations of the CSO variables as a function of the rainfall parameters for the El Vado CSO. R

^{2}is the coefficient of determination of the PLSR.-N is the number of components used to build the PLSR model, and X is the percentage of variability explained by the model.

CSO Variable | Regression Coefficients (PLSR) | N | X (%) | R^{2} | |||||
---|---|---|---|---|---|---|---|---|---|

${\mathbf{C}}_{\mathbf{1}}$ | ${\mathbf{C}}_{\mathbf{2}}$ | ${\mathbf{C}}_{\mathbf{3}}$ | ${\mathbf{C}}_{\mathbf{4}}$ | ${\mathbf{C}}_{\mathbf{5}}$ | ${\mathbf{C}}_{\mathbf{6}}$ | ||||

${\mathrm{Q}}_{\mathrm{max}}$ | 7.710 | 33.740 | 9.892 | 1.217 | 2.300 | −29.932 | 2 | 92.2 | 0.81 |

${\mathrm{C}}_{\mathrm{mean}}$ | −8.428 | −0.584 | −26.091 | −0.989 | 2.079 | 373.142 | 4 | 98.0 | 0.62 |

${\mathrm{Tur}}_{\mathrm{mean}}$ | 0.404 | 1.792 | 0.513 | −0.516 | 0.207 | 170.928 | 2 | 92.2 | 0.60 |

${\mathrm{COD}}_{\mathrm{mean}}$ | 16.281 | −11.664 | 23.326 | −1.399 | 3.480 | 279.929 | 4 | 99.7 | 0.71 |

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**MDPI and ACS Style**

Montalvo-Cedillo, C.; Jerves-Cobo, R.; Domínguez-Granda, L.
Determination of Pollution Loads in Spillways of the Combined Sewage Network of the City of Cuenca, Ecuador. *Water* **2020**, *12*, 2540.
https://doi.org/10.3390/w12092540

**AMA Style**

Montalvo-Cedillo C, Jerves-Cobo R, Domínguez-Granda L.
Determination of Pollution Loads in Spillways of the Combined Sewage Network of the City of Cuenca, Ecuador. *Water*. 2020; 12(9):2540.
https://doi.org/10.3390/w12092540

**Chicago/Turabian Style**

Montalvo-Cedillo, César, Rubén Jerves-Cobo, and Luis Domínguez-Granda.
2020. "Determination of Pollution Loads in Spillways of the Combined Sewage Network of the City of Cuenca, Ecuador" *Water* 12, no. 9: 2540.
https://doi.org/10.3390/w12092540