1. Introduction

2. Materials and Methods

2.2. Wastewater Characterization

To determine the quality of wastewater discharged into Buenaventura Bay, a characterization campaign was conducted. The Fecal Coliforms (FC) were determined according to the Standard Methods for the Examination of Water and Wastewater [10]. The 695 wastewater discharge locations were georeferenced, and 100 (14,39%) of these were selected as a sample for characterization. Figure 2 shows the location of the sampled wastewater discharges.

Based on the characterization data, the discharges were categorized into three groups based on low, medium, and high flow. An average flow was calculated for each category. An estimated total wastewater discharge flow of 694 L/s was determined to flow into Buenaventura Bay. Table 1 displays the flows used for the categories of wastewater discharges in the simulations.

Table 1. Discharge flows were considered in the simulations.

Table 1. Discharge flows were considered in the simulations.

Discharge Type	Flow (L/S)	Amount Discharges	Total Flow (L/s)
Low	0,74	316	233,84
Medium	1,01	252	254,52
High	1,62	127	205,74

2.2. Hydrodynamic and Water Quality Models Description

A coupling scheme combining the RMA10 3D hydrodynamic and RMA11 water quality models was used to simulate the hydrodynamic and water quality conditions in Buenaventura Bay. The RMA10 model simulates the velocity, pressure, and sediment fields in three dimensions [11,12,13,14]. The system of equations that the model solves is described from equations (1) to (6).

Figure 2. Location of wastewater discharges (red dots), blue line represents the coastline, Google Earth image.

Figure 2. Location of wastewater discharges (red dots), blue line represents the coastline, Google Earth image.

The equations of movement in the three components of the cartesian field are shown by equations (1)–(3):

$$\rho .\left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)-\frac{\partial }{\partial x}\left({\mathsf{\epsilon }}_{\mathit{xx}}\frac{\partial u}{\partial x}\right)-\frac{\partial }{\partial y}\left({\mathsf{\epsilon }}_{\mathit{xy}}\frac{\partial u}{\partial y}\right)-\frac{\partial }{\partial z}\left({\mathsf{\epsilon }}_{\mathit{xz}}\frac{\partial u}{\partial z}\right)+\frac{\partial p}{\partial x}-{\Gamma }_x=0,$$

(1)

$$\rho .\left(\frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z}\right)-\frac{\partial }{\partial x}\left({\mathsf{\epsilon }}_{\mathit{yx}}\frac{\partial v}{\partial x}\right)-\frac{\partial }{\partial y}\left({\mathsf{\epsilon }}_{\mathit{yy}}\frac{\partial v}{\partial y}\right)-\frac{\partial }{\partial z}\left({\mathsf{\epsilon }}_{\mathit{yz}}\frac{\partial v}{\partial z}\right)+\frac{\partial p}{\partial y}-{\Gamma }_y=0,$$

(2)

$$\rho .\left(\frac{\partial w}{\partial t}+u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}\right)-\frac{\partial }{\partial x}\left({\mathsf{\epsilon }}_{\mathit{zx}}\frac{\partial w}{\partial x}\right)-\frac{\partial }{\partial y}\left({\mathsf{\epsilon }}_{\mathit{zy}}\frac{\partial w}{\partial y}\right)-\frac{\partial }{\partial z}\left({\mathsf{\epsilon }}_{\mathit{zz}}\frac{\partial w}{\partial z}\right)+\frac{\partial p}{\partial z}+\mathsf{\rho }\rho .g-{\Gamma }_z=0$$

(3)

The continuity equation is presented in equation (4):

$$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$$

(4)

Advection–diffusion processes are presented in equation (5):

$$\frac{\partial s}{\partial t}+u\frac{\partial s}{\partial x}+v\frac{\partial s}{\partial y}+w\frac{\partial s}{\partial z}-\frac{\partial }{\partial x}\left(D_x\frac{\partial s}{\partial x}\right)-\frac{\partial }{\partial y}\left(D_Y\frac{\partial s}{\partial y}\right)-\frac{\partial }{\partial z}\left(D_z\frac{\partial s}{\partial z}\right)-\theta s=0,$$

(5)

And the equation of state is presented in equation (6):

$$\rho =F\left(s\right),$$

(6)

Where x, y, and z are the coordinates of the Cartesian system; $u$, $v$, and $w$ are the velocities in the directions of the Cartesian system, p is the water pressure, t is time, ${\mathsf{\epsilon }}_{\mathrm{xx}}{,\mathsf{\epsilon }}_{\mathrm{xy}}{,\mathsf{\epsilon }}_{\mathrm{xz}}{,\mathsf{\epsilon }}_{\mathrm{yx}}{,\mathsf{\epsilon }}_{\mathrm{yy}}{,\mathsf{\epsilon }}_{\mathrm{yz}}{,\mathsf{\epsilon }}_{\mathrm{zx}}{,\mathsf{\epsilon }}_{\mathrm{zy}}{,\mathsf{\epsilon }}_{\mathrm{zz}}$ are the eddy turbulence coefficients, $\mathrm{g}$ is the acceleration due to gravity, $D_x$, $D_Y$, and $D_z$ are the eddy diffusion coefficients, $\rho$ is the density of water, ${\Gamma }_x$, ${\Gamma }_y$, and ${\Gamma }_z$ are the external forces; $s$ is the salinity, and $\theta s$ is the salinity source/sink.

The RMA11 model, which uses the finite element method, has been used successfully to model water quality in estuaries, bays, lakes, and rivers [15,16,17,18]. It receives the velocity, temperature, and salinity fields from the RMA10 model and uses them to solve the advection-diffusion constituent transport equations [15]. The water quality relationships implemented in RMA11 are derived from QUAL2E, and for more information, the reader is referred to Brown and Barnwell [19]. In RMA11, coliform transport is modeled using three loss parameters: settling, decay in darkness, and light–sensitive decay. The equation for coliform growth (GC) is given by:"

$$\mathrm{GC}=–\left(K_{C1}+K_{C2}+K_{C3}/d\right)\ast C_C$$

(7)

where $C_C$ is the concentration of the coliform, (MPN/100mL), $K_{C1}$ is the coliform die–off rate in darkness – temperature adjusted (1/day), $K_{C2}$ is the coliform die–off rate due to light - temperature adjusted (1/day), $K_{C3}$ is the coliform settling rate–temperature adjusted (m/day) and $d$ is the water depth (m).

The temperature values computed in RMA11 were used to adjust the rate coefficients in the source/sink terms. These coefficients are input at 20°C and then corrected to the actual temperature (T) using Equation (8):

$$X_t=X_{20}{\theta }^{\left(T-20\right)}$$

(8)

where, $X_t$ is the value of the coefficient at the local computed temperature $X_{20}$ is the value of the coefficient at 20°C, $\theta$ is a dimensionless constant coefficient usually set to be 1,07 [20]. This correction was applied to $K_{C1}$ and, $K_{C3}$, While $K_{C2}$ dependent on the light intensity and is given for equation (9):

$$K_{C2}=2,3026\frac{\left[L_{i}exp{\left(-\lambda z_d\right)}^{0.7}\right]}{L_c}$$

(9)

where $L_i$ is the light intensity expressed in MJ/m²–hr, $L_c$ is the coliform light coefficient (hr.[ MJ/m²–hr]^0.7), $\lambda$is the light extinction coefficient (1/m), and $z_d$ is the depth below the water surface for 3D (m).

2.3. Model Set up for Buenaventura Bay

The simulation domain was selected to cover an area of 430 km² and included both the inner and outer bay. The finite element mesh was created to closely follow the irregular coastline of the bay, using Mesh2D software [21,22]. The resulting mesh consisted of 19.672 elements, with lengths ranging from 15 to 500 meters, and 43.604 nodes. The triangular elements in the mesh were equilateral, which helped reduce the computational efforts. Figure 3 shows the resulting mesh generated by Mesh2D.

The bathymetry data used in the study were obtained from the CIOH nautical charts of the study area and digitized and interpolated in the finite element mesh nodes. The interpolated bathymetry is shown in Figure 4. The RMA 10 model used sigma coordinates and modified the system of equations to account for changes in the water surface elevation due to tides. The details of the modification can be found in the references Marthanty et al. [11] and Fosati et al. [12]. The finite element mesh was discretized into five layers in the vertical direction.

The open boundaries at the southeast, southwest, and northwest of the outer bay were forced with current, water level, salinity, and temperature data from the HYCOM global model [23]. Wind direction and speed, solar radiation, humidity, and air temperature data were taken from a meteorological station and considered uniform over the simulation domain. The simulation model was run for one year (2021) to determine the effect of wastewater discharges on Buenaventura Bay. Fresh water from the Dagua (66,10 m³/s), Achicayá (98,90 m³/s), Humane (30 m³/s), Gamboa (30 m³/s), Aguacate (10 m³/s), San Antonio (20 m³/s), Hondo (10 m³/s), and Agua Dulce (80 m³/s) rivers and estuaries were considered in the model. Mean flows of each river and estuary and mean temperature of 28°C were considered. Average fecal coliform concentrations of 28.960 and 4.724 MPN/100mL, were included in the Dagua and Achicaya rivers, respectively, as reported by Vivas et al. [9].

Figure 4. Simulation domain bathymetry, built-up area with black.

Figure 4. Simulation domain bathymetry, built-up area with black.

3. Results

3.1. Characterization of Wastewater Discharges

The results of the FC concentration of the characterizations of the wastewater discharges to Buenaventura Bay are shown in Table 1. In the measurement campaigns, an average concentration of 8 × 10⁸ MPN/100mL was found.

Table 2. Concentration of FC in wastewater discharge.

Table 2. Concentration of FC in wastewater discharge.

Parameter	Unit	Maximum	Mean	Minimum
Fecal Coliform	MPN/100mL	2 × 1010	8 × 108	7 × 103

3.2. FC Concentration in the Water Column

16 measurement campaigns were carried out to determine the concentration of FC, 8 corresponded to the calibration phase of the water quality model, from February to March, one every week, and 8 in the validation period, from October to November. Mean values of 2,8 × 10³ MPN/100mL were found for the calibration stage and 1,8 × 10³ MPN/100mL for the validation. Table 2 shows the maximum, minimum, and average values of the sampling campaigns for each data set.

Table 2. Concentration of FC in the Wastewater Discharge.

Table 2. Concentration of FC in the Wastewater Discharge.

	Unit	Maximum	Mean	Minimum
calibration	MPN/100mL	5× 103	3 × 103	1.2 × 103
validation	MPN/100mL	2.4× 103	1.4 × 103	4× 102

The one-way anova did not show significant differences (p= 0,478) between the two samples sets taken for the calibration and validation of the water quality model; therefore, it can be presumed that despite the difference in the rainy seasons in which the samples were taken, the concentrations tend to be similar given their origin, the discharge of wastewater into Buenaventura Bay.

3.3. Calibration Hydrodynamic Model

3.3.1. Sea Level

Values of 0,602 and 0,620 were obtained for the RSME estimator in the calibration periods in February-March and the validation periods in October-November, respectively. The SKILL showed values of 0,747 and 0,742 for the same periods. The comparison between the results of the model and the field measurements for tides at station T1 is presented in Figure 6.

3.3.3. Water Quality Model

The water quality model showed a predictive ability of 0,716 in the calibration stage and 0,799 in validation. A value close to 1 in the "skill" indicates high predictive ability, meaning the model is capable of accurately predicting data. A value close to 0 indicates low predictive ability, meaning the model is unable to predict data accurately. Given the favorable results obtained, it is considered that the model is capable of accurately predicting the water quality data in Buenaventura Bay, regarding FC. The RMSE values were 1 x 10³ and 1,13 x 10³ for calibration and validation, respectively. The graphical comparison of the field-measured data at station T2 and the model results is presented in Figure 9.

3.3.2. Currents

Evaluating the performance estimators of the model found an RMSE of 0,007 m/s and a Skill of 0,998 for the magnitude of the currents and an RMSE of 9,87 degrees and SKILL of 0,992 for the direction of the currents, both confirmed the excellent performance of the model to reproduce current data in the Bay of Buenaventura. The graphical comparison of the current roses for the data measured in the field and the model results confirm the results of these estimators (Figure 7).

Figure 6. Sea water level comparation for simulations and measurements for, a. calibration in February, b. calibration in March, c. validation in October, and c. validation in November.

Figure 6. Sea water level comparation for simulations and measurements for, a. calibration in February, b. calibration in March, c. validation in October, and c. validation in November.

Figure 7. Currents roses comparation comparison for simulations and measurements for the calibration period.

Figure 7. Currents roses comparation comparison for simulations and measurements for the calibration period.

Similar behavior was found in the evaluation of the model during the validation period. For the speed of the current, the RSME was 0,007 m/s and the predictive ability was 0,998, while for the direction of the current, the values were 7,71 degrees and 0,995 for the RSME and SKILL, respectively. The current roses resulting from the validation period (October - November) are shown in Figure 8; this corresponds to the comparison of the measured and simulated current data at station T1.

Figure 8. Currents roses comparation comparison for simulations and measurements for the validation period.

Figure 8. Currents roses comparation comparison for simulations and measurements for the validation period.

Figure 9. Comparison of fecal coliform concentration in the calibration and validation of the water quality model.

Figure 9. Comparison of fecal coliform concentration in the calibration and validation of the water quality model.

3.3.4. Discharge Reduction Scenario

The concentration of FC in the Bay of Buenaventura for the current scenario, according to the results of the RMA11 model, is presented in Figure 10. The current scenario measures the effects of the 695 untreated wastewater discharges. The highest concentrations of FC was obtained in the San Antonio estuary, where most of the Untreated wastewater discharges were generated in Buenaventura. Maximum concentrations of 1,45 × 10⁷ MPN/100mL of FC were found in this scenario.

The Colombia´s Law contemplates a limit concentration of 200 MPN/100mL of FC for primary contact; this value was used as a reference for the analysis of the impact on the reduction of discharge points in the Bay of Buenaventura. The time step of the water quality model was 15 min, and it was run for one year (2021) equivalent to 35.040 results per node. For each node, the frequency of the data that exceeds the reference limit concentration established by the Colombian standard was found, from this analysis the frequency of affected areas with concentrations greater than 200 MPN/100mL was found, the result of this analysis It is presented in Figure 11. This is the base scenario to analyze the differences with the proposed discharge reduction scenarios. The areas with a frequency of 100% of values with a concentration greater than 200 MPN/100mL are presented in red in Figure 11. A modification was made to the water quality model with respect to the adjustment parameters found in the calibration and validation phase, to determine the effects of wastewater discharges on the quality of the water in the Bay of Buenaventura, the concentrations of FC in the tributaries that reach the bay were set at zero. This assumption allows knowing the impact of the discharges generated in the urban areas without other interferences.

Figure 10. Spatial distribution of the maximum concentration of FC in the Bay of Buenaventura in the current scenario.

Figure 10. Spatial distribution of the maximum concentration of FC in the Bay of Buenaventura in the current scenario.

It can be noted that the current situation of 695 untreated wastewater discharge into the Bahía de Buenaventura has its greatest effect on the concentration of FC inside the estuary and in the vicinity of the discharges that corresponding to the most internal of it. In this area, there is a frequency of 100% of the occurrence of values that violate the norm. In the middle or central part of the bay, the effects of levels that violate the standard are between 50% and 70%, while outside the bay, the effects are less than 20%. That is, in this section of the Bahía de Buenaventura, only 20% of the time there are concentrations greater than 200 MPN/100mL of FC that are related to the wastewater discharges generated by the urban settlement that occurs in the city of Buenaventura (Figure 11).

The reduction of wastewater discharges was proposed to go from 695 to 6 (Figure 5a), that concentrate the flow of the previous ones; this situation is analyzed in scenario two that increases the concentration of FC in the Buenaventura Bay with respect to the current situation (scenario one) the maximum concentration obtained in this scenario is 1,45 × 10⁷ MPN/100mL; this situation is shown in figure 12.

The maximum concentration in the Scenario three is 3,21 × 10⁷ MPN/100mL of FC. Concentrating the untreated wastewater discharges at two points (Figure 5b) generates twice the concentration of the 6-discharge scenario and 2,2 times the concentration as the current scenario with 695 discharges. (Figure 13)

When a wastewater treatment system was considered for these two discharge points (Figure 5b), the concentration of FC is drastically reduced, reaching maximum concentrations of 5,32× 10⁵ MPN/100mL, which correspond to the lowest concentrations of all scenarios studied. In addition to the low concentrations, a notable reduction in the area affected by FC in Buenaventura Bay can be observed in Figure 14.

Figure 11. Frequency of areas affected by concentrations higher than 200 MPN/100mL in the water column scenario acts.

Figure 11. Frequency of areas affected by concentrations higher than 200 MPN/100mL in the water column scenario acts.

Figure 12. Spatial distribution of the maximum fecal coliform concentration in Buenaventura Bay in scenario two.

Figure 12. Spatial distribution of the maximum fecal coliform concentration in Buenaventura Bay in scenario two.

The last scenario studied (Figure 15) belongs to the trend situation, which answers the question, What will happen if sanitation solutions are not implemented?. The assumptions made for this scenario contemplate population growth according to the local demographic dynamics (population growth rate of 3%) and consider that the current discharges are conserved over time. In 25 years, Buenaventura is projected to double its population (1,050 × 10⁶ inhabitants) and generate 1,45 m³/s of untreated wastewater if the current situation persists. Under these considerations, it was found that the maximum concentration of FC in the bay of Buenaventura increases by a factor of three to a maximum concentration of 4,32 x 10⁷ MPN/100mL. This is undoubtedly the highest concentration of all scenarios studied and justifies the urgent need to adopt a sanitation and discharge reduction plan.

Figure 13. Spatial distribution of the maximum fecal coliform concentration in Buenaventura Bay in scenario three.

Figure 13. Spatial distribution of the maximum fecal coliform concentration in Buenaventura Bay in scenario three.

4. Discussion

Figure 14. Spatial distribution of the maximum fecal coliform concentration in Buenaventura Bay in scenario four.

Figure 14. Spatial distribution of the maximum fecal coliform concentration in Buenaventura Bay in scenario four.

Figure 15. Spatial distribution of the maximum fecal coliform concentration in Buenaventura Bay in scenario five.

Figure 15. Spatial distribution of the maximum fecal coliform concentration in Buenaventura Bay in scenario five.

Figure 18. Frequency of areas affected by concentrations higher than 200 MPN/100 ml in different scenarios, a. scenario two, b. scenario three, c. scenario four, and d. scenario five.

Figure 18. Frequency of areas affected by concentrations higher than 200 MPN/100 ml in different scenarios, a. scenario two, b. scenario three, c. scenario four, and d. scenario five.

Figure 19. Frequency exceeding in areas affected by concentrations higher than 200 MPN/100 ml in scenario four, inner part of Buenaventura Bay.

Figure 19. Frequency exceeding in areas affected by concentrations higher than 200 MPN/100 ml in scenario four, inner part of Buenaventura Bay.

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