Evaluation of the Role of Self-cleaning Capacity on Marine Environmental Carrying Capacity: A Case of Ganh Rai Bay, Vietnam

Economic activities are constantly increasing in the southern key economic region (SKER), especially in Ho Chi Minh City (HCMC), which leads to the influx of large amounts of wastewater from this region into Ganh Rai Bay (GRB). The problem of assessing the marine environmental carrying capacity (MECC) of coastal areas is urgent, and the role of self-cleaning must be elucidated. Four typical pollution parameters were selected: ammonium (NH4+), biological oxygen demand (BOD), phosphate (PO43−), and coliforms. The study aims to propose a framework to assess the impact of the role of self-cleaning on MECC and to apply the proposed framework to GRB as a case study. A series of models were used to simulate hydrodynamics, and an advection–diffusion model with an ecological parameter set was used for water quality modelling. The land–ocean interactions in the coastal zone model were used to calculate the GRB and East Sea retention time. Finally, a multiple linear regression model was used to clarify the relationship between the MECC and self-cleaning factors. Calculation results show that the self-cleaning factor increased the MECCAmmonium by 60.30% in the dry season and 22.75% in the wet season; similar to MECCBOD, MECCPhosphate increased by 5.26%, 0.21% (dry season), and 11.04%, 0.72% (wet season), respectively. MECCCColiforms in the dry season increased by 14.83%; in the wet season, MECCColiforms doubled. The results provide medium-and long-term solutions to improve the water quality of the GRB, especially the selection of activities that conserve the ecological system and improve the self-cleaning capacity of the bay.

Vietnam has a coastline of over 3,260 km with 114 large and small estuaries, which annually discharge approximately 847 billion m 3 of water into the sea, accompanied by many nutrients and pollutants (Luu 2016).Estuaries, bays, and lagoons are rich in aquatic resources with extraordinary biodiversity and beautiful landscapes (Luu 2016).As Vietnam faces an increasing coastal pollution trend, determining the role of anthropogenic factors is required to achieve a reasonable and feasible solution for managing and exploiting the coastal zone at the national level (Government, 2018).
Coastal areas are inhabited by dense populations, with approximately 40% of the global population living within 100 km of the coast (Statham 2012).Over the past centuries, increasing population density and rapid socioeconomic development have led to increased discharging of pollutants from the mainland into coastal waters (Jickells 1998;Syvitski et al. 2005;Smith et al. 2010;Elliott 2014).Land-based inputs contribute to more than 75% of marine pollutants (Pravdlc 1995;Williams 1996).Pollutants from land-based sources, when they exceed the carrying capacity of the marine environment, pose a significant threat to marine ecosystems and the health of coastal inhabitants (Trinh 1997;Graymore et al. 2010;Borja et al. 2010;Kang & Xu 2012;Elliott 2013).Therefore, the estimation of pollutant discharge from land to coastal areas and assessment of marine capacity are the basis for pollution control and mitigation (Jarvie et al. 1997;Tuncer et al. 1998;Strong et al. 2015;Wolanski & Elliott 2016;Groeneveld et al. 2018).The issues listed have raised the urgency to study the coastal water environment's Marine Environmental Carrying Capacity (MECC) (GESAMP 1986;Bui & Tran 2022).Despite different approaches, the studies carried out to put the ideas of GESAMP into practice were carried out (Liao et al. 2013;Thu et al. 2013Thu et al. , 2016;;Li et al. 2014Li et al. , 2015;;Long et al. 2014Long et al. , 2019;;Thao et al. 2017).In a recent study by Bui & Tran (2022), the approach used the mass balance principle to determine the allowable load on water bodies (Thu et al. 2013;Luu 2016) to assess the MECC.This study used hydrodynamic, ecological, and retention time models to determine the MECC.
Ecosystems are critical in balancing and playing a selfcleaning role in conserving coastal water resources (Lee et al. 2008).Without maintaining a self-cleaning capacity, other measures to clean and preserve water quality may not be effective (Luu 2016).Lee et al. (2008) conducted a selfcleaning assessment of Yeoja Bay, Korea, using an approach that considers ecological factors, such as phytoplankton, zooplankton, and oxygen consumption from benthic animals.The role of the natural ecosystem in self-cleaning capacity has been noted through ECO-parameters calibrated and tested based on measured data, the application case in Da Nang semienclosed bay (Bui & Tran 2022).
The ecosystem of GRB is characterised by marine species adapted to the brackish saltwater environment and is an abundant food source for aquatic systems.The phytoplankton recorded included silic algae (Bacillariophyta), diopteran algae (Dinophyta), and blue algae (Cyanophyta) (HCMC DNRE 2015;Thanh et al. 2017).The concentration of ammonium (NH 4 + ) in the bay water will be partly reduced by photosynthesis.Like terrestrial plants, the zooplankton is highly diverse in Ganh Rai Bay.There is a mixture of marine species, such as Acartia negligens, Lucifer hanseni, Lucifer penicillifer, Penilia avirostris, Pontella latifurca, Pontella fera, Paracalanus aculeatus, Sagitta enflata, and Sagitta seratodentata.These are associated with typical saltwater open sea species, such as Canthocalanus pauper, Eucalanus subcrassus, with coastal pale salt species, such as Temora discaudata, Oikopleura rufescens, Heterocypris anomala, Limnoithona sinensis, Microcyclops varicans, and with species like Acartia erythracea that are adapted to low salinity (HCMC DNRE 2015;Thanh et al. 2017).In addition to consuming phytoplankton as a food source, zooplankton absorbs nutrients (NH 4 + ) to survive and grow.At the same time, products from zooplankton excretion and death processes strongly reduce dissolved oxygen (DO) concentrations and increase BOD and NH 4 + concentrations in the bay water environment.
In addition, GRB is a coastal area, and the transition between the sea and the mainland constantly receives wastewater; therefore, it is necessary to quantify the pollutant load from rivers (Broman & Robèrt 2017;Pradhan et al. 2017).In the study area, six rivers, especially the Thi Vai River, carry wastewater from economic activities in three provinces: HCM City, Dong Nai, and Ba Ria-Vung Tau upstream.In addition, Ganh Rai Bay is influenced by natural factors leading to hydrodynamic changes in space-time, so MECC, hydraulic factors, and pollutant loads from incoming rivers can be determined (Lee et al. 2008;Liao et al. 2013;Li et al. 2014Li et al. , 2015)).
This study aimed to assess MECC concerning hydrodynamic and anthropogenic factors but mainly focused on the self-cleaning capacity of water bodies.A research framework was proposed to meet this objective and applied to specific cases of the GRB and HCMC areas.The results of this study are significant, helping managers come up with solutions to develop Ganh Rai Bay in the direction of ecotourism, ensuring improved self-cleaning capacity and regulating discharge into the water body.

Study Area
GRB is located in the South East Sea of Vietnam, adjacent to the Can Gio biosphere reserve (Fig. 1).The bay contains brackish water, where three large rivers Long Tau, Dong Tranh, and Thi Vai from SKER and three small rivers from the Ba Ria-Vung Tau Province pour into the bay.The front facing the sea is the Can Gio estuary.The GRB area has outstanding resources with a well-developed port system: Vung Tau, Cai Map ports with beautiful beaches, rich wetlands, a rich mangrove ecosystem, and a diversity of minerals, creating a large potential for socioeconomic development such as tourism, seaports, aquaculture, and fishing.In addition to its critical position in water transportation, GRB is also a large fishing ground with many aquaculture farms, such as shrimp, fish, and bivalve species such as clams and oysters.Mangrove forests are biosphere reserves that nurture fish and shrimp species when they are young.Currently, GRB is also affected by numerous damaging factors, including environmental pollution at seaports and estuaries, such as the Cua Lap port and Thi Vai River.
In the area of GRB, there were 206 species belonging to 8 phyla along with the juvenile larvae group (Larva), mainly phylum Arthropoda with 129 species, Protozoa with 31 species, and Rotifera has 12 species (HCMC DNRE 2015), particularly in three areas of the Dong Tranh, Long Tau, and Cai Mep estuaries.More diversity was recorded, with 70 species belonging to 10 different phyla, the main structure being the phylum Copepoda with 42 species (HCMC HEPA 2015;Thanh et al. 2017).
The benthic fauna of Ganh Rai Bay recorded 389 species belonging to 235 genera, 136 families, 47 orders, 13 classes, six phyla, and the larval group, focusing on Mollusca.There are 155 species, 120 species of angiosperms (Annelida), and 100 species of Arthropoda (HCMC DNRE 2015), especially in the three areas of the Dong Tranh, Long Tau, and Cai Mep estuaries.Seventy species with the main structure are still in the phylum Annelida with 39 species and the phylum Arthropoda with 17 species (HCMC HEPA 2015;Thanh et al. 2017).The number of benthic species in Ganh Rai Bay focuses mainly on the main classes of bivalves (Bivalvia), Polychaeta (Polychaeta), and Crustaceans (Crustacea), which are considered to be the prominent representatives of the ecosystem.benthic animals in GRB.
Water quality in GRB is generally directly affected by socioeconomic activities from urban areas and according to the environmental planning for the period of 2020-2025, this area will receive a large amount of wastewater so the Bay has tended to be significantly polluted (Nam 2022).Besides, the proposal to establish a Can Gio marine protected area in the list of marine protected zones under the fisheries protection and exploitation planning in the period 2021-2030, with a vision to 2050 of the Vietnamese Ministry of Agriculture and Rural Development (MONRE 2021), will certainly improve the bay water environment quality.
The study area is limited by four points: A (106°50′3.70ʺE,10°23′39.50ʺN),B (106°50′4.19ʺE,10°18′56.56ʺN),C ( 107° 9′54.38ʺE,10°18′48.15ʺN),and D (107° 9′56.55ʺE,10°24′5.48ʺN),with six edges, WQ1, WQ2, WQ3, WQ10, WQ11, and WQ12 at six river estuaries (Fig. 2).The bay has an average depth of 2-5 m and a maximum depth of 22 m.The bay has an open structure, a long sandy shoreline, is inclined to the southeast, and has a tropical monsoon climate with an average annual temperature of 26.80 °C, the highest temperature of the year was 42 °C, and the lowest was 17.3 °C.There are two seasons each year: the wet season from May to October, and the dry season from November to April.The average temperature in the seasons is similar, with a difference of approximately 0.5 °C.
In this study, to run hydrodynamic models, meteorological data were extracted from the results of running the Weather Research & Forecasting Model (WRF) version 3.8 (Skamarock et al. 2008).This model was calibrated and validated before simulation.The global meteorological dataset with grid 1° × 1° was used as input data for the Weather Research and Forecasting (WRF) (Skamarock et al. 2008;Powers et al. 2017).The simulation time was from 6:00 pm on 31 December 2015 to 6:00 pm on 31 December 2016 with 3 regions, including D1 (encircling the entire Vietnam), D2 (circling the southern provinces of Vietnam), and D3 (covering the southern provinces of Vietnam) surrounding the provinces of Ho Chi Minh, Binh Duong, and Dong Nai, including GRB.The results of the meteorological model were extracted at Can Gio station (Open-Meteo 2022) and compared with the field-measured data to verify simulation results (Minh-Thu et al. 2020).Wind input data, including speed and direction, were obtained from the WRF.
The grid in Can Gio Bay was divided as follows: the grid coverage was approximately 118.5 km 2 for the entire bay area, and the type of grid used was a triangular grid with 5441 and 3276 nodes.The section sizes were 10, 35.5, and 9 km, respectively.The calculation time in this study was selected as 2016 with a time step of 30 s.The reason for choosing this timeline was to take advantage of the real field data set measured by the SIWRP (SIWRP 2016(SIWRP , 2019)).Input wave data including wave height, wave period, average wave direction, direction standard deviation were collected from Metocean data portal DHI for 2016 (DHI 2016), then this parameter set is calibrated and verified based on the real wave data measured for the study area provided by the Southern Institute Of Water Resources Research (SIWRR).At the location adjacent to the East Sea, the boundary water level values over time were extracted from the Mike Toolbox.The boundaries for temperature and salinity were obtained from SIWRP (2016).At six estuaries, WQ1-WQ3, WQ10-WQ12 (Fig. 2), the average discharge values of the river in the wet and dry seasons were used.Input boundary values at estuaries, such as discharge and salinity, were based on collected datasets such as Table 1, Table S1.GRB is influenced by the East Sea, and the semidiurnal tidal regime has four main tidal components including the principal solar semidiurnal M 2 = 12.42 cm, larger lunar elliptic semidiurnal N 2 = 12.66 cm, principal solar semidiurnal S 2 = 12.00 cm, and lunisolar semidiurnal K 2 = 11.97 cm components that are used to simulate hydrodynamics (Ninh 2009).The hydrodynamic parameters for calibration and confirmation include eddy viscosity, roughness height, and horizontal and vertical dispersion coefficients.In this study, we used the Coriolis force

Ecological Model
Ecohydrodynamic models were used to simulate the GRB's water quality to clarify the marine ecosystem's self-cleaning capacity.The three-dimensional ecological model module for a substance is described by ( 1) where C is the concentration, t is time, u, v, and w are the mean velocity components, K x , K y , and K z are eddy diffusion coefficients, and dC/dt is the biogeochemical variation term.

Eco-hydrodynamic model (ED)
MIKE 21/3 coupled model was used to clarify the relationship between hydrodynamic, anthropogenic factors and MECC (DHI 2017a, b).This package of hydrodynamic models can be applied to estuaries and coastal areas and has been widely implemented (Dong et al. 2018;Doan et al. 2019;Bui and Pham, 2022).The hydrodynamic (HD), wave spectrum (SW), and ecological (ECO) models were the three basic components used in this study.The models allow for the calculation of the interaction between flow, wave, and water quality using a combination of HD, SW, and ECO models (DHI 2017a, b;Dong et al. 2018;Doan et al. 2019;Bui and Pham 2022).This combination allows the simulation of not only the flow but also biogeochemical processes, especially decomposition and photosynthesis, which play important roles in the selfcleaning process of GRB.

LOICZ
Land-ocean interactions in coastal zones (LOICZ) model is a box model used to estimate the retention time of water, material balance, and nutrient status, and is widely applied in coastal water bodies (Gordon et al. 1996;Xu et al. 2013;Kiwango et al. 2018).
At a steady state and assuming no internal sources/sinks and if terrestrial and atmospheric sources of water can be assumed to be completely fresh or approximately, the general salt budget can be expressed as follow: and the water retention time T in a water body can be expressed as follows: (5) where V sys is the bay volume, V x is the water exchange volume, V R is the residual flow volume, S sys is the system salinity, S ocn is the oceanic salinity (Thu et al. 2013;Bui & Tran 2022).

MECC Assessment Model
During the 1976-2002 period, the Group of Experts on the Scientific Aspects of Marine Environmental Protection (GESAMP) made 47 reports on various technical topics related to pollution, protection, and marine conservation (Wells et al. 2002).In 1986, GESAMP published the document: "Environmental carrying capacity-An approach to preventing marine pollution" (GESAMP 1986).The efforts of the international community have created a scientific and practical basis for calculating MECC for several bays around the world (Lee et al. 2008;Liao et al. 2013;Li et al. 2014Li et al. , 2015)).In this study, as applied to GRB, based on volumetric data and water retention time combined with data on pollutant content in water bodies and national water quality standards, the MECC was calculated as follows: where C CR is the average concentration of pollutants in the study water body, which is extracted from the results of running the ecohydrodynamic model, considering the water body's self-cleaning process; C ST is the allowable S2); V sys is the average water body volume in wet and dry seasons; T is the water retention time (Thu et al. 2013;Bui & Tran 2022).

Multiple Linear Regression Model
Multiple linear regression (MLR) (Tai et al. 2010(Tai et al. , 2012;;Herrig et al. 2015) was established to clarify the multiple linear correlations of the MECC with the volume of the water body V sys and the concentration C CR obtained from the modelling results.The detailed MLR models were constructed using the following equation: where α is the cut-off point on the vertical axis, β 1 , β 2 are the slopes or regression coefficients (parameters), and ε is a random variable (error term).This equation was considered for the case that presents the relationship between the MECC concentration (C MECC ) and two factors: average volume of the water body x 1 (V sys ) and the average concentration of x 2 (C CR ).The obtained fundamental results were linear regression equations showing the multivariable correlation between MECC and variables (x 1 , x 2 ).

Model Setup
Choosing the optimal set of parameters for hydrodynamic and water quality simulation models is an important step in ensuring the accuracy of MECC determination results.MIKE 21/3 HD was used for hydrodynamic simulation (DHI 2018) and therefore, it was necessary to establish spatial, temporal, mesh resolution, and initial and boundary conditions.Data on background concentrations, boundary concentrations, and input conditions for the hydrodynamic and ecological models were collected from local sources (Table 1 and S1).The time period of the hydrodynamic modelling was from 00:00 on January 1, 2016 to 23:00 on December 25, 2016.Nash-Sutcliffe (NSE), coefficient of determination (R 2 ), per cent bias (PBIAS), and repeat-sales regression (RSR) indices (Table 3) were used to evaluate the accuracy of the calibration and verification steps.The selected seasonal correction period was 00:00 on January 1, 2016 to 23:00 on February 28, 2016, and the verification time was from 00:00 on October 1, 2016 to 23:00 on November 25, 2016.
The measured datasets used for calibration and verification are presented in Tables 1 and S2.The real dataset to measure the water level at the Aval station was used for the hydrodynamic calibration and verification steps (Fig. 2).The set of criteria used to evaluate the accuracy of the simulation results is presented in Table 3 (Moriasi et al. 2007).The results of calibration and verification are shown in Table S3.The set of validated hydrodynamic parameters included a roughness height if 0.8 m, eddy horizontal viscosity of 0.1 (m 2 /s), eddy vertical viscosity of 0.3 m 2 /s, horizontal dispersion of 38 m 2 /s, and vertical dispersion of 0.15 m 2 /s.In this study, four pollution parameters were selected: ammonium (NH 4 + ), biological oxygen demand (BOD), phosphate (PO 4 3− ), and coliforms, with background, boundary, and initial values given in Tables 1 and S1.Calibrated and validated results of the ecological parameter set were made based on a comparison with the fieldmeasured data as shown in Tables S3.Four field-measurement positions were selected: CB6, CB7, CB8, and CB9.The set of calibrated ECO parameters is presented in Table S4.

Framework and Implementation Steps
The research framework is shown in Fig. 4. Data groups related to natural factors, including meteorology, hydrology, and oceanography, were used as inputs for the hydrodynamic modelling.In this context, the field-measured dataset (Tables 1 and S1) is used as the initial boundary conditions for the calibration and validation of processes.The calibration and validation results are shown in Tables S3, with attention to Table 3.A set of hydrodynamically calibrated parameters was used to run the hydrodynamic module.The hydrodynamic running results were used to serve the step of calibrating and validating the eco-parameter set.Next, to perform a water quality simulation for the study area, the set of field-measured data in Table 1 was used to calibrate and validate the ecological parameter set.The calibration and validation results are shown in Tables S4.The result of this step is the calibrated set of eco-parameters (Table S4).Next, hydrodynamic and water quality simulations were performed, and the results in this step were used to calculate the retention time using the LOICZ model.The water quality simulation results were directly used to calculate the MECC.This step resulted in the seasonal retention time T and concentration of the selected pollutant CCR.The results of the MECC calculation using the ECO parameter set were compared with those of the model running without using the ECO parameter set used to evaluate the self-cleaning role.When the self-cleaning factor is not considered, pollutant transport, in this case, takes place by an advection-diffusion mechanism, and the pollutant is considered inert.
Self-cleaning by biochemical processes occurring in the water environment inside the GRB is considered a crucial issue in decontaminating the water source and completely removing initial unsustainable organic contaminants.In these processes, compounds are changed qualitatively, leading to biochemical decomposition of the original substance and generation of other substances that are, in most cases, harmless, such as carbonic acid (H 2 CO 3 ) and water (H 2 O).However, this also causes the dissolved oxygen (DO) concentration to be reduced, which in several cases could lead to oxygen deficiency and an increase in BOD concentration because of biochemical reactions.In this model, organic biochemical decompositions do not directly participate in mutual reactions with other substances and only interact with themselves, which does not consider chemical reactions occurring with other substances.Organic matter is directly oxidised by DO, as the degree of mutual chemical reactions among them in the bay is minimal compared to biochemical oxidation processes (Fig. 3).

Hydrodynamic Assessment
The following phrases were used for the current speeds in Ganh Rai: current speed,

Dry Season
Flow during high tide: The maximum flow rate is 119.266cm/s, the direction of movement is 89.1°, and is located at 107°9.802′E and 10° 19.139′N.During the tidal cycle, the frequency of weak currents was approximately 76.55%, the frequency of moderate current was 18.21%, and the frequency of the quite strong and strong current was 4.58% and 0.66%, respectively.
Current at low tide: The maximum flow rate is 158.913cm/s, and the direction of travel is 179.1° and is located at 106° 59.830′ and 10°27.629′°N.During the tidal cycle, the frequency of weak currents was approximately 69.11%, the frequency of moderate current was 13.22%, and the frequency of the quite strong and strong current was 5.99% and 11.68%, respectively (Fig. S1).

Wet Season
Flow during high tide: The maximum flow rate is 128.019cm/s, the direction of movement is 179.1° and is located at 107° 9.335′E and 10° 18.753′N.During the tidal cycle, the frequency of weak currents was approximately 71.97%, the frequency of moderate current was 21.55%, and the frequency of the quite strong and strong current was 3.78% and 2.70%, respectively.
Low tide current: The maximum flow rate is 173.117cm/s in the 179.1° direction and is usually located at 106°59.830′E and 10°27.629′N.Tide velocities are lower during spring tides.Statistics from the simulation results show that the flow in the distribution area is 70.65% weak, 10.18% medium, 9.65% quite strong, and 9.52% strong (Fig. S1).
The assessment results of water exchange time in GRB were established based on the LOICZ model with the input dataset shown in Table S5 and Fig. S2.The calculation results of water retention time for GRB were τ = 2.84 (days) in the wet season and τ = 4.09 (days) in the dry season.The bay volume was calculated by taking the total depth value of each grid cell (extracted from the GIS) and the water level height at that grid cell (extracted from Mike) multiplied by the area of the study vicinity.The parameter series V sys received in the form of a time series by hour is used to find the correlation between MECC with two factors concentration and volume.

Water Quality Assessment BOD 5
During the dry season, average BOD 5 ranged from 0.035 to 6.93 mg/l.Most of the bay had a BOD 5 concentration of less than 0.75 mg/l; however, in the Cha Va and Dinh river mouths, BOD 5 reached 6.93 mg/l.The distribution and spread of BOD 5 in the wet season were the same as in the dry season.However, the concentration of BOD 5 in the wet season was higher than that in the dry season, at approximately 3.9 mg/l (Figs.S3, S4), (Table 4).

+
In the dry season, the average NH 4 + from 0.01 to 1.69 mg/l.Most of the bay had a NH 4 + concentration of < 0.5 mg/l; however, in the Cai Mep area, the NH 4 + concentration peaked at 1.02 mg/l.The distribution and spread of NH 4 + in the wet season were the same as in the dry season.However, the concentration of NH 4 + in the wet season was lower than that in the dry season, at approximately 0.12 mg/l (Figs.S3, S4), (Table 4).

PO 4 3−
During the dry season, the average PO 4 3− concentration was < 0.1.Most of the bay had a PO 4 3− concentration of less than 0.05 mg/l; however, in the Cha Va and Dinh river mouths, PO 4 3− reached 0.11 mg/l.The range of PO 4 3− distribution and spread in the wet season was the same as that in the dry season.However, the PO 4 3− concentration in the wet season was lower than that in the dry season, at approximately 0.06 mg/l (Figs.S3, S4), (Table 4).

Coliforms
During the dry season, the average coliforms concentration was < 719 mg/l.Most of the bay had a coliforms concentration of less than 581 mg/l; however, in the Cha Va and Dinh river mouths, coliforms reached 2884 mg/l.Coliform distribution and spread range in the wet season were the same as in the dry season.However, the coliforms concentration in the wet season was more prominent than in the dry season, at approximately 3681 mg/l.(Figs.S3, S4) (Table 4).

MECC Assessment
Based on the calculation results of the retention time, the volume of the bay is shown in subsection Hydrodynamic Assessment, the simulation results of concentrations of four selected parameters (NH 4 + , PO 4 3− , BOD 5 , and Coliform) are presented in subsection Water Quality Assessment, and MECC is shown in Table 5.These were determined according to the wet and dry seasons.Table 5 presents the MECC results.The calculation results showed the assimilative capacity MECC of ammonia, BOD5, and phosphate substances increases by 24.28%, 3.36%, and 0.23% (dry season), and 17.52%, 7.74%, and 0.95% (wet season).

MECC Dependence on Hydrodynamic and Anthropogenic Factors
The MECC value is a function of time t, denoted by y, and is found to be dependent on the volume and concentration.Denote where index i = 1,2,3,4, corresponding to ammonium, BOD, phosphate, and coliform, j = 1.2, corresponding to the dry season and wet season, index x 1 corresponds to the concentration of substances to be considered for MECC calculation, and index x 2 corresponds to the volume of GRB water.
Formula (11) means (MECC over time t for a substance i) = α + β 1 (concentration) + β 2 (volume) + ε.where α is the cut-off point on the vertical axis, β 1 and β 2 are slopes or regression coefficients (parameters), and ε is a random variable (error term).As for the relationship y i,j = i,j + i x 1,i,j + 2,i,j x 2,i,j , the regression results show the correlation relationship between MECC with concentrations x 1, i, j and volume x 2,i,j over time for each indicator and in the wet and dry seasons, as shown in Table 6.
Table 6 shows that the correlation coefficients are greater than 0.98, indicating that concentration and volume factors explain over 98% of the concentration variation for the criteria considered, except for coliforms only.reached R = 0.5921.Based on these results, a univariate analysis was performed for each concentration and volume factor (Table 5).On the other hand, the results from the p value showed that both of the above two factors, the concentration of C and the volume of V, were statistically significant, with both p values < 0.05 (Table 7).This shows that although both of the above factors influence MECC, it is mainly due to the effect of volume V, and the influence of C concentration is lower.

Self-Cleaning Capacity Assessment
The MECC calculation results are listed in Table 5. Selfcleaning capacity significantly increases the load capacity of ammonia in the dry season, reaching 3984.47 (tonne/month) an increase of 60.30% compared to 2485.62 (tonne/month) otherwise compared to the case of neglect the self-cleaning capacity.During the wet season, MECC Ammonium reached 7867.74 (tonne/month), an increase of 22.75% compared to 6409.80 (tonne/month) if the self-cleaning capacity factor was not taken into account.Similar to BOD 5 , phosphate, the self-cleaning ability helps MECC BOD5 , MECC Phosphate increase by 5.26%, 0.21% (dry season) and 11.04%, 0.72% (wet season), respectively.With the coliform indicator in the dry season, when self-cleaning capacity is considered, MECC Coliforms = 11,843,105 (tonne/month) increases by 14.83% if self-cleaning capacity is not taken into account.In the wet season, in the scenario with self-cleaning ability, MECC Coliforms = 12,668,211 (tons/month) increased three times compared to MECC Coliforms when not considering the sudden increase in self-cleaning capacity, leading to a sharp decrease in MECC with 3,971,304 (tonne/ month) (Table 5).11,843,105.43 12,668,211.35 10,313,194.38 3,971,304.14

Discussion
The order of the BOD decomposition equation in this study is built according to the rule of first-order reaction with the first-order decomposition rate coefficient at 20 °C with the value K 3 = 0.50 day −1 along with the Arrhenius temperature coefficient for the entire BOD decomposition to θ 3 = 1.02 and a half-saturated oxygen concentration level of HS_ BOD = 0.05 mg/L.(Table S4).
Nutrients such as ammonium (NH 4 + ) in the water environment of the bay are partly degraded by photosynthesis; similar to terrestrial plants, phytoplankton also have chlorophyll to absorb sunlight associated with the consumption of CO 2 , water, and nutrients, thereby creating chemical energy and providing O 2 for the aquatic environment.These processes could produce peak O 2 levels of up to P max = 3.50 g O 2 /m 2 /day in the bay.Simultaneously, primary productivity was formed, increasing the population mass of phytoplankton, which was reflected in this model based on the NH 4 + uptake coefficient of phytoplankton with UN p = 0.066 mg NH 4 + -N/mg O 2 .In contrast, in respiration and the dying process, DO concentration declines because of consumption, decay, and mineralisation, releasing back into the aquatic environment with several inorganic components of nitrogen.This is reflected through the respiratory rate coefficient of R 2 = 3.00 g O 2 /m 2 /day (at 20 °C with the Arrhenius temperature adjustment coefficient for heterotrophic respiration θ 2 = 1.05) and NH 4 + release coefficient is Y BOD = 0.10 mg NH 4 + -N/mg BOD.(Table S4).In addition to consuming phytoplankton as a food source and absorbing nutrients (NH 4 + ) with the coefficient UN b = 0.109 mg NH 4 + -N/mg O 2 , in order to survive and develop, zooplankton also perform the same heterotrophic respiration process as phytoplankton with a respiratory rate coefficient R 2 = 3.00 g O 2 /m 2 /day (20 °C), and the Arrhenius temperature adjustment coefficient for this process is θ 2 = 1.05; simultaneously, products from the excretion and death processes of zooplankton continued to strongly reduce DO concentration, and the BOD and NH 4 + concentrations in the GRB increased.
Similar to NH 4 + , phosphate (PO 4 3− ) is a nutrient for the development of a wide range of algae and plankton groups.The source of PO 4 3− in the bay is commonly domestic wastewater, which contains animal faeces, industrial wastewater from several groups of food-producing industries, and runoff from chemically fertilised fields (such as Phospho and NPK fertilisers).In this model, it can be seen that the rate of PO 4 3− released from the BOD of organic matter is Y 2 = 0.009 g PO 4 3− -P/g BOD, whereas the PO 4 3− concentration levels are absorbed by the phytoplankton groups which reach UP p = 0.009 mg PO 4 3− -P/mg O 2 .Phosphate (PO 4 3− ) from discharge sources was also partly deposited and sedimented in the bottom areas of the bay.In the bay bottom area, benthic fauna (or zoobenthos) play an important role in the processes of absorbing and resolving sediments to the bottom from the water column with a settling rate of 0.80 m/day, and a process of re-suspending the water column from the bottom (known as resuspension) at 0.50 g/ m 2 /day.Part of the re-infiltration of PO 4 3− from the bottom sediments frequently leads to a sudden change in the water quality of the bay, and bottom sediment respiration processes also consume a large amount of oxygen, which results in the degradation of the DO concentration.The oxygen demand for sedimentation in this model was adjusted at SOD = 0.50 g O 2 /m 2 /day along with the corresponding Arrhenius temperature adjustment coefficient of 1.00.Furthermore, because most of the city's domestic wastewater is received, the NH 4 + and PO 4 3− concentrations in the Saigon River are often quite high in the inner city areas.Nevertheless, some of the above pollutants (NH 4 + and PO 4 3− ) have also been strongly reduced in the estuary area, because when the Dong Nai and Saigon rivers confluence, the self-cleaning capacity also increases considerably.
Moreover, inorganic products of nitrogen (NH 4 + ) released during decomposition and mineralisation for both phytoplankton and zooplankton continue to participate in the nitrogen conversion cycle, including nitrification, to form nitrite (NO 2 − ) and nitrate (NO 3 − ), and denitrification to generate free nitrogen (N 2 ).These processes occur under the complex influence of decomposition conditions and sea temperature; in this model, they are corrected with the nitrification coefficients K 4 = 1.54 ngày −1 (at 20 °C) with the corresponding Arrhenius temperature adjustment coefficients θ 4 = 1.13; in addition, a denitrification coefficient K 6 = 1.00 ngày −1 (at 20 °C) with the corresponding Arrhenius temperature adjustment coefficient θ 6 = 1.16.When the nitrification process occurs, the DO content in the bay is also used by the groups of bacteria with an O 2 demand of up to 4.47 g O 2 /g NH 4 + , causing the DO concentration to continue to decline and be limited by the half-saturated O 2 concentration coefficient of HS_nitr = 0.05 mg O 2 /L.(Table S4).Coliform groups characterised by Escherichia coli (or E. coli) are a group of specific indicator microorganisms, indicating that the aquatic environment is contaminated with faeces and contains pathogenic bacteria.In particular domestic wastewater sources that have not been treated are discharged into the Saigon River and its confluence tributaries flowing through the inner city of Ho Chi Minh City before pouring into GRB.When Coliform bacteria decompose, they also increase the content of organic matter in the bay.In this study, these organics were biodegradable with a first-order Faecal Coliform decomposition coefficient of K dF = 0.70 day −1 along with the Arrhenius temperature adjustment coefficient of θ = 1.09.(Table S4).
In the scenario in which there is a Can Gio marine protected area, the effects on the MECC and water quality of GRB could shift in a positive direction.This can be simulated and reported in the model through the increased values of the potential parameters, as shown in Table S6.The simulation results show that, in the case of construction of Can Gio biodiversity conservation area, the MECC increases from 2 to 4% in the dry season and from 0.7 to 44% in the wet season, depending on each substance (Table S7).

Conclusion
A framework for assessing the role of natural and anthropogenic factors in the marine environmental carrying capacity of the bay was developed in this study.Natural factors, including meteorology, hydrology, and oceanography, were considered.The influencing factors, including anthropogenic, included six river flows that carried pollutants into the bay.The research framework includes four models: hydrodynamics (HD), water quality simulation (ECO), retention time calculation (LOIZC), and marine environmental carrying capacity (MECC).
Hydrodynamic factors and water quality were simulated after the calibration and validation steps of the hydrodynamic models based on the field-measured dataset.
The MECC was calculated for GRB, which receives wastewater from the most economically active provinces in southern Vietnam, namely, HCMC, Dong Nai, and Ba Ria-Vung Tau.For the two parameters NH 4 + , BOD 5 , the MECC calculation results showed that two indicators, NH 4 + and BOD 5 , still had load capacities in both the wet and dry seasons..
Based on the MECC calculation results and the hourly concentration and volume of water, multiple linear regression functions were built to clarify the role of natural and anthropogenic factors in MECC formation.The study area results showed that the system volume role was more significant than current concentration.This shows that hydrodynamic factors play an essential role in determining MECC in the region.Therefore, the proposed approach and methods can be applied to similar regions.Chi Minh City University of Technology (HCMUT), VNU-HCM for this study.

Data and Materials Availability
We declare that all data relating to this manuscript are truthful and we will gladly share it with any interested readers or at the request of the editor board.

Declarations
Conflict of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Ethical Approval
The authors declare: The manuscript is not submitted to more than one journal for simultaneous consideration.The manuscript is original and not have been published elsewhere in any form or language (partially or in full), unless the new work concerns an expansion of previous work.The manuscript is not split up into several parts to increase the quantity of submissions and submitted to various journals or to one journal over time (i.e.'salami-slicing/publishing').Results are presented clearly, honestly, and without fabrication, falsification or inappropriate data manipulation.We adhere to disciplinespecific rules for acquiring, selecting and processing data.We have provided all data and proper mentions of other works.
Consent to Participate I consent to participate publish my manuscript entitled "Evaluation of the role of self-cleaning capacity on marine environmental carrying capacity: a case of Ganh Rai bay, Vietnam " to the Archives of Environmental Contamination and Toxicology (AECT).
Consent to Publication I consent to publish my manuscript entitled "Evaluation of the role of self-cleaning capacity on marine environmental carrying capacity: a case of Ganh Rai bay, Vietnam "to the Archives of Environmental Contamination and Toxicology (AECT).

Fig. 2
Fig. 2 Field data and boundary monitoring stations

Fig. 4
Fig. 4 Framework and implementation steps

Table 4
The simulation results of concentration of NH 4

Table 6
Multivariable correlation equation L t,DO = F(C, V)

Table 7
Synthesis of values in univariable linear regression analysis