Optimal Water Quality Management Considering ...

Optimal Water Quality Management Considering Spatial and Temporal Variations in a Tidal River Huapeng Qin, Jingjing Jiang, Guangtao Fu & Ying Zheng

Water Resources Management An International Journal - Published for the European Water Resources Association (EWRA) ISSN 0920-4741 Volume 27 Number 3 Water Resour Manage (2013) 27:843-858 DOI 10.1007/s11269-012-0218-7

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Author's personal copy Water Resour Manage (2013) 27:843–858 DOI 10.1007/s11269-012-0218-7

Optimal Water Quality Management Considering Spatial and Temporal Variations in a Tidal River Huapeng Qin & Jingjing Jiang & Guangtao Fu & Ying Zheng

Received: 30 July 2011 / Accepted: 15 November 2012 / Published online: 28 November 2012 # Springer Science+Business Media Dordrecht 2012

Abstract There is an increasing need to establish wastewater treatment facilities for improving water quality of heavily polluted rivers in rapidly urbanizing areas. Optimization models are widely used to determine the pollutant removal levels at different pollution sources, with the aim of minimizing the wastewater treatment cost and satisfying certain water quality criteria. Water quality is usually evaluated in a prescribed space or time point. Thus it cannot reflect the overall status of a tidal river that has significant spatio-temporal variations. In this paper, new spatio-temporal water quality criteria, which consider the water quality violation against specified water quality standards during the whole simulation period of time for the entire river simulated, are proposed and then applied to optimization of a wastewater treatment system in Shenzhen, China. The results indicate that the optimization based on the proposed criteria facilitates an improved performance of wastewater treatment systems in terms of water quality along the whole river during a long time period, instead of just in a prescribed space or time point. Furthermore, use of the new criteria derives a better Pareto front of cost and water quality in terms of convergence and coverage compared with the conventional criteria and thus they are recommended as the water quality criteria to measure spatial and temporal variation in a tidal river for wastewater treatment system planning. Keyword Water quality management . Optimization . Spatial variation . Temporal variation . Tidal river

H. Qin (*) : J. Jiang : Y. Zheng Key Laboratory for Urban Habitat Environmental Science and Technology, School of Environment and Energy, Peking University Shenzhen Graduate School, 518055 Shenzhen, China e-mail: [email protected] G. Fu Centre for Water Systems, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK

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1 Introduction In many urbanizing areas, river water quality has deteriorated due to increasing wastewater discharges from domestic and industrial sources (Fu et al. 2009; Karn and Harada 2001; Qin et al. 2010; Singh et al. 2007). To protect the receiving water from adverse impacts, it is required to determine the pollutant removal levels at a number of pollution sources along the river and develop (or upgrade) a wastewater treatment system in a cost-effective manner (Burn and Yulianti 2001). Many optimization approaches have been developed to provide optimal water quality management plans and assess mitigation and adaption strategies for potential urbanization and climate change in urban catchments(Butler and Schutze 2005; Cho et al. 2004; Fu et al. 2010; Tufail and Ormsbee 2009). These approaches are usually an integration of a water quality simulation model and an optimization algorithm (Vemula et al. 2004; Saadatpour and Afshar 2007). The water quality models are used to predict water quality in the river under various management strategies; while the optimization algorithms, such as genetic algorithms (GA), are used to find optimal solutions to minimize the cost of wastewater treatment and achieve water quality requirement of the receiving water body. The water quality criteria herein refer to water quality indicators whose values have to satisfy specific standards set by authorities. Many water quality criteria have been formulated in the literature. Most water quality criteria are defined to ensure that the worst water quality along a river meets specified water quality standards. That is, only the check point with the worst concentration is taken into consideration (Cho et al. 2004; Rauch and Harremoës 1999; Tufail and Ormsbee 2009). These criteria can be expressed as constraints in an optimization model (Qin and Huang 2009; Zhu et al. 2009). In this way, the typical optimal wastewater treatment problem can be formulated as a single objective optimization problem that aims to minimize the wastewater treatment cost for the entire river catchment, subject to constraints on satisfaction of specified water quality standards at all the check points along the river. Water quality criteria based on frequency (or magnitude) of water quality standard violation have also been proposed. Because of natural variability and anthropogenic influence, water quality in a river usually has the feature of temporal and spatial variation (Awadallah and Yousry 2012; Bu et al. 2010; Pillsbury and Byrne 2007), and it is unreasonable to disallow any standard violations in the river (Borsuk et al. 2002). To reflect the variation of water quality, the U.S. EPA guidelines for state water quality assessments instruct that a water body is listed as impaired if more than 10 % of the samples taken over a specified time and space from that water body violate water quality standards (Borsuk et al. 2002). Indicators such as number of violations, magnitude of maximum violations, duration of violations, and total magnitude of violations at the checkpoints can be expressed either as additional objectives or as constraints in the optimization model (Butler and Schutze 2005; Cardwell and Ellis 1993; Tufail and Ormsbee 2009; Yandamuri et al. 2006). Aggregated water quality criteria have been used to reduce the number of criteria for optimization problems as many-objective problems have more complex trade-offs and are more computationally intractable. Yandamuri et al. (2006) proposed an overall performance measure that is expressed as a weighted sum of several individual performance measures, including the number of dissolve oxygen (DO) standard violations, magnitude of maximum DO standard violations and magnitude of total DO standard violations over all the checkpoints considered within the system. Fu et al. (2008) used a combined criterion for solving multi-objective optimal control problems that integrates the extreme concentrations and the durations breaching critical thresholds. All the aforementioned water quality criteria have some limitations when they are used as objectives for optimal control of urban wastewater treatment systems. Traditionally, the water

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quality criteria are evaluated at several prescribed reaches or check points at a specific time step (e.g., when the worst water quality happens). This cannot reflect the continuous water quality variation in space and time. Furthermore, river data (water flow and quality) have a very specific spatio-temporal dependence structure, which can be represented by correlations between data at different locations and times (Clement and Thas 2009). The spatio-temporal dependence structure has been largely ignored in the previous studies in terms of definition of water quality criteria. Therefore, the comprehensive characterization of the spatial and temporal variation of water quality in a river cannot be accurately captured by the existing criteria. Driven by the implementation of the EU Water Framework Directive (WFD) (Council of the European Communities 2000), there is an increasing need to evaluate water quality covering the whole river and for a long time period, rather than just at the prescribed locations or times. Moreover, due to the periodic tidal effects and heterogeneous wastewater discharges along the river, the water quality in a tidal river has significant spatio-temporal variation. To facilitate the performance of wastewater treatment systems with the goal to improve water quality along a whole river during a long time period, the spatial and temporal variation of water quality should be considered in optimization of wastewater treatment systems. Therefore, the objectives of this paper are: 1) to propose new water quality criteria, which can accurately capture the spatial and temporal variation of water quality in a tidal river; and 2) to investigate the impacts of the newly developed spatio-temporal water quality criteria in multi-objective optimization of the wastewater treatment system of Shenzhen, China.

2 Material and Methods 2.1 Study Area The Shenzhen River is located in the rapidly urbanizing coastal region of Southeastern China, and forms the administrative border between mainland China and Hong Kong (Fig. 1). The total catchment area of the Shenzhen River is 312 km2. The river is a typical tide-affected river with a length of 14 km. It drains southwest into the Deep Bay, which joins the Pearl River estuary on its seaward side. The northern catchment area of the Shenzhen River is highly urbanized. There are three WWTPs (Luofang, Binhe and Caopu) in this area, however, the wastewater treatment rate was only 74 %, and around 3.1×105 m3/d of wastewater was discharged into the Shenzhen River without treatment in 2007. In addition, the effluents from the WWTPs are considered as major pollutant sources due to the low pollutant removal efficiency of the WWTPs. For example, the average biochemical oxygen demand (BOD5) pollutant removal rate is only around 80 %, and the BOD5 load from the effluents of the WWTPs accounted for 36 % of the total BOD5 load discharged into the river from the northern catchment (EPBSZ 2007). The southern catchment area of the Shenzhen River is rural, and its pollutant load accounts for a relatively small percentage of the total pollutant load discharged into the river (EPDHK 2007). The water quality in the Shenzhen River has seriously deteriorated (EPBSZ 2007). Many engineering measures have been proposed to improve the water environment in the Shenzhen River. According to the wastewater system planning in the northern catchment (Shenzhen Urban Planning and Land Resources Bureau 2003), two new WWTPs (Shawan and Pudixia) will be built at different stages before 2020 to improve the wastewater treatment capacity (Fig. 1); and the existing WWTPs will be upgraded and provided with secondary or tertiary treatment to improve the pollutant removal efficiency, as with the two new plants. Trade-offs between the investment in WWTPs and water quality improvement


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Fig. 1 A general view of the Shenzhen River catchment

should be carefully considered in the decision making process. And use of appropriate water quality criteria, which can reflect the spatio-temporal variations of water quality, plays an important role in evaluation of the effectiveness of different wastewater treatment solutions. 2.2 Water Quality Criteria Many water quality models can be used to simulate continuous variations of river water quality with both space and time. Figure 2 gives an example of spatial and temporal distribution of water quality (BOD5) in the Shenzhen River.

Fig. 2 Spatial and temporal distribution of water quality in a river


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To reflect the variation of water quality with space or time, we propose the following water quality criteria (assuming the smaller the concentration the better the water quality). (1)

Rtj, the rate of the accumulative time with water quality violation at a prescribed reach j to the whole simulation time (T): T P

Rtj ¼

$ti d ij

i

T

ð1Þ

where d ij ¼

(2)

1; when Cij Cs 0; when Cij < Cs

Cij is the concentration of one pollutant of concern at time i and reach j; Cs is the water quality standard; Δti is the time step in model simulation. Rsi, the rate of the accumulative length of reaches with water quality violation at a prescribed time i to the whole length of a river simulated (L): L P

Rsi ¼

(3)

$lj d ij

j

L

ð3Þ

where, Δlj is a space step in model simulation. Rst, the relative frequency of the water quality violation during a T period of time for a whole river: T ;L P

Rts ¼ (4)

ð2Þ

$ti $lj d ij

i;j

T L

ð4Þ

Mst, the relative magnitude of the water quality violation during a T period of time for a whole river: T;L P

Mst ¼

$ti $lj d ij Cij Cs

i;j

T L Cs

ð5Þ

Rtj and Rsi are the traditional criteria, which can reflect the temporal variation of water quality at a specific reach and the spatial variation at a specific time, respectively. The two criteria have been widely used in previous studies. Whereas, Rst and Mst are the newly developed spatio-temporal criteria in the paper, which can consider both spatial and temporal variations of water quality in a river. The former criterion reflects the frequency of water quality violation in space or time, but the latter reflects the magnitude of water quality violation. Since BOD5 is one of the main pollutants in the Shenzhen River and it is taken as representative water quality indicator in the study. To analyze the impacts of spatiotemporal criteria on wastewater treatment optimization, 6 different criteria with varying


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spatio-temporal scales are considered as shown in Table 1. BOD-Rst and BOD-Mst are two criteria considering tempo-spatial variation of water quality against the specified water quality standards. However, BOD-Rt, mid-stream and BOD-Rt, down-stream are two criteria proposed based on temporal water quality violation at a specific reach; and BOD-Rs, flood and BOD-Rs, ebb are spatial water quality violation at a specific time. 2.3 Optimization Model 2.3.1 Multi-Objective Optimization Problem Formulation The objectives of the optimization model are to minimize the cost of wastewater treatment and minimize the frequency or magnitude of water quality violation against the specified water quality standards for the water body of the Shenzhen River. The two-objective optimization problem can be mathematically represented as follows: min F ðH; W Þ ¼ ffcost ðH; W Þ; fviolation ðHÞg H ¼ fη1 ; η2 ; ; η5 g 2 4H W ¼ fw1 ;w2 ; ; w5 g 2 4W

ð6Þ

where η1, η2, …η5 are pollutant removal rates corresponding to the 5 WWTPs in the catchment; ΩH is the feasible solution space of H, and each pollutant removal rate is considered in the range of [0.80, 0.94]; w1, w2, …, w5 are wastewater treatment types for the 5 WWTPs; ΩW is the feasible solution space of W, and Activated sludge, Oxidation ditch and A2/O are considered as the feasible treatment types in the study since the three types of wastewater treatment are widely used in China; fcost (H, W) is the function of total wastewater treatment cost; fviolation(H) is one of the water quality criteria in Table 1 and is evaluated using the water quality model. A 10 mg/l threshold is chosen for BOD5 concentrations in the case study according to the V class of Environmental Quality Standards for Surface Water in China (GB3838-2002). The same concepts could also be applied to the management of other pollutants. 2.3.2 Wastewater Treatment Cost Function The treatment cost for each plant was calculated using empirical treatment cost functions, and the total wastewater treatment cost in the catchment is simply the sum of the treatment Table 1 Criteria used for the assessment of water quality violation Name

Definition of criterion

BOD-Rst

relative frequency of BOD5 violation during a period of time (T) for a whole river

BOD-Rt, mid-stream

rate of the accumulative time with BOD5 violation at a prescribed mid-stream reach to the whole simulation time (T)

BOD-Rt, down-stream

rate of the accumulative time with BOD5 violation at a prescribed down-stream reach to the whole simulation time (T)

BOD-Rs, ebb

rate of the accumulative length of reaches with BOD5 violation at a prescribed time in ebb tide to the whole length of a river (L)

BOD-Rs, flood

rate of the accumulative length of reaches with BOD5 violation at a prescribed time in flood tide to the whole length of a river (L)

BOD-Mst

relative magnitude of BOD5 violation during a T period of time for a whole river


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cost for each plant. The treatment cost for a WWTP includes the capital construction cost and annual operation cost. However, for the sake of simplifications, we only considered the operation cost in the study and the capital cost is assumed to be the same for each plant. Generally, the cost functions are based on the treatment type, wastewater treatment quantity and pollutant removal rate. The measured data from a total of 169 WWTPs in China (Yang 2006) were used to derive the treatment cost function for each wastewater treatment type. And the power functions of the three wastewater types, Activated sludge, Oxidation ditch and A2/O, can be expressed as follows, respectively: Cost ¼ 0:298Q0:798 þ 2:85Q0:798 η1:73 BOD

ð7Þ

Cost ¼ 3:54Q0:600 þ 6:76Q0:600 η1:01 BOD

ð8Þ

Cost ¼ 2:090Q0:622 þ 7:759Q0:622 η1:64 BOD

ð9Þ

where Cost is the treatment cost (104 Yuan) of a WWTP, Q is the wastewater treatment quantity (L/s) and ηBOD is the removal efficiency of BOD5 (%). 2.3.3 Unsteady Water Quality Model In the study, the water quality criteria are evaluated by an unsteady water quality model. In this model, the Saint-Venant equation (Chanson 2004) and convection–dispersion equation (Jain and Singh 2003) are coupled as follows @A @Q þ ¼q @t @x

ð10Þ

@Q @ ðuQÞ @ @Q @Z gn2 QjQj þ " þ gA þ ¼0 @t @x @x @x @x AR4=3

ð11Þ

@C @ ðuC Þ @ @C þ Dx þ KC ¼ Sc @t @x @x @x

ð12Þ

where x is longitudinal distance; t is time; u is cross section averaged flow velocity; Q is flow discharge; q is lateral increment of discharge per unit length of x; A is cross-sectional area; Z is water level; g is gravitational acceleration, ε is effective viscosity coefficient; n is roughness coefficient; R is hydraulic radius; C is cross-section averaged concentration of specific pollutant; Dx is longitudinal dispersion coefficient; K is decay coefficient; and Sc is source intensity. The studied reach of the Shenzhen River was equally divided into 144 segments with length of 100 m for each in the model. The downstream boundary condition was given by the typical tidal stage at Tsim Bei Tsui, as shown in Fig. 1, and the upstream boundary information was obtained from the measurements of discharge and pollutant concentration. Shawan, Pudixia and Caopu WWTPs and their discharge points are located in the upper parts of the tributaries of the Shenzhen River. After the WWTP discharge and the tributary


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flow are mixed, the tributary flows into the main river. While the effluents from Luofang and Binhe WWTPs flow into the main river directly. The Preissmann scheme and upwind weighting scheme were adopted to solve the Saint-Venant equation and convection–dispersion equation, respectively. The model parameters, including the effective viscosity coefficient, roughness coefficient, longitudinal dispersion coefficient, and decay coefficient in Eqs. (11) and (12), have been calibrated by trial and error using the measured data of March 1994 (Ni and Qin 2001; Peking Univ. et al. 1995). The model was then validated against measured data of May 2004 (Qin et al. 2011). Figure 3 shows the spatial variation of BOD5 along the river. Normalized standard error for the average BOD5 in a tidal period is 3.8 %. Figure 4 shows the temporal variation of BOD5 concentrations for the May 2004 event at station A and B, and the predicted BOD5 in the two stations have normalized standard errors of 4.4 % and 5.9 %, respectively. The validation results indicated that the water quality model has the ability to simulate the spatial and temporal variation of water quality in the Shenzhen River. For simulation, typical spring tides at Tsim Bei Tsui and the mean discharge of the Shenzhen River in dry seasons were selected according to historical hydrological data. According to the data of dry seasons (from October to February), the flow of 90 % exceedance probability in the Shenzhen River is only 1.2×105 m3/d. Pollutant loads in 2007 were considered as baseline condition. And the effects of the wastewater system planning in the northern catchment on the pollutant loads were evaluated. However, for simplicity, pollutant loads from the southern catchment were considered as constant in this study. 2.3.4 Optimization Algorithm A powerful multiobjective genetic algorithm technique known as Nondominated Sorting Genetic Algorithm-II (NSGA-II) (Deb et al. 2002) is used to generate the optimal trade-offs between the objectives. In this study, each of the alternative wastewater treatment solutions (treatment type and pollutant removal rate of each WWTP) generated from the NSGA-II module is sent to the water quality simulator and the predicted spatial and temporal variations of BOD in the river are evaluated (against the BOD standard specified). The solution is also sent to wastewater treatment cost functions and the total wastewater treatment cost is estimated. Following this, the wastewater treatment solution is sent to the NSGA-II module for fitness function evaluation. After this, these solutions are sorted according to the fast nondominated approach to identify different levels of nondominated fronts. Subsequently new populations are created using the tournament selection operator Fig. 3 Measured and calculated BOD5 along the Shenzhen River in 2004


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Fig. 4 Comparison of temporal variations of measured and calculated BOD5

and crowded comparison operator. This process is repeated until the specified stopping criterion is achieved and the final set of nondominated solutions is stored in an output file. For the control optimization problem in this paper, the control parameters include five BOD removal rates and five treatment types. Recall that the BOD removal rate is constrained by an interval [0.80, 0.94] and the treatment type has three options (Activated sludge, Oxidation ditch and A2/O), so NSGA II only needs to handle box constraints, simply by sampling within the intervals. In the optimization process of the GA, we set the values of the genetic parameters to 100 for population size, 90 % for crossover and 1 % for mutation probability. We continued the converging process for 200 generations.

3 Results and Discussion In the case study, six different optimization instances are developed for the wastewater treatment optimization by considering the cost and one of the six water quality criteria in Table 1. 3.1 Optimal Solutions Under BOD-Rst (MOP1) Taken Rst of BOD5 as water quality criteria, the multi-objective optimization problem (MOP1) is defined: Minimizing total treatment cost and percentage of BOD violation during a T period of time for the whole river (BOD-Rst). The optimization results are represented by the “upside down triangles” in Fig. 5. The trade-offs between cost and BOD-Rst has different characteristics at different parts of the curve. In the upper part of the curve, BOD-Rst slowly decreases from 84 % to 70 % as the annual treatment cost increases from 103 to 107 million Yuan. The reason is that BOD5 concentrations in this part of the curve are much worse than the prescribed water quality standard for most times and reaches simulated and the increase in the annual treatment cost has little impact on BOD-Rst. However, BOD-Rst quickly decreases from 70 % to 55 % as the treatment cost increases around 107 million Yuan because BOD5 concentrations at most time and reaches are close to the water quality standard when the treatment cost approaches to 107 million Yuan. In the lower part of the curve, BOD-Rst decreases gradually from 55 % to 0 as wastewater treatment cost increases to more than 113 million Yuan. 3.2 Optimal Solutions Under BOD-Rt, mid-stream (MOP2) or BOD-Rt, down-stream (MPO3) There are two water quality monitoring points represented by A and B in Fig. 1, 7.5 km and 12 km from the upstream boundary (Sanchakou), respectively. Point A is at the middle-stream reach and B is at the down-stream reach. Thus Points A and B are used to analyze the effect of


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Fig. 5 Pareto optimal solutions from MOP1, 2 and 3

selecting different spatial points for evaluating the river water quality violation. Two sets of multi-objective optimization problems are defined: (1) Minimizing total treatment cost and BOD violation at the mid-stream reach (BOD-Rt, mid-stream), denoted as MOP2; (2) Minimizing total treatment cost and BOD violation at the down-stream reach (BOD-Rt, down-stream), denoted as MOP3. The optimization results for MOP2 are represented by the “crosses” in Fig. 5. BOD-Rt, mid-stream is 100 % when the annual treatment cost is less than 107 million Yuan. It decreases to 60 % when the treatment cost increases to 110.2 million Yuan. And then BOD-Rt, mid-stream quickly decreases to 0 % as wastewater treatment cost increases to more than 112 million Yuan. The results from MOP3, represented by the “pluses”, show that BOD-Rt, down-stream is 45 % when the annual treatment cost is 103 million Yuan. It decreases to 0 % as wastewater treatment cost increases to more than 109 million Yuan. Furthermore, to achieve the same percentage of BOD5 violation (or the same level of water quality criteria) the total treatment cost of MOP2 is much more than that of MOP3. The reason is that the river has spatial variation of water quality and the water quality in the mid-stream reach is much worse than that in the down-stream reach. The large gaps between the curves with “crosses” and “pluses” illustrate the significant impacts of water quality criteria at different locations on the optimal solutions. Likewise, at the upper and middle parts of the curves, the total treatment cost to achieve the same level of water quality criteria of MOP1 is more than that of MOP3, but less than that of MOP2, because the water quality criteria (BOD-Rst) in MPO1 reflects the average water quality during the T period of time for a whole river. However, at the lower part of the curves where the water quality criteria are less than 20 %, the Pareto optimal curve of MOP2 is better than that of MOP1 in Fig. 5. The reason is that Point A is not the worst point in the river, and the water quality in the point becomes better than the average water quality of the river when the BOD-Rt, mid-stream decreases to less than 20 %. The results indicate that when the water quality criteria are evaluated based on the water quality at a prescribed spatial


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point, the pollution may be underestimated if water quality at the prescribed check point is better than that at other points, or overestimated it if water quality at the prescribed check point is worse than that at other points. To compare the optimal solutions of MOP1, MOP2 and MOP3 using the water quality criteria with the same meanings, all the solutions in the Pareto fronts of MOP2 and MOP3 were re-evaluated using BOD-Rst, and their new criteria values in the sense of BOD-Rst were plotted and represented by the “dots” and “circles” in Fig. 5, respectively. The results indicate that at the upper parts of the curves where the BOD-Rst is more than 70 %, the solution points of MOP3 can reach the Pareto front of MOP1 but there are only several points with large gaps in the Pareto front. For MOP2, it is obvious that there is only one solution at the upper curve as is in the original MOP3 Pareto front. At the lower parts of the curves, the solution points of both MOP2 and MOP3 are worse than those of MOP1. The comparisons clearly show that the BODRst based optimization provides a better Pareto optimal front in terms of coverage and quality in solutions compared with those from the other two criteria. 3.3 Optimal Solutions Under BOD-Rs,

ebb

(MOP4) or BOD-Rs, flood (MOP5)

The Shenzhen River is influenced by the irregular mixed diurnal tide of the South China Sea with tide period of 24.8 h. Statistical analysis of tidal records at Tsim Bei Tsui indicates that the average, maximum, and minimum tidal stages are -0.15, 0.45, and -0.85 m, respectively. To analyze the effect of selecting different temporal points for checking the water quality violation, the times with maximum and minimum tidal stages were taken as the checking points during flood and ebb tide, respectively. Two sets of multi-objectives optimization problems are defined: Minimizing total treatment cost and BOD violation at ebb tide (BOD-Rs, ebb), denoted as MOP4; and Minimizing total treatment cost and BOD violation at flood tide (BOD-Rs, flood), denoted as MOP5. As shown by the curve with “crosses” in Fig. 6, BOD-Rs, ebb is 100 % when the annual treatment cost is less than 106 million Yuan. Similar to MOP1, a steep drop in water quality criteria from 95 % to 70 % is observed around 107.2 million Yuan in treatment cost. This is because BOD5 concentrations at most reaches during ebb tide are close to the water quality standard when the treatment cost is close to 107.2 million Yuan. After that BOD-Rs, ebb decreases to 0 % as wastewater treatment cost increases to more than 112.5 million Yuan. As shown by the curve with “pluses” in Fig. 6, BOD-Rs, flood is 65 % when the annual treatment cost is 103 million Yuan. It decreases to 0 % as wastewater treatment cost increases to more than 112.7 million Yuan. The large gaps between the curves with “crosses” and “pluses” illustrate the significant impacts of water quality criteria at different time periods on the optimal solutions. To achieve a certain water quality objective with percentage of BOD violation>20 %, the total treatment cost under MOP5 is less than that under MOP4. However, to achieve a certain water quality objective with percentage of BOD violation20 %, the water quality during flood tide is usually better than that at ebb tide due to the dilution effect of tide. In this case, it is cheaper to improve the water quality to the same BOD violation level during flood tide than during ebb tide. However, when the wastewater treatment rate is improved and the percentage of BOD violation