Today, one of the most important aspects of urban planning and management is the issue of environmental protection. It is necessary to consider the effects of urban development on the environment in urban planning to achieve sustainable economic and industrial development. In this paper, an optimal planning structure has been developed to reduce the pollution load of Khorramabad River, Lorestan Province, Iran. The developed fuzzy trading-ratio system was programmed based on risk-based fuzzy analysis for nine dischargers of biochemical oxygen demand (BOD5) as a water quality index and optimized using a genetic algorithm. The calibrated and verified model was utilized to simulate the BOD5 concentration at checkpoints of the river using four data sets of water quality collected from 2018 to 2021 in August (2018, 2019 and 2020 for calibration and 2021 for verification). The results showed that BOD5 exchange in the downstream stations is in critical condition. Optimization to reduce the cost of wastewater treatment showed that the proposed model could be economically improved by about 11%. The feasible domain of risk changes was assessed at three levels of 30, 60 and 90%, with the maximum value of the objective function calculated for the alcohol factory and the minimum value obtained for the flour factory.

• An optimal planning structure has been developed to reduce the pollution load using risk-based trading-ratio system.

• Multi-objective optimization has been implemented to find the fuzzy responses.

• The rate of BOD5 exchange between pollutant sources showed that location, distance and flow rate were significantly important in BOD5 exchange.

### Graphical Abstract

Graphical Abstract
Graphical Abstract

The growth of population and industries has increased the pollution load discharge beyond the self-purification capacity of the river and endangered the river ecosystem (Karasakal et al. 2020; Hatamkhani & Moridi 2021; Quan et al. 2021, 2022; Ren & Khayatnezhad 2021). Therefore, it is necessary to determine strategies to maintain environmental standards and reduce the cost of wastewater treatment (Ge et al. 2019; Moridi 2019; Chen et al. 2021; G. Li et al. 2021a, 2021b). Moreover, one of the important issues that has been considered by researchers and policy makers in recent decades is the quality management of river systems (Lindang et al. 2017; Shi et al. 2021) to make optimal use of water resources (Lalehzari et al. 2013; Wang et al. 2021, 2022; Zhu et al. 2021). A major part of the decision-making framework in the field of water resources management was dedicated to the development of quantitative-qualitative management models of river systems (Nikoo et al. 2016; Li et al. 2019; G. He et al. 2021; L. He et al. 2021). In addition, river water quality control with economic approaches is an important part of quality management and environmental issues (Hatamkhani & Moridi 2021; Tao et al. 2021).

Urban, industrial and agricultural wastewaters discharged into rivers with various pollutants are associated with adverse effects on the river ecosystem (Zhang et al. 2019a; Gholamin & Khayatnezhad 2021; Guo et al. 2021; A. Li et al. 2021). These effluents increase the suspended solids in water and drastically reduce the dissolved oxygen in the water, thereby reducing or completely disrupting the possibility of river self-purification. Sustainable water quality management should be able to measure pollutants, predict the effects of pollutants on water quality, and determine the water quality. Different studies have been conducted to evaluate the effect of pollution load on landuse (Bai et al. 2020) and river network (Zhang et al. 2019b; Liu et al. 2020). Feizi Ashtiani et al. (2015) investigated the application of the genetic algorithm method in the qualitative planning of river systems in critical situations. In this research, the quality management policies of rivers have been formulated according to objectives such as minimizing treatment costs, minimizing the total violations of river water quality standards, and equalizing the amount of pollution treatment of pollutant sources. The model proposed in this study is definite and non-seasonal and the results showed the appropriate efficiency of the genetic algorithm method in the qualitative planning of river systems. Ma et al. (2020) proposed the idea of seasonal pollution load management in river systems. The application of the linear model proposed in this method showed the importance of seasonal policies in reducing the costs of quantitative and qualitative operation of the river.

The simulation-optimization models have been widely used to optimize the waste load allocation in river systems. In a case study, the wastewater discharge volume for each pollutant source was estimated using optimization algorithms to minimize the treatment costs considering downstream water quality constraints (Saberi & Niksokhan 2017; Liu et al. 2021; L. Zhang et al. 2022). Farjoudi et al. (2021) suggested a probabilistic framework for water quality management to solve conflicts between the Environmental Protection Agency and polluters in river systems. Therefore, the model structure was simulated using QUAL2Kw and particle swarm optimization was applied to minimize the wastewater discharge. The effect of river flow uncertainty on the optimal solution was evaluated by Monte Carlo and Latin hypercube sampling (Ma et al. 2021; Xu et al. 2021; J. Zhang et al. 2022; L. Zhang et al. 2022). The results of the probabilistic model showed a reduction of 95% in waste load. Yousefi & Moridi (2022) developed a simulation-optimization model by coupling the soil and water assessment tool and non-dominated sorting differential evolution algorithm. The proposed model was implemented to increase agricultural revenue and decrease nutrient discharge to the Minab reservoir. The results of optimization showed that the total nitrogen load decreased by 70% compared to the current condition.

Moreover, application of fuzzy theory in water resources management was addressed by policy makers to find a feasible domain of responses. Mujumdar & Subbarao (2004) presented a fuzzy pollution load allocation model in which the cost functions were examined directly. But fuzzy utility functions were provided for discharge units that indirectly consider system costs. Asgari et al. (2021) developed an innovative index based on the fuzzy inference system for assessing the quality drinking waters in the Hamadan province, Iran. Results of the sensitivity analysis using fuzzy theory showed that the parameters NO3, Na, hardness, and NO2 have the most impact on the water quality index scores.

Since the pollution and environmental problems of rivers have been higher in all countries, especially in industrialized and developed countries, a major part of the studies in the field of quality management of water resources has been devoted to the development of quantitative and qualitative management models of river systems. Accordingly, in this research, the management of the river system with the approach of pollution permit clearance is studied. Moreover, considering the need for planning for the future, Iran is currently facing an environmental crisis, which doubles the importance of planning in the field of environmental protection. Today, most cities in Iran, including Khorramabad, face environmental pollution issues, including surface and underground pollution. The economic parameters resulting from the optimal utilization of the capacity to accept pollution of water resources systems and the reduction of pollution treatment costs are among the main objectives in the quality management of water resources. Optimal economic conditions in the quality management of river systems were considered between the pollution sources in the decision model. Therefore, in order to develop the decision framework, each source is assigned a permit to discharge the pollution. In this paper, a new structure for real-time pollution load in river quality management is presented so that while maintaining water quality at the desired level, the optimal trade model is presented and important uncertainties are considered.

### Simulation model

A simulation model was used to predict the behavior of the system which is divided into four stages. In the first step, the necessary information was collected and summarized to enter the calibration model. In the next step, the governing equations of the system are formulated by MATLAB programming. The model was calibrated and verified based on the collected information. Finally, it can be used to simulate the effects of different plans on the water allocation strategies.

The integration of simulation models has been widely used for the quality management of rivers. In this study, the river is first divided into several intervals, which can be divided into periods when there is a sudden change in the flow rate or quality of the river (Figure 1). Based on this classification, the desired parameters in the governing equations are calculated in each interval and are usually considered constant during it. Then the mathematical optimization equations were provided to achieve the optimal goals including the minimization of the treatment costs along with the existing constraints for the quality variables and the problem was solved with a genetic algorithm and the optimal values of the decision variables were obtained.

Figure 1

Location of Khorramabad River in Lorestan province, Iran.

Figure 1

Location of Khorramabad River in Lorestan province, Iran.

Close modal
The simulation model has been developed with emphasis on the amount of biochemical oxygen demand (BOD5). The following equation shows the flow balance in the river.
(1)
where, i = river interval number; = river discharge in i; = discharge of the sub-branch. Equation (2) is the equilibrium equation of BOD5.
(2)
where, = concentration at the beginning of i; = Concentration at the end of the range; = BOD5 concentration in the sub-branch at the beginning of i. Equilibrium equation of dissolved oxygen is obtained:
(3)
where, C = oxygen deficiency; M = oxygen deficiency at thebeginning of interval; G = oxygen deficiency at the beginning of branch i. Changes in the amount of oxygen deficiency can be written as follows:
(4)
where, kc = degradation coefficient of BOD5; k2 = aeration coefficient. To estimate the time of the critical water quality conditions (tc) in terms of dissolved oxygen concentration, Equation (5) was formulated:
(5)
Moreover, the critical oxygen deficiency, BOD5 removal equation and water treatment efficiency equations are summarized in Equations (6)–(8), respectively.
(6)
(7)
(8)
where, = the amount of critical solution oxygen deficiency; = the required treatment efficiency in the sub-branch at the beginning of the interval i; = BOD5 concentration of wastewater in the sub-branch at the beginning of the interval i.

One of the effective methods in the field of river quality management which is addressed with an economic approach, is the tradable discharge permit (TDP). In this study, the trading-ratio system (TRS) proposed by Hung & Shaw (2005) was used to trade pollution discharge permits. This system determines the TRS values by considering the rate of river self-purification and the pattern of pollutant distribution to present the optimal trade model with the application of the genetic algorithm. TRS has three main features: (1) the capacity to accept the pollution load of each area is calculated by considering the transfer load from the upstream areas; (2) trading coefficients between the regions are determined according to the transmission coefficients; and (3) TRS minimizes the cost of the entire system.

In the trading-ratio system, it is necessary to divide the river into several sections from upstream to downstream. The following steps were considered in the trading ratio framework.

The allowable discharge for each interval was determined based on the water quality standard and flow characteristics.
(9)
where, = the degradation coefficient of pollutant from k to i. Equation (10) was used under critical condition.
(10)
The objective function in the optimization model minimizes the cost required to reduce the pollution load in the system. The details of the optimization relations are as follows:
(11)
subject to:
(12)
where, = the cost of a pollution reduction for source i; = the pollutant discharge of source i after trading. In Equation (12) the first phrase on the right in this regard expresses the amount of pollution load purchased by the unit according to trade ratios. = the amount of pollution load that the source i buys from the source k. The second term on the right in Equation (12) is the amount of pollution load that the source i sells to other sources. It should be noted that upstream sources cannot receive pollution from downstream sources because the trading-ratio = 0 where i > k.

#### Uncertainty analysis

Definitive simulation models of water resources systems do not take into account the uncertainties in hydrological parameters and variables. These models are generally used for initial decisions and general comparisons between different options, and for more accurate decisions, indeterminate models should be used. Uncertain simulation models make it possible to consider the probabilistic properties of some system variables (such as river discharge and pollution loads). One of the accurate methods of uncertain simulation of water resource systems is multi-objective optimization. In this method, initial values are randomly generated for each variable and the system is established based on the non-dominated theory and genetic algorithm. The output of the proposed model is two extreme points that are obtained by maximization and minimization of the objective function.

The fuzzy model of pollution load allocation is an important component in the optimal quality management of river systems (Sun & Khayatnezhad 2021; Sun et al. 2021). These models use the basic concepts of fuzzy set theory (Zadeh 1965), fuzzy decision theory (Bellman & Zadeh 1970), fuzzy mathematical programming (Zimmermann 1978) and fuzzy resource allocation (Kindler 1992). In this paper, the risk of violating water quality standards is calculated using fuzzy set theory. The concentration levels related to low water quality are defined as the fuzzy set. Each concentration level in the fuzzy set is assigned a membership value in the range [0, 1]. Mathematically, the set is defined as follows:
(13)
The membership value indicates the concentration level corresponds to the concept of low water quality. Here, is the concentration of the dissolved oxygen (DO) variable at the station i. For the discrete mode, the fuzzy risk is determined as follows:
(14)
where is equal to the minimum and maximum concentration levels obtained from the optimization process. The fuzzy membership function is expressed as follows:
(15)
where, is the fuzzy membership function; is a non-zero positive number that shows the shape of the membership function at point l and its value can be chosen by decision makers based on their understanding of water quality according to a given value.

#### Non-dominated sorting genetic algorithm (NSGAII)

The extreme points of the feasible domain are the fuzzy responses that have been estimated by non-dominated sorting genetic algorithm (NSGAII). NSGAII is a multi-objective optimization technique developed by Deb et al. (2002) based on the domination theory and genetic algorithm. Genetic algorithms are an attractive method that have so far had limited applications in pollution load allocation problems. Genetic algorithms are especially suitable for solving multi-objective optimization problems and can easily calculate the exchange curve between different goals with one run and with acceptable computation time.

Genetic algorithms, a technique for searching for optimal solutions, were first proposed by Holland (1975). The logic behind genetic algorithms is simple. First, an initial set of solutions to the problem is created. In the next step, several superior solutions are selected and a new set of solutions is created by combining them using special operators called mutation and crossover. The selection process is usually a random process that gives a better chance of choosing better solutions. When the generation of a new population of chromosomes is complete, this set replaces the existing population. This process is repeated until a significant improvement is not observed in the best chromosome of the set.

### Description of the study area

The city of Khorramabad in Lorestan province, Iran is located at 48° 21″ longitude and 30° 43″ latitude with 35 km2 area and 1,180 m height above sea level. The northern part of the city is mountainous and the southern part has an almost plain landscape. Between the plains and valleys of the city, the width of the city is minimized and is about 1,100 m. Khorramabad River (north-south direction) passes through the city. Khorramabad River consists of two rivers, Robat and Karganeh, which are connected in the center of the city. In this paper, the general title of Khorramabad River is used for Karganeh and Robat rivers. Figure 1 shows the situation of the study area.

#### Climatic and meteorological conditions

The main source of precipitation is from the Mediterranean and the Black Sea to the plateau of Iran; it falls during autumn and winter and the effect of physiographic and climatic characteristics on this phenomenon is a determining factor in the quality-quantity (Hou et al. 2021; Huang et al. 2021; Tian et al. 2021) and temporal and spatial distribution of precipitation in the region. According to information and statistics collected from the amount of rainfall in different parts of Lorestan province, this province is among the semi-humid areas (average annual rainfall between 250 and 500 mm) in the south and humid areas (average rainfall of 500–1,000 mm) in the north of the province.

The climate of Khorramabad region is Mediterranean with mild winters and warm summers. Atmospheric precipitation often occurs in the form of rain in autumn and winter and to a considerable extent in spring, and only occasionally in winter there is a small amount of snow.

#### Hydrological conditions of the region

The Khorramabad River, which flows through the city of Khorramabad, is fed by the Karganeh, Rimla, and Bastam watersheds, located north of Khorramabad. A summary of the physiographic results for the Khorramabad River basin and Karganeh and Kaka Sharaf tributaries is shown in Table 1.

Table 1

Geographic characteristics of the study areas

Area (km2381 538 401 1,650
Perimeter (km) 100 105 100 192
Height from sea level (m) 1,751 1,692 1,697 1,676
River length (km) 20 34 36 47
Slope (%) 1.45 1.03 2.64 0.84
Area (km2381 538 401 1,650
Perimeter (km) 100 105 100 192
Height from sea level (m) 1,751 1,692 1,697 1,676
River length (km) 20 34 36 47
Slope (%) 1.45 1.03 2.64 0.84

Quantitative and qualitative study of river water requires knowledge of changes and fluctuations in the amount of water in different months of water shortage (July, August and September) and waterlogging (January, February and March). To know the causes of these fluctuations, it is necessary to study the water sources that recharge the river, including springs and runoff along with the factors affecting these fluctuations. The main water consumption of Khorramabad River is divided into four categories: agricultural, industrial, urban and rural consumption. The average, maximum and minimum annual discharges of this station are 11.5, 19.2 and 5.6 m3/s, respectively. The average annual discharge of the Karganeh River is reported to be 4.9 m3/s.

#### Water pollutants

Pollutants entering the Khorramabad River are divided into three categories: urban, agricultural and industrial. Urban and industrial pollutants can affect river water quality from point and non-point sources. Urban and industrial wastewaters are called point sources because they are collected through a network through a pipe or canal and discharged into a river from one point. In general, point pollution sources can be treated by proper treatment of wastewater before discharge into the river. Moreover, wastewater and agricultural runoff that is discharged into the river from a number of points are known as non-point sources.

Rivers are one of the important sources of water supply in a natural ecosystem. Therefore, it is necessary to identify the sources of their contaminants. In general, any factor to the extent that it changes the quality of water and causes it not to be used for its specific use, has created water pollution. Therefore, a water can be considered polluted when the amount of the substance or its pollutants in terms of consumption is more than the allowable international or regional standards.

#### Industrial pollution sources

Khorramabad city is considered as a semi-industrial city with 28% of all industries in Lorestan province. A large number of small and large industrial units are located around and near the Khorramabad River and along its route, which directly and indirectly cause its pollution. Some industries discharge wastewater directly into the river, while others discharge it into the river after incomplete treatment. In this paper, combined samples were prepared and analyzed from the pollutant sources of nine important industries whose wastewater now enters the river (with or without treatment). The results of pollution analysis of these pollutant sources are listed in Table 2.

Table 2

Water quality parameters of pollutant sources

Pollution sourcespHTemperatureTurbidityECBOD5CODTSS
CNTUμS/cmmg/Lmg/Lmg/L
PS1 Fish farming 7.1 28 84 485 148 1,950 1,100
PS2 Parsylon company 7.1 21 31 512 129 2,750 1,128
PS3 Flour factory 6.2 19 52 2,320 195 1,150 1,510
PS4 Cheese factory 6.5 21 452 549 165 295 620
PS5 Industrial town 7.8 19 38 810 362 1,270 1,052
PS6 Milk factory 6.9 20 25 620 89 160 412
PS7 Refrigerator factory 7.1 20 32 1,280 89 192 682
PS8 Agro-industry Company 6.2 17 23 1,250 95 182 921
PS9 Alcohol factory 51 >1,000 41,200 42,000 60,500 2,400
Pollution sourcespHTemperatureTurbidityECBOD5CODTSS
CNTUμS/cmmg/Lmg/Lmg/L
PS1 Fish farming 7.1 28 84 485 148 1,950 1,100
PS2 Parsylon company 7.1 21 31 512 129 2,750 1,128
PS3 Flour factory 6.2 19 52 2,320 195 1,150 1,510
PS4 Cheese factory 6.5 21 452 549 165 295 620
PS5 Industrial town 7.8 19 38 810 362 1,270 1,052
PS6 Milk factory 6.9 20 25 620 89 160 412
PS7 Refrigerator factory 7.1 20 32 1,280 89 192 682
PS8 Agro-industry Company 6.2 17 23 1,250 95 182 921
PS9 Alcohol factory 51 >1,000 41,200 42,000 60,500 2,400

EC, electrical conductivity; COD, chemical oxygen demand; TSS, total suspended solids.

##### Fish farming

Fish farming is one of the sources of river pollution, the details of which are summarized in Table 2 and Figure 2 (shown as PS1). The volume of wastewater produced in the salmon pond is about 310 m3/day. This volume of wastewater is discharged directly upstream of the fish pond and no wastewater treatment process takes place.

Table 3

Quantities and quality of Khorramabad River in August 2020

Source noRiver
Discharger
DO (mg/l)BOD5 (mg/l)V (m/s)Q (m3/s)Q (m3/day)BOD5 (mg/l)T °C
PS1 5.20 6.38 2.70 45 48,000 51
PS2 3.80 9.88 2.60 3.9 775 129 21
PS3 4.20 9.47 2.59 3.8 200 195 19
PS4 4.00 9.88 2.50 3.85 1.5 165 19
PS5 3.50 9.26 2.10 3.6 36 362 21
PS6 4.50 7.82 2.24 3.65 250 89 20
PS7 4.70 9.88 2.31 3.7 37 89 20
PS8 5.00 7.00 2.67 3.95 110 95 17
PS9 4.80 11.93 2.46 3.75 150 42,000 51
Source noRiver
Discharger
DO (mg/l)BOD5 (mg/l)V (m/s)Q (m3/s)Q (m3/day)BOD5 (mg/l)T °C
PS1 5.20 6.38 2.70 45 48,000 51
PS2 3.80 9.88 2.60 3.9 775 129 21
PS3 4.20 9.47 2.59 3.8 200 195 19
PS4 4.00 9.88 2.50 3.85 1.5 165 19
PS5 3.50 9.26 2.10 3.6 36 362 21
PS6 4.50 7.82 2.24 3.65 250 89 20
PS7 4.70 9.88 2.31 3.7 37 89 20
PS8 5.00 7.00 2.67 3.95 110 95 17
PS9 4.80 11.93 2.46 3.75 150 42,000 51

DO, dissolved oxygen; V, velocity; Q, flow discharge; T, temperature.

Figure 2

Chemical parameters measured in the pollutant sources.

Figure 2

Chemical parameters measured in the pollutant sources.

Close modal
##### Parsylon company

Parsylon produces 13,500 tonnes/year of nylon yarn and has 1,450 workers. A residential town has also been established near Parsylon Company, which currently has a population of 500 people. The amount of industrial wastewater produced in this factory is 650 m3/day, which is treated with human wastewater from the factory as well as human wastewater from a residential town in an activated sludge system. The amount of human wastewater is 125 m3/day. In total, the capacity of the wastewater treatment system is 775 m3/day and an average of 32 m3/h of wastewater enters the system.

##### Flour factory

Due to the development of Khorramabad, the flour factory is located inside the city. The volume of wastewater produced by the factory is 200 m3/day of industrial and human wastewater. The wastewater is directly discharged in the Khorramabad River.

##### Milk factory

This factory is located at the beginning of Khuzestan road and produces 75 tonnes of various dairy products daily. Lorestan Milk Factory produces 250 m3/day of industrial wastewater. This amount of wastewater, in addition to the staff wastewater, enters an aerobic and anaerobic lagoon system. Due to the nature of the wastewater, and the active units in the production of dairy products which are highly polluting, if it is not properly treated, it will be one of the important sources of water and soil pollutants. The results of the chemical analysis of the effluent of Lorestan milk factory are listed in Table 2.

##### Refrigerator factory

The amount of wastewater produced in Lorestan Refrigeration Factory is 12 m3/day of human wastewater and 25 m3/day of industrial wastewater, which are treated in two separate systems. Human wastewater is treated in a continuous sludge system with continuous aeration and then discharged into the Khorramabad River. In an industrial wastewater treatment system, oil and grease emulsions are first broken down and separated into floating materials. Suspended materials in the effluent are separated by coagulation and precipitation, and finally the effluent is discharged into the environment after chemical treatment.

##### Industrial town

This pollutant source (PS5 in Table 2), which is located in the south of Khorramabad city, produces about 1.5 m3 of human wastewater with a daily consumption of 2 m3 of water, which is treated in a wastewater treatment system using activated sludge method.

##### Industrial white cheese

The volume of wastewater of 36 m3 was daily produced in the industrial white cheese factory, which was discharged in the agricultural lands without treatment and then it is a pollutant source of Khorramabad River.

##### Agro-industry company

The volume of wastewater produced by this complex is about 110 m3/day. More details of the wastewater quality have been summarized in Table 2.

##### Alcohol factory

The volume of wastewater produced by the alcohol factory is about 150 m3/day. About 45 m3/day of sewage with very high pollution load enters Khorramabad River without any treatment.

##### Human (urban) contaminant resources

Khorramabad River is located in the thalweg elevation of Khorramabad city and due to the considerable slope, all residential sewage of this city flows into this river. The main sources of urban pollution in the Khorramabad River include solid and liquid wastes that are discharged from residential areas into this river. There are many residential complexes around Khorramabad River and along its route from Robat village to Cham Anjir, which pollute the river in various ways such as discharging human sewage into the river (both directly and indirectly), runoff, washing clothes, etc.

Unfortunately, accurate and reliable statistics on human wastewater discharged into the river are not available. Therefore, the amount of produced wastewater and BOD5 wastewater of the studied cities and villages have been estimated with the help of per capita wastewater. The water consumption per capita in Khorramabad city is estimated as about 260 liters per person per day. About 12–17% of this amount is wasted on green space irrigation, laundry, air conditioners, etc. and 13–18% is wasted in the water supply network. The wastewater production per capita is assumed to average 220 liters per person per day.

One of the most important aspects of wastewater pollution is the presence of organic matter. Because these substances are unstable, they become stable mineral substances by absorbing oxygen and oxidation. In order to determine the exact amount of municipal sewage pollution, it is necessary to have a sewage collection network, which is not possible in the city of Khorramabad. Organic load and other characteristics of urban wastewater can sometimes not be the same even for different cities of one country and depend on the type of nutrition, health and cultural conditions, customs and other factors. According to studies conducted by consulting engineers for water and wastewater design and research, the per capita amount of BOD5 is estimated at about 45 grams per day per person. Depending on the population, the average amount of BOD5 and its weight can be obtained. The per capita amount of suspended solids in municipal wastewater in Khorramabad city is estimated by water and wastewater consulting engineers to be about 1.15 times BOD5. Therefore, the per capita amount of suspended solids is estimated at 52 grams per day per person.

### Water quality of river

The efficiency of the proposed model was evaluated using quantitative and qualitative case information of Khorramabad River. The study area includes part of this river with a length of about 45 km that passes through Khorramabad city. Pollutant sources in the study area include six non-point sources and nine point sources that discharge wastewater from Khorramabad into the river. The study area was divided into 27 areas. This division was done so that there was only one discharge source in each area.

Qualitative and quantitative parameters of the river and pollutant sources are summarized in Table 3. The velocity and flow rate of the river are almost the same in different stations. Furthermore, the concentration of BOD5 in the river is significantly different from that of the pollutant sources. The highest pollutant volumes are from PS2 and the highest pollutant concentrations are from PS1 and PS9.

### Validation and calibration of river simulation model

The BOD5 concentration in the river was simulated using the Streeter–Phelps equation (Streeter & Phelps 1925). Calibration of BOD5 degradation coefficient and river aeration coefficient was performed along the river and in order to minimize the difference between the calculated BOD5 and the predicted values with three data sets for calibration (August 2018–2020) and one data set for verification (August 2021). Graphical results of calibration and verification showed that the simulated BOD5 values were acceptable for the river. Furthermore, the following error coefficients are used to evaluate the model, the results of which are summarized in Figure 4. To evaluate the accuracy of simulation, four evaluation parameters were used including root mean square error (RMSE) (Equation (16)), mean absolute error (MAE) (Equation (17)), the percentage of bias (PBIAS, Equation (18)), and Nash–Sutcliffe (NS) (Equation (19)).
(16)
(17)
(18)
(19)
where, os and om are the simulated and measured values of water quality, respectively, n is the number of pollutant sources and i is the station number of the river. A comparison of these criteria is shown in Figure 3. The results of both simulations have the necessary reliability to predict.
Figure 3

Evaluation indicators of calibration/verification process for BOD5 (mg/l).

Figure 3

Evaluation indicators of calibration/verification process for BOD5 (mg/l).

Close modal
Figure 4

Minimum and maximum costs corresponding to different treatment percentages.

Figure 4

Minimum and maximum costs corresponding to different treatment percentages.

Close modal

### Treatment cost analysis

One of the effective parameters in pollution load allocation models is pollution load treatment costs. Due to the inaccuracy in calculating the cost functions of pollutants and considering that the estimation of cost functions has complexities, in this study using fuzzy regression of uncertainties in estimating cost functions was examined. In this paper, due to the nonlinearity of the cost functions of the pollutants, the cost functions were estimated using fuzzy nonlinear regression. In classical linear regression, for each series of input variables, only a specific value is calculated for the output variable, while fuzzy regression estimates the range of possible values for the output variable. These values are determined by a possible distribution that is represented by membership function. Therefore, unlike the usual regressions that attribute the difference between the measured values and the estimated values to the model error, in fuzzy regression this difference is related to the degree of fuzziness. Nonlinear fuzzy regression was first introduced by Guo & Tanaka (2006) and includes the following steps:

First, a polynomial function was considered with the following general form for the regression output function, which is called the optimal function:
(20)
where, Y(x) = a fuzzy output function, x = certain input variable, n = the degree of the proposed function, which is initially considered to be one, and Ai is a fuzzy number with a triangular membership function whose center is a, and whose amplitude of change is twice ci.
Therefore, maximization and minimization of the following should be considered as two objective functions in NSGAII model.
(21)
(22)
where, are the values of the primary data on which the regression is based. is a certain number and is defined as a domain. The value of is calculated according to Equation (22). m is the number of initial data used for regression. From solving the above optimization problem, the variables of the problem are ai, Ci.

It should be noted that if these equations have a solution, the objective value is zero (J = 0), which is proved in Guo et al. (2022). Therefore, at first assume that the appropriate function is linear and n = 1. If no response is found for the equations, a unit is added to the degree of the proposed function and the optimization equations are solved again. This process continues until a solution is found for the optimization equations.

By specifying the general form of regression, the following relationships are optimized:
(23)
(24)

Basic information is needed to estimate cost functions using fuzzy regression. The cost corresponding to the percentage of pollution treatment, 30, 60 and 90%, was obtained from different factories. To calculate the minimum and maximum cost of each unit, a minimum value of 0.85 was calculated and a maximum value of 1.15 times the calculated cost was considered.

#### Fuzzy responses of treatment cost

Three levels of 30, 60 and 90% were defined for wastewater treatment at each pollutant source and the fuzzy responses of the developed model were compared for minimum and maximum costs. Figure 4 compares the range of cost fuzzy changes based on the mentioned criteria. Alcohol factory and Parsylon Company have the most changes, respectively. The results showed that fuzzy analysis was able to estimate the potential risk for economic evaluation of projects. The economic risk obtained from fuzzy simulation is 30.2%.

#### Estimating the coefficient of the fuzzy extended trading-ratio system

Fuzzy trading-ratio coefficients () for each interval, Ei and initial fuzzy numbers of have been calculated using the calibrated model and the proposed fuzzy extended trading-ratio system (FETRS) formulation as shown in Figure 5 and Table 4, respectively. Moreover, the values of the fuzzy triangular numbers αi obtained by fuzzy regression are shown in Table 5.

Table 4

Treatment efficiency and allowable discharge for different pollutant sources

Interval no.123456789
2.46 2.30 2.38 2.10 1.10 2.76 2.87 3.10 3.54
19.3 53 8.5 12.7 16.45 6.8 11.4 9.7
Interval no.123456789
2.46 2.30 2.38 2.10 1.10 2.76 2.87 3.10 3.54
19.3 53 8.5 12.7 16.45 6.8 11.4 9.7
Table 5

Fuzzy coefficient of the triangular membership for cost function

Cost function coefficientDischarger number
2.02 2.25 10.7 3.64 8.36 7.02 16.4 4.42 16.9 15.8
1.41 1.57 7.46 2.54 5.64 4.64 11.5 2.98 11.4 9.75
Cost function coefficientDischarger number
2.02 2.25 10.7 3.64 8.36 7.02 16.4 4.42 16.9 15.8
1.41 1.57 7.46 2.54 5.64 4.64 11.5 2.98 11.4 9.75
Figure 5

Fuzzy trading-ratio coefficients () for different intervals.

Figure 5

Fuzzy trading-ratio coefficients () for different intervals.

Close modal

After obtaining the optimal trading model by TRS, the wastewater treatment cost before and after trading was compared (Table 6). The results showed that the application of the risk-based extended trading-ratio model can reduce the cost of water treatment by more than 11%.

Table 6

Comparison of the wastewater treatment costs

Total cost (US$)Cost reduction (%) Before trading 352 Risk-based trading 313 11.2 Total cost (US$)Cost reduction (%)

### BOD5 exchange

The rate of BOD5 exchange between pollutant sources is shown in Figure 6. The results showed that location, distance and flow rate were significant in BOD5 exchange. Industrial towns have not played an effective role in increasing BOD5 exchange due to pollution control. Point pollutant sources can affect the flow of pollution in a shorter time and more quickly. The end part of the river (PS6, PS7, PS8, and PS9 in Figure 6) has more complex conditions for BOD5 pollutants and especially the location of the alcohol factory at the end of the network has increased the concentration of pollutants in the downstream rural areas.

Figure 6

BOD5 exchange between pollutant sources.

Figure 6

BOD5 exchange between pollutant sources.

Close modal

The effort of the last decade to explain sustainable development highlights the need for all countries to recognize the sustainability and protection of environmental resources. This research has developed a fuzzy risk-based method for allocating pollution load from nine pollutant sources of Khorramabad River. BOD5 concentration was considered a water quality index. The results showed that the developed trading-ratio model was able to determine the optimal amount of wastewater discharge according to the flow conditions and the BOD5 concentration as the main constraints. Furthermore, the application of the maximum and minimum uncertainty model predicted the probability of each event based on the feasible domain. The results of this forecast can determine the maximum risk available for each strategy and give the choice to the decision model. The economic evaluation of wastewater treatment showed that in the proposed model, treatment costs will be reduced by at least 11%. An important consequence of this study is the development of a decision model that can be used for other chemical contaminants as well. Future research can be developed in the form of a probabilistic prediction model to involve different river flow regimes in the decision-making process. To create a sustainable model of water management in this region, it is necessary to link the developed model in to the structure of an agricultural water allocation system based on land use improvement.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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