An Optimization Model for Water Management Based on Water Resources and Environmental Carrying Capacities: A Case Study of the Yinma River Basin, Northeast China

: In this study, an inexact two-stage stochastic programming (ITSP) model was developed for supporting water resources allocation for the four main water use sectors (industry, municipal, environmental, and agriculture) and total amount control of the pollutant emissions. The Yinma River Basin in northeast China was selected for a case study. A number of scenarios corresponding to different ﬂow levels were examined. The ﬂow levels reﬂect different probabilities of water resource availability and environmental carrying capacity. The results revealed that the optimal allocation strategies for each sector depend on water resource carrying capacity, wastewater treatment capacity, the total amount of regional control, and the water environment carrying capacity. Water ecology projects were identiﬁed that are needed to treat contaminated water and to address the insufﬁcient carrying capacity for pollutant emissions generated in water-using processes. The results will be helpful for establishing sensible water management systems that integrate the development and utilization of water resources and protect the environment, and for providing a basis for water pollution prevention plans, the model can be used to guide management interventions to improve the water environment by regional pollutant emission control and the improvement of carrying capacity in the Yinma River


Introduction
Water resources play an essential role in human survival, sustainable socioeconomic development, and the eco-environment [1]. However, as a result of rapid population growth and socioeconomic development, excessive exploitation of water causes severe shortages of water resources and the destruction of water ecosystems, especially in water-stressed areas [2,3]. At the same time, wastewater discharge leads to the deterioration of the water environment quality, creating further water resource problems [4,5]. In addition, there are many uncertainties in the water environment system, such as the variability in the availability of water resources, variability in the development of technology, variability of demand, and the complexity of the interconnected processes (e.g., water utilization, recycling, wastewater treatment, and discharge) [6]. In practice, these uncertainties generate enormous challenges for water resources allocation and water quality management. Therefore, effective optimization approaches to water management in complex, uncertain conditions are necessary. Water management issues that need to be optimized include water resources allocation and utilization, water quality management, environmental protection, and regional development.

Study Area
The Yinma River (43°14′-44°53′ N, 125°30′-126°15′ E) is located in the central part of Jilin Province, China. The river originates in Panshi County and flows through Shuangyang District, Yongji County, Jiutai District, and Dehui City, before flowing into the Second Songhua River, after the junction with the Yitong River in Nong'an County. The river has a total length of 387.5 km, and the Yinma River Basin has an area of more than 8056 km 2 (this does not include the Yitong River) [41].
In this study, in order to clearly reflect different water environmental functions, and relationships between water utilization, pollutants generation, and discharge directions, the Yinma River Basin was divided into 11 water environment zones (i = 1-11 represent I, II, III, IV, V, VI, VII, VIII, IX, X, and XI) and eight administrative regions (j = 1-8 represent Panshi, Yongji, Shuangyang, Jiutai, Dehui, Yitong, Changchun, and Nongan). The zones and regions are shown in Figure 2. Table 1 lists the relationships between regional pollutant emissions and receiving water, including pollutant emission directions and proportions. The values show the proportion of pollutant emissions generated from region j and discharged into the water environment zone i.

Study Area
The Yinma River (43 • 14 -44 • 53 N, 125 • 30 -126 • 15 E) is located in the central part of Jilin Province, China. The river originates in Panshi County and flows through Shuangyang District, Yongji County, Jiutai District, and Dehui City, before flowing into the Second Songhua River, after the junction with the Yitong River in Nong'an County. The river has a total length of 387.5 km, and the Yinma River Basin has an area of more than 8056 km 2 (this does not include the Yitong River) [41].
In this study, in order to clearly reflect different water environmental functions, and relationships between water utilization, pollutants generation, and discharge directions, the Yinma River Basin was divided into 11 water environment zones (i = 1-11 represent I, II, III, IV, V, VI, VII, VIII, IX, X, and XI) and eight administrative regions (j = 1-8 represent Panshi, Yongji, Shuangyang, Jiutai, Dehui, Yitong, Changchun, and Nongan). The zones and regions are shown in Figure 2. Table 1 lists the relationships between regional pollutant emissions and receiving water, including pollutant emission directions and proportions. The values show the proportion of pollutant emissions generated from region j and discharged into the water environment zone i.   Table 1. Relationships between regional pollutant emission and receiving water.

Model Development
This study considers long-run programming. The planning horizon covers 15 years with five years per period (i.e., 2016-2020, 2021-2025, and 2026-2030), and has three scenarios for flow levels (low, medium, and high), reflecting different probabilities of available water resources and water environmental carrying capacities. The applicability of the engineering improvements differed in different water environment zones and necessitated an adjustment in the initial allocation of water resources, to balance pollutants amount discharged into the rivers and water environmental carrying capacities. The ITSP method is considered suitable for addressing the local issues. The inexact, two-stage, stochastic  Table 1. Relationships between regional pollutant emission and receiving water.

Water Zones
Administrative Regions

Model Development
This study considers long-run programming. The planning horizon covers 15 years with five years per period (i.e., 2016-2020, 2021-2025, and 2026-2030), and has three scenarios for flow levels (low, medium, and high), reflecting different probabilities of available water resources and water environmental carrying capacities. The applicability of the engineering improvements differed in different water environment zones and necessitated an adjustment in the initial allocation of water resources, to balance pollutants amount discharged into the rivers and water environmental carrying capacities. The ITSP method is considered suitable for addressing the local issues. The inexact, two-stage, stochastic programming model for integrating engineering technologies and water resources allocation in the Yinma River Basin can be formulated as follows: where f ± is the total expected system benefit (10 4 RMB) over the planning periods.
(1) Water utilization benefits where j denotes the controlling administrative region; k denotes the water use sectors (k = 1 for industry, k = 2 for municipal, k = 3 for the environment, and k = 4 for agriculture); t denotes different periods in the planning horizon (t = 1 is 2016-2020, t = 2 is 2021-2025, and t = 3 is 2026-2030); L t denotes length of period t, and the values are fixed at 5 years; NB ± jkt represents water-use benefit for each sector k in region j (10 4 RMB/10 4 m 3 ); W ± jkt represents pre-allocation of water resources for sector k during period t in region j (10 4 m 3 /year); and RW ± jkt represents reused water resources for sector k during period t in region j (10 4 m 3 /year).
(2) Water shortage penalty where h denotes various scenarios of runoff in every period (h = 1, 2, and 3 for low, medium, and high levels, respectively); p h denotes the occurrence probability of scenario h; PNB ± jkt represents the reduction of net benefit to sector k per unit of water resource not delivered (10 4 RMB/10 4 m 3 ); and DW ± jkth represents the allocation deficit of water resources for sector k during period t in region j under scenario h (10 4 m 3 /year).
(3) Water supply cost where CW ± jkt represents the costs of water supply of sector k during period t in region j (10 4 RMB/10 4 m 3 ); and CRW ± jkt is the cost of reused water supply for sector k during period t in region j (10 4 RMB/10 4 m 3 ).
(4) Wastewater treatment cost Water 2018, 10, 565 6 of 21 where CWW ± jkt represents the costs of wastewater treatment for sector k during period t in region j (10 4 RMB/10 4 m 3 ); CRWT ± jkt denotes the costs of wastewater reclamation for sector k during period t in region j (10 4 RMB/10 4 m 3 ).
(5) Environmental capacity improvement cost where i is the water environment zone; l is the engineering required for carrying capacity improvement (l = 1, 2, 3, 4, 5, 6, and 7 are wetland, ecological floating bed, ecological corridor, pre-tank construction, conservation forest, dredging engineering, and artificial aeration, respectively); EQ ± ilt is the quantity of engineering l in zone i during period t; CER ± ilt is the cost of engineering l in zone i. Constraints: (1) Water supply constraints where AWQ ± th denotes available water resources under scenario h during period t (10 4 m 3 /year). (2) Demand constraints of water use sectors where WD ± minjkt represents the minimum water resources requirement of sector k during period t in region j (10 4 m 3 /year); and WD ± maxjkt represents the maximum water resources requirement of sector k during period t in region j (10 4 m 3 /year).
(3) Regional wastewater treatment capacity constraints where α jkt is the wastewater emission coefficient for sector k during period t in region j; β jkt is the wastewater concentration treatment coefficient for sector k during period t in region j; and ATW ± jkt represents the wastewater treatment capacity of sector k during period t in region j (10 4 tons).
(4) Regional wastewater reuse capacity constraints where ξ jkt is the wastewater reuse rate of sector k during period t in region j.
(5) Constraints for the total emissions of water pollutants Water 2018, 10, 565 where r is the controlled water pollutant (r = 1 for chemical oxygen demand (COD), r = 2 for ammonia nitrogen (NH 4 -N)); EC ± krt represents the concentration of pollutant r after wastewater treatment by sector k during period t (mg/L); SC ± krt represents the concentration of pollutant r without treatment from sector k during period t (mg/L); and TED ± jrt represents the total amount of pollutant r during period t in region j (tons).
(6) Water environment carrying capacity constraint where IDR krt represents the river load ratio of pollutant r from sector k during period t; X ij is the receiving ratio of water zone i from region j; EER ± ilrt is the improvement in the carrying capacity for pollutant r by engineering l in zone i during period t; ER ± ilt is the maximum quantity constraint for engineering l in zone i during period t; and ALD ± irth is the carrying capacity (tons) of pollutant r in zone i during period t under scenario h.

(7) Engineering constraints for carrying capacity improvement
The objective is to maximize the total system benefit in the river basin, which includes the related benefit from the water use sectors under the pre-allocation of water resources; the penalties when the permitted allocation is not delivered; and the cost of water supply, wastewater treatment, wastewater reclamation, and engineering to improve the water environment carrying capacity. The constraints are for the relationships between decision values and water quality requirements, including the available water resources, regional total amount controlled, water carrying capacity, and ecological engineering.
Using an interactive algorithm, the ITSP model can be transformed into two deterministic sub-models that correspond to the lower and upper bounds of the desired objective function value. By solving the two sub-models, DW − jkth , RW + jkt , EQ − ilt and DW + jkth , RW − jkt , EQ + ilt were obtained and formed the final solution of the ITSP model as Table 2 lists the initial water resources allocation strategies in the Yinma River Basin; these were determined based on the latest 10 years of regional water resource consumption in each sector and on development planning for the river basin. Table 2. Initial water resource allocation in the Yinma River Basin (10 4 m 3 /year).

Regions
Departments Periods  Table 3 lists the optimal water resources pre-allocation for the Yinma River Basin. The table indicates that the optimal allocation is close to the lower boundary of the initial water resource allocation-a result of the higher water shortage probability, and because a lower pre-allocation would be more reasonable for different water use sectors and would lead to lower penalties caused by water resource deficits [22].  show the reused water allocation for the industrial, municipal, and environment sectors. Figure 3 indicates different tendencies for reused water allocation for industry in the three periods. In Regions 2, 4, and 8 the allocations of reused water increase gradually over time because of higher water consumption and reuse rates. For example, in Region 2, the amounts were 951 × 10 4 , 1085 × 10 4 , and 1225 × 10 4 m 3 /year in three periods. However, in Regions 1 and 7, the amounts of reused water show an opposite trend; the values are 368.8 × 10 4 , [237.3, 297.2] × 10 4 , [20.1, 220.7] × 10 4 m 3 /year, and 1022 × 10 4 m 3 /year, 0, and 0, in three periods, respectively. There are two reasons for this trend: (1) the water resources pre-allocation was obtained that was close to the maximum water resource requirements; and (2) more water consumption results in more wastewater generation, which would be constrained by wastewater treatment capacity. For these reasons, higher pre-allocations of water resources might lead to wasting of water resources. Figures 4 and 5 show reused water allocations for the municipal and environment sectors, all of which were generated by the municipal sector. From these figures, it can be seen the amount of the reused water allocation for the two sectors has clear differences. The amount of reused water allocated to the environment sector increased gradually over time, which is the opposite of the municipal sector. The main reason for this trend is that the environment sector generates more benefits through water consumption and has a higher water requirement; when the water resource allocation meets the minimum water resource requirement, more reused water was allocated to the environment sector. Table 3. Optimal water resource pre-allocations for the Yinma River Basin (10 4 m 3 /year).

Regions
Departments Periods consumption and has a higher water requirement; when the water resource allocation meets the minimum water resource requirement, more reused water was allocated to the environment sector.   Water 2018, 10, x FOR PEER REVIEW 9 of 20 consumption and has a higher water requirement; when the water resource allocation meets the minimum water resource requirement, more reused water was allocated to the environment sector.      Figure 6 show emissions of the main pollutants (COD and NH 4 -N) during the study periods. These figures indicate that emissions of the two pollutants generally decreased over time and were influenced by optimal water resource allocation and by control of total regional pollution. For example, in Region 7, from Period 1 to 3, the amount of COD emissions were 5365.  4 -N values were the same. The main reason for this trend might be that low industrial water use efficiency, and high generation and discharge coefficients lead to increased pollutant emissions in these regions. Additionally, the results show that in the Yinma River Basin, agricultural non-point pollution is the main source of pollution, and far exceeds pollution from other sources. However, in Region 7, the industrial sector was the largest source of NH 4 -N, and it was clearly different from the other regions. The explanation for this is that the economy in Region 7 is dominated by industry with high NH 4 -N emissions.     For the purpose of water environment protection, pollutant quantities discharged into the river should not exceed the environmental carrying capacity. Figures 7 and 8 show the relationships between pollutant emission load and environmental carrying capacity for COD and NH 4 -N, respectively. The figures reveal that the amounts of pollutant discharged into the river decreased over time, because of reductions in regional pollutant emissions. However, the amounts were still far in excess of the environmental carrying capacities. For example, in Zone 9, the amounts of COD discharged into the river were [6638.2, 6812.7], [6196.2, 6376.0], and [5625.4, 5982.0] tons/year in three periods, which was much more than the carrying capacities of 2610.0, 2370.0, and 2130.0 tons/year. Only in Zone 10 were the pollutant amounts less than the carrying capacity. In general, there was a large imbalance between the amounts of pollutants and the environmental carrying capacities. To increase the water environment safety of the Yinma River, improvements to the water environment carrying capacity should be carried out in addition to pollutant emission reduction.  For the purpose of water environment protection, pollutant quantities discharged into the river should not exceed the environmental carrying capacity. Figures 7 and 8 show the relationships between pollutant emission load and environmental carrying capacity for COD and NH4-N, respectively. The figures reveal that the amounts of pollutant discharged into the river decreased over time, because of reductions in regional pollutant emissions. However, the amounts were still far in excess of the environmental carrying capacities. For example, in Zone 9, the amounts of COD discharged into the river  .0] tons/year in three periods, which was much more than the carrying capacities of 2610.0, 2370.0, and 2130.0 tons/year. Only in Zone 10 were the pollutant amounts less than the carrying capacity. In general, there was a large imbalance between the amounts of pollutants and the environmental carrying capacities. To increase the water environment safety of the Yinma River, improvements to the water environment carrying capacity should be carried out in addition to pollutant emission reduction.  Table 7 lists the strategies and quantities of ecological engineering for improving the water environment carrying capacity of the Yinma River. Figures 9 and 10 show the improvements in COD and NH4-N carrying capacities, respectively. These engineering projects would not be suitable for each water zone, and the quantities are constrained by the environmental conditions, resulting in different projects in different water zones. Zone 1 is the furthest upstream zone of the Yinma River and has few non-point agricultural pollutant emissions and has good water quality. Consequently, the engineering of wetlands and conservation forests would be selected, with areas of [13,16]  t=1 t=2 t=3 t=1 t=2 t=3 t=1 t=2 t=3 t=1 t=2 t=3 t=1 t=2 t=3 t=1 t=2 t=3 t=1 t=2 t=3t=1 t=2 t=3 t=1 t=2 t=3 t=1 t=2 t=3 t=1 t=2 t=3

Water Environment Carrying Capacity Improvement
Carrying  Table 7 lists the strategies and quantities of ecological engineering for improving the water environment carrying capacity of the Yinma River. Figures 9 and 10 show the improvements in COD and NH 4 -N carrying capacities, respectively. These engineering projects would not be suitable for each water zone, and the quantities are constrained by the environmental conditions, resulting in different projects in different water zones. Zone 1 is the furthest upstream zone of the Yinma River and has few non-point agricultural pollutant emissions and has good water quality. Consequently, the engineering of wetlands and conservation forests would be selected, with areas of [13,16] ha and [60, 70] ha, and capacity improvements of 310 and [42. 5, 43.5] tons/year for COD and NH 4 -N, respectively. In Zone 3, pre-tank construction should be carried out to meet the water quality target of the lower reservoir, and dredging engineering should be carried out to improve the contaminated water quality of the river, with volumes of [0, 25] × 10 4 m 3 . Zone 6 is the main pollutant receiving water body of Region 5 and has a severely contaminated status. To address the pollution in Zone 6,[140,150]    These projects that aim to improve water environment carrying capacity would not only reduce the pollutant overload, but also improve and restore the ecological environment in the Yinma River. Figures  11 and 12      These projects that aim to improve water environment carrying capacity would not only reduce the pollutant overload, but also improve and restore the ecological environment in the Yinma River. Figures  11 and 12     These projects that aim to improve water environment carrying capacity would not only reduce the pollutant overload, but also improve and restore the ecological environment in the Yinma River. Figures 11 and 12 Figure 11. Surplus COD carrying capacity for the Yinma River.

Water Environment Carrying Capacity Improvement
Lower bound Upper bound Surplus carrying capacity of NH 4 -N: tons/year Figure 11. Surplus COD carrying capacity for the Yinma River.   Water Units Projects l = 1 l = 2 l = 3 l = 4 l = 5 l = 6 l = 7 i = 1 [13,16] Lower bound Upper bound Surplus carrying capacity of NH 4 -N: tons/year

Conclusions
In this study, an ITSP model was developed for the management of water resources and environmental carrying capacity under uncertainties. The model was applied to the Yinma River Basin, where water shortages and high degrees of contamination are found that are typical for China. The proposed model can simultaneously deal with uncertainties presented as interval values and probability distributions by integrating the IPP and TSP methods. By solving the ITSP model, the optimal water resources allocations for the four main water use sectors were determined for the planning periods under different scenarios. In addition, the amounts of pollutant emission from the different sectors in the administrative regions were obtained. These results, constrained by regional total amount control, can provide a basis for regional emission permit systems for the different sectors. Furthermore, water environment improvement schemes should be formulated for each sector to remediate the effects of contamination, and to reconcile the total regional amounts of pollution and environmental carrying capacities. The results would be valuable for guiding the optimal allocation of water resources and water quality management in the Yinma River Basin.
The aim of this study was to use the ITSP model to create a water management system that combined water resources allocation with water environment treatment strategies. This system considered water environment improvement projects together with water resources allocation and total pollutant limits for the first time. The results suggest that this approach is applicable and effective for the management of water resources allocation and water quality in the Yinma River Basin, and that the approach could also be applied in other water-stressed or contaminated areas. However, there is still much room for improvement in the proposed model. This model does not consider the decision risk under uncertainty. In addition, details such as different water sources, climate change influence on the water resources availability, the water use pattern in different sectors, and efficiencies of different wastewater treatment methods were not modeled in this study. Further studies are needed to address these limitations.