Drainage basin water pollution control compensation method considering population flow and medium

Abstract

The invention is suitable for the field of water pollution control compensation methods, and provides a drainage basin water pollution control compensation method considering population flow and a medium, the method comprises the following steps: analyzing cost and income factors affecting water pollution control behaviors of upstream and downstream regions of a drainage basin; quantitatively analyzing the influence of population flow on cost and income; upstream and downstream government water pollution control revenue functions are constructed, and an equilibrium solution is solved; and empirically analyzing an influence rule of population flow on game equilibrium. Population flow is brought into a drainage basin ecological compensation analysis framework, and the pollution control cooperation relation of upstream and downstream governments under the influence of the population flow is considered. The problem of deviation caused by insufficient consideration of the population flow problem is solved.

Description

Technical Field

[0001] The present invention relates to the field of water pollution control and compensation methods, and in particular to a basin water pollution control and compensation method and medium taking population mobility into consideration. Background Art

[0002] Ecosystems provide humans with a variety of direct and indirect services that are crucial to their survival and development. Among them, water supply directly meets basic human needs and is an indispensable resource for human life and production. With population growth and industrialization, the amount of sewage discharged into rivers across various regions has increased significantly, far exceeding the rivers' own purification capacity, resulting in frequent water pollution. Water pollution poses a persistent threat to human health, the environment, and sustainable development. The enormous costs pose challenges to the sustainability of water pollution control. Furthermore, since river basins often span multiple regions or countries, pollutants migrate with the flow of water, potentially triggering interregional conflicts. Therefore, it is necessary to effectively coordinate the interests of different regions to incentivize the active participation of relevant parties in water pollution control.

[0003] Watershed ecological compensation is an incentive system that provides compensation to organizations and individuals that agree to carry out watershed ecological protection. Current research on ecological compensation focuses on mechanism design methods, calculation of compensation standards, and evaluation of compensation implementation effectiveness. Research on mechanism design methods has always been a core issue in the field of watershed ecological compensation, including the determination of compensation entities and compensation methods.

[0004] Regarding compensation entities, basin-scale approaches typically prioritize upstream and downstream governments based on the natural flow of the river. This approach is further refined to include mainstream and tributary governments, as well as left and right bank governments, within the analytical framework. Furthermore, given the need for external oversight, central government or river basin management committees are increasingly being considered as regulatory bodies. Regional approaches typically focus on a specific region within the basin, establishing a compensation mechanism between the local government and polluting enterprises. Furthermore, after factoring in public oversight, the analysis gradually incorporates the local government, polluting enterprises, and local residents as compensation entities.

[0005] Compensation methods typically include two approaches. One is a fixed-amount payment, and the other is a cost-sharing approach, where the compensator shares a certain percentage of the pollution control costs of the compensated party. Compared to the fixed-amount approach, the cost-sharing approach provides more flexible implementation by providing compensation based on actual pollution control investments. Game theory provides a rational and effective decision-making framework for participants in cost-sharing ecological compensation. By modeling and analyzing the interactions and decision-making processes of participants, fair and effective cost-sharing schemes can be identified, thereby promoting cooperation to achieve pollution control and emission reduction goals. Given the fluid and long-term nature of water pollution in a river basin, participants representing various regional interests must engage in a dynamic process of interaction to reach game equilibrium. Differential games can describe the process of pollutant removal in a river basin and depict the dynamic process of strategy selection and game equilibrium achieved by each participant within a continuous-time system. Therefore, dynamic analysis of river basin water pollution control based on differential game theory is currently a predominant research approach.

[0006] In summary, the research on watershed ecological compensation mechanism is gradually developing and improving. However, there are still some problems. Existing research rarely considers the impact of population mobility in the design method of watershed ecological compensation mechanism. The mobility of population between regions will have an impact on local water resource consumption, which in turn affects the pollution control effect of the region and ultimately affects the implementation of the watershed ecological compensation mechanism. Insufficient consideration of the impact of population mobility can easily lead to large deviations in research results. Based on this, the present invention incorporates population mobility into the watershed ecological compensation analysis framework and considers the pollution control cooperation relationship between upstream and downstream governments under the influence of population mobility. A simulation analysis is carried out using Henan Province and Shandong Province in the lower reaches of the Yellow River as an example. Summary of the Invention

[0007] The present invention provides a watershed water pollution control compensation method and medium taking into account population mobility, so as to solve the technical problems mentioned in the background technology.

[0008] A watershed water pollution control compensation method considering population mobility, the method comprising:

[0009] Analyze the cost and benefit factors that affect water pollution control in upstream and downstream areas of the basin;

[0010] Quantitatively analyze the impact of population mobility on costs and benefits;

[0011] Construct the water pollution control benefit function of upstream and downstream governments and find the equilibrium solution;

[0012] Empirically analyze the impact of population mobility on game equilibrium.

[0013] As a further technical solution of the present invention, the step of analyzing the cost and benefit factors affecting water pollution control in upstream and downstream areas of the basin includes:

[0014] Setting 1: Assume that the pollution control efforts of upstream and downstream governments are A and B respectively, representing the policies, personnel and financial investment made for water pollution control;

[0015] Assumption 2: The pollution control costs of upstream and downstream governments are quadratic functions of pollution control efforts. and c1 and c2 represent the pollution control cost coefficients of upstream and downstream governments, respectively;

[0016] Setting 3: To motivate the upstream government to carry out water environment governance and ensure the water environment requirements of the region, the downstream government will provide ecological compensation to the upstream government by sharing part of the upstream region's environmental protection investment. Let the proportion of the downstream government's share of the upstream government's environmental protection investment in period t be χ(t), 0≤χ(t)≤1;

[0017] Assumption 4: Pollutant emission reduction in the basin is the result of pollution control by upstream and downstream governments, and is a dynamic process that changes over time t. The dynamic change of pollutant emission reduction over time is described by the differential equation in Formula 1:

[0018] Formula 1:

[0019] In the formula, q(t) represents the pollutant emission reduction in the basin at time t, and the system initial state is set to q(0) ≥ 0, α>0, β>0 represent the pollutant elimination per unit pollution control effort of the upstream and downstream governments, δ represents the emission reduction attenuation coefficient caused by factors such as aging of sewage treatment equipment, and A and B represent the pollution control efforts of the upstream and downstream governments, respectively.

[0020] Setting 5: The basin benefit level in period t is expressed as S(t)=S0+λA(t)+μB(t)+ηq(t), where S0>0 represents the initial welfare status of the basin, λ and μ represent the impact coefficients of the upstream and downstream governments' water ecological environment governance levels on the basin benefit level, and η>0 represents the impact coefficient of the basin emission reduction on the basin benefit level.

[0021] Setting 6: The goal of the upstream and downstream governments of the basin is to pursue the optimal level of benefits under the optimal level of water environment governance in an infinite interval. It is assumed that the upstream and downstream regions of the basin have the same discount rate in an infinite interval, denoted as ρ.

[0022] As a further technical solution of the present invention, the steps of quantitatively analyzing the impact of population mobility on costs and benefits are as follows:

[0023] The available water resources upstream and downstream in period t are π u and π dWithout considering water diversion from outside the basin, the available water resources are related to the local water production and population. Since population migration will cause changes in the available water resources upstream and downstream, π u and π d The expressions for π are u =w u -e u +p×u 1per ,π d =w d -e d -p×u 2per ; Among them, w u and w d represent the water yield of the upstream and downstream areas during period t, e u and e d represents the total water consumption of the resident population in the upstream and downstream areas during period t, p represents the population migration during period t, u 1per and u 2per Represents the per capita water consumption in the upstream and downstream areas respectively.

[0024] As a further technical solution of the present invention, the steps of constructing the upstream and downstream government water pollution control benefit functions and finding the equilibrium solution include:

[0025] There are two main decision-making methods for upstream and downstream governments regarding water pollution compensation: independent and master-slave. Independent decision-making means that upstream and downstream governments are on equal footing, and both aim to maximize their respective regional benefits. Master-slave decision-making means that the downstream government is in a dominant position and provides ecological compensation to the upstream government by sharing part of the upstream government's environmental protection investment. On this basis, both regional governments aim to maximize their respective regional benefits.

[0026] Independent decision making:

[0027] The upstream and downstream government benefit functions are constructed as shown in Formula 2-3:

[0028] Formula 2:

[0029] Formula 3:

[0030] In order to ensure that Equation 1 has a unique continuous solution q(t), it is necessary to construct a set of bounded, continuous, and differentiable value functions V1(q) and V2(q); therefore, the Hamilton-Jacobi-Bellman-Fleming (HJB) equations for the upstream and downstream governments are constructed as shown in Equation 4-5:

[0031] Formula 4:

[0032] Formula 5:

[0033] By maximizing the first-order conditions for A and B on the right side of Formulas 4 and 5, we can obtain:

[0034] Formula 6:

[0035] Formula 7:

[0036] Substitute Formula 6-7 into the HJB equation of Formula 4-5 and assume that the function V i The expression of (q) is in linear form, and the game equilibrium solution under independent decision-making can be obtained as shown in Formula 8-9:

[0037] Formula 8:

[0038] Formula 9:

[0039] Substituting the calculated game equilibrium solution into Formula 4-5, we can obtain the optimal benefits of the upstream and downstream governments under this equilibrium condition as shown in Formula 10-11:

[0040] Formula 10:

[0041] Formula 11:

[0042] Master-slave decision making:

[0043] When the downstream government provides ecological compensation to the upstream government by sharing part of the upstream government's environmental protection investment, the upstream and downstream government benefit functions are constructed as shown in Formula 12-13:

[0044] Formula 12:

[0045] Formula 13:

[0046] Following the same steps as above, the HJB equations for upstream and downstream governments are constructed as shown in Formulas 14-15:

[0047] Formula 14:

[0048] Formula 15:

[0049] The game equilibrium solution of this equation is shown in Formula 16-17:

[0050] Formula 16:

[0051] Formula 17:

[0052] Substitute Formula 16 and Formula 17 into Formula 15, solve the first-order condition for maximizing χ(t), and calculate the optimal sharing ratio, as shown in Formula 18:

[0053] Formula 18:

[0054] Under this equilibrium condition, the optimal benefits of upstream and downstream governments when adopting ecological compensation are shown in Formula 19-20:

[0055] Formula 19:

[0056] Formula 20:

[0057] As a further technical solution of the present invention, the empirical analysis of the impact of population mobility on game equilibrium includes: the impact of population mobility on the degree of pollution control efforts, the impact of population mobility on the sharing ratio, the impact of population mobility on the amount of pollutant control and the impact of population mobility on the benefits of upstream and downstream governments.

[0058] Another object of the present invention is to provide a storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for compensating for water pollution control in a river basin that takes population flow into consideration.

[0059] Beneficial effects achieved by the present invention:

[0060] This proposed compensation method for water pollution control in a river basin that considers population mobility, based on the perspective of a coupled natural-social system, constructs a multi-agent compensation method for upstream and downstream governments under population mobility. This method can help decision-makers more scientifically assess the interests of all parties involved in water pollution control, develop reasonable compensation mechanisms, and promote cooperation and coordination between upstream and downstream governments. Furthermore, this method simulates and analyzes a game model using actual data from Henan and Shandong provinces in the lower reaches of the Yellow River, deeply exploring the constraints and influencing factors of population mobility on establishing ecological compensation between upstream and downstream governments, thus increasing the reliability of the results. The method includes: analyzing the cost and benefit factors that influence water pollution control behavior in upstream and downstream areas of the river basin; quantitatively analyzing the impact of population mobility on costs and benefits; constructing a water pollution control benefit function for upstream and downstream governments and finding an equilibrium solution; and empirically analyzing the influence of factors such as population mobility on the game equilibrium.

[0061] Interregional population mobility affects local water resource consumption, which in turn impacts regional pollution control effectiveness and ultimately the implementation of watershed ecological compensation mechanisms. Insufficient consideration of the impact of population mobility can easily lead to significant deviations in research results. This paper incorporates population mobility into the watershed ecological compensation analysis framework, considering the collaborative relationship between upstream and downstream governments in pollution control under the influence of population mobility. This addresses the bias caused by insufficient consideration of population mobility. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a schematic diagram of a watershed water pollution control compensation method taking population mobility into consideration, provided by an embodiment of the present invention.

[0063] Figure 2 This is a flow chart of a method for compensating for water pollution control in a river basin that takes population mobility into consideration, provided by an embodiment of the present invention.

[0064] Figure 3 It is the impact of population mobility on the pollution control efforts of upstream and downstream governments.

[0065] Figure 4 It is the impact of population mobility on the sharing ratio.

[0066] Figure 5 It is the impact of population mobility on the amount of pollutant control.

[0067] Figure 6 It is the impact of population mobility on Henan Province’s income.

[0068] Figure 7 It is the impact of population mobility on Shandong Province’s income. DETAILED DESCRIPTION

[0069] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0070] In the description of the present invention, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, a feature specified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0071] See also Figures 1 to 2 The embodiment of the present invention provides a watershed water pollution control compensation method taking into account population mobility, the method comprising:

[0072] Analyze the cost and benefit factors that affect water pollution control in upstream and downstream areas of the basin;

[0073] Quantitatively analyze the impact of population mobility on costs and benefits;

[0074] Construct the water pollution control benefit function of upstream and downstream governments and find the equilibrium solution;

[0075] Empirically analyze the impact of population mobility on game equilibrium.

[0076] In an embodiment of the present invention, the step of analyzing the cost and benefit factors affecting water pollution control actions in upstream and downstream areas of a river basin includes:

[0077] Since the actual situation is too complex to be described by a model, some assumptions are made about the cost and benefit factors involved.

[0078] Scenario 1: To achieve sustainable economic and social development, water quality must be stable and improving, so both upstream and downstream governments will manage the water environment. Assume that the pollution control efforts of the upstream and downstream governments are A and B, respectively, representing the policies, personnel, and financial investment in water pollution control.

[0079] Assumption 2: The pollution control costs of upstream and downstream governments are quadratic functions of pollution control efforts. and c1 and c2 represent the pollution control cost coefficients of upstream and downstream governments, respectively;

[0080] Setting 3: Due to the transboundary mobility of water resources in a river basin, water environment governance in upstream areas will affect both the local and downstream water environment quality. On the other hand, water environment governance in downstream areas will only affect the local water environment quality and will not affect the upstream water environment quality. To motivate the upstream government to conduct water environment governance and ensure the water environment requirements of the region, the downstream government will provide ecological compensation to the upstream government by sharing part of the upstream government's environmental protection investment. Let the proportion of the downstream government's share of the upstream government's environmental protection investment in period t be χ(t), 0≤χ(t)≤1.

[0081] Assumption 4: Pollutant emission reduction in the basin is the result of pollution control by upstream and downstream governments, and is a dynamic process that changes over time t. The dynamic change of pollutant emission reduction over time is described by the differential equation in Formula 1:

[0082] Formula 1:

[0083] Where, q(t) represents the pollutant emission reduction in the basin at time t, and the system initial state is set to q(0) ≥ 0, α>0, β>0 represent the pollutant elimination amount per unit pollution control effort of the upstream and downstream governments, δ represents the emission reduction attenuation coefficient caused by factors such as aging of sewage treatment equipment, and A and B represent the pollution control efforts of the upstream and downstream governments, respectively.

[0084] Assumption 5: The level of watershed benefits is closely related to the water environment governance level of upstream and downstream governments and the pollutant emission reduction of the entire basin. The watershed benefit level in period t is expressed as S(t) = S0 + λA(t) + μB(t) + ηq(t), where S0 > 0 represents the initial welfare state of the basin, λ and μ represent the coefficients of the water ecological environment governance level of upstream and downstream governments on the watershed benefit level, and η > 0 represents the coefficient of the impact of the watershed emission reduction on the watershed benefit level.

[0085] Setting 6: The goal of the upstream and downstream governments of the basin is to pursue the optimal level of benefits under the optimal level of water environment governance in an infinite interval. It is assumed that the upstream and downstream regions of the basin have the same discount rate in an infinite interval, denoted as ρ.

[0086] In the embodiment of the present invention, the steps of quantitatively analyzing the impact of population mobility on costs and benefits are as follows:

[0087] The available water resources upstream and downstream in period t are π u and π d Without considering water diversion from outside the basin, the available water resources are related to the local water production and population. Since population migration will cause changes in the available water resources upstream and downstream, π u and π d The expressions for π are u =w u -e u +p×u 1per ,π d =w d -e d -p×u 2per ; Among them, w u and w d represent the water yield of the upstream and downstream areas during period t, e u and e d represents the total water consumption of the resident population in the upstream and downstream areas during period t, p represents the population migration during period t, u 1per and u 2per Represents the per capita water consumption in the upstream and downstream areas respectively.

[0088] In an embodiment of the present invention, the steps of constructing the upstream and downstream government water pollution control benefit functions and finding the equilibrium solution include:

[0089] There are two main decision-making methods for upstream and downstream governments regarding water pollution compensation: independent and master-slave (i.e., adopting an ecological compensation strategy). Independent decision-making means that the upstream and downstream governments of the basin are on an equal footing, and both aim to maximize their respective regional benefits. Master-slave decision-making means that the downstream government is in a dominant position and provides ecological compensation to the upstream government by sharing part of the upstream government's environmental protection investment. On this basis, both regional governments aim to maximize their respective regional benefits. Therefore, this paper analyzes these two decision-making scenarios.

[0090] Independent decision making:

[0091] Based on the above settings, the upstream and downstream government revenue functions are constructed as shown in Formula 2-3:

[0092] Formula 2:

[0093] Formula 3:

[0094] In order to ensure that Equation 1 has a unique continuous solution q(t), it is necessary to construct a set of bounded, continuous, and differentiable value functions V1(q) and V2(q); therefore, the Hamilton-Jacobi-Bellman-Fleming (HJB) equations for the upstream and downstream governments are constructed as shown in Equation 4-5:

[0095] Formula 4:

[0096] Formula 5:

[0097] By maximizing the first-order conditions for A and B on the right side of Formulas 4 and 5, we can obtain:

[0098] Formula 6:

[0099] Formula 7:

[0100] Substitute Formula 6-7 into the HJB equation of Formula 4-5 and assume that the function V i The expression of (q) is in linear form, and the game equilibrium solution under independent decision-making can be obtained as shown in Formula 8-9:

[0101] Formula 8:

[0102] Formula 9:

[0103] Substituting the calculated game equilibrium solution into Formula 4-5, we can obtain the optimal benefits of the upstream and downstream governments under this equilibrium condition as shown in Formula 10-11:

[0104] Formula 10:

[0105] Formula 11:

[0106] Master-slave decision making:

[0107] When the downstream government provides ecological compensation to the upstream government by sharing part of the upstream government's environmental protection investment, the upstream and downstream government benefit functions are constructed as shown in Formula 12-13:

[0108] Formula 12:

[0109] Formula 13:

[0110] Following the same steps as above, the HJB equations for upstream and downstream governments are constructed as shown in Formulas 14-15:

[0111] Formula 14:

[0112] Formula 15:

[0113] The game equilibrium solution of this equation is shown in Formula 16-17:

[0114] Formula 16:

[0115] Formula 17:

[0116] Substitute Formula 16 and Formula 17 into Formula 15, solve the first-order condition for maximizing χ(t), and calculate the optimal sharing ratio, as shown in Formula 18:

[0117] Formula 18:

[0118] Under this equilibrium condition, the optimal benefits of upstream and downstream governments when adopting ecological compensation are shown in Formula 19-20:

[0119] Formula 19:

[0120] Formula 20:

[0121] In an embodiment of the present invention, the empirical analysis of the impact of population mobility on game equilibrium includes: the impact of population mobility on the degree of pollution control efforts, the impact of population mobility on the sharing ratio, the impact of population mobility on the amount of pollutant control, and the impact of population mobility on the benefits of upstream and downstream governments.

[0122] In this embodiment, Henan Province and Shandong Province in the lower reaches of the Yellow River are used as examples for simulation analysis. The parameter values ​​are derived from the water resources bulletins and statistical yearbooks of Henan Province and Shandong Province. The values ​​of each parameter are as follows: u Take 24.94 billion m 3 , e u Take 22.8 billion m 3 ,u 1per Take 318.87m 3 , w d Take 24.98 billion m 3 , e d Take 22.34 billion m 3 ,u 2per Take 443.70m 3 , α is 0.6, β is 0.6, δ is 0.2, λ is 0.6, μ is 0.6, η is 0.5, and ρ is 0.2. The influence of factors such as population mobility on game equilibrium is as follows:

[0123] (1) The impact of population mobility on pollution control efforts

[0124] Taking P = 0, 10, 20, 30, 40 and 50 respectively, we can get the impact of population mobility changes on the pollution control efforts of upstream and downstream governments, as follows: Figure 3 (a)-(d) show that, overall, downstream governments exert greater pollution control efforts than upstream governments. For upstream governments, the effects of population mobility on pollution control efforts are opposite under independent decision-making and eco-compensation strategies. Under independent decision-making, pollution control efforts increase with increasing population outflow, increasing by 1% for every 100,000 people outflow. Under eco-compensation strategies, pollution control efforts slowly decrease with increasing population outflow, decreasing by 0.2% for every 100,000 people outflow. For downstream governments, pollution control efforts gradually decrease as the number of people moving to downstream areas increases.

[0125] (2) The impact of population mobility on the burden-sharing ratio

[0126] The impact of population mobility on the burden sharing ratio is as follows: Figure 4 As shown in Figure 2, the shared burden ratio under the eco-compensation strategy decreases linearly with increasing population migration. When there is no population migration, downstream governments will bear 10.3% of upstream pollution control costs. When the number of migrants exceeds 650,000, the shared burden ratio drops to zero, meaning that without external incentives, the eco-compensation mechanism cannot be established.

[0127] (3) Impact of population mobility on pollutant control

[0128] Taking P = 0 and 50 respectively, we can get the impact of population mobility changes on the pollutant elimination of upstream and downstream governments, as follows: Figure 5 As shown in (a) and (b), the amount of pollutant removal using the eco-compensation strategy is higher than that using the independent decision-making strategy. As the number of migrants increases, the total amount of pollutant removal using both the independent decision-making and eco-compensation strategies decreases, with the eco-compensation strategy showing a greater decrease, gradually approaching the total amount of pollutant removal using the independent decision-making strategy.

[0129] (4) The impact of population mobility on upstream and downstream government revenues

[0130] Taking P = 0, 20 and 50 respectively, we can get the impact of population mobility changes on the upstream (Henan Province) government revenue, as follows: Figure 6 As shown in (a)-(c). When population outflow is below the critical value, regardless of the upstream population outflow, the benefits of ecological compensation are greater than those of independent decision-making. As population outflow increases, the benefits under both decisions increase and gradually converge.

[0131] Similarly, taking P = 0, 20 and 50 respectively, we can obtain the impact of population mobility changes on the government revenue of the downstream (Shandong Province), as follows: Figure 7 As shown in the figure, overall, when eco-compensation is implemented, downstream benefits are higher than when independent decisions are made. As the influx of upstream population to downstream increases, Shandong Province's benefits gradually decrease. Furthermore, as population mobility increases, the benefits under the two decisions gradually approach each other.

[0132] This paper proposes a compensation method for water pollution control in a river basin that takes population mobility into account. Starting from the perspective of a coupled natural-social system, it constructs a multi-party interest compensation method for upstream and downstream governments in the river basin under population mobility, addressing the bias caused by insufficient consideration of population mobility. This method can help decision-makers more scientifically assess the interests of all parties involved in water pollution control in the river basin, develop a reasonable compensation mechanism, and promote cooperation and coordination between upstream and downstream governments. The method includes: analyzing the cost and benefit factors that influence water pollution control in upstream and downstream areas of the river basin; quantitatively analyzing the impact of population mobility on costs and benefits; constructing a water pollution control benefit function for upstream and downstream governments and finding an equilibrium solution; and empirically analyzing the influence of factors such as population mobility on the game equilibrium.

[0133] A storage medium stores a computer program, which, when executed by a processor, implements the steps of a watershed water pollution control and compensation method that takes population flow into consideration.

[0134] It should be noted that, in this document, the term "comprises" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article, or apparatus that includes a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0135] The above are only preferred embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A watershed water pollution control compensation method considering population mobility, characterized in that: The method comprises: Analyze the cost and benefit factors that affect water pollution control in upstream and downstream areas of the basin; Quantitatively analyze the impact of population mobility on costs and benefits; Construct the water pollution control benefit function of upstream and downstream governments and find the equilibrium solution; Empirically analyze the impact of population mobility on game equilibrium.

2. A watershed water pollution control compensation method considering population mobility according to claim 1, characterized in that: The steps of analyzing the cost and benefit factors affecting water pollution control in upstream and downstream areas of the basin include: Setting 1: Assume that the pollution control efforts of upstream and downstream governments are A and B respectively, representing the policies, personnel and financial investment in water pollution control; Assumption 2: The pollution control costs of upstream and downstream governments are quadratic functions of pollution control efforts. and c1 and c2 represent the pollution control cost coefficients of upstream and downstream governments, respectively; Setting 3: To motivate the upstream government to carry out water environment governance and ensure the water environment requirements of the region, the downstream government will provide ecological compensation to the upstream government by sharing part of the upstream region's environmental protection investment. Let the proportion of the downstream government's share of the upstream government's environmental protection investment in period t be χ(t), 0≤χ(t)≤1; Assumption 4: Pollutant emission reduction in the basin is the result of pollution control by upstream and downstream governments, and is a dynamic process that changes over time t. The dynamic change of pollutant emission reduction over time is described by the differential equation in Formula 1: Formula 1: In the formula, q(t) represents the pollutant emission reduction in the basin at time t, and the system initial state is set to q(0) ≥ 0, α>0, β>0 represent the pollutant elimination per unit pollution control effort of the upstream and downstream governments, δ represents the emission reduction attenuation coefficient caused by factors such as aging of sewage treatment equipment, and A and B represent the pollution control efforts of the upstream and downstream governments, respectively. Setting 5: The watershed benefit level in period t is expressed as S(t) = S0 + λA(t) + μB(t) + ηq(t), where S0 > 0 represents the initial welfare status of the watershed, λ and μ represent the impact coefficients of the upstream and downstream governments' water ecological environment governance levels on the watershed benefit level, and η > 0 represents the impact coefficient of the watershed emission reduction on the watershed benefit level. Setting 6: The goal of the upstream and downstream governments of the basin is to pursue the optimal level of benefits under the optimal level of water environment governance in an infinite interval. It is assumed that the upstream and downstream regions of the basin have the same discount rate in an infinite interval, denoted as ρ.

3. The method for compensation of water pollution control in a river basin considering population mobility according to claim 1 is characterized in that: The steps for quantitatively analyzing the impact of population mobility on costs and benefits are as follows: The available water resources upstream and downstream in period t are π u and π d Without considering water diversion from outside the basin, the available water resources are related to the local water production and population. Since population migration will cause changes in the available water resources upstream and downstream, π u and π d The expressions for π are u =w u -e u +p×u 1per ,π d =w d -e d -p×u 2per ; Among them, w u and w d represent the water yield of the upstream and downstream areas during period t, e u and e d represents the total water consumption of the resident population in the upstream and downstream areas during period t, p represents the population migration during period t, u 1per and u 2per Represents the per capita water consumption in the upstream and downstream areas respectively.

4. The method for compensation of water pollution control in a river basin considering population mobility according to claim 1 is characterized in that: The steps of constructing the upstream and downstream government water pollution control benefit functions and finding the equilibrium solution include: There are two main decision-making methods for upstream and downstream governments regarding water pollution compensation: independent and master-slave. Independent decision-making means that upstream and downstream governments are on equal footing, and both aim to maximize their respective regional benefits. Master-slave decision-making means that the downstream government is in a dominant position and provides ecological compensation to the upstream government by sharing part of the upstream government's environmental protection investment. On this basis, both regional governments aim to maximize their respective regional benefits. Independent decision making: The upstream and downstream government benefit functions are constructed as shown in Formula 2-3: Formula 2: Formula 3: In order to ensure that there is a unique continuous solution q(t) for Formula 1, it is necessary to construct a set of bounded, continuous, and differentiable value functions V1(q) and V2(q); therefore, the HJB equations for the upstream and downstream governments are constructed as shown in Formula 4-5: Formula 4: Formula 5: By maximizing the first-order conditions for A and B on the right side of Formulas 4 and 5, we can obtain: Formula 6: Formula 7: Substitute Formula 6-7 into the HJB equation of Formula 4-5 and assume that the function V i The expression of (q) is in linear form, and the game equilibrium solution under independent decision-making can be obtained as shown in Formula 8-9: Formula 8: Formula 9: Substituting the calculated game equilibrium solution into Formula 4-5, we can obtain the optimal benefits of the upstream and downstream governments under this equilibrium condition as shown in Formula 10-11: Formula 10: Formula 11: Master-slave decision making: When the downstream government provides ecological compensation to the upstream government by sharing part of the upstream government's environmental protection investment, the upstream and downstream government benefit functions are constructed as shown in Formula 12-13: Formula 12: Formula 13: Following the same steps as above, the HJB equations for upstream and downstream governments are constructed as shown in Formulas 14-15: Formula 14: Formula 15: The game equilibrium solution of this equation is shown in Formula 16-17: Formula 17: Substitute Formula 16 and Formula 17 into Formula 15, solve the first-order condition for maximizing χ(t), and calculate the optimal sharing ratio, as shown in Formula 18: Formula 18: Under this equilibrium condition, the optimal benefits of upstream and downstream governments when adopting ecological compensation are shown in Formula 19-20: Formula 19: Formula 20:

5. The method for compensation of water pollution control in a river basin considering population mobility according to claim 1 is characterized in that: The empirical analysis of the impact of population mobility on game equilibrium includes: the impact of population mobility on the degree of pollution control efforts, the impact of population mobility on the sharing ratio, the impact of population mobility on the amount of pollutant control, and the impact of population mobility on the benefits of upstream and downstream governments.

6. A storage medium, characterized in that The storage medium stores a computer program, which, when executed by a processor, implements the steps of a watershed water pollution control and compensation method taking into account population flow as described in any one of claims 1 to 5.

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