Method for determining suitable area of lake based on ecological water use efficiency

By constructing a response function for the ecological water use efficiency of lakes and determining the optimal suitable area of ​​lakes using the first derivative method, the problem of the correlation between the synergistic effect of lakes and vegetation and water resource utilization was solved, thus realizing the healthy maintenance of lake ecosystems and efficient management of water resources.

CN122636030APending Publication Date: 2026-08-25XINJIANG INST OF ECOLOGY & GEOGRAPHY CHINESE ACAD OF SCI
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Patent Information

Application Number
CN202611068366.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-07-17
Publication Date
2026-08-25

AI Technical Summary

Technical Problem

In existing technologies, methods for determining the suitable water surface area of ​​lakes fail to comprehensively consider the synergistic effect between lakes and lakeside vegetation, lack correlation analysis between ecological benefits and water resource occupation, and lack a complete chain from area determination to management decisions, resulting in low lake ecosystem health and low water resource utilization efficiency.

Method used

By acquiring remote sensing monitoring data of the target lake area, the ecological water use efficiency is calculated, a response function of lake surface area and ecological water use efficiency is constructed, the optimal suitable lake area is determined by the first derivative extreme value method, a suitable area range is set, and differentiated management and control measures are formulated.

Benefits of technology

It has enabled quantitative assessment of the ecological benefits of lakes, ensured the integrity and health of the lake-vegetation complex ecosystem, improved the efficiency of water resource utilization in arid areas, and provided precise management measures from area monitoring to water replenishment, maintenance, and control.

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Abstract

The present application relates to the technical field of ecological hydrology and water resources management, and discloses a method for determining suitable area of lake based on ecological water use efficiency, comprising: obtaining multi-source remote sensing monitoring data of target lake area in historical years, extracting lake area, normalized vegetation index, vegetation area and land use type area in each year; calculating ecological environment quality index based on land use type area; calculating ecological water use efficiency; drawing a scatter plot of lake area and ecological water use efficiency in multiple years, conducting quadratic polynomial regression fitting, and constructing a response function between lake area and ecological water use efficiency; determining the optimal lake suitable area threshold by using the first derivative extreme value method, calculating the maximum ecological water use efficiency value, and determining the lake suitable area interval to implement lake ecological management; the present application realizes quantitative evaluation of ecological benefits of lakes in arid regions and accurate determination of suitable area.
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Description

Technical Field

[0001] This invention relates to the fields of ecohydrology and water resources management, specifically to a method for determining the suitable area of ​​lakes based on ecological water use efficiency. Background Technology

[0002] As the final destination of water resources in arid regions, terminal lakes play crucial ecological roles in maintaining biodiversity, regulating local climate, and preventing wind erosion, thus acting as stabilizers for ecological security in these areas. However, under the dual pressures of climate change and human activities, lakes in arid regions generally face shrinking areas and ecological degradation. Determining the appropriate surface area of ​​these lakes is of great significance for developing ecological water replenishment plans, optimizing water resource allocation, and maintaining the health of lake ecosystems.

[0003] Currently, existing methods for determining the suitable water surface area of ​​lakes have the following main shortcomings: (1) Using a single ecological indicator as the threshold basis lacks comprehensive benefit consideration. Existing methods often employ minimum ecological water level or single-species habitat requirement methods, which only consider maintaining the basic morphology of the lake or the survival of a certain indicator species as constraints, failing to comprehensively consider the synergistic benefits of multiple ecological elements such as lakeside vegetation zones and wetland ecosystems. The minimum area determined by such methods often only prevents the lake from drying up and is insufficient to support the complete function of the lake ecosystem.

[0004] (2) Lack of quantitative expression of the synergistic effect between lake water and lakeside vegetation There is a close water-ecological relationship between lakes and lakeside vegetation in arid regions: when the lake surface area is too small, the lakeside vegetation degrades due to the drop in groundwater level; when the lake surface area is too large, the lakeside vegetation is submerged and dies, which in turn reduces the quality of the ecological environment. However, most existing methods study water and vegetation as independent objects, failing to construct a mechanism for expressing their synergistic effects and making it difficult to identify the marginal impact of water surface expansion on vegetation ecology.

[0005] (3) No ecological benefit output and water resource occupation benefit relationship has been established. Lake ecological protection requires a large amount of water resources. Under the hard constraint of total water resources in arid areas, simply pursuing the largest lake surface area or the highest water level often leads to inefficient use or even waste of water resources. Current technology lacks an indicator system and calculation method to compare the ecological benefits with the amount of water resources occupied by the lake surface area, making it difficult to answer the core management question of what area is optimal.

[0006] (4) Failed to provide a complete technical chain from area determination to management decision-making. Most existing studies only provide recommended values, failing to establish a quantitative correlation between the degree of area deviation and management response measures. This makes it difficult for technical solutions to directly serve the actual decision-making of water resource management departments. There is a disconnect between research findings and operational management, resulting in a low application conversion rate. Summary of the Invention

[0007] To address the aforementioned shortcomings in existing technologies, this invention provides a method for determining the suitable area of ​​lakes based on ecological water use efficiency. This method solves the technical problems in existing technologies, such as the inability to comprehensively reflect the synergistic benefits of lakes and vegetation due to reliance on a single ecological threshold indicator, the inability to identify the marginal benefit inflection point of water resource utilization due to the lack of correlation analysis between ecological benefits and water resource occupation, and the difficulty in directly supporting refined water resource management decisions due to the lack of a complete chain from area determination to differentiated management measures.

[0008] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: Obtain historical year-by-year remote sensing monitoring data of the target lake area, and extract the lake surface area, normalized vegetation index, vegetation area and land use type area for each year; Calculate the ecological environment quality index based on the area of ​​land use type; Ecological water use efficiency is calculated based on lake surface area, normalized vegetation index, vegetation area and ecological environment quality index. The annual lake surface area and ecological water use efficiency of the target lake area were obtained. A scatter plot was drawn with the lake surface area as the abscissa and the ecological water use efficiency as the ordinate. The least squares method was used to perform a quadratic polynomial regression fitting on the scatter data to construct the response function between the lake surface area and the ecological water use efficiency. Based on the response function between lake surface area and ecological water use efficiency, the optimal suitable lake area is determined by the first derivative extreme value method, the maximum ecological water use efficiency value is calculated, and the suitable lake area range is determined for lake ecological management.

[0009] The present invention has the following beneficial effects: The proposed method for determining the suitable area of ​​lakes based on ecological water use efficiency constructs a comprehensive evaluation index for ecological water use efficiency, establishes a quadratic polynomial response function between lake surface area and ecological water use efficiency, uses the first derivative extreme value method combined with threshold segmentation to determine the optimal suitable lake area and suitable area range, and formulates three-level differentiated management rules from area monitoring to water replenishment / maintenance / control based on the suitable area range. This achieves quantitative assessment of the ecological benefits of lakes in arid areas and accurate determination of the suitable area, ensuring the integrity and health of the lake-vegetation complex ecosystem, improving the utilization efficiency of limited water resources in arid areas, and providing water resource management departments with complete technical support from area monitoring to differentiated management measures for water replenishment, maintenance, and control. Attached Figure Description

[0010] Figure 1 This is a flowchart illustrating the method for determining the suitable area of ​​a lake based on ecological water use efficiency proposed in this invention. Detailed Implementation

[0011] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0012] The specific embodiments of this invention are as follows: like Figure 1 As shown, the method for determining the suitable area of ​​a lake based on ecological water use efficiency includes the following steps: Step 1: Obtain historical remote sensing monitoring data of the target lake area year by year, and extract the lake surface area, normalized vegetation index, vegetation area and land use type area for each year.

[0013] In this step, Landsat satellite imagery data of the target lake area from 2000 to 2023 was acquired annually using the Google Earth Engine platform. Based on the Landsat satellite imagery data, basic indicators such as the lake surface area, normalized difference vegetation index, vegetation area, and land use type area of ​​the target lake area were extracted annually, serving as the basis for calculating all subsequent indicators. The Landsat satellite imagery data has a ground spatial resolution of 30m, meaning the ground area corresponding to each pixel is... They are the same, both are The specific extraction process for each indicator is as follows: (1) Lake surface area ( (km²) Based on Landsat satellite imagery data, the Normalized Difference Water Index (NDWI) is calculated pixel-by-pixel; the formula for calculating the NDWI for each pixel is as follows:

[0014] In the formula, For pixels Normalized water index; For pixels Reflectivity in the green light band; For pixels Near-infrared reflectivity; Will The pixels identified as water bodies are summed up within the target lake area to obtain the lake's surface area. The formula for this calculation is as follows:

[0015] In the formula, The lake's surface area; The pixels identified as water bodies within the target lake area ( The total number of pixels; For pixels The corresponding ground area is (30 m × 30 m = 900 m²).

[0016] (2) Normalized Difference Vegetation Index Based on Landsat series satellite imagery data, the normalized vegetation index (NDI) is calculated pixel-by-pixel; the formula for calculating the NDI for each pixel is as follows:

[0017] In the formula, For pixels Normalized Difference Vegetation Index; For pixels Near-infrared reflectivity; For pixels The reflectivity of the red light band.

[0018] (3) Vegetation area (VA, km²) Based on the normalized vegetation index of each pixel, The pixels are identified as having vegetation cover, and the areas of all pixels identified as having vegetation cover within the target lake area are summed to obtain the vegetation area. The calculation formula is as follows:

[0019] In the formula, The area is the vegetation area; The area within the target lake region was identified as having vegetation cover. The total number of pixels, For pixels Normalized Difference Vegetation Index; For pixels The corresponding ground area is (30m × 30m = 900m²).

[0020] (4) Land use type area, including grassland area, water area, unused land area, and construction land area; Based on Landsat series satellite imagery data, supervised classification or random forest classification methods were used pixel by pixel to classify the land use type of each pixel in the target lake area into four categories: grassland, water area, unused land, and construction land.

[0021] The number of pixels classified as grassland, water area, unused land, and construction land is counted separately, and then multiplied by the area of ​​a single pixel to obtain the area of ​​each land use type. The calculation formula is as follows:

[0022]

[0023]

[0024]

[0025] In the formula, , , , These are grassland area, water area, unused land area, and construction land area, respectively. , , , These represent the number of pixels divided into grassland, water area, unused land, and built-up land, respectively. , , , For pixels Pixel Pixel Pixel The corresponding ground area is (30m × 30m = 900m²).

[0026] Step 2: Calculate the ecological environment quality index based on the land use type area.

[0027] Specifically, the formula for calculating the ecological environment quality index is:

[0028]

[0029] In the formula, For ecological environment quality index; The grassland area is (km²). The area of ​​the water body (km²) Area of ​​unused land (km²); The total area (km²) of the target lake region; The normalized coefficient for the habitat quality index is 458.5, calibrated based on historical measured data of the target lake area.

[0030] Step 3: Calculate the ecological water use efficiency based on the lake surface area, normalized vegetation index, vegetation area, and ecological environment quality index.

[0031] Specifically, the formula for calculating ecological water use efficiency is:

[0032] In the formula, Ecological water use efficiency is dimensionless and represents the comprehensive ecological benefits supported by a unit lake surface area. The ecological environment quality index is dimensionless. The area is the vegetation area; The normalized vegetation index is the mean of all pixels within the target lake area, and is dimensionless. The lake's surface area.

[0033] Step 4: Obtain the annual lake surface area and ecological water use efficiency of the target lake area. Plot a scatter plot with lake surface area as the x-axis and ecological water use efficiency as the y-axis. Use the least squares method to perform a quadratic polynomial regression fitting on the scatter data to construct the response function between lake surface area and ecological water use efficiency.

[0034] Specifically, the process of constructing the response function between lake surface area and ecological water use efficiency is as follows: (1) Obtain the annual lake surface area and ecological water use efficiency of the target lake area, and generate year-paired scatter data, represented as:

[0035] In the formula, Total number of historical years; , , The first Year, No. Year, No. The lake's surface area in [year]; , , The first Year, No. Year, No. Annual ecological water use efficiency.

[0036] (2) Draw a scatter plot with the lake surface area as the horizontal axis and the ecological water use efficiency as the vertical axis.

[0037] In this invention, to obtain the annual lake surface area and ecological water use efficiency of the target lake area from 2000 to 2023, 24 sets of paired scatter plot data are generated, namely: To construct a scatter plot of scatter data paired across 24 years.

[0038] (3) Based on the scatter plot, construct a quadratic polynomial model, which is expressed as:

[0039] In the formula, For ecological water use efficiency; The lake's surface area; , , These are all model coefficients to be solved; (4) Based on the quadratic polynomial model, with the goal of minimizing the sum of squared residuals, the least squares method is used for parameter estimation, generating the solved model coefficients, which are expressed as:

[0040]

[0041] In the formula, It is the sum of squared residuals; , , These are all the model coefficients after the solution was obtained; Let be the independent variable that minimizes the objective function; where The purpose is to ensure that the objective function has an inverted U-shaped form.

[0042] (5) Substituting the solved model coefficients into the quadratic polynomial model, the response function between lake surface area and ecological water use efficiency is obtained, expressed as: .

[0043] Step 5: Based on the response function between lake surface area and ecological water use efficiency, the optimal suitable lake area is determined by the first derivative extreme value method, the maximum ecological water use efficiency value is calculated, and the suitable lake area range is determined in order to implement lake ecological management.

[0044] Specifically, based on the response function between lake surface area and ecological water use efficiency, the optimal suitable lake area is determined using the first derivative extreme value method, and the process of calculating the maximum ecological water use efficiency value is as follows: (1) Find the first derivative of the response function between lake surface area and ecological water use efficiency, and obtain the equation of the tangent slope, which is expressed as:

[0045] In the formula, For ecological water use efficiency; The lake's surface area; , All of these are the model coefficients after the solution is obtained.

[0046] (2) Set the tangent slope equation to zero and solve it to obtain the stationary point based on the lake surface area, which is expressed as:

[0047]

[0048] In the formula, The location is based on the lake's surface area.

[0049] (3) Find the second derivative of the equation for the slope of the tangent line, expressed as:

[0050] because ,therefore According to the second derivative criterion, the stationary point based on the lake surface area is a local maximum point.

[0051] (4) Determine the optimal suitable area of ​​the lake, expressed as:

[0052] In the formula, The optimal suitable area for a lake.

[0053] (5) Based on the optimal suitable area of ​​the lake, calculate the maximum ecological water use efficiency value, expressed as:

[0054] In the formula, This represents the maximum ecological water use efficiency value. These are the coefficients of the solved model.

[0055] Specifically, the process of determining the appropriate area range for lakes in order to implement lake ecological management is as follows: (1) Set threshold coefficient ; In this step, considering the inherent dynamic fluctuations of lake ecosystems and the systematic errors present in the remote sensing data inversion process, this invention does not use the optimal suitable area of ​​the lake. Instead of using a single rigid target value, a threshold coefficient is introduced. ( (), used to define the ecologically acceptable efficiency retention ratio; Threshold coefficient The determination is based on the ecological sensitivity of the target lake area, specifically: For ecologically sensitive lakes (such as ecologically fragile lakes that are significantly affected by external disturbances), take... This means that the ecological water use efficiency must be no less than 95% of the maximum value; For lakes with good ecological stability, take This means that ecological water use efficiency is allowed to decrease by no more than 10% from its maximum value, in order to retain more flexible management space.

[0056] (2) Based on the threshold coefficient and the optimal suitable area of ​​the lake, a target threshold is set, expressed as:

[0057] In the formula, Let be the target threshold, and be dimensionless; (3) Substituting the target threshold into the response function between lake surface area and ecological water use efficiency, we obtain a quadratic equation based on lake surface area, which is expressed as: ; (4) By rearranging the terms of the quadratic equation based on the lake surface area, a standard quadratic equation is generated, which is expressed as: ; (5) Solve the standard form of the quadratic equation in one variable, that is, use the quadratic equation quadratic formula to obtain two real roots based on the lake surface area, which are expressed as:

[0058]

[0059] In the formula, , These are the first and second solid roots, respectively, based on the lake surface area, and .

[0060] (6) Based on the two real roots of the lake surface area, determine the lower and upper limits of the suitable lake area, expressed as:

[0061]

[0062] In the formula, , These represent the lower and upper limits of the suitable area for lakes, respectively, in km². (7) Based on the lower and upper limits of the suitable area of ​​a lake, the suitable area range of a lake is obtained, which is expressed as: ; Furthermore, the ecological water use efficiency corresponding to any lake surface area within the suitable lake area range is not lower than the target threshold, that is: For any interval All of them have: .

[0063] (8) Based on the suitable area range of the lake, implement lake ecological management, specifically as follows: when At that time, it indicated that the target lake had shrunk severely, and the ecological water replenishment plan was activated to prioritize its restoration to its original state. above; when When the target lake is in a suitable range, the status quo should be maintained and dynamic monitoring should be implemented. when When the target lake has expanded excessively, the amount of water flowing into the lake should be controlled, and appropriate discharge should be carried out to lower the water level.

[0064] In summary, the method for determining the suitable area of ​​lakes based on ecological water use efficiency proposed in this invention achieves the following technical effects: (1) Constructing an ecological water use efficiency index: The ecological environment quality index (ecosystem service value), normalized vegetation index and vegetation area (vegetation water consumption) are incorporated into a unified framework, realizing the quantitative correlation between lake ecological benefit output and water resource occupation, and filling the technical gap in the quantitative method of synergistic optimization of lake ecological benefit-water occupation in arid areas.

[0065] (2) The inverted U-shaped response law between lake area and ecological benefits was revealed and a quantitative response function was constructed: a quadratic polynomial response function between lake area and ecological water use efficiency was established by fitting multi-year time series data. From an empirical perspective, the ecological mechanism that ecological degradation occurs when the lake area is too small and benefits are diluted when the lake area is too large was verified, providing a quantifiable mathematical basis for determining the appropriate area.

[0066] (3) Achieved dual spatial identification of peak point + suitable range: Unlike the existing technology that only gives a single threshold, this invention determines the optimal lake suitable area threshold by the first derivative extreme value method and determines the lake suitable area range by the threshold segmentation method, providing management departments with a multi-level decision-making basis that combines target value and acceptable fluctuation range.

[0067] (4) A complete technical chain from area determination to management decision-making has been constructed: an end-to-end technical process of area measurement → safety assessment → efficiency calculation → curve fitting → extreme value solution → interval determination → management response has been established, and remote sensing monitoring data is directly converted into three types of operable management instructions: water replenishment plan, maintenance monitoring and water level control, which solves the problem of the transformation gap between research results and business management.

[0068] (5) Make full use of multi-source remote sensing data and have strong operability: Based on Landsat (30 m resolution) and MODIS (250 m resolution) publicly available and free remote sensing data, the time covers 24 years from 2000 to 2023. The method does not rely on the ground-based well network and can be quickly extended to other arid lakes.

[0069] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0070] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for determining the suitable area of ​​a lake based on ecological water use efficiency, characterized in that, Includes the following steps: Obtain historical year-by-year remote sensing monitoring data of the target lake area, and extract the lake surface area, normalized vegetation index, vegetation area and land use type area for each year; Calculate the ecological environment quality index based on the area of ​​land use type; Ecological water use efficiency is calculated based on lake surface area, normalized vegetation index, vegetation area and ecological environment quality index. The annual lake surface area and ecological water use efficiency of the target lake area were obtained. A scatter plot was drawn with the lake surface area as the abscissa and the ecological water use efficiency as the ordinate. The least squares method was used to perform a quadratic polynomial regression fitting on the scatter data to construct the response function between the lake surface area and the ecological water use efficiency. Based on the response function between lake surface area and ecological water use efficiency, the optimal suitable lake area is determined by the first derivative extreme value method, the maximum ecological water use efficiency value is calculated, and the suitable lake area range is determined for lake ecological management.

2. The method for determining the suitable area of ​​a lake according to claim 1, characterized in that, The process of obtaining historical remote sensing monitoring data for the target lake area and extracting the lake surface area, normalized vegetation index, vegetation area, and land use type area for each year is as follows: Acquire Landsat series satellite imagery data of the target lake area over historical years; Based on Landsat satellite imagery data, the normalized water index for each pixel is calculated and expressed as: in, For pixels Normalized water index; For pixels Reflectivity in the green light band; For pixels Near-infrared reflectivity; Will The pixels identified as water bodies are summed, and the lake surface area is obtained by accumulating the areas of all pixels identified as water bodies within the target lake area, represented as: in, The lake's surface area; The total number of pixels identified as water bodies within the target lake area; For pixels The corresponding ground area; Based on Landsat satellite imagery data, the normalized vegetation index (NDI) for each pixel is calculated and expressed as: in, For pixels Normalized Difference Vegetation Index; For pixels Near-infrared reflectivity; For pixels Reflectivity in the red light band; Based on the normalized vegetation index of each pixel, The pixels are identified as having vegetation cover, and the areas of all pixels identified as having vegetation cover within the target lake area are summed to obtain the vegetation area, which is represented as: in, The area is the vegetation area; The total number of pixels within the target lake area that are identified as having vegetation cover; For pixels The corresponding ground area; Based on Landsat series satellite imagery data, the land use type of each pixel within the target lake area is divided into grassland, water area, unused land and construction land; The number of pixels classified as grassland, water area, unused land, and construction land is counted separately, and then multiplied by the area of ​​a single pixel to obtain the area of ​​each land use type. The calculation formula is as follows: in, , , , These are grassland area, water area, unused land area, and construction land area, respectively. , , , These represent the number of pixels divided into grassland, water area, unused land, and built-up land, respectively. , , , For pixels Pixel Pixel Pixel The corresponding ground area.

3. The method for determining the suitable area of ​​a lake according to claim 1, characterized in that, The formula for calculating the ecological environment quality index is: in, For ecological environment quality index; This is the normalized coefficient of the habitat quality index; The area of ​​grassland; The area of ​​the water body; This refers to the area of ​​unused land. The total area of ​​the target lake region.

4. The method for determining the suitable area of ​​a lake according to claim 1, characterized in that, The formula for calculating ecological water use efficiency is: in, For ecological water use efficiency; For ecological environment quality index; The area is the vegetation area; The mean normalized vegetation index of all pixels within the target lake area.

5. The method for determining the suitable area of ​​a lake according to claim 1, characterized in that, The process of constructing the response function between lake surface area and ecological water use efficiency is as follows: Obtain the annual lake surface area and ecological water use efficiency of the target lake area, and generate year-paired scatter plot data, represented as follows: in, Total number of historical years; , , The first Year, No. Year, No. The lake's surface area in [year]; , , The first Year, No. Year, No. Annual ecological water use efficiency; Plot a scatter plot with the lake surface area on the x-axis and the ecological water use efficiency on the y-axis. Based on the scatter plot, a quadratic polynomial model is constructed, represented as follows: in, For ecological water use efficiency; The lake's surface area; , , These are all model coefficients to be solved; Based on a quadratic polynomial model, with the objective of minimizing the sum of squared residuals, the least squares method is used for parameter estimation, generating the solved model coefficients, expressed as: in, It is the sum of squared residuals; , , These are all the model coefficients after the solution was obtained; The independent variable is the one that minimizes the objective function; Substituting the solved model coefficients into the quadratic polynomial model, we obtain the response function between lake surface area and ecological water use efficiency, expressed as: 。 6. The method for determining the suitable area of ​​a lake according to claim 1, characterized in that, Based on the response function between lake surface area and ecological water use efficiency, the optimal suitable lake area is determined using the first derivative extreme value method. The process of calculating the maximum ecological water use efficiency is as follows: Finding the first derivative of the response function between lake surface area and ecological water use efficiency yields the equation for the tangent slope, which is expressed as: in, For ecological water use efficiency; The lake's surface area; , These are all the model coefficients after the solution was obtained; Setting the tangent slope equation to zero and solving it yields the stationary point based on the lake surface area, expressed as: in, The location is based on the lake's surface area; Find the second derivative of the equation for the slope of the tangent line, expressed as: ; According to the second derivative criterion, the stationary point based on the lake surface area is a local maximum point. Therefore, the stationary point is taken as the optimal suitable lake area, expressed as: in, The optimal suitable area for a lake; Based on the optimal suitable area of ​​the lake, the maximum ecological water use efficiency is calculated and expressed as follows: in, This represents the maximum ecological water use efficiency value. These are the coefficients of the solved model.

7. The method for determining the suitable area of ​​a lake according to claim 6, characterized in that, The process of determining the appropriate area range for lakes in order to implement lake ecological management is as follows: Based on the ecological sensitivity of the target lake area, a threshold coefficient is set. ; Based on the threshold coefficient and the optimal suitable area of ​​the lake, a target threshold is set, expressed as: in, The target threshold; Substituting the target threshold into the response function between lake surface area and ecological water use efficiency, we obtain a quadratic equation based on lake surface area, expressed as: ; By rearranging the terms of the quadratic equation in one variable based on the lake surface area, we can obtain a standard form quadratic equation in one variable, which can be expressed as: ; Solving the standard form of the quadratic equation in one variable yields two real roots based on the lake surface area, expressed as: in, , These are the first and second solid roots, respectively, based on the lake surface area; Based on the two real roots of the lake surface area, the lower and upper limits of the suitable lake area are determined, expressed as: in, , These represent the lower and upper limits of the suitable area for lakes, respectively. Based on the lower and upper limits of the suitable area for lakes, the suitable area range for lakes is obtained, represented as: ; Implement lake ecological management based on the appropriate area range of the lake.

8. The method for determining the suitable area of ​​a lake according to claim 7, characterized in that, Based on the suitable area range of the lake, the process of implementing lake ecological management is as follows: when At that time, it indicated that the target lake had shrunk severely, and the ecological water replenishment plan was activated to prioritize its restoration to its original state. above; when When the target lake is in a suitable range, the status quo should be maintained and dynamic monitoring should be implemented. when When the target lake has expanded excessively, the amount of water flowing into the lake should be controlled, and appropriate discharge should be carried out to lower the water level.