Slope-to-terrace project social ecological benefit evaluation and space optimization method based on linear optimization model

Abstract

The invention provides a slope-to-terrace project social ecological benefit evaluation and spatial optimization method based on a linear optimization model, and the method comprises the following steps: (1) obtaining the multi-source data of a region, determining the area and distribution of land suitable for slope-to-terrace in each small watershed, and (2) evaluating the water and soil conservation benefits of slope-to-terrace construction of each small watershed. (3) evaluating economic benefits brought by grain yield increase after slope-to-terrace conversion of each small watershed, and (4) setting two targets of maximum water and soil conservation benefits and maximum crop value-added benefits and constraint conditions of slope-to-terrace total amount control by taking the slope-to-terrace conversion area in each watershed as a variable, simulating and optimizing the ecological and economic benefits of slope-to-terrace conversion, and obtaining a slope-to-terrace conversion result. And determining a spatial pattern of slope-to-terrace in the small watershed under different target weights and constraint conditions. According to the method, the optimal slope-to-terrace construction number of each small watershed under different target priority scenes is quantified through a space optimization mode, and accurate evaluation of regional slope-to-terrace social ecological benefits is realized.

Description

Technical Field

[0001] The invention relates to the field of soil and water conservation, and specifically to a social ecological benefit evaluation and spatial optimization method of a slope-to-terrace project based on a linear optimization model. Background Art

[0002] For areas with serious soil and water loss problems, comprehensive soil and water conservation measures need to be implemented, such as slope-to-grain terraces, slope-to-fruit terraces, soil conservation farming, and returning farmland to forests. Slope-to-terrace projects play an important role in maintaining arable land resources, reducing soil loss, and promoting food production. In the site selection and construction process of slope-to-terrace projects, how to coordinate its soil and water conservation benefits and economic benefits is the key to promoting a win-win situation between soil and water conservation and food security. However, among the various water conservation measures including slope-to-terrace construction based on small watersheds, the spatial layout of measures for the coordinated optimization of ecological and economic benefits at the small watershed level has not yet been clarified, and it is impossible to carry out targeted layout optimization according to regional realities. In conventional slope-to-terrace projects, some only consider ecological benefits, and fail to comprehensively consider the economic benefits of crop value-added. Summary of the invention

[0003] In view of the deficiencies of the above-mentioned prior art, the present invention provides a social-ecological benefit evaluation and spatial optimization method for slope-to-terrace conversion based on a linear optimization model, constructs a soil and water conservation benefit and crop value-added economic benefit model for slope-to-terrace conversion projects on a small watershed scale based on the linear optimization method, analyzes the trade-off relationship between the two types of objectives, and proposes a corresponding spatial optimization layout.

[0004] The technical solution provided by the present invention is a method for evaluating the social ecological benefits and optimizing the space of a slope-to-terrace project based on a linear optimization model, comprising the following steps:

[0005] (1) Obtain multi-source data of the region to determine the area and distribution of land suitable for terrace conversion in each small watershed;

[0006] (2) Using the Chinese soil loss equation model combined with local rainfall, vegetation, slope, and soil characteristics, the soil and water conservation benefits per unit area of ​​slope terraces in different watersheds were quantified;

[0007] (3) Combine field survey data with the GAEZ database to determine the increase in crop yield and value added per unit area brought about by slope-terracing in different small watersheds;

[0008] (4) Taking the area of ​​slope-to-terrace conversion in each watershed as the variable, two objective functions of maximizing the benefit of soil and water conservation and maximizing the benefit of crop value-added as well as the constraint conditions for controlling the total amount of slope-to-terrace conversion were set. The ecological and economic benefits of slope-to-terrace conversion were simulated and optimized, and the spatial pattern of slope-to-terrace conversion in small watersheds under different objective weights and constraint conditions was determined.

[0009] Furthermore, the specific process of step (1) is as follows:

[0010] (1-1) Obtain the scope of cultivated land based on land use data, extract slope information based on digital elevation data, and determine the area of ​​sloping cultivated land in the region;

[0011] (1-2) The original high-resolution images were preprocessed using the Google Earth Engine platform. A land use training set including terraces was extracted through visual interpretation. The classification feature set of the high-resolution images was constructed through band index feature calculation, grayscale texture feature extraction, principal component transformation and feature fusion. The terraces in the region were classified and extracted using random forest to determine their area and range, thereby ultimately determining the spatial distribution and number of sloping farmland and terraces in each watershed.

[0012] Furthermore, the preprocessing in step (1-2) includes any one or more of resampling, cropping and mosaicking.

[0013] Furthermore, the calculation formula of the Chinese soil loss equation in step (2) is:

[0014] A=R×K×LS×B×E×T (1)

[0015] Where: A is the soil erosion modulus, unit: t·hm -2 ·a -1 ; R is the rainfall erosivity factor, unit: MJ·mm·hm -2 ·a -1 ; K is the soil erodibility factor, unit: Mg·h·MJ -1 mm -1 ; The remaining factors are dimensionless, LS is the slope length and slope factor, B is the vegetation coverage and biological measures factor, E is the engineering measures factor, and T is the tillage measures factor;

[0016] The soil and water conservation benefit of terraces is the difference between the soil erosion amount when the terraces are not built and the soil erosion amount of the existing terraces. The specific calculation formula is as follows:

[0017] SE t =R×K×LS×B×(E p -E t )×T (2)

[0018] Among them, SE t represents the soil and water conservation benefit value of terraces, E p With E t Respectively represent the values ​​of soil and water conservation engineering measures factor E for sloping farmland and terraced fields.

[0019] Furthermore, the specific process of step (3) is as follows:

[0020] First, the mean crop yield of the region is obtained through the GAEZ database. Then, the yield coefficients of different slopes are adjusted. The specific crop yield changes are shown in the following formula:

[0021]

[0022] where α i is the area of ​​sloping farmland with different slope categories, which are divided into six categories according to the slope conditions: <6°, 6–10°, 10–15°, 15–20°, 20–25°, and >25°, β i Represents the yield coefficient of different slopes and regions, G ave The mean yield per unit area of ​​each crop, G is the total yield;

[0023] The formula for the crop value-added economic benefits brought by the slope-to-terrace project is as follows:

[0024]

[0025] Among them, EC t It indicates the increase in agricultural product output value brought by the slope-to-terrace project, in yuan. represents the yield of the nth crop in the terraced field, in units of t, represents the yield of the nth crop on sloping farmland, in t, P n is the unit price of the nth crop, in yuan / t.

[0026] Furthermore, the crops include corn, wheat, potatoes, rice, rapeseed, soybeans, peanuts, cotton, tobacco and sunflower seeds, and the unit price of the crops is based on the source price at the place of origin.

[0027] Furthermore, in step (4)

[0028] Goal 1: Maximize the benefits of soil and water conservation.

[0029]

[0030] f1 i =a i (6)

[0031] Where: f1 i represents the target coefficient, n is the number of small watersheds, a i represents the average soil erosion coefficient of the cultivated land that can be converted into terraces in small watershed i, X i is the area of ​​the slope-terraced conversion in the i-th small watershed, Fval1 represents the soil and water conservation benefit value of the slope-terraced conversion, and the unit is t;

[0032] Objective 2: Maximize the crop value-added benefits, that is, maximize the economic benefits of crop value-added from slope-to-terrace conversion. The following two scenarios are considered in this objective:

[0033] Scenario 1: Maximizing the increase in crop yield after converting slopes to terraces

[0034]

[0035] f2 i =v i (8)

[0036] Scenario 2: Considering the spatial distribution of population among river basins on the basis of increasing output value

[0037]

[0038] f2 i =pp i ×v i (10)

[0039] where f2 i represents the target coefficient, pp i The population distribution coefficient of the watershed within the small watershed i is dimensionless and takes values ​​between 0 and 1. i It indicates the output value improvement coefficient brought by the conversion of slope to terrace per unit area, in units of 10,000 yuan / hm2 2 , X i The area of ​​sloping cultivated land.

[0040] Furthermore, the constraint conditions in step (4) include a cost function and a constraint function.

[0041] The cost function is the ratio of the target slope of sloping farmland to the average slope of existing terraces in a watershed.

[0042]

[0043] S i It indicates the difficulty of sloping farmland construction in small watershed i, ranging from 0 to 1, with higher values ​​indicating more difficulty, and dimensionless; i is the average slope of the target cultivated land in the watershed, Ter_s i is the average slope of existing terraces in the basin;

[0044] The constraint function includes the following conditions:

[0045]

[0046] Per is the proportion of cultivated land area converted from slope to terrace (ranging from 10% to 90%, with an interval of 10%, for a total of 9 cases), A represents the total area of ​​target sloping cultivated land in the entire study area, and U represents the total area of ​​target sloping cultivated land in each small watershed.

[0047] Furthermore, the overall objective function of the ecological and economic benefits of slope-to-terrace conversion is as follows:

[0048]

[0049] Where Fval is the total target, w is the weight coefficient (the value is 0-1, 0.01 is the interval, a total of 101 cases), sf1 i With sf2 i f1 i With f2 i The coefficients after normalization.

[0050] The present invention uses high-resolution image data to extract the spatial distribution of terraces in the study area at the scale of a small watershed, combines the Chinese soil loss equation to evaluate the water and soil conservation of terraces and slope-to-terrace construction, and uses the global agricultural ecological zoning data set and survey data to quantify the grain output and output value of unit terrace construction. Based on the linear optimization method, two scenarios and a combination of 909 weights for each scenario are constructed to evaluate the water and soil conservation benefits and crop value-added economic benefits of slope-to-terrace projects at the scale of a small watershed, analyze the trade-off between the two types of goals, and propose a corresponding spatial optimization layout. The present invention quantifies the trade-off between water conservation and crop value-added economic benefits in slope-to-terrace project construction through a spatial optimization method and provides a series of non-inferior solutions for management departments. The research results can provide a reference basis for high-standard farmland construction, small watershed comprehensive management, etc., provide a scientific reference for regional slope-to-terrace construction work, and promote the sustainable development of ecology and economy. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a flow chart of the method of the present invention;

[0052] Figure 2 It is the basic situation of terraced fields and sloping farmland in the embodiment;

[0053] Figure 3 is the grid distribution of terraced fields and sloping farmland in the embodiment;

[0054] Figure 4 is a spatial result diagram of various soil erosion factors in the embodiment;

[0055] Figure 5 is a spatial distribution map of soil and water conservation benefits of terraced fields in the embodiment;

[0056] Figure 6is a spatial distribution map of the population in the watershed and the added economic benefits of terraced crops in the embodiment;

[0057] Figure 7 is a coefficient spatial distribution difference diagram of each watershed in the linear optimization of the embodiment;

[0058] Figure 8 It is a spatial distribution diagram of the optimal area allocation of the slope-to-terrace project in each watershed under the different proportions of slope-to-terrace in the embodiment;

[0059] Fig. 9 It is the trade-off relationship between the area of ​​slope-to-terracing, the economic benefit of crop value-added and the benefit of soil and water conservation under different scenarios in the embodiment and the result of target value change;

[0060] Fig.10 It is a non-inferior solution under different slope-to-staircase ratio scenarios in the embodiment. DETAILED DESCRIPTION

[0061] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0062] like Figure 1 The method for evaluating the social ecological benefits and optimizing the space of the slope-to-terrace project based on the linear optimization model shown in the figure includes the following steps:

[0063] (1) Obtain multi-source data of the region to determine the area and distribution of land suitable for terrace conversion in each small watershed;

[0064] (2) Using the Chinese soil loss equation model combined with local rainfall, vegetation, slope, and soil characteristics, the soil and water conservation benefits per unit area of ​​slope terraces in different watersheds were quantified;

[0065] (3) Combine field survey data with the GAEZ database to determine the increase in crop yield and value added per unit area brought about by slope-terracing in different small watersheds;

[0066] (4) Taking the area of ​​slope-to-terrace conversion in each watershed as the variable, two objective functions of maximizing the benefit of soil and water conservation and maximizing the benefit of crop value-added as well as the constraint conditions for controlling the total amount of slope-to-terrace conversion were set. The ecological and economic benefits of slope-to-terrace conversion were simulated and optimized, and the spatial pattern of slope-to-terrace conversion in small watersheds under different objective weights and constraint conditions was determined.

[0067] Example 1

[0068] 1. Taking Danjiangkou City as an example, a series of basic data such as social economy and natural climate were used. The sources and descriptions of various data are shown in Table 1.

[0069] Table 1 Basic data information

[0070]

[0071] 2. Obtain multi-source data in the region to determine the potential area of ​​slope-to-terrace conversion in the study area, including digital elevation models, high-resolution images, land use data, etc., to determine the area and distribution of land suitable for slope-to-terrace conversion in each small watershed in the study area. The land use data is 2018-2022, with a resolution of 30m, taken from the CLCD dataset; the high-resolution images are Gaofen-1 images, Google Maps ETM+ sensor data, etc.; the digital elevation model is GDEMV2. The specific process is as follows: First, the scope of cultivated land is obtained based on land use data, and the slope and other information are extracted based on digital elevation data to determine the area of ​​sloping cultivated land in the region. However, some of them are already terraces. The terraces in the sloping cultivated land are eliminated, and the remaining area is the area that can be converted from slope to terrace, so as to determine the maximum area of ​​slope-to-terrace conversion in each watershed, which is used as constraint A in the subsequent optimization. The original high-resolution images were resampled, cropped, and mosaicked using the Google Earth Engine (GEE) platform. The land use training set, including terraces, was extracted using visual interpretation methods. The classification feature set of the high-resolution images was constructed by band index feature calculation, grayscale texture feature extraction, principal component transformation, and feature fusion. The terraces in Danjiangkou City were classified and extracted using random forests to determine the area and range of the terraces, thereby ultimately determining the spatial distribution and number of sloping farmland and terraces in each basin of the study area.

[0072] The main features selected include spectral features, index features and texture features, and a total of 30 features are fused for high-resolution image classification (see Table 2).

[0073] Table 2 High-resolution image classification feature set

[0074]

[0075]

[0076] The training and validation samples were selected by visual interpretation. The classification was based on the "Land Use Classification" standard and the land use status map, and seven categories were identified: terraces, grasslands, construction land, forest land, water bodies, unused land and cultivated land. The study area was divided into 50 equal-area grid areas, and 1-2 random samples were selected from each area for each type of land use. The total number of samples exceeded 400, and there were no less than 50 sample points for each type of land use. The training samples and validation samples were allocated in a ratio of 7:3 to ensure that they obeyed the same distribution. The results showed that the overall land use classification accuracy and Kappa coefficient exceeded 0.9, among which the user accuracy and producer accuracy of terrace identification reached 0.83 and 0.82 respectively.

[0077] 3. Soil and Water Conservation Benefit Assessment Method

[0078] The CSLE model is selected to estimate the soil and water conservation amount (soil erosion modulus) in the present invention. The calculation formula of the CSLE equation is:

[0079] A=R×K×LS×B×E×T (1) where A(t·hm -2 ·a -1 ) is the soil erosion modulus, R (MJ·mm·hm -2 ·a -1 ) is the rainfall erosivity factor, K (Mg·h·MJ -1 mm -1 ) is the soil erodibility factor. The remaining factors are dimensionless, namely the slope length and slope factor LS, the vegetation coverage and biological measures factor B, the engineering measures factor E, and the tillage measures factor T. The calculation of the R, K, and LS factors refers to the "Technical Guidelines for Dynamic Monitoring of Soil and Water Loss in Hubei Province in 2022"; the calculation of the B factor is based on the forest understory coverage in the region; and the E and T factors are directly assigned according to the specific land use conditions. The present invention mainly considers the main soil and water conservation measures in the study area-the horizontal terraces on the ridge, and assigns it a value of 0.084 with reference to the "Guidelines"; for tillage measures, the area belongs to the Qinba Mountain area where dry land is double-cropped and one-cropped and paddy fields are double-cropped, and the T value of the area is 0.403.

[0080] The soil and water conservation benefit of terraces in the present invention refers to the difference between the soil erosion amount of existing terraces and the amount of soil erosion when the terraces are not built. The specific calculation formula is as follows:

[0081] SE t =R×K×LS×B×(E p -E t )×T (2)

[0082] Among them, SE t represents the soil and water conservation benefit value of terraces, E p With E t Respectively represent the values ​​of soil and water conservation engineering measures factor E for sloping farmland and terraced fields.

[0083] 4. Methods for evaluating the economic benefits of crop value-added

[0084] The present invention defines the economic benefits of crop value-added as the increase in output value brought about by the increase in crop yield after the implementation of the slope-to-terrace project. The steps for determining the crop yield per unit area of ​​sloping cultivated land are as follows: First, the mean crop yield of the study area is obtained through the GAEZ database. The main crops include corn, wheat, potatoes, rice, rapeseed, soybeans, peanuts, cotton, tobacco and sunflower seeds; then, adjustments are made based on the yield coefficients of different slopes. The specific crop yield changes are shown in the following formula:

[0085]

[0086] where α i The area of ​​sloping farmland with different slope categories is divided into six categories according to the slope conditions: <6°, 6–10°, 10–15°, 15–20°, 20–25°, and >25°. i represents the yield coefficient of different slopes and regions (see Table 3), G ave The mean yield per unit area of ​​each crop (in ton), G is the total yield (in ton).

[0087] Table 3 Yield coefficient of sloping farmland

[0088]

[0089] Field research revealed that the increase in crop yields after the slope-to-terrace project in the region was as follows: corn increased by 31%, potatoes by 36%, wheat by 75%, tobacco by 0.84%, and the rest of the crops were calculated based on an average increase of 47%. Based on this, the increased crop yield after the slope-to-terrace project was calculated, and the unit price of the crop was referenced to the source price of the production area. The specific unit price is shown in Table 4.

[0090] Table 4 Crop unit price table

[0091]

[0092] The formula for the crop value-added economic benefits brought by the slope-to-terrace project is as follows:

[0093]

[0094] Among them, EC t It indicates the increase in agricultural product output value brought by the slope-to-terrace project (in yuan). represents the yield of the nth crop in the terraced field (in t), represents the yield of the nth crop on sloping farmland (in tons), P n is the unit price of the nth crop (in yuan / t).

[0095] 5. Small watershed scale spatial optimization model

[0096] The present invention uses MATLAB 2018b software to construct a spatial optimization model for slope-to-terrace conversion in Danjiangkou City. The optimization object is the sloping farmland with a slope between 5-25° in the small watershed. The scope is determined by referring to the construction standard of slope-to-terrace conversion (Plan for the Construction of High-standard Farmland in Hubei Province (2022-2030)). This part of sloping farmland is referred to as target sloping farmland in the following text. The optimization result is whether to carry out slope-to-terrace conversion construction. The optimization goal is to maximize the water and soil conservation benefits and grain value-added benefits brought by slope-to-terrace conversion. The specific optimization method is as follows:

[0097] (1) Objective function

[0098] Goal 1: Maximize the benefits of soil and water conservation from slope-to-terrace conversion, i.e. prioritize soil and water conservation benefits

[0099]

[0100] f1 i =a i (6)

[0101] Where f1 represents the target coefficient, n is the number of small watersheds (79), a represents the average soil erosion coefficient of the cultivated land that can be converted into terraces in small watershed i, and is obtained by multiplying the average value of the factors R, K, LS, B, and T in each watershed and the numerical value of the change in the E factor after the slope-to-terrace conversion, and multiplying it by the area represented by the unit grid (unit: t / hm 2 ). i is the area of ​​the slope-to-terrace conversion of the i-th small watershed (hm 2 ). Fval1 represents the soil and water conservation benefit value of slope-to-terrace conversion, in units of t.

[0102] Objective 2: To maximize the economic benefits of crop value-added from converting slopes to terraces, that is, giving priority to crop value-added benefits. Two scenarios are considered in this objective.

[0103] Scenario 1: Maximizing the increase in crop yield after converting slopes to terraces

[0104]

[0105] f2 i =v i (8)

[0106] Scenario 2: Considering the spatial distribution of population among river basins on the basis of increasing output value

[0107]

[0108] f2 i =pp i ×v i (10)

[0109] Where f2 represents the target coefficient 2, pp represents the population distribution coefficient of the basin in the small basin i (dimensionless, value 0-1), which is calculated by subtracting the population of each small basin from the minimum population of all basins in the city and then dividing it by the difference between the maximum and minimum populations in the basins of the city; v represents the output value improvement coefficient brought about by the slope conversion per unit area (unit: 10,000 yuan / hm2 2 ), X is the area of ​​sloping cultivated land.

[0110] (2) Cost function and constraint function

[0111] The present invention also designs a cost function, which believes that the greater the ratio of the target sloping farmland slope to the average slope of existing terraces in a certain watershed, the higher the construction difficulty and cost will be. The specific formula is as follows:

[0112]

[0113] S i It indicates the difficulty of sloping farmland construction in small watershed i, ranging from 0 to 1, with higher values ​​indicating more difficulty, and dimensionless; i is the average slope of the target cultivated land in the watershed, Ter_s i It is the average slope of existing terraces in the basin.

[0114] Set the constraint function for converting the target sloping farmland into terraces in each small watershed:

[0115]

[0116] Per is the proportion of cultivated land area converted from slope to terrace, ranging from 10% to 90% with an interval of 10%. A represents the total area of ​​target sloping cultivated land in the entire study area, and U represents the total area of ​​target sloping cultivated land in each small watershed.

[0117] The overall objective function of the present invention is as follows:

[0118]

[0119] Among them, Fval is the total goal, w is the weight coefficient (the value is 0-1, 0.01 is the interval), and there are 101 weight values. Since 9 conditions are designed for the proportion of cultivated land area in the slope-to-terrace restriction conditions, there are a total of 909 combinations of different weights. Due to the difference in order of magnitude between Fval1 and Fval2, the coefficients f1 and f2 of the two are normalized by normal standardization during linear optimization, and the processed coefficients are sf1 and sf2 respectively.

[0120] The present invention obtains the basic situation of the spatial distribution of terraced fields and target sloping farmland in Danjiangkou City (see below). Figure 2 ), the results show that there are 79 small watersheds in Danjiangkou City, with the largest area of ​​about 239.56km 2 , with a minimum area of ​​approximately 14.05km 2 Overall, the area distribution of terraces and target sloping farmland is mainly concentrated in the central and northern parts of the basin, while the distribution in the south is relatively small. In terms of slope, the average slope of terraces in Danjiangkou City is about 12.94°, while the average slope of target sloping farmland is about 14.01°. In addition, the average slope of terraces and target sloping farmland in each small watershed is similar in spatial distribution, showing a pattern of high slopes in the southwest and gentle slopes in the east and north.

[0121] The present invention further analyzes the spatial differences in the distribution of terraces and target sloping farmland (see below). Figure 3 ). The results show that the overall distribution of the constructed terraces and the target sloping farmland that can be developed into terraces in the future is similar, and presents a certain staggered distribution pattern. The distribution center of the terraces is biased to the southwest compared with the target sloping farmland, but in general, the distribution of the center of gravity of the two is similar. Through the standard deviation ellipse analysis of land use distribution, it is found that the standard deviation ellipse area of ​​the existing terraces is 1316.91km 2 , and the standard deviation ellipse area of ​​the target sloping farmland is 1208.47km 2 The standard deviation ellipse area of ​​terraces is about 8.97% higher, indicating that the spatial concentration of the target sloping farmland in Danjiangkou City is slightly higher, while the distribution of terraces in the city is more dispersed.

[0122] The spatial results of soil erosion factors in Danjiangkou City are shown in Figure 4 In order to quantify the soil and water conservation benefits brought by terraces, the present invention calculates the soil erosion amount when the existing terraces are assumed to be sloping farmland, and obtains the difference between the terraces and sloping farmland, thereby obtaining the soil and water conservation benefits of terraces in each small watershed (such as Figure 5 The total amount (10,000 tons) and the soil and water conservation benefits of terraced fields per unit grid area (t / 0.09hm 2 ).

[0123] In order to quantify the economic benefits of crop value-added brought by the conversion of slopes into terraces, the crop output value increase of existing terraces compared with sloping farmland was obtained by referring to the crop output value calculation method (e.g. Figure 6 The results show that the areas with higher crop output value increase of terraces are distributed in the eastern and northern basins of Danjiangkou City, most of which are located around the Danjiangkou Reservoir, while the crop output value increase in the southwest of the city is relatively small. By comparing the population in the basin, it can be found that the crop value-added economic benefits generated by the slope-to-terrace project in the densely populated basin are generally higher, indicating that the existing terrace construction is in line with the laws of natural and social development, and tends to be carried out in locations with a large population and good planting conditions.

[0124] The present invention extracts the coefficient values ​​required in each small watershed, and its specific spatial distribution is as follows: Figure 7 The coefficient of target one is the amount of soil and water conservation per hectare of terraced fields after the slope is converted to terraced fields. Figure 6The average water and soil conservation benefits of the existing terraces shown in are similar, and the water and soil conservation benefits per unit area brought by the basin terraces on the southwest side are higher. The original coefficient of Target 2 (Scenario 1 of Target 2) is the increase in crop output value that may be brought about by the construction of terraces per hectare. It can be found that the coefficient value in the central and northern regions under this target is significantly higher, while the value in the southwest region is lower. At the same time, since the economic benefits of crop value-added brought about by slope-to-terrace conversion are for local farmers, Scenario 2 of Target 2 is set: It is believed that in areas with more and denser population distribution, more consideration should be given to increasing crop output value and carrying out slope-to-terrace conversion projects. This will be conducive to the efficient use of terrace projects by farmers and reduce the possibility of their abandonment.

[0125] In terms of cost coefficient, the present invention assumes that the level of construction of slope-to-terrace conversion in each basin is related to the existing terraces. If the slope of the newly added slope-to-terrace conversion project is greater than the slope of the existing terraces, the construction difficulty will be greater, and vice versa. The results show that the slope values ​​of the target sloping farmland in the north and southeast regions are relatively different from those of the existing terraces, resulting in a higher cost coefficient (see Figure 7 ).

[0126] The present invention analyzes the distribution optimization results of the slope-to-terrace project in the watershed under different scenarios and the trade-off relationship between soil and water conservation benefits and crop value-added through a linear optimization method.

[0127] (1) Spatial differences in optimization results based on different objectives

[0128] The optimization objectives were set as the highest soil and water conservation benefit ("Goal 1 Priority" scenario), the highest crop value-added economic benefit ("Goal 2 Priority" scenario), and the two with equal weights ("Trade-off" scenario). In the optimization solution process, different slope-to-terrace area restrictions were used. At the same time, the solution results were divided into two scenarios (considering population distribution scenario and not considering population distribution scenario) based on the coefficient of Goal 2. The spatial distribution of slope-to-terrace projects in the basin under different scenarios is shown below. Figure 8 From the spatial distribution results of each scenario, in the "Goal One Priority" scenario, priority is given to the construction of slope-to-terraced land in the river basins in the southwest. In the "Goal Two Priority" scenario, priority is given to the construction of slope-to-terraced land in the river basins in the central part, and there is basically no construction area in the river basins in the southwest. In the "Trade-off" scenario, the optimization results weighed the two types of goals to obtain a more compromised optimization result. Comparing Scenario 1 with Scenario 2, it was found that under the priority of crop value-added benefits, the slope-to-terraced land area allocated to the river basins in Scenario 2 was concentrated in the eastern part and the river basins around the Danjiangkou Reservoir, which is in line with Figure 5 The distribution of population in China.

[0129] At the same time, the water and soil conservation benefits and crop value-added brought by linear optimization under each scenario were analyzed (see Table 5). When pursuing water and soil conservation benefits first (i.e., "Goal One Priority"), the two types of benefit values ​​and the spatial allocation of slope-to-terrace conversion in Scenario 1 and Scenario 2 are the same, and the highest water and soil conservation benefit is to reduce erosion by about 3.207 million tons. When pursuing crop value-added benefits first (i.e., "Goal Two Priority"), the benefit value of Scenario 2 will be slightly lower than that of Scenario 1, and the highest crop value-added economic benefit value is about 187.45 million yuan. In addition, we compared the differences in specific benefit values ​​of each small watershed under different scenarios. Taking the scenario of completing 90% of the slope-to-terrace conversion ratio under Scenario 1 as an example, in terms of water and soil conservation benefits, the "Goal One Priority" scenario has an average of about 2,500 tons of soil and water conservation higher than the "Goal Two Priority" scenario, and the highest difference is about 116,000 tons. The "trade-off" scenario has an average of about 1,400 tons more soil and water conservation than the "Goal 2 Priority", with the highest difference of about 48,400 tons. In terms of economic benefits, the "Goal 2 Priority" scenario has an average increase of about 118,000 yuan compared with the "Goal 1 Priority" scenario, with the highest difference of about 3.769 million yuan. At this time, the "trade-off" scenario has an average increase of about 79,000 yuan compared with the "Goal 1 Priority" scenario, with the highest difference of about 3.769 million yuan.

[0130] Table 5 Benefit values ​​of linear optimization results under each scenario

[0131]

[0132]

[0133] In order to reveal the trade-off between the economic benefits of crop value-added and the benefits of soil and water conservation, the objective function was constructed by 101 sets of weights at each slope-to-terrace ratio during the optimization process, and the optimization solution was performed. The results showed that as the slope-to-terrace area increased, the values ​​of the economic benefits of crop value-added and the benefits of soil and water conservation also increased accordingly ( Fig. 9 (a) with Fig. 9 (d)). At the same time, there is an obvious trade-off between the social and economic benefits and the soil and water conservation benefit goals. With the increase in the area of ​​​​slope-to-terrace conversion, the soil and water conservation benefits of goal 1 and the economic benefits of crop value-added of goal 2 have increased. At the same time, under the restrictions of the slope-to-terrace conversion area between scenario 1 and scenario 2, the range of the curve values ​​is similar, and the target value distribution is similar to an arc ( Fig. 9 (b) with Fig. 9 (e)). Among them, the non-inferior solution (non-inferior solution means that in the given set of available options, no solution that can improve each criterion can be found.) shows that with the improvement of soil and water conservation benefits, the added value of crops has decreased, which shows that there is a certain trade-off relationship between the two goals, and it is impossible to achieve the maximum soil and water conservation benefits and crop added value at the same time. Fig. 9 (c) and Fig. 9(f) shows the change of each target value (normalized) with the weight under different weight combinations. In general, the higher the weight of the target value, the higher its value will be. Fig. 9 As shown in Figure (c), when the slope-to-ladder ratio is low (such as 10% slope-to-ladder ratio), the total target value shows a pattern of first decreasing and then increasing. As the slope-to-ladder ratio increases, the total target value will show a linear downward trend. In Figure (f), the change trend of the total target value is that it increases with the increase of the weight coefficient.

[0134] In practical applications, non-inferior solutions are usually the solution sets that decision makers pay more attention to. This solution set provides feasible solutions when multiple objectives are weighed against each other. For example, when the crop value-added benefit is more than 44 million yuan or the soil and water conservation benefit is more than 846,000 tons at a 20% slope-to-terrace ratio, the solution set at this time is a non-inferior solution; this part of the solution set provides decision makers with higher soil and water conservation benefits or higher crop value-added benefits. Fig.10 The proportion of non-inferior solutions in all solution sets under different weight coefficients was further analyzed (the situation in scenario 1 is the same as that in scenario 2). The results show that when the weight coefficient is close to 0 or 1, more non-inferior solutions can be generated, and the total number and proportion of non-inferior solutions also increase accordingly. In practical applications, decision makers can choose a non-inferior solution for implementation and application based on local actual conditions, policy orientation, etc.

[0135] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for evaluating the social ecological benefits and spatial optimization of slope-to-terrace projects based on a linear optimization model, characterized in that: The steps include: (1) Obtain multi-source data of the region to determine the area and distribution of land suitable for terrace conversion in each small watershed; (2) Using the Chinese soil loss equation model combined with local rainfall, vegetation, slope, and soil characteristics, the soil and water conservation benefits per unit area of ​​slope terraces in different watersheds were quantified; (3) Combine field survey data with the GAEZ database to determine the increase in crop yield and value added per unit area brought about by slope-terracing in different small watersheds; (4) Taking the area of ​​slope-to-terrace conversion in each watershed as the variable, two objective functions were set, namely, maximizing the benefit of soil and water conservation and maximizing the benefit of crop value-added, as well as the constraint conditions for controlling the total amount of slope-to-terrace conversion. The ecological and economic benefits of slope-to-terrace conversion were simulated and optimized, and the spatial pattern of slope-to-terrace conversion in small watersheds under different objective weights and constraint conditions was determined.

2. The method for evaluating the social ecological benefits and optimizing the space of a slope-to-terrace project based on a linear optimization model according to claim 1 is characterized in that: The specific process of step (1) is as follows: (1-1) Obtain the scope of cultivated land based on land use data, extract slope information based on digital elevation data, and determine the area of ​​sloping cultivated land in the region; (1-2) The original high-resolution images were preprocessed using the Google Earth Engine platform. A land use training set including terraces was extracted through visual interpretation. The classification feature set of the high-resolution images was constructed through band index feature calculation, grayscale texture feature extraction, principal component transformation and feature fusion. The terraces in the region were classified and extracted using random forest to determine their area and range, thereby ultimately determining the spatial distribution and number of sloping farmland and terraces in each watershed.

3. The method for evaluating the social ecological benefits and optimizing the space of a slope-to-terrace project based on a linear optimization model according to claim 2 is characterized in that: The preprocessing in step (1-2) includes any one or more of resampling, cropping and mosaicking.

4. The method for evaluating the social ecological benefits and optimizing the space of a slope-to-terrace project based on a linear optimization model according to claim 1 is characterized in that: The calculation formula of the Chinese soil loss equation in step (2) is: A=R×K×LS×B×E×T (1) Where: A is the soil erosion modulus, unit: t·hm -2 ·a -1 ; R is the rainfall erosivity factor, unit: MJ·mm·hm -2 ·a -1 ; K is the soil erodibility factor, unit: Mg·h·MJ -1 mm -1 ; The remaining factors are dimensionless, LS is the slope length and slope factor, B is the vegetation coverage and biological measures factor, E is the engineering measures factor, and T is the tillage measures factor; The soil and water conservation benefit of terraces is the difference between the soil erosion amount when the terraces are not built and the soil erosion amount of the existing terraces. The specific calculation formula is as follows: SE t =R×K×LS×B×(E p -E t )×T (2) Among them, SE t represents the soil and water conservation benefit value of terraces, E p With E t Respectively represent the values ​​of soil and water conservation engineering measures factor E for sloping farmland and terraced fields.

5. The method for evaluating the social ecological benefits and optimizing the space of a slope-to-terrace project based on a linear optimization model according to claim 1 is characterized in that: The specific process of step (3) is as follows: First, the mean crop yield of the region is obtained through the GAEZ database. Then, the yield coefficients of different slopes are adjusted. The specific crop yield changes are shown in the following formula: where α i is the area of ​​sloping farmland of different slope categories, β i Represents the yield coefficient of different slopes and regions, G ave The mean yield per unit area of ​​each crop, G is the total yield; The formula for the crop value-added economic benefits brought by the slope-to-terrace project is as follows: Among them, EC t It indicates the increase in agricultural product output value brought by the slope-to-terrace project, in yuan. represents the yield of the nth crop in the terraced field, in units of t, represents the yield of the nth crop on sloping farmland, in t, P n is the unit price of the nth crop, in yuan / t.

6. The method for evaluating the social ecological benefits and optimizing the space of a slope-to-terrace project based on a linear optimization model according to claim 5 is characterized in that: The crops include corn, wheat, potatoes, rice, rapeseed, soybeans, peanuts, cotton, tobacco and sunflower seeds, and the unit price of the crops is based on the source price at the place of origin.

7. The method for evaluating the social ecological benefits and optimizing the space of a slope-to-terrace project based on a linear optimization model according to claim 1 is characterized in that: Objective 1 in step (4): maximizing the benefits of soil and water conservation, f1 i =a i (6) Where: f1 i represents the target coefficient, n is the number of small watersheds, a i represents the average soil erosion coefficient of the cultivated land that can be converted into terraces in small watershed i, X i is the area of ​​the slope-terraced conversion in the i-th small watershed, Fval1 represents the soil and water conservation benefit value of the slope-terraced conversion, and the unit is t; Objective 2: Maximize the crop value-added benefits, that is, maximize the economic benefits of crop value-added from slope-to-terrace conversion. The following two scenarios are considered in this objective: Scenario 1: Maximizing the increase in crop yield after converting slopes to terraces f2 i =in i (8) Scenario 2: Considering the spatial distribution of population among river basins on the basis of increasing output value f2 i =pp i ×v i (10) where f2 i represents the target coefficient, pp i The population distribution coefficient of the watershed within the small watershed i is dimensionless and takes values ​​between 0 and 1. i It indicates the output value improvement coefficient brought by the conversion of slope to terrace per unit area, in units of 10,000 yuan / hm2 2 , X i The area of ​​sloping cultivated land.

8. The method for evaluating the social ecological benefits and optimizing the space of a slope-to-terrace project based on a linear optimization model according to claim 7 is characterized in that: The constraints in step (4) include a cost function and a constraint function. The cost function is the ratio of the target slope of sloping farmland to the average slope of existing terraces in a watershed. S i It indicates the difficulty of sloping farmland construction in small watershed i, ranging from 0 to 1, with higher values ​​indicating more difficulty, and dimensionless; i is the average slope of the target cultivated land in the watershed, Ter_s i is the average slope of existing terraces in the basin; The constraint function includes the following conditions: Where Per is the proportion of cultivated land area converted from slope to terrace, A represents the total area of ​​target sloping cultivated land in the entire study area, and U represents the total area of ​​target sloping cultivated land in each small watershed.

9. The method for evaluating the social ecological benefits and optimizing the space of a slope-to-terrace project based on a linear optimization model according to claim 8 is characterized in that: The overall objective function of the ecological and economic benefits of slope-to-terrace conversion is as follows: Where Fval is the total target, w is the weight coefficient, sf1 i With sf2 i f1 i With f2 i The coefficients after normalization.

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