Regional water resource accessibility evaluation method based on river network accessibility and water resource quantity

Abstract

The invention discloses a regional water resource accessibility evaluation method based on river network accessibility and water resource quantity. The method comprises the following steps: step 1, collecting terrain, river network, rainfall and water network engineering data of a to-be-analyzed region; step 2, determining a river network accessibility evaluation index, determining an evaluation scale according to evaluation requirements, performing space grid division on an evaluation region, and calculating an evaluation index value on a space grid; step 3, performing normalization processing on the evaluation indexes; 4, determining the accessibility of the river network through a factor analysis method; and 5, evaluating and analyzing the reachability of the regional water resources by combining the reachability of the river network and the quantity of the water resources. According to the method, the evaluation model is established, the river network accessibility and the water resource quantity are comprehensively considered, the regional water resource accessibility is evaluated, and the independent influence of the river network layout or the water resource quantity on the water resource accessibility is clarified, so that the actual effect of water network engineering construction is clearly expressed, and the understanding of the water network is improved; and the planning level of water network management and water network engineering is improved.

Description

Technical Field

[0001] The invention relates to the field of river network evaluation and management, and proposes a regional water resource accessibility evaluation method based on water network accessibility and water resource quantity. Background Art

[0002] Water resource accessibility is a common indicator to describe the availability and convenience of regional water resources. Specifically, it refers to the difficulty of obtaining water from the river network at any point in the region. Water resource accessibility is the key to determining the amount of water used and the efficiency of water use. Therefore, it is of great significance to understand the role of water network projects and further optimize the water network pattern to explore the impact of water network projects on regional water resource accessibility and its spatial distribution. At present, the research on water resource accessibility is mainly based on indicators such as water intake distance, elevation difference, runoff, land use, and river connectivity. The indicators are weighted to calculate accessibility through hierarchical analysis, fuzzy synthesis, TOPSIS, etc. There are limitations in the selection of indicators, and the combination method is greatly affected by subjective factors. The accessibility evaluation results lack clear practical significance. In areas with dense river networks but scarce water resources, water accessibility is low, and water accessibility can be improved by obtaining additional water through water diversion projects; in areas with abundant water resources, accessibility is low due to the lack of river networks as transportation channels, and accessibility needs to be improved through the construction of water network projects. Previous accessibility evaluations mixed river network characteristic indicators and runoff, making it difficult to identify the key factors affecting water resource accessibility. Summary of the invention

[0003] Based on the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a regional water resource accessibility evaluation method based on river network accessibility and water resource quantity, aiming to establish a water resource accessibility evaluation system including river network accessibility and water resource quantity, clarify the impact of water network engineering construction, and enhance the comprehensive understanding of the water network pattern by the river basin management department. Therefore, innovative methods are needed to construct a water resource accessibility evaluation model. On the basis of determining the river network accessibility through factor analysis and combining the water resource quantity, the above problems can be well solved. The water resource accessibility evaluation model established based on this is of great significance.

[0004] The present invention provides a method for evaluating regional water resource accessibility based on river network accessibility and water resource quantity, comprising:

[0005] Collect data on topography, river network, precipitation, water network engineering and water diversion in the area to be evaluated, and obtain spatial sample points from the area to be evaluated;

[0006] Select terrain indicators, river spatial structure indicators and river network topological structure indicators as river network accessibility evaluation indicators, extract various evaluation indicator values ​​within spatial sample points, and use the mean values ​​of various evaluation indicators as sample data;

[0007] The normalized evaluation indicators are combined into a sample matrix X, and the covariance matrix S of the sample matrix is ​​calculated. After determining the appropriate evaluation indicators, the orthogonal factor model of the sample matrix is ​​established, and the expression is:

[0008] X=μ+AF+ε

[0009] The parameters of the above formula satisfy

[0010] Where, F=(F1,F2,…,F m ) T is the set of common factors of the sample matrix X, m is the number of common factors, μ=(μ1,μ2,…,μ K ) T is the mean of the sample matrix X, ε=(ε1,ε2,ε3,…,ε K ) T is a special factor set of the sample matrix X, mE(ε) is the mean of the variable ε, var(ε) is the covariance of each element in the variable ε, is a diagonal matrix, is the variance of the Kth variable, I is the covariance matrix of the common factors, cov(F,ε) is the covariance between the variable F and the variable ε, A=(a Km ) K×m is the factor loading matrix of the sample matrix X, cov(X,F)=A,CD=AA T , A T is the factor loading transposed matrix, and D is the covariance matrix of the special factor; A and D are obtained by the following process:

[0011] i) Decompose the covariance matrix S of the sample matrix, the expression is:

[0012]

[0013] In the formula, λ1, λ2, ...λ K is the eigenvalue of the covariance matrix, and λ1≥λ2≥…≥λ K ≥0,l1,l2,…,l K is the corresponding eigenvector, T stands for transpose;

[0014] ii) Estimate the relevant parameters through the principal component method and determine the number of common factors m, so as to obtain the variance of the factor loading matrix and the variance estimate of the special factors, expressed as:

[0015]

[0016] In the formula, s KK is the diagonal element of the sample covariance matrix S, diag(BB T) is the matrix B, the transposed matrix B T The diagonal matrix of ;

[0017] Perform an orthogonal rotation on the common factor with the largest variance to obtain the rotated factor score matrix Z, which is expressed as:

[0018]

[0019] Where Γ is an orthogonal matrix, then the factor orthogonal model after rotation is: X = μ + AΓZ + ε;

[0020] Variance contribution through common factors The weighted calculation of river network accessibility H is expressed as:

[0021]

[0022] In the formula, Z m is the element of the rotated factor score matrix Z;

[0023] Combining river network accessibility and natural water resources, the water resource accessibility W of the area to be evaluated is evaluated, and the expression is:

[0024] W=H·R

[0025] Where R is the runoff of the catchment area and H is the accessibility of the river network.

[0026] In some embodiments, the terrain indicator d is formally defined K , river spatial structure index z K and river network topological structure index g K , the expression is:

[0027] d 1,2,...,K1 =[d 1,2,...,K1,1 ,d 1,2,...,K1,2 ,…,d 1,2,...,K1,N ]

[0028] z 1,2,...,K2 =[z 1,2,...,K2,1 ,z 1,2,...,K,2 ,…,z 1,2,...,K2,N ]

[0029] g 1,2,...,K3 =[g 1,2,...,K3,1 ,g 1,2,...,K,2 ,…,g 1,2,...,K3,N ]

[0030] In the formula, N is the number of samples, d is 1,2,...,K1 is the K1th evaluation index terrain index value of all samples, z 1,2,...,K2 is the K2th evaluation index river spatial structure index value of all samples, g 1,2,...,K3It is the K3th evaluation index of river network topology index value of all samples.

[0031] In some embodiments, determining a suitable evaluation index further comprises performing a KMO test and a Bartlett sphericity test on the sample to determine a suitable evaluation index.

[0032] In some implementations, the part with a large covariance eigenvalue is determined as a common factor, and the number of common factors m is set.

[0033] In some embodiments, the positive or negative sign of the connecting symbol in the expression of river network accessibility H depends on the positive or negative meaning of the common factor. If it is positive, the connecting symbol is +, and if it is negative, the connecting symbol is -.

[0034] In some embodiments, the expression of the average runoff is:

[0035] R=A r ·P·α

[0036] Where R is the runoff of the catchment area, A r is the catchment area, P is the average annual precipitation in the catchment area, and α is the runoff coefficient of the catchment area;

[0037] The multi-year average runoff R is used as an estimate of natural water resources.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1) By establishing an evaluation model, comprehensively considering river network accessibility and water resources, evaluating regional water resource accessibility, clarifying the independent impact of river network layout or water resources on water resource accessibility, and making the actual role of water network project construction clearly expressed, it is conducive to enhancing the understanding of water networks and improving the level of water network management and water network project planning;

[0040] 2) Common factors were introduced, and the variance contribution of common factors was weighted to calculate the river network accessibility, which more effectively improved the influence and pertinence of the dominant factors in the evaluation model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of the regional water resource accessibility evaluation method based on river network accessibility and water resource quantity of the present invention;

[0042] Figure 2 It is a schematic diagram of the specific process of determining river network accessibility through factor analysis;

[0043] Figure 3 It is the spatial distribution map of river network accessibility;

[0044] Figure 4 It is the spatial distribution map of water resources;

[0045] Figure 5 It is the spatial distribution map of water resource accessibility. DETAILED DESCRIPTION

[0046] The technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0047] The technical solution of the present invention is described below in conjunction with specific embodiments and drawings.

[0048] like Figure 1 As shown, the regional water resource accessibility evaluation method based on river network accessibility and water resource quantity of the present invention has the following specific process:

[0049] Step 1: Collect the topography, river network, precipitation, water network engineering and water diversion data of the area to be evaluated; specifically, the collected data are regional digital elevation data, river line vector data in 2019, precipitation data of rain gauges from 2003 to 2018, vector data of the South-to-North Water Diversion Middle Route Project, and water diversion data of the South-to-North Water Diversion Middle Route Project from 2014 to 2021;

[0050] Step 2: Select and calculate the river network accessibility evaluation indicators. The specific steps are as follows:

[0051] Step 2-1: According to the evaluation cost, the evaluation scale is determined to be 1km*1km. According to the evaluation scale, the area to be evaluated is divided into square grids of equal area in ArcGIS, which are used as spatial sample points.

[0052] Step 2-2, select three types of indicators, namely terrain indicators, river spatial structure indicators and river network topological structure indicators, as evaluation indicators, collect various indicators contained in each grid, calculate the mean of various indicators respectively, and use the mean as sample data; according to previous studies, the indicators characterizing terrain mainly include elevation, undulation, slope, distance, etc., the indicators describing the spatial structure of rivers mainly include river network density, box dimension, branch ratio, river curvature, etc., and the indicators describing the topological structure of river networks mainly include the number of nodes, edge point rate, degree, proximity center, betweenness center, clustering coefficient, average path length, etc. Select indicators with spatial distribution characteristics and large spatial differentiation in the study area. Specifically, select water intake distance (Distance), elevation difference (Elevation), slope (Slope) as terrain indicators, river network density (Density), box dimension (Density) as well as river network density (Density). f ) as the river spatial structure index, degree (Degree), closeness center (CC), and betweenness center (BC) as the river network topological structure index;

[0053] Step 2-3, formally define the terrain index dK , river spatial structure index z K and river network topological structure index g K , the expression is:

[0054] d 1,2,...,K1 =[d 1,2,...,K,1 ,d 1,2,...,K,2 ,…,d 1,2,...,K1,N ]

[0055] z 1,2,...,K2 =[z 1,2,...,K,1 ,z 1,2,...,K,2 ,…,z 1,2,...,K2,N ]

[0056] g 1,2,...,K3 =[g 1,2,...,K,1 ,g 1,2,...,K,2 ,…,g 1,2,...,K3,N ]

[0057] Where N is the number of samples, which is used as the sample index here, N = 1, 2, ..., d 1,2,...,K1 is the K1th evaluation index river network topology structure index value, z 1,2,...,K2 is the K2 evaluation index and river spatial structure index value of all samples, g 1,2,...,K3 is the K3 evaluation index river network topology index value of all samples; among them, the river spatial structure index calculation unit is 10km*10km grid, the river network topology calculation result is a linear index, which is extended to the entire study area through kernel density estimation, and K1+K2+K3=K;

[0058] Step 3: normalize the evaluation index. The general formula for normalization is as follows:

[0059]

[0060] In the formula, x is the normalized value of the evaluation index, T is the initial value of the evaluation index, and T max is the initial maximum value of the evaluation index; T min is the initial minimum value of the evaluation index;

[0061] Step 4: Determine the river network accessibility through factor analysis, such as Figure 2 The specific processing is as follows:

[0062] Step 4-1, combine the normalized evaluation indicators into a sample matrix X, expressed as:

[0063]

[0064] In the formula, x 1,K ,...x N,Kare the 1st to Kth evaluation indicators of the 1st to Nth samples after normalization;

[0065] Calculate the covariance matrix S of the sample matrix, the expression is as follows:

[0066]

[0067] In the formula, s KK are the elements in the covariance matrix;

[0068] Step 4-2, perform KMO test and Bartlett sphericity test on the samples to test the appropriate evaluation indicators;

[0069] The general KMO test expression followed is:

[0070]

[0071] In the formula, Represents the correlation coefficient between two elements i and j to be tested, Represents the partial correlation coefficient between two elements i and j to be tested.

[0072] The general Bartlett sphericity test expression followed is:

[0073] (1) Assume that the covariance matrices of all samples are equal (spherical):

[0074] (2) Calculate the evaluation index statistic χ 2 , the expression is:

[0075]

[0076] Where, |S| is the determinant of the population covariance matrix;

[0077] (3) Calculate the degrees of freedom df, the expression is:

[0078]

[0079] In the formula, K is the number of evaluation indicators;

[0080] (4) Conduct the hypothesis test in (1): According to the evaluation index statistic X 2 and degrees of freedom df to find the corresponding critical value from the chi-square distribution table. If the calculated χ 2 > the critical value, reject the null hypothesis; otherwise, do not reject the null hypothesis.

[0081] It can be deduced from this that in the present invention, when the sample satisfies the KMO test coefficient KMO>0.6 and the significance level coefficient p<0.05, the factor analysis result of the evaluation index is judged to be appropriate;

[0082] Step 4-3, after judging that the evaluation index is suitable, establish the orthogonal factor model X of the sample matrix X, expressed as:

[0083] X=μ+AF+ε

[0084] The parameters of the above formula satisfy

[0085] Where, F=(F1,F2,…,F m ) T is the set of common factors of the sample matrix X, m is the number of common factors, μ=(μ1,μ2,…,μ K ) T is the mean of the sample matrix X, ε=(ε1,ε2,ε3,…,ε K ) T is a special factor set of the sample matrix X, E(ε) is the mean of the variable ε, var(ε) is the covariance of each element in the variable ε, is a diagonal matrix (K×K), is the variance of the Kth variable, I is the covariance matrix of the common factors, which is the unit matrix (m×m), cov(F,ε) means to find the covariance between the variable F and the variable ε, A=(a Km ) K×m is the factor loading matrix (K×m) of the sample matrix X. From the model conditions, it can be deduced that cov(X,F)=A, SD=AA T , A T is the factor loading transposed matrix, and D is the covariance matrix (K×K) of the special factor; A and D are unknown and are obtained by the following process:

[0086] i. Estimate the covariance of common factors by the principal component method described below, determine the part with larger covariance eigenvalue as the common factor, and set the number of common factors m;

[0087] ii. Decompose the covariance matrix S of the sample matrix, the expression is:

[0088]

[0089] In the formula, λ1, λ2, ...λ K is the eigenvalue of the covariance matrix, and λ1≥λ2≥…≥λ K ≥0,l1,l2,…,l K is the corresponding eigenvector, That is, the error term, and T represents the transpose;

[0090] The common factor m, which approximately represents the principal component of the original variable, is introduced. m is used as the larger part of the eigenvalue, so that the variance of the factor loading matrix and the variance estimation of the special factor can be obtained. The expression is:

[0091]

[0092] In the formula, s KK is the diagonal element of the sample covariance matrix S, diag(BB T ) is the matrix B, the transposed matrix B T The diagonal matrix of ;

[0093] Through the common factor F j Variance Contribution Reflects the common factor F j The total impact on all variables is an indicator of the relative importance of common factors. j Variance Contribution The calculation formula is as follows:

[0094]

[0095] Among them, common factors refer to the common factors shared by the original variables, and special factors refer to the factors that only appear in the corresponding single original variable;

[0096] Step 4-4, perform orthogonal rotation of the common factors with the largest variance, so that the square of each factor loading is transformed to 0 and 1 in columns, so as to highlight the actual significance of each common factor. Perform orthogonal rotation on the factor model X = μ + AF + ε, the expression is:

[0097]

[0098] Where Γ is an orthogonal matrix, the factor orthogonal model after rotation is X = μ + AΓZ + ε, and Z is the factor score matrix after rotation (m × 1);

[0099] Step 4-5, by common factor variance contribution The weighted calculation of river network accessibility H is expressed as:

[0100]

[0101] In the formula, Z m is the element of the rotated factor score matrix Z;

[0102] The positive or negative sign of the connection symbol depends on the positive or negative meaning of the common factor. If it is positive, the connection symbol is +, and if it is negative, the connection symbol is -.

[0103] The characteristic roots, factor loadings, and variance contributions of the orthogonal model before and after rotation are shown in Tables 1 and 2. According to the eigenvalue greater than 1, three common factors were selected, and the cumulative variance contribution was 79.708%.

[0104] Table 1

[0105]

[0106]

[0107] Table 2

[0108]

[0109] From the rotated factor loads, we can see that the loads of factor 1, degree, CCY, and BCY are large, reflecting the impact of river network connectivity on accessibility; the loads of factor 2, density, box dimension, and distance are large, reflecting the impact of the difficulty of water acquisition on accessibility; the loads of factor 3, height difference and slope, are large, reflecting the impact of terrain on accessibility. Each common factor has a clear practical significance; factor 1 and factor 2 have a positive impact on accessibility, and the connection sign is positive, while factor 3 has a negative impact on accessibility, and the connection sign is negative. The calculation results are as follows: Figure 3 shown.

[0110] Step 5: Combine river network accessibility and water resources to conduct water resources accessibility evaluation and analysis in the area to be evaluated;

[0111] Step 5-1: Estimate the amount of natural water resources and use the runoff coefficient method to calculate the multi-year average runoff. The expression is:

[0112] R=A r ·P·α

[0113] Where R is the runoff of the catchment area, A r is the catchment area, P is the average annual precipitation in the catchment area, and α is the runoff coefficient of the catchment area;

[0114] Among them, the multi-year average runoff R is used as the estimated value of natural water resources;

[0115] Step 5-2: Count the amount of water transferred from outside the area to be evaluated, add the amount of natural water resources, and determine the actual amount of water resources in the area to be evaluated, including the amount of water transferred from outside + the amount of natural water resources, such as Figure 4 As shown,

[0116] Step 5-3, combining river network accessibility and natural water resources to evaluate the water resource accessibility W of the area to be evaluated;

[0117] W=H·R

[0118] ,like Figure 5shown.

[0119] To sum up, the present invention comprehensively considers the river network accessibility and water resources, and evaluates the regional water resources accessibility by establishing an evaluation model, clarifies the independent influence of river network layout or water resources on water resources accessibility, and makes the actual role of water network engineering construction clearly expressed, which is conducive to enhancing the understanding of water networks and improving the level of water network management and water network engineering planning.

[0120] The implementation steps of a regional water resource accessibility evaluation method based on river network accessibility and water resources involved in the above specific embodiments are only used to help understand the specific methods and core ideas of the present invention. There will be changes in the specific implementation methods and application scopes, and they are not intended to limit the present invention. For those skilled in the art, any modifications, equivalent substitutions, improvements or changes made based on the inventive concept of this application should be included in the protection scope of the present invention.

Claims

1. A method for evaluating regional water resource accessibility based on river network accessibility and water resource quantity, characterized in that: include: Collect data on topography, river network, precipitation, water network engineering and water diversion in the area to be evaluated, and obtain spatial sample points from the area to be evaluated; Select terrain indicators, river spatial structure indicators and river network topological structure indicators as river network accessibility evaluation indicators, extract various evaluation indicator values ​​within spatial sample points, and use the mean values ​​of various evaluation indicators as sample data; The normalized evaluation indicators are combined into a sample matrix X, and the covariance matrix S of the sample matrix is ​​calculated. After determining the appropriate evaluation indicators, the orthogonal factor model of the sample matrix X is established, and the expression is: X=μ+AF+ε The parameters of the above formula satisfy Where, F=(F1,F2,…,F m ) T is the set of common factors of the sample matrix X, m is the number of common factors, μ=(μ1,μ2,…,μ K ) T is the mean of the sample matrix X, ε=(ε1,ε2,ε3,…,ε K ) T is a special factor set of the sample matrix X, E(ε) is the mean of the variable ε, var(ε) is the covariance of each element in the variable ε, is a diagonal matrix, is the variance of the Kth variable, I is the covariance matrix of the common factors, cov(F,ε) is the covariance between the variable F and the variable ε, A=(a Km ) K×m is the factor loading matrix of the sample matrix X, cov(X,F)=A, SD=AA T , A T is the factor loading transposed matrix, D is the covariance matrix of the special factor; A and D are obtained by the following process: i) Decompose the covariance matrix S of the sample matrix, the expression is: In the formula, λ1, λ2, ...λ K is the eigenvalue of the covariance matrix, and λ1≥λ2≥…≥λ K ≥0,l1,l2,…,l K is the corresponding eigenvector, T stands for transpose; ii) Estimate the relevant parameters through the principal component method and determine the number of common factors m, so as to obtain the variance of the factor loading matrix and the variance estimate of the special factors, expressed as: In the formula, s KK is the diagonal element of the sample covariance matrix S, diag(BB T ) is the matrix B, the transposed matrix B T The diagonal matrix of ; Perform an orthogonal rotation on the common factor with the largest variance to obtain the rotated factor score matrix Z, which is expressed as: Where Γ is an orthogonal matrix, then the factor orthogonal model after rotation is: X = μ + AΓZ + ε; Variance contribution through common factors The weighted calculation of river network accessibility H is expressed as: In the formula, Z m is the element of the rotated factor score matrix Z; Combining river network accessibility and natural water resources, the water resource accessibility W of the area to be evaluated is evaluated, and the expression is: W=H·R Where R is the runoff of the catchment area and H is the accessibility of the river network.

2. The regional water resource accessibility evaluation method based on river network accessibility and water resource quantity as claimed in claim 1, characterized in that: Formal definition of terrain index d K , river spatial structure index z K and river network topological structure index g K , the expression is: d 1,2,...,K1 =[d 1,2,...,K1,1 ,d 1,2,...,K1,2 ,…,d 1,2,...,K1,N ] With 1,2,...,K2 =[of 1,2,...,K2,1 ,With 1,2,...,K,2 ,…,With 1,2,...,K2,N ] g 1,2,...,K3 =[g 1,2,...,K3,1 ,g 1,2,...,K3,2 ,…,g 1,2,...,K3,N ] In the formula, N is the number of samples, d is 1,2,...,K1 is the K1th evaluation index terrain index value of all samples, z 1,2,...,K2 is the K2th evaluation index river spatial structure index value of all samples, g 1,2,...,K3 It is the K3th evaluation index of river network topology index value of all samples.

3. The regional water resource accessibility evaluation method based on river network accessibility and water resource quantity as claimed in claim 1, characterized in that: The determining of the appropriate evaluation index further includes performing a KMO test and a Bartlett sphericity test on the sample to determine the appropriate evaluation index.

4. The regional water resource accessibility evaluation method based on river network accessibility and water resource quantity as claimed in claim 1, characterized in that: The part with large covariance eigenvalue is determined as the common factor, and the number of common factors m is set.

5. The regional water resource accessibility evaluation method based on river network accessibility and water resource quantity as claimed in claim 1, characterized in that: The positive or negative value of the connection symbol in the expression of river network accessibility H depends on the positive or negative meaning of the common factor. If it is positive, the connection symbol is +, and if it is negative, the connection symbol is -.

6. The regional water resource accessibility evaluation method based on river network accessibility and water resource quantity as claimed in claim 1, characterized in that: The expression of the average runoff is: R=A r ·P·a Where R is the runoff of the catchment area, A r is the catchment area, P is the average annual precipitation in the catchment area, and α is the runoff coefficient of the catchment area; The multi-year average runoff R is used as an estimate of natural water resources.

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