Ecological and hydrological zoning methods

3.4.1 Overview of the main partitioning methods

There are many methods of partitioning, including qualitative methods, quantitative methods and a combination of the two methods. Qualitative method is a method or perspective that studies things from the inherent stipulations of things based on the attributes of social phenomena or things and the contradictory changes in movement. It is based on generally recognized axioms, a set of deductive logic and a large number of historical facts, and describes and explains the things under study based on the contradictions of things. To conduct qualitative research, we must directly grasp the main aspects of the characteristics of things based on certain theories and experiences, and temporarily ignore the quantitative differences in homogeneity. Qualitative partitioning methods mainly include the traditional dominant factor method, sequential method, merger method, etc. Quantitative analysis refers to analyzing the quantitative relationship between components or properties of a research object; it can also quantitatively analyze and compare certain properties, characteristics, and interrelationships of several objects, and the research results are also used "Quantity" is described. In recent years, with the development of statistical science, remote sensing and geographic information systems, a large number of quantitative zoning methods have emerged, mainly including system clustering methods, fuzzy clustering methods, artificial neural network methods, GIS methods, comprehensive integration methods, etc. . Among them, the cluster analysis method is applicable to biology, medicine, meteorology, geology and all other disciplines involving classification. After comparison, this study selected the cluster analysis method and used SP SS software to implement it.

3.4.2 Cluster analysis method

Cluster analysis refers to the analysis process of grouping a collection of physical or abstract objects into multiple classes composed of similar objects. It is an important human behavior. The goal of cluster analysis is to collect data and classify them on the basis of similarity. Clustering originates from many fields, including mathematics, computer science, statistics, biology, and economics. In different application fields, many clustering techniques have been developed. These technical methods are used to describe data, measure the similarity between different data sources, and classify data sources into different clusters.

Cluster analysis, also known as group analysis, point group analysis, cluster group analysis, etc., is a quantitative method for studying multi-element things classification problems. The basic principle of cluster analysis is to use mathematical methods to quantitatively determine the close relationship between samples based on the similarity and closeness of the attributes or characteristics of variables (or indicators), and use mathematical methods according to the degree of this close relationship. Classify them step by step, and gather closely related classifications into a small classification unit, and distantly related classifications into a large classification unit, until all samples or variables are gathered to form a complete classification system diagram. Also called a pedigree diagram, it is used to display the differences of classified objects (individuals or indicators) more naturally and intuitively (Guo Zhigang, 2001).

Cluster analysis can objectively reflect the inherent combination relationship between these variables or regions. Its basic feature is that there is no need to know the classification structure of the classification object in advance. It only requires a batch of geographical data, then selects the classification statistics or indicators, and performs calculations according to certain method steps. Finally, a picture can be obtained naturally and objectively. Complete classification system diagram. In fact, the partitioning process is essentially a clustering process.

From a statistical point of view, cluster analysis is a method of simplifying data through data modeling. Traditional statistical clustering analysis methods include systematic clustering, decomposition, joining, dynamic clustering, ordered sample clustering, overlapping clustering and fuzzy clustering. Cluster analysis tools using k-means, k-center point and other algorithms have been added to many well-known statistical analysis software packages, such as SP SS, SAS, etc. Below is a brief description of the most commonly used system clustering methods and fuzzy clustering methods.

Systematic clustering analysis is currently the most commonly used method at home and abroad, also known as hierarchical clustering analysis. The basic idea of ??systematic clustering is: first, first treat n samples as a class, and specify the distance between samples and the distance between classes; secondly, select the pair with the smallest distance and merge it into a new class, and calculate The distance between the new class and other classes; then, merge the two classes with the smallest distance, thus reducing one class at a time until all samples become one class (Yuan Qingke et al., 1995). The principle is that individuals in the same category have greater similarities, while individuals in different categories have greater differences. Systematic clustering conforms to the basic principles of zoning and is the most commonly used quantitative analysis method in zoning work. Common distances include absolute value distance, Euclidean distance, Minkov distance, Chebyshev distance, Mahalanobis distance, and Rankine distance. There are many methods to define the distance between classes, mainly including: class average method, center of gravity method, intermediate distance method, longest distance method, shortest distance method, square deviation method, and density estimation method.

Fuzzy cluster analysis method is a mathematical method that uses fuzzy mathematical language to describe and classify things according to certain requirements. Fuzzy cluster analysis generally refers to constructing a fuzzy matrix based on the attributes of the research object itself, and On this basis, the clustering relationship is determined based on a certain degree of membership, that is, the fuzzy relationship between samples is quantitatively determined using fuzzy mathematics, so that clustering can be performed objectively and accurately. Because fuzzy clustering obtains the degree of uncertainty that the sample belongs to each category, it expresses the betweenness of the sample class attributes, that is, it establishes the uncertainty description of the category by the sample, and can more objectively reflect the actual things, thus becoming a cluster. Analytical research mainstream.

The objects discussed in fuzzy clustering analysis are not given any pattern in advance for classification reference, and are required to be classified according to the respective attribute characteristics of the samples. Clustering is to divide the data set into multiple classes or clusters so that the data differences between each class are as large as possible and the data differences within classes are as small as possible, which is to "minimize the similarity between classes and maximize the similarity within classes." "similarity" principle. The basic process of fuzzy clustering analysis: ① Calculate the similarity coefficient between samples or variables and establish a fuzzy similarity matrix; ② Use fuzzy operations to perform a series of synthetic transformations on the similarity matrix to generate a fuzzy equivalent matrix; ③ Finally, according to different interception levels λ performs interception classification on the fuzzy equivalent matrix.

In terms of analysis method, this book adopts Hierachical cluster analysis. There are two forms of systematic clustering: one is to classify the research object itself and cluster the samples, which is called Q-type clustering; the other is to cluster the observation indicators of the research object, which is called R-type clustering . According to the characteristics of ecological and hydrological zoning, Q-type clustering is used in this book. Cluster analysis can be easily performed using SP SS software. The clustering steps are as follows:

3.4.2.1 Index selection

The object of cluster analysis is samples, and the samples can reflect Its characteristics are characterized by several indicators. The effect of cluster analysis largely depends on the selection of samples and clustering indicators. Indicators refer to characteristics that can accurately reflect a certain aspect of the research object based on the research object and purpose. The selected indicators should be representative, adaptable, measurable and independent, and there should be obvious differences between indicators (Qu Yongling et al., 2005).

3.4.2.2 Data Standardization

After the zoning indicators are selected, due to the differences in the dimension, magnitude and magnitude of changes in the indicators, different properties, different dimensions, and different Statistical statistics of the magnitude of quantitative changes together will likely highlight the role of certain indicators with particularly large magnitudes in classification, while suppressing or even excluding the role of some indicators with smaller magnitudes in classification, so that each indicator will be weighted unequally. Participate in operational analysis. In order to avoid these shortcomings, appropriate and necessary processing and transformation of data are often performed to eliminate dimensional differences and unify each indicator within a certain, relatively uniform numerical range, that is, to The data is standardized.

Standardization of data is also called dimensionless and normalization of data. It is a method to eliminate the influence of the dimension of each indicator through simple mathematical transformation. The SP SS software cluster analysis menu provides the following four categories of dimensionless processing methods for indicators (Han Shengjuan, 2008):

The first is the extreme value method. The SPSS software provides three extreme methods of equations (3.1) to (3.3):

Eco-environmental benefit assessment of the Henan water-receiving area of ??the South-to-North Water Diversion Middle Route Project

That is, each The value of a variable is divided by the full range of values ??that the variable takes. After standardization, the value range of each variable is limited to -1 to 1.

Eco-environmental benefit assessment of the Henan water-receiving area of ??the South-to-North Water Diversion Middle Route Project

That is, the difference between each variable value and the minimum value is divided by the full range of the variable's value. After standardization, the value range of each variable is limited to 0 to 1.

Eco-environmental benefit assessment of the water-receiving area in Henan Province of the South-to-North Water Diversion Middle Route Project

That is, dividing each variable value by the maximum value of the variable. After standardization, the maximum value of each variable is 1.

The extremalization method nondimensionalizes variable data by using the maximum and minimum values ??of the variables to convert the original data into data within a specific range, thereby eliminating the impact of dimension and order of magnitude. , the problem of different measures is addressed by changing the weight of variables in the analysis. This method is only related to the maximum and minimum values ??of the variable during the dimensionless process of the variable, which makes this method overly dependent on the two extreme values ??when changing the weight of each variable. Extreme values ??in this data should be used with caution.

The second is the standardization method, that is, the difference between each variable value and its mean value is divided by the standard deviation of the variable. After being dimensionless, the average value of each variable is 0 and the standard deviation is 1, thereby eliminating the influence of dimension and magnitude. It can be expressed in detail as:

Ecological and environmental benefits of the water-receiving area in Henan Province for the middle route of the South-to-North Water Diversion Project Evaluation

In the formula: p>

Xj——The arithmetic mean of the jth variable, ;

Sj——The standard deviation of the jth variable, .

After the standardized transformation of the standard deviation, it becomes:

Eco-environmental benefit assessment of the water-receiving area in Henan Province for the South-to-North Water Diversion Middle Route Project

The second type of method is the standardized method It is the most commonly used method at present. When the original data presents a normal distribution, it is more reasonable to use this method for dimensionless data processing.

The third is the averaging method, that is, each variable is divided by the average value of the variable. After standardization, the mean value of each variable is 1, and the standard deviation is the coefficient of variation of the original variable.

Assessment of the ecological environment benefits of the water-receiving areas in Henan for the South-to-North Water Diversion Middle Route Project

This method not only eliminates the influence of dimensions and magnitudes, but also retains the information on the degree of difference in the values ??of each variable. The greater the degree of variables, the greater the impact on the comprehensive analysis.

The fourth is the standard deviation method, that is, each variable is divided by the standard deviation of the variable. After dimensionality, the standard deviation of each variable is 1.

Eco-environmental benefit assessment of the water-receiving areas in Henan Province for the Middle Route of the South-to-North Water Diversion Project

The difference between it and the standardized method is only in the mean value of each variable after non-dimensionalization. The mean value of each variable after the standardized method is processed is 0, and the mean value of each variable after the standard deviation method is the ratio of the original variable mean value and the standard deviation, that is, the reciprocal of the coefficient of variation, which will produce some error information for the analysis.

Since the ecological and hydrological zoning indicators selected in this study come from different sources, their dimensions and quantities are inconsistent, and their change amplitudes are also different, they are not comparable. If the index value is directly used for calculation, the effect of variables with large absolute values ??will be highlighted and the effect of variables with small absolute values ??will be weakened. Before statistical analysis and calculation, the data must be standardized and transformed to eliminate the differences between them and balance the effects of each indicator. Since it is necessary to retain the numerical relationships in actual values ??as much as possible during ecological and hydrological zoning, through the above research, the most suitable indicator standardization method available in SP SS software is the second one - the standardization method, so this study selected this method. Perform data standardization.

3.4.2.3 Calculation of distance

Distance is usually used to measure the dissimilarity between two objects, that is, to define the distance between units. Commonly used distance measurement methods are shown in Table 3.1.

Table 3.1 Table of commonly used distance measurement methods

If you choose different distances, the clustering results will be different. Currently, there are no clear principles or theoretical basis for the choice of standardization methods and similarity measures. In geographical partitioning and classification research, several distances are often used for calculation and comparison, and a more appropriate distance is selected for clustering. After comparative analysis, this book chooses the Euclidean distance square method.

3.4.2.4 Clustering method selection

The quality of the clustering results depends on the similarity comparison method used by the clustering method. The selected clustering method should be able to reproduce the inherent Categorical groups and are sensitive to errors or outliers within a data group.

There are many methods for comparing the similarity (distance between classes) of systematic clustering, such as the longest distance method (the distance between two classes is calculated by the distance of the farthest sample between the two classes). represents, it is space expansion), shortest distance method (the distance between two categories is represented by the distance between the nearest samples between the two categories, it is space compression), centroid distance method (the distance between two categories is represented by the center of gravity The distance between two categories is represented by the distance between them, which is non-monotonic), the class average method (the squared distance between two categories is represented by the average square distance between pairs of elements of each type, which has space preservation and monotonicity) and the deviation sum of squares method ( The square distance between two categories is expressed by the sum of squared deviations increased after the two categories are classified. During the clustering process, the variance of each indicator within the category is minimized, the variance between categories is as large as possible, and it also has monotonicity), etc.

According to research, the class average method and the deviation sum of squares method can make full use of the information of each sample and are better methods for type merging and partitioning, so they are the main methods for partitioning. Through comparative analysis, this study adopts the deviation sum of squares method.

3.4.2.5 Determination of the number of clusters

Select the number of clusters according to the clustering requirements. The research object can be divided into several areas according to a certain threshold. With different objects in the research area and different area sizes, the thresholds must be different. Therefore, the determination of the threshold needs to be determined based on the research object and purpose.

3.4.2.6 Clustering result analysis

The pedigree diagram obtained from cluster analysis needs to be manually analyzed and adjusted. Cluster analysis combines different partition units together, but this analysis is a type of merging, and the result may not comply with the regional ***yoke principle. This requires researchers to make adjustments based on the principles of zoning and the characteristics of the research objects to obtain the required results. Computers are only an important tool to assist in zoning research. Researchers must identify, adjust and filter computer results based on the research objects.

3.4.3 Establishing an indicator system

Scientific and reasonable establishment of an indicator system is the theoretical basis for dividing ecological and hydrological regions and the basis for cluster analysis. The determination of the indicator system and the selection of each indicator should be based on the principle of reflecting the differentiation laws of ecological and hydrological systems in different regions as much as possible. The structure, function and formation process of the eco-hydrological system are extremely complex. They are affected by many factors and are the result of the combined effects of various factors. Therefore, when selecting indicators for the division of ecological and hydrological zones during the research process, we should comprehensively consider and grasp the dominant factors on the basis of a comprehensive analysis of each element, so as to grasp the essence of the ecological and hydrological systems in different regions without Make the indicator system too complex or repetitive.

Based on the theoretical basis and principle requirements of ecological and hydrological zoning, an ecological and hydrological zoning index system for the water-receiving areas in Henan is established.

The elements to determine its eco-hydrological zoning mainly include natural elements, land use elements, socio-economic elements and soil erosion elements, and the eco-hydrological zoning index system is divided into 4 levels, namely target layer (A) and element layer (B). , factor layer (C) and indicator layer (D), the factor analysis at each level is as follows:

1) Target layer (A). The establishment of an ecological and hydrological zoning index system is the basic work and key step of ecological and hydrological zoning. The system integrates the main factors and factors that affect ecohydrology, and systematically reflects the role of nature, land and soil erosion on ecological hydrology.

2) Feature layer (B). The element layer is a comprehensive reflection of various ecological and hydrological influencing factors, including natural elements (B1), land use elements (B2), and soil and water loss elements (B3).

3) Factor layer (C). The factor layer includes topographic factors (C1), climate and hydrological factors (C2), various land use proportion factors (C3), and soil and water loss intensity factors (C4).

4) Indicator layer (D). The indicator layer is the specific embodiment of the influencing factors of the ecological and hydrological system, and is selected and determined according to the specific conditions of the region. Topographic factors mainly include indicators such as average altitude; climate and hydrological factors mainly include indicators such as annual groundwater depth and multi-year average precipitation depth; various land use proportion factors refer to the area proportions of various land use types, including the proportion of water to the total land area, cultivated land Indicators such as the proportion of total land area; water and soil erosion intensity factors mainly include indicators such as the proportion of soil water erosion area that is mild or above.

Table 3.2 lists the structural components of the first three levels of the ecological and hydrological zoning system.

Table 3.2 Ecological and hydrological zoning indicator system structure table

3.4.4 Ecological and hydrological zoning process

This book uses the systematic clustering method to carry out ecological and hydrological zoning. Systematic clustering is implemented using the cluster analysis function of SPSS (Statistical Program for Social Science). The method steps of ecological and hydrological zoning are: first collect data according to zoning units, use statistical analysis software to standardize the data of various indicators and perform systematic cluster analysis, generate a clustering dendrogram of each element, and rationalize the clustering results adjustment, and finally generate an ecological and hydrological zoning map. The zoning process is shown in Figure 3.1.

Fig.3.1 Step chart of eco-hydrological regionalization

Fig.3.1 Step chart of eco-hydrological regionalization