# Identifying Influencing Factors of Regional Agricultural Drought Vulnerability Based on PSR-TGRC Method

Authors: Dongxing Zhang; Wenkai Cao; Bing Qi
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

Regional agricultural drought vulnerability (RADV) is a complex nonlinear problem caused by the interaction of multiple factors, and an objective and systematic method is proposed by this paper to identify its influencing factors, which plays an important role in preventing and regulating the risks of regional agricultural drought. Firstly, to provide a reference for the evaluation problem in selecting the number of factors, the influencing factors affecting RADV are revealed by using the method of phase space reconstruction (PSR). Secondly, to rank the importance of influencing factors, a grey trend relational analysis (TGRA) method is proposed, considering the dynamic development relationship between the RADV index and the influencing factors and integrating the absolute and relative variation of sequences in each corresponding period. Finally, to reduce the collinearity between the influencing factors, a grey trend relational clustering (TGRC) analysis method is proposed. According to the above steps, the process of identifying factors based on PSR-TGRC method is formed. Taking Henan Province as an example, 14 main influencing factors and their effects on RADV are identified from all 42 factors, and the identification results which are consistent with the actual drought relief work show the rationality and practicality of PSR-TGRC method and provide theoretical support for formulating strategies of regional agricultural disaster prevention and mitigation.


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## Body

## 1. Introduction

With the acceleration of global warming and the intensity of human activities, the frequency and destructiveness of drought disasters (drought for short), which seriously threatens agricultural production, farmers’ property security, and livelihood security, are gradually increasing and restricting the sustainable development of regional economy and society. Preventing and mitigating disasters has become a hot and wide concern issue in the international community and academia [1, 2]. The accumulation of RADV, which refers to the state of loss caused by the threat of drought in agricultural production [3], provides an intrinsic basis for the eventual outbreak of agricultural drought, and it is important to reduce drought losses and promote sustainable agricultural development by reducing RADV [4]. At present, the research on reducing the degree of RADV mainly focuses on the use of mathematical tools or intelligent algorithms to build vulnerability assessment models [5–8]. Scientific and reasonable influencing factors are the basis for obtaining accurate evaluation results. However, the requirements on the selection and quantity of factors are different [9–11], and there is no corresponding explanation and measurement standard for the selection of factors, which may directly affect the stability and accuracy of the evaluation of RADV. Therefore, it is necessary to make a reasonable and quantitative analysis for the factors affecting the RADV, determine the optimal number of factors affecting the evaluation of RADV, and identify the main influencing factors that need to be adjusted by intervening.Obtaining the number of influencing factors accurately can effectively reduce the subjectivity of factors’ selection in the evaluation problems. From the perspective of chaos theory, a method that quickly obtains the number of influencing factors by reconstructing the phase space of RADV index and calculating the correlation dimensions byG-P algorithm [12, 13] was proposed. Chen and Gu obtained the number of factors affecting energy production and consumption by PSR [14]. Zhou researched the number of factors affecting the drought-affected area of Guangdong Province from 1950 to 1999 by PSR [15]. Xu et al. researched the number of factors affecting the total power of agricultural machinery in Heilongjiang Province by PSR [16]. In this paper, based on RADV index [17, 18], the number of factors affecting the evaluation of RADV is excavated by PSR, the subjectivity of factor selection is reduced, and the efficiency of data collection is improved.The common identification methods of factors are the following: expert consultation and empirical knowledge [19], theoretical analysis [20], frequency analysis [21], network analysis [22], analytic hierarchy process [23], principal component analysis [24], and DEMATEL [25], and they have greatly promoted the scientificity and reliability of factors identification. However, in sudden natural disasters such as agricultural drought, there are often uncertainties such as inconsistent or incomplete data information as a result of different statistical paths. In addition, the formation mechanism of agricultural drought is complex and is influenced by many factors and coupled with human factors’ interference; agricultural drought-related data often do not have a typical distribution law, so it is difficult to identify the RADV factors by using traditional theoretical analysis or statistical methods. Grey relational analysis and grey relational clustering analysis in Grey System theory do not require a large number of samples or the samples with statistical rules, so they are suitable for the identification of RADV factors [26].Due to the obvious dynamic development characteristics between the influencing factors and the degree of RADV, to better measure the proximity level of the relative changes, the correlation between sequences is measured by the greyT-type relational analysis [27–29]. In this paper, with the full use of data information, the changing trend between data sequences is reflected from the absolute and relative amount of data changes, and a method of the grey trend relational analysis (TGRA) method is proposed, the same as the method of grey trend relational clustering (TGRC) analysis method, which is based on TGRA. Finally, the PSR-TGRC method is applied to the factor identification of RADV in Henan Province, and the managerial implications to reduce the RADV in Henan Province are proposed according to the identification results.The main contributions of this paper are listed as follows:(1)
The influencing factors of RADV are quantitatively analyzed with the perspective of chaos theory, which provides a dimensional reference for the factors’ selection in RADV assessment and reduces the subjectivity of threshold selection in relational clustering.(2)
Considering the absolute and relative amount of data changes, a grey relational analysis method based on trend of data changes is proposed, which measures the correlation degree comprehensively between RADV index and influencing factors, as well as the positive and negative correlation of development trends.(3)
Considering the perspectives of nature, economy, society, and so forth, a relatively comprehensive collection of RADV influencing factors has been constructed, and the main influencing factors in Henan Province and the influencing factors that need to be implemented urgently for intervention have been identified through the PSR-TGRC method, which will help in solving the agricultural drought warning in Henan Province.The rest of this paper is organized as follows. Section2 proposes the factor identification process based on PSR-TGRC method. Section 3 applies the PSR-TGRC method to obtain the identification results of the influencing factors of RADV. Section 4 gives managerial implications according to the identification results. Section 5 gives the conclusions of this paper.


## 2. Influencing Factors Identification Process Based on the PSR-TGRC Method

In the process of factors identification, screening the main influencing factors and identifying their directions on the development trend of RADV are two key issues that need to be solved. Most of the factors are directly selected according to the relational threshold, but how to determine the threshold often lacks explanation, and the influence direction of factors on RADV lacks recognition.Given the above problems, in Section2.1, this paper puts forward the PSR method to reconstruct the RADV index, which quantifies the numbers of influencing factors, and provides a reference for the dynamic selection of relational clustering thresholds. In Section 2.2, firstly, this paper constructs a collection of influencing factors, and the TGRA method is proposed, which analyzes the correlation degree between the RADV index and the influencing factors, ranks the importance of the factors, and identifies the direction of the influencing factors on the development trend of RADV. Secondly, a TGRC method is proposed to analyze the collinearity between the influencing factors and reduce the redundancy between the factors. Finally, according to the number of main influencing factors, the ranking, and clustering results, the appropriate threshold is determined to identify the main influencing factors objectively and comprehensively. The methodology flow is shown in Figure 1.Figure 1
The methodology flow of this paper.


### 2.1. Determining the Number of Main Influencing Factors

#### 2.1.1. RADV Index

The RADV is a complex process of material and energy exchange with the outside world and it is influenced by natural conditions, technology, economy, policies, and other factors. The RADV index is a measure of RADV, which is based on the relationship between grain yield reduction and agricultural drought. The specific method is as follows.For each year of a region, the RADV index is obtained by using the crop under-receiving index for the current year divided by the corresponding drought index, and the formula is(1)X0=X0′X0″=H^/HR^/R.In formula (1), X0 is the RADV index of a region, X0′ is the crop under-receiving index, X0″ is the drought index of a region, and the crop under-receiving index X0′ is obtained by the expected output value H^ of a region divided by the actual output value in the current year. In order to eliminate the influence of technological progress and other factors on grain production, the autoregressive method in SPSS software is used to autoregress the data in time sequences at a time interval of 3 years, and then the expected value of grain production is obtained. Drought index X0″ is obtained by using the regional multiyear average rainfall R^ divided by the actual rainfall R for the year.


#### 2.1.2. PSR Method

By identifying the chaotic connotation of RADV index, the number of influencing factors affecting the RADV can be obtained by PSR method. The key of PSR method is to determine the delay time and the correlation dimensions [30]. In this section, the autocorrelation function method and G-P algorithm are used to calculate the delay time τ and the correlation dimensions Dm of RADV index, respectively [31].Definition 1.
For RADV indexX0=x0t1,x0t2,…,x0tn, the delay time is τ, and the autocorrelation function is(2)Rτ=Ex0ta−X¯0x0ta+τ−X¯0σ2.
In function (2), ta=t1,t2,…,tn−τ, X¯0 is the average of RADV index X0, and σ is the standard deviation of RADV index X0.
Using SPSS data analysis software, the autocorrelation function value of RADV indexX0 is calculated, and the corresponding delay time τ is found when the autocorrelation function value first approaches zero.
The reconstructed phase space isX=X1,X2,…,XNT, and each component in the space is Xb=xtb,xtb+τ,…,xtb+m−1τ; b=1,2,…,N, where xtb is the point of phase space, m is the embedding dimension, N is the number of phase points in the reconstructed phase space, and tN=tn−m−1τ.
The specific steps of theG-P algorithm are as follows.
Suppose that there are some phase points inm-dimensional phase space:(3)Xb=xtb,xtb+τ,…,xtb+m−1τ,Xe=xte,xte+τ,…,xte+m−1τ.
In the above equation,b,e=1,2,…,N and b−e>τ. The distance between the pair points is recorded as dbe=Xb−Xe. Given a distance value of r, the G-P algorithm checks how many pairs of points Xb,Xe have a distance dbe<r among the N points embedding in the phase space and marks the proportion of the pairs whose distance is less than r in all pairs as correlation function Cr, which indicates how many state points are interrelated, that is, the density of phase points in the phase space, which reflects the correlation degree and regularity degree of system motion.(4)Cr=1N2∑b=1N∑e=1Nθr−Xb−Xe.
From the above equation,θx=1x=r−Xb−Xe>0,0x=r−Xb−Xe<0. is Heaviside function.
The fractal dimension of RADV index isD=limr⟶0lnCr/lnr, which is the correlation dimension. In the actual calculation process, for different embedding dimension m, there is a corresponding D, which can be marked as Dm. For RADV index, when m increases to mc, Dm will no longer change significantly with m and become saturated; then the embedding dimension mc is the saturation embedding dimension. Dm and mc are the lower and upper number limits of main factors associated with the RADV index, respectively.


### 2.2. Identifying the Main Influencing Factors

#### 2.2.1. Constructing a Collection of RADV Influencing Factors

To identify the main influencing factors of RADV, the paper first constructs a collection of influencing factors as the basis of factor selection. RADV is mainly affected by both sensitivity and recovery factors. Sensitivity refers to the sum of the factors that exacerbate the drought hazards in agriculture; that is, the more sensitive the agricultural system, the greater the drought vulnerability of the agricultural system. Recovery refers to the sum of the various favorable factors to mitigate the harm of agricultural drought; that is, the more restorative the agricultural system, the weaker the drought vulnerability of the agricultural system. Considering that the RADV is the result of the joint action of natural environmental and socioeconomic systems [32], by excluding uncontrollable factors, with the principles of scientificity, integrity, and data availability, the influencing factors in existing studies are summarized, and a collection of RADV influencing factors is initially constructed from both sensitivity and recovery, as shown in Table 1.Table 1
A collection of RADV influencing factors.
Guideline layerInfluencing factorsInfluencing directionsInfluencing factorsInfluencing directionsSensitivityWater consumption per 10000 yuan GDP of agriculturalX1+Proportion of agricultural output valueX2+Water consumption per unit value added of agricultureX3+Total agricultural water consumptionX4+Per capita living water consumption of rural residentsX5+Per capita water resourcesX6−Average water consumption per mu of farmland irrigationX7+Multiple-crop indexX8+Cover rate of forestX9−Proportion of watered land areaX10+Population densityX11+Proportion of agricultural populationX12+Per capita arable land areaX13−Proportion of grain planting areaX14+Proportion of water field areaX15+Proportion of autumn grain crop planting areaX16+Proportion of corn planting areaX17+Proportion of summer grain crop planting areaX18+Proportion of rice planting areaX19+Proportion of wheat planting areaX20+RecoveryPer capita disposable income of rural householdsX21−Per capita fiscal incomeX22−Per capita GDPX23−Intensity of R&D fundingX24−Consumption level of rural residentsX25−Number of rural labor resourcesX26−Rural electricity consumptionX27−Total power of agricultural machinery per unit areaX28−Pure amount of fertilizer application per unit areaX29−Use of plastic film per unit areaX30−Mechanical harvest area of agricultural yearX31−Waterlogging control areaX32−Soil erosion control areaX33−Proportion of water-saving irrigation areaX34−Total reservoir capacityX35−Per capita grain yieldX36−Grain unit area yieldX37−Corn unit area yieldX38−Wheat unit area yieldX39−Rice unit area yieldX40−Summer grain unit area yieldX41−Autumn grain unit area yieldX42−


#### 2.2.2. Ranking the Importance of Influencing Factors Based on TGRA Method

The paper holds that the perspective of the absolute and relative amount of data changes can not only make full use of data information but also reflect the trend of data change more comprehensively. Therefore, based on the absolute and relative amount of data changes, the trend change is defined, and the grey trend relational coefficient is given by the composition ratio and difference of the trend change amount, and the symbol function is introduced to reflect the positive and negative correlations between the time sequences; then the TGRA method is proposed, which can rank the influencing factors according to the grey trend relational degree.Definition 2.
Suppose that the time sequence on intervalf,g is Xϕ=xϕt1,xϕt2,…,xϕtn, ϕ=0,1,2,…,l; then(5)xϕΔtk=xϕtk−xϕtk−1,Dϕ=∑k=2nxϕΔtkn−1,xϕ′Δtk=xϕtk−xϕtk−1xϕtk−1,Dϕ′=∑k=2nxϕ′Δtkn−1,zϕΔtk=α·xϕΔtkDϕ+β·xϕ′ΔtkDϕ′,respectively, represent the absolute amount of data change, mean of absolute amount of data change, relative amount of data change, mean of relative amount of data change, and the trend amount of data change of time sequences Xϕ from point of time tk−1 to point of time tk.
In the above equation,Δtk=tk−tk−1,f,g=∪k=2nΔtk,Δtk∩Δtk−1=∅,g>f≥0,k=2,3,…,n; α and β represent the emphasis on the absolute and relative amount of data changes, respectively, and α+β=1.Definition 3.
Suppose that the RADV index on intervalf,g is X0=x0t1,x0t2,…,x0tn; the influencing factor is Xi=xit1,xit2,…,xitni=1,2,…,u; then(6)ξ0itk=sgnz0Δtk⋅ziΔtk⋅11+1/2z0Δtk−ziΔtk+1/21−minz0Δtk,ziΔtk/maxz0Δtk,ziΔtk,others,1,z0Δtk=ziΔtk=0,is the grey trend relational coefficient between the RADV index X0 and the influencing factor Xi from the point of time tk−1 to point of time tk.
In the above equation,sgnz0Δtk⋅ziΔtk is a symbolic function used to reflect the positive and negative correlations between the RADV index X0 and the influencing factor Xi. When z0Δtk⋅ziΔtk≥0, sgnz0Δtk⋅ziΔtk=1, and ξ0itk>0, which indicates that X0 and Xi change in the same direction during the period from the point of time tk−1 to the point of time tk, that is, positive correlation. When z0Δtk⋅ziΔtk<0, sgnz0Δtk⋅ziΔtk=−1, and ξ0itk<0, which indicates that X0 and Xi change in the opposite direction during the period from the point of time tk−1 to the point of time tk, that is, negative correlation.Definition 4.
Suppose that the RADV index on intervalf,g is X0=x0t1,x0t2,…,x0tn; the influencing factor is Xi=xit1,xit1,…,xitni=1,2,…,u; then,(7)γ0i=1b−a∑k=2nΔtk⋅ξ0itk,is the trend grey relational degree between the RADV index X0 and the influencing factor Xi.
When−1≤γ0i<0, X0 is negatively correlated with Xi, and the larger γ0i, the stronger the negative correlation. When 0<γ0i≤0, X0 is positively correlated with Xi, and the larger γ0i, the stronger the positive correlation. When γ0i=0, X0 is not related to Xi.Theorem 1.
The grey trend relational degreeγ0i has the following properties:(1)
Normativity.γ0i≤1; when x0tk=λxitk, λ is a nonzero constant, and γ0i=1 is established.(2)
Symmetry.γX0,Xi=γXi,X0.(3)
Proximity. The closer sequencesX0 and Xi are, the larger γ0i is.(4)
Uniqueness and comparability.(5)
Isotony. After dimensionless processing such as initialization in the same direction, multiplication, averaging, and percentage, the grey trend relational degree is not changed, so the sequence does not produce ordinal effects.Proof .
(1) Normativity. Ifx0tk=λxitk, λ is a nonzero constant; then(8)x0Δtk=x0tk−x0tk−1=λxitk−λxitk−1=λxiΔtk,x0′Δtk=x0tk−x0tk−1x0tk−1=λxitk−λxitk−1λxitk−1=xi′Δtk,λ>0,λxitk−λxitk−1λxitk−1=−xi′Δtk,λ<0,D0=∑k=2nx0Δtkn−1=∑k=2nλxiΔtkn−1=λDi,λ>0,∑k=2nx0Δtkn−1=∑k=2nλxiΔtkn−1=−λDi,λ<0,D0′=∑k=2nx0′Δtkn−1=∑k=2nxi′Δtkn−1=Di′,z0Δtk=α⋅x0ΔtkD0+β⋅x0′ΔtkD0′=α⋅λxiΔtkλDi+β⋅xi′ΔtkDi′=ziΔtk,λ>0,α⋅λxiΔtk−λDi+β⋅xi′Δtk−Di′=−ziΔtk,λ<0,and therefore(9)z0Δtk−ziΔtk=1−minz0Δtk,ziΔtkmaxz0Δtk,ziΔtk=0,sgnz0Δtk⋅ziΔtk=1,λ>0,−1,λ<0,and then(10)γ0i=1b−a∑k=2nΔtk⋅1=1,λ>0,1b−a∑k=2nΔtk⋅−1=−1,λ<0.
Namely,γ0i=1.
From the derivation of formulas (6) and (7), it can be seen that the properties in (2)-(6) are obviously valid.
(5) Isotony. Taking the same direction initialization as an example, sequencesX0 and Xi are normalized, and the normalized sequences are noted as X0Δ and XiΔ; then(11)x0Δtk=x0tkx0t1,x0Δtk−1=x0tk−1x0t1,x0ΔΔtk=x0Δtk−x0Δtk−1=x0tkx0t1−x0tk−1x0t1=x0Δtkx0t1,x0ΔΔtk=x0Δtk−x0Δtk−1=x0tkx0t1−x0tk−1x0t1=x0Δtkx0t1,x0′ΔΔtk=x0Δtk−x0Δtk−1x0Δtk−1=x0tk−x0tk−1⋅x0t1x0t1⋅x0tk−1=x0′Δtk,x0t1>0,−x0′Δtk,x0t1<0,D0Δ=∑k=2nx0ΔΔtkn−1=∑k=2nx0Δtkn−1⋅x0t1=D0x0t1,x0t1>0,−D0x0t1,x0t1<0,D0′Δ=∑k=2nx0′ΔΔtkn−1=∑k=2nx0′Δtkn−1=D0′,and therefore(12)z0ΔΔtk=α⋅x0ΔΔtkD0Δ+β⋅x0′ΔΔtkD0′Δ=α⋅x0Δtk⋅x0t1x0t1⋅D0+β⋅x0′ΔtkD0′=z0Δtk,x0t1>0,α⋅x0Δtk⋅x0t1−x0t1⋅D0+β⋅−x0′ΔtkD0′=−z0Δtk,x0t1<0.
Similarly,(13)xiΔΔtk=xiΔtkxit1,xi′ΔΔtk=xi′Δtk,xit1>0,−xi′Δtk,xit1<0,DiΔ=Dixit1,xit1>0,−Dixit1,xit1<0,Di′Δ=Di′,ziΔΔtk=ziΔtk,xit1>0,−ziΔtk,xit1<0,sgnz0ΔΔtk⋅ziΔΔtk=sgnz0Δtk⋅ziΔtk=1,x0t1>0,xit1<0,sgn−z0Δtk⋅−ziΔtk=1,x0t1>0,xit1<0,ziΔΔtk−zjΔΔtk=ziΔtk−ziΔtk,minziΔΔtk,zjΔΔtkmaxziΔΔtk,zjΔΔtk=minziΔtk,zjΔtkmaxziΔtk,zjΔtk.
Therefore, after the initialization in the same direction, the grey trend relational coefficient is unchanged, the same as the grey trend relational degree. Similarly, it can be proved that the dimensionless processing such as multiplication in the same direction, averaging, and percentage does not change the grey trend relational degree.


#### 2.2.3. Clustering the Influencing Factors Based on TGRC Method

Depending on the grey trend relational degree between the RADV indexX0 and the influencing factor sequence Xi, the importance of the influencing factors can be ranked, but the main influencing factors cannot be filtered entirely according to the degree of importance, since some influencing factors may fall into the same category, which will not only increase the redundancy of data collection but also reduce the comprehensiveness of the factor screening. Therefore, it is necessary to cluster the influencing factors and merge the similar factors. TGRC is a method that is based on TGRA, constructing grey trend correlation matrix of the influencing factors and clustering the influencing factors by selecting appropriate relational threshold.Definition 5.
Assume that there are influencing factor sequencesXi=xit1,xit2,…,xitn and Xj=xjt1,xjt2,…,xjtn on interval f,g. For all i≤j, i=1,2,…,u, according to formulas (4) and (6), the grey trend relational degree between Xi and Xj is calculated, and the upper triangular matrix is obtained:(14)Y=γ11γ12…γ1uγ22…γ2u⋱⋮γuu,is the grey trend relational matrix of the influencing factors.
From the above equation,γii=1, and the relational threshold takes r∈0,1, which can be set according to the needs of the actual problem. When γij≥r, Xi and Xj are treated as the same influencing factors, and they are grouped into the same category. If γih≥r appears at the same time and h=1,2,…,u, but i≠j≠h, TGRC takes the smallest influencing factor of Xi,Xj,Xh in the label i,j,h as the representative of each category and combines the other two influencing factors into one with the smallest label to become a category. By traversing the whole grey trend correlation matrix, according to the relational threshold, the clustering results can be obtained, and the similar influencing factors merged.


## 2.1. Determining the Number of Main Influencing Factors

### 2.1.1. RADV Index

The RADV is a complex process of material and energy exchange with the outside world and it is influenced by natural conditions, technology, economy, policies, and other factors. The RADV index is a measure of RADV, which is based on the relationship between grain yield reduction and agricultural drought. The specific method is as follows.For each year of a region, the RADV index is obtained by using the crop under-receiving index for the current year divided by the corresponding drought index, and the formula is(1)X0=X0′X0″=H^/HR^/R.In formula (1), X0 is the RADV index of a region, X0′ is the crop under-receiving index, X0″ is the drought index of a region, and the crop under-receiving index X0′ is obtained by the expected output value H^ of a region divided by the actual output value in the current year. In order to eliminate the influence of technological progress and other factors on grain production, the autoregressive method in SPSS software is used to autoregress the data in time sequences at a time interval of 3 years, and then the expected value of grain production is obtained. Drought index X0″ is obtained by using the regional multiyear average rainfall R^ divided by the actual rainfall R for the year.


### 2.1.2. PSR Method

By identifying the chaotic connotation of RADV index, the number of influencing factors affecting the RADV can be obtained by PSR method. The key of PSR method is to determine the delay time and the correlation dimensions [30]. In this section, the autocorrelation function method and G-P algorithm are used to calculate the delay time τ and the correlation dimensions Dm of RADV index, respectively [31].Definition 1.
For RADV indexX0=x0t1,x0t2,…,x0tn, the delay time is τ, and the autocorrelation function is(2)Rτ=Ex0ta−X¯0x0ta+τ−X¯0σ2.
In function (2), ta=t1,t2,…,tn−τ, X¯0 is the average of RADV index X0, and σ is the standard deviation of RADV index X0.
Using SPSS data analysis software, the autocorrelation function value of RADV indexX0 is calculated, and the corresponding delay time τ is found when the autocorrelation function value first approaches zero.
The reconstructed phase space isX=X1,X2,…,XNT, and each component in the space is Xb=xtb,xtb+τ,…,xtb+m−1τ; b=1,2,…,N, where xtb is the point of phase space, m is the embedding dimension, N is the number of phase points in the reconstructed phase space, and tN=tn−m−1τ.
The specific steps of theG-P algorithm are as follows.
Suppose that there are some phase points inm-dimensional phase space:(3)Xb=xtb,xtb+τ,…,xtb+m−1τ,Xe=xte,xte+τ,…,xte+m−1τ.
In the above equation,b,e=1,2,…,N and b−e>τ. The distance between the pair points is recorded as dbe=Xb−Xe. Given a distance value of r, the G-P algorithm checks how many pairs of points Xb,Xe have a distance dbe<r among the N points embedding in the phase space and marks the proportion of the pairs whose distance is less than r in all pairs as correlation function Cr, which indicates how many state points are interrelated, that is, the density of phase points in the phase space, which reflects the correlation degree and regularity degree of system motion.(4)Cr=1N2∑b=1N∑e=1Nθr−Xb−Xe.
From the above equation,θx=1x=r−Xb−Xe>0,0x=r−Xb−Xe<0. is Heaviside function.
The fractal dimension of RADV index isD=limr⟶0lnCr/lnr, which is the correlation dimension. In the actual calculation process, for different embedding dimension m, there is a corresponding D, which can be marked as Dm. For RADV index, when m increases to mc, Dm will no longer change significantly with m and become saturated; then the embedding dimension mc is the saturation embedding dimension. Dm and mc are the lower and upper number limits of main factors associated with the RADV index, respectively.


## 2.1.1. RADV Index

The RADV is a complex process of material and energy exchange with the outside world and it is influenced by natural conditions, technology, economy, policies, and other factors. The RADV index is a measure of RADV, which is based on the relationship between grain yield reduction and agricultural drought. The specific method is as follows.For each year of a region, the RADV index is obtained by using the crop under-receiving index for the current year divided by the corresponding drought index, and the formula is(1)X0=X0′X0″=H^/HR^/R.In formula (1), X0 is the RADV index of a region, X0′ is the crop under-receiving index, X0″ is the drought index of a region, and the crop under-receiving index X0′ is obtained by the expected output value H^ of a region divided by the actual output value in the current year. In order to eliminate the influence of technological progress and other factors on grain production, the autoregressive method in SPSS software is used to autoregress the data in time sequences at a time interval of 3 years, and then the expected value of grain production is obtained. Drought index X0″ is obtained by using the regional multiyear average rainfall R^ divided by the actual rainfall R for the year.


## 2.1.2. PSR Method

By identifying the chaotic connotation of RADV index, the number of influencing factors affecting the RADV can be obtained by PSR method. The key of PSR method is to determine the delay time and the correlation dimensions [30]. In this section, the autocorrelation function method and G-P algorithm are used to calculate the delay time τ and the correlation dimensions Dm of RADV index, respectively [31].Definition 1.
For RADV indexX0=x0t1,x0t2,…,x0tn, the delay time is τ, and the autocorrelation function is(2)Rτ=Ex0ta−X¯0x0ta+τ−X¯0σ2.
In function (2), ta=t1,t2,…,tn−τ, X¯0 is the average of RADV index X0, and σ is the standard deviation of RADV index X0.
Using SPSS data analysis software, the autocorrelation function value of RADV indexX0 is calculated, and the corresponding delay time τ is found when the autocorrelation function value first approaches zero.
The reconstructed phase space isX=X1,X2,…,XNT, and each component in the space is Xb=xtb,xtb+τ,…,xtb+m−1τ; b=1,2,…,N, where xtb is the point of phase space, m is the embedding dimension, N is the number of phase points in the reconstructed phase space, and tN=tn−m−1τ.
The specific steps of theG-P algorithm are as follows.
Suppose that there are some phase points inm-dimensional phase space:(3)Xb=xtb,xtb+τ,…,xtb+m−1τ,Xe=xte,xte+τ,…,xte+m−1τ.
In the above equation,b,e=1,2,…,N and b−e>τ. The distance between the pair points is recorded as dbe=Xb−Xe. Given a distance value of r, the G-P algorithm checks how many pairs of points Xb,Xe have a distance dbe<r among the N points embedding in the phase space and marks the proportion of the pairs whose distance is less than r in all pairs as correlation function Cr, which indicates how many state points are interrelated, that is, the density of phase points in the phase space, which reflects the correlation degree and regularity degree of system motion.(4)Cr=1N2∑b=1N∑e=1Nθr−Xb−Xe.
From the above equation,θx=1x=r−Xb−Xe>0,0x=r−Xb−Xe<0. is Heaviside function.
The fractal dimension of RADV index isD=limr⟶0lnCr/lnr, which is the correlation dimension. In the actual calculation process, for different embedding dimension m, there is a corresponding D, which can be marked as Dm. For RADV index, when m increases to mc, Dm will no longer change significantly with m and become saturated; then the embedding dimension mc is the saturation embedding dimension. Dm and mc are the lower and upper number limits of main factors associated with the RADV index, respectively.


## 2.2. Identifying the Main Influencing Factors

### 2.2.1. Constructing a Collection of RADV Influencing Factors

To identify the main influencing factors of RADV, the paper first constructs a collection of influencing factors as the basis of factor selection. RADV is mainly affected by both sensitivity and recovery factors. Sensitivity refers to the sum of the factors that exacerbate the drought hazards in agriculture; that is, the more sensitive the agricultural system, the greater the drought vulnerability of the agricultural system. Recovery refers to the sum of the various favorable factors to mitigate the harm of agricultural drought; that is, the more restorative the agricultural system, the weaker the drought vulnerability of the agricultural system. Considering that the RADV is the result of the joint action of natural environmental and socioeconomic systems [32], by excluding uncontrollable factors, with the principles of scientificity, integrity, and data availability, the influencing factors in existing studies are summarized, and a collection of RADV influencing factors is initially constructed from both sensitivity and recovery, as shown in Table 1.Table 1
A collection of RADV influencing factors.
Guideline layerInfluencing factorsInfluencing directionsInfluencing factorsInfluencing directionsSensitivityWater consumption per 10000 yuan GDP of agriculturalX1+Proportion of agricultural output valueX2+Water consumption per unit value added of agricultureX3+Total agricultural water consumptionX4+Per capita living water consumption of rural residentsX5+Per capita water resourcesX6−Average water consumption per mu of farmland irrigationX7+Multiple-crop indexX8+Cover rate of forestX9−Proportion of watered land areaX10+Population densityX11+Proportion of agricultural populationX12+Per capita arable land areaX13−Proportion of grain planting areaX14+Proportion of water field areaX15+Proportion of autumn grain crop planting areaX16+Proportion of corn planting areaX17+Proportion of summer grain crop planting areaX18+Proportion of rice planting areaX19+Proportion of wheat planting areaX20+RecoveryPer capita disposable income of rural householdsX21−Per capita fiscal incomeX22−Per capita GDPX23−Intensity of R&D fundingX24−Consumption level of rural residentsX25−Number of rural labor resourcesX26−Rural electricity consumptionX27−Total power of agricultural machinery per unit areaX28−Pure amount of fertilizer application per unit areaX29−Use of plastic film per unit areaX30−Mechanical harvest area of agricultural yearX31−Waterlogging control areaX32−Soil erosion control areaX33−Proportion of water-saving irrigation areaX34−Total reservoir capacityX35−Per capita grain yieldX36−Grain unit area yieldX37−Corn unit area yieldX38−Wheat unit area yieldX39−Rice unit area yieldX40−Summer grain unit area yieldX41−Autumn grain unit area yieldX42−


### 2.2.2. Ranking the Importance of Influencing Factors Based on TGRA Method

The paper holds that the perspective of the absolute and relative amount of data changes can not only make full use of data information but also reflect the trend of data change more comprehensively. Therefore, based on the absolute and relative amount of data changes, the trend change is defined, and the grey trend relational coefficient is given by the composition ratio and difference of the trend change amount, and the symbol function is introduced to reflect the positive and negative correlations between the time sequences; then the TGRA method is proposed, which can rank the influencing factors according to the grey trend relational degree.Definition 2.
Suppose that the time sequence on intervalf,g is Xϕ=xϕt1,xϕt2,…,xϕtn, ϕ=0,1,2,…,l; then(5)xϕΔtk=xϕtk−xϕtk−1,Dϕ=∑k=2nxϕΔtkn−1,xϕ′Δtk=xϕtk−xϕtk−1xϕtk−1,Dϕ′=∑k=2nxϕ′Δtkn−1,zϕΔtk=α·xϕΔtkDϕ+β·xϕ′ΔtkDϕ′,respectively, represent the absolute amount of data change, mean of absolute amount of data change, relative amount of data change, mean of relative amount of data change, and the trend amount of data change of time sequences Xϕ from point of time tk−1 to point of time tk.
In the above equation,Δtk=tk−tk−1,f,g=∪k=2nΔtk,Δtk∩Δtk−1=∅,g>f≥0,k=2,3,…,n; α and β represent the emphasis on the absolute and relative amount of data changes, respectively, and α+β=1.Definition 3.
Suppose that the RADV index on intervalf,g is X0=x0t1,x0t2,…,x0tn; the influencing factor is Xi=xit1,xit2,…,xitni=1,2,…,u; then(6)ξ0itk=sgnz0Δtk⋅ziΔtk⋅11+1/2z0Δtk−ziΔtk+1/21−minz0Δtk,ziΔtk/maxz0Δtk,ziΔtk,others,1,z0Δtk=ziΔtk=0,is the grey trend relational coefficient between the RADV index X0 and the influencing factor Xi from the point of time tk−1 to point of time tk.
In the above equation,sgnz0Δtk⋅ziΔtk is a symbolic function used to reflect the positive and negative correlations between the RADV index X0 and the influencing factor Xi. When z0Δtk⋅ziΔtk≥0, sgnz0Δtk⋅ziΔtk=1, and ξ0itk>0, which indicates that X0 and Xi change in the same direction during the period from the point of time tk−1 to the point of time tk, that is, positive correlation. When z0Δtk⋅ziΔtk<0, sgnz0Δtk⋅ziΔtk=−1, and ξ0itk<0, which indicates that X0 and Xi change in the opposite direction during the period from the point of time tk−1 to the point of time tk, that is, negative correlation.Definition 4.
Suppose that the RADV index on intervalf,g is X0=x0t1,x0t2,…,x0tn; the influencing factor is Xi=xit1,xit1,…,xitni=1,2,…,u; then,(7)γ0i=1b−a∑k=2nΔtk⋅ξ0itk,is the trend grey relational degree between the RADV index X0 and the influencing factor Xi.
When−1≤γ0i<0, X0 is negatively correlated with Xi, and the larger γ0i, the stronger the negative correlation. When 0<γ0i≤0, X0 is positively correlated with Xi, and the larger γ0i, the stronger the positive correlation. When γ0i=0, X0 is not related to Xi.Theorem 1.
The grey trend relational degreeγ0i has the following properties:(1)
Normativity.γ0i≤1; when x0tk=λxitk, λ is a nonzero constant, and γ0i=1 is established.(2)
Symmetry.γX0,Xi=γXi,X0.(3)
Proximity. The closer sequencesX0 and Xi are, the larger γ0i is.(4)
Uniqueness and comparability.(5)
Isotony. After dimensionless processing such as initialization in the same direction, multiplication, averaging, and percentage, the grey trend relational degree is not changed, so the sequence does not produce ordinal effects.Proof .
(1) Normativity. Ifx0tk=λxitk, λ is a nonzero constant; then(8)x0Δtk=x0tk−x0tk−1=λxitk−λxitk−1=λxiΔtk,x0′Δtk=x0tk−x0tk−1x0tk−1=λxitk−λxitk−1λxitk−1=xi′Δtk,λ>0,λxitk−λxitk−1λxitk−1=−xi′Δtk,λ<0,D0=∑k=2nx0Δtkn−1=∑k=2nλxiΔtkn−1=λDi,λ>0,∑k=2nx0Δtkn−1=∑k=2nλxiΔtkn−1=−λDi,λ<0,D0′=∑k=2nx0′Δtkn−1=∑k=2nxi′Δtkn−1=Di′,z0Δtk=α⋅x0ΔtkD0+β⋅x0′ΔtkD0′=α⋅λxiΔtkλDi+β⋅xi′ΔtkDi′=ziΔtk,λ>0,α⋅λxiΔtk−λDi+β⋅xi′Δtk−Di′=−ziΔtk,λ<0,and therefore(9)z0Δtk−ziΔtk=1−minz0Δtk,ziΔtkmaxz0Δtk,ziΔtk=0,sgnz0Δtk⋅ziΔtk=1,λ>0,−1,λ<0,and then(10)γ0i=1b−a∑k=2nΔtk⋅1=1,λ>0,1b−a∑k=2nΔtk⋅−1=−1,λ<0.
Namely,γ0i=1.
From the derivation of formulas (6) and (7), it can be seen that the properties in (2)-(6) are obviously valid.
(5) Isotony. Taking the same direction initialization as an example, sequencesX0 and Xi are normalized, and the normalized sequences are noted as X0Δ and XiΔ; then(11)x0Δtk=x0tkx0t1,x0Δtk−1=x0tk−1x0t1,x0ΔΔtk=x0Δtk−x0Δtk−1=x0tkx0t1−x0tk−1x0t1=x0Δtkx0t1,x0ΔΔtk=x0Δtk−x0Δtk−1=x0tkx0t1−x0tk−1x0t1=x0Δtkx0t1,x0′ΔΔtk=x0Δtk−x0Δtk−1x0Δtk−1=x0tk−x0tk−1⋅x0t1x0t1⋅x0tk−1=x0′Δtk,x0t1>0,−x0′Δtk,x0t1<0,D0Δ=∑k=2nx0ΔΔtkn−1=∑k=2nx0Δtkn−1⋅x0t1=D0x0t1,x0t1>0,−D0x0t1,x0t1<0,D0′Δ=∑k=2nx0′ΔΔtkn−1=∑k=2nx0′Δtkn−1=D0′,and therefore(12)z0ΔΔtk=α⋅x0ΔΔtkD0Δ+β⋅x0′ΔΔtkD0′Δ=α⋅x0Δtk⋅x0t1x0t1⋅D0+β⋅x0′ΔtkD0′=z0Δtk,x0t1>0,α⋅x0Δtk⋅x0t1−x0t1⋅D0+β⋅−x0′ΔtkD0′=−z0Δtk,x0t1<0.
Similarly,(13)xiΔΔtk=xiΔtkxit1,xi′ΔΔtk=xi′Δtk,xit1>0,−xi′Δtk,xit1<0,DiΔ=Dixit1,xit1>0,−Dixit1,xit1<0,Di′Δ=Di′,ziΔΔtk=ziΔtk,xit1>0,−ziΔtk,xit1<0,sgnz0ΔΔtk⋅ziΔΔtk=sgnz0Δtk⋅ziΔtk=1,x0t1>0,xit1<0,sgn−z0Δtk⋅−ziΔtk=1,x0t1>0,xit1<0,ziΔΔtk−zjΔΔtk=ziΔtk−ziΔtk,minziΔΔtk,zjΔΔtkmaxziΔΔtk,zjΔΔtk=minziΔtk,zjΔtkmaxziΔtk,zjΔtk.
Therefore, after the initialization in the same direction, the grey trend relational coefficient is unchanged, the same as the grey trend relational degree. Similarly, it can be proved that the dimensionless processing such as multiplication in the same direction, averaging, and percentage does not change the grey trend relational degree.


### 2.2.3. Clustering the Influencing Factors Based on TGRC Method

Depending on the grey trend relational degree between the RADV indexX0 and the influencing factor sequence Xi, the importance of the influencing factors can be ranked, but the main influencing factors cannot be filtered entirely according to the degree of importance, since some influencing factors may fall into the same category, which will not only increase the redundancy of data collection but also reduce the comprehensiveness of the factor screening. Therefore, it is necessary to cluster the influencing factors and merge the similar factors. TGRC is a method that is based on TGRA, constructing grey trend correlation matrix of the influencing factors and clustering the influencing factors by selecting appropriate relational threshold.Definition 5.
Assume that there are influencing factor sequencesXi=xit1,xit2,…,xitn and Xj=xjt1,xjt2,…,xjtn on interval f,g. For all i≤j, i=1,2,…,u, according to formulas (4) and (6), the grey trend relational degree between Xi and Xj is calculated, and the upper triangular matrix is obtained:(14)Y=γ11γ12…γ1uγ22…γ2u⋱⋮γuu,is the grey trend relational matrix of the influencing factors.
From the above equation,γii=1, and the relational threshold takes r∈0,1, which can be set according to the needs of the actual problem. When γij≥r, Xi and Xj are treated as the same influencing factors, and they are grouped into the same category. If γih≥r appears at the same time and h=1,2,…,u, but i≠j≠h, TGRC takes the smallest influencing factor of Xi,Xj,Xh in the label i,j,h as the representative of each category and combines the other two influencing factors into one with the smallest label to become a category. By traversing the whole grey trend correlation matrix, according to the relational threshold, the clustering results can be obtained, and the similar influencing factors merged.


## 2.2.1. Constructing a Collection of RADV Influencing Factors

To identify the main influencing factors of RADV, the paper first constructs a collection of influencing factors as the basis of factor selection. RADV is mainly affected by both sensitivity and recovery factors. Sensitivity refers to the sum of the factors that exacerbate the drought hazards in agriculture; that is, the more sensitive the agricultural system, the greater the drought vulnerability of the agricultural system. Recovery refers to the sum of the various favorable factors to mitigate the harm of agricultural drought; that is, the more restorative the agricultural system, the weaker the drought vulnerability of the agricultural system. Considering that the RADV is the result of the joint action of natural environmental and socioeconomic systems [32], by excluding uncontrollable factors, with the principles of scientificity, integrity, and data availability, the influencing factors in existing studies are summarized, and a collection of RADV influencing factors is initially constructed from both sensitivity and recovery, as shown in Table 1.Table 1
A collection of RADV influencing factors.
Guideline layerInfluencing factorsInfluencing directionsInfluencing factorsInfluencing directionsSensitivityWater consumption per 10000 yuan GDP of agriculturalX1+Proportion of agricultural output valueX2+Water consumption per unit value added of agricultureX3+Total agricultural water consumptionX4+Per capita living water consumption of rural residentsX5+Per capita water resourcesX6−Average water consumption per mu of farmland irrigationX7+Multiple-crop indexX8+Cover rate of forestX9−Proportion of watered land areaX10+Population densityX11+Proportion of agricultural populationX12+Per capita arable land areaX13−Proportion of grain planting areaX14+Proportion of water field areaX15+Proportion of autumn grain crop planting areaX16+Proportion of corn planting areaX17+Proportion of summer grain crop planting areaX18+Proportion of rice planting areaX19+Proportion of wheat planting areaX20+RecoveryPer capita disposable income of rural householdsX21−Per capita fiscal incomeX22−Per capita GDPX23−Intensity of R&D fundingX24−Consumption level of rural residentsX25−Number of rural labor resourcesX26−Rural electricity consumptionX27−Total power of agricultural machinery per unit areaX28−Pure amount of fertilizer application per unit areaX29−Use of plastic film per unit areaX30−Mechanical harvest area of agricultural yearX31−Waterlogging control areaX32−Soil erosion control areaX33−Proportion of water-saving irrigation areaX34−Total reservoir capacityX35−Per capita grain yieldX36−Grain unit area yieldX37−Corn unit area yieldX38−Wheat unit area yieldX39−Rice unit area yieldX40−Summer grain unit area yieldX41−Autumn grain unit area yieldX42−


## 2.2.2. Ranking the Importance of Influencing Factors Based on TGRA Method

The paper holds that the perspective of the absolute and relative amount of data changes can not only make full use of data information but also reflect the trend of data change more comprehensively. Therefore, based on the absolute and relative amount of data changes, the trend change is defined, and the grey trend relational coefficient is given by the composition ratio and difference of the trend change amount, and the symbol function is introduced to reflect the positive and negative correlations between the time sequences; then the TGRA method is proposed, which can rank the influencing factors according to the grey trend relational degree.Definition 2.
Suppose that the time sequence on intervalf,g is Xϕ=xϕt1,xϕt2,…,xϕtn, ϕ=0,1,2,…,l; then(5)xϕΔtk=xϕtk−xϕtk−1,Dϕ=∑k=2nxϕΔtkn−1,xϕ′Δtk=xϕtk−xϕtk−1xϕtk−1,Dϕ′=∑k=2nxϕ′Δtkn−1,zϕΔtk=α·xϕΔtkDϕ+β·xϕ′ΔtkDϕ′,respectively, represent the absolute amount of data change, mean of absolute amount of data change, relative amount of data change, mean of relative amount of data change, and the trend amount of data change of time sequences Xϕ from point of time tk−1 to point of time tk.
In the above equation,Δtk=tk−tk−1,f,g=∪k=2nΔtk,Δtk∩Δtk−1=∅,g>f≥0,k=2,3,…,n; α and β represent the emphasis on the absolute and relative amount of data changes, respectively, and α+β=1.Definition 3.
Suppose that the RADV index on intervalf,g is X0=x0t1,x0t2,…,x0tn; the influencing factor is Xi=xit1,xit2,…,xitni=1,2,…,u; then(6)ξ0itk=sgnz0Δtk⋅ziΔtk⋅11+1/2z0Δtk−ziΔtk+1/21−minz0Δtk,ziΔtk/maxz0Δtk,ziΔtk,others,1,z0Δtk=ziΔtk=0,is the grey trend relational coefficient between the RADV index X0 and the influencing factor Xi from the point of time tk−1 to point of time tk.
In the above equation,sgnz0Δtk⋅ziΔtk is a symbolic function used to reflect the positive and negative correlations between the RADV index X0 and the influencing factor Xi. When z0Δtk⋅ziΔtk≥0, sgnz0Δtk⋅ziΔtk=1, and ξ0itk>0, which indicates that X0 and Xi change in the same direction during the period from the point of time tk−1 to the point of time tk, that is, positive correlation. When z0Δtk⋅ziΔtk<0, sgnz0Δtk⋅ziΔtk=−1, and ξ0itk<0, which indicates that X0 and Xi change in the opposite direction during the period from the point of time tk−1 to the point of time tk, that is, negative correlation.Definition 4.
Suppose that the RADV index on intervalf,g is X0=x0t1,x0t2,…,x0tn; the influencing factor is Xi=xit1,xit1,…,xitni=1,2,…,u; then,(7)γ0i=1b−a∑k=2nΔtk⋅ξ0itk,is the trend grey relational degree between the RADV index X0 and the influencing factor Xi.
When−1≤γ0i<0, X0 is negatively correlated with Xi, and the larger γ0i, the stronger the negative correlation. When 0<γ0i≤0, X0 is positively correlated with Xi, and the larger γ0i, the stronger the positive correlation. When γ0i=0, X0 is not related to Xi.Theorem 1.
The grey trend relational degreeγ0i has the following properties:(1)
Normativity.γ0i≤1; when x0tk=λxitk, λ is a nonzero constant, and γ0i=1 is established.(2)
Symmetry.γX0,Xi=γXi,X0.(3)
Proximity. The closer sequencesX0 and Xi are, the larger γ0i is.(4)
Uniqueness and comparability.(5)
Isotony. After dimensionless processing such as initialization in the same direction, multiplication, averaging, and percentage, the grey trend relational degree is not changed, so the sequence does not produce ordinal effects.Proof .
(1) Normativity. Ifx0tk=λxitk, λ is a nonzero constant; then(8)x0Δtk=x0tk−x0tk−1=λxitk−λxitk−1=λxiΔtk,x0′Δtk=x0tk−x0tk−1x0tk−1=λxitk−λxitk−1λxitk−1=xi′Δtk,λ>0,λxitk−λxitk−1λxitk−1=−xi′Δtk,λ<0,D0=∑k=2nx0Δtkn−1=∑k=2nλxiΔtkn−1=λDi,λ>0,∑k=2nx0Δtkn−1=∑k=2nλxiΔtkn−1=−λDi,λ<0,D0′=∑k=2nx0′Δtkn−1=∑k=2nxi′Δtkn−1=Di′,z0Δtk=α⋅x0ΔtkD0+β⋅x0′ΔtkD0′=α⋅λxiΔtkλDi+β⋅xi′ΔtkDi′=ziΔtk,λ>0,α⋅λxiΔtk−λDi+β⋅xi′Δtk−Di′=−ziΔtk,λ<0,and therefore(9)z0Δtk−ziΔtk=1−minz0Δtk,ziΔtkmaxz0Δtk,ziΔtk=0,sgnz0Δtk⋅ziΔtk=1,λ>0,−1,λ<0,and then(10)γ0i=1b−a∑k=2nΔtk⋅1=1,λ>0,1b−a∑k=2nΔtk⋅−1=−1,λ<0.
Namely,γ0i=1.
From the derivation of formulas (6) and (7), it can be seen that the properties in (2)-(6) are obviously valid.
(5) Isotony. Taking the same direction initialization as an example, sequencesX0 and Xi are normalized, and the normalized sequences are noted as X0Δ and XiΔ; then(11)x0Δtk=x0tkx0t1,x0Δtk−1=x0tk−1x0t1,x0ΔΔtk=x0Δtk−x0Δtk−1=x0tkx0t1−x0tk−1x0t1=x0Δtkx0t1,x0ΔΔtk=x0Δtk−x0Δtk−1=x0tkx0t1−x0tk−1x0t1=x0Δtkx0t1,x0′ΔΔtk=x0Δtk−x0Δtk−1x0Δtk−1=x0tk−x0tk−1⋅x0t1x0t1⋅x0tk−1=x0′Δtk,x0t1>0,−x0′Δtk,x0t1<0,D0Δ=∑k=2nx0ΔΔtkn−1=∑k=2nx0Δtkn−1⋅x0t1=D0x0t1,x0t1>0,−D0x0t1,x0t1<0,D0′Δ=∑k=2nx0′ΔΔtkn−1=∑k=2nx0′Δtkn−1=D0′,and therefore(12)z0ΔΔtk=α⋅x0ΔΔtkD0Δ+β⋅x0′ΔΔtkD0′Δ=α⋅x0Δtk⋅x0t1x0t1⋅D0+β⋅x0′ΔtkD0′=z0Δtk,x0t1>0,α⋅x0Δtk⋅x0t1−x0t1⋅D0+β⋅−x0′ΔtkD0′=−z0Δtk,x0t1<0.
Similarly,(13)xiΔΔtk=xiΔtkxit1,xi′ΔΔtk=xi′Δtk,xit1>0,−xi′Δtk,xit1<0,DiΔ=Dixit1,xit1>0,−Dixit1,xit1<0,Di′Δ=Di′,ziΔΔtk=ziΔtk,xit1>0,−ziΔtk,xit1<0,sgnz0ΔΔtk⋅ziΔΔtk=sgnz0Δtk⋅ziΔtk=1,x0t1>0,xit1<0,sgn−z0Δtk⋅−ziΔtk=1,x0t1>0,xit1<0,ziΔΔtk−zjΔΔtk=ziΔtk−ziΔtk,minziΔΔtk,zjΔΔtkmaxziΔΔtk,zjΔΔtk=minziΔtk,zjΔtkmaxziΔtk,zjΔtk.
Therefore, after the initialization in the same direction, the grey trend relational coefficient is unchanged, the same as the grey trend relational degree. Similarly, it can be proved that the dimensionless processing such as multiplication in the same direction, averaging, and percentage does not change the grey trend relational degree.


## 2.2.3. Clustering the Influencing Factors Based on TGRC Method

Depending on the grey trend relational degree between the RADV indexX0 and the influencing factor sequence Xi, the importance of the influencing factors can be ranked, but the main influencing factors cannot be filtered entirely according to the degree of importance, since some influencing factors may fall into the same category, which will not only increase the redundancy of data collection but also reduce the comprehensiveness of the factor screening. Therefore, it is necessary to cluster the influencing factors and merge the similar factors. TGRC is a method that is based on TGRA, constructing grey trend correlation matrix of the influencing factors and clustering the influencing factors by selecting appropriate relational threshold.Definition 5.
Assume that there are influencing factor sequencesXi=xit1,xit2,…,xitn and Xj=xjt1,xjt2,…,xjtn on interval f,g. For all i≤j, i=1,2,…,u, according to formulas (4) and (6), the grey trend relational degree between Xi and Xj is calculated, and the upper triangular matrix is obtained:(14)Y=γ11γ12…γ1uγ22…γ2u⋱⋮γuu,is the grey trend relational matrix of the influencing factors.
From the above equation,γii=1, and the relational threshold takes r∈0,1, which can be set according to the needs of the actual problem. When γij≥r, Xi and Xj are treated as the same influencing factors, and they are grouped into the same category. If γih≥r appears at the same time and h=1,2,…,u, but i≠j≠h, TGRC takes the smallest influencing factor of Xi,Xj,Xh in the label i,j,h as the representative of each category and combines the other two influencing factors into one with the smallest label to become a category. By traversing the whole grey trend correlation matrix, according to the relational threshold, the clustering results can be obtained, and the similar influencing factors merged.


## 3. Identification Results and Analysis

Henan Province is located in the center of the Huang-Huai-Hai Plain, which is a typical grain export province in China. However, due to the influence of the monsoon climate, drought occurs frequently, posing a huge threat to food security [33], and the research on drought issues needs to be strengthened urgently. In this paper, Henan Province is selected as the research object; the main influencing factors of RADV are identified by the PSR-TGRC method to reduce the degree of RADV and provide theoretical support for reducing agricultural drought losses.


### 3.1. Data Sources

In this paper, the annual precipitation comes from the China Meteorological Data Network from 1960 to 1998, and the annual precipitation comes from the Henan Provincial Water Resources Bulletin from 1999 to 2018, containing 19 typical meteorological stations in Henan Province (Anyang, Xinxiang, Zhengzhou, Nanyang, Xinyang, etc.). The data of the remaining factors mainly comes from the China Statistical Yearbook, the China Rural Statistical Yearbook, the China Science and Technology Statistical Yearbook, and the Henan Provincial Statistical Yearbook from 2012 to 2018.


### 3.2. Identification Results

#### 3.2.1. The Number of Main Influencing Factors of RADV in Henan Province

In order to identify the number of influencing factors of RADV in Henan Province, the PSR method is used to reconstruct the RADV index and calculate the RADV index of Henan Province from 1960 to 2018 according to formula (1), as shown in Figure 2.Figure 2
RADV index in Henan Province.After using the SPSS software to calculate the delay time of the RADV index in Henan Province, it is found that the autocorrelation function value of the RADV index changes with the delay timeτ, as shown in Figure 3. It can be seen from the figure that when τ=3, the autocorrelation function value is −0.036 and it is approximately 0 for the first time, so the delay time of the RADV index in Henan Province is 3.Figure 3
The curve of autocorrelation function with delay time.Taking the RADV index sequence from 1960 to 2018 in Henan Province as the object of PSR, theG-P algorithm is realized by MATLAB R2018b. By analyzing the change characteristics of the correlation dimension and the embedding dimension, the number of factors affecting RADV in Henan Province is explored. The relationship between embedding dimension and correlation dimension is shown in Figure 4.Figure 4
The relationship between embedding dimensionm and correlation dimension Dm.It can be found from Figure4 that when the embedding dimension m=14, the correlation dimension Dm reaches a saturation value of 4.36, which indicates that the RADV index of Henan Province is a chaotic time sequence, and the number of variables required to describe the chaotic sequence is 5 to 14; that is, when evaluating the degree of RADV, 5 to 14 main influencing factors must be selected for the evaluation. The result is basically consistent with the number of factors affecting RADV in the existing literatures [3, 9, 10].


#### 3.2.2. The Main Influencing Factors of RADV in Henan Province

The main influencing factors of Henan Province from 2012 to 2018 are identified based on TGRA and TGRC; the former is to identify the main influencing factors, and the latter is to identify the influence trend of factors on RADV. The RADV index of Henan Province from 2012 to 2018 showed an overall increasing trend (as shown in Figure2). If the influencing factors on RADV of Henan Province have the same direction as the grey trend relational degree, the development trend of influencing factors has a positive effect on the increase of RADV in Henan Province, and it is denoted as X+. If the influencing factors on the RADV of Henan Province have the opposite direction as the grey trend relational degree, the development trend of influencing factors has a negative effect on the increase of RADV in Henan Province, and it is denoted as X−.According to formulas (6) and (7), the grey trend relational degree between the 42 factors in Table 1 and the RADV index in Henan Province were calculated, in which α=β=0.5. According to formula (14), 20 influencing factors of sensitivity level and 22 influencing factors of recovery level were analyzed by grey trend relational clustering.In this paper, taking 14 influencing factors as examples, since they can more comprehensively represent the factors needed in the evaluation of RADV in Henan Province, the main influencing factors are screened out. According to the principle of comprehensiveness, the numbers of selected sensitivity factors and recovery factors should be balanced as far as possible, and they are clustered into 7 categories, respectively, to determine the clustering threshold and the main influencing factors. Taking sensitivity factors as an example, the grey trend relational degrees between 20 sensitivity factors and the RADV index are calculated according to formulas (6) and (7) and combined with the influencing direction of sensitivity factors of RADV and the direction of sensitivity factors on the development trend of RADV. The importances of influencing factors in Henan Province are ranked as follows:(15)X6−>X17+>X5−>X7−>X13+>X15+>X9−>X4−>X18+>X19+>X2−>X14−>X16−>X10+>X2−>X3+>X11−>X12+>X20+>X8−.A clustering analysis of 20 sensitivity factors is performed according to Definition5, and the clustering results between the 20 sensitivity factors at different thresholds are shown in Table 2.Table 2
Clustering results of sensitivity factors of RADV in Henan Province.
ThresholdrClustering results0.8362X1,X3,X11,X120.6823X1,X3,X11,X12,X14,X18,X200.6313X1,X3,X2,X13,X4,X7,X11,X12,X14,X18,X200.6069X1,X3,X2,X13,X4,X7,X5,X19,X10,X14,X18,X20,X11,X120.5843X1,X3,X2,X11,X12,X13,X4,X7,X5,X19,X10,X14,X18,X200.5593X1,X3,X2,X11,X12,X13,X4,X7,X5,X10,X14,X18,X19,X200.5269X1,X3,X4,X7,X2,X11,X12,X13,X5,X10X14,X18,X19,X200.5166X1,X3,X4,X7,X2,X8,X11,X12,X13,X5,X10X14,X16,X18,X19,X200.5153X1,X2,X3,X4,X7,X8,X11,X12,X13,X5,X10X14,X16,X18,X19,X200.5131X1,X2,X3,X4,X7,X8,X10,X11,X12,X13,X14,X16,X18,X19,X200.4793X1,X2,X3,X4,X7,X8,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X200.4411X1,X2,X3,X4,X5,X6,X7,X8,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X20According to the clustering of sensitivity factors under different thresholds, when thresholdr selects 0.5166, the sensitivity factors can be divided into 7 categories, and the main sensitivity factors can be identified by combining the ranking results of 20 sensitivity factors. The identification results can be found in Table 3. The recovery factors and the identification process of sensitivity factors are similar, so the detailed process will not be listed in this paper.Table 3
The identification results of main influencing factors of RADV in Henan Province.
Calculation methodIdentification resultsGuideline layerSensitivity factorsRecovery factorsGrey trend relational analysisX6−,X17+,X5−,X7−,X13+,X15+,X9−X36+,X29+,X40−,X42+,X31+,X33−,X30−GreyT-type relational analysisX6−,X17+,X13+,X5−,X15+,X9−,X12+X36+,X29+,X40−,X38+,X31+,X37+,X33−Grey rate of change relational analysisX6−,X17+,X18+,X7−,X9−,X2−,X15+X28+,X38+,X29+,X40−,X33−,X25−,X35+Grey comprehensive relational analysisX1,X2,X4,X6,X19,X17,X8X23,X31,X33,X22,X21,X27,X28


### 3.3. Results Analysis

During the period from 2012 to 2018, the main influencing factors of sensitivity in order of importance are per capita water resourcesX6, the proportion of corn planting area X17, per capita living water consumption of rural residents X5, average water consumption per mu of farmland irrigation X7, per capita arable land area X13, the proportion of water field area X15, and cover rate of forest X9. The main influencing factors of recovery in order of importance are per capita grain yield X36, pure amount of fertilizer application per unit area X29, rice unit area yield X40, autumn grain unit area yield X42, mechanical harvest area of agricultural year X31, soil erosion control area X33, and use of plastic film per unit area X30. In general, the influencing factors of RADV in Henan Province are mainly related to natural resources, agricultural industrial structure, agricultural attention, agricultural water efficiency, residents’ awareness of water conservation, water and soil conservation measures, and so forth, and the identification results are consistent with the actual drought relief work in Henan Province [34].The increasing trend of the proportion of corn planting areaX17 and the proportion of water field area X15, as well as the increase of per capita arable land area X13, per capita grain yield X36, pure amount of fertilizer application per unit area X29, and autumn grain unit area yield X42, and the decreasing trend of mechanical harvest area of agricultural year X31 are the main influencing factors driving the increase of RADV in Henan Province. Therefore, we should focus on adjusting the trend of these factors in order to reduce the RADV in Henan Province.In addition, per capita water resourcesX6, cover rate of forest X9, rice unit area yield X40, soil erosion control area X33, and use of plastic film per unit area X30, as well as the per capita living water consumption of rural residents X5, and the reduction of the average water consumption per mu of farmland irrigation X7 are the main influencing factors to inhibit the increase of RADV in Henan Province. It is shown that the development trend of these influencing factors is better, which has not yet caused threat to the increase of RADV in Henan Province; and, based on affirming the preliminary work, the above influencing factors should continue to be controlled to prevent their evolution from causing disaster.


### 3.4. Comparative Analysis

The greyT-type relational analysis [28], the grey rate of change relational analysis [29], and the grey comprehensive relational analysis [26] are used to perform relational clustering analysis to compare the identification results of influencing factors. The specific results (ranked by the importance of influencing factors) are shown in Table 3.There are some differences in the influencing factors of RADV in Henan Province obtained by different grey relational analysis methods. The first three kinds of grey relational analysis methods can distinguish the influence trend of factors on the degree of RADV in Henan Province from 2012 to 2018, and the difference in the identification results of factors is small, in which the ranking result of grey trend relational analysis method adjusts the different ranking of greyT-type relational analysis method and grey rate of change relational analysis method, while the grey comprehensive relational analysis method is quite different from the first three grey relational analysis methods.There are two main reasons for the above differences:(1)
The aspect of structure selection of relational analysis method. The first three grey relational analysis methods take the perspective of data composition ratio and composition difference to define the correlation degree, while the grey comprehensive relational analysis method takes the perspective of data composition difference to define the correlation degree.(2)
The aspect of data selection. The greyT-type relational analysis method and the grey rate of change relational analysis method select the absolute and relative amount of data in each period, respectively, while the grey comprehensive relational analysis method selects the absolute and relative amount between data points and ignores the amount of change in the development of data.In this paper, the grey trend relational analysis method integrates the idea of grey comprehensive relational analysis method on data selection, and the dynamic development characteristics of the RADV index and the influencing factors are fully considered. The trend change is defined by selecting the absolute and relative amount of data changes in each period, and correlation degree between the RADV index and the influencing factors is measured. Therefore, it will be more comprehensive and objective to examine the correlation of the RADV index and the influencing factors by using the grey trend relational analysis method.


## 3.1. Data Sources

In this paper, the annual precipitation comes from the China Meteorological Data Network from 1960 to 1998, and the annual precipitation comes from the Henan Provincial Water Resources Bulletin from 1999 to 2018, containing 19 typical meteorological stations in Henan Province (Anyang, Xinxiang, Zhengzhou, Nanyang, Xinyang, etc.). The data of the remaining factors mainly comes from the China Statistical Yearbook, the China Rural Statistical Yearbook, the China Science and Technology Statistical Yearbook, and the Henan Provincial Statistical Yearbook from 2012 to 2018.


## 3.2. Identification Results

### 3.2.1. The Number of Main Influencing Factors of RADV in Henan Province

In order to identify the number of influencing factors of RADV in Henan Province, the PSR method is used to reconstruct the RADV index and calculate the RADV index of Henan Province from 1960 to 2018 according to formula (1), as shown in Figure 2.Figure 2
RADV index in Henan Province.After using the SPSS software to calculate the delay time of the RADV index in Henan Province, it is found that the autocorrelation function value of the RADV index changes with the delay timeτ, as shown in Figure 3. It can be seen from the figure that when τ=3, the autocorrelation function value is −0.036 and it is approximately 0 for the first time, so the delay time of the RADV index in Henan Province is 3.Figure 3
The curve of autocorrelation function with delay time.Taking the RADV index sequence from 1960 to 2018 in Henan Province as the object of PSR, theG-P algorithm is realized by MATLAB R2018b. By analyzing the change characteristics of the correlation dimension and the embedding dimension, the number of factors affecting RADV in Henan Province is explored. The relationship between embedding dimension and correlation dimension is shown in Figure 4.Figure 4
The relationship between embedding dimensionm and correlation dimension Dm.It can be found from Figure4 that when the embedding dimension m=14, the correlation dimension Dm reaches a saturation value of 4.36, which indicates that the RADV index of Henan Province is a chaotic time sequence, and the number of variables required to describe the chaotic sequence is 5 to 14; that is, when evaluating the degree of RADV, 5 to 14 main influencing factors must be selected for the evaluation. The result is basically consistent with the number of factors affecting RADV in the existing literatures [3, 9, 10].


### 3.2.2. The Main Influencing Factors of RADV in Henan Province

The main influencing factors of Henan Province from 2012 to 2018 are identified based on TGRA and TGRC; the former is to identify the main influencing factors, and the latter is to identify the influence trend of factors on RADV. The RADV index of Henan Province from 2012 to 2018 showed an overall increasing trend (as shown in Figure2). If the influencing factors on RADV of Henan Province have the same direction as the grey trend relational degree, the development trend of influencing factors has a positive effect on the increase of RADV in Henan Province, and it is denoted as X+. If the influencing factors on the RADV of Henan Province have the opposite direction as the grey trend relational degree, the development trend of influencing factors has a negative effect on the increase of RADV in Henan Province, and it is denoted as X−.According to formulas (6) and (7), the grey trend relational degree between the 42 factors in Table 1 and the RADV index in Henan Province were calculated, in which α=β=0.5. According to formula (14), 20 influencing factors of sensitivity level and 22 influencing factors of recovery level were analyzed by grey trend relational clustering.In this paper, taking 14 influencing factors as examples, since they can more comprehensively represent the factors needed in the evaluation of RADV in Henan Province, the main influencing factors are screened out. According to the principle of comprehensiveness, the numbers of selected sensitivity factors and recovery factors should be balanced as far as possible, and they are clustered into 7 categories, respectively, to determine the clustering threshold and the main influencing factors. Taking sensitivity factors as an example, the grey trend relational degrees between 20 sensitivity factors and the RADV index are calculated according to formulas (6) and (7) and combined with the influencing direction of sensitivity factors of RADV and the direction of sensitivity factors on the development trend of RADV. The importances of influencing factors in Henan Province are ranked as follows:(15)X6−>X17+>X5−>X7−>X13+>X15+>X9−>X4−>X18+>X19+>X2−>X14−>X16−>X10+>X2−>X3+>X11−>X12+>X20+>X8−.A clustering analysis of 20 sensitivity factors is performed according to Definition5, and the clustering results between the 20 sensitivity factors at different thresholds are shown in Table 2.Table 2
Clustering results of sensitivity factors of RADV in Henan Province.
ThresholdrClustering results0.8362X1,X3,X11,X120.6823X1,X3,X11,X12,X14,X18,X200.6313X1,X3,X2,X13,X4,X7,X11,X12,X14,X18,X200.6069X1,X3,X2,X13,X4,X7,X5,X19,X10,X14,X18,X20,X11,X120.5843X1,X3,X2,X11,X12,X13,X4,X7,X5,X19,X10,X14,X18,X200.5593X1,X3,X2,X11,X12,X13,X4,X7,X5,X10,X14,X18,X19,X200.5269X1,X3,X4,X7,X2,X11,X12,X13,X5,X10X14,X18,X19,X200.5166X1,X3,X4,X7,X2,X8,X11,X12,X13,X5,X10X14,X16,X18,X19,X200.5153X1,X2,X3,X4,X7,X8,X11,X12,X13,X5,X10X14,X16,X18,X19,X200.5131X1,X2,X3,X4,X7,X8,X10,X11,X12,X13,X14,X16,X18,X19,X200.4793X1,X2,X3,X4,X7,X8,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X200.4411X1,X2,X3,X4,X5,X6,X7,X8,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X20According to the clustering of sensitivity factors under different thresholds, when thresholdr selects 0.5166, the sensitivity factors can be divided into 7 categories, and the main sensitivity factors can be identified by combining the ranking results of 20 sensitivity factors. The identification results can be found in Table 3. The recovery factors and the identification process of sensitivity factors are similar, so the detailed process will not be listed in this paper.Table 3
The identification results of main influencing factors of RADV in Henan Province.
Calculation methodIdentification resultsGuideline layerSensitivity factorsRecovery factorsGrey trend relational analysisX6−,X17+,X5−,X7−,X13+,X15+,X9−X36+,X29+,X40−,X42+,X31+,X33−,X30−GreyT-type relational analysisX6−,X17+,X13+,X5−,X15+,X9−,X12+X36+,X29+,X40−,X38+,X31+,X37+,X33−Grey rate of change relational analysisX6−,X17+,X18+,X7−,X9−,X2−,X15+X28+,X38+,X29+,X40−,X33−,X25−,X35+Grey comprehensive relational analysisX1,X2,X4,X6,X19,X17,X8X23,X31,X33,X22,X21,X27,X28


## 3.2.1. The Number of Main Influencing Factors of RADV in Henan Province

In order to identify the number of influencing factors of RADV in Henan Province, the PSR method is used to reconstruct the RADV index and calculate the RADV index of Henan Province from 1960 to 2018 according to formula (1), as shown in Figure 2.Figure 2
RADV index in Henan Province.After using the SPSS software to calculate the delay time of the RADV index in Henan Province, it is found that the autocorrelation function value of the RADV index changes with the delay timeτ, as shown in Figure 3. It can be seen from the figure that when τ=3, the autocorrelation function value is −0.036 and it is approximately 0 for the first time, so the delay time of the RADV index in Henan Province is 3.Figure 3
The curve of autocorrelation function with delay time.Taking the RADV index sequence from 1960 to 2018 in Henan Province as the object of PSR, theG-P algorithm is realized by MATLAB R2018b. By analyzing the change characteristics of the correlation dimension and the embedding dimension, the number of factors affecting RADV in Henan Province is explored. The relationship between embedding dimension and correlation dimension is shown in Figure 4.Figure 4
The relationship between embedding dimensionm and correlation dimension Dm.It can be found from Figure4 that when the embedding dimension m=14, the correlation dimension Dm reaches a saturation value of 4.36, which indicates that the RADV index of Henan Province is a chaotic time sequence, and the number of variables required to describe the chaotic sequence is 5 to 14; that is, when evaluating the degree of RADV, 5 to 14 main influencing factors must be selected for the evaluation. The result is basically consistent with the number of factors affecting RADV in the existing literatures [3, 9, 10].


## 3.2.2. The Main Influencing Factors of RADV in Henan Province

The main influencing factors of Henan Province from 2012 to 2018 are identified based on TGRA and TGRC; the former is to identify the main influencing factors, and the latter is to identify the influence trend of factors on RADV. The RADV index of Henan Province from 2012 to 2018 showed an overall increasing trend (as shown in Figure2). If the influencing factors on RADV of Henan Province have the same direction as the grey trend relational degree, the development trend of influencing factors has a positive effect on the increase of RADV in Henan Province, and it is denoted as X+. If the influencing factors on the RADV of Henan Province have the opposite direction as the grey trend relational degree, the development trend of influencing factors has a negative effect on the increase of RADV in Henan Province, and it is denoted as X−.According to formulas (6) and (7), the grey trend relational degree between the 42 factors in Table 1 and the RADV index in Henan Province were calculated, in which α=β=0.5. According to formula (14), 20 influencing factors of sensitivity level and 22 influencing factors of recovery level were analyzed by grey trend relational clustering.In this paper, taking 14 influencing factors as examples, since they can more comprehensively represent the factors needed in the evaluation of RADV in Henan Province, the main influencing factors are screened out. According to the principle of comprehensiveness, the numbers of selected sensitivity factors and recovery factors should be balanced as far as possible, and they are clustered into 7 categories, respectively, to determine the clustering threshold and the main influencing factors. Taking sensitivity factors as an example, the grey trend relational degrees between 20 sensitivity factors and the RADV index are calculated according to formulas (6) and (7) and combined with the influencing direction of sensitivity factors of RADV and the direction of sensitivity factors on the development trend of RADV. The importances of influencing factors in Henan Province are ranked as follows:(15)X6−>X17+>X5−>X7−>X13+>X15+>X9−>X4−>X18+>X19+>X2−>X14−>X16−>X10+>X2−>X3+>X11−>X12+>X20+>X8−.A clustering analysis of 20 sensitivity factors is performed according to Definition5, and the clustering results between the 20 sensitivity factors at different thresholds are shown in Table 2.Table 2
Clustering results of sensitivity factors of RADV in Henan Province.
ThresholdrClustering results0.8362X1,X3,X11,X120.6823X1,X3,X11,X12,X14,X18,X200.6313X1,X3,X2,X13,X4,X7,X11,X12,X14,X18,X200.6069X1,X3,X2,X13,X4,X7,X5,X19,X10,X14,X18,X20,X11,X120.5843X1,X3,X2,X11,X12,X13,X4,X7,X5,X19,X10,X14,X18,X200.5593X1,X3,X2,X11,X12,X13,X4,X7,X5,X10,X14,X18,X19,X200.5269X1,X3,X4,X7,X2,X11,X12,X13,X5,X10X14,X18,X19,X200.5166X1,X3,X4,X7,X2,X8,X11,X12,X13,X5,X10X14,X16,X18,X19,X200.5153X1,X2,X3,X4,X7,X8,X11,X12,X13,X5,X10X14,X16,X18,X19,X200.5131X1,X2,X3,X4,X7,X8,X10,X11,X12,X13,X14,X16,X18,X19,X200.4793X1,X2,X3,X4,X7,X8,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X200.4411X1,X2,X3,X4,X5,X6,X7,X8,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X20According to the clustering of sensitivity factors under different thresholds, when thresholdr selects 0.5166, the sensitivity factors can be divided into 7 categories, and the main sensitivity factors can be identified by combining the ranking results of 20 sensitivity factors. The identification results can be found in Table 3. The recovery factors and the identification process of sensitivity factors are similar, so the detailed process will not be listed in this paper.Table 3
The identification results of main influencing factors of RADV in Henan Province.
Calculation methodIdentification resultsGuideline layerSensitivity factorsRecovery factorsGrey trend relational analysisX6−,X17+,X5−,X7−,X13+,X15+,X9−X36+,X29+,X40−,X42+,X31+,X33−,X30−GreyT-type relational analysisX6−,X17+,X13+,X5−,X15+,X9−,X12+X36+,X29+,X40−,X38+,X31+,X37+,X33−Grey rate of change relational analysisX6−,X17+,X18+,X7−,X9−,X2−,X15+X28+,X38+,X29+,X40−,X33−,X25−,X35+Grey comprehensive relational analysisX1,X2,X4,X6,X19,X17,X8X23,X31,X33,X22,X21,X27,X28


## 3.3. Results Analysis

During the period from 2012 to 2018, the main influencing factors of sensitivity in order of importance are per capita water resourcesX6, the proportion of corn planting area X17, per capita living water consumption of rural residents X5, average water consumption per mu of farmland irrigation X7, per capita arable land area X13, the proportion of water field area X15, and cover rate of forest X9. The main influencing factors of recovery in order of importance are per capita grain yield X36, pure amount of fertilizer application per unit area X29, rice unit area yield X40, autumn grain unit area yield X42, mechanical harvest area of agricultural year X31, soil erosion control area X33, and use of plastic film per unit area X30. In general, the influencing factors of RADV in Henan Province are mainly related to natural resources, agricultural industrial structure, agricultural attention, agricultural water efficiency, residents’ awareness of water conservation, water and soil conservation measures, and so forth, and the identification results are consistent with the actual drought relief work in Henan Province [34].The increasing trend of the proportion of corn planting areaX17 and the proportion of water field area X15, as well as the increase of per capita arable land area X13, per capita grain yield X36, pure amount of fertilizer application per unit area X29, and autumn grain unit area yield X42, and the decreasing trend of mechanical harvest area of agricultural year X31 are the main influencing factors driving the increase of RADV in Henan Province. Therefore, we should focus on adjusting the trend of these factors in order to reduce the RADV in Henan Province.In addition, per capita water resourcesX6, cover rate of forest X9, rice unit area yield X40, soil erosion control area X33, and use of plastic film per unit area X30, as well as the per capita living water consumption of rural residents X5, and the reduction of the average water consumption per mu of farmland irrigation X7 are the main influencing factors to inhibit the increase of RADV in Henan Province. It is shown that the development trend of these influencing factors is better, which has not yet caused threat to the increase of RADV in Henan Province; and, based on affirming the preliminary work, the above influencing factors should continue to be controlled to prevent their evolution from causing disaster.


## 3.4. Comparative Analysis

The greyT-type relational analysis [28], the grey rate of change relational analysis [29], and the grey comprehensive relational analysis [26] are used to perform relational clustering analysis to compare the identification results of influencing factors. The specific results (ranked by the importance of influencing factors) are shown in Table 3.There are some differences in the influencing factors of RADV in Henan Province obtained by different grey relational analysis methods. The first three kinds of grey relational analysis methods can distinguish the influence trend of factors on the degree of RADV in Henan Province from 2012 to 2018, and the difference in the identification results of factors is small, in which the ranking result of grey trend relational analysis method adjusts the different ranking of greyT-type relational analysis method and grey rate of change relational analysis method, while the grey comprehensive relational analysis method is quite different from the first three grey relational analysis methods.There are two main reasons for the above differences:(1)
The aspect of structure selection of relational analysis method. The first three grey relational analysis methods take the perspective of data composition ratio and composition difference to define the correlation degree, while the grey comprehensive relational analysis method takes the perspective of data composition difference to define the correlation degree.(2)
The aspect of data selection. The greyT-type relational analysis method and the grey rate of change relational analysis method select the absolute and relative amount of data in each period, respectively, while the grey comprehensive relational analysis method selects the absolute and relative amount between data points and ignores the amount of change in the development of data.In this paper, the grey trend relational analysis method integrates the idea of grey comprehensive relational analysis method on data selection, and the dynamic development characteristics of the RADV index and the influencing factors are fully considered. The trend change is defined by selecting the absolute and relative amount of data changes in each period, and correlation degree between the RADV index and the influencing factors is measured. Therefore, it will be more comprehensive and objective to examine the correlation of the RADV index and the influencing factors by using the grey trend relational analysis method.


## 4. Managerial Implications

According to the above main influencing factors driving or inhibiting the increase of RADV in Henan Province, the corresponding managerial implications are put forward to reduce the RADV in Henan Province.For the main factors driving the increase of RADV in Henan Province, the specific measures are as follows:(1)
Optimizing the planting structure of crops, reducing production according to market changes, selecting drought-tolerant crop varieties, and making full use of rainfall and irrigation water to reduce the yield losses of crops caused by water shortage.(2)
Actively protecting arable land, strictly controlling the conversion of arable land to nonarable land, and increasing effective arable land area to improve land quality and utilization efficiency.(3)
Increasing the amount of farm manure and decreasing phosphorus-containing chemical fertilizer applied in land to promote agricultural production to avoid destroying the ecological balance.(4)
Giving full play to the supporting and guiding role of agricultural machinery purchase subsidies and other policy projects, focusing on improving the level of agricultural mechanization, improving agricultural production efficiency, and promoting farmers’ income to improve the ability of drought resistance and disaster prevention by developing modern agriculture.For the main factors inhibiting the increase of RADV in Henan Province, the specific measures are as follows:(1)
Strengthening the publicity of drought and water conservation and guiding enterprises and the masses to raise awareness of drought and water conservation to increase the utilization rate of water resources.(2)
Increasing forest cover area and greening efforts, optimizing tree species and forest structure, improving forest quality, and strengthening the construction of large areas of forest corridors, such as wetland parks and other forest ecological spaces between Zhengzhou, the provincial capital, and surrounding cities.(3)
Strengthening the construction, maintenance, and management of farmland water conservancy infrastructure, improving agricultural irrigation technology, and the reuse rate of industrial water to reduce the loss of water resources.(4)
Paying attention to the integration of soil erosion control with the local pillar industries, the people’s poverty alleviation, and the adjustment of industrial structure and increasing the construction of water and soil conservation measures such as slope conversion, small-scale water conservancy, and water storage projects, water conservation forests, and economic forests.(5)
Increasing the promotion of high-quality agricultural film, improving the efficiency of agricultural film use from the perspectives of screening the best uncovering period of crops, and strengthening the drought management of seedlings to minimize the losses caused by drought.


## 5. Conclusions

As for the influencing factor identification of RADV, a PSR-TGRC method is proposed. From the aspects of sensitivity and recovery, 42 influencing factors are selected to construct a collection of RADV influencing factors. Using the method of PSR in chaos theory, the number of influencing factors of RADV is quantitatively analyzed. Then, considering the absolute and relative amount of data changes in each period, the grey trend relational analysis method and the grey trend relational clustering analysis method are proposed. The PSR-TGRC method is applied to identify the influencing factors of RADV in Henan Province, while three other grey relational analysis methods are selected for comparative analysis, which verifies the effectiveness and superiority of PSR-TGRC method. Finally, combined with the main influencing factors and effects of RADV in Henan Province in 2012–2018, the corresponding measures are put forward.In this paper, the province is chosen as the research unit, and the PSR-TGRC method is used to identify the influencing factors of RADV, which can provide a reference for the selection of influencing factors in the subsequent evaluation process. Next, in the evaluation and study, the research areas should be refined and the differences of agricultural drought problems within regions should be deeply analyzed. In addition, this paper gives more consideration to human factors but less consideration to natural factors, such as topography, soil vegetation, and other factors on the formation of agricultural drought and postdisaster recovery. The collection of RADV influencing factors can be updated with the improvement of data.



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*Source: 9933152-2021-07-19.xml*