Agricultural drought risk assessment is helpful in quantitatively understanding agricultural drought and scientifically guiding disaster prevention and mitigation. Therefore, according to the characteristics of attribute uncertainty and index weight subjectivity in agricultural drought risk assessment, an attribute interval identification model combined with grey relational analysis was established to evaluate agricultural drought risk. Firstly, the agricultural drought risk evaluation index system was established from four aspects: disaster, exposure, vulnerability and resistance. Then, the objective weights of the indicators were calculated using the grey relational method. Finally, the agricultural drought risk in Zhengzhou was evaluated by qualitative analysis and probabilistic analysis. Qualitative analysis results showed that the agricultural drought risk in Zhengzhou is at the level of moderate drought. The probability analysis showed that the probability of Zhengzhou City being in a moderate drought is 79.5%, and the probability of being in a severe drought is 20.5%. In addition, the superiority of the attribute interval identification model in agricultural drought risk assessment was further verified by comparative analysis. This research provides a new method for regional agricultural drought risk assessment. Furthermore, it can provide support for management departments to further understand the regional drought risk level and improve the efficiency of drought risk management.

  • The probability corresponding to the agricultural drought risk level should be considered.

  • Interval values are used instead of fixed values to quantify the evaluation indicators.

  • Gray correlation is introduced to construct an interval attribute recognition and evaluation model.

  • The construction of an evaluation index system is very important.

  • The dynamic changes of indicator values should be taken seriously.

Graphical Abstract

Graphical Abstract
Graphical Abstract

Drought is a natural disaster with a complex formation mechanism, long duration and wide influence, which has seriously affected agricultural production, human life and economic development (Cong et al. 2017; Schwalm et al. 2017; Zhang et al. 2017; Zhao et al. 2021). The critical impact of drought on socio-economic and ecological systems has become a frontier issue in the field of climate change research (Jiang & Wang 2021). A related IPCC report pointed out that between 2030 and 2052, the global average temperature will rise by 1.5 °C from that before the second industrial revolution, and climate change and other factors will significantly increase the possibility of extreme droughts in the future (Schwalm et al. 2017). In recent years, the impact of drought on agricultural production has shown an increasing trend. Approximately 7% of the world's large-scale food production losses result in drought (Lesk et al. 2016). The area affected by agricultural droughts accounted for 56.2% of the area affected by multiple meteorological disasters (Wang et al. 2007). With the constant increase in the frequency of drought disasters and the continuous expansion of the scope of influence, the degree of drought in various regions is further intensified. Meanwhile, these regions are facing severe drought disaster risk situations due to the increasingly severe form of climate warming (Han et al. 2019). Therefore, the effective identification of agricultural drought risk levels will not only support governments and disaster reduction departments to grasp the relevant information on drought losses in a timely manner, but also to formulate response measures for disaster prevention and mitigation scientifically. This is a major strategic issue related to regional social economy, food security, ecological security, and even national security.

Global research on agricultural drought disasters originated in the late 19th century. However, research on agricultural drought disaster risk has only emerged in the past 50 years (Han et al. 2019). Dong et al. (2019) constructed a risk-matrix-based assessment method for regional agricultural drought risk chain transmission, and carried out agricultural drought risk assessment in the Huaihe River Basin of Anhui Province. Kamruzzaman et al. (2018) calculated the drought index and drought hazard index from both socio-economic and physical indicators based on the Markov chain to assess agricultural drought risk status in the western region of Bangladesh under the background of global climate change from 1960 to 2011. Obviously, the above research has improved the accuracy of drought risk assessment to a certain extent. However, because the risk factors of regional agricultural drought disasters have the characteristics of diversity, variability and uncertainty, etc, it is necessary to establish a more comprehensive evaluation index from the perspective of hazard, exposure, vulnerability and resistance. In addition, accurately assessing the characteristics and laws of the spatial distribution of disaster risks appears to be insufficient. Therefore, this study comprehensively considers the complexity and uncertainty of drought risk, and establishes evaluation indicators from the aspects of drought hazard, exposure, vulnerability and resistance. The attribute interval recognition model is introduced to solve the problem of index attribute value uncertainty and ambiguity in the drought risk assessment. The model can accurately assess the risk level of regional drought disasters and provide theoretical support for regional agricultural high-quality development and ecological protection.

The remaining content of this paper is organized as follows. The literature review in the second section reviews related research on agricultural drought risk assessment theory, agricultural drought risk assessment index system and attribute interval identification method. The third section is the research method, which constructs the index system and attribute recognition evaluation model of regional agricultural drought risk assessment. The fourth section is a case analysis, using the constructed index system and methods to evaluate the agricultural drought risk in Zhengzhou. The fifth section is the conclusion, summarizing and proposing the limitations of the research.

Regional agricultural drought risk is a compound factor of the interaction between natural and manufactured disasters. It is necessary to accurately identify the drought risk to reduce drought losses. Nowadays, the research on regional agricultural drought risk mainly focuses on three aspects: choosing the theoretical method of risk assessment, establishing the risk assessment index system and determining the weight of the risk assessment index. This section reviews the literature from the two aspects of agricultural drought risk assessment theoretical methods and agricultural drought risk assessment indicators, and further reviews the application of the attribute interval recognition method.

Theoretical methods of agricultural drought risk assessment

In recent years, the research on agricultural drought disaster risk assessment systems can be summarized into the following two aspects: (1) Based on historical data and meteorological drought index. For instance, derived from 30 years of agricultural disaster statistics in Heilongjiang Province, Xing et al. (2017) used the fuzzy comprehensive evaluation method to analyze the characteristics and risk levels of agro-meteorological disasters caused by meteorological disasters. In view of the daily meteorological data of 90 meteorological stations in the study area, Shen et al. (2017) calculated the standardized precipitation evapotranspiration index (SPEI) (Li et al. 2017) for multiple time-scales from 1961 to 2014, and further discussed the effectiveness of the SPEI in northeast China. Chen et al. (2018) used daily meteorological data from 1953 to 2016 in the Zhanghe Irrigation District of Hubei to calculate the monthly standardized precipitation index (SPI) (Wang et al. 2015), relative humidity index (M) (Farahmand et al. 2015) and Palmer drought index (PDSI) (Ma et al. 2015), using calculated data to compare with actual drought records to analyze its seasonal drought characteristics. In view of the precipitation data of 15 meteorological stations in Anhui Province from 1965 to 2014, Li et al. (2018) investigated the characteristics of temporal and spatial changes in Anhui Province by using the percentage of precipitation anomaly as a drought indicator. Zhang et al. (2019b) further evaluated the meteorological drought in Fujian Province derived from daily temperature, precipitation and wind-speed meteorological data from 1961 to 2017 combined with the Mediterranean Climate Index (MCI) (Kutiel & Türkeş 2017). Naz et al. (2020) collected monthly precipitation data from ten stations for 37 years (1980–2017) of Pakistan's meteorological department (PMD), and used the standard precipitation index (SPI) to analyze the drought trend on a three-month cumulative time-scale in Balochistan. (2) Based on disaster system theory and statistical methods. Zhang & Guo (2016) evaluated the agricultural drought risk in Zhoukou from the two levels of disaster-causing and disaster-bearing on the basis of the information diffusion model of fuzzy mathematics theory. Qu et al. (2015) used the fuzzy comprehensive evaluation method derived from regional disaster system theory to quantitatively and qualitatively evaluate agricultural drought risk at the national level. Xu et al. (2021) established an agricultural drought risk assessment model on the basis of the grey matter element analysis method, and evaluated agricultural drought risk in 18 regions of Henan Province in 2019. Li & Zhang (2020) assessed the risk of agro-meteorological disasters in Henan Province in view of the grey neural network model.

However, this research found that there are still some deficiencies in agricultural drought assessment on the grounds of historical data and statistical methods. For instance, in fuzzy mathematics methods it is difficult to distinguish the difference between two adjacent categories. The matter-element extension method often takes the interval's midpoint as optimal when calculating the degree of relevance, thereby omitting significant constraints, resulting in differences between the results and the actual situation. The neural network method is not only limited by the knowledge bottleneck in application, but also has very high requirements for the size of the data set. Therefore, on account of the complexity and uncertainty of drought risk assessment, it is necessary to further explore regional agricultural drought risk assessment methods.

Agricultural drought risk assessment indicators

In terms of determining the weights of evaluation indicators, He et al. (2017) took Shaanxi Province as the research object. An evaluation index system and evaluation method of agricultural drought risk in view of the combination of principal component analysis and analytic hierarchy process (Sahani et al. 2019) were proposed. Ai et al. (2021) used the analytical hierarchy process to determine the weight coefficients of each indicator in the model, and evaluated the drought disaster risk in Jiangxi Province. Deriving from the principle of set pair analysis and fuzzy theory, Liang et al. (2019) established a fuzzy set pair evaluation method to assess the risk of agricultural drought disasters in Bozhou, Anhui Province, in 2012. Pei et al. (2021) used the correlation coefficient test method to select the main factors affecting drought disasters from the three aspects of nature, agriculture and social economy, and conduct drought risk analysis. Chang et al. (2017) used the principal component analysis method to study the natural drought zoning of Yunnan Province. According to the multi-level fuzzy comprehensive evaluation results, a study on agricultural drought risk zoning in Yunnan was carried out. Sahana et al. (2021) integrated the analytic hierarchy process (AHP), entropy weight method, TOPSIS method and other aggregation techniques to conduct agricultural drought risk assessments across India.

In summary, these research methods are highly subjective or reliant on statistical data. In addition, the calculation process of these methods is complicated, which can easily lead to unobjective research results. Furthermore, these methods did not consider the uncertain characteristics of agricultural drought disaster risk and the incompleteness of the data obtained. In addition, most of the evaluation index values in the above methods are of constant value, ignoring the dynamic changes of specific index values during the drought risk assessment process, which brings difficulties to the macro-management of drought disaster risks.

Research on attribute interval recognition method

Cheng (1997) proposed a new evaluation method attribute recognition theoretical model that can effectively solve the problem of ordered segmentation (Li & Ning 2002). On the basis of traditional attribute recognition theory, Li introduced the concept of the attribute measurement interval, expanded the evaluation index into a small range, and constructed a new systematic evaluation method (Li et al. 2013). Based on the ordered segmentation and attribute recognition criterion, interval value is used to quantify the evaluation index to effectively identify and compare things. The attribute interval method uses the interval to represent the degree of measurement of an element with a specific attribute, which can accurately express the uncertainty between the component and the attribute set. It can not only solve the uncertainty of evaluation indicators, but also evaluate the risk degree through qualitative analysis and probability analysis. This method has been widely used in hillside stability evaluation (Wu et al. 2016), earthquake secondary fire evaluation (Liu & Wang 2017), coal seam floor water inrush risk evaluation (Li et al. 2015), natural gas pipeline accident consequence evaluation (Li et al. 2021) and flood accident evaluation (Yuan & Zhou 2004; Zou et al. 2012). Although this method is widely used in risk assessment, there are few specific studies on agricultural drought risk uncertainty.

Reviewing the above literature, the research deficiencies are as followed: (1) In agricultural drought risk assessment, the current model ignores some important influencing factors when screening the influencing factors, resulting in a big difference between the assessment results and the actual situation. Meanwhile, most of the existing models can only provide a qualitative or semi-quantitative drought risk level instead of a probability of occurrence corresponding to the drought level. (2) In the process of determining the index weight, the determination method is subjective. The calculation process is complex, ignoring the uncertain characteristics of agricultural drought risk and the incompleteness of the obtained data. (3) Most evaluation methods usually set the index value as a constant value, ignoring the dynamic changes of certain index values during the drought risk assessment process, which brings difficulties to the macro-management of drought disaster risks. Therefore, this paper introduces the attribute interval measurement model into the regional agricultural drought risk assessment, and uses interval values instead of fixed values to quantify the evaluation indicators. The dynamically changing characteristics of the data are also considered in the evaluation process. For the combinations of the comprehensive attribute measurement calculated by attribute interval recognition, two methods of qualitative analysis and probabilistic analysis are used to evaluate and analyze the risk level. Moreover, grey correlation analysis is used to determine the index weights, which overcomes the subjectivity of traditional methods and makes the evaluation results more convincing. The interval attribute identification model constructed in this paper evaluates the level and probability of agricultural drought disasters by considering the dynamics of the data on the basis of objectively determining the weights of the indicators.

On the basis of attribute recognition theory, the attribute interval recognition model (AIRM) was firstly proposed by Chinese scholars in 2002 (Li & Ning 2002). It developed concepts such as the upper and lower bound attribute measurement interval and the average coefficient. The interval number is used to evaluate the uncertainty of the index. Agricultural drought risk assessment is a complex system, in which the assessment process is affected by uncertain factors (Liang et al. 2019). In addition, objectively determining the indicator weights is crucial to the accuracy of the evaluation results (Zhang & Yang 2007). Therefore, on the basis of introducing the grey relational analysis method to determine the objective weight, this paper constructs an attribute interval identification model to evaluate the regional agricultural drought risk. It effectively solves the qualitative description measurement problem in drought risk assessment. First of all, this research establishes a regional agricultural drought disaster risk assessment index system. Secondly, this study constructs an attribute interval recognition and evaluation model. Then the single-index attribute measurement is selected to determine the value of each attribute, and the grey relational analysis model is applied to determine the weight of each attribute. The comprehensive attribute measurement value is determined based on the single-index attribute measurement value and weight. Finally, because the comprehensive attribute measures obtained by the attribute interval recognition calculation have multiple combinations, qualitative analysis and probabilistic analysis are used to identify and classify regional agricultural drought risks. Therefore, the regional agricultural drought risk assessment system in this paper is mainly composed of a single-index attribute measurement and analysis system, a multi-index comprehensive attribute measurement and analysis system, and an attribute identification and analysis system. The model flow chart is shown in Figure 1.

Figure 1

Flow chart of the evaluation model of the attribute interval recognition method.

Figure 1

Flow chart of the evaluation model of the attribute interval recognition method.

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Establishment of index system and evaluation standard

The formation process of drought is complicated, and there are many influencing factors of drought. On the basis of regional disaster system theory and natural disaster theory, this paper constructed the agricultural drought risk assessment index system and method. Derived from the principles of scientificity, comparability, operability and data accessibility (Zhang et al. 2011; Dai et al. 2020; Xu et al. 2021), this research established an index system for agricultural drought risk assessment from the perspectives of hazards, exposure, vulnerability and resistance. On this basis, this study evaluated the agricultural drought risk in Zhengzhou.

Hazard is primarily used to describe the extent of damage caused by drought (Zhang et al. 2020b). Existing studies have developed indicators such as annual precipitation (Zhang et al. 2019a), annual precipitation variation coefficient (Longobardi & Boulariah 2022), average water resources per ha (Qu 2018), and crop soil moisture (Yuan & Zhou 2004) to describe the characteristics of drought risk. Combining the features of agricultural drought, this paper selects annual average precipitation and annual average temperature as indicators to evaluate the risk of drought. The higher the average annual precipitation in an area, the lower the risk of drought in that area. Otherwise, the region will be at greater risk of drought.

Exposure is mainly used to describe the range of production factors affected by drought when it occurs (Liu et al. 2021). The exposure to agricultural drought is mainly reflected in the sown area of crops (Luo et al. 2020). Existing studies have used indicators such as the gross agricultural production value per planted area (Yang 2015; Xu 2016), the proportion of arable land (Zhang & Wang 2018), and the per capita arable land area (He et al. 2016) to describe the characteristics of exposure. This paper refers to related literature (Qin et al. 2013; Qu et al. 2015; Yang et al. 2018) and the characteristics of the study area, and according to the principle of data availability, two indicators, the per capita arable land area and the proportion of agricultural production to gross domestic product (GDP), were selected to measure the degree of drought exposure.

Vulnerability refers to the ability of the planting environment of crops to buffer the negative effects of drought in the process of drought under constant natural environment conditions (Kim et al. 2015). Existing studies have applied the ratio of irrigated dry land to arable land (Qin et al. 2013), the ratio of irrigated paddy land to arable land (Wu et al. 2018), the ratio of rain-fed agriculture to arable land (Zhang & Wang 2018), the extent of water resources development and utilization (He et al. 2017; Luo et al. 2020), the amount of water supplied by projects (Zhao et al. 2013), and the area of water-saving irrigation (Xu et al. 2013; Qu 2018) to describe the characteristics of vulnerability. Since the existing statistical data cannot meet the above characteristics at the scale of the city, under the conditions of comprehensive research area characteristics and the principle of data availability, this research selects the proportion of grain output per unit area and agricultural water consumption to describe the characteristics of vulnerability.

Resistance refers to the ability of human beings to reduce drought losses by organizing drought-relief actions when a drought occurs (Sun et al. 2013). Existing studies have generated the per capita net income of farmers (Jin et al. 2014), the number of motorized wells per unit area (Liang et al. 2013), the profitable storage capacity per unit area (He et al. 2016), the total power of machinery per unit area (Palchaudhuri & Biswas 2016), and the rural labor force per unit area (Sahana et al. 2021) to characterize disaster prevention and mitigation capabilities. Because of the difficulty of obtaining some data, this paper selects the total power of agricultural machinery per unit area and per capita GDP to describe disaster prevention and mitigation capabilities. The agricultural drought risk assessment indicators are shown in Table 1.

Table 1

Agricultural drought risk assessment indicators

Evaluation subsystemIndicatorsUnitIndicator source
hazard annual average precipitation (mm Xu et al. (2021)  
annual average temperature ( Palchaudhuri & Biswas (2016), Yuan & Zhou (2004)  
exposure per capita arable land (ha/person He et al. (2013), Yang et al. (2018)  
the proportion of agricultural production/GDP (Qin et al. (2013)  
vulnerability grain production per unit area (kg/ha Xu et al. (2013)  
proportion of agricultural water consumption (Palchaudhuri & Biswas (2016), Yang (2015)  
resistance total power of agricultural machinery per unit area (kWh/ha Liang et al. (2013)  
GDP per capita (RMB Jin et al. (2014)  
Evaluation subsystemIndicatorsUnitIndicator source
hazard annual average precipitation (mm Xu et al. (2021)  
annual average temperature ( Palchaudhuri & Biswas (2016), Yuan & Zhou (2004)  
exposure per capita arable land (ha/person He et al. (2013), Yang et al. (2018)  
the proportion of agricultural production/GDP (Qin et al. (2013)  
vulnerability grain production per unit area (kg/ha Xu et al. (2013)  
proportion of agricultural water consumption (Palchaudhuri & Biswas (2016), Yang (2015)  
resistance total power of agricultural machinery per unit area (kWh/ha Liang et al. (2013)  
GDP per capita (RMB Jin et al. (2014)  

Attribute interval recognition and evaluation model

Definition 1: Let be the evaluation space of the evaluation object, and the evaluation object has m evaluation indexes . The attribute measurement value of each evaluation index is , and there are K evaluation levels for each evaluation object. This paper constructs the corresponding attribute space C for the regional agricultural drought risk level. Based on the attribute measure function, this research determines the classification standard of each evaluation index, and writes the corresponding classification standard interval matrix as shown in Table 2, where represents the lower limit value of the -th evaluation index corresponding to the -th evaluation level; represents the upper limit value of the -th evaluation index corresponding to the -th evaluation level. At the same time, the matrix expression form of the classification criteria of risk grades is shown in Equations (1) and (2):
formula
(1)
formula
(2)
where if , then , ; if , then , .
Table 2

Classification standard of evaluation index

Evaluation indexEvaluation grade
(    
     
     
     
     
Evaluation indexEvaluation grade
(    
     
     
     
     

Single-index attribute measurement

According to the attribute measurement of the evaluation index , the single-index attribute measurement function can be used to determine whether it belongs to the single-index attribute measurement of the drought risk level . Due to the complexity and uncertainty characteristics of agricultural drought disasters, the value range of the -th evaluation index in the actual drought risk assessment is . The single-index attribute measurement is calculated by constructing an attribute measurement function, and the attribute measurement interval is expressed as .

When and , , the calculation method of single-index attribute measurement is as Equations (3)–(8). In the calculation, takes the lower limit and the upper limit of the index value range respectively for calculation.

① When , there is
formula
(3)
② When , there is
formula
(4)
③ When , there is
formula
(5)
④ When , there is
formula
(6)
⑤ When , there is
formula
(7)
where or .
⑥ When , there is
formula
(8)
where or .
Therefore, for , two single-index attribute measurement matrices are obtained, as Equations (9) and (10):
formula
(9)
formula
(10)
In the same way, for , two single-index attribute measurement matrices can be obtained after the calculation of the single-index attribute measurement, as shown in Equations (11) and (12):
formula
(11)
formula
(12)

Through the above calculation and analysis, the single-index attribute measurement function can be obtained, as shown in Figure 2. The vertical coordinates and in the figure represent the attribute measurement value, and the value range is [0, 1], which is dimensionless. The same below.

Figure 2

Single-index attribute measurement function.

Figure 2

Single-index attribute measurement function.

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Determine attribute weight

Grey relational analysis is based on sample data as a model calculation basis. The calculated grey relational degree is considered to describe the closeness of the relationship between the factors (Liu et al. 2013c). Grey relational analysis distinguishes the weight of system factors, determines the sequence relationship of factors, and divides the primary behavior of the system (Yuan et al. 2014); and this method can measure the degree of correlation between factors according to the degree of similarity or difference in the development of factors, revealing the characteristics and degree of dynamic correlation of things (Liu et al. 2013a, 2013b). At present, grey relational analysis is widely used in economics (Cui & Cai 2021), management (Fu et al. 2012) and other fields to determine attribute weights (Zhu & Lv 2020; Su 2021).

In this paper, the classic Deng's grey system correlation analysis model is used to solve the problem of attribute weights (Tan & Deng 1995). When calculating the grey relational degree, the index data needs to be processed without dimension. The benefit index adopts Equation (13), and the cost index adopts Equation (14) (Wu et al. 2021):
formula
(13)
formula
(14)
Definition 2: Suppose is the system behavior characteristic sequence, , is the correlation factor sequence, the point correlation coefficient is as in Equation (15), and the gray correlation degree of and is as Equation (16) (Tan & Deng 1995):
formula
(15)
formula
(16)
where is the resolution coefficient, which is usually 0.5 (Luo et al. 2018).
Then, Equation (17) is used to obtain the weight value of each attribute:
formula
(17)

Attribute recognition analysis

According to the single-index attribute measurement matrix calculated according to Equations (3)–(8), four comprehensive attribute measures of the risk level can be obtained accordingly, as shown in Equation (18):
formula
(18)
where is the weight of the -th evaluation index that satisfies .

The purpose of attribute recognition is to judge which evaluation level the evaluation object belongs to from the comprehensive attribute measure . On the basis of determining comprehensive attribute measurement, the confidence criterion is used for attribute recognition. The value of the confidence coefficient generally satisfies 0.6–0.7.

①When , it is considered that is the evaluation level corresponding to slight risk, is the evaluation level corresponding to low risk, , is the evaluation level corresponding to high risk, that is, . If:
formula
(19)
is satisfied, the evaluation object is considered to belong to the level.
②When , at this time, it is considered that is the evaluation level corresponding to high risk, is the evaluation level corresponding to medium risk, , is the evaluation level corresponding to slight risk, that is, . If:
formula
(20)
is satisfied, the evaluation object is considered to belong to the level.

Since there are combinations of comprehensive attribute measures calculated by attribute interval recognition, this paper adopts two methods of qualitative analysis and probabilistic analysis to evaluate and analyze the risk level.

(1) Qualitative analysis

This paper calculates the average value of the comprehensive attribute measurement corresponding to the -th evaluation level as shown in Equation (21):
formula
(21)
obtained by Equation (21) is based on the confidence criterion to discriminate the risk level of the evaluation object.

(2) Probabilistic analysis

Define vectors and . Then Equations (9) and (10) can be expressed as Equation (22):
formula
(22)
Then Equations (11) and (12) can be expressed as Equation (23):
formula
(23)
where and are the two single-index attribute measurement vectors calculated from the -th evaluation index measurement value of the evaluation object; and are the two single-index attribute measurement vectors calculated from the -th evaluation index measurement value of the evaluation object.
This research calculates the average value of , , and to get Equation (24):
formula
(24)
Thus, the two single-index attribute measurement matrices are obtained as:
formula
(25)
where .
and are arranged and combined according to the sequence to construct an -order matrix , that is, the vector composed of the single-index attribute measurement of the -th index of the evaluation object is taken as the -th row of . In this way, there are combinations of matrix in total.
formula
(26)
where means choosing one from and .
Therefore, the matrix can be expressed as Equation (27):
formula
(27)
where , and is an -dimensional column vector, which is the column k of matrix . Then the comprehensive attribute measurement calculation formula corresponding to matrix is Equation (28):
formula
(28)
where is the weight vector of the evaluation index.

Finally, for each matrix obtained by calculation, the confidence level is used to evaluate the risk level. Each matrix corresponds to a risk level , that is, there are combinations of . Then according to , take the number of 1, 2, , K levels respectively, and calculate their proportions.

Model calculation steps

Step 1: According to the evaluation index classification standard, Equations (1)–(8) are used to construct the attribute measurement function of a single index.

Step 2: According to the attribute measurement function constructed in step 1, Equations (9)–(12) are used to calculate the single-index attribute value matrices , , and .

Step 3: Use Equations (13)–(17) to solve the weight value of a single attribute.

Step 4: Use Equations (18) to obtain four comprehensive attribute matrices , , and .

Step 5: Use Equations (21) to determine the comprehensive attribute measure for qualitative analysis, and determine the drought risk level of the evaluation object according to the judgment results of Equations (19) and (20).

Step 6: Use Equations (22)–(28) to calculate the comprehensive attribute measure for probability analysis, and determine the probability value of the drought risk level of the rating object according to the judgment results of Equations (19) and (20).

Zhengzhou is located in the lower reaches of the Yellow River, with a geographical location of north latitude and east longitude . The terrain transitions from mountains and hills to plains, showing a stepped character. At the intersection of the middle and lower reaches of the Yellow River and the northeastern flank of the Funiu Mountains to the Huanghuai Plain, it faces the Yellow River to the north, Mount Song to the west, and the vast Huanghuai Plain to the southeast. The middle and low mountains in the west and southwest are composed of Songshan and Jishan, respectively. Zhengzhou has a continental monsoon climate in the north temperate zone, with frequent alternating between cold and warm groups. Spring, summer, autumn and winter are four distinct seasons. Winter is long, dry and cold with little rain and snow. The spring is dry with little rain. The average temperature is about 14, and the sunshine time is about 2,400 h. Zhengzhou's multi-year average precipitation is 4.26 cm/year (Hu et al. 2021), and total water resources are 1.124 billion cubic metres (Zhang et al. 2020a). The per capita water resource is 179 cubic metres, which means it is a severely water-deficient area. The particular topography has formed a disaster-prone environment, causing frequent natural disasters in Zhengzhou, among which drought has become the most severe natural disaster affecting Zhengzhou. This paper evaluates the drought risk of Zhengzhou based on statistical data from 2014 to 2018. The data comes from the database of the National Bureau of Statistics of China.

Based on the construction of an agricultural drought risk assessment index system, this research formulates the corresponding agricultural drought risk level. The drought assessment standards promulgated by the National Flood Control and Drought Relief Headquarters divide agricultural drought into four levels: mild drought disasters, moderate drought disasters, severe drought disasters and extreme drought disasters, which provide a reference for the classification of drought disaster indicators (Luo et al. 2020). In addition, this paper refers to the relevant literature rating standards and the suggestions of experts and scholars (Dai et al. 2020; Luo et al. 2020; Xu et al. 2021). According to the actual characteristics of Zhengzhou, this paper finally divides these evaluation indicators into four levels: level I means mild drought, level II means moderate drought, level III means severe drought, level IV means extreme drought. That is, the higher the level of the assessment value of the region, the greater the corresponding drought risk. Table 3 shows the interval value of each indicator.

Table 3

Classification standards of agricultural drought risk assessment index

IndexRisk level
Mild drought (level I)Moderate drought (level II)Severe drought (level III)Extreme drought (level IV)
annual average precipitation (600–700 500–600 400–500 300–400 
annual average temperature (14–15 15–16 16–17 17–18 
per capita arable land (1.3–1.8 0.8–1.3 0.3–0.8 0–0.3 
proportion of agricultural production/GDP (0–8 8–16 16–24 24–32 
proportion of grain output per unit area (5,000–6,000 4,000–5,000 3,000–4,000 2,000–3,000 
proportion of agricultural water consumption (15–30 30–45 45–60 60–75 
total power of agricultural machinery per unit area (18–23 13–18 8–13 3–8 
GDP per capita (7–9 5–7 3–5 1–3 
IndexRisk level
Mild drought (level I)Moderate drought (level II)Severe drought (level III)Extreme drought (level IV)
annual average precipitation (600–700 500–600 400–500 300–400 
annual average temperature (14–15 15–16 16–17 17–18 
per capita arable land (1.3–1.8 0.8–1.3 0.3–0.8 0–0.3 
proportion of agricultural production/GDP (0–8 8–16 16–24 24–32 
proportion of grain output per unit area (5,000–6,000 4,000–5,000 3,000–4,000 2,000–3,000 
proportion of agricultural water consumption (15–30 30–45 45–60 60–75 
total power of agricultural machinery per unit area (18–23 13–18 8–13 3–8 
GDP per capita (7–9 5–7 3–5 1–3 

Regional agricultural drought risk assessment

Step 1: According to the evaluation index classification standard, Equations (1)–(8) are used to construct the attribute measurement function of a single index, as shown in Figure 3.

Figure 3

Attribute measurement function of agricultural drought risk evaluation index.

Figure 3

Attribute measurement function of agricultural drought risk evaluation index.

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Based on the above analysis, this paper evaluated the agricultural drought risk in Zhengzhou. The data of Section 3.1 are collected and sorted out, and the value range of the evaluation indicators in Zhengzhou is shown in Table 4.

Table 4

Value range of evaluation indicators in Zhengzhou

IndexIndex lower limit ()Indicator upper limit ()
annual average precipitation (533.2 656.8 
annual average temperature (15.4 16.5 
per capita arable land (0.487 0.604 
proportion of agricultural production/GDP (1.914 2.862 
proportion of grain output per unit area (3,717 4,841 
proportion of agricultural water consumption (20.439 28.146 
total power of agricultural machinery per unit area (13.718 18.236 
GDP per capita (7.299 10.135 
IndexIndex lower limit ()Indicator upper limit ()
annual average precipitation (533.2 656.8 
annual average temperature (15.4 16.5 
per capita arable land (0.487 0.604 
proportion of agricultural production/GDP (1.914 2.862 
proportion of grain output per unit area (3,717 4,841 
proportion of agricultural water consumption (20.439 28.146 
total power of agricultural machinery per unit area (13.718 18.236 
GDP per capita (7.299 10.135 
Step 2: According to the attribute measurement function constructed in step 1, Equations (9)–(12) are used to solve the single-index attribute value matrices ,, and based on Table 4.
formula
formula
formula
formula

Step 3: Obtain the weight of each indicator as .

Step 4: Perform comprehensive attribute measurement analysis. Then this paper uses qualitative and probabilistic analysis to analyze the agricultural drought risk in Zhengzhou.

Step 5: The attribute measure obtained by Equations (18) and (21) is: . When evaluating the risk level, the confidence coefficient takes a value of 0.65. According to Equations (19) and (20), can be obtained, which means that the agricultural drought risk level of Zhengzhou is the level. This result indicates that Zhengzhou City is a moderately arid area.

Step 6: Matrix and matrix are obtained by Equation (24). By permuting and combining matrix and matrix , this paper can get 28 combinations, that is, there are 256 combinations of matrix in total. For each matrix obtained by calculation, confidence criteria are used to assess the level of risk.

The analysis results show that among the 256 ordered combinations of matrices and , 124 combinations are , and the corresponding risk level is the level; 32 combinations are , and the corresponding risk level is grade. Therefore, this study can consider that the probability of occurrence of grade drought risk in Zhengzhou is 79.5%, and the probability of occurrence of grade drought risk is 20.5%. This result indicates that the probability of Zhengzhou City being in a moderate drought is 79.5%, and the probability of being in a severe drought is 20.5%. Under normal weather conditions, there will be no extreme drought in Zhengzhou.

Comparative analysis

This paper used qualitative analysis to evaluate the agricultural drought risk in Zhengzhou, and it can be seen that the agricultural drought risk in Zhengzhou belongs to the level. Using the probability analysis method to evaluate the agricultural drought risk in Zhengzhou, it can be concluded that the probability of agricultural drought risk in Zhengzhou belonging to the grade is 79.5%. The probability of belonging to the grade is 20.5%. In order to further verify the effectiveness of the method in this paper, it is compared with the cloud model analysis method and the set pair analysis method. The results are shown in Table 5.

Table 5

Comparison and analysis table of drought risk assessment in Zhengzhou

Risk level (probability) method
attribute interval recognition qualitative analysis 100% 
probabilistic analysis 79.5% 20.5% 
cloud model analysis 100% 
set pair analysis 100% 
Risk level (probability) method
attribute interval recognition qualitative analysis 100% 
probabilistic analysis 79.5% 20.5% 
cloud model analysis 100% 
set pair analysis 100% 

As can be seen from Table 5, the risk of agricultural drought in Zhengzhou was evaluated using the cloud model and set pair analysis. It can be seen that the probability that the agricultural drought risk in Zhengzhou belongs to the level is 100%, which means the agricultural drought risk in Zhengzhou is that of moderate drought. The cloud model and set pair analysis of the agricultural drought risk assessment results for Zhengzhou are consistent with the qualitative analysis assessment results adopted in this paper, which further verifies the effectiveness of the model in this paper. However, when using the membership principle of the cloud model to evaluate the disaster level, once a large membership occurs, other data sizes will affect the accuracy of decision-making results, resulting in the loss of some useful information. The attribute interval recognition method proposed in this paper will not lose part of the useful information when grading. It can reflect the degree of disaster loss, and its accuracy is high. The specific performance is: probability analysis shows that 79.5% of the drought risk in Zheng-zhou may be in a moderate drought, and 20.5% may be in a severe drought.

Based on the attribute interval identification model, the agricultural drought risk in Zhengzhou is evaluated. This model can well overcome the complex, uncertain and ambiguous characteristics of the influencing factors of regional agricultural drought risk. The main conclusions are as follows: (1) Aiming at the current situation that the evaluation index system of agricultural drought risk is not perfect, this paper selected eight indicators from four aspects to evaluate regional agricultural drought risk through statistical analysis and literature collection. According to the data collection and literature review, the classification standard of the agricultural drought risk evaluation index was formed. The evaluation system was verified to be suitable for regional agricultural drought risk assessment by evaluating the agricultural drought risk in Zhengzhou. This paper further optimizes the index system of regional agricultural drought risk assessment. (2) In the existing assessment methods, fixed values are often used to assess drought risk (Xu et al. 2013; Palchaudhuri & Biswas 2016; Qu 2018). It is easy to ignore the characteristics of dynamic changes of index values in drought risk assessment. In this paper, the interval value quantitative evaluation index was used to overcome the uncertainty and fuzziness of the index, and it provides a new reference method for analyzing drought risk and other systems with uncertain data characteristics. (3) Since the existing model cannot accurately give the corresponding probability of the drought level, this paper used qualitative analysis and probabilistic analysis in the case analysis to evaluate the agricultural drought risk of Zhengzhou. The grey relational analysis method was used to determine the weight of each influencing factor, and the probability value of the agricultural drought risk level was accurately given, which shows that the model constructed in this paper is effective. In summary, this model has a specific reference value for the implementation of regional agricultural drought risk assessment and strategic protection, and also has a certain reference value for the government in regional water resources management and planning, drought prevention and mitigation.

The attribute interval recognition evaluation method provides an effective evaluation method when the data is interval value. It can provide a scientific basis for agricultural drought prevention and control, and has reference value for regional agricultural drought risk assessment. However, there are still some areas for improvement in this paper. Firstly, the threshold setting of the evaluation criteria for drought indicators is subject to a certain degree of subjectivity. Future research needs to further develop a more objective method for classifying the thresholds of drought disaster risk assessment indicators. Secondly, this paper only adopts four years of data values in the drought disaster risk assessment, and future research needs to consider more extended time series to improve the applicability of the model further. Finally, the model in this paper only uses the objective evaluation method to determine the index weights. The introduction of the combined weighting method into regional agricultural drought risk assessment deserves further study.

The authors acknowledge with gratitude Henan Province Philosophy and Social Science Planning Project (2020BJJ046), Key Scientific Research Projects of Higher Education Institutions in Henan Province (21A790013) and Postgraduate Innovative Project of North China University of Water Resources and Electric Power (No.YK2020-09, No.YK2020-29). This research would not have been possible without their financial support.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Data cannot be made publicly available; readers should contact the corresponding author for details.

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