Vulnerability Assessment of Soil and Water Loss in Loess Plateau and Its Impact on Farmers’ Soil and Water Conservation Adaptive Behavior

Abstract

Analyzing vulnerability and adaptation to soil and water loss is an important part of the study on the human–environment relationship in the Loess Plateau. It has also provided a new perspective for studying the farmers’ adoption behavior of soil and water conservation technology in the soil erosion area of the Loess Plateau. Based on the Turner vulnerability framework, this paper constructs a household-scale index system of soil and water loss vulnerability in the Loess Plateau and evaluates the soil and water loss vulnerability in the Loess Plateau using the field survey data of the Loess Plateau applied entropy method. Finally, we use the binary logistic model to estimate the impact mechanism of farmers’ soil erosion vulnerability on farmers’ adoption behavior of soil and water conservation technology. The main conclusions are as follows: (1) In the total sample, susceptibility > exposure > adaptability, whereas in the Shaanxi and Gansu subsample, susceptibility > adaptability > exposure. The Ningxia subsample was similar to the total sample. For each index, Ningxia > Gansu > Shaanxi; (2) The exposure and susceptibility of soil and water loss have a positive impact on farmers’ adoption behavior of soil and water conservation technology, and natural capital has a positive impact on farmers’ adoption behavior of soil and water conservation technology. Physical capital has a positive impact on farmers’ adoption behavior of biological measures. Financial capital has a negative impact on farmers’ adoption behavior of biological measures and farming measures. Social capital has a positive impact on farmers’ adoption behavior of engineering measures and biological measures; (3) Overall, the marginal effect of the adoption behavior of farmers’ soil and water conservation techniques, adaptability > susceptibility > exposure. Therefore, it is necessary to strengthen the monitoring of soil and water loss, encourage the government and farmers to respond in time, and reduce the losses caused by soil erosion. Enriching the capital endowment of farmers, breaking through the endowment restriction of farmers’ adoption of soil and water conservation technology.

1. Introduction

Agriculture is highly dependent on resource conditions and affected by the natural environment [1]. Natural disasters can cause huge losses to agriculture [2], which makes farmers face more uncertainty, instability, and more exogenous production risks in agricultural production [3]. Natural disasters such as precipitation, rainstorm, drought, collapse, landslide, mountain torrent, debris flow, wind and sand, and soil erosion occur from time to time in the Loess Plateau [4], making it one of the areas with the most serious soil erosion and the most fragile ecological environment in the world. Soil erosion of the Loess Plateau, southwest rocky desertification, and desertification in the northwestern part are the three major ecological disasters in China, which seriously restrict the sustainable development of industry and agriculture. Serious soil erosion not only causes the reduction of land productivity and threatens national food security [5], but also causes the deterioration of the ecological environment, threatens national ecological security, and affects the sustainable development of a coupled human–environment system [6]. In response to the increasingly severe agricultural ecological environment problems, China Central Document No. 1 has repeatedly proposed “carrying out land greening operations to promote desertification, rocky desertification and soil erosion comprehensive control”, vigorously promoting the construction of an ecological civilization. Therefore, solving the problem of soil erosion in the Loess Plateau is of great significance for improving the ecological and environmental problems in China.

Turner proposed a vulnerability analysis framework of the coupled human–environment systems [7]. It contains exposure, susceptibility and adaptability three aspects under the background of human and environmental conditions, and analyzes the interaction between the elements. The human–environment conditions of the system determine its sensitivity to any set of exposures. These conditions include both social and biophysical capital that influences the existing coping mechanisms, which take effect as the impacts of the exposure are experienced, as well as those coping mechanisms adjusted or created because of the experience [7]. The vulnerability theory and evaluation centered on the coupled human–environment systems have attracted more and more attention from the current academic circles [8]. At present, this framework has been widely recognized by researchers, it can provide scientific basis and guidance for sustainable development. Academic circles have applied the Turner vulnerability framework to different fields and evaluated it from the aspects of poverty vulnerability [9], social vulnerability [10], climate vulnerability [11], drought vulnerability [12,13], flood vulnerability [14], urban high temperature heat wave vulnerability [15], natural disasters vulnerability and so on. Poverty vulnerability refers to the possibility of been trapped in poverty [9]. Social vulnerability focuses on the exposure sensitivity and adaptability of groups or individuals under the change of climate and social economic system [10]. For climate vulnerability, the key words of the fourth IPCC assessment report in 2007 were exposure sensitivity and adaptability. The definition of vulnerability adds to the exposed content [11]. Many scholars have studied disaster vulnerability. For example, Wilhelmi et al. [12] set up a framework for agricultural drought vulnerability. Shuai Hong et al. [14] quantitatively analyzed the flood disasters vulnerability of peasant households. Xie Pan et al. [15] evaluated the vulnerability of high temperature and heat wave disasters in cities. The results of vulnerability assessment are scientific, pertinent and applicable. Farmers are the main subjects of economic activity in the human–environment coupling system and the most direct unit of natural resources utilization [16]. They are the main bearers and the most direct perceivers of the consequences of ecological deterioration, such as soil erosion [17]. Therefore, it is necessary to evaluate the vulnerability of soil and water loss in the Loess Plateau at the scale of farmers. Turner’s framework of vulnerability “exposure–susceptibility–adaptability” provides an analytical framework to analyze soil and water loss vulnerability. According to the survey data of farmers, from the three dimensions of exposure, susceptibility and adaptability, this paper selects explanatory indicators to build an index system for soil and water loss vulnerability, and uses the entropy method to calculate the vulnerability index, exposure, susceptibility and adaptability of farmers in the Loess Plateau. The vulnerability of soil erosion is a state in which natural, social and economic factors in human–environment systems are disturbed by soil erosion, which affects the ability of human–environment systems to cope with soil erosion. It is important to understand when and why human–environment systems are vulnerable to soil erosion, and what can be done to reduce the vulnerability. Research and evaluation on the vulnerability of soil and water loss has gradually become a prerequisite for formulating policies to mitigate and prevent soil erosion. At the same time, farmers are the main body of soil and water loss control and rural ecological construction [18]. Farmers adopt a series of adaptive measures to reduce the adverse effects of soil and water loss on agricultural output. Risk-averse farmers take adaptive measures to reduce potential production losses and risks of soil erosion [19]. Practice shows that soil and water conservation measures (engineering measures, biological measures and tillage measures, etc.) have the functions of preventing soil erosion, improving land productivity, reducing poverty and realizing agricultural transformation [20], and can reduce the production risk caused by soil erosion. To a certain extent, the management of soil erosion depends on farmers’ adoption of soil and water conservation technologies. Relevant scholars have studied the influencing factors of farmers’ adoption behavior of soil and water conservation technology. A large number of studies have shown that individual characteristics (gender, age, education level, etc.), family management characteristics (income level, scale of agricultural operation, part-time behavior, labor force status), regional economic development level, and policy factors (agricultural technology training, extension system, government support, etc.) are the basic factors for farmers to adopt soil and water conservation measures [21,22,23]. However, there is a lack of empirical research on the impact of soil erosion vulnerability on farmers’ adoption behavior of soil and water conservation technology from the perspective of human–environment coupling system-centric vulnerability theory.

This paper constructs a household-scale index system of soil and water loss vulnerability in the Loess Plateau based on the Turner vulnerability framework. As the matrix of soil erosion vulnerability is usually large and complicated, the evaluation process usually involves the procedures of colleting criteria data, inputting missing data, normalizing actual data, weighting criteria and aggregating normalized data and the associated weights [24]. Even though all the steps are important for the quality of vulnerability evaluation, the weight step seem to have the greatest impact [25]. Index weighting is the key link to evaluate the vulnerability of soil erosion at the scale of peasant households. There are two main methods to determining the weight of indicators: subjective evaluation and objective evaluation. Subjective evaluation mainly focuses on the Analytic Hierarchy Process and the Delphi method. Objective evaluation methods mainly use the correlation coefficient method, the entropy weight method, and the factor analysis method [26,27]. In general, the subjective evaluation method determines the importance of each index according to subjective judgment, which has the advantages of a clear concept, simplicity, and feasibility; however, it is more easily interfered with by subjective factors, thus can affect the scientific rigor of the research results. According to the standardized data of each index, the objective evaluation method automatically entrust weight according to certain rules. Its advantages are rigorous calculation and objective evaluation. Entropy [28] is a widely used method. Compared with other methods, using the entropy method to determine weights can eliminate subjective interference and make the evaluation results more scientific and reasonable. The concept of entropy originated from the thermodynamics concept in physics, mainly reflecting the degree of chaos of the system, which has been widely used in the field of sustainable development evaluation and vulnerability assessment. Zinatizadeh et al. [29] selected 44 explanatory indicators to build an index system for the evaluation of sustainability of urban areas from three aspects, including social and welfare progress, economic growth, and environmental protection, and uses the entropy method to obtain the criteria weights, and then to calculate the urban sustainability in Kermanshah. The research results show that the entropy method was an appropriate approach to study the sustainable development of Kermanshah city, Kermanshah city is in a critical condition, and is far from sustainable development. Weiwei Li et al. [30] applied the entropy methods to evaluate the sustainability of the 34 prefecture-level and cities in Northeastern China, the evaluation results indicated that the progress of cities sustainable development in Northeastern China was slow from the year 2012 to 2016. Munier [31] used the entropy method to weight the selected sustainability indicators used to measure the state of a city. Yan Tingwu et al. [32] evaluated the natural disaster vulnerability and market risk vulnerability of farmers in poor areas of China through the entropy method; the results showed that farmers’ natural disaster vulnerability is higher than the market risk vulnerability, showing that natural disasters are more likely to cause losses than market risks for farmers. The entropy weight method is a mathematical method for calculating a comprehensive index based on the comprehensive consideration of the amount of information provided by various factors. As an objective and comprehensive weighting method, the entropy weight method mainly determines the weight according to the amount of information transmitted by each indicator to the decision maker. Soil erosion vulnerability is a comprehensive index based on the comprehensive consideration of the amount of information provided by various factors. Therefore, in order to avoid the bias caused by subjective factors, this paper uses the entropy method to empower the indicators of farmers’ soil erosion vulnerability.

In view of this, firstly, based on the Turner vulnerability framework, this paper constructs a household-scale index system of soil and water loss vulnerability in the Loess Plateau, then, we use entropy method to evaluate soil and water loss vulnerability in the Loess Plateau using the field survey data of the Loess Plateau. Finally, we use the binary logistic model to evaluate the impact mechanism of farmers’ soil erosion vulnerability on farmers’ adoption behavior of soil and water conservation technology. These are also the innovations of this article.

2. Theoretical Analysis Framework

Turner proposed a vulnerability analysis framework for human–environment coupling systems [7]. It includes three aspects: exposure, susceptibility, and adaptability in the context of human and environmental conditions and their interaction. It also analyzes the interaction between elements. Among them, human–environmental conditions determine exposure and susceptibility and affect the response mechanism of the system [7,33].

Essentially, the vulnerability of the coupled human–environment system belongs to ecological vulnerability, which determines that it is mainly characterized by ecological problems and natural disasters [34]. For the Loess plateau region, where soil erosion is serious, its vulnerability is characterized by soil erosion. As for the stress and impact of natural disasters on the human–environment system, most of them are studied at a macro scale, but lack research from a micro perspective. As the main economic activity subject and the most direct unit of natural resource utilization in the system, farmers have become the most direct bearers of soil erosion disturbance. The impact of soil erosion on farmers’ agricultural production is very serious [13]. Therefore, it is necessary to evaluate the vulnerability of soil and water loss in the Loess Plateau from the scale of farmers. Therefore, based on the framework of vulnerability analysis of Turner’s human–environment coupling system, this paper chooses farmers as the object of investigation and analysis in the basic unit of rural human–environment coupling systems, takes soil erosion as a disturbance factor, and is based on previous research and field research. Exposure, susceptibility, and adaptability are chosen as the three dimensions to characterize rural households’ soil and water loss vulnerability [13]. Drawing on related research, this paper defines the vulnerability of soil erosion as the natural, social, and economic factors in the human–environment system that are disturbed by soil erosion. It makes agricultural production easy and sensitive to the threat of soil erosion and causes losses, which affects the human–environment system’s ability to cope with soil erosion [35].

Exposure reflects the degree of a human–land system suffering disasters or dangers, which determines the potential loss of the system under the impact of disasters, and mainly depends on the probability of human and regional exposure to dangerous events. For soil erosion, exposure is the pressure of soil erosion on farmers. According to its characteristics, the frequency of soil erosion occurrences is chosen to describe the exposed characteristics. Susceptibility is related to the critical condition of the system being destroyed [9], which reflects the susceptibility of the system to external disturbance. For soil erosion, susceptibility is the susceptibility of the system to soil erosion disturbance [36]. This paper chooses the degree of loss of agricultural production and operation caused by soil and water loss to farmers to measure susceptibility. Adaptability refers to the ability of the system to deal with disaster events. As well as the recovery ability from disaster losses, it reflects the degree of avoidable damage of the system and determines the actual loss of the system under the influence of disaster events. As far as soil erosion is concerned, adaptability is the farmer’s ability to accommodate and recover from soil erosion disturbances. It is represented by physical capital, natural capital, financial capital, social capital, and human capital at the household scale [13]. Among them, physical capital reflects housing type, tool type, and agricultural machinery quantity; natural capital reflects cultivated land area and forest land area; financial capital reflects household total income and loans; social capital reflects village cadres, number of contacts, trust, and mutual assistance; whereas human capital reflects education, part-time employment, and the size of the labor force [37,38].

The vulnerability index of farmers is composed of exposure index, susceptibility index and adaptability index, but there are different calculation formulas for vulnerability calculation. The vulnerability calculation formula vulnerability = exposure + susceptibility − adaptability adopted by IPCC is widely quoted [39]. The values of exposure, susceptibility and adaptability are calculated by entropy method. The vulnerability (v) is calculated by using the formula vulnerability = exposure + susceptibility − adaptability. The above formula shows: the higher the exposure, the higher the vulnerability; the higher the susceptibility, the higher the vulnerability; and the lower the adaptability, the higher the vulnerability. Exposure and susceptibility can increase the vulnerability of the system, and the increase of adaptability can reduce the vulnerability of the system.

Accordingly, the index system of vulnerability to soil and water loss based on the household scale is set forth in

Table 1. Indicator assessment system of rural household soil and water loss vulnerability.

	Dimension	Index	Effect
Indicator system of rural household soil and water loss vulnerability	Exposure (e)	Is there frequent soil erosion in your area?	+
	Susceptibility (s)	The risk of loss to your agricultural production and operation caused by soil and water loss	+
	Adaptability (a): human capital (hc)	Education, part-time employment, the number of labor force	−
	physical capital (pc)	Housing type, tool type, agricultural machinery quantity	−
	natural capital (nc)	Cultivated land area, forest land area	−
	financial capital (fc)	Household total income, loan	−
	social capital (sc)	Village cadres, number of contacts, trust, mutual assistance	−

Note: (+) in the table indicates a positive indicator and (−) indicates a negative indicator.

.

3. Data Sources, Variable Selection, and Model Methods

3.1. Data Sources

Based on the above theoretical analysis framework, the data used in this study mainly come from the large-scale field survey conducted by the research group in the Loess Plateau from October to November 2016. Shaanxi, Gansu, and Ningxia were selected as the research areas. The sample selection is representative. There are three reasons. First, in the national soil and water conservation plan (2015–2030) promulgated by the State Council in 2015, China has 23 key state-level soil and water loss prevention zones and 17 key treatment areas, The Loess Plateau region has 7 key state-level soil and water loss prevention zones and 5 key treatment areas [40]. The key soil prevention zones and key treatment areas are mostly distributed in the Shaanxi and Gansu provinces; therefore, evaluation of soil and water vulnerability in the area has great practical significance. Second, in 1998, the construction of a soil and water conservation demonstration zone in the city of Xifeng in the Gansu province and Suide County in the Shaanxi province played a typical exemplary role in the area’s governance and development. Since the implementation of the world bank loan project for soil and water conservation in 1994, a systematic and complete scientific work system has been established in the aspects of project management, investment operation, monitoring and evaluation, and science and technology popularization. It has played a good role in guiding the management of soil and water conservation and ecological environment construction in the Yellow River basin. The government provided preferential policies, such as preferential technical services and material supply, and further mobilized the enthusiasm of the masses and the community to invest in soil and water conservation. Three provinces (regions) have implemented a project of returning farmland to forests and compensated farmers who participate in afforestation. Third, the research area is not only the main area of agricultural development, but also a serious area of soil erosion. Soil erosion has a serious impact on farmers’ agricultural production and even affects food security. Farmers adopt certain soil and water conservation technologies to control soil erosion in the specific agricultural practice. The study of farmers’ soil and water conservation behavior is of great practical significance.

This paper adopts cluster, stratified and random sampling methods to select the sample area, selecting Mizhi County, the Yuyang district and Suide County in the city of Yulin in the Shaanxi Province, the Xifeng district and Huan County in the city of Qingyang in the Gansu Province, and the Yuanzhou district, Pengyang county, and Xiji County in the city of Guyuan in Ningxia as the research areas. Through the stratified random sampling method, the investigation group selected 1–5 towns in each of the above counties, randomly selected 2–5 villages in each town, and in each village randomly selected 15–20 farmers. The survey sample ultimately included 8 counties, 30 towns, 72 villages, and 1200 farmers in the 3 provinces (districts) of Shaanxi, Gansu, and Ningxia. The form of survey was one-to-one interviews with farmers. We obtained 1200 household questionnaires, and we deleted questionnaires with missing important indicators. Finally, 1152 valid questionnaires were obtained, and the effective rate of the questionnaire was 96%. The survey involved the capital endowment of farmers, the occurrence of natural disasters, and the adoption of water and soil conservation technologies.

Table 2. The basic situation of the sample farmers.

Variable	Classified	House-Hold	Ratio /%	Variable	Classified	House-Hold	Ratio /%
Gender	Men	1114	96.7	Education level	Illiteracy	250	21.70
	Female	38	3.3		Primary school	267	23.18
Age	Under 30 years old	21	1.83		Junior middle school	519	45.05
	31–40 years old	128	11.11		High school	109	9.46
	41–50 years old	334	28.99		College graduate or above	7	0.61
	50 years old and above	334	58.07	Agricultural income ratio	25% and below	600	52.08
Labor quantity	1 and below	94	10.5		25–49%	214	18.58
	2	451	39.15		50–74%	128	11.11
	3	201	17.45		75% and above	210	18.23
	4	256	22.22	Off-farm Employment	Yes	489	42.45
	5 and above	150	13.02		No	663	57.55

shows the basic information of sample farmers. A total of 96.7% of the households interviewed were male. Because men have a certain final decision-making power in the family, men’s wishes can represent the final decision-making intention of the family. A total of 72.74% of the people in rural households were 41–60 years old, while 58.07% of the respondents were over 51 years old, so the trend of aging in rural migrant workers was obvious. A total of 66.55% of respondents were primary schools graduates and below, while 89.83% of them were junior middle school graduates and below, and the education level was generally low. A total of 42.45% of the farmers interviewed were engaged in concurrent production, and the level of household farming was relatively high. The proportion of household labor force in 2–4 households was 76.48%, at a medium-scale level.

The proportion of agricultural income was relatively low, and 70.66% of rural households’ income mainly came from non-agricultural income.

Table 3. Distribution of sample farmers and farmers’ adoption behavior of soil and water conservation technology.

Province	County (District)	Frequency and Percent (%)	Engineering Measures Frequency and Percent (%)	Biological Measures Frequency and Percent (%)	Tillage Measures Frequency and Percent (%)
Shaanxi	Mizhi County	228 (19.79)	82 (35.96)	172 (75.77)	4 (1.75)
	Yuyang District	75 (6.51)	15 (20)	60 (80)	0 (0)
	Suide County	80 (6.94)	17 (21.25)	58 (72.5)	0 (0)
Gansu	Xifeng district	185 (16.06)	88 (47.57)	37 (20)	26 (14.05)
	Huan County	200 (17.36)	178 (89)	81 (40.5)	65 (32.5)
Ningxia	Yuanzhou District	151 (13.11)	140 (92.72)	78 (51.66)	50 (33.11)
	Pengyang	200 (16.06)	185 (92.5)	119 (59.5)	80 (40)
	Xiji County	33 (2.86)	28 (84.85)	18 (54.55)	16 (48.48)
Total	-	1152	733 (63.63)	623 (54.08)	241 (20.92)

shows the specific distribution of sample farmers and the technical application of soil and water conservation for farmers in counties (districts). According to the survey, 63.63% of the sample farmers had adopted engineering soil and water conservation technology, 54.08% of the sample farmers had adopted biological soil and water conservation technology, for example, planting grass and afforestation, and 20.92% had adopted tillage technology.

3.2. Variable Selection

The dependent variable of this study is the adoption of soil and water conservation technology. Soil and water conservation technology is a technical package consisting of several sub technologies, including engineering measures, biological measures, and tillage measures. We asked farmers whether they had adopted engineering measures, biological measures, and tillage measures. The independent variable of this paper is the three dimensions of vulnerability of soil and water loss: Exposure, susceptibility and adaptability.

Table 4. Explanation and statistical description of sample variables.

Variable	Variable Specification	MEAN	SD
Dependent variable
Engineering measures	Whether a farmer has adopted or not? Yes = 1, no = 0	0.64	0.48
Biological measures	Whether a farmer has adopted or not? Yes = 1, no = 0	0.54	0.49
Tillage measures	Whether a farmer has adopted or not? Yes = 1, no = 0	0.21	0.41
Exposure (e)	Is there frequent soil erosion in your area? 1 = almost no, 2 = very little, 3 = general, 4 = regular, 5 = frequent	2.57	1.12
Susceptibility (s)	The risk of loss to your agricultural production and operation caused by the soil and water loss: Very low = 1, Lower = 2, uncertainty = 3, higher = 4, very high = 5. The higher the value, the higher the sensitivity to the risk of loss to the natural environment	3.51	1.56
Adaptability (a)
Human capital (hc)
Education	Illiteracy = 1, Primary school = 2, Junior middle school = 3, High school = 4, College graduate or above = 5	2.44	0.95
Off-farm Employment	Whether to engage in off-farm work or not? Yes = 1, no = 0	0.42	0.49
Labor quantity	The labor number of your family	3	1.48
Physical capital (pc)
Housing type	1 = concrete, 2 = brick, 3 = brick wood, 4 = civil, 5 = stone kiln	2.84	1.37
Agricultural machinery quantity	Number of household farm machinery (unit)	0.44	0.55
Tool type	Number of family transport vehicles (unit)	0.97	0.73
Natural capital (nc)
Cultivated land area	Your cultivated and land area (mu)	11	10.95
Forest land area	Your forest land area (mu)	3.47	6.39
Financial capital (fc)
Household total income	Total household income < 1 million = 1, 1–3 million = 2, 3–5 million = 3, 5–10 million = 4, >10 million = 5	2.54	1.16
Loan	Whether to borrow or not: Yes = 1, no = 0	0.32	0.48
Social capital (sc)
Village cadres	Yes = 1, no = 0	0.18	0.38
Number of contacts	0–20 = 1, 20–50 = 2, 50–100 = 3, >100 = 4	2.03	0.99
Mutual trust	The degree of mutual trust between people: No = 1, little = 2, general = 3, a lot = 4, much=5	3.72	0.99
Mutual assistance	Do you think people around you help each other? No = 1, little = 2, general = 3, a lot = 4, much=5	3.84	0.87

shows the definition and assignment of variables and descriptive statistical analysis.

3.3. Model Selection

3.3.1. Entropy Method

The entropy method calculates the information entropy of the index and determines the weight of the index according to the influence of the relative change degree of the index on the system. According to information theory, entropy is a measurement of the degree of disorder in a system, and information is a measurement of ordering. In the index data matrix X, the greater the degree of discretization of the data, the smaller the information entropy, the greater the amount of information it provides, and the greater the impact of the index has on the comprehensive evaluation; hence, its weight should be greater, and vice versa. The main steps are as follows:

(1) Constructing the basic matrix, $x=\left(x_{ij}\right)$, $x_{ij}$ represents the observation value of the jth index of the ith farmer household. i = 1, …, m. There are 1152 sample farmer households in this paper, so the maximum value of m is 1152, j = 1, …, n. There are 16 indicators in this study (Table 1). The maximum value of n is 16.

Normalization of data: when the larger the index value the more favorable the system, the calculation method of a positive index value is adopted: $x^{\prime }{}_{ij}=\frac{x_{ij}-\min \left\{x_{ij}\right\}}{\max \left\{x_{ij}\right\}-\min \left\{x_{ij}\right\}}$; when the smaller the index value the more favorable the system, the calculation method of a negative index value is adopted: $x^{\prime }{}_{ij}=\frac{\max \left\{x_{ij}\right\}-x_{ij}}{\max \left\{x_{ij}\right\}-\min \left\{x_{ij}\right\}}$. $\min \left\{x_{ij}\right\}$, $\max \left\{x_{ij}\right\}$ are the maximum and minimum value of the basic matrix $X=(x_{ij})$.

(2) Calculate the weight of the item j of the ith farmer household. Using the above matrix to generate a new matrix, the corresponding relationship between the elements in the matrix and the above matrix is as follows:

$$y_{ij}=\frac{x^{\prime }{}_{ij}}{{\displaystyle \sum _{i=1}^m{x}^{\prime }{}_{ij}}}$$

(1)

(3) Calculate the information entropy $e_j$ of the jth index:

$$e_j=-k{\displaystyle \sum _{i=1}^m{y}_{ij}\ln y_{ij}}$$

(2)

In the formula, $k>0$, $\ln$ is the natural logarithm, $e_j\ge 0$. The constant $k$ in the formula is related to the sample $m$, $k=1/\ln m$, In this study, m = 1152, so $k$ = 1/ln1152, $0\le e_j\le 1$.

(4) Calculate the information entropy redundancy $g_j$:

$$g_j=1-e_j$$

(3)

(5) Calculate the weight of each index:

$$W_j=\frac{g_j}{{\displaystyle \sum _{j=1}^m{g}_j}},j=1,2\dots m$$

(4)

(6) Compute the comprehensive evaluation value of each index:

$$f_i={\displaystyle \sum _{j=1}^n{w}_j{x}_{ij}}$$

(5)

In the formula, $f_i$ is the vulnerability evaluation value of the ith peasant household.

Based on 1152 household survey data collected in the Loess Plateau, the data of 16 indicators in Table 1 are substituted into Formulas (1)–(5) to calculate the exposures (e), susceptibility (s) and adaptability (a) evaluation values of total samples and subsamples.

3.3.2. Binary Logistic Regression Model

Logistic regression analysis is suitable for regression analysis with dependent variables as two classified variables, which is an ideal model for analyzing individual decision-making behavior. The variables explored in this study are whether farmers adopt soil and water conservation technology or not. The results include adoption and non-adoption, so this paper chose a binary logistic regression model to quantitatively analyze exposures (e), susceptibility (s), physical capital (pc), natural capital (nc), financial capital (fc), social capital (sc), and human capital (hc) influencing farmers’ adoption behavior of soil and water conservation technology. Specific models are as follows:

$$p=\frac{\exp (z)}{1+\exp (z)}$$

(6)

In Formula (6), $z$ represents the linear combination of explanatory variable (e, s, hc, pc, nc, fc, sc); e, exposure; s, susceptibility; hc, human capital; pc, physical capital; nc, natural capital; fc, financial capital; sc, social capital. The exposure, susceptibility, physical capital, natural capital, financial capital, social capital, and human capital in Table 1 are calculated by the entropy method. The expression of $z$ is:

$$z={\beta }_0+{\beta }_{1}e+{\beta }_{2}s+{\beta }_{3}hc+{\beta }_{4}pc+{\beta }_{5}nc+{\beta }_{6}fc+{\beta }_{7}sc$$

(7)

In Formula (7), ${\beta }_0$ is a constant term, ${\beta }_1-{\beta }_7$ respectively represent the regression coefficients of explanatory variables (e, s, hc, pc, nc, fc, sc).

In the process of statistical analysis of data, the probability of farmers’ soil and water conservation technology adoption behavior is set as $p(y=1)$, 0 ≤ $p$ ≤ 1. The probability of farmers not adopting technology is 1 − $p(y=1)$. In logistic regression analysis, Logit transform for P is usually used:

$$\mathrm{logitp}=\ln (\frac{p}{1-p})={\beta }_0+{\beta }_{1}e+{\beta }_{2}s+{\beta }_{3}hc+{\beta }_{4}pc+{\beta }_{5}nc+{\beta }_{6}fc+{\beta }_{7}sc$$

(8)

Formula (8) is the logistic regression equation to be estimated the farmers’ soil and water conservation technology adoption behavior model.

The coefficients of the binary logistic regression model were estimated by maximum likelihood methods using Stata 14.0.

4. Results and Analysis

4.1. Descriptive Statistical Analysis

Exposure.

Table 5. Soil and water loss exposure in different studied area (Frequency).

Province	Almost No	Very Little	General	Regular	Frequent
Shaanxi	128	131	53	46	25
Gansu	55	177	85	50	18
Ningxia	39	80	62	144	51
Total	222	388	200	240	94

shows soil and water loss exposure in different studied area. A total of 80.73% of farmers in the total sample indicated that soil erosion had occurred in the area. A total of 28.99% of the peasant households indicated that soil erosion often occurred in the area. A total of 66.58% of the peasant households in the Shaanxi province indicated that there had been soil erosion, while 85.71% of the peasant households in the Gansu province indicated that there had been soil erosion. A total of 89.84% of the farmers in Ningxia indicated that there had been soil erosion.

Table 6. Soil and water loss exposure and farmers’ soil and water conservation technology adoption (Frequency and Percent (%)).

Exposure	Engineering Measures		Biological Measures		Tillage Measures
	Not adopted	Adopted	Not adopted	Adopted	Not adopted	Adopted
Almost no	152 (39.18)	236 (60.82)	190 (48.97)	198 (51.03)	320 (82.47)	68 (17.53)
Very little	64 (32)	136 (68)	99 (49.5)	101 (50.5)	155 (77.5)	45 (22.5)
General	47 (19.58)	193 (80.42)	113 (47.08)	127 (52.92)	170 (70.83)	70 (29.17)
Regular	12 (22.22)	42 (77.78)	14 (25.93)	40 (74.07)	33 (61.11)	21 (38.89)
Frequent	6 (12.5)	42 (87.5)	23 (47.92)	25 (52.08)	26 (54.17)	22 (45.83)

shows the relationship between exposure and farmers’ adoption behavior of soil and water conservation technology. Among the 930 farmers who suffered from soil erosion, 69.78% of them adopted engineering measures, 52.80% of them adopted biological measures, and 24.30% of them adopted farming measures. For engineering measures and biological measures, regardless of the frequency of soil erosion the proportion adopting measures is larger than the proportion not adopting measures.

When soil erosion occurs frequently, the proportion of farmers adopting engineering measures is more than 77.78%. The proportion of farmers adopting biological measures is more than 52.08%. Overall, with the increasing frequency of soil erosion, the proportion of farmers adopting soil and water conservation technology showed an increasing trend.

Susceptibility.

Table 7. Susceptibility of soil erosion in sample area (Frequency and Percent (%)).

Province	1 Few	2 Lower	3 Uncertainty	4 Higher	5 Very High
Shaanxi	148	37	27	109	62
Gansu	56	21	30	83	195
Ningxia	44	16	46	99	179
Total	248 (21.53)	74 (6.42)	103 (8.94)	291 (25.26)	436 (37.85)

shows susceptibility of soil erosion in sample area. A total of 63.11% of farmers in the total sample thought soil erosion is higher and very high. A total of 44.65% of farmers in Shaanxi believed that soil erosion is higher and very high. A total of 72.21% of farmers in Gansu believed that soil erosion is higher and very high. A total of 72.39% of farmers in Ningxia thought that soil erosion is higher and very high.

Table 8. Soil and water loss susceptibility and farmers’ soil and water conservation technology adoption (Frequency and Percent (%)).

	Engineering Measures		Biological Measures		Tillage Measures
Susceptibility	Not adopted	Adopted	Not adopted	Adopted	Not adopted	Adopted
1	160 (64.52)	88 (35.48)	95 (38.31)	153 (61.69)	234 (94.35)	14 (5.65)
2	40 (54.05)	34 (45.95)	21 (28.38)	53 (71.62)	65 (87.84)	9 (12.16)
3	32 (31.07)	71 (68.93)	49 (47.57)	54 (52.43)	76 (73.79)	27 (26.21)
4	91 (31.27)	200 (68.73)	156 (53.61)	135 (46.39)	215 (73.88)	76 (26.12)
5	96 (22.02)	340 (77.98)	208 (47.71)	228 (52.29)	321 (73.62)	115 (26.38)

shows the relationship between susceptibility and farmers’ adoption behavior of soil and water conservation technology. Susceptibility and farmers’ adoption behavior of soil and water conservation technology. Among the farmers who believed that soil erosion is serious, 68.73% adopted engineering measures, 46.39% adopted biological measures, and 26.12% adopted farming measures. Among the farmers who believed that soil erosion is very serious, 77.98% of the farmers adopted engineering measures, 52.29% adopted biological measures, and 26.38% adopted farming measures. Overall, the more serious soil erosion is, the higher the proportion of farmers adopting soil and water conservation technology.

4.2. Farmers’ Vulnerability Assessment of Soil and Water Loss

To understand the exposures (e), susceptibility (s), adaptability (a) and vulnerability (v), following the steps of the entropy method, the survey data from 1152 households for 16 indicators in Table 1 were substituted into Formula (1) to Formula (5) to calculate the exposures (e), susceptibility (s) and adaptability (a) evaluation value of the total samples and subsamples, and the vulnerability (v) was calculated using the formula v = e + s − a. The results of the vulnerability assessment of soil and water loss based on the household scale are shown in

Table 9. Assessment results of soil and water loss vulnerability.

	Total Sample	Shaanxi Province	Gansu Province	Ningxia Province
Exposure (e)	0.54	0.36	0.4	0.85
Susceptibility (s)	1.05	0.82	1.16	1.18
Adaptability (a)	0.52	0.49	0.53	0.54
Vulnerability (v)	1.07	0.69	1.04	1.48

. To facilitate a comparative analysis, the subsample evaluation results of the three locations in Shaanxi, Gansu, and Ningxia are also listed. In the total sample, susceptibility (1.05) > exposure (0.54) > adaptability (0.52), whereas in Shaanxi, susceptibility (0.82) > adaptability (0.49) > exposure (0.36), and in the Gansu subsamples, susceptibility (1.16) > adaptability (0.53) > exposure (0.4). In the Ningxia subsample, susceptibility (1.18) > exposure (0.85) > adaptability (0.54). It can be seen that susceptibility is the greatest in the total sample and subsample, indicating that soil erosion is very serious in the Loess Plateau, which seriously affects agricultural output and causes loss of agricultural income. Regarding vulnerability, Ningxia (1.48) > Gansu (1.04) > Shaanxi (0.69); regarding exposure, Ningxia (0.85) > Gansu (0.4) > Shaanxi (0.36), as shown in Table 5. A total of 66.58% of the peasant households in the Shaanxi province indicated that there had been soil erosion, while 85.71% of the peasant households in the Gansu province indicated that there had been soil erosion, and a total of 89.84% of the farmers in Ningxia indicated that there had been soil erosion. Regarding susceptibility, Ningxia (1.18) > Gansu (1.16) > Shaanxi (0.82), as shown in Table 6. A total of 44.65% of farmers in Shaanxi believed that soil erosion was higher and very high, a total of 72.21% of farmers in Gansu believed that soil erosion is higher and very high, a total of 72.39% of farmers in Ningxia thought that soil erosion is higher and very high. The ecological environment in Ningxia is relatively fragile. Drought and wind, sparse vegetation, active wind erosion activities, low environmental carrying capacity, weak self-repairing ability and natural purification function give the ecological environment in Ningxia obvious vulnerability and variability, and low ecological stability. Regarding adaptability, Ningxia (0.54) > Gansu (0.53) > Shaanxi (0.49). This shows that the values are different.

4.3. Econometric Model Test on Vulnerability of Soil and Water Loss Impacts Farmers’ Adoption Behavior of Soil and Water Conservation

SPSS (version 19.0) (IBM SPSS Statistics, Multiple collinearity, DU Qiang, China) was used to verify the multicollinearity of the independent variable. The variance expansion factor (VIF) <2 satisfies the independence principle, and there is no serious collinearity problem.

Following the steps of the entropy method, the 1152 household survey data of 16 indicators in Table 1 were substituted into Formula (1) to Formula (5) to calculate the exposures (e), susceptibility (s), physical capital (pc), natural capital (nc), financial capital (fc), social capital (sc), and human capital (hc) evaluation value of the total samples. In the Stata 14.0 software, the binary logistic regression model was used to test the effects of exposures (e), susceptibility (s), physical capital (pc), natural capital (nc), financial capital (fc), social capital (sc), and human capital (hc) on farmers’ adoption of engineering measures, biological measures, and tillage measures. The estimated results of Formulas (6)–(8) are shown in

Table 10. Logistic regression results of farmers’ adoption behavior of soil and water conservation technology.

	Response Variables
Explanatory Variables	Engineering Measures		Biological Measures		Tillage Measures
	Coefficient	Standard Errors	Coefficient	Standard Errors	Coefficient	Standard Errors
Exposure (e)	0.22 ***	0.06	0.05 *	0.03	0.18 ***	0.04
Susceptibility (s)	0.32 ***	0.05	0.19 ***	0.04	0.23 ***	0.06
Adaptability (a)
human capital (hc)	0.19	0.24	0.05	0.21	−0.14	0.27
physical capital (pc)	0.12	0.25	0.50 **	0.22	0.38	0.27
natural capital (nc)	4.15 ***	0.29	1.19 ***	0.26	1.27 ***	0.26
financial capital (fc)	0.04	0.29	−0.98 ***	0.26	1.15 ***	0.30
social capital (sc)	0.38 ***	0.189	0.30 *	0.16	0.23	0.19
Constant	−5.05 ***	0.57	−0.54	0.43	−5.31 ***	0.58
Log likelihood	−608.15965		−763.24438		−517.43392
LR chi2 (7)	272.20		59.73		145.91
Pseudo R2	0.1937		0.0377		0.1236
Prob > chi2	0.0000		0.0000		0.0000

Note: *, ** and *** respectively represented significant tests at 10%, 5% and 1% levels.

.

In terms of the influence of soil and water loss from exposure on farmers’ adoption behaviors of soil and water conservation technology, the soil and water loss from exposure showed significantly positive effects on engineering technology, biological technology and tillage technology of 1%, 10%, and 1%, respectively, indicating that the more frequently soil erosion occurs, the greater the probability of farmers adopting soil and water conservation technology to mitigate the impacts and losses caused by soil erosion.

In terms of the impact of soil and water loss susceptibility on farmers’ adoption behavior of soil and water conservation technology, the susceptibility of soil and water loss to engineering technology, biological technology, and tillage technology showed a significant positive impact of 1%. This shows that the more serious the soil erosion affect, the greater the probability of farmers adopting soil and water conservation technology to mitigate the impacts and losses caused by soil erosion.

With respect to the influence of adaptability of soil and water loss on farmers’ adoption behavior of soil and water conservation technology, natural capital has a significant positive impact on engineering technology, biological technology, and farming technology of 1%. This shows that the greater the natural capital, the more water and soil conservation technology will be adopted, because the cultivated land areas and woodland areas selected represent farmers’ natural capital. The larger the cultivated land area and the larger the forest area, the more likely it is that farmers’ main income source will be agriculture, and the stronger their dependence on the farmland. Therefore, agricultural management is more valued, and the impact of soil erosion on them is greater. The probability of farmers adopting soil and water conservation technology is greater. Physical capital has a 5% positive effect on farmers’ adoption of biological technology. This shows that the more abundant the material capital, the more water and soil conservation technology will be adopted. For example, the more quantities of agricultural machinery in physical capital represent farmers’ attention to agricultural production, the more likely it is that soil and water conservation technology will be used. Economic capital has a significant negative impact on biological technology and farming technology of 1%. The possible explanation is that the higher the total household income, the higher the level of family business and the higher the non-agricultural income, whereas a lower agricultural income represents farmers relying more on non-agricultural income than on agricultural income, so they do not attach importance to agricultural production and reduce the adoption of water and soil conservation technology. Soil and water conservation technology requires investment into a certain amount of labor. Agricultural income is not the main source of income for the family. It does not pay enough attention to agricultural production. It may not care about the environment of agricultural production. Therefore, the higher the total household income, the lower the adoption of soil and water conservation technology. Social capital has a significant positive impact on the adoption of engineering technology and biotechnology of 1% and 10%, respectively. Small water conservation projects in engineering measures, forestation and grass planting in biological measures require the collective action of farmers. Research shows that social capital can encourage farmers to participate in collective action. Therefore, the richer the social capital, the probability of farmers adopting soil and water conservation technology is greater.

It can be seen that the soil erosion characteristics (frequency and severity) directly affect exposure and susceptibility. In the face of soil erosion, the degree of recovery of farmers depends on adaptability. Capital endowments determine the inherent ability of farmers to deal with disturbances, and mitigate and eliminate the impact of soil erosion. These results are consistent with other research done in the field of drought vulnerability. Research shows that differences in drought characteristics (frequency, intensity, and duration) directly affect the degree of exposure. According to field research, the increase in the frequency, intensity, and duration of drought has led to changes in household income and livelihood systems. Faced with this change, the degree of recovery of farmers depends on adaptability. Capital endowments determine the inherent ability of farmers to cope with drought disturbances [25].

4.4. Marginal Effect Analysis

To further study the specific influence mechanism and influence the degree of the exposures (e), susceptibility (s), physical capital (pc), natural capital (nc), financial capital (fc), social capital (sc), and human capital (hc) on farmers’ adoption of soil and water conservation technology, a marginal effect analysis was carried out, and the results are shown in

Table 11. Analysis of marginal effects.

	Response Variables
Explanatory Variables	Engineering Measures		Biological Measures		Tillage Measures
	Coefficient	Standard Errors	Coefficient	Standard Errors	Coefficient	Standard Errors
Exposure(e)	0.05 ***	0.01	0.01 *	0.006	0.027 ***	0.006
Susceptibility(s)	0.06 ***	0.011	0.05 ***	0.01	0.03 ***	0.009
Adaptability(a)
human capital(hc)	0.04	0.05	0.01	0.05	−0.02	0.04
physical capital(pc)	0.02	0.05	0.12 **	0.05	0.06	0.04
natural capital(nc)	0.86 ***	0.09	0.29 ***	0.06	0.19 ***	0.04
financial capital(fc)	0.01	0.06	−0.24 ***	0.06	−0.17 ***	0.04
social capital(sc)	0.08 **	0.04	0.07 *	0.04	0.03	0.03

Note: *, ** and *** respectively represented significant tests at 10%, 5% and 1% levels.

.

Table 11 shows that exposure increased by one grade. The probability of farmers adopting engineering soil and water conservation technology increased by 5%, and the probability of farmers adopting biological soil and water conservation technology increased by 1%. The probability of farmers adopting soil and water conservation technology of farming increased by 2.7%. Susceptibility increased by one level. The probability of farmers adopting engineering soil and water conservation technology increased by 6%, and the probability of farmers adopting biological soil and water conservation technology increased by 5%. The probability of farmers adopting soil and water conservation technology of farming increased by 3%. From the perspective of adaptability, capital endowment plays an important role in promoting farmers’ adoption of soil and water conservation technologies, such as engineering, biological, and tillage. When physical capital was increased by one level, the probability of farmers adopting biological soil and water conservation technology increased by 12%. When natural capital was upgraded by one level, the probability of farmers adopting engineering soil and water conservation technology increased by 86%, the probability of farmers adopting biological soil and water conservation technology increased by 29%, and the probability of farmers adopting soil and water conservation technology increased by 19%. When economic capital was upgraded by one level, farmers’ probability of using soil and water conservation technology decreased by 24%, and farmers’ probability of using soil and water conservation techniques reduced by 17%. When social capital was upgraded by one level, the probability of farmers adopting engineering soil and water conservation technology increased by 8%, and the probability of farmers adopting biological soil and water conservation technology increased by 7%.

5. Conclusions and Implications

Based on the Turner vulnerability framework, this paper constructs a household-scale index system of soil and water loss vulnerability in the Loess Plateau and evaluates the soil and water loss vulnerability in the Loess Plateau using the entropy evaluation method applied to field survey data of the Loess Plateau. The mechanism of influence of soil erosion vulnerability on farmers’ adoption behavior of soil and water conservation technology was assessed using a binary logistic model. The main conclusions are as follows: (1) Among the 930 farmers who suffered from soil erosion, 69.78% of them adopted engineering measures, 52.80% of them adopted biological measures, and 24.30% of them adopted farming measures. A total of 63.11% of farmers in the total sample thought soil erosion was higher and very high. (2) The results of vulnerability assessment of soil and water loss were based on the household scale. In the total sample, susceptibility > exposure > adaptability, whereas in the Shaanxi and Gansu subsample, susceptibility > adaptability > exposure. The Ningxia subsample was consistent with the total sample. For various indicators, Ningxia > Gansu > Shaanxi. Their differences were large. (3) The exposure and susceptibility of soil and water loss had a positive impact on farmers’ adoption behavior of soil and water conservation technology, and natural capital had a positive impact on farmers’ adoption of soil and water conservation technology. Social capital had a positive impact on farmers’ adoption of engineering technology and biotechnology. (4) Exposure increased by one grade. The probability of farmers adopting engineering soil and water conservation technology increased by 5%, and the probability of farmers adopting biological soil and water conservation technology increased by 1%. The probability of farmers adopting soil and water conservation technology of farming increased by 2.7%. Susceptibility increased by one level. The probability of farmers adopting engineering soil and water conservation technology increased by 6%, and the probability of farmers adopting biological soil and water conservation technology increased by 5%. The probability of farmers adopting soil and water conservation technology of farming increased by 3%. From the perspective of adaptability, capital endowment plays an important role in promoting farmers’ adoption of soil and water conservation technologies, such as engineering, biological and tillage. When physical capital was raised one level, the probability of farmers adopting biological soil and water conservation technology increased by 12%. When natural capital was upgraded by one level, the probability of farmers adopting engineering soil and water conservation technology increased by 86%, the probability of farmers adopting biological soil and water conservation technology increased by 29%, and the probability of farmers adopting soil and water conservation technology increased by 19%. When economic capital was upgraded by one level, farmers’ probability of using soil and water conservation technology decreased by 24%, and farmers’ probability of using soil and water conservation techniques reduced by 17%. When social capital was upgraded by one level, the probability of farmers adopting engineering soil and water conservation technology increased by 8%, and the probability of farmers adopting biological soil and water conservation technology increased by 7%.

Based on the above findings, the following policy implications can be drawn: (1) We should intensify monitoring of soil erosion. It can be seen from the survey that the frequency of soil erosion is relatively high in the Loess Plateau, which seriously affects agricultural production. Increasing the intensity of disaster monitoring will help the government and farmers to respond promptly and reduce the losses caused by soil erosion; (2) The government needs to strengthen and popularize soil and water conservation technologies, provide effective information on soil and water conservation technologies, and mitigate the negative impacts of soil erosion. Although the conclusion of the study indicates that soil and water conservation technology play a positive role in slowing down the risk of production caused by soil erosion, field data show that 56.34% of farmers adopt engineering measures, 42.62% of households adopt biological measures, and 19.62% of households adopt farming measures. Therefore, it is of great potential and space to propagate and popularize soil and water conservation technology for the Loess Plateau region where soil erosion is serious; (3) It is necessary to enrich the capital endowment of farmers and break through the endowment constraint of farmers’ adoption of soil and water conservation technology. We should further promote land transfer and guide the transfer of land to large households, in order to improve farmers’ technology adoption behavior of soil and water conservation, improve farmers’ social capital and promote collective action.

There are also limitations in this research. First, the evaluation index of the soil and water loss vulnerability may not reflect the real situation completely due to the limitations of accessing related data. It also needs to test its validity and practicability in other cities in China. Second, this paper does not distinguish between different types of natural disasters; therefore, there is no in-depth analysis of the relationship between different natural disasters and farmers’ adoption behavior of soil and water conservation technology. Third, because there is only one year of data, there is a lack of sustainability assessment of vulnerability. Therefore, in the future, we will try to further deepen and expand the research.