Evaluating Agricultural Sustainability Based on the Water–Energy–Food Nexus in the Chenmengquan Irrigation District of China

: Agriculture is one of the largest consumers of water and energy. This paper evaluated the agricultural sustainability of the Chenmengquan irrigation district of China based on the water–energy–food nexus. One objective weighting method and one subjective weighting method were integrated, based on game theory, and a matter–element model was constructed to evaluate agricultural sustainability for the research region. The sensitivity of each index to the evaluation class was also analyzed. The results showed that agricultural sustainability was moderate in 2006–2012 and high in 2012–2015. The indexes, which represent water-use e ﬃ ciency and yield per unit area of crops, had higher sensitivities in the context of the present case study. The results also indicated that agricultural sustainability had a comparatively positive trend between 2012 and 2015, and that pesticide utilization was the most important issue for agricultural sustainability. The approach of using the combination of a weighting method, based upon game theory, and the use of the matter–element model provides a guide for the evaluation of agricultural sustainability.


Introduction
The issue of agricultural sustainability has received considerable critical attention in the world with the changing environment and the growing population [1]. In the case of limited arable land resources, in order to satisfy the expected demands for food, agriculture must be transformed, in order to feed a growing global population and provide the basis for economic growth and poverty reduction [2]. More than 80% of agricultural production growth by 2050 is expected to come from increased productivity on presently cultivated land [3]. However, intensive agricultural practices have resulted in serious environmental degradation, including groundwater level decline, the loss of biodiversity, and soil and water pollution [4]. Improving agricultural sustainability is the inevitable choice for agricultural development in the future. Operationalizing the assessment of agricultural sustainability is an important premise in order to promote it. The assessment of agricultural sustainability aims to provide an efficient tool for decision-makers to determine which actions should be preferentially taken in an attempt to promote agricultural sustainability [5]. the agricultural population is 185,000. The total area of the irrigation district is approximately 20,000 ha. The main crops in the irrigation district are wheat, maize, and vegetables. With the continuous adjustment of the proportion of different crop acreages, the vegetable planting area has increased substantially. The study area is located in the mid-latitude zone and belongs to the warm, temperate, semi-humid monsoon climate. Rainfall varies greatly in different seasons. The average annual precipitation is 673 mm  and 70% of the annual precipitation is concentrated between June and September [24].
Irrigation plays an important role for agriculture in the study area. Irrigation water is mainly supplied by the Yellow River and groundwater. With increased use of water for agriculture the exploitation of groundwater gradually exceeded the recharge, resulting in the continuous decline of the groundwater level in 2000-2006. Since 2006, the administrative department has promoted the protection of groundwater. However, there are still other problems like soil and water pollution caused by the excessive application of fertilizer and pesticide.

Methods
Based on the above introduction, the steps of the proposed methodology are shown in Figure 2. Irrigation plays an important role for agriculture in the study area. Irrigation water is mainly supplied by the Yellow River and groundwater. With increased use of water for agriculture the exploitation of groundwater gradually exceeded the recharge, resulting in the continuous decline of the groundwater level in 2000-2006. Since 2006, the administrative department has promoted the protection of groundwater. However, there are still other problems like soil and water pollution caused by the excessive application of fertilizer and pesticide.

Methods
Based on the above introduction, the steps of the proposed methodology are shown in Figure 2.

Index System
To assess agricultural sustainability, representative indexes are identified in Table 1 through a comprehensive perspective based on WEFN (ci represents index number, i = 1, 2, …, 10). Irrigation plays an important role in increasing the output of agricultural products. However, it also faces the practical problems of improving the efficiency of agricultural water use and controlling the total amount of water used. Cao et al. proposed an evaluation index for agricultural water use effect based on water footprint (WF) and irrigation development [25]. The indexes c1 (agricultural blue water proportion), c2 (water-use efficiency), and c3 (irrigation proportion of arable land), which represent agricultural water use effects, were used as indexes in the water sector.
The index c1 (agricultural blue water proportion) is based on the concept of WF proposed by Hoekstra [26]. It indicates the dependence of agriculture on irrigation water. The index expression for c1 is given in Equation (1), as the ratio between agricultural blue water footprint (AWFb) and the agricultural water footprint (AWF).
AWFb and AWF are calculated as in Equations (2) ETb,cr and ETg,cr (in mm) are the blue and green evapotranspiration components of a given crop, which are computed by the CropWat ® software. Scr (in ha) is the total area cultivated of a given crop.
The index c2 (water-use efficiency) is essential regarding the water consumption. It has a high correlation with the infrastructural performance of the irrigation network, the farm management

Index System
To assess agricultural sustainability, representative indexes are identified in Table 1 through a comprehensive perspective based on WEFN (c i represents index number, i = 1, 2, . . . , 10). Irrigation plays an important role in increasing the output of agricultural products. However, it also faces the practical problems of improving the efficiency of agricultural water use and controlling the total amount of water used. Cao et al. proposed an evaluation index for agricultural water use effect based on water footprint (WF) and irrigation development [25]. The indexes c 1 (agricultural blue water proportion), c 2 (water-use efficiency), and c 3 (irrigation proportion of arable land), which represent agricultural water use effects, were used as indexes in the water sector.
The index c 1 (agricultural blue water proportion) is based on the concept of WF proposed by Hoekstra [26]. It indicates the dependence of agriculture on irrigation water. The index expression for c 1 is given in Equation (1), as the ratio between agricultural blue water footprint (AWF b ) and the agricultural water footprint (AWF).
AWF b and AWF are calculated as in Equations (2) and (3) ET b,cr and ET g,cr (in mm) are the blue and green evapotranspiration components of a given crop, which are computed by the CropWat ® software. S cr (in ha) is the total area cultivated of a given crop.
The index c 2 (water-use efficiency) is essential regarding the water consumption. It has a high correlation with the infrastructural performance of the irrigation network, the farm management techniques, and irrigation methods. The index c 3 (irrigation proportion of arable land) is the ratio of effective irrigated area to arable land area. The effective irrigated area is the area of farmland which is relatively flat, has a certain water source and irrigation facilities, and can be irrigated normally in an average year. The data of c 2 (water-use efficiency) and c 3 (irrigation proportion of arable land) were derived from the Statistical Yearbook of Jinan City.

Energy
The energy consumed by agriculture can be divided into direct energy and indirect energy [27]. Direct energy includes fuel and electricity mainly used for irrigation and agricultural machinery's operation. Indirect energy refers to the energy used to produce fertilizers and pesticides. In this research, energy consumption intensity is expressed by four indicators: c 4 (energy utilization for irrigation amount per arable land), c 5 (agricultural machinery power per arable land), c 6 (fertilizer utilization amount per arable land), and c 7 (pesticide utilization amount per arable land).
The index c 4 (energy utilization for irrigation amount per arable land) is given in Equation (4) where S represents the area of the arable land and E ir represents energy utilization for irrigation, which refers to the energy requirement from-source-to-field. It not only depends on the specific water source, but also on the distribution of irrigation systems, the characteristics of the conveyance with their respective water losses and operational pressures [28]. For simplicity, the energy requirement for conveyance was not included, hence the water source was assumed to be on-farm [29]. For surface irrigation, the energy for surface water transport was mainly driven by gravity. Consequently, energy used for groundwater abstraction was computed as E ir , shown in Equation (5) where Volume g represents the gross amount of water from a groundwater source. η represents the pump efficiency; and H t , H lift , and H pr represent the total hydraulic head, the elevation head, and the nominal operating pressure of the irrigation system, respectively. The data of c 5 (agricultural machinery power per arable land), c 6 (fertilizer utilization amount per arable land), and c 7 (pesticide utilization amount per arable land) were derived from the Statistical Yearbook of Jinan City.

Food
The indexes of the food sector were formulated according to the actual agriculture production in the given area. Wheat, maize, and vegetables make up more than 90% of the arable land at the study site. Because different crops have different attributes, it is not rigorous to use the total output value or total yield of all crops as the index. In this research, the index c 8 (yield per unit area of wheat), c 9 (yield per unit area of maize), and c 10 (yield per unit area of vegetables) were used to represent the food productivities of the arable land. The data of these indexes were calculated from data on gross yields and planting areas given in the Statistical Yearbook of Jinan City.

Calculation of the Weights
In a comprehensive evaluation, the weight reflects the significant performance of each basic indicator or dimension criterion [30,31]. Major factors act on sustainability in different degrees. Thus, each major factor must be assigned with a weight. Selecting the appropriate weight determination method is the key step of the comprehensive evaluation work. Weight calculation methods primarily include objective weighting methods and subjective evaluation methods. Objective weighting methods are represented by the entropy method [32] and the coefficient of variation (CV) method [33]. Subjective weighting methods are represented by the analytic hierarchy process (AHP) method [34] and the Delphi method [35].
Each type of those methods has its own advantages and disadvantages. Objective weighting methods depend on objective data completely, whereas subjective weighting methods are influenced by human-subjective experience inevitably. The combination weighting method [36] combines the subjective weighting method with the objective method based on game theory, so that the weight can reflect the subjective and objective information simultaneously. The central idea is to minimize the deviations of different weights calculated by different methods. In this study, subjective weights were determined by the G1 method, whereas objective weights were acquired by the entropy method.

The G1 Method
The G1 method (order relation analysis) is an improved method based on the analytic hierarchy process (AHP) [21]. This method does not require a consistency check, so a large amount of calculations can be avoided. The method consists of three steps: Firstly, the order of the evaluation indexes has to be determined The number of the evaluation indexes is n. " " indicates that the index on the left side of the symbol is more important.
Secondly, the importance ratio assignments of adjacent evaluation indexes are determined.
The reference assignments for r i are shown in Table 2.  The index c i−1 is slightly more important than index c i 1. 4 The index c i−1 is fairly more important than index c i 1. 6 The index c i−1 is strongly more important than index c i 2.0 The index c i−1 is extremely more important than index c i Finally, the weights of indexes are calculated where w 1 n , w 1 i , and w 1 i represent the weights of the indexes c n , c i−1 , and c i using the G1 method, respectively.

The Entropy Method
The entropy method is based on objective data. Therefore, it can avoid personal subjective interference. Supposing the number of evaluation objects is m and the number of evaluation indexes is n, the original data matrix can be expressed as: X = {x ij } m×n (j = 1, 2, 3, . . . , m; I = 1, 2, 3, . . . , n).
In the process of the calculation, negative and extreme values cannot be used directly because of the concept of logarithm and entropy. Thus, the index data needs to be normalized in advance. The normalized indexes can be divided into positive type and negative type, as shown in Equations (11) and (12): The entropy measure is calculated using the following equation: where The weights of indexes are obtained as: where w 2 i denotes the weight of the index x i using entropy method.

Combination Weighting Rule
If L types of methods are used to assign weights to an index; a weight vector set can be constructed: The linear combination of L weight vectors can be represented by Equation (15): where w is a possible weight vector obtained through L types of methods, and α k is the coefficient of the kth method. Searching for the most ideal weight vector can be aided by optimizing the coefficients α k in the Formula (15). Based on game theory [37,38], the goal of the optimization is to minimize the deviation between w and the various w T k : The optimal first-order derivative conditions can be converted to the following linear system of equations: α 1 , α 2 , . . . , α L can be computed mathematically and normalized, as in Equation (18): The combination weights of indexes can be obtained as: where w represents (w 1 , w 2 , . . . , w i , . . . ,w n ).

Matter-Element Model
The matter-element theory has been widely applied to mathematics and system theory [39]. The matter-element model consists of objects, characteristics, and values [40]. Therefore, agricultural sustainability as the evaluation object can be regarded as a composite whole with different characteristics and corresponding values. The attribute diversity of agricultural sustainability can be assumed as an incompatibility problem. The extension method aims to solve this type of problem by combining indexes with different attributes to deduce a comprehensive result [36].

Determining the Matter-Element
The matter-element is the basic element to describe objects (R), which is constituted of a given object (N), a characteristic (C), and the value of the characteristic (V). The matter-element is defined according to by Equation (20):

Determining the Classical Domain and the Controlled Domain Matter-Element Matrix
The classical domain matter-element matrix can be expressed as Equation (21): where t represents the tth class of agricultural sustainability. R t is the matrix of the classical domain in the tth class. N t is the agricultural sustainability in tth class. V ti is the value range of the ith index in the tth class, with the lower bound of a ti and the upper bound of b ti . The controlled domain matter-element matrix can be expressed as Equation (22): where R p represents the matter-element of the controlled domain. V pi is the value range of the ith index in all classes, with the lower bound of a pi and the upper bound of b pi .

Correlation Degree between Each Index and Each Class
The correlation degree determines whether one index belongs to a sustainability class and how much it belongs there. The value of the correlation degree was calculated according to the following functions. where where x ij is the value of the ith index of the jth object. K t (x ij ) is the value of correlation degree between the ith index of the jth object and the tth class. c ij belongs to the tth class if K t ( Combined with the corresponding weights according to Section 3.2, the integrated correlation degree K t (N j ) between N j and the tth class is shown in Equation (26).
where N j is the jth object and o represents the number of all the classes. In conclusion, N j belongs to the tth class if K t (N j ) = max [K t (N j )] (t = 1, 2, . . . , o).

The Weights of Indexes
Subjective weights were calculated by the G1 method, as stated in Section 3.2.1. The order of the evaluation indexes is c 4 , c 2 , c 7 , c 6 , c 1 , c 10 , c 8 , c 9 , c 5 , and finally, c 3 . The importance ratio assignments of the adjacent evaluations are c 4 /c 2 = 1.2; c 2 /c 7 = 1; c 7 /c 6 = 1; c 6 /c 1 = 1.2; c 1 /c 10 = 1; c 10 /c 8 = 1; c 8 /c 9 = 1.2; c 9 /c 5 = 1; c 5 /c 3 = 1. It should be noted that the G1 method is a subjective method, so that the order and order and ratios of the indexes have to be defined according to study site characteristics and research objectives on a case-by-case basis.
Objective weights were calculated by the entropy method, as stated in Section 3.2.2. According to the combination weighting rule, α 1 = 0.915 and α 2 = 0.085. Subjective weights, objective weights, and synthetic weights of indexes are shown in Table 3.

The Classical Domain and the Controlled Domain
Agricultural sustainability classes reflect the degree of agricultural sustainability [41]. The degree of agricultural sustainability was divided into five classes: very low, low, moderate, high, and very high. Thus, as described in Section 3.3.2, the classical domain and the controlled domain are listed in Table 4. The classical domain of each index was determined by data from Jinan over the past 30 years. The controlled domain was determined by minimum or maximum values of the indexes of the research site.

Determination of the Sustainability Class
For each object to be evaluated, the correlation between each index and each evaluation class can be calculated by Equations (23)- (25). For example, Table 5 shows the correlation degree and evaluation class of each index in 2015. K 1 (c 1 ) = −0.050, K 2 (c 1 ) = −0.023, K 3 (c 1 ) = 0.062, K 4 (c 1 ) = −0.021, and K 5 (c 1 ) = −0.038. Thus, c 1 belongs to the moderate class because K 3 (c 1 ) is the maximum of all of the classes. The correlation degree between each index and evaluation class is shown in Figure 3. Evaluation results of each index from 2006 to 2015 are shown in Table 6. For simplicity, I, II, III, IV, and V represent very low, low, moderate, high, and very high, respectively.     Index  2006  2007  2008  2009  2010  2011  2012  2013  2014  2015   c 1  III  III  III  III  III  II  III  II  II  III  c 2  III  III  III  III  III  III  III  III  III  III  c 3  IV  IV  IV  IV  III  III  IV  IV  IV  IV  c 4  I  I  III  II  III  III  III  IV  III  IV  c 5  III  III  III  III  III  III  III  III  III  III  c 6  III  III  III  III  III  III  III  III  III  III  c 7  IV  II  II  II  II  II  II  II  II  II  c 8  III  III  IV  IV  IV  IV  IV  IV  IV  IV  c 9  IV  IV  IV  IV  IV  IV  III  III  III  III  c 10  IV  IV  III  III  IV  IV  IV  IV  IV  IV Combined with the corresponding weights in Table 3, the integrated correlation degree between each year and evaluation class was calculated by Equation (26), as shown in Figure 4. Thus, the final evaluation results of every year were obtained as shown in Table 7.   c1 Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅱ Ⅲ Ⅱ Ⅱ Ⅲ c2 Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ c3 Ⅳ Ⅳ Ⅳ Ⅳ Ⅲ Ⅲ Ⅳ Ⅳ Ⅳ Ⅳ c4 Ⅰ Ⅰ Ⅲ Ⅱ Ⅲ Ⅲ Ⅲ Ⅳ Ⅲ Ⅳ c5 Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ c6 Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ c7 c10 Ⅳ Ⅳ Ⅲ Ⅲ Ⅳ Combined with the corresponding weights in Table 3, the integrated correlation degree between each year and evaluation class was calculated by Equation (26), as shown in Figure 4. Thus, the final evaluation results of every year were obtained as shown in Table 7

Analysis and Discussion
The level of agricultural sustainability was promoted from class III to class IV in 2013 (Table 7), and the level was steady in class III before 2013. A higher degree of correlation to a given class indicates that the state in a given evaluation class is more stable, or that there is a greater tendency to convert to this class. Thus, it is worth noting that the integrated correlation degree of class IV was continuously increasing in 2013-2015 ( Figure 2). It indicates that the state of agricultural sustainability in class IV was more and more stable. In the meantime, in regard to the other classes, the integrated correlation degree of class V was also growing, whereas the integrated correlation degree of class III was constant. Cumulatively, reflecting that agricultural sustainability was in a comparatively positive trend.
The above-mentioned analysis path can be extended to analyze the sustainable development of each index. The index c 1 (agricultural blue water proportion) was switching back and forth between class II and class III. Besides, there was no obvious upward trend for the correlation degree of class IV. The evaluation result of c 3 (irrigation proportion of arable land) was one class higher than that of c 1 . The trends of those two indexes were similar. This shows that the dependencies of agriculture on irrigation and irrigation intensity have not been effectively alleviated in recent years. The index c 2 (water-use efficiency) ranked class IV in all the years and the correlation degree to class V kept increasing. This shows that water-use efficiency was improved. The improvement of water-use efficiency benefited from the renovation of irrigation infrastructure and the optimization of irrigation methods (i.e., sprinkler or drip irrigation) in the Chenmengquan irrigation district. The index c 4 (energy utilization for irrigation amount per arable land) experienced a leap from class I to class IV in 10 years, which can be attributed to the increase of the groundwater table caused by the regional groundwater protection by the administrative department [42]. The indexes c 5 (agricultural machinery power per arable land) and c 6 (fertilizer utilization amount per arable land) were both in class III all the time and their correlation degrees to class III were significantly higher than those to other classes. This suggests that the sustainability classes of c 5 and c 6 will not change in the short term. The amount of fertilizer utilization did not decrease effectively. Except for 2006, c 7 (pesticide utilization amount per arable land) was always in class II and the correlations to the two adjacent classes were still much lower than class II. It performed the worst of all the indexes. Regarding the use of pesticide, adequate attention should be paid by the administrative department. In the period 2010-2015, c 8 (yield per unit area of wheat) and c 10 (yield per unit area of vegetable) were both in class IV, and both of their correlation degrees with class IV, were getting close to the correlation degrees of class V. Those results showed that the productivity of wheat and vegetables was gradually increasing. However, the productivity of maize was getting worse, which can be demonstrated by the fact that c 9 (yield per unit area of maize) dropped down from class IV to class III after 2012.
In addition, the sensitivity of the indexes was analyzed in this research. The simplest form of sensitivity analysis includes varying one index by a given amount at a time in the model and examining the impact of such change on the result of the model [43]. Consider that agricultural sustainability consists of multiple indexes which have different attributes. Each index value was given certain changes (−5%, −10%, +5%, and +10%) in double-directions [44]. The evaluation result of agricultural sustainability in 2015 did not change with the variations of the indexes. However, the evaluation results of c 2, c 8, c 9 , and c 10 were changed, as shown in Table 8. Compared with other indexes, these four indexes had higher sensitivities. The variations of c 8 (yield per unit area of wheat), c 9 (yield per unit area of maize), c 10 (yield per unit area of vegetable), and c 2 (water-use efficiency) had a strong influence on the evaluation results of corresponding indexes.
It is worth noting that the proposed procedure cannot be generalized to other contexts and should be considered site-specific. The indexes need to be selected according to the characteristics of the agriculture in other research regions.  III  III  III  IV  III  c 8  IV  IV  V  V  IV  c 9  III  II  III  III  III  c 10  IV  III  IV  V  IV

Conclusions
This paper proposes an index-based approach to evaluate agricultural sustainability in a given area based on the concept of the WEFN. The index system was established in the dimensions of agricultural water use, the intensity of agricultural energy use, and food productivity. The index system can not only reflect the agricultural sustainability comprehensively, but also avoid the influence of scale variation. In this premise, the evaluation approach integrated the combination weighting method and the matter-element model. The matter-element model was applied to quantify the fuzzy concept of agricultural sustainability. The combination weighting method gave each index a more scientific weight. The methodology was implemented in a case research, on an irrigation district in Jinan City of China, which is characterized by highly intensive agricultural practices. The results show the evaluation classes of agricultural sustainability in the study area. From 2006 to 2012, the level of agricultural sustainability was class III (moderate). From 2013 to 2015, the level of agricultural sustainability was class IV (high). At the same time, the results indicate the trend of the state change and the single index information. The agricultural sustainability was in a comparatively positive trend after 2012. Excessive use of pesticides was a shortcoming of agricultural practices in the study area. The results derived from the sensitivity analysis indicated that c 2 (water-use efficiency), c 8 (yield per unit area of wheat) , c 9 (yield per unit area of maize), and c 10 (yield per unit area of vegetable) had higher sensitivities. The research results could be applied both for scientific and decision-making purposes. The methodology is suitable to evaluate agricultural sustainability.
Author Contributions: C.L. conceived the original research and drafted the manuscript; Z.Z. guided the execution of the research; S.L. and B.F. assisted in developing the research design; Q.L. contributed to the collection and processing of data; J.T. contributed to editing the manuscript.