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Study areaChina is one of the countries with the poorest per capita water resources in the world while also having the largest water consumption in the world. In 2018, China’s total water consumption was 601.55 billion m3, with 369.31 billion m3 of water used in agriculture, accounting for 61.4% of the total water2. Agriculture is the most important industrial sector in water resource consumption. However, due to regional and climate differences, the distribution of agricultural water resources is uneven, and the shortage of water resources seriously affects agricultural development in water-deficient areas.Figure 1 shows the agricultural water consumption in China by province for 2007 and 2018. The agricultural water consumption includes farmland irrigation water consumption (classified as paddy field, irrigated land, vegetable field, groundwater exploitation), forest, animal husbandry, fishery, and livestock (classified as forest and fruit, grassland, fish pond, animal husbandry, groundwater exploitation), domestic water consumption of rural residents and rural ecological environment water consumption. Previous studies have mainly considered the irrigation water consumption of the planting industry as the research object at the provincial or regional levels (e.g., eastern, central, and western regions). Few were able to consider all 31 provinces in China and have comprehensively assessed water consumption and water use efficiency in the various types of agricultural production3,4,5,6,10,16,17,22,23,24,25,30. In this study, the agricultural water use efficiency and its influencing factors are assessed based on the agricultural water consumption of agriculture, forestry, animal husbandry, and fishery in China.Figure 1Agricultural water consumption in China by province for (a) 2007 and (b) 2018. Note: Map created using ArcGIS [10.2], (http://www.esri.com/software/arcgis).Full size imageResearch methodIn this study, the agricultural water use efficiency (under the common frontier and the group frontier) is calculated using the super-efficiency slacks-based measure (Super-SBM) model. The significant factors affecting water-use efficiency are then analyzed through the threshold regression model.Super-efficiency SBM modelData envelopment analysis (DEA) is an efficiency evaluation method proposed by Charnes31, a famous American operational research scientist. While traditional radial and angular DEA models do not require the specific form of the estimation function, they ignore the relaxation of variables and result in efficiency values in the range of 0 to 1. If there are multiple efficiency value of decision making units(DMUs) with an efficiency value of 1, these values cannot be compared. The efficiency of the super efficiency DEA model can be greater than 1, which means that the efficiency level of all decision-making units can be compared.To avoid the problem of slack variables, Tone (2001) proposed the SBM model, which is a non-radial and non-angular DEA analysis method based on the relaxation variable measure16,17,18,19,20,32. The SBM model of unexpected output solves the slack problem of input and output variables, minimizing deviations in the efficiency measurement. The super-efficiency SBM model combines the super-efficiency DEA model and the SBM model. It is also one of the methods based on data envelopment analysis, which can measure the efficiency of all decision-making units and the slack of input and output variables.Assume n to be the decision-making units, each of which has m inputs, expected output r1, and unexpected output r2. Let X (X ∈ Rm), Yd (Yd ∈ Rs1), and Yu (Yu ∈ Rs2) be matrices, such that (X=[{x}_{1},dots ,{x}_{n}]in {R}^{m*n}) and (Y=[{y}_{1}^{d}, dots ,{ y}_{n}^{d}in {R}^{{r}_{1}*n}). The form of the super-efficiency SBM model is as follows1,17,19,54:$$min=frac{frac{1}{m}sum_{i=1}^{m}(overline{x}/{x}_{ik})}{1/left({r}_{1}+{r}_{2}right)*(sum_{r=1}^{{r}_{1}}overline{{y}^{d}}/{y}_{rk}^{d}+sum_{q=1}^{{r}_{2}}overline{{y}^{u}}/{y}_{qk}^{u}}.$$
(1)
Among them,$$overline{x}ge sum_{j=1ne k}^{n}{x}_{ij}{lambda }_{j}, i=1,dots ,m;$$
(2)
$$overline{{y}^{d}}le sum_{j=1,ne k}^{n}{y}_{rj}^{d}{lambda }_{j}, r=1,dots ,{s}_{1};$$
(3)
$$overline{{y}^{d}}ge sum_{j=1,ne k}^{n}{y}_{qj}^{u}{lambda }_{j}, q=1,dots ,{s}_{2};$$
(4)
$${lambda }_{y}ge 0,j=1,dots ,n;jne 0;$$
(5)
$$overline{x}ge {x}_{k},k=1,dots ,m;$$
(6)
$$overline{{y}^{d}}le {y}_{k}^{d},d=1,dots ,{r}_{1};$$
(7)
$$overline{{y}^{u}}ge {y}_{k}^{u},b=1,dots ,{r}_{2}.$$
(8)
Based on the Super-SBM model (Eq. 1) and its constraint formula, the agricultural water use efficiency for the different provinces was calculated for the period 2007–2018 using Maxdea 8 ultra software.Threshold effectConsidering the differences in economic development and technical levels, the agricultural water use in different regions of China shows characteristics of time-series evolution, spatial heterogeneity, and unbalanced spatial distribution. There is a non-linear relationship between the influencing factors of agricultural water use efficiency, which suggests the existence of certain threshold characteristics33,34. This means that for a particular determinant, agricultural water use efficiency would be affected differently depending on whether the parameter has crossed the threshold. In this study, the threshold panel model proposed by Hansen is used. The threshold value of the threshold variable is taken as the critical point, and the regression equation is divided into different stage intervals to analyze the influence of threshold variables on the explained variables at different stages . Therefore, according to the relationship between agricultural water use efficiency and its influencing factors in different regions, the following single threshold regression model is set:$${Y}_{it}=alpha {X}_{it}+{beta }_{1}{T}_{it}Ileft({T}_{it}le {gamma }_{1}right)+{beta }_{2}{T}_{it}Ileft({T}_{it} >{gamma }_{1}right)+C+{varepsilon }_{it},$$
(9)
such that i is the province; t is the year; Yit and Tit are the explanatory variables and explained variables, respectively; Xit is the control variable that has a significant impact on the explained variables; Tit is threshold variable, which changes with the different explanatory variables; γ is a specific threshold value; α is the corresponding coefficient vector; β1 and β2 represent the influence coefficients of the threshold variable Tit on the explained variable Yit in the case of ({T}_{it}le {gamma }_{1}) and ({T}_{it} >{gamma }_{1}) , respectively; C is a constant; ε is random disturbance term, ({varepsilon }_{it}sim i.i.d.N(0,{sigma }^{2})); and, I (·) is an indicative function. After obtaining the estimated value of each parameter, two tests need to be carried out: (1) establish whether the threshold effect is significant; and (2) determine whether the estimated threshold value is equal to the true value. In addition, the above equation assumes that only one threshold exists. For two or more thresholds, the model would have to be adjusted according to the data.Based on the panel data of 31 provinces in China from 2007 to 201844,45,46, Stata15.0 software was used to perform threshold regression on seven variables: per capita water resources, rural labor force, disposable income, government’s attention, foreign trade dependence, industrial structure, and gross domestic product (GDP). The threshold effect of each factor can be analyzed, and the impact on agricultural water consumption can be assessed using the threshold value.Variable selection and data sourceThe super-efficiency SBM model was used in calculating the agricultural water use efficiency for the 31 provinces in China from 2007 to 2018. The input–output indicators were defined before the calculations, as shown in Extended Data Table 1.The selection of input–output factors to measure the utilization efficiency of agricultural water resources follows the principles of availability and operability. The input variables included: (1) agricultural water consumption, (2) the number of employees in agriculture, forestry, animal husbandry, and fishery, (3) the total power of agricultural machinery, and (4) the expenditure of local finance on agriculture, forestry, and water affairs. In terms of output, the added value in agriculture, forestry, animal husbandry, and fishery (based on 2007) was used as the expected output, while ammonia nitrogen emission, agricultural chemical oxygen demand emission, and agricultural carbon emission comprised the unexpected output.This study considered the scale of carbon emissions released by the agricultural system. According to existing research, agricultural carbon emissions are associated with rural environmental pollution35. The main consequence of agricultural pollutant emissions is soil pollution, which leads to rural groundwater pollution36,37,39,40,41,41. The deterioration of groundwater quality adversely affects the development of the agricultural economy and threatens the safety of the drinking water supply for rural residents.The threshold regression model was used to investigate the convergence of agricultural water use efficiency and observe the changes in agricultural water consumption under different influencing factors. The control variables include the following: water resource endowment, the number of agricultural labor, the income level of rural residents, industrial structure, the degree of government’s attention, the degree of dependence on foreign trade, and the level of economic development, as shown in Extended Data Table 2. For water resource endowment (WR), WR is expressed in per capita water resource (m3 / person). Zhang Lixiao45,46 and previous studies have shown a negative correlation between water resource endowment and water resource utilization. For agricultural labor (ah), the variable is expressed by the number of people engaged in agriculture, forestry, animal husbandry, and fishery (10,000 people). Past studies suggest rural population affects the consumption of agricultural water resources47,50,51,52,53,52. For income levels, rural residents’ income level is indicated by the per capita disposable income of rural households. Wang Xueyuan et al.3 and Han Qing et al.53 argue that the increase in the rural residents’ income would limit agricultural water consumption. For industrial structure (× 2), which is expressed by the proportion of industrial added value in GDP, research has shown water resource efficiency would vary under different industrial structures54,57,56. For the government’s attention degree (GA), the variable is expressed by the proportion of agriculture, water affairs, and forestry spending in the total financial expenditure. The government’s support for comprehensive agricultural development and infrastructure and technology upgrading for agricultural, forestry, and water conservation significantly affects water resource utilization efficiency16,56,59,58. For the degree of dependence on foreign trade (open), the parameter is indicated by the proportion of the total import and export of agricultural and sideline products in the GDP. Changes in import demand can reduce or increase the consumption and pollution of water resources. Likewise, export demand changes, especially in high water-consuming and high polluting products, can significantly improve or degrade water resource efficiency. And for the level of economic development, expressed in terms of GDP, the level of regional economic development plays a positive role in promoting the efficiency of water resource utilization59,62,61. More

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