Design of DEA water efficiency evaluation model for cotton field irrigation in Xinjiang

Xinjiang in China is located in the middle of Eurasia, with low annual rainfall and high evaporation, which is a typical continental arid area. Because of its vast area and a large area of cultivated land per capita, it has gradually developed into the most important agricultural production area in China. Cotton, as an important cash crop in Xinjiang, due to its significant regional advantages and unique climate environment, has increased its planting area year by year, from 940,000 hm² in 2002 to 2254,000 hm² in 2017. In the past 15 years, the planting area of cotton has expanded by 2.4 times, accounting for more than 75% of the total cotton planting area in China, and the cotton output has accounted for more than 85% of the total output in China (Qiao et al. 2021). Therefore, the renewal of agricultural machinery and the development of cultivation techniques in Xinjiang are of great significance to further reduce the cost of cotton planting and increase cotton yield. Water resources are directly related to human survival and socioeconomic development. With the rapid development of China's economy, the consumption and demand for water resources in all walks of life are gradually increasing. As a country short of water resources, China is facing a major problem in improving the utilization efficiency of water resources (Zhang et al. 2020). Water resources are the lifeblood of agricultural development, and limited water resources carrying capacity has become an important factor restricting the sustainable development of agriculture. Although agricultural water consumption is relatively high, the efficiency of farmland water utilization in Xinjiang is far from the expected value due to excessive water consumption and low efficiency of management measures.

Huang & Qu (2021) constructed the comprehensive evaluation index system and index classification standard of water efficiency in the Hetao irrigation area, using the improved entropy method to weight the evaluation index, combining the set pair analysis theory (SPA) and variable fuzzy set theory (VFS), and applied the SPA–VFS coupling model to carry out the classification evaluation of water efficiency in Hetao irrigation area. The results show that the water efficiency grade of Hetao irrigation area obtained by SPA–VFS coupling model is grade III, which is consistent with the evaluation results of VFS model and SPA model, indicating that the SPA–VFS coupling model is reasonable and feasible for the classification evaluation of water efficiency of Hetao irrigation area; the stable ranges of the level eigenvalues obtained by SPA–VFS coupling model and VFS model are 3.12–3.17 and 3.00–3.33, respectively. The stable range of SPA–VFS coupling model is significantly smaller than that of VFS model. The evaluation results are more reliable and more suitable for the level evaluation of water efficiency in the Hetao irrigation area. Yu et al. (2020) proposed an intelligent precision irrigation decision-making model for ginseng planting under the Internet of Things. The environmental information such as soil moisture content and air temperature and humidity are collected in real-time through the information acquisition and transmission module, and the information is transmitted to the information processing module through ZigBee network for comparative analysis with the knowledge base threshold. In the irrigation decision-making execution module, combined with the standard threshold of the collected environmental data knowledge base, the decision-making mathematical model is established to calculate the water demand of ginseng, predict the irrigation time and the optimal amount of irrigation, feedback the decision-making results to the control terminal, and control the irrigation valve through the single chip microcomputer to realize accurate irrigation.

The above existing methods can not accurately predict irrigation water consumption, resulting in large errors in water efficiency evaluation. Therefore, an evaluation method of irrigation water efficiency of the cotton fields in Xinjiang based on super efficiency DEA model is proposed.

The data envelopment analysis (DEA) method is a nonparametric estimation method. Its main idea is to explore the reasons for the mismatch between the input and output of non-DEA effective units and the improvement direction by projective analysis on the production front, and then adjust the input of resources and the output of benefits, so as to maximize the input and output efficiency of decision making units (DMUs) (Adhikari et al. 2020; Baloch et al. 2021). The DEA method can evaluate the relative efficiency among different DMUs (DMUs) with multiple input and output variables, and has the advantage that it does not require a specific production function form for multiple input and output indicators. The evolution of DEA method can be divided into three stages.

When calculating the efficiency of the DMU, C is excluded from the reference set of DMUs, so the production frontier changes from ABCD to ABD, when the LOC'/lOC is greater than 1 (lOC', lOC is OC 'and OC length). For the original DEA inefficient decision-making unit E, in the DEA model, the frontier of efficiency is still ABCD, which is consistent with the efficiency obtained in the DEA model, and is still lOE'/lOE < 1 (lO', lOE is O'and OE length).

The analysis of water resources utilization efficiency belongs to the problem of efficiency evaluation of more inputs and more outputs. Because the water resources utilization efficiency involves many aspects, this paper intends to quantify the water resources utilization efficiency from the perspectives of ‘water resources conditions-water use conditions-social economy’ and ‘water use conditions-social economy’ (Ye et al. 2019; Lenka et al. 2021). Thus, the indicators obtained include those that reflect the conditions of water resources, water use, and economics, as shown in Table 1.

Because the genetic algorithm has the characteristics of global search and high efficiency, the genetic algorithm is used to obtain the global optimal solution of super-efficient DEA. Genetic search in space of vector can improve the value of the vector in the process of genetic evolution, and it is a method to solve the super efficiency DEA model. The global optimal solution of the model can be transformed into a linear programming problem by bringing the vector values from the genetic search into the objective function.

⁠, u represent the relevant weight vector, if we want to call the unit equal or effective proportion, then all the DMU j meet ⁠, and the unit p is the best efficiency.

In the solution of the super efficiency DEA model, if the of the DMU is positive, the DMU is the best efficiency.

In the above formula, represents the vector combination of cotton field irrigation water data, and represents the interference component.

According to the information fusion results of irrigated cotton field irrigation water, principal component analysis and adaptive game decision-making are carried out to evaluate and test the cotton field irrigation water of the irrigation system (Liu et al. 2019; Sarangi et al. 2019).

• A.
  The prediction of crop water evapotranspiration in cotton field adopts the following calculation formula:

  

  (13)

In the above formula, L represents crop evapotranspiration in the cotton field; represents crop coefficient in the cotton field; represents soil moisture correction coefficient in the cotton field; represents crop evapotranspiration in reference cotton field (Garibay et al. 2019).

• B.

  Prediction of evapotranspiration of reference cotton field

The evapotranspiration of reference cotton field mainly reflects the influence of meteorological factors on the evapotranspiration of reference cotton field. According to the correlation analysis of the evapotranspiration of the reference cotton field and meteorological factors, the highest correlation factor can be selected to determine the temperature factor, so as to predict the evapotranspiration of the reference cotton field (Han et al. 2019).

Through analyzing the change of crop temperature with time, the relationship between temperature and crop growth cycle is analyzed, as shown in Table 2.

In the above formulas, represent the meteorological factors during the warming period and the cooling period, respectively; represent the power of the natural logarithms during the warming period and the cooling period, respectively; T represents the temperature (Li et al. 2019).

The actual correction value is obtained by multiplying the difference between the temperature actually measured 10 days prior to the start of the forecast and the historical trend value for the same period by a daily attenuation factor (Younis et al. 2020). The sum of the former measured values and the actual corrected values is the final predicted temperature. The accuracy of temperature forecasts can be effectively improved if the real-time weather forecast information is published and the forecast value is properly corrected.

In the above formula, represents the amount of groundwater recharge; represents the evapotranspiration of crops in cotton fields on day i; represents the empirical coefficient relating to the soil in cotton fields in irrigated areas; and represents the depth of groundwater.

In the above formula, ⁠, respectively, represent the soil volume moisture content, cotton crop evapotranspiration, effective rainfall, cotton crop irrigation, and groundwater recharge in the wet area on day i; represents the soil volume moisture content in the wet area; ⁠, respectively, represent the water increased due to planned wetting, the wetting ratio of irrigated crop groups and the water increased in the wet layer (Zare et al. 2020).

In the above formula, V represents the predicted water consumption; represents the soil water capacity of the cotton field; represents the minimum suitable water content of the cotton field.

Taking the irrigation water demand value corresponding to the redundancy rate as the processing object, the maximal point of the scale efficiency function is calculated in the plane range. By synthesizing the data of irrigation water demand and actual usage in the irrigation area of cotton fields with the same attributes, the dual linear processing method is adopted to add a constraint condition at the critical point, and the optimal solution is the most value of the constraint condition in the calculation formula (19). When eliminating the weak effective effect in the optimal solution, the scale in the irrigation area of cotton fields is estimated to drive the parameters, and the critical point and the optimal value are continuously combined into the above calculation formula (18). When the relaxation parameter is a numerical value of 1, the redundancy rate calculated at this time is the correlation coefficient of the final demand usage. Under the control of the coefficients, the DEA model was used to determine the environmental impact variables of cotton fields.

Based on the actual cotton irrigation data in a certain region in 2020 and meteorological data in the same period, the cotton field water holding capacity was 0.33 cm³/cm³, the minimum suitable soil water content was 0.155 cm³/cm³, and the groundwater recharge was negligible. Two time periods from 1 August 2020 to 10 August 2020 and from 20 August 2020 to 30 August 2020 were selected to verify the prediction model of water consumption for water-fertilizer and gas coupling water-saving irrigation equipment in small and medium-sized cotton fields.

The samples from 1 August to 10 August 2020 and 20 August to 30 August 2020 are divided into training sets and test sets. A total of 10 groups of training data are obtained from the two groups, as shown in Table 3.

In order to guarantee the sampled data to be uniform order of magnitude, the input and output sample data should be preprocessed by using the mapminmax function in MATLAB toolbox.

The actual irrigation water consumption is shown in Table 4.

It can be seen from Figure 3 that the comprehensive evaluation method of water efficiency in the Hetao irrigation area proposed in Huang & Qu (2021) and the evaluation method of irrigation water efficiency based on the Internet of things proposed in Yu et al. (2020) are quite different from the actual value. The maximum error of water consumption at three-time points is 100,000 m³. The irrigation water consumption predicted by the proposed method is basically similar to the actual value, and the maximum water consumption error is 5,000 m³.

As can be seen from Figure 4, the predicted irrigation water consumption using the proposed method is basically similar to the actual value and the error is negligible. The comprehensive assessment method for water use efficiency of the Hetao irrigation area proposed in Huang & Qu (2021) and the assessment method for water use efficiency of irrigation based on the Internet of Things proposed in Yu et al. (2020) differ greatly from the actual value. Therefore, the application of water-fertilizer and gas coupling water-saving irrigation model for small- and medium-sized cotton fields is more reasonable and consistent with the actual value.

According to Figures 5 and 6, compared with the references, the irrigation water efficiency of the proposed method can be as high as 90% during irrigation period 1 and irrigation period 2. This experiment shows that the proposed method has ideal practical performance.

In order to solve the problem of large errors in the irrigation water use efficiency evaluation method, a new method based on super efficiency DEA model was proposed in the Xinjiang cotton field. The DEA model of super efficiency is established to adjust the predicted and actual amount of irrigation water use. This paper constructs a statistical series model of cotton field irrigation water information, fuses the information of cotton field irrigation water, and constructs a prediction model of water consumption by crop evapotranspiration, groundwater recharge and soil moisture. After establishing the index data set, the numerical relationship between demand and usage was defined to evaluate the irrigation water use efficiency of cotton fields in Xinjiang. Experimental results show that the irrigation water consumption prediction of the proposed method has high accuracy, and the irrigation water use efficiency can reach 90%, which shows that the proposed method has better practicability.

The research is supported by Project of Renovation Capacity Building for the Young Sci-Tech Talents Sponsored by Xinjiang Academy of Agricultural Sciences (No.xjnkq-2020011).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.