Evaluation and Prediction of Agricultural Water Use Efficiency in the Jianghan Plain Based on the Tent-SSA-BPNN Model

Abstract

The Jianghan Plain (JHP) is a key agricultural area in China where efficient agricultural water use (AWUE) is vital for sustainable water management, food security, environmental sustainability, and economic growth. This study introduces a novel AWUE prediction model for the JHP, combining a BP neural network with the Sparrow Search Algorithm (SSA) and an improved Tent Mixing Algorithm (Tent-SSA-BPNN). This hybrid model addresses the limitations of traditional methods by enhancing AWUE forecast accuracy and stability. By integrating historical AWUE data and environmental factors, the model provides a detailed understanding of AWUE’s spatial and temporal variations. Compared to traditional BP neural networks and other methods, the Tent-SSA-BPNN model significantly improves prediction accuracy and stability, achieving an accuracy (ACC) of 96.218%, a root mean square error (RMSE) of 0.952, and a coefficient of determination (R²) of 0.9939, surpassing previous models. The results show that (1) from 2010 to 2022, the average AWUE in the JHP fluctuated within a specific range, exhibiting a decrease of 0.69%, with significant differences in the spatial and temporal distributions across various cities; (2) the accuracy (ACC) of the Tent-SSA-BPNN prediction model was 96.218%, the root mean square error (RMSE) was 0.952, and the coefficient of determination (R²) value was 0.9939. (3) Compared with those of the preoptimization model, the ACC, RMSE, and R² values of the Tent-SSA-BPNN model significantly improved in terms of accuracy and stability, clearly indicating the efficacy of the optimization. (4) The prediction results reveal that the proportion of agricultural water consumption has a significant impact on AWUE. These results provide actionable insights for optimizing water resource allocation, particularly in water-scarce regions, and guide policymakers in enhancing agricultural water management strategies, supporting sustainable agricultural development.

1. Introduction

In the Jianghan Plain (JHP), annual water shortages have reduced crop yields by up to 20% in recent years, highlighting the urgent need for improved agricultural water use efficiency (AWUE). Water resources, as critical inputs for agricultural production, are essential for sustainable food systems. Their efficient use is not only vital for enhancing agricultural productivity but also aligns with global sustainability objectives, particularly those set out in the United Nations Sustainable Development Goals (SDGs), such as SDG 2 (Zero Hunger) and SDG 6 (Clean Water and Sanitation) [1]. Efficient management of water resources is essential for addressing pressing global challenges, such as food security, climate change adaptation, and agricultural resilience. However, regions like the JHP, with its specific climatic and hydrological characteristics, present distinct challenges compared to more temperate or arid zones. While arid regions focus on water conservation and efficient irrigation practices, and temperate regions contend with moderate variability in rainfall, the JHP faces the dual challenge of managing both water scarcity during dry spells and water excess during heavy rainfall, which complicates the development of sustainable agricultural practices. This dynamic requires more nuanced and adaptable water management strategies, making it an ideal case study for regions with similar hydrological variability. With the world’s population projected to exceed 9 billion by 2050, the demand for water resources is increasing, particularly in arid and semi-arid regions where water scarcity poses a major constraint on agricultural productivity [2]. This issue is further exacerbated by climate change, which intensifies the frequency and severity of water-related stresses, further emphasizing the need for effective water use in agriculture. Specifically, China, as the largest developing country globally, utilizes more than 60% of its total water resources for agriculture, facing the challenges of water scarcity and uneven distribution [3]. The JHP, a crucial grain-producing region in central China, faces distinctive agricultural water management challenges that set it apart from other global regions. The area’s vulnerability to frequent natural disasters, such as droughts and floods, combined with significant spatial and temporal variations in water availability, exacerbates the complexity of managing agricultural water resources. Unlike more temperate regions where water availability is relatively stable, the JHP is situated in a semi-humid climate zone with extreme fluctuations in water supply, making it more prone to water scarcity during dry spells and water excess during the rainy season. This unique hydrological variability, coupled with the rapid urbanization and increasing water demand, intensifies the need for efficient water use and targeted management strategies. Consequently, optimizing water resource management in the JHP not only addresses local agricultural and economic challenges but also offers insights applicable to other regions facing similar water stress issues globally. Given the critical importance of water in the region’s agricultural production, the JHP’s unique water management challenges—marked by fluctuating water supply and increasing demand—underscore the urgent need for targeted studies on AWUE. Addressing these challenges through efficient water use is not only vital for ensuring food security and stable agricultural production in the JHP but also serves as a model for other semi-humid and water-scarce regions globally. Consequently, the evaluation and prediction of AWUE in the JHP have both theoretical and practical value for guiding the scientific management and optimization of regional water resources while also offering insights into the sustainable use of water resources in analogous regions worldwide.

AWUE is a measure of the crop yield or economic value that can be produced per unit of water in agricultural production [4]. Conducting an assessment of AWUE facilitates the development and implementation of effective water management strategies, optimizing the utilization of agricultural water resources and enhancing agricultural production efficiency [5]. Recent research on AWUE has relied primarily on total factor measures, utilizing efficiency analysis models such as data envelopment analysis (DEA) [6,7,8], stochastic frontier analysis (SFA) [9,10,11], and Super-Efficiency SBM (SE-SBM) models [12]. For example, Mu et al. utilized the SE-DEA model to measure AWUE levels in municipalities in the Northwest Region [7]; Riera and Bruemmer applied the SFA model to assess AWUE levels in the Krishna River Basin [13]; and Zhi et al. employed the non-directional distance function to evaluate AWUE levels in the Bohai Rim urban agglomeration [14]. However, these models have inherent limitations: DEA fails to account for random errors and is sensitive to the choice of inputs and outputs [15], whereas SFA requires large datasets and assumes constant technical efficiency, which may not be applicable in all settings [16]. The SE-SBM model, also known as the super-efficiency slacks-based measure, is a nonparametric method used to evaluate the efficiency of decision-making units (DMUs), especially in the presence of undesirable outputs. The SE-SBM model, which considers both desired outputs (e.g., crop yield) and undesirable outputs (e.g., carbon emissions), offers a more comprehensive framework for evaluating AWUE, capturing both the economic and the environmental dimensions of agricultural water use [17]. Moreover, it can be adapted to various data structures and scales, making it a versatile tool for assessing AWUE across diverse regions. Consequently, this paper evaluates AWUE and analyzes its temporal and spatial characteristics by constructing an AWUE evaluation index system and selecting the SE-SBM model for scientific assessment.

Conducting predictions of AWUE and establishing a scientific prediction model can provide theoretical support for achieving the sustainable use of water resources [18]. Currently, most predictions related to water use efficiency (WUE) focus on plant growth efficiency [19], water use efficiency [20], and water resource carrying capacity [21], with relatively few studies addressing AWUE. Given the limitations of traditional prediction methods in water resource systems, this paper develops a novel prediction model for AWUE in the JHP, combining the strengths of the SE-SBM model for AWUE evaluation with a BP neural network (BPNN) optimized by the Sparrow Search Algorithm (SSA). The BPNN model, which stands for the backpropagation neural network, is a multilayer feedforward neural network trained through the backpropagation algorithm. The Tent chaotic mapping method is also introduced. Tent chaotic mapping is a type of chaotic mapping that exhibits complex aperiodic behavior through a simple equation and is extremely sensitive to initial conditions, which makes it potentially advantageous in areas such as security and efficient high-power transmission [22]. The SSA is a novel swarm intelligence optimization algorithm inspired by the foraging and anti-predation behaviors of sparrows. It simulates the biological group characteristics of the foraging and anti-predation behaviors of sparrows, aiming at solving the global optimization problem with high precision and high efficiency [23]. This integrated approach addresses the shortcomings of traditional models, enhancing prediction accuracy and stability in complex, nonlinear systems. Currently, common water resource predictions primarily utilize traditional models [24,25], including gray prediction models [26,27] and regression analysis models. Traditional prediction models often lack flexibility when addressing the complexities and dynamics of the real world. While traditional prediction models may yield better results under specific conditions, their accuracy (ACC) often fails to meet satisfactory levels when confronted with the complexities of the real world [28,29]. In complex nonlinear chaotic systems, such as water resource systems, traditional models with linear fitting capabilities exhibit limited explanatory power, leading to suboptimal model fitting and reduced credibility and ACC in carbon emission predictions [30]. To address the limitations of traditional prediction methods, researchers have begun to employ intelligent algorithm models, particularly neural network (NN) models, for water resource system prediction. Neural networks can automatically learn features from raw data, thereby minimizing the need for manual feature engineering. The ability of neural networks to capture and model complex nonlinear relationships is critical in AWUE, as the factors influencing efficiency are typically nonlinear and multivariate [31]. Currently, numerous researchers have conducted NN prediction studies in agriculture [32], industry [33], and energy [34], demonstrating that NN model predictions often outperform traditional linear models. However, there has been no research employing NN for comprehensive AWUE predictions. Possible reasons include the NN model’s tendency to converge to local optima, making ensuring the accuracy and stability of prediction results in complex water resource systems challenging [35]. Additionally, the NN model requires a substantial number of samples for pretraining, whereas water resource accounting typically spans years with fewer data samples, leading to inherent limitations in sample size and reduced confidence in prediction results [36]. By applying an optimized BPNN model, this study aims to significantly improve the accuracy and robustness of AWUE predictions, offering valuable insights for regional water resource management and policy formulation. First, the SE-SBM measures AWUE in the Jianghan Plain, followed by the construction of an NN model on the basis of accounting results and relevant AWUE prediction variables. The NN model is then optimized via the SSA, culminating in the use of the optimized NN for AWUE.

The remainder of this paper is organized as follows. Section 2.1 and Section 2.2 delineates the objects of study and the research area. Section 2.3–Section 2.6 outlines the modeling processes for the SE-SBM method, Tent chaotic mapping, BPNN, k-fold cross-validation, SSA, and Tent-SSA-BPNN. In Section 3, the AWUE of the JHP is measured in detail, and spatiotemporal analysis is conducted via the natural breakpoint method (NBM), standard deviation ellipse (SDE), Moran index (MI), and center of gravity model (CGM). The prediction model subsequently undergoes variable correlation analysis, NN parameter setting and training, comparison of prediction results, NN cross-validation, and performance evaluation. Finally, the validated Tent-SSA-BPNN model is employed to predict the AWUE of the Jianghan Plain. Section 4 and Section 5 provide a discussion of the results and a concise summary. The technological roadmap of this study is presented in Figure 1.

2. Materials and Methods

2.1. Study Area

The JHP is a significant geographic region in China, situated in the central reaches of the Yangtze River and encompassing the south-central part of Hubei Province, which includes areas such as Jingzhou, Xiantao, Qianjiang, and Tianmen. This region is recognized for its fertile land and ample water resources, and it serves as one of China’s key food production bases [37]. The geographical features of the JHP include low, flat terrain; a dense network of rivers; numerous lakes; and plentiful water systems, which create favorable conditions for agricultural development [38,39]. This study focuses on eight city-level administrative divisions, namely, Wuhan, Yichang, Jingmen, Xiaogan, Jingzhou, Xiantao, Qianjiang, and Tianmen (Figure 2).

2.2. Data Sources

The data presented in this paper are primarily derived from eight cities in the JHP for the period 2008–2022, and the study’s data primarily originate from the China Statistical Yearbook, China Water Resources Statistical Yearbook, China Rural Statistical Yearbook, China Environmental Statistical Yearbook, China Carbon Accounting Database, National Bureau of Statistics data, the Statistical Yearbook of the eight cities in the JHP, and the Water Resources Bulletin for the period 2008–2021. The 2008–2022 period was selected because of the availability of consistent and comprehensive data within this timeframe, which allows for the analysis of recent trends and changes in AWUE. Additionally, this period encompasses significant policy developments and climatic events that may have influenced water resource management and AWUE in the Jianghan Plain, thereby providing a relevant context for the study. While these sources are diverse and reputable, it is important to acknowledge potential limitations. Government-published statistics may be subject to reporting biases or inconsistencies due to varying data collection methodologies across different years and regions. Additionally, the use of linear interpolation and linear trend methods to estimate missing data can introduce uncertainties, potentially affecting the reliability of the results. To mitigate these issues, the study employs data validation techniques and sensitivity analyses to assess the robustness of the findings against data quality concerns. Data for certain years remain unpublished due to governmental restrictions, and data for some indicators are absent. The missing data were estimated and interpolated via linear interpolation and linear trend methods.

2.3. Establishing a System of Indicators for Assessing the Efficiency of Water Use in Agriculture

This study establishes an evaluation system for AWUE in the JHP. The data used in this study were collected from official agricultural reports and regional statistics for the period 2008–2022. The dataset covers various regions of the JHP, including both urban and rural areas, and includes data at the provincial level. The spatial resolution of the data is based on administrative boundaries, with annual data being used to evaluate AWUE. The data were pre-processed to remove outliers and missing values, ensuring their reliability for analysis. The data cleaning steps included removing extreme outliers on the basis of agricultural output and water usage thresholds and imputing missing values via interpolation techniques. In previous studies [40,41,42], the following input–output evaluation index system for AWUE was developed, as illustrated in

Table 1. Selected indicators for the evaluation of AWUE.

Primary Indicators	Secondary Indicators	Measurable Indicators
Input	Land	Agricultural land area
	Water Resources Labor	Agricultural water consumption
		Ecological water consumption
	Technological Advancement	Agricultural labor force
	Capital	Total power of agricultural machinery at the end of the year
	Land	Amount of agricultural materials applied
Output	Desired outputs	Gross agricultural output
	Undesired outputs	Carbon emissions from agriculture

.

The following indicators were selected as inputs: the area of major agricultural land as a land input indicator, agricultural water consumption, and ecological water consumption as indicators of water resources, the agricultural labor force as a labor input indicator, the total power of agricultural machinery at the end of the year as an indicator of technological progress, and the number of agricultural materials applied as a capital input indicator. The expected output indicator is the gross value of agricultural output (GVA), which comprehensively reflects the utilization of water resources during agricultural production and is closely related to agricultural economic outcomes. The variables selected for this study were based on key indicators of AWUE, including agricultural land area, agricultural water consumption, and the agricultural labor force. The dataset includes annual data from 2010 to 2022, with each sample representing a specific year for a given region within the JHP. A total of 13 regional units were considered, with multiple samples collected for each region across the years to allow for interannual comparisons. The desired output indicator is the total agricultural output value, which comprehensively reflects the utilization of water resources in agricultural production and is closely related to agricultural economic outcomes, thereby significantly indicating the economic benefits of agricultural water resource use. The non-desired output indicator is total agricultural carbon emissions, defined as the sum of carbon dioxide emissions generated during the agricultural production process [43]. The utilization of total agricultural carbon emissions as a non-desired output indicator enhances the understanding and improvement of agricultural water resource efficiency while also reflecting the ecological effects and environmental impacts of water resource use. This approach supports the goals of sustainable agricultural development and environmental protection. This paper references the agricultural carbon emission formula employed in prior studies [44,45]. The carbon emission estimation formula is as follows:

$$E={\displaystyle \sum E_i}={\displaystyle \sum (T_i}{\delta }_i)$$

(1)

where $E$ represents the total carbon emissions from agriculture, $E_i$ denotes the carbon emissions from various carbon sources, $T_i$ indicates the amount of each carbon source, and ${\delta }_i$ refers to the carbon emission factor for each carbon source. The identified carbon sources include fertilizers, pesticides, agricultural films, diesel fuel, irrigation, and tilling. The agricultural carbon emission coefficients were derived by quantifying and standardizing various carbon emission sources in agricultural activities, with values of 0.8956, 4.9341, 5.18, 0.5927, 20.476 kg/hm², and 312.6 kg/km², respectively.

2.4. Superefficiency Slack-Based Measure Model (SE-SBM)

The super-efficiency slack-based measure model (SE-SBM) is a nonparametric method for evaluating the efficiency of decision-making units (DMUs) that account for undesirable outputs [46]. The SE-SBM model is a robust tool for evaluating efficiency; by incorporating the concept of super-efficiency, it can distinguish efficiency differences between decision-making units more precisely, thereby providing a refined basis for decision-making [47]. The SE-SBM model was implemented via Python 3.7 with the pyDEA library for efficiency analysis. The model was run on a computer with an Intel i7 processor and 16 GB of RAM. The SE-SBM model is expressed as follows:

$${\phi }_{k_t}=\min {\displaystyle \frac{1/m{\displaystyle {\sum }_{i=1}^m(\overline{x}/x_{ik})}}{1/(s1+s2)({\displaystyle {\sum }_{p=1}^{s_1}\overline{y^d}/{y_{pk}}^d+{\displaystyle {\sum }_{q=1}^{s_2}\overline{y^u}/{y_{qk}}^u)}}}}$$

(2)

$$\overline{x}\ge {\displaystyle \sum _{j=1,\ne k}^n{x}_{ij}{\lambda }_j};\overline{y^d}\ge {\displaystyle \sum _{j=1,\ne k}^n{y_{pj}}^d{\lambda }_j};\overline{y^u}\ge {\displaystyle \sum _{j=1,\ne k}^n{y_{qj}}^u{\lambda }_j}$$

(3)

$${\displaystyle \sum _{j=1,\ne k}^n{\lambda }_j}=1,{\lambda }_j\ge 0$$

(4)

$$\overline{x}\ge x_{ik};\overline{y^d}\le {y_{pk}}^d;\overline{y^u}\le {y_{qk}}^u$$

(5)

$$j=1,...,n(j\ne k);p=1,...,s1;q=1,...,s2;i=1,...,m$$

(6)

where ${\phi }_{k_t}$ represents the AWUE of the k-th DMU in the t-th period. If ${\phi }_{k_t}$ < 1, the decision-making unit is deemed inefficient; if ${\phi }_{k_t}$ ≥ 1, the unit is considered effective. A larger value of ${\phi }_{k_t}$ < 1 indicates higher efficiency. Here, ${\mathrm{x}}_{\mathrm{ik}}$, ${\mathrm{y}}_{\mathrm{pk}}^{\mathrm{d}}$, ${\mathrm{y}}_{qk}^u$, and ${\lambda }_j$ denote the i-th input, p-th desired output, q-th non-desired output, and j-th linear combination coefficient of the k-th DMU, respectively.

2.5. The Tent-SSA-BP Model

The Tent-SSA-BP model integrates three distinct methods: Tent chaotic mapping, the SSA, and the back propagation neural network (BPNN). The model was developed in two key phases. In the first phase, Tent chaotic mapping was employed to initialize the population for the SSA due to its ability to enhance search diversity and avoid local optima. Tent chaotic mapping is a form of chaotic system that exhibits sensitive dependence on initial conditions, making it highly effective for global optimization tasks where avoiding local minima is critical. Previous research has shown that chaotic systems like Tent mapping are capable of providing more diverse and evenly distributed initial populations, which can improve the convergence rate and overall performance of optimization algorithms [48]. Furthermore, the chaotic nature of Tent mapping is particularly suited for complex, nonlinear problems such as the AWUE prediction, where traditional initialization methods might fail to explore the solution space effectively [49]. The second phase involved optimizing the BPNN through the SSA, where the network weights and biases were adjusted iteratively on the basis of the search results of the SSA. The BPNN’s performance was evaluated via a training dataset from 2010 to 2020, and model testing was conducted with data from 2021 to 2022. This model optimizes the weights and biases of the BPNN through the introduction of Tent chaotic mapping, whereas the population dynamics of the SSA further enhance the optimization of network parameters. By synthesizing the strengths of these three methodologies, the model aims to enhance the performance of the BPNN in regression prediction tasks. The computations for optimization and prediction via the Tent-SSA-BPNN model were carried out in MATLAB R2020a with custom scripts developed for model training and evaluation. The training process was executed on a system with an NVIDIA GTX 1080 GPU to accelerate the training of the neural network.

2.5.1. BPNN (Back Propagation Neural Network)

The BPNN is a neural network (NN) model that is trained via a backpropagation algorithm [50]. The model maps input data to output data through connections and computations among multiple layers of neurons, adjusting the weights and biases during training via the backpropagation algorithm to minimize the error between the predicted and actual outputs [51].

2.5.2. Selection of Variables

The selection of variables for predicting AWUE efficiency was based on several criteria. First, the predictor variables must be representative of the key factors influencing agricultural water use efficiency in the JHP. The selected variables include per capita water resources (WRPCs), the share of surface water supply (SCWS), and the share of agricultural water consumption (SAWC). These variables were chosen because they directly reflect the availability of water resources and the allocation of water between agricultural and other uses, which are crucial determinants of AWUE in the region. Additionally, these indicators are easily accessible from reliable governmental data sources, enhancing the credibility and accuracy of the model. The correlation between these variables and AWUE has been validated in previous studies, which demonstrated their importance in explaining variations in agricultural water use efficiency [52]. Furthermore, the number of predictor variables should be limited, as the sample size for AWUE efficiency is relatively small, and an excessive number of variables may lead to underfitting or overfitting of the model. Consequently, this paper proposes the use of three indicators, per capita water resources (WRPCs), the share of surface water supply (SCWS), and the share of agricultural water consumption (SAWC), as predictor variables for constructing the BPNN. To verify the rationale for selecting per capita water resources of the JHP, SCWS relative to total water supply, and SAWC with respect to total water consumption as input variables, it is essential to analyze the correlation between these input variables and the output variables. The Spearman correlation coefficient method serves as a nonparametric measure of correlation, assessing the relationship between the ranks of two variables rather than the actual values of the variables [53,54]. This method is particularly applicable when the data do not conform to a normal distribution or when the data are hierarchical. Spearman’s correlation coefficient is calculated as follows:

$$R=1-{\displaystyle \frac{6{\displaystyle \sum _{i=1}^n{D}^2}}{n(n^2-1)}}$$

(7)

where R represents the Spearman correlation coefficient, D denotes the difference in rank between each pair of data, and n indicates the total number of samples. The values of R range from −1 to 1, where R = 1 indicates a perfect positive correlation, R = −1 signifies a perfect negative correlation, and R = 0 denotes no correlation.

To mitigate the effects of multicollinearity among variables, it is essential to analyze the correlation between the input variables [55]. The variance inflation factor (VIF) method is employed to measure the degree of covariance among the variables, and it is calculated as follows [56,57]:

$$x_1={\beta }_0+{\beta }_1{x}_2+{\beta }_2{x}_3$$

(8)

$$VIF={\displaystyle \frac{1}{1-R^2}}$$

(9)

where VIF represents the variance inflation factor, x₁ denotes variable 1, x₂ denotes variable 2, x₃ denotes variable 3, and R² indicates the coefficient of determination.

2.5.3. Selection of Evaluation Indicators

Evaluating the predictive effectiveness of neural networks (NNs) typically involves several metrics that provide a comprehensive overview of the model’s performance [58]. The evaluation metrics selected in this paper include accuracy (ACC), the root mean square error (RMSE), and the coefficient of determination (R²). The ACC measures the accuracy of a classification model’s predictions, indicating the proportion of samples correctly classified by the model [59]. The RMSE quantifies the predictive accuracy of a regression model by calculating the square root of the mean of the squared differences between the model’s predicted and actual values [60]. The coefficient of determination (R²) assesses the goodness-of-fit of a regression model, indicating how well the model explains the variability in the data [61]. The formulas for the three indicators are presented below:

$$\mathrm{ACC}=1-{\displaystyle \frac{100\%}{n}}{\displaystyle \sum _{i=1}^n\left|\frac{y_i-\widehat{y_i}}{y_i}\right|}$$

(10)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2}}$$

(11)

$$R^2={\displaystyle \frac{{\left(n{\displaystyle \sum _{i=1}^n{y}_i}\cdot \widehat{y_i}-{\displaystyle \sum _{i=1}^n{y}_i}\cdot {\displaystyle \sum _{i=1}^n\widehat{y_i}}\right)}^2}{\left[n{\displaystyle \sum _{i=1}^n{\widehat{y_i}}^2}-{\left({\displaystyle \sum _{i=1}^n\widehat{y_i}}\right)}^2\right]\times \left[n{\displaystyle \sum _{i=1}^n{y}_i^2}-{\left({\displaystyle \sum _{i=1}^n{y}_i}\right)}^2\right]}}$$

(12)

where n represents the sample size of the dataset, $y_i$ denotes the true value of the i-th sample, and $\widehat{y_i}$ indicates the predicted value of the i-th sample.

2.6. Optimizing BP Neural Network Methods

2.6.1. K-Fold Cross-Validation (KFCV)

Given the limited sample size for AWUE prediction, it is necessary to enhance the training and test set samples by dividing the dataset via k-fold cross-validation (KFCV) [62]. KFCV is a statistical technique utilized for evaluating and comparing the performance of machine learning models. This technique divides the dataset into K equal-sized subsets, each of which serves as a test set in turn, while the remaining K − 1 subsets constitute the training set. This process is repeated K times, with each iteration selecting a different subset as the test set [63]. Ultimately, the results of the K evaluations are averaged to derive an estimate of model performance. KFCV is a robust model evaluation technique that yields more accurate and reliable predictive models for AWUE through extensive training and validation.

2.6.2. Traditional SSA

Traditional back propagation neural networks (BPNNs) encounter issues such as local optimization, vanishing or exploding gradients, prolonged training times, and challenges in structure selection [64]. The SSA is a group intelligence optimization technique that simulates the foraging and antipredation behaviors of sparrows. The core principle of the SSA is to leverage interactions and information sharing among individuals in a group to increase search efficiency and identify the global optimal solution. The traditional SSA is defined as follows:

Step 1: Initialization. Randomly generate the positions of a flock of sparrows, each representing a potential solution.

Step 2: Fitness assessment. The fitness value for each sparrow is calculated, typically on the basis of an objective function.

Step 3: The leader (producer) updates. The leader updates its position according to the following formula:

$$X_{i,j}^{t+1}=\left\{\begin{array}{ccc}Q\cdot e^{{\displaystyle \frac{X_{uorst}^t-X_{i,j}^t}{t^2}}}\hfill & \mathrm{if}i>{\displaystyle \frac{n}{2}}\hfill & \hfill \\ X_P^{t+1}+\parallel X_{i,j}^t-X_P^{t+1}\parallel \cdot A^{+}\cdot L\hfill & \mathrm{otherwise}\hfill & \hfill \end{array}\right.$$

(13)

where $X_{worst}$ represents the current worst position, $X_P$ denotes the leader’s position, A is a random matrix, $A^{+}$ is the pseudoinverse of A, and L indicates the learning factor.

Step 4: Followers (joiners) update. The followers adjust their positions on the basis of the leader’s location.

$$X_{i,j}^{t+1}=X_{best}^t+\beta \cdot \Vert X_{i,j}^t-X_{best}^t\Vert$$

(14)

where $X_{best}$ represents the current global optimal position and where $\beta$ denotes the step control parameter.

Step 5: Update (Sparrow that Perceives Danger). When sparrows detect a potential threat, they adopt an avoidance strategy, and the formula for updating their position is as follows:

$$X_{i,j}^{t+1}=X_{i,j}^t+k\cdot \left({\displaystyle \frac{\Vert X_{i,j}^t-X_{worst}^t\Vert }{(f_i-f_w)+\epsilon }}\right)$$

(15)

where k represents a random number, $f_i$ denotes the current sparrow fitness value, $f_w$ indicates the worst fitness value, and $\epsilon$ is a small constant introduced to avoid division by zero.

Step 6: Iteration. Repeat Steps 2–5 until the stopping conditions are met, such as reaching the maximum number of iterations or achieving satisfactory solution quality.

Step 7: Output the optimal solution. After the algorithm, the optimal solution is identified.

2.6.3. Optimizing the SSA

To enhance the diversity and homogeneity of the initialized population, Tent chaotic mapping is employed for population initialization [65]. Integrating Tent chaotic mapping into the sparse search algorithm (SSA) can significantly enhance the diversity and search capability of the algorithm, particularly in avoiding local optima and improving the global search efficiency [66]. To further increase the global optimization accuracy (ACC) of the algorithm, perturbations are introduced to the positions of individuals with varying fitness levels: for individuals with higher fitness, Gaussian variation [67] is applied for position adjustment; for individuals with lower fitness, Tent perturbation [66] is utilized for position adjustment.

The Tent chaotic mapping, which has been successfully applied in optimization tasks [68], is formulated as follows:

$$x_{n+1}=\left\{\begin{array}{ll}r\cdot x_n\hfill & \mathrm{if}{x}_n<0.5,\hfill \\ r\cdot (1-x_n)\hfill & \mathrm{if}{x}_n\ge 0.5,\hfill \end{array}\right.$$

(16)

where r is a chaos parameter that typically assumes values between 2 and 4, $x_n$ represents the current iteration value, and $x_n$ takes values between 0 and 1.

The Gaussian variation is calculated as:

$$X_{new}=X_{old}+N(\mu ,{\sigma }^2)$$

(17)

$X_{new}$ is the new individual after mutation. $X_{old}$ is the original individual, and $N(\mu ,{\sigma }^2)$ is a normally distributed random value with a mean of $\mu$ and a variance of ${\sigma }^2$. The mean and variance are equivalent to those of the original individual.

To address the challenges of the SSA, Tent chaotic mapping, Gaussian variation, and Tent perturbation are sequentially introduced for enhancement, resulting in specific implementation steps for the improved Tent-SSA. The specific steps include parameter setting, initialization, population division, position updating, recalculation, position perturbation, and information output. On the basis of the aforementioned strategy of the improved SSA, the traditional BPNN is optimized to enhance its convergence performance and global search capability, thereby improving the ACC and stability of AWUE prediction. The overall flow of the optimized BPNN model (Tent-SSA-BPNN) incorporating the improved SSA is illustrated in Figure 3.

3. Results

3.1. Spatio-Temporal Analysis of AWUE in the JHP

3.1.1. Changes in the Time Dimension of AWUE in the JHP

In this study, the SE-SBM model was employed to construct the global frontier surface, and the AWUE values of the JHP from 2010 to 2021 were calculated via MATLAB 2022 software. Seven representative years were selected for analysis: the efficiency values and their averages across the JHP for 2010, 2012, 2014, 2016, 2018, 2020, and 2022 (Figure 4).

Figure 4 shows the time-varying trends of AWUE in the JHP from 2010 to 2022. The average AWUE value fluctuated within a specific range, with a decrease of 0.69% over the study period. Yichang City presented the highest mean AWUE value of 1.394, indicating more efficient use of agricultural water, whereas Tianmen City presented the lowest mean AWUE value of 0.464, suggesting room for improvement in water resource utilization. As a vital rice production region in China, AWUE in the JHP has significant implications for demonstration and guidance. The results derived from the SE-SBM model indicate that AWUE in the JHP exhibited an overall fluctuating trend during the study period, with no clear monotonic increase or decrease. An increase in AWUE necessitates a balance among various factors. For example, technological advancements may enhance water use efficiency; however, they often require increased investment in resources and capital. Consequently, AWUE may exhibit fluctuating trends due to trade-offs among various factors.

3.1.2. Spatial Dimensions of AWUE in the JHP

Spatial Distribution of AWUE in the JHP Under the NBM

To intuitively analyze the changes in the spatial distribution of AWUE across cities, the results were visualized via the natural breakpoint grading method [69] in ArcGIS 10.4, as shown in Figure 5. Employing the NBM alongside prior studies [70,71], AWUE is classified into five categories: I (Optimal Efficiency Class), II (High-Efficiency Class), III (Moderate Efficiency Class), IV (Low-Efficiency Class), and V (Extremely Low-Efficiency Class).

Among the cities, Yichang City exhibited relatively high water resource efficiency during the study period, whereas Tianmen City and the mean value were lower. The spatial patterns of AWUE in cities such as Wuhan, Yichang, and Xiaogan showed consistent year-to-year improvements, reflecting effective water management practices. In contrast, the cities of Jingmen and Jingzhou presented more fluctuating trends, which may be influenced by regional factors such as changes in agricultural practices or climate conditions. Yichang City maintained relatively high water resource efficiency throughout the study period and ranked first in most years. Between 2018 and 2021, Wuhan demonstrated greater AWUE and implemented more effective water management measures, including water allocation, usage quotas, monitoring, and management strategies, to ensure efficient agricultural water use [72]. In Yichang City, AWUE has gradually increased in recent years, reflecting improvements in water management practices. However, the decline observed in 2021 highlights the importance of consistent agricultural management practices, as changes in irrigation methods or farming techniques can influence water use efficiency [73]. The average values for Jingmen and Xiaogan remain relatively stable but declined in 2021, possibly due to unusual climatic events, such as reduced rainfall leading to drought in some areas or increased flooding temperatures [74]. AWUE in Jingzhou and Xiantao exhibited significant fluctuations, which may be attributed to changes in agricultural structure and cultivation patterns. These adjustments, such as shifts in crop types and farming practices, have a direct impact on the efficiency of agricultural water use in these regions. In 2018, Jingzhou City implemented the “Rural Revitalization” plan, resulting in changes to the planting structure, including a decrease in the area allocated for grains, oilseeds, and cotton, alongside an increase in the area designated for melons, fruits, and vegetables. Concurrently, Jingzhou City has promoted regenerative rice planting and an integrated rice-farming model, and by 2020, the area designated for the “shrimp and rice co-crop” farming model is expected to expand further. Similarly, Xiantao City is adjusting its agricultural structure and planting patterns, promoting agricultural industrialization, and increasing the area allocated for vegetable facilities, integrated farming, and aquaculture [75,76]. The averages for Qianjiang City and Tianmen City also fluctuated over the years, but the overall trend remained relatively stable. However, the city of Qianjiang significantly increased in 2021, with technological advancements and improved management likely playing a crucial role [77].

Spatial Differentiation Analysis of AWUE in the JHP via the SDE Method

By utilizing the AWUE measurement results in the JHP from 2010 to 2022, this study explores the spatial distribution of AWUE through the application of the SDE method [78]. SDEs visualize the spatial distribution characteristics of data by calculating the mean center, standard deviation, and rotation angle of a dataset to generate an ellipse [79]. This study uses the latitude and longitude coordinates of eight prefecture-level cities in the JHP, employing the AWUE of each city as weights. The SDE model calculates the center of gravity coordinates, the standard deviations of the long and short semi-axes, and the rotation angle to thoroughly analyze the spatial distribution direction of AWUE, its dynamic characteristics, and the degree of discretization within the JHP. The center coordinates of the SDE for each year in the JHP were calculated Via ArcGIS 10.4 software, and the parameters were compiled into a summary table (Figure 6).

By utilizing the six data points presented in Figure 6, this analysis examines the spreading, orientation, and shape characteristics of the elliptical difference. Analyzing the spreading characteristics, the area of the ellipse from 2010 to 2022 initially increased but then decreased, rising from 238.85 million square kilometers in 2010 to a peak of 264.33 million square kilometers in 2012 before gradually declining to 261.15 million square kilometers in 2022. This change suggests that AWUE in the JHP exhibited a trend of agglomeration and growth in the early years but began to optimize from 2012 onward, reflecting a reduction in the degree of agglomeration. In terms of directional characteristics, the rotation angle of the center point decreased from 81.51° in 2010 to 80.66° in 2022, indicating a weak counterclockwise rotation trend; thus, the direction of AWUE in the JHP remains relatively stable, primarily oriented along the “northeast–southwest” axis. With respect to shape characteristics, as illustrated in Figure 7, the ellipse exhibits a more pronounced expansion in the X direction, whereas the change in the Y direction is relatively minimal. The minor change in the rotation angle suggests a slight alteration in the directional trend, indicating that the ellipsoid shape becomes more balanced and “rounded”, reflecting a weakening of the directional trend.

The Centroidal Geometry Method (CGM) is utilized to analyze the characteristics of spatial distribution within the regional economy by calculating the weighted average position of economic activities across subregions, thereby determining the centroid of these activities [80,81]. This model effectively reflects trends in spatial concentration and changes in the distribution of economic activities, serving as a robust tool for research on regional economic development, planning, and policy formulation. This study aims to explore the spatial center characteristics of AWUE in the JHP from 2010–2021 via economic CGM and to analyze the trajectory of the center of gravity to understand the evolutionary trends and development gaps in the spatial layout of AWUE.

Using ArcGIS 10.4, the center of gravity of AWUE in the JHP from 2010 to 2022 was plotted, revealing that the center of gravity consistently remained in Tianmen City. The migration trajectory indicates that AWUE has exhibited cyclical and unstable changes over the past few years, along with notable development gaps. The migration trajectory further illustrates that AWUE has exhibited cyclical and unstable changes in recent years, highlighting a development gap, with an overall trend of movement toward the southeast. The specific migration trajectory is as follows: Northwest China (2010–2012) → East China (2012–2014) → Northwest China (2014–2016) → Southwest China (2016–2020) → Southeast China (2020–2022).

Spatial Correlation Analysis Based on Moran’s Index (MI) Approach

This study employed the MI [82] to assess both the global and local spatial correlations of AWUE in the JHP. The global MI of AWUE in the JHP was calculated, and the results are presented in

Table 2. Global MI analysis of AWUE in the JHP.

Year	2010	2012	2014	2016	2018	2020	2022
Moran’I	−0.248	0.439	0.053	0.113	0.067	−0.128	0.061
Z	−0.446	2.011	0.622	1.084	0.674	0.063	0.864
P	0.328	0.05	0.213	0.139	0.225	0.475	0.194

. With respect to the changes in global MI values, the values for the JHP exhibited volatility from 2010 to 2021. The MI value of −0.091 in 2010 indicates a slight negative spatial correlation, whereas the values for 2012, 2016, and 2021 are 0.439, 0.601, and 0.117, respectively, reflecting positive spatial correlations in these years and denoting areas of high AWUE. In terms of time series trends, the MI values for the JHP demonstrate significant volatility. For example, the higher positive values in 2012 and 2016 signify strong spatial aggregation, whereas the negative value in 2020 denotes spatial dispersion. The Z values of 2.011 and 2.123 for 2012 and 2016, respectively, reached significance, indicating that spatial aggregation was statistically significant during these years. In contrast, the Z values for other years were lower, suggesting that spatial aggregation was not significant. The p values of 0.050 for 2012 and 0.029 for 2016 were below or close to the traditional significance level of 0.05, further supporting the conclusion that spatial aggregation was significant. Higher p values in other years reflected weaker statistical significance. The spatial correlation in the JHP exhibited a dynamic trend, suggesting that the spatial distribution and interaction of AWUE may have been influenced by various factors in different years.

The localized MI offers insights into the local characteristics of spatial data related to AWUE in the JHP, providing a foundation for further spatial analysis and decision-making. Using the Geoda platform, scatter plots of the Moran index for AWUE in the JHP were generated for the years 2012 and 2016 (Figure 8). The analysis of Figure 8 reveals that the Moran scatter plot of AWUE in the JHP is primarily distributed in the first and third quadrants, demonstrating clustering characteristics among regions with similar AWUE levels. This suggests that certain areas of the JHP effectively manage and utilize agricultural water resources, leading to regions with efficient water use. The scatter points in the third quadrant are primarily clustered around regions that efficiently utilize agricultural water resources, indicating a spatial correlation among these areas, which is likely attributable to similar resource allocation, policy measures, or agricultural production structures. While a limited number of scatter points are found in the second quadrant, this may indicate areas with inefficient AWUE that necessitate further management and improvement.

The quadrants corresponding to each province are plotted in the scatterplot of the MI for 2012 and 2022, presented in

Table 3. Quadrant table of prefecture-level cities in the JHP.

Quadrant	First Quadrant	Second Quadrant	Third Quadrant	Fourth Quadrant
2012	Wuhan, Tianmen	Jingzhou, Jingmen, Yichang	Xiantao	Qianjiang, Xiaogan
2016	Jingzhou	Wuhan, Yichang	Xiantao, Qianjiang, Tianmen	Jingmen, Xiaogan
2020	Qianjiang, Xiaogan	Wuhan, Jingzhou, Jingmen	Tianmen	Xiantao, Yichang
2022	Jingmen	Wuhan, Jingzhou	Xiantao, Tianmen	Yichang, Xiaogan, Qianjiang

. Cities are classified into distinct quadrants on the basis of their spatial relevance. In 2012, Wuhan was situated in the first quadrant (high–high), while Jingzhou, Jingmen, and Yichang occupied the second quadrant (low–high); Xiantao, Qianjiang, and Tianmen were placed in the third quadrant (low–low), and Xiaogan was found in the fourth quadrant (high–low). By 2016, Wuhan and Jingzhou continued to occupy the first quadrant; however, Jingmen, Xiaogan, Yichang, and Wuhan had transitioned to the second quadrant, whereas Tianmen, Qianjiang, and Xiantao remained in the third quadrant. This distribution indicates that reverse agglomeration has emerged as a predominant factor, alongside significant spatial differences.

3.2. Predictive Analysis of AWUE in the JHP via the Tent-SSA-BPNN

3.2.1. Correlation Analysis

In this study, three indicators were selected as predictor variables: water resources per capita (WRPC), the share of surface water supply (SCWS), and the share of agricultural water use (SAWC). To verify the rationality of selecting per capita water resources, SCWS in total water supply, and SCWS in total water use as input variables, it is essential to analyze the correlation between these input variables and the output variables. The Spearman correlation coefficient method was used to calculate the correlation between the three indicators and AWUE; the results are presented in

Table 4. Correlation analysis table.

Indicator	Correlation Coefficient	Significance	Sample Size
WRPC	0.402	0.122	13
SCWS	0.822 ***	0	13
SAWC	0.909 ***	0	13

“***” represents the highest level of statistical significance, usually indicating a p-value less than 0.001.

. Table 4 indicates that AWUE in the JHP is correlated with SCWS.The correlation coefficients of 0.822 and 0.903 for SCWS and SAWC, respectively, are significant at the 1% level, indicating a strong correlation between AWUE in the JHP and both SCWS and SAWC. Thus, SCWS and SAWC, as input variables, effectively reflect changes in AWUE efficiency in the JHP. The correlation coefficient between AWUE and WRPC in the JHP is 0.473, whereas the correlation coefficient between AWUE and WRPC is 0.402, indicating a moderate correlation [83]. Although WRPC demonstrates a significant correlation, given the limited number of selected variables and its potential impact on the water resource status in actual production activities, this variable is retained as an input variable.

The variance inflation factor (VIF) method was employed to calculate the variance inflation factors (VIFs) for WRPC, SCWS, and SAWC in the JHP; the results are presented in

Table 5. Variable variance inflation factor analysis.

Indicator	VIF	Sample Size
WRPC	6.772	13
SCWS	6.521	13
SAWC	4.105	13

. The variance inflation factors for the three indicators are less than 10, indicating a weak correlation among the input variables and suggesting that the multicollinearity effect can be disregarded [84]. Consequently, these three indicators can serve as independent variables for predicting AWUE in the JHP, making the NN prediction model constructed with WRPC, SCWS, and SAWC a viable approach.

3.2.2. Model Parameter Setting and Training

The dataset was randomly divided into five mutually exclusive subsets, each containing sample sizes of 2, 2, 3, 3, and 3, totaling 13 samples. In each iteration, a different subset is designated as the test set, while the remaining four subsets serve as the training set; this process is repeated five times. The input variables include WRPC, SCWS, and SAWC, whereas the output variable is AWUE in the JHP; all the data are normalized before analysis. The new function is utilized to establish the BPNN; the activation functions for the hidden layer and output layer are the Tansig and Purelin functions, respectively, and the training algorithm employs the trail function, which integrates the gradient descent method with the Gauss–Newton method. Given the small sample size, the NN is configured with a single hidden layer, and the number of neurons in this layer is determined by traversing the empirical interval [85,86], where n1 represents the number of input variables, and n2 denotes the number of output variables. In conjunction with previous research, the maximum number of training epochs for the NN is set to 100, with a learning rate of 0.01. Additionally, the individual size of the sparrow population in the SSA is established at 100, the number of iterations is set to 20, the proportion of discoverers is 60%, the proportion of vigilantes is 20%, and the early warning threshold is 0.6. Training and prediction are conducted following the completion of the model setup according to the aforementioned parameters.

3.2.3. Model Training Prediction Results

The error iteration convergence process of the Tent-SSA-BPNN model is illustrated in Figure 9. Analysis reveals that during the 1st to 6th iterations, the error convergence speed is rapid; from the 6th to the 14th iterations, this speed slows down and approaches stability because the model becomes trapped in a local optimal solution, resulting in decreased convergence performance. From the 14th to the 19th iterations, the error decreases rapidly, and after 20 iterations, it stabilizes and no longer changes, indicating that the model has reached the global optimal solution. Overall, the Tent-SSA-BPNN model rapidly completes the iterative error convergence process, indicating its strong convergence performance. Furthermore, the Tent-SSA-BPNN model effectively escapes local optimal solutions, highlighting its robust global search optimization capability.

The prediction results and relative errors of the Tent-SSA-BPNN model for AWUE in the JHP are presented in

Table 6. Variance inflation factors.

Year	Real Value	Predicted Value	Relative Error Values
2010	0.910	0.898	1.319
2011	0.885	0.869	1.808
2012	0.829	0.832	0.362
2013	0.898	0.889	1.002
2014	0.869	0.873	0.460
2015	0.851	0.842	1.058
2016	0.830	0.822	0.964
2017	0.854	0.839	1.756
2018	0.897	0.888	1.003
2019	0.985	0.995	1.015
2020	1.113	1.121	0.719
2021	0.877	0.885	0.912
2022	0.869	0.874	0.575

, which indicates that the maximum relative error between the predicted and actual values is 1.808%, whereas the minimum relative error is 0.362%, and the average relative error is 0.996%. The prediction error of the Tent-SSA-BPNN model for AWUE in the JHP is significantly less than 5%, indicating that the model has high prediction accuracy. Figure 10 shows the model prediction fitting plot. The scatter points of the predicted and actual values are closely clustered around the trend line, with a correlation coefficient of 0.98851, indicating a strong correlation between the predicted and actual values and a high degree of model fit.

3.2.4. NN Cross-Validation

Owing to the inherent limitations of AWUE prediction stemming from the small sample size, the results of individual predictions may be contingent and unconvincing. To increase the credibility of the AWUE prediction results, 5-fold cross-validation (FFCV) is employed to evaluate the indicators of the Tent-SSA-BPNN model. Each data point in the dataset is utilized as both training and test data for multiple validations, compensating for the limitations posed by the small sample size in predicting agricultural carbon emissions. The results of the FFCV are presented in

Table 7. Results of FFCV.

I (Fold)	R2	ACC	RMSE	Average R2	Average ACC	Average RMSE
1	0.9931	95.52	0.85	0.9939	96.218	0.952
2	0.9924	94.49	0.87
3	0.9947	96.68	0.69
4	0.9955	96.92	1.15
5	0.9938	97.48	1.2

. The FFCV evaluation of the tent-SSA-BPNN model for AWUE in the JHP yielded an accuracy (ACC) of 96.218% and a root mean square error (RMSE) of 0.952, indicating that the discrepancies between the predicted values and the actual values obtained by the model across different training and test sets are minimal, affirming the model’s predictive capability for AWUE. The R² value derived from the FFCV of the model is 0.9939, indicating a strong correlation between the predicted and actual values. These findings suggest that the model has excellent fitting ability across different training and testing sets, confirming that the Tent-SSA-BPNN model is a reliable and stable predictor of AWUE.

3.2.5. Model Performance Comparison

To further validate the predictive efficacy of the Tent-SSA-BPNN model, the results from multiple runs of the Tent-SSA-BPNN were compared with those from the BPNN model, the SSA neural network model (SSA-BPNN), and another widely used optimization algorithm, the gray wolf algorithm neural network (GWO-BPNN) [87], on the AWUE dataset in the JHP. The accuracy (ACC), root mean square error (RMSE), and R² values for each model after five runs are presented in Figure 11.

Analysis of Figure 11 reveals that the fluctuation range of accuracy (ACC), root mean square error (RMSE), and R² for the BPNN is relatively large, indicating significant instability in the BPNN’s prediction results for AWUE. The robustness of the BPNN is inadequate. In contrast, the stability of the ACC, RMSE, and R² for the NNs optimized by the single SSA or GWO algorithms is significantly greater than that of the BPNN, highlighting the necessity of algorithmic optimization for the BPNN. Compared with the aforementioned models, the performance of the Tent-SSA-BPNN model has further improved, achieving an ACC of 95% or above, an RMSE of 1.2 or below, and an R² value of 0.99 or above, significantly outperforming the NNs optimized by single algorithms. This demonstrates that the global search capability and optimization accuracy of the Tent-SSA-BPNN model have been greatly enhanced, enabling it to identify the global optimal solution of the objective function accurately, thereby improving the optimization effect of the SSA on NN performance. The Tent-SSA-BPNN model is characterized by strong stability, accuracy (ACC), and robustness, significantly enhancing the reliability of AWUE prediction and demonstrating excellent capability in carbon emission prediction.

3.2.6. Prediction of AWUE in the JHP

Following the validation of the Tent-SSA-BPNN model, the AWUE in the JHP was predicted, thereby providing a theoretical foundation for the formulation of a rational AWUE policy. The trends of WRPC, SCWS, and SAWC are projected for the next five years. Analyzing the trends of these three indicators from 2010 to 2022, the average annual change rates for WRPC, SCWS, and SAWC were found to be 15.57%, 19.57%, and 8.55%, respectively. Using the average rates of change, future values for the three indicators were established under two scenarios: a continuous increase and a continuous decrease. This yields eight combinations of the three indicators. The Tent-SSA-BPNN model was utilized to predict these eight scenarios, with the findings illustrated in Figure 12.

The eight preset scenarios are visually represented, with “+” indicating an increasing factor, “−” indicating a decreasing factor, and three distinct symbols denoting WRPC, SCWS, and SAWC. As illustrated in Figure 12, when the values of the three indicators—WRPC, SCWS, and SAWC—continuously increase or decrease (i.e., “+ + +“ and “− − −”), the value of AWUE increases or decreases correspondingly. When SAWC, along with the other two indicators, continuously increases or decreases (i.e., “+ + +” and “− − −”), AWUE correspondingly reflects these changes. Specifically, when “+ + +” and “− − −” are present, AWUE will demonstrate an increasing or decreasing trend, indicating a positive correlation between the values of the three indicators and AWUE. By comparing “+ + +” with “- + +”, “+ − +”, and “+ + −” and analyzing scenarios in which one indicator decreases while the others increase, it is evident that when SAWC continuously decreases, AWUE tends to decrease; when SCWS continuously decreases, AWUE remains stable; and when WRPC continuously decreases, AWUE initially increases before stabilizing. This suggests that SAWC positively influences the AWUE value in the JHP. These findings indicate that SAWC exerts the most significant influence on AWUE, whereas WRPC has the least impact on AWUE in the JHP. By comparing “− − −” with “+ − −” and “− + −” with “− − +”, the continuous increase in one indicator while the other two indicators remain constant is analyzed. When WRPC continuously increases, the AWUE value tends to stabilize; when SAWC continuously increases, AWUE first stabilizes and then increases; and when SCWS continuously increases, AWUE tends to decrease. This finding reinforces the conclusion that SAWC significantly influences AWUE in the JHP. The results of “+ − +” and “+ − −”, as well as “− +” and “− +”, are summarized in the following table, which compares “+ − +” with “+ − −”, “− +” with “+ + −”, and “+ + −” with “+ − −”. By analyzing the differences between scenarios in which two indicators decline compared with scenarios where one indicator declines, it is evident that the overall AWUE value decreases more significantly when two indicators decline. Furthermore, as long as SAWC declined, the overall AWUE value demonstrated a downward trend. By comparing “+ + +” with “− + +”, “+ − −” with “+ + +”, and “+ − −” with “− − +” to analyze the effects of WRPC and SCWS on AWUE values, when SCWS increases and WRPC decreases, the AWUE value is greater than when WRPC increases and SCWS decreases, indicating that SCWS exerts a more significant effect on AWUE than WRPC does, which is consistent with the conclusions drawn in the previous section.

In summary, the degree of influence of the three indicators on AWUE in the JHP is ranked as follows: SAWC > SCWS > WRPC, with SAWC exerting the most significant influence. This underscores the importance of optimizing agricultural water management, improving irrigation efficiency, and minimizing water waste. Effective agricultural water management not only improves agricultural productivity but also positively affects the overall sustainable use of water resources.

4. Discussion

This study aimed to evaluate and predict AWUE in the JHP, addressing key research questions related to the spatial and temporal variations in AWUE and the performance of predictive models. The SE-SBM model was employed for AWUE calculations, whereas the improved Tent-SSA-BPNN model was utilized to predict AWUE trends. Our findings provide insights into the spatial disparities in AWUE across different cities and demonstrate the effectiveness of the Tent-SSA-BPNN model in improving prediction accuracy. The results revealed a slight downward trend in AWUE across the JHP, with notable spatial and temporal variations observed among cities. These trends suggest that while some regions are making progress in optimizing water use, others are experiencing stagnation or decline. The disparity between cities such as Wuhan and smaller cities like Qianjiang highlights the need for region-specific strategies in water management and agricultural practices. The evaluation metrics of the Tent-SSA-BPNN prediction model outperform those of the single algorithm optimization model, demonstrating robust predictive performance. The analysis predicts that SAWC has a greater impact on AWUE in the JHP than WRPC and SCWS.

From a theoretical perspective, most previous studies focused on predicting outcomes via traditional models or constructing conventional BPNNs [88]. The improved Tent-SSA-BPNN model outperforms traditional models due to its unique integration of global optimization from SSA and nonlinear prediction capabilities from BPNN. The model avoids local optima, enhancing prediction accuracy. Furthermore, Tent chaotic mapping increases the diversity of the initial population, preventing early convergence to suboptimal solutions, which is a common issue with traditional methods. This results in more robust and reliable predictions of AWUE trends. The improved Tent-SSA-BPNN model in this study outperforms traditional models because of its ability to combine the global search capability of the SSA with the nonlinearity capture of the back propagation neural network (BPNN). The SSA optimizes the BPNN’s weights and biases more effectively by avoiding local optima, thus improving the prediction accuracy. Additionally, Tent chaotic mapping enhances the SSA’s ability to explore the solution space by increasing the diversity of the initial population, which further contributes to the model’s robustness. Furthermore, a comparison of multiple runs with the BPNN, SSA-BPNN, and GWO-BPNN models indicates that the traditional BPNN has addressed its previous shortcomings regarding stability. All evaluation metrics surpass those of the models optimized by single algorithms, demonstrating that the improved SSA significantly enhances the global search capability and optimization accuracy of neural networks, leading to marked improvements in their performance. This confirms that the Tent-SSA-BPNN model exhibits strong stability, accuracy, and robustness as a predictive model for agricultural water resources. This study addresses the gap in AWUE prediction and offers new insights for related research in this area. Previous studies, such as those by Wang et al. (2024) and Zhang et al. (2023), have relied heavily on methods like DEA and SFA for efficiency analysis [89,90]. While these approaches are useful, they struggle with nonlinear relationships and multidimensional datasets, limiting their predictive power. In contrast, the Tent-SSA-BPNN model, by incorporating a global optimization algorithm (SSA) and a nonlinear neural network (BPNN), addresses these challenges effectively, offering a more precise and adaptable tool for AWUE analysis. This study builds on and improves previous work by integrating these cutting-edge techniques. In contrast, the improved Tent-SSA-BPNN model used in this study successfully overcomes these limitations by incorporating a global search algorithm and nonlinear prediction model, offering a more accurate and reliable tool for AWUE analysis. These findings align with recent research on optimizing prediction models for AWUE, but they extend previous work by demonstrating the practical applicability of the Tent-SSA-BPNN model in a real-world setting [41]. From a practical standpoint, improving AWUE in the JHP has significant implications for water resource management and agricultural policy. By optimizing water resource allocation, the Tent-SSA-BPNN model can inform policy decisions aimed at enhancing water use efficiency across different regions. The Tent-SSA-BPNN model offers policymakers crucial insights for enhancing water resource allocation strategies. This model can effectively pinpoint areas within the JHP where implementing advanced irrigation technologies, such as drip or sprinkler systems, would yield the most significant reductions in water waste. Moreover, the model’s predictive capabilities enable policymakers to strategically prioritize water conservation measures in regions facing the highest risk of water scarcity, thus promoting a more focused and efficient allocation of resources. For agricultural practitioners, the model’s predictive ability can assist in making informed decisions about crop selection, irrigation practices, and resource allocation, ultimately improving productivity while reducing water consumption. These findings emphasize the role of AWUE optimization in ensuring the sustainable development of agriculture in water-scarce regions.

In light of the findings of this study, the JHP should undertake the following measures to increase AWUE levels. First, strengthening the management and optimal allocation of water resources is essential. Given the significant disparities in AWUE among the cities of the JHP discussed earlier, rational allocation and effective management of water resources must be ensured through the establishment and enhancement of a comprehensive water resources management system [91]. Second, the agricultural planting structure should be adjusted on the basis of the climate and soil conditions of the JHP to promote water-saving and efficient agricultural practices [92]. Third, it is important to promote water-saving irrigation technologies, such as drip and sprinkler irrigation, which can significantly reduce water waste.

Although this research aims to analyze AWUE accounting and forecasting comprehensively in the JHP, it inevitably has certain limitations. The limitations are as follows:

(1)

AWUE changes significantly over time, and the research may be limited by the speed of obtaining the latest data. This limitation may prevent the findings from fully reflecting the current situation.

(2)

AWUE varies among different regions and crop types, and a single model may not adequately represent the characteristics of all JHP agricultural regions, which may affect the universality of the predictive results.

(3)

The JHP encompasses a vast area, exhibiting variations in water resource conditions and agricultural development models across different regions. Consequently, this study may not be able to address all regions comprehensively, which may limit the conclusions drawn.

In light of these limitations, future research should prioritize the following:

(1)

Enhance the techniques for data collection and processing. An efficient algorithm has been developed for processing large-scale agricultural water resource data, aimed at improving processing speed and accuracy while minimizing the impact of data errors on research outcomes.

(2)

This study aims to investigate the short-term and long-term impacts of natural disasters, such as floods and droughts, on AWUE and to propose corresponding coping strategies and plans.

(3)

Incorporate climate change factors, including precipitation and temperature, into the model to analyze their impacts on AWUE and enhance the adaptability of forecasts in the future.

5. Conclusions

In the face of increasing water scarcity and the need for agricultural sustainability, improving AWUE is crucial for ensuring the sustainable management of water resources and food security. This study focuses on the JHP and AWUE, employing the SE-SBM model for evaluation and the enhanced Tent-SSA-BPNN model for prediction. The novel integration of Tent chaotic mapping with SSA and BPNN significantly improves the accuracy and robustness of AWUE predictions. By offering a more reliable forecasting tool, this research addresses key challenges in water resource management and agricultural sustainability in water-scarce regions. The findings indicate that AWUE in the JHP showed a slight downward trend from 2010 to 2022, with notable spatial and temporal disparities across regions. The use of the Tent-SSA-BPNN model allowed for precise modeling of these variations, enhancing the understanding of how environmental and agricultural factors interact to shape water use efficiency. The Tent-SSA-BPNN model achieved an impressive prediction accuracy of 96.218% (ACC) and an RMSE of 0.952, outperforming traditional models and confirming its robust performance in predicting AWUE. The findings are presented below.

(1)

From 2010 to 2022, the AWUE in the JHP exhibited a slight downward trend. The AWUE values in the JHP ranked from highest to lowest are as follows: Yichang > Xiaogan > Jingmen > Wuhan > Jingzhou > Qianjiang > Xiantao > Tianmen.

(2)

This section discusses the spatial distribution characteristics and dynamic change trends of AWUE in the JHP. The overall trend indicates that the center of gravity of AWUE migrated eastward and southward. The SDE indicates that AWUE in the JHP initially exhibited agglomeration growth; however, from 2012, it began to optimize, resulting in a decreased degree of agglomeration. The direction of distribution remained relatively stable, predominantly along the “northeast–southwest” axis. The distribution has a more uniform elliptical shape. The MI illustrates the dynamic trend of spatial correlation in the JHP, with high positive values in 2012 and 2016 signifying strong spatial aggregation, whereas negative values in 2020 suggest spatial dispersion.

(3)

WRPC, SCWS, and SAWC were chosen as predictive variables to forecast the AWUE of the JHP. The FFCV was used to assess the prediction results. The results indicated that the ACC and RMSE predicted by the Tent-SSA-BPNN model were 96.218% and 0.952, respectively. The R² value was 0.9939, demonstrating the high accuracy and fit of the model’s prediction results.

(4)

The results of multiple evaluations of the Tent-SSA-BPNN model, along with the BPNN, SSA-BPNN, and GWO-BPNN models, were compared. The findings indicate that the ACC of the Tent-SSA-BPNN model remains stable at approximately 96%, whereas the RMSE remains below 1.2. The R² value consistently exceeds 0.99, addressing the stability shortcomings of the traditional BPNN. All evaluation metrics surpass those of the single algorithm optimization models, demonstrating that the enhanced SSA significantly improves the global search capability and optimization accuracy of the BPNN, thus positively affecting the performance optimization of neural networks. The Tent-SSA-BPNN model serves as an agricultural carbon emission forecasting model characterized by strong stability, accuracy, and robustness.

(5)

By incorporating WRPC, SCWS, and SAWC, the Tent-SSA-BPNN model was employed to predict the AWUE of the JHP for the next five years. The results indicated that the three indicators were positively correlated with AWUE, with their influence ranked as follows, from greatest to least: SAWC > SCWS > WRPC. Furthermore, SAWC has a dominant influence on AWUE, indicating that managing SAWC can effectively regulate AWUE.

(6)

The Tent-SSA-BPNN model represents a significant advancement in AWUE prediction by integrating Tent chaotic mapping and SSA with the BPNN. Compared with traditional methods, this innovation allows for more accurate predictions and robust performance. Its potential applications extend beyond the JHP, offering valuable insights for sustainable agriculture in water-scarce regions globally. The model can also be adapted for predicting AWUE in other industries, contributing to broader water resource management strategies.

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The findings of this study underscore the critical importance for policymakers and agricultural stakeholders to integrate these insights into their water resource management strategies and agricultural methodologies. The Tent-SSA-BPNN model presents a robust framework that enhances AWUE prediction capabilities and optimizes water allocation, thereby offering a scalable approach to address water scarcity concerns and promote sustainable agricultural development. Furthermore, researchers should continue to refine and test the Tent-SSA-BPNN model in different regions and contexts, advancing its applicability and contributing to global efforts to ensure water sustainability and food security.