Spatiotemporal Evolution and Driving Mechanisms of Water–Energy–Food Synergistic Efficiency: A Case Study of Irrigation Districts in the Lower Yellow River

Abstract

As an integrated framework linking resource use and environmental sustainability, the WEF (Water–Energy–Food) system plays a vital role in achieving sustainable agricultural development. Focusing on the irrigation districts in the lower reaches of the Yellow River, this study constructed and applied a Super-Undesirable-SBM (super-efficiency undesirable slacks-based measure) model and a GTWR (geographically and temporally weighted regression) model from a WEF perspective to systematically analyze the spatiotemporal evolution and driving mechanisms of WEFSE (Water–Energy–Food Synergistic Efficiency) from 2000 to 2020. The overall WEFSE exhibited a continuous upward trend, with the spatial pattern gradually shifting from the southwest to the northeast and regional disparities becoming more pronounced. The efficiency demonstrated a significant positive spatial autocorrelation, indicating a stable clustering pattern of “high–high” and “low–low” efficiency areas. In terms of driving mechanisms, WEFSE evolved from being dominated by socio-economic drivers to a composite system jointly influenced by ecological and structural factors. Among these, PD (population density) and WP (proportion of water area) had increasingly positive effects, whereas PRE (precipitation) and NDVI (normalized difference vegetation index) imposed notable constraints. Meanwhile, PCL (proportion of cultivated land), GP (proportion of grassland), and AT (average temperature) exhibited significant spatial differentiation. This study highlights that the assessment of WEFSE and identification of its driving mechanisms using the Super-Undesirable-SBM and GTWR models can help to uncover the spatiotemporal dynamics of agricultural resource utilization, providing methodological support and decision-making insights for optimizing resource allocation and promoting sustainable development in the Yellow River irrigation districts and other complex agricultural systems.

1. Introduction

Against the backdrop of global climate change and population growth, the environmental impacts of agricultural irrigation—a key measure for ensuring food security—are increasingly drawing attention [1]. Irrigation currently accounts for 15% of the overall energy consumption and greenhouse gas emissions from agricultural operations [2], consuming 1896 gigawatts of energy yearly and producing 216 million tons of carbon dioxide. Groundwater pumping accounts for 89% of total energy consumption, with diesel pumps accounting for the majority of this usage. Global irrigation energy consumption and carbon emissions are predominantly concentrated in Asia and North America, with India, China, the United States, Pakistan, and Iran contributing the most [3]. In line with the WEF (water–energy–food) nexus framework advocated by the FAO (Food and Agriculture Organization of the United Nations) and other international initiatives, these intertwined pressures highlight the need to jointly manage water, energy and food systems rather than relying on isolated sectoral policies [4,5]. As climate change and population expansion increase pressure on food production, this task will become even more difficult if we do not successfully improve water and land utilization efficiency. Therefore, conducting in-depth research on the utilization efficiency of agricultural water, land, and energy resources, and on promoting their efficient and coordinated use, has become a critical issue concerning national food security, global ecosystem health, and sustainable development [6].

As sustainable agricultural development has become a core goal, research on agricultural waste and land-use efficiency has expanded. In this context, the agricultural water cycle, which couples blue, green and gray water with land resources to support irrigation, crop growth and the assimilation of agricultural pollutants, provides an important basis for analyzing the joint use of water and land in agriculture [7]. Existing work mainly concentrates on efficiency measurement, spatial-temporal patterns and driving mechanisms, and commonly applies composite indicators, DEA (Data Envelopment Analysis) and SFA (Stochastic Frontier Analysis). The basic DEA model is a non-parametric frontier approach that evaluates the relative efficiency of decision-making units in multi-input–multi-output settings without specifying a production function or performing dimensional standardization [8,9].

To better depict the transformation from water–land inputs to agricultural outputs, DEA has been extended in several directions. Network and two-stage DEA models portray internal production stages of regional water and land utilization, Malmquist DEA captures dynamic changes in efficiency and matching, and DEA–Tobit models add a second-stage censored regression to explain how external factors affect bounded DEA scores [10,11,12,13]. SBM-DEA (Super-efficiency and slack-based measure DEA) defines efficiency through input–output slacks and allow comparison among units on or above the frontier, while also incorporating undesirable outputs such as carbon emissions; these models support evaluations of grain-production efficiency and multi-resource systems including water–land–energy [14,15,16]. Windows-DEA, by contrast, treats panel data as a series of overlapping time windows to track time-varying efficiency and coupling coordination, as shown in studies of cities in the Yellow River Basin [17].

At the level of research objects, scholars have gradually moved from single-factor efficiency to coupled resource systems. Internationally, WEF nexus assessments have been conducted for water-scarce agricultural regions such as India, sub-Saharan Africa and the Mediterranean, using composite indicators, optimization and DEA-type models to explore cross-sectoral trade-offs and coordination [18,19,20]. Provincial WEF efficiency and its spatial clustering or environmental drivers have been assessed using super-efficiency, network and three-stage DEA models [21,22], while WLEF (water–land–energy–food) nexus has been examined by embedding emergy and ecological footprint within a super-efficiency SBM-DEA framework with undesirable outputs [23]. Under RCP–SSP (Representative Concentration Pathway–Shared Socioeconomic Pathway) scenarios-which combine climate-forcing trajectories with socio-economic development pathways to characterize plausible future climate and development conditions-multi-objective optimization models simulate optimal water–land allocation in irrigation districts [24]. At the technical scale, smart irrigation strategies that integrate the Internet of Things, remote sensing and closed-loop model predictive control, together with AHP–entropy weighting, SBM-DEA and coordinated development models for system resilience, further refine the analysis of agricultural water-use efficiency [25,26]. Compared with these provincial- or basin-scale studies that mostly employ static super-efficiency or network DEA models for WEF systems, this study adopts a Super-Undesirable-SBM DEA model at the irrigation-district scale in the lower reaches of the Yellow River, explicitly treating gray-water-related pollution as an undesirable output and using the resulting 2000–2020 panel of WEFSE (Water–Energy–Food Synergistic Efficiency) values to describe its long-term evolution. Furthermore, instead of only comparing efficiency levels, we couple the dynamic WEFSE results with a GTWR model to reveal how socio-economic, hydrological and ecological drivers of WEFSE vary across both space and time, thereby providing a finer, management-oriented decomposition of WEFSE evolution within irrigation districts.

In summary, although existing studies have advanced the analysis of agricultural water and land-use efficiency, they still lack an evaluation framework that jointly reflects the sustainability of agricultural systems and integrates water, land and energy inputs with ecological and environmental constraints. To address this gap, this study takes 40 irrigation districts in the lower reaches of the Yellow River as decision-making units, integrates the concepts of blue, green and gray water into an agricultural WEF indicator system, and applies a Super-Undesirable-SBM model to measure the efficiency of agricultural water, land and energy resource utilization from 2000 to 2020. The results identify efficiency weaknesses and binding constraints across irrigation districts and provide a quantitative basis for optimizing the coordinated management of water, land and energy resources in the Yellow River irrigation districts.

2. Materials and Methods

2.1. Study Area

The study area encompasses the irrigation districts in the lower reaches of the Yellow River. There are 40 of these districts, and they are divided according to the locations of water intake. Geographically, the Yellow River irrigation districts are primarily located on the North China Plain, a vital grain-producing region in China, between 114°49′ E~119°06′ E and 34°33′ N~38°13′ N (Figure 1). The riverbed in the lower reaches is significantly higher than the surrounding terrain, coupled with substantial net flow, creating favorable conditions for water diversion and irrigation. Since the establishment of the Yellow River irrigation districts, the water supply for farmland in the study area has gradually stabilized, ensuring consistent high yields for major crops such as wheat and corn, thereby strengthening national food security. The study area is characterized by a warm temperate and a semi-humid monsoon climate with four distinct seasons. Summers are typically hot and rainy, whereas winters are cold and dry. Most of the annual precipitation occurs during the summer months (June to September), accounting for more than 70% of the yearly total [27]. In contrast, spring droughts are particularly pronounced, as precipitation in March and April accounts for less than 10% of the annual total. The region experiences abundant solar radiation, with annual sunshine duration ranging from 2300 to 2800 h [28], which creates favorable conditions for enhancing crop yield and quality. For example, wheat requires lots of sunlight during the spring season, and the favorable light conditions in the Yellow River irrigation districts guarantee high yields. This study investigates the utilization efficiency of agricultural water, land, and energy resources, taking winter wheat as a representative grain crop.

2.2. Data Sources

Data on the natural geography and agricultural production of the irrigation districts in the lower reaches of the Yellow River were systematically collected for the period of 2000 to 2020. This time window was chosen because the key remote sensing and statistical datasets used in this study become reliably available and comparable at the irrigation-district scale from around 2000 onward, whereas most harmonized series for the explanatory variables currently extend only to 2020. Extending the analysis to 2025 would involve mixing data of different quality or temporal completeness, which may weaken the consistency and robustness of the results. Meanwhile, the period 2000–2020 remains sufficiently long to capture the major phase of recent climate- and policy-related changes in the study area. Agricultural data were mainly derived from the annual statistical yearbooks of the prefecture-level cities in the study area; meteorological data were obtained from the National Meteorological Science Data Sharing Service Center of China; grain price data were sourced from the China Agricultural Product Price Survey Yearbook; and data on crop irrigation quotas were derived from Irrigation Quotas for Major Crops in Shandong Province, provided by the Shandong Provincial Institute of Water Resources Research. The data of each irrigation district were processed based on the proportional area of the prefecture-level cities where they are located, using the area ratio as a weighting factor to convert the city-level data into irrigation-district-level data.

2.3. Input and Output Variables

2.3.1. Water Resource Input Indicator

In traditional DEA models, water resources were usually treated as a single input indicator. To more comprehensively reflect water resource consumption, this study refined the water resource input into two components: blue water and green water [29].

$$x_{1,j}=W_{green,i}+W_{blue,i}$$

(1)

where i indexes the irrigation districts (i = 1, 2, …, n) in the lower reaches of the Yellow River, and t denotes the year. $x_{1,j}$ denotes the agricultural water resource input in the i-th irrigation district (m³), $W_{green,i}$ denotes the agricultural green water resource input in the i-th irrigation district (m³), and $W_{blue,i}$ denotes the agricultural blue water resource input in the i-th irrigation district (m³).

Green water input refers to the effective precipitation stored in the land and ultimately consumed through evapotranspiration during the crop growth period [30]. The green water resource input in each irrigation district was determined based on the effective precipitation and the crop planting area, and was calculated as follows:

$$W_{green,i}={\displaystyle \sum }_{c=1}^c{A}_{i,c}\times P_{e,i,c}\times 10$$

(2)

where denotes the number of grain crop types, $A_{i,c}$ denotes the planting area of the c-th grain crop in the i-th irrigation district (hm²), and $P_{e,i,c}$ denotes the effective precipitation during the growth period of the c-th grain crop in the i-th irrigation district (mm).

The land water balance method, which had been developed based on the approach of the Land Conservation Service of the United States Department of Agriculture (USDA-SCS), was used to estimate the effective precipitation. This method dynamically calculates crop evapotranspiration, precipitation infiltration, and changes in land water storage to estimate effective precipitation. The specific calculation formula was expressed as follows [31]:

$$\begin{array}{ll}{P}_e=P\left(4.17-0.02P\right)/4.17\hfill & P<83\hfill \\ P_e=41.7+0.1P\hfill & P\ge 83\hfill \end{array}$$

(3)

where $P_e$ denotes the effective precipitation (mm), and $P$ denotes the total precipitation (mm).

In agricultural production, blue water input refers to the amount of water extracted from natural sources such as surface water and groundwater for agricultural irrigation [32]. In this study, the distribution ratio of agricultural irrigation water among different crops was determined based on the gross irrigation quota and the planting area of each crop. Once the statistical data of total agricultural irrigation water use had been collected, the total blue water input for grain production in each irrigation district was calculated. The specific calculation method was as follows [33]:

$$W_{blue,i}={\displaystyle \sum _{c=1}^C{\alpha }_{i,c}}{W}_{IR,i}$$

(4)

$${\alpha }_{i,c}={\displaystyle \frac{I_{i,c}{A}_{i,c}}{{\displaystyle \sum _{c=1}^C{I}_{i,c}}{A}_{i,c}}}$$

(5)

where $C$ denotes the number of all crop types, ${\alpha }_{i,c}$ denotes the proportion of irrigation water used for the c-th crop in the i-th irrigation district relative to the total agricultural irrigation water use, $W_{\mathrm{IR},i}$ denotes the agricultural irrigation water use in the i-th irrigation district (m³), and $I_{i,c}$ denotes the irrigation quota of the c-th crop in the i-th irrigation district (m³/hm²).

2.3.2. Cultivated Land Resource Input Indicators

Considering the multiple cropping and intercropping practices in agricultural production, as well as the existence of idle or abandoned farmland in some regions, the traditional statistical data on cultivated land area could not accurately reflect the actual utilization level of cultivated land resources. Therefore, this study selected the total sown area of crops as the indicator to measure the input of cultivated land resources. The specific calculation formula was as follows [34]:

$$x_{2,i}={\displaystyle \sum }_{c=1}^c{A}_{i,c}$$

(6)

where $A_{i,c}$ denotes the planting area of the c-th grain crop in the i-th irrigation district (hm²).

2.3.3. Energy Input Indicators

Energy input serves as a fundamental driving force for economic and social development and is also a key indicator for measuring the scale of regional energy consumption. In this study, the total energy consumption was selected as a proxy variable for energy input. The specific conversion coefficients are shown in

Table 1. Conversion coefficients for various types of energy.

Indicator	Conversion Coefficient
Electricity	3.6 MJ/kwh
Diesel	43.5 MJ/kg
Fertilizer	51.67 MJ/kg
Pesticide	100 MJ/kg
Plastic film	104.7 MJ/kg

[35].

A wide variety of energy data were involved in this study. To ensure consistency and accuracy in the accounting process, all energy consumption data were converted into standard coal equivalents (tce) during the calculation and analysis stage. The conversion coefficients adopted in this study were based on the General Principles for Calculation of Comprehensive Energy Consumption (GB/T 2589-2020) [36], with the specific conversion factor of 1 tce = 29,307.6 MJ.

2.3.4. Social Benefit Output Indicators

Grain yield refers to the total amount of grain harvested within a year, including both summer and autumn grain yields categorized by harvest season. The specific calculation method was as follows [37]:

$$y_{1,i}={\displaystyle \sum }_{c=1}^c{y}_{1,i,c}$$

(7)

where $y_{1,i}$ denotes the grain yield of the i-th irrigation district (t), and $y_{1,i,c}$ denotes the yield of the c-th grain crop in the i-th irrigation district (t).

2.3.5. Economic Benefit Output Indicators

Grain output value refers to the total monetary value of grain products, reflecting the economic results of agricultural production in irrigation districts during the study period. The grain output value was calculated as follows [38]:

$$y_{2,i}={\displaystyle \sum }_{c=1}^c{y}_{1,j,c}\times P_{r,j,c}$$

(8)

where $y_{2,i}$ denotes the grain output value of the i-th irrigation district (yuan), and $P_{r,j,c}$ denotes the price of the c-th grain crop in the i-th irrigation district (yuan/t).

Referring to the China Agricultural Product Price Survey Yearbook (2018), the grain prices of Shandong Province were used in this study. The unit price of wheat was 2580 yuan per ton.

2.3.6. Ecological Benefit Undesirable Output of Carbon Emissions

Carbon emissions refer to the total amount of greenhouse gases directly or indirectly released into the atmosphere by human activities, which are used to quantify the impact of human activities on the global climate system [39]. In the process of agricultural water and land resource development and utilization, carbon emissions are closely related to the use of irrigation, fertilizers, and pesticides, and constitute the main source of greenhouse gas emissions in agricultural systems [40,41]. In this study, carbon emissions were regarded as an undesirable output in the efficiency evaluation system of agricultural water and land resource utilization, representing the negative ecological effect. The carbon emissions generated from agricultural production activities can be converted into carbon dioxide equivalents (CO₂-eq) based on the global warming potential (GWP) parameters. According to the method proposed by the Intergovernmental Panel on Climate Change (IPCC), the carbon emissions from grain production were calculated by summing the products of the carbon emission coefficients of different agricultural inputs and the corresponding amounts of fossil energy consumption. The specific calculation formula was as follows [42]:

$$b_{1,i}={\displaystyle \sum }_{e=1}^E{\displaystyle \frac{A_i}{A_i^{*}}}{\beta }_e{E}_{i,e}$$

(9)

where $b_{1,i}$ denotes the carbon emissions of the i-th irrigation district (kg), $E_{i,e}$ denotes the amount of the e-th type of agricultural energy used in the i-th irrigation district, $A_i$ denotes the sown area of grain crops in the i-th irrigation district (hm²), $A_i^{*}$ denotes the total sown area of all crops in the i-th irrigation district (hm²), and ${\beta }_e$ denotes the carbon emission coefficient (CO₂-equivalent conversion factor) of the e-th type of agricultural energy.

The carbon emission coefficients of agricultural energy in the study area were determined based on previous research [43,44], and are listed in

Table 2. Carbon emission coefficients of agricultural inputs.

Indicator	Carbon Emission Coefficients
Electricity	0.801 kg(C)/kw·h
Diesel	0.59 kg(C)/kg
Fertilizer	2.12 kg(C)/kg
Pesticide	4.93 kg(C)/kg
Plastic film	5.18 kg(C)/kg

.

The gray water discharge was used in this study to measure agricultural non-point source pollution. Gray water refers to the volume of freshwater required to dilute the pollutants generated from agricultural production activities in freshwater bodies to the maximum allowable concentration under environmental standards [45].

In this study, the gray water is chosen as an ecological indicator to assess the impact of agricultural activities on water pollution. The gray water is defined as the amount of water required to dilute pollutant loads to acceptable concentrations, effectively quantifying water pollution while considering different pollutant sources and pathways [46]. This method has been widely applied in agricultural systems, particularly in evaluating nitrogen pollution caused by agricultural activities such as fertilizer and pesticide use. In complex hydrological environments, gray water can effectively assess water pollution levels in areas like paddy fields, thus providing valuable support for agricultural water pollution management [47].

Furthermore, gray water has been applied to assess nitrogen-related non-point source pollution and quantify agricultural water pollution at the regional scale. This application not only confirms its effectiveness as an ecological indicator in agricultural production systems but also provides a reliable tool for managing agricultural water pollution [48].

The gray water in agricultural production mainly originates from fertilizer runoff, pesticide runoff, and livestock wastewater [49]. In the North China Plain, the problem of excessive nitrogen fertilizer application is particularly severe during agricultural production. Therefore, in this study, the gray water discharge was calculated based on the total nitrogen input from chemical fertilizers. The specific calculation formula was as follows:

$$b_{2,i}={\displaystyle \frac{1000\alpha P_{N,i}}{\left(c_{\max }-c_{\mathrm{nat}}\right)}}$$

(10)

where $b_{2,i}$ denotes the gray water discharge of the i-th irrigation district (m³), $P_{N,i}$ denotes the total nitrogen input for grain production in the i-th irrigation district (kg), $\alpha$ denotes the leaching rate of total nitrogen, $c_{\max }$ denotes the maximum allowable concentration of total nitrogen in water bodies (mg/L), and $c_{\mathrm{nat}}$ denotes the background concentration of total nitrogen in natural water bodies (mg/L).

Leaching refers to the process in which soluble substances in the land move downward with water flow and eventually leave the root zone of crops, entering deeper land layers, groundwater, or surface water. The average leaching rate (α) of total nitrogen under the winter wheat–summer maize rotation system in the North China region was 25% [50]. There is no explicit standard for the total nitrogen concentration in agricultural irrigation water in the study area. According to the Integrated Discharge Standard of Water Pollutants along the South-to-North Water Diversion Project in Shandong Province, the maximum allowable total nitrogen concentration for agricultural discharge is 60 mg/L. Therefore, in this study, the maximum allowable concentration of total nitrogen in water bodies ($c_{\max }$) was set to 60 mg/L. In the absence of measured data, the background concentration of total nitrogen in natural water bodies ($c_{\mathrm{nat}}$) was assumed to be 0 mg/L.

The conceptual framework of water-energy-food synergistic efficiency in the irrigation districts of the lower Yellow River is shown in Figure 2.

2.4. Development of the WEFSE Measurement Model

In the process of agricultural production, water, cultivated land and energy are three key factors that support the sustainable development of agriculture [51]. However, in practice it is often difficult for these inputs to increase or decrease in the same proportion, and agricultural production is accompanied by non-point source pollution and greenhouse gas emissions that are usually ignored in traditional efficiency accounting. To comprehensively and accurately evaluate the integrated utilization of water, land and energy resources while reflecting ecological performance, this study adopts an input-oriented Super-Efficiency Slacks-Based Measure model with undesirable outputs under constant returns to scale. Inputs and desirable outputs are assumed to be strongly disposable, whereas undesirable outputs are treated as weakly disposable, recognizing that reducing pollution generally requires additional resource inputs or technological improvement rather than costless abatement.

Compared with radial DEA models (such as CCR/BCC) and the traditional Super-SBM model, the Super-Undesirable-SBM framework is better suited to the agricultural WEF context for two reasons. First, as a non-radial, slack-based model it evaluates efficiency by explicitly incorporating input and output slacks, which allows heterogeneous redundancies of water, land and energy inputs and shortfalls in desirable outputs to be identified instead of imposing a uniform proportional contraction or expansion. Second, it directly incorporates environmental pressure indicators-such as agricultural non-point source pollution and greenhouse gas emissions-as undesirable outputs, so that higher emissions translate into larger slack and lower efficiency scores. In this way, the model simultaneously captures the economic performance and ecological effects of agricultural production, and the resulting WEFSE provides an efficiency measure with clearer environmental significance. The following model follows Tone’s slacks-based measure with undesirable outputs [52,53]:

$$\min WEFSE={\displaystyle \frac{\frac{1}{m}{\displaystyle \sum _{i=1}^m\frac{{\widehat{x}}_i}{x_{io}}}}{\frac{1}{s_1+s_2}\left({\displaystyle \sum _{r=1}^{s_1}\frac{{\widehat{y}}_r^g}{y_{ro}^g}}+{\displaystyle \sum _{r=1}^{s_2}\frac{y_{ro}^b}{{\widehat{y}}_r^b}}\right)}}\hspace{1em}\mathrm{s}.\mathrm{t}.\hspace{1em}\left\{\begin{array}{l}\widehat{x}\ge {\displaystyle \sum _{j\ne o}{\lambda }_j}{x}_j,\hfill \\ {\widehat{y}}^g\le {\displaystyle \sum _{j\ne o}{\lambda }_j}{y}_j^g,\hfill \\ {\widehat{y}}^b\ge {\displaystyle \sum _{j\ne o}{\lambda }_j}{y}_j^b,\hfill \\ \widehat{x}\ge x_o,\hspace{1em}{\widehat{y}}^g\le y_o^g,\hspace{1em}0\le {\widehat{y}}^b\le y_o^b,\hfill \\ {\lambda }_j\ge 0.\hfill \end{array}\right.$$

(11)

where

$x_{io}$ denotes the i-th input;

${\widehat{x}}_i$ denotes the projected value of the i-th input;

$y_{ro}^g$ denotes the r-th desirable output;

$y_{ro}^b$ denotes the r-th undesirable output;

${\widehat{y}}_r^g$ denotes the projected value of the r-th desirable output;

${\widehat{y}}_r^b$ denotes the projected value of the r-th undesirable output;

$S_1,S_2$ denote the numbers of desirable and undesirable output items.

2.5. Spatial Autocorrelation

Based on the analysis of WEFSE in the Yellow River irrigation districts of the lower reaches, this study further examined their spatial autocorrelation characteristics to provide a reference for promoting regional coordinated development. This study applied spatial autocorrelation analysis to examine the WEFSE of the Yellow River irrigation districts in the lower reaches by calculating the Global Moran’s I and Local Moran’s I. This approach revealed the spatial distribution patterns of WEFSE and provided a theoretical basis for promoting regional sustainable development.

2.5.1. Global Spatial Autocorrelation

Global spatial autocorrelation is represented by the Global Moran’s I proposed by Moran, which is used to describe the spatial autocorrelation of the study area [54]. The calculation formula of the Global Moran’s I is expressed as follows:

$$I={\displaystyle \frac{n{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{w}_{ij}(x_i-\overline{x})(x_j-\overline{x})}}}{{\displaystyle \sum _{i=1}^n{(x_i-\overline{x})}^2{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{w}_{ij}}}}}}$$

(12)

where

$n$ denotes the number of spatial units (regions);

$x_i$ denotes the attribute value of region i;

$x_j$ denotes the attribute value of region j;

$w_{ij}$ denotes the spatial weight between region i and region j.

In this study, the spatial weight matrix was determined using the distance matrix method. The Global Moran’s I represents the overall spatial autocorrelation of the study area, with values ranging from −1 to 1. When I > 0, it indicates a positive spatial autocorrelation of the attribute values, characterized by a “spatial clustering” pattern in which high values are adjacent to high values and low values are adjacent to low values. When I < 0, it indicates a negative spatial autocorrelation, characterized by a “spatial dispersion” pattern in which high values are adjacent to low values.

The basic null hypothesis of the spatial autocorrelation test is that the spatial distribution of geographical elements within the study area follows a random pattern [55]. Based on this assumption, this study employed the statistical variable Z to test the significance of the Global Moran’s I.

$$Z(I)={\displaystyle \frac{I-E(I)}{\sqrt{VAR(I)}}}$$

(13)

where $E(I)$ denotes the expected value of the Global Moran’s I, and $VAR(I)$ denotes the variance of the Global Moran’s.

$$E(I)={\displaystyle \frac{-1}{n-1}}$$

(14)

$$VAR(I)=E(I^2)-E{(I)}^2$$

(15)

In this study, the Global Spatial Autocorrelation analysis of the WEFSE was conducted for 40 irrigation districts in the Yellow River irrigation districts of the lower reaches during 2000–2020, using the Moran’s I method in GeoDa software 1.22.0.20. In this study, the statistical significance of the Global Moran’s I was tested using the Z-test, with the number of Monte Carlo simulations set to 999. At the 95% confidence level (i.e., α = 0.05), if the calculated p-value is less than 0.05 and the absolute value of the Z statistic is greater than 1.96, the null hypothesis is rejected, indicating that the spatial distribution of the study object exhibits statistically significant spatial autocorrelation. Conversely, if the p-value is greater than 0.05, the null hypothesis is not rejected, implying that the spatial distribution pattern of the variable does not significantly differ from a random distribution [56].

2.5.2. Local Spatial Autocorrelation

The Local Moran’s I represents the spatial autocorrelation between a spatial unit i and its neighboring units, with values ranging from −1 to 1. Similar to the Global Moran’s I, when I_i > 0, it indicates that the attribute values of spatial unit i are similar to those of its neighbors; when I_i < 0, it indicates that the attribute values of spatial unit i differ greatly from those of its neighbors. The significance of the Local Moran’s I was also tested using the Z-statistic [57].

$$Z(I_i)={\displaystyle \frac{I_i-E(I_i)}{\sqrt{VAR(I_i)}}}$$

(16)

where $E(I_i)$ denotes the expected value of the Local Moran’s I, and $VAR(I_i)$ denotes the variance of the Local Moran’s I.

$$E(I_i)={\displaystyle \frac{-{\displaystyle \sum _{j=1}^n{w}_{ij}}}{n-1}}$$

(17)

In this study, the Local Indicators of Spatial Association (LISA) cluster map was employed to identify the spatial association patterns of local regions. The LISA cluster map reveals four types of spatial relationships that are statistically significant. The first two represent spatial clustering patterns, including the “high–high” (H–H) type, where high values are surrounded by high values, and the “low–low” (L–L) type, where low values are surrounded by low values. The latter two represent spatial outlier patterns, including the “high–low” (H–L) type, where high values are surrounded by low values, and the “low–high” (L–H) type, where low values are surrounded by high values [58]. In this study, the significance level was set at 0.05. Only when the absolute value of the Z-statistic exceeded 1.96 (p < 0.05) were the corresponding spatial units classified into one of the four types described above and displayed on the map.

2.6. Geographically and Temporally Weighted Regression Model

Building on the identification of the spatial distribution characteristics of WEFSE in the Yellow River irrigation districts of the lower reaches, further analysis of its influencing factors is of great significance for revealing the causes of efficiency differences and optimizing regional development pathways. In this study, the Geographically and Temporally Weighted Regression (GTWR) model was applied to systematically investigate the driving factors of WEFSE from three aspects: socio-economic conditions, meteorological environment, and ecological land use. The model aims to reveal the spatiotemporal autocorrelation mechanisms of WEFSE, clarify the influence intensity and spatial heterogeneity of each factor, and provide empirical support and decision-making references for improving regional WEFSE and achieving sustainable development. The GTWR model was first proposed to integrate temporal effects into the traditional Geographically Weighted Regression (GWR) model, thereby enabling the simultaneous handling of non-stationarity in both spatial and temporal dimensions, and Equations (18)–(20) in this study follow the model specification, estimator and spatio-temporal distance function proposed by Huang et al. [59]. The basic form of the GTWR model is expressed as follows:

$$Y_i={\beta }_0(u_i,v_i,t_i)+{\displaystyle \sum _k{\beta }_k}(u_i,v_i,t_i)X_{ik}+{ϵ}_i$$

(18)

where $Y_i$ denotes the dependent variable at observation point i, $(u_i,v_i,t_i)$ denote the spatial and temporal coordinates of observation point i, ${\beta }_0(u_i,v_i,t_i)$ denotes the intercept term at observation point i, ${\beta }_k(u_i,v_i,t_i)$ denotes the local regression coefficient of the independent variable $x_k$ at observation point i, and ${ϵ}_i$ denotes the random error term.

The parameter estimation of the model is implemented through the weighted least squares (WLS) method, and its matrix expression is as follows:

$$\widehat{\beta }(u_i,v_i,t_i)={[X^{T}W(u_i,v_i,t_i)X]}^{-1}{X}^{T}W(u_i,v_i,t_i)Y$$

(19)

where $W(u_i,v_i,t_i)$ is an n × n diagonal matrix, whose diagonal elements represent the spatiotemporal weights of other observation points with respect to regression point i. The spatiotemporal weights depend on the spatiotemporal distance, where observation points that are closer in space and time are assigned greater weights. The spatiotemporal distance is calculated as follows:

$${(d_{ij}^{ST})}^2=\lambda [{(u_i-u_j)}^2+{(v_i-v_j)}^2]+\mu {(t_i-t_j)}^2$$

(20)

where $\lambda ,\mu$ denote the scaling factors used to balance the influence of spatial and temporal distances measured in different units.

3. Results

3.1. Results of WEFSE Measurement

Using Equations (1)–(11), the input and output indicators of 40 irrigation districts in the lower reaches of the Yellow River were calculated. These input and output values were then substituted into the Super-Undesirable-SBM model to obtain the WEFSE results for the 40 irrigation districts (Figure 3).

The map in Figure 3 is dominated by light blue and dark blue colors during 2000–2006, indicating that initially, the efficiency values of most irrigation districts were relatively low. As time progressed, the proportion of warm colors in the map gradually increased, and by 2017–2020, large areas of red appeared. During 2000–2020, the average WEFSE of all irrigation districts increased steadily from 0.55 to 0.87, representing a cumulative growth of 58.1%. This indicates that throughout the study period, the overall efficiency levels of all irrigation districts showed continuous and significant improvement. The Bojili, Taochengpu, Xiaokaihe, and Weishan irrigation districts gradually exhibit warmer colors after 2009, suggesting that these districts maintained relatively high efficiency and represent as long-term examples of high-performance irrigation areas. In particular, the Xiaokaihe irrigation district experienced a remarkable increase in efficiency, rising from a medium level of 0.55 in 2000 to 1.04 in 2020. In contrast, the Renmin Shengli Canal and Qucun irrigation districts are dominated by blue or light-colored areas up to 2020, indicating that their efficiency levels have shown the least improvement among all of the irrigation districts. For example, the efficiency of the Renmin Shengli Canal irrigation district showed some improvement, with its efficiency value increasing from 0.52 in 2000 to 0.71 in 2020, its absolute efficiency level consistently remained among the lowest of all of the irrigation districts, and the gap between it and the efficiency level of the leading districts continued to widen over time. In the earlier years, the relatively uniform color distribution indicates that the irrigation districts generally had low efficiency levels and that the differences among them were not significant. In more recent years, the colors are much more diverse and although the overall efficiency levels increased, the differences in efficiency between districts also became more pronounced. This pattern is primarily driven by the more favorable diversion and surface-water supply conditions in the northeastern part of the lower Yellow River, together with the fact that this area has been a key focus of recent agricultural water-saving and irrigation-modernization projects.

To further explore the regional differentiation of the irrigation districts in the lower reaches of the Yellow River, this study selected data from five years—2000, 2005, 2010, 2015, and 2020—and used the ArcGIS 10.8 software to map the spatial distribution patterns of WEFSE across the irrigation districts (Figure 4). The irrigation efficiency exhibited significant dynamic evolution, and in the initial stage of the study, the efficiency pattern exhibited a spatial characteristic of “high in the southwest and low in the northeast.” High-efficiency irrigation districts were mainly concentrated in the southwestern part of the study area, forming early efficiency peaks. However, the overall efficiency level was relatively low, with values ranging from 0.40 to 0.68. As time progressed, the area with the highest efficiency gradually shifted along the southwest–northeast axis, and by the end of the study period, the northeastern region had replaced the southwest as the area of highest efficiency, with most values exceeding 0.82.

Overall, the agricultural WEFSE in the irrigation districts of the lower reaches of the Yellow River exhibited a significant trend of evolution from overall inefficiency to widespread efficiency during 2000–2020. In the early years, the efficiency levels among the irrigation districts exhibited minor differences and remained generally low. Over time, sustained technological progress and management optimization continuously promoted efficiency improvement, thereby driving the gradual evolution of the spatial distribution pattern. From the initial pattern of “high in the southwest and low in the northeast,” the spatial structure gradually evolved into a new configuration characterized by “high in the northeast and overall improvement,” indicating a dynamic rebalancing of resource allocation and development priorities across regions. This transformation not only reflects the spatial reorganization of production factors but also demonstrates the considerable reshaping of agricultural system efficiency due to policy orientation, infrastructure upgrades, and the promotion of water-saving technologies.

3.2. Analysis of the Spatial Autocorrelation of WEFSE

To further investigate the spatial autocorrelation characteristics of WEFSE in the Yellow River irrigation districts, this study employed Global Moran’s I to perform a spatial autocorrelation test on the efficiency data from 2000 to 2020. The Moran’s I values for all years were positive and significant, indicating that the agricultural WEFSE in the Yellow River irrigation districts exhibited a significant positive spatial autocorrelation. In other words, high-efficiency areas tended to be adjacent to other high-efficiency areas, while low-efficiency areas were clustered together.

As shown in

Table 3. Global Moran’s I indices of water–energy–food synergistic efficiency.

Year	Moran’s I	Z	Significance
2000	0.2353	2.4824	*
2001	0.6639	6.5369	*
2002	0.4901	4.9559	*
2003	0.5070	5.2643	*
2004	0.5357	5.3214	*
2005	0.6368	6.0379	*
2006	0.6958	6.9127	*
2007	0.7539	7.2962	*
2008	0.8179	7.8855	*
2009	0.4522	4.5050	*
2010	0.4030	4.1872	*
2011	0.5420	5.4074	*
2012	0.4913	5.0161	*
2013	0.4748	4.7995	*
2014	0.6431	6.8092	*
2015	0.7009	7.1250	*
2016	0.6240	6.2094	*
2017	0.7056	6.9335	*
2018	0.6128	6.0585	*
2019	0.6277	6.1437	*
2020	0.6020	5.8057	*

Note: NS indicates that the result does not pass the 0.05 significance test, and * indicates that the result is significant at the 0.05 level.

, the Global Moran’s I values of WEFSE for the 40 irrigation districts from 2000 to 2020 were all positive and significant. The empirical analysis confirmed that the WEFSE of the irrigation districts exhibited a significant positive spatial autocorrelation, forming a distinct spatial pattern characterized by “hot spots” (high-value clusters) and “cold spots” (low-value clusters). From a temporal perspective, the Moran’s I value in 2000 was 0.2353, the lowest of all the years. Although spatial clustering existed, its intensity was relatively weak. From 2001, the Moran’s I value increased sharply to 0.6639 and continued to fluctuate at a high level, eventually reaching its peak in 2008. During this period, spatial clustering became increasingly pronounced and reached its maximum intensity in 2008. From 2009 to 2013, the Moran’s I value declined slightly, indicating weakening spatial clustering intensity. Although minor fluctuations were observed after this point, the values generally remained relatively high, ranging from 0.6020 to 0.7056, reflecting a mature and stable pattern of strong spatial clustering. Overall, the spatial clustering pattern of WEFSE in the irrigation districts of the lower reaches of the Yellow River underwent strengthening during 2000–2020. Specifically, the intensity of spatial clustering increased rapidly from 2000 and reached its peak in 2008, and although fluctuations occurred after this point, it remained high for an extended period. This trend indicates that the spatial differentiation pattern of WEFSE among regions evolved from weak to strong, with spatial disparities persisting and becoming consolidated at a high level. These findings highlight the urgent need to promote cross-regional collaborative governance and targeted policy interventions to break development barriers and advance the overall improvement and balancing of the spatial layout of WEFSE.

To further investigate the spatial autocorrelation characteristics of WEFSE between each irrigation district of the lower reaches of the Yellow River and its neighboring districts, this study conducted a local spatial autocorrelation analysis for the years 2000, 2005, 2010, 2015, and 2020 using Moran scatterplots and LISA cluster maps. The results are shown in Figure 5 and Figure 6.

In the Moran scatterplots, each Yellow River irrigation district is classified into one of four types of spatial clustering: high–high (HH), low–low (LL), low–high (LH), or high–low (HL). The blue line denotes the linear regression line, whose slope corresponds to Moran’s I. During 2000–2020, the Moran’s I values were 0.2353, 0.6368, 0.4030, 0.7009, and 0.6020, respectively, revealing an overall trend of “initial strengthening–subsequent fluctuation–eventual stabilization.” In 2000, the Moran’s I value was only 0.235, indicating weak spatial autocorrelation. The points representing the study units in the HH and LL quadrants are scattered, and the spatial clustering effect is not obvious. By 2005, the index had risen rapidly to 0.637, and the number of HH and LL units had increased significantly, suggesting that the clustering of high and low-value areas had become much more pronounced. In 2010, the Moran’s I value declined slightly, indicating weakening of the spatial clustering effect. By 2015, it approached its peak (0.701), showing strong positive spatial autocorrelation and suggesting that the WEFSE among irrigation districts was relatively high. Although the Moran’s I value decreased slightly in 2020, it remained high, indicating overall narrowing of regional differences and stability of the spatial clustering pattern.

To further examine the local spatial autocorrelation characteristics of WEFSE within the study area, we constructed LISA cluster maps of WEFSE. In 2000, most spatial units showed no significant spatial relationship, with only a few low–low clusters sporadically distributed in the southwestern irrigation districts. After 2005, the number of high–high and low–low relationships increased markedly, and the spatial clustering effect became more pronounced. In 2010, the following fluctuations occurred: the number of high–high units decreased, while the number of low–low units increased. By 2015, both high–high and low–low clusters had expanded again and continued to do so through 2020. These results indicate that the WEFSE in the region significantly improved and exhibited strong positive spatial associations among the irrigation districts. Overall, the northern areas consistently showed high–high clustering, while the southern areas were dominated by low–low clustering. The spatial pattern gradually stabilized, and the number of heterogeneous areas was relatively small, suggesting that the region was mainly characterized by homogeneous clustering.

From 2000 to 2020, the overall spatial pattern of the study area evolved from a dispersed state with no significant spatial relationships to a clustered and stable one. In the early years, the spatial autocorrelation among the units was relatively weak, but high–high and low–low clusters gradually emerged and became consolidated after 2015, forming a stable contrasting pattern characterized by high–high clustering in the north and low–low clustering in the south. The long-term existence of this spatial differentiation pattern is closely related to differences in regional natural resource availability, adjustments in industrial layout, and the strength of policy support. To achieve a higher level of coordinated and balanced development among irrigation districts, it is necessary to further strengthen regional collaborative governance, promote the rational flow and optimal allocation of resources, and facilitate the transformation of low–low and heterogeneous areas to areas of high–high clustering.

3.3. Driving Mechanisms of the Spatial Autocorrelation of WEFSE

To reveal the spatiotemporal differentiation patterns of the WEF system, this study employed the GTWR model. In constructing the indicator system for assessing influencing factors, this study referred to the eleven potential risk factors proposed by the FAO in 2014 for the WEF system; these include population growth, urbanization rate, dietary diversification, cultural and social beliefs, climate change, government governance, sectoral decision-making, international trade, industrial development, agricultural upgrading, and technological innovation. Moreover, the unique geographical location and natural conditions of the Yellow River irrigation districts were taken into account, and an extensive review of the relevant literature was conducted. On this basis, following the principles of representativeness and data availability in indicator selection, this study selected the following factors and examined their impacts on the WEFSE of the Yellow River irrigation districts: NLI (nighttime light index), PRE (precipitation), AT (average temperature), PD (population density), PCL (proportion of cultivated land), GP (proportion of grassland), WP (proportion of water area), and NDVI (normalized difference vegetation index). The details of these factors are shown in

Table 4. Factors influencing water–energy–food synergistic efficiency.

Variable	Dimension	Indicator	Variable Number
Independent variable	Socio-economic factors	NLI	X1
		PD	X2
		PCL	X3
	Meteorological factors	AT	X4
		PRE	X5
	Ecological land-use factors	GP	X6
		WP	X7
		NDVI	X8
Dependent variable		WEFSE	Y

. NLI is used as a proxy for the level of socio-economic development and agricultural input intensity; PRE and AT characterize the hydro-climatic conditions that determine water availability, crop water demand and drought or flood risk; PD reflects population agglomeration and the associated pressure on food demand and resource utilization; and PCL, GP and WP jointly describe the land-use structure and the relative dominance of cropland, grassland and surface water within each irrigation district. NDVI is included as an ecological indicator of cropland vegetation status, as it reflects canopy greenness and photosynthetic activity and has been widely used to capture vegetation responses to water availability, drought and irrigation in agricultural regions, thereby providing additional information on the ecological conditions under which WEFSE evolves [60,61]. In this study it is treated as an ecological factor that may constrain WEFSE under limited water and land resources.

The years 2000 and 2020 were selected as representative periods. The spatial autocorrelation of the influencing factors was visualized using ArcGIS 10.8 software, and the final analytical results are presented in Figure 7. These results, respectively, illustrate the spatial autocorrelation effects of NLI, PRE, AT, PD, PCL, GP, WP, and NDVI on the WEFSE of the Yellow River irrigation districts.

To examine potential multicollinearity among the explanatory variables, the VIF (variance inflation factor) was calculated (

Table 5. Variance inflation factor values of the explanatory variables.

Indicator	VIF
NLI	3.1790
PD	2.6606
PCL	3.4298
AT	1.6356
PRE	1.0347
GP	1.3456
WP	1.8722
NDVI	2.2749

). All VIF values are below 5, indicating that multicollinearity is not a concern.

The GTWR model employs a fixed kernel function, and the optimal spatiotemporal bandwidth is automatically determined through the AICc (Corrected Akaike Information Criterion) minimization criterion. This configuration maintains a balance between model flexibility and parameter stability, enabling the model to effectively capture the spatiotemporal variations in WEFSE.

The diagnostic results indicate that the GTWR model achieves satisfactory performance, with well-behaved residuals and stable parameter estimates. A comparison with the global OLS (Ordinary Least Squares) model and the GWR (Geographically Weighted Regression) model further reveals that GTWR substantially outperforms both OLS and GWR in terms of AICc and goodness-of-fit (

Table 6. Comparison of model results.

Model	AICc	R2	Adjusted R2
OLS	2070.18	0.3254	0.3189
GWR	1719.26	0.6013	0.5975
GTWR	1264.16	0.8035	0.8016

), confirming its superior ability to capture the spatiotemporal heterogeneity of WEFSE.

Based on the GTWR model, the spatial distributions of the regression coefficients for each explanatory variable in 2000 and 2020 indicate that the effects of socio-economic and natural environmental factors on the dependent variable exhibited distinct spatiotemporal variations across the study area. Overall, the dominant mechanism has gradually shifted from being primarily constrained by socio-economic factors to a new pattern characterized by the deep coupling and mutual balance among socio-economic, natural environmental, and ecological land-use factors.

In terms of socio-economic factors, NLI was relatively high in the northern and central regions in 2000, with coefficients ranging from 0.355 to 0.455, whereas it was lower in the southern regions (−0.506 to −0.318). This indicates that urbanization and economic activities in the northern and central regions had a significant positive effect on agricultural efficiency, while their influence in the south was weaker or even negative. By 2020, the positive effect of NLI had further expanded toward the central and southern regions, with coefficients increasing to 0.007–0.441. PD showed an overall negative effect in 2000 (−0.193 to −0.023), reflecting the resource and environmental pressures caused by the early-stage population concentration. By 2020, the coefficients in the central and northern regions had shifted from negative to positive, reaching up to 0.404, while those in the southern regions remained negative, indicating pronounced regional differentiation. PCL exhibited an overall negative correlation in 2000 (−0.310 to −0.032), with the lowest values observed in the southwestern region. This suggests that limited cultivated land per capita placed widespread constraints on development. In 2020, the coefficients in the central and southern regions had shifted from negative to positive (0.087–0.296), while those in the northern and peripheral areas remained negative, with the lowest value reaching −0.372, reflecting the spatiotemporal heterogeneity in the distribution of cultivated land resources.

In terms of meteorological factors, more complex regional differences were observed. In 2000, AT showed a positive correlation in the southwestern region, with coefficients ranging from −0.059 to 0.301, while it was negative in the northeastern and central regions, ranging from approximately −0.335 to −0.157. By 2020, the coefficients in the northeastern region had shifted from negative to positive, reaching 0.168–0.526, whereas those in the central region remained negative. In 2000, PRE exhibited a “positive in the south and negative in the north” pattern, with coefficients ranging from −0.139 to 0.228. By 2020, the correlation was negative across the entire region, with the lowest value of −0.231 in the south and the weakest value of −0.099 in the north, indicating that the impact of precipitation had shifted from spatial differentiation to overall inhibition. This suggests that additional rainfall increasingly failed to alleviate water stress and instead tended to aggravate mismatches between water availability and crop water demand. One plausible explanation is that, under recent climate change, more intense and uneven rainfall events, together with the limited adaptability of local irrigation and drainage systems, have increased waterlogging risk and reduced the effective utilization of precipitation for improving WEFSE.

In terms of ecological land-use factors, GP showed a positive correlation in the southwestern region in 2000, with coefficients ranging from 0.082 to 0.264, while it was negative in the northern region (−0.291 to −0.221). By 2020, the correlation in the southern region was a strongly negative, with coefficients ranging from −4.532 to −1.708, whereas those in the northern and central regions had increased to 0.151–0.860, forming a spatial pattern characterized by “southern constraints and northern drivers.” In 2000, WP was high in the northeastern region, with coefficients ranging from 0.116 to 0.305, while it was negative in the central region and close to zero in the southern region. Several higher-value areas were also observed along the periphery. By 2020, the high-value areas had shifted southward, with coefficients in the southwestern region generally exceeding 0.491 and reaching up to 1.356 in some localities, becoming key zones for efficiency improvement. In contrast, the high values in the northeastern region had weakened significantly, with some areas turning negative, while the central region had developed extensive medium- and high-value areas, indicating that water resource utilization efficiency had markedly improved and a new regional support pattern had emerged. In 2000, NDVI showed a positive correlation in the central region, with coefficients ranging from 0.066 to 0.370, while most areas in the southwestern and northeastern regions exhibited weak effects, and some localities even showed negative correlations, indicating a dual effect. By 2020, the correlation had turned negative across the entire region, with the strongest negative values (−0.669) observed in the northeast, and negative correlations also occurred in the central and southwestern regions, indicating that there was no longer a promoting effect on vegetation growth, but rather, a limiting effect.

Table 7. Descriptive statistics of Geographically and Temporally Weighted Regression coefficient estimates.

Factor	Mean β	Std. Dev.	Min β	Max β	Q1	Q3
NLI	0.0772	0.3094	−0.6112	0.6712	−0.1936	0.3571
PD	−0.0479	0.1679	−0.3229	0.2843	−0.1207	0.0172
PCL	−0.0207	0.2003	−0.6499	0.6539	−0.2029	0.1827
AT	−0.0934	0.2836	−0.5443	0.4035	−0.2249	0.0085
PRE	−0.1440	0.1205	−0.6794	0.2964	−0.3088	0.0394
GP	−0.1086	0.6279	−4.5324	2.1602	−0.1950	0.1331
WP	0.0787	0.2182	−0.6199	1.3562	−0.0421	0.1481
NDVI	−0.2102	0.2877	−0.6740	0.3703	−0.5028	0.0478

provides a quantitative summary of GTWR coefficients. According to the descriptive statistics, there are significant differences in the mean values and variability of each influencing factor. The mean of NLI is 0.0772, with a standard deviation of 0.3094, indicating significant regional differences and suggesting that this factor has a prominent impact across different regions. The mean of PD is −0.0479, with a standard deviation of 0.1679, indicating small variability and suggesting that its impact on WEFSE is relatively stable. The means of PCL and NDVI are −0.0207 and −0.2102, respectively, with moderate standard deviations, indicating that these factors have a more balanced impact across regions. The standard deviation of GP is large, and the range of extreme values is notable, indicating that this factor has a significant and spatially variable impact on WEFSE. Overall, NLI and GP show greater variability, highlighting their stronger impact on resource utilization efficiency, while factors like PD, PCL, and NDVI show smaller variability, indicating their more balanced and stable effects.

In summary, the above analysis reveals that from 2000 to 2020, different factors exhibited not only distinct spatial differentiation but also significant changes in their overall value ranges and degrees of dispersion. To more intuitively investigate the differences and evolutionary characteristics of the coefficients for each factor, we plotted boxplots of the factor coefficients from 2000 to 2020 (Figure 8). In each boxplot, the red line denotes the median.

In terms of socio-economic factors, the median coefficient of NLI is approximately 0.2 in 2000 and rises to a peak of 0.45 by 2007, indicating that the promoting effect of urbanization on efficiency was strongest during this period. However, the expansion of the box also reflects pronounced spatial heterogeneity of this positive influence. Thereafter, the effect is reversed, with the median coefficient decreasing to −0.1 between 2013 and 2015, accompanied by significant expansion of the box, indicating the intensification of spatial differentiation. By the end of the study period, the coefficients stabilize around zero, and the box narrows, suggesting that the relationship between the two entered a stage of low-level equilibrium. The coefficient of PD remains negative from 2000 to 2009, reaching a minimum of −0.25, with a relatively narrow box, indicating that the inhibitory effect was widespread. After 2010, the coefficient shifts from negative to positive, reaching up to 0.25, while the box expands, suggesting that the population scale effect strengthened and spatial disparities increased. The coefficient of PCL was negative from 2000 to 2007, reaching a minimum of −0.4. It rebounds after 2008 and peaks at 0.1 in 2010, then fluctuates around zero with the box becoming narrower, indicating that the influence gradually tended toward neutrality.

In terms of meteorological factors, the median coefficient of AT is positive from 2000 to 2005, reaching 0.2 in 2004, but declines to a trough of −0.45 in 2009, accompanied by expansion of the box, indicating that the inhibitory effect of rising temperature intensified. By 2017, the coefficient rebounds to 0.4, with the box expanding again, reflecting increased volatility in the temperature effect. The coefficient of PRE is positive from 2000 to 2004, reaching a peak of 0.1 in 2003, indicating that precipitation acted as a favorable factor for improving efficiency during this period. Subsequently, it turns negative, with the median coefficient dropping to −0.2 in 2011 and the box continuing to expand. By the end of the study period, the coefficients fluctuate below zero and gradually converge, suggesting that the negative impact of precipitation stabilized.

Regarding ecological land-use factors, the median coefficient of GP remained approximately zero over the study period. However, a considerable number of negative outliers emerge after 2015, with the minimum value dropping below −4.0. This suggests that, in certain regions, a higher proportion of grassland exerted a pronounced inhibitory effect-likely due to grassland degradation, overgrazing, or desertification-which substantially diminished the land and water conservation functions of these ecosystems. The coefficient of WP remained at a low positive level (0.0–0.1) from 2000 to 2013, with a relatively narrow box. After 2014, the median value increases to approximately 0.2, and the box expands markedly, indicating strengthening of the positive influence of the WP and widening of spatial heterogeneity. The coefficient of NDVI is positive from 2000 to 2008, with median values ranging from 0.0 to 0.1, indicating a stable promoting effect on efficiency. After 2009, it turns negative, reaching −0.6 in 2017 and stabilizing at around −0.5 by the end of the study period. The box becomes narrower, suggesting that its effect shifted from promotion to inhibition and then stabilized.

Overall, the factors influencing WEFSE in the study area underwent substantial structural changes from 2000 to 2020, shifting from dominance by natural constraints to guidance by socio-economic drivers. Their effects were nonlinear and dynamic, showing non-monotonic trends, significant spatial autocorrelation, and stage-specific reversals in direction. The spatial distribution of efficiency demonstrated a gradual transition from the southwest to the northeast, reflecting a gradient of evolution from low-efficiency to high-efficiency regions.

4. Discussion

This study revealed the spatiotemporal evolution characteristics of the WEFSE in the irrigation districts of the lower reaches of the Yellow River from 2000 to 2020. The overall efficiency level continuously improved, indicating that, the optimization of water conservancy infrastructure, the widespread adoption of water-saving agricultural technologies, and the transformation of farming practices have jointly improved of resource use efficiency over the past two decades [62,63]. This spatial differentiation pattern was mainly driven by the combined effects of natural resource availability, cultivated land concentration, and economic input intensity, which is consistent with a previous study that identified a pattern of “high efficiency in the east and low efficiency in the west, with significant spatial clustering” [64]. In contrast, the southwestern region has long maintained a relatively low efficiency level due to constraints such as water scarcity, poor land conditions, and a weak economic foundation [65]. Recent studies on the irrigation districts in the lower reaches of the Yellow River have shown that irrigation districts located in the northeastern part of the lower Yellow River have more reliable surface-water diversion conditions and have received more intensive investments in canal rehabilitation and water-saving irrigation projects, which jointly reinforce their efficiency advantage over other districts in the same basin [66,67].

The analysis of the evolution of dominant factors showed that, in the early stage of the study period, efficiency was mainly driven by socio-economic factors such as NLI [68]; in the middle stage, the economic effects weakened while environmental constraints intensified; and in the later stage, the positive effects of PD and WP became significantly stronger, whereas PRE and NDVI emerged as major negative constraints [69,70].As the regional climate has warmed and precipitation has become more variable in terms of timing and intensity, additional rainfall is increasingly prone to occur in forms that exceed the regulating capacity of existing irrigation–drainage systems and soils, so that it aggravates waterlogging and mismatches between water supply and crop water demand instead of alleviating water stress and improving WEFSE [71,72]. This conclusion is consistent with several studies investigating the impacts of climate and vegetation on land moisture and agricultural drought [73], as well as on the evolution of driving factors within the WEF system. This trend is generally consistent with the empirical findings of existing studies on the irrigation districts in the lower reaches of the Yellow River [74], which emphasized that ecological coverage and hydrological anomalies have gradually replaced single economic inputs as the dominant forces driving system evolution. Overall, with the intensification of climate change and the evolution of ecological land-use structures, environmental constraints are becoming an increasingly important external limiting factor for further WEFSE improvement.

At the macro level, the overall findings indicate that improving agricultural WEFSE in the irrigation districts of the lower Yellow River should rely less on simply expanding inputs and more on promoting high-efficiency, water-saving irrigation, optimizing cropping and land-use structures, and strengthening ecological conservation and basin-scale coordination of water allocation [75]. First, the efficiency analysis shows a steady increase in WEFSE from 2000 to 2020, accompanied by a widening gap between high and low efficiency irrigation districts when undesirable outputs are considered; this is broadly consistent with basin-scale studies that find an overall rise in agricultural water efficiency in the Yellow River Basin but persistent regional disparities driven by differences in economic development and water-resource endowments [76], implying that macro-level policy should shift from input-oriented growth to efficiency-oriented growth with stronger support for lagging districts. Second, the spatial autocorrelation analysis reveals a clear and persistent pattern of high-efficiency clustering in the northeastern part of the study area and low-efficiency clustering in the southwest, which echoes the significant “high–high” and “low–low” clustering of existing studies for the Yellow River Basin suggesting that northeastern high-efficiency districts can be developed as demonstration zones for advanced water-saving irrigation and refined water–land matching, while southwestern low-efficiency districts require targeted investment in infrastructure upgrading and structural adjustment [77,78]. Third, the GTWR results indicate a staged shift in the dominant drivers of WEFSE-from early promotion mainly associated with socio-economic factors such as NLI to a growing influence of climatic and ecological constraints related to PRE, AT, NDVI [79], this calls for regionally adaptive measures that combine basin-wide promotion of water-saving technologies and ecological restoration with local policies tailored to the efficiency level, spatial position and dominant driving factors of each irrigation district.

Although this study revealed the long-term evolutionary characteristics of efficiency in the Yellow River irrigation districts, it has certain limitations. First, the selection of efficiency indicators primarily relied on existing statistical data and derived products. Some key variables, such as NDVI, NLI, are based on remote sensing or modeled datasets that may be affected by sensor noise, atmospheric conditions, interpolation and resampling procedures, as well as scale inconsistencies. These data uncertainties may introduce bias into the measurement of WEFSE. In addition, factors such as ecosystem services and within-district land-quality differences were not fully quantified, so the efficiency evaluation may not have captured some underlying micro-level mechanisms. Methodologically, the analysis was conducted mainly at a macro-regional scale using a GTWR framework that assumes short-term spatiotemporal stationarity within the bandwidth window; the local coefficients therefore describe spatial associations rather than strict causal relationships, and rapid intra-annual changes may be underrepresented. Future research could enrich the indicator system, incorporate higher-resolution and multi-source datasets, and combine short-term time-series with micro-scale field investigations to better identify the dynamic evolution and underlying drivers of agricultural WEFSE, thereby strengthening the robustness and policy relevance of the results for the sustainable management of irrigation districts in the lower reaches of the Yellow River.

Looking ahead, agricultural WEFSE research faces significant challenges due to increasing hydro-climatic variability and the complex interactions between WEF systems. To address these challenges, future studies should focus on developing dynamic models that integrate local climate data and specific crop requirements to better predict system responses under changing environmental conditions. Improving data collection methods, such as integrating real-time soil moisture sensors and satellite data, will provide more accurate and timely assessments. Additionally, combining water-efficient irrigation techniques with renewable energy sources can enhance the sustainability and resilience of irrigation systems, ensuring more adaptive solutions in the face of ongoing climate change.

5. Conclusions

This study focused on the irrigation districts in the lower reaches of the Yellow River and constructed a dynamic DEA and GTWR model from the perspective of the WEF system to systematically analyze the spatiotemporal evolution characteristics and driving mechanisms of WEFSE from 2000 to 2020. The main conclusions are as follows:

(1)

When undesirable outputs were considered, the overall WEFSE of the irrigation districts showed a steady upward trend, while regional disparities gradually widened. The spatial pattern and relative ranking of high- and low-efficiency districts remained largely stable. Over time, the efficiency pattern evolved from scattered high-efficiency areas in the southwest to a more continuous high-efficiency belt in the northeast, forming a clear southwest–northeast gradient.

(2)

During the study period, the WEFSE of the irrigation districts exhibited an increasingly strong positive spatial autocorrelation. Moran’s I showed an overall upward trend, indicating a stable spatial spillover effect and pronounced “high–high” and “low–low” clustering. The northeastern irrigation districts stayed in persistent high-efficiency clusters, whereas the southwestern districts formed low-efficiency clusters, reflecting marked regional gaps in resource allocation and institutional responsiveness.

(3)

The driving mechanisms of WEFSE showed clear stage differentiation. In the early stage, WEFSE was mainly driven by NLI; in the middle stage, economic effects weakened and environmental constraints strengthened; and in the later stage, PD and WP became the core positive factors, while PRE and NDVI evolved into major negative constraints. The impacts of PCL, GP and AT exhibited clear spatial heterogeneity. Overall, the system shifted from a single socio-economic driving pathway to a composite mechanism jointly dominated by ecological and structural factors.

In conclusion, the assessment of efficiency and its driving mechanisms from on the perspective of the WEF system can facilitate the exploration of more scientific resource allocation pathways in heterogeneous regions, providing methodological support and practical insights for the sustainable transformation of the Yellow River irrigation districts and other complex agricultural systems.