Analysis of Water Resource Utilization Efficiency and Its Driving Factors in the Water-Receiving Area of the Tao River Diversion Project

Abstract

To solve the spatial water resources shortage, lots of water diversion projects have been constructed for sustaining development. As the water resource utilization efficiency (WRUE) is assumed not to decrease after the operation of water diversion projects, it is necessary to analyze the WRUE and its driving factors in a water-receiving area. Taking the Tao River Diversion Project as a case study, a Super-SBM (Super Slack-Based Measure) model and the Malmquist–Luenberger index are applied in estimating the WRUE values in the seven counties or districts in the water-receiving area of the Tao River Diversion Project. Spatial autocorrelation and a geographical detector are applied to explore the patterns and influencing factors. The results show that there is significant spatial variation in WRUE across the water-receiving areas from 2010 to 2019. High-efficiency areas maintain or improve their efficiencies, while low-efficiency areas show a stagnant or declining trend. The nondecreasing premise of WRUE is not fully satisfied in any area and at any time. The water diversion project is found to be a key driver for the shifting spatial patterns of WRUE from a cold spot dominance to a stronger hot spot agglomeration. The influencing factors on WRUE’s spatial differentiation are also dynamic with the operation of the water diversion project. Therefore, our study will not only help to assess the benefits of the Tao River Diversion Project, but can also provide many valuable insights for water resource planning.

1. Introduction

Water allocation has emerged as a global concern, and this challenge intensifies with the widening gap between water supply and demand. Such a predicament is further shaped by water management strategies, water footprint performance, and the accessibility of alternative water sources. Moreover, water scarcity is not merely a product of natural constraints; it is also a scarcity driven by social factors [1]. Water resources are among the most fundamental resources for human survival because of their importance to social, economic, and ecological systems [2,3]. Due to the uneven temporal and spatial distribution of water resources in China, water resources shortage is becoming a critical hindrance for its social and economic development [4]. To solve the water resources shortage issue, lots of water diversion projects have been constructed for sustaining development [5,6]. However, there is a premise that the efficiency of water resource utilization (WRUE) will not decrease. The differences in WRUE between the no-diversion project period and the operation period of the diversion project can help us not only test the no-decrease WRUE premise but also assess the benefits of the diversion project in the receiving area of the water diversion project for sustaining its operation [7,8,9].

WRUE reflects the efficiency of the multi-input and multi-output of a water diversion project in terms of a decision-making unit (DMU). To assess this type of efficiency, Data Envelopment Analysis (DEA) was developed through a scalar indicator that ranges between 0 (i.e., the worst) and 1 (i.e., the best) by Charnes et al. [10,11]. It is a non-parametric method for relative efficiency evaluation, and does not require the prior determination of functional relationships, and is not subjective in the weighting of the ineffective factors of the DMU. Although DEA has been widely applied in the assessment of WRUE, it can only classify the DMU as either efficient or inefficient rather than fully rank all the DMUs [12]. And only economic benefits of WRUE were taken into account and the slack variables between the input and output of the DMU were neglected [3,10,13]. However, it failed to take into account the unwanted output of wastewater and its actual WRUE production process cannot be reflected. To address these issues, Tone proposed a non-radial and non-angular SBM (Slack-Based Measure) model [4]. The model directly incorporates the slack variables into the objective function, avoiding the selection bias of radial and angular directions. For ranking the effective DMU [14], Tone proposes the Super-SBM model for taking non-desired outputs into account [12]. As the undesirable outputs (e.g., wastewater), traditional DEA models (e.g., CCR and BCC) [10,15] require their indirect processes to incorporate non-expected outputs, and they may distort the original efficiency information. However, a Super-SBM and the Malmquist–Luenberger (ML) index can directly embed undesirable outputs into the objective function, reflecting the trade-off between expected outputs and undesirable outputs in the production process, which is more consistent with the efficiency evaluation context of DMUs involving pollution emissions [16]. To rank the efficient DMUs, conventional DEA models often classify multiple DMUs as “fully efficient (efficiency value = 1)” and fail to distinguish their relative superiority [15]. The Super-SBM addresses this limitation by adjusting the slacks of inputs and outputs, enabling the precise ranking of efficient DMUs. Meanwhile, the ML index further refines the dynamic efficiency differences among efficient units by decomposing the total factor productivity (TFP) into technical change and efficiency change, which is unavailable in the traditional Malmquist index, which ignores undesirable outputs. Compared with alternative models such as EBM (mixed-orientation but weak in ranking) or SBM-DEA (without super-efficiency ranking function), the combination of the Super-SBM (static efficiency and ranking) and the ML index (dynamic TFP change) [17] fully matches the need to evaluate both the static efficiency and dynamic evolution of DMUs with dual characteristics of expected and undesirable outputs of water diversion. The redundancy of input and the insufficiency of output in each county or district in the water-receiving area for a water diversion project can be quantified by the slack variables and are used for determining their WRUE values. If its efficiency value is greater than 1, it can be determined through the super-efficiency mechanism, and the WRUE values of different counties or districts in the study area can be ranked [4,15]. Since water resource utilization not only produces economic benefits, but also generates non-desired outputs such as wastewater in daily life, agriculture, and industrial production, the Super-SBM model will be applied in assessing the WRUE of the receiving area of a water diversion project.

The differences in water resource allocation among various administrative regions within the water-receiving area and the imperfect trust mechanism among stakeholders, along with the incomplete technical policies for water resource utilization in some regions and the insufficient application of advanced water-saving technologies, have become key factors affecting the overall WRUE in the water-receiving area [1]. The aim of our study is to show a way to assess the WRUE of a water diversion project and figure out the impact factors for optimizing water resource development in its water-receiving area. The changes in WRUE before and after the operation of the water diversion project can test the no-decrease WRUE premise. The Methodology including the study area and dataset is presented in Section 2. Section 3 covers the Results and Discussion, and Conclusions are drawn in Section 4.

2. Methodology

2.1. Study Area

To solve the arid and water-scarce areas in the central part of Gansu Province in China, the Tao River Diversion Project was built to divert water from the Tao River, a first-class tributary of the Yellow River. The project has a wide receiving area, a long water diversion canal line, and benefits a large number of people. It is the largest inter-basin water diversion project in Gansu Province in China [18,19,20]. The project began operation in 2014 and reached its designed supply capacity in 2017. The water-receiving area spans 34°50′–36°26′ N and 103°29′–105°38′ E, covering the central and southeastern Gansu Province and including Yuzhong, Huining, Anding, Tongwei, Longxi, Weiyuan, and Linta counties or districts (Figure 1).

2.2. Data Sources

As the water-receiving area refers to seven counties or districts, data in these areas from 2010 to 2019 were collected. The investment in fixed assets, the population, as well as domestic, industrial, and agricultural water use were taken as input indicators while the regional gross domestic product (GDP), the industrial gross output value, and the agricultural gross output value were taken as output indicators for the water utilization system. The discharge of wastewater was taken as the undesired output indicator. These data were mainly obtained from the Gansu Water Resources Statistical Yearbook [21], the Gansu Province Water Resources Bulletin [22], and the Gansu Province Development Yearbook [23].

2.3. Research Methods

To take the undesired output indicator into account, the Super-SBM model is applied to estimate the WRUE of the study area. After determining the total factor productivity of water resources by the Malmquist index, the influencing factors of the WRUE spatial changes will be figured out by a geographic detector in the water-receiving area.

2.3.1. The Super-SBM Model

The SBM model evaluates the performance of a DMU based on its input excesses and output shortfalls, but it can only be applied in a DMU with no slack (zero-slack) [10] and fails to discriminate between SBM-efficient units. As the Super-SBM model can measure the Super-SBM efficiency score of an SBM-efficient DMU, it has been proposed to remove the unit under assessment from the technology. The super-efficiency score of an efficient unit may exceed 1 while the super-efficiency score of an inefficient unit remains the same as its SBM efficiency score. The Super-SBM model can rank the unit based on its Super-SBM efficiency score [14]. Therefore, the Super-SBM model incorporates the input, expected output, and undesired output. The redundancy of input and the insufficiency of output in each county or district can be quantified by the slack variables and are used for determining their WRUE values. If an efficiency value is greater than 1, it can be determined through the super-efficiency mechanism, and the WRUE values of different counties or districts in the study area can be ranked. The excess in input and the insufficiency in output of each county or district can be specifically analyzed according to the slack variable results from the model [4,15].

$$\mu =min{\displaystyle \frac{1-\frac{1}{J}{\sum }_{j=1}^J{s}_j^x/x_{n_j^{\prime }}^{t^{\prime }}}{1+\frac{1}{K+L}\left({\sum }_{k=1}^K{s}_k^y/y_{n_k^{\prime }}^{t^{\prime }}+{\sum }_{l=1}^L{s}_l^z/z_{n_l^{\prime }}^{t^{\prime }}\right)}}$$

(1)

$$subject to \left\{\begin{array}{c}{\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{n=1}^N}{\sigma }_n^t{x}_{n_j}^t+s_j^x=x_{n_j^{\prime }}^{t^{\prime }} (j=1,\dots ,J)\\ {\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{n=1}^N}{\sigma }_n^t{y}_{n_k}^t-s_k^y=y_{n_k^{\prime }}^{t^{\prime }} (k=1,\dots ,K)\\ {\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{n=1}^N}{\sigma }_n^t{z}_{n_l}^t+s_l^z=z_{n_l^{\prime }}^{t^{\prime }} (l=1,\dots ,L)\\ {\sigma }_n^t\ge 0,s_j^x\ge 0,s_k^y\ge 0,s_l^z\ge 0,(n=1,\dots ,N)\end{array}\right.$$

where μ denotes the value of WRUE; J, K, and L are the number of input factors, desirable output factors, and undesirable output factors. They are 5, 3, and 1, respectively, in our case study. N is the number of counties and is 7 here. The terms $x_{k_j^{\mathrm{\prime }}}^{t^{\mathrm{\prime }}}$, $y_{k_k^{\mathrm{\prime }}}^{t^{\mathrm{\prime }}},$ and $z_{k_l^{\mathrm{\prime }}}^{t^{\mathrm{\prime }}}$ correspond to the input vector, the desirable output vector, and the undesirable output vector of the k′ counties at t′ period, respectively. $x_{k_j}^t$, $y_{k_k}^t$, and $z_{k_l}^t$ are the matrices representing the inputs, desirable outputs, and undesirable outputs of the k counties at t period, respectively. T is the total number of time periods and is 10 in our case study (e.g., the research period covers 2010 to 2019, T = 10). The vectors ($s_j^x,s_k^y,s_l^z$) and ${\sigma }_n^t$ denote the input and output slack and the weight of N × T DMUs at t period, respectively.

2.3.2. Malmquist Index

To take the undesired outputs into efficiency analysis, Chung and Fare, based on the output-oriented directional distance function within the framework of the Malmquist index, obtained the M index including undesired outputs, which was subsequently named the Malmquist–Luenberger index. The index provides an important tool for efficiency analysis including undesired outputs and has been widely applied [16,17,24,25].

$$M_c^{t+1}\left(x^t,y^t,x^{t+1},y^{t+1}\right)={\left[{\displaystyle \frac{E_c^t(x^{t+1},y^{t+1})}{E_c^t\left(x^t,y^t\right)}}.{\displaystyle \frac{E_c^{t+1}(x^{t+1},y^{t+1})}{E_c^{t+1}\left(x^t,y^t\right)}}\right]}^{{\displaystyle \frac{1}{2}}}$$

(2)

where M denotes the TFP index. If M > 1, there is an improvement in the TFP level while there is a decline in the TFP level if M < 1. E_c^t(x^t, y^t) is the efficiency value of input x ^t and output y ^t during period t where x and y are input variables and output variables, respectively; t is the time periods; c stands for Constant Returns to Scale (CRS).

$$M_c^{t+1}=E{C}_c\times T{C}_c=\mathit{PEC}\times \mathit{SEC}\times T{C}_c$$

(3)

where ${\mathit{EC}}_c$ is the technological efficiency change index; ${TC}_c$ is the technological change index; PEC is the pure technical efficiency change index; and SEC is the scale efficiency change index. If ${\mathit{EC}}_c$ > 1, there is an improvement in technological efficiency while the decision-making units have not fully utilized the existing technologies if ${\mathit{EC}}_c$ < 1. ${\mathit{EC}}_c$ can be estimated by the Equation (4). ${\mathit{TC}}_c$ reflects the impact of production technology progress on decision-making units (DMUs). If ${\mathit{TC}}_c$ > 1, it indicates technological progress or technological innovation while vice versa. ${\mathit{TC}}_c$, PEC, and SEC can be estimated by the following Equations (5)–(7).

$$E{C}_c={\displaystyle \frac{E_c^{t+1}(x^{t+1},y^{t+1})}{E_c^t\left(x^t,y^t\right)}}$$

(4)

$$T{C}_c={\left[{\displaystyle \frac{E_c^t(x^{t+1},y^{t+1})}{E_c^{t+1}\left(x^{t+1},y^{t+1}\right)}}·{\displaystyle \frac{E_c^t(x^t,y^t)}{E_c^{t+1}\left(x^t,y^t\right)}}\right]}^{{\displaystyle \frac{1}{2}}}$$

(5)

$$\mathit{PEC}={\displaystyle \frac{E_v^{t+1}(x^{t+1},y^{t+1})}{E_v^t(x^t,y^t)}}$$

(6)

$$SEC={\displaystyle \frac{E_c^{t+1}(x^{t+1},y^{t+1})/E_v^{t+1}\left(x^{t+1},y^{t+1}\right)}{E_c^t(x^t,y^t)/E_v^t(x^t,y^t)}}$$

(7)

2.3.3. Spatial Autocorrelation Analysis

(1)

Global Spatial Autocorrelation

To figure out a global spatial autocorrelation analysis of the WRUE, Moran’s I index [26,27] was selected and can be estimated by the Equation (8).

$$Moran\prime s I={\displaystyle \frac{\sum _{i=1}^N\sum _{j=1}^M{W}_{ij}(x_i-\overline{x})(x_j-\overline{x})}{S^2\sum _{i=1}^N\sum _{j=1}^M{W}_{ij}}}$$

(8)

$$S^2={\displaystyle \frac{1}{N}}\sum _{i=1}^N{\left(x_i-\overline{x}\right)}^2$$

(9)

where x_i, x_j are the WRUE values of the i-th and j-th county or district; N is the total number of counties and districts; W_ij is the adjacent spatial weight matrix between i-th and j-th county or district. If the i-th county or district is adjacent to the j-th county or district, W_ij = 1; otherwise, W_ij = 0. The significance test is carried out according to z =$(I-E(I\left)\right)/\sqrt{\left(Var\right(I\left)\right)}$. The value range of I is [−1, 1]. When I > 0, there is spatial agglomeration of WRUE; when I < 0, there is a spatial divergent distribution of WRUE; when I = 0, there is no spatial autocorrelation of WRUE and is taken as a random state.

(2)

Local Spatial Cold and Hot Spot Analysis

According to the WRUE values, local cold and hot spot analyses are applied to identify the spatial agglomeration and dispersion phenomena within a region, as well as the existence of hot spots (i.e., high-value agglomeration areas) and cold spots (i.e., low-value agglomeration areas) in different spatial positions [28,29]. The analysis is carried out through the G_i* statistical index as the Equation (10).

$$G_i^{*}={\displaystyle \frac{\sum _{j=1}^N{W}_{ij}{x}_j}{\sum _{i=1}^n{x}_i}}$$

(10)

$$Z(G_i^{*})={\displaystyle \frac{G_i^{*}-E\left(G_i^{*}\right)}{\sqrt{Var\left(G_i^{*}\right)}}}$$

(11)

where G_i* is the Getis–Ord G_i statistic; E(G_i*) and Var(G_i*) are the expectation and coefficient of variation of G_i*, respectively; Z(G_i*) is the statistical test value in Equation (11). If Z(G_i*) is positive and significant, it indicates high-value spatial agglomeration; if Z(G_i*) is negative and significant, it indicates low-value spatial agglomeration.

2.3.4. Geographical Detector

To detect spatial heterogeneity and reveal its driving factors of WRUE [12], a geographical detector is applied here to judge the similarity of the spatial distribution between the driving factors based on the spatial hierarchical heterogeneity of WRUE [30] in the water-receiving area of the Tao River Diversion Project.

$$q=1-{\displaystyle \frac{\sum _{k=1}^K{N}_k{\sigma }_k^2}{N{\sigma }^2}}$$

(12)

where q is the explanatory power of each factor on the WRUE, and its value range is [0, 1]. k = 1, 2, …, K is the stratification of the driving factor; N_k is the number of counties or districts for the kth factor; σ²_k is the variance of the kth factor; and σ² is the variance of the whole study area.

The influencing factors of WRUE can be summarized, as shown in

Table 1. Indicators of the driving factors of WRUE.

Influencing Factors	Variable	Unit	Data Source
Natural Resources Conditions	Annual Precipitation (x1)	m3/person	National Meteorological Science Data Center of the China Meteorological Administration (2010–2019)
Population Size	Permanent Population of a Year (x2)	10,000 people	Gansu Development Yearbook (2011–2020)
Population Quality Level	Proportion of Population with or above the Junior College Education (x3)	%	Gansu Development Yearbook (2011–2020)
Water Use Structure	Proportion of Agricultural Water Use (x4)	%	Gansu Water Conservancy Yearbook (2010–2019)
	Proportion of Industrial Water Use (x5)	%	Gansu Water Conservancy Yearbook (2010–2019)
Urban Development Level	Urbanization Rate (x6)	%	Gansu Development Yearbook (2011–2020)
Science and Technology Development Level	Proportion of Science and Education Expenditure in Fiscal Expenditure (x7)	%	Gansu Development Yearbook (2011–2020)
Economic Development Level	Per Capita GDP (x8)	RMB	Gansu Development Yearbook (2011–2020)
	Investment in Fixed Assets (x9)	RMB 100 million	Gansu Development Yearbook (2011–2020)
Water Consumption	Water Consumption/GDP (x10)	RMB m3/10,000	Gansu Water Conservancy Yearbook (2010–2019)

Notes: The National Meteorological Science Data Center of the China Meteorological Administration, https://www.cma.gov.cn/. https://data.cma.cn/; Gansu Water Conservancy Yearbook (2010–2019), https://slt.gansu.gov.cn; Gansu Development Yearbook (2011–2020), https://tjj.gansu.gov.cn.

.

As a big cross-basin water diversion project in Gansu Province, the main function of the Tao River Diversion Project is to alleviate persistent water scarcity in its water-receiving areas. In addition to the water supply, the project will also restructure the coupled water–ecology–economy–society system as a pivotal role in the arid regions of Northwest China. This role requires a benefit assessment from multiple dimensions, long time horizons, and spatial heterogeneity. Therefore, water resource utilization efficiency (WRUE) was adopted as a central performance metric to capture how effectively inputs are transformed into desirable outputs while accounting for environmental constraints.

Traditional DEA models have difficulty in handling undesirable outputs and cannot further discriminate among decision-making units (DMUs) that have a score of 1. To overcome these limitations, the Super-SBM model explicitly incorporates slack and undesirable outputs (e.g., wastewater), enabling realistic production characterization and complete ranking of efficient DMUs. Because WRUE evolves with project progress, policy adjustments, and socio-economic change, the temporal dynamics were analyzed using the Malmquist–Luenberger index, which decomposes total factor productivity into efficiency change and technical change, thereby distinguishing catch-up from frontier shifts. Given that the study area spans multiple administrative units, the spatial dependence was examined with global Moran’s I and local Getis–Ord G_i* statistics implemented to identify overall autocorrelation as well as hot and cold spot clusters. Finally, to reveal determinants and their interactions, a geographical detector was employed to quantify each factor’s explanatory power for the spatial variance in WRUE. This integrated framework provides DMU-level diagnostics of input redundancies and output shortfalls while it yields macro-level insights into regional coordination and spatiotemporal evolution, thereby informing optimal water resource allocation, targeted policy design, and the sustainable operation of the Tao River Diversion Project with aligned economic, social, and ecological benefits.

3. Results and Discussion

3.1. Analysis of WRUE

The WRUE of each county/district in the water-receiving area of the Tao River Diversion Project is listed in

Table 2. The WRUE in the water-receiving areas of the Tao River Diversion Project from 2010 to 2019 (The * in the table indicates the year when benefits were first realized).

Region	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	Average
Yuzhong	1.199	1.311	1.337	1.325	1.325	1.122	1.054	1.033	1.269 *	1.359	1.233
Huining	1.200	1.511	1.337	1.271	1.229	1.160 *	1.159	1.223	1.620	1.670	1.338
Anding	1.329	1.345	1.320	2.305	2.581	2.676 *	2.516	2.466	2.136	1.972	2.065
Tongwei	1.467	1.737	1.676	1.254	1.244	1.189	1.106	1.174	1.036 *	1.024	1.291
Longxi	1.055	1.021	1.034	1.004	0.499	0.398 *	0.493	0.386	0.407	0.369	0.667
Weiyuan	1.011	0.395	1.021	1.021	1.008	1.185 *	1.191	0.390	1.107	1.094	0.942
Lintao	0.393	0.328	0.372	0.405	0.400	0.409 *	0.399	0.351	0.375	0.310	0.374
Average	1.093	1.093	1.157	1.226	1.184	1.163	1.131	1.003	1.136	1.114	1.130

and shown in Figure 2. As the average values of WRUE in various counties or districts during 2010 to 2019 are shown in Figure 2, there are significant gaps in efficiency among different counties or districts. The high levels of WRUE over a long time can be found in Anding District (2.065), Huining County (1.338), and Yuzhong County (1.233). They show their strong capacities to translate water inputs into desired outputs. Significantly lower efficiencies can be found in Lintao County (0.374), Weiyuan County (0.942), and Longxi County (0.667) due to their restricted factors such as industrial structure, water resource management level, and supporting infrastructure.

From 2010 to 2019, WRUE generally increased, then stabilized, and finally declined slightly. The average value rose from 1.093 to 1.226 during 2010–2014, reflecting gradual improvement in most areas and enhanced benefit conversion. Affected by the adjustment period after water diversion, the average value remained between 1.003 and 1.163 during 2015–2017, and regional water resource utilization entered a stable period. From 2018 to 2019, the average value slightly dropped to 1.114, and the efficiency of some regions declined slightly, consistent with the ongoing optimization of water allocation and industrial restructuring.

Following the implementation of water diversion in 2015 for Anding District, Longxi County, Weiyuan County, Lintao County, and Huining County, and in 2018 for Yuzhong County and Tongwei County, regional efficiency changes diverged. Anding District stayed above 2.0 after 2015, and Yuzhong County rose to 1.269 after 2018, indicating that enhanced water supply reliability directly supported gains in utilization efficiency with notable benefit conversion. In contrast, Longxi County dropped to 0.398 after 2015, and Lintao County remained low at around 0.4; in these cases, efficiency did not increase and even declined or grew slowly, likely due to initial-stage misalignments in management mechanisms and limited industrial absorptive capacity. Huining County remained between 1.1 and 1.7 after 2015, indicating a relatively mature utilization pattern.

As shown in Figure 2, Anding District remained at a high level over an extended period and sustained its peak after the 2015 diversion, underscoring efficient utilization. Lintao County consistently occupied the lower range, reflecting long-term low efficiency. The polylines for Yuzhong and Huining rose markedly after diversion, indicating a positive effect on efficiency, whereas those for Longxi and Weiyuan fluctuated substantially, pointing to instability in the post-diversion phase. So, the WRUE in the water-receiving areas is determined by regional endowments, diversion timing, management mechanisms, and industrial structure. There are clear spatial disparities and temporal differentiation. High-efficiency areas refine the utilization modes, while low-efficiency areas need to prioritize industrial upgrading and management innovation to strengthen their ability to convert water inputs into economic and social benefits.

3.2. Analysis of Total Factor Productivity of Water Resources Based on Malmquist Index

The Malmquist–Luenberger (ML) index and its decomposition of WRUE in the water-receiving areas of the Tao River Diversion Project from 2010 to 2019 are listed in

Table 3. The ML index and decomposition of WRUE in the water-receiving areas from 2010 to 2019.

Year	Total Factor Productivity Change	Technical Efficiency Change	Pure Technical Efficiency Change	Scale Efficiency Change	Technological Progress Change
2010	1.138	0.947	0.909	1.096	1.202
2011	1.186	0.963	1.065	0.900	1.360
2012	1.343	1.226	0.995	1.230	1.115
2013	1.122	1.071	1.387	0.926	1.070
2014	0.973	0.936	0.970	0.971	1.088
2015	0.975	0.969	2.992	0.855	1.006
2016	1.003	1.004	0.989	1.025	1.000
2017	1.079	0.867	0.963	0.869	1.307
2018	1.508	1.323	1.107	1.281	1.130
2019	1.142	0.962	0.898	1.164	1.185
Average	1.147	1.027	1.227	1.032	1.146

. The total factor productivity (TFP) index shows an overall increase, with an average value of 1.147. The TFP of water resource utilization in the water-receiving areas is increased to 14.7% over 2010–2019 and exhibits a positive long-term trend. TFP has increased by 34.3% and 50.8%, respectively. The values of TFP are 1.343 and 1.508 in 2012 and 2018 while they are 0.973 and 0.975 in 2014 and 2015, respectively. There are short-term fluctuations. From the technical efficiency aspect, it exhibits an increasing trend with an average value of 1.027, implying a 2.7% overall gain and a long-term improvement trend in production technology utilization; even the lower values of technical efficiency can be found in 2014 (0.936) and 2017 (0.867) due to the low utilization of the existing technologies. Especially, the values of technical efficiency increase by 22.6% and 32.3% in 2012 (1.226) and 2018 (1.323), respectively. Pure technical efficiency achieved notable long-term growth with improvements in technical management, with an average value of 1.227, representing a 22.7% overall increase and making it the main contributor to technical efficiency growth. The water-receiving areas make progress in promoting water-saving technologies and improving water allocation mechanisms. The values of pure technical efficiency increased by 38.7% and 10.7% in 2013 (1.387) and 2018 (1.107), respectively. It reaches the breakthrough phase where the value of pure technical efficiency exceeds 0.99 in most years. There is a high basic level of technical management, with fluctuations mainly caused by technological innovation or adjustments.

The values of scale efficiency show a slight overall increase, with an average value of 1.032, indicating that scale effects provided support for technical efficiency growth but contributed less than pure technical efficiency. The values of scale efficiency increased by 23.0% and 28.1% in 2012 (1.230) and 2018 (1.281), where there is a good match between the scale of water resource inputs and outputs while the values of scale efficiency are below 1 in 2011 (0.900) and 2017 (0.869), indicating input–output mismatch and the loss of scale efficiency. Technological progress achieves significant long-term growth and serves as a core driver of TFP with an average value of 1.146, reflecting the sustained advances in innovation, equipment upgrading, and process improvement in water resource utilization. The TFP of water resource utilization in the water-receiving areas shows an upward trend from 2010 to 2019, with the main driving forces being improvements in technological progress and pure technical efficiency. However, there are also clear temporal fluctuations, mainly arising from the changes in technical efficiency, especially scale efficiency. In the future, it is necessary to stabilize scale efficiency, optimize the matching between the input scale and output demand, and continuously strengthen technological progress and pure technical efficiency to promote innovation and management optimization.

The ML index and its decomposition results of WRUE in the seven counties or districts of the water-receiving areas of the Tao River Diversion Project are listed in

Table 4. The ML index and decomposition of WRUE in each district of the water-receiving area.

Region	Total Factor Productivity Change	Technical Efficiency Change	Pure Technical Efficiency Change	Scale Efficiency Change	Technological Progress Change
Yuzhong	1.143	1.015	1.018	0.999	1.111
Huining	1.078	1.039	1.047	0.994	1.032
Anding	1.025	1.017	3.311	1.028	1.040
Tongwei	1.034	0.974	0.960	1.024	1.061
Longxi	1.081	0.919	0.923	0.994	1.216
Weiyuan	1.423	1.226	1.013	1.186	1.316
Lintao	1.244	0.997	1.008	0.987	1.248
Average	1.147	1.027	1.227	1.032	1.146

. There are significant improvements in TFP in Lintao (1.244) and Weiyuan (1.423). Moderate growths can be found in Yuzhong (1.143), Longxi (1.081), Tongwei (1.034), and Huining (1.078) while the smallest rise is found in Anding. In terms of technical efficiency, its value is increased by 22.6% in Weiyuan (1.226) while slight increases can be found in Anding (1.017), Yuzhong (1.015), and Huining (1.039). The lower values can be found in Tongwei (0.974), Longxi (0.919), and Lintao (0.997). Regarding pure technical efficiency, a leading technical management capability can be found in Anding (3.311) while a slight increase can be found in Weiyuan (1.013), Yuzhong (1.018), and Huining (1.047). However, a lower value below 1 has been found in Longxi (0.923), reflecting its short-term bottlenecks. In terms of scale efficiency, good matches between the input scale and output can be found in Weiyuan (1.186), Anding (1.028), and Tongwei (1.024), but lower values that are below 1 can be found in Huining (0.994), Yuzhong (0.999), and Lintao (0.987). In terms of technological progress, a lead in innovation can be found in Lintao (1.248) and Weiyuan (1.316) while there are slight increases in Anding (1.040), Tongwei (1.061), Yuzhong (1.111), Longxi (1.216), and Huining (1.032). It can be found that the core drivers of WRUE in the seven counties or districts are pure technical efficiency and technological progress. There are mismatches in input–output scales and decrease trends in technical efficiency, implying the differences among the counties or the districts; especially, the coordination between technological innovation and scale optimization should be strengthened in Weiyuan, Anding, and Lintao while Longxi and Huining should focus on the bottlenecks in technical efficiency among the counties or districts.

3.3. Analysis of Spatial Correlation of WRUE

3.3.1. Global Spatial Autocorrelation Analysis of WRUE

There is not obvious global spatial correlation of WRUE in the water-receiving areas of the Tao River Diversion Project. According to the data in

Table 5. The global spatial autocorrelation index of WRUE in the water-receiving areas of the Tao River Diversion Project.

Year	I	Z *	p
2010	0.200	1.245	0.213
2015	−0.050	0.386	0.700
2018	0.459	1.561	0.118

Note: * Z is the standardized statistic of I.

, the spatial autocorrelation significance test values Z for WRUE range from −1.65 to 1.65 in 2010, 2015, and 2018. The WRUEs are randomly spatially distributed. All the spatial autocorrelation significance test p-values are greater than 0.10, which suggests that their confidence levels are less than 90% and the spatial correlations of WRUE are not significant. The global Moran’s I index of WRUE in 2010 and 2018 is greater than 0; the Moran’s I index in 2015 is less than 0, so the spatial autocorrelation of WRUE in the water-receiving areas is a changing trend of “weak positive correlation–weak negative correlation–relatively strong positive correlation.” From 2010 to 2018, the global Moran’s I index is increased by 0.259, so the global spatial autocorrelation of WRUE gradually strengthened, and the clustering effects of spatial distribution are also increased. The operation of the water diversion is the key driving factor of the changes in the spatial autocorrelation of WRUE in some counties or districts of water-receiving areas in 2015 and 2018. The WRUE of counties or districts will be further improved after water diversion, even if their efficiencies are high (e.g., Anding District and Huining County). And these counties or districts are surrounded by areas with high value, which promotes the positive development of the overall Moran’s I index. As water diversion can improve the water resource pipeline networks and allocation mechanisms, the relevance among counties and districts will be strengthened and triggered by the spatial spillover of technology and industries. As technologies from high-value areas are effectively absorbed from their surrounding regions, the efficiency gaps will be narrowed. Thus, the spatial correlation of efficiencies in the water-receiving areas shows a weak negative correlation in 2015. However, the spatial correlation of efficiency in the water-receiving areas is found to be a relatively strong positive correlation in 2018 due to the slower speed of technology absorption in surrounding counties or districts compared to the agglomeration speed of high-value areas.

3.3.2. Local Spatial Cold and Hot Spot Analysis of WRUE

The global Moran’s I index can only reflect the overall spatial distribution of WRUE; it cannot reflect the local spatial correlation and the degree of correlation. According to the global autocorrelation analysis, a local spatial cold and hot spot analysis of WRUE can be carried out to identify the correlation and agglomeration characteristics of the local space. The spatial distributions of the cold and hot spots of WRUE in the water-receiving areas of the Tao River Diversion Project in 2010, 2015, and 2018 are shown in Figure 3. There is only cold spot agglomeration with no significant hot spot areas in 2010. Its spatial pattern of WRUE in the water-receiving areas can be dominated by “low-value area agglomeration.” The obvious spatial agglomerations are hard to be found in high-value areas; then, the overall efficiency distribution exhibits the characteristics of “low-level agglomeration and high-level dispersion.” However, hot spot agglomeration emerged while cold spot areas disappeared in 2015. The high-value areas are found to form spatial agglomeration, and the spatial differentiation of regional efficiency starts to shift towards “high-value agglomeration.”, especially in Huining County. The coverages of the hot spot agglomeration areas are found to be expanded and their significances are also found to be improved in 2018 but the cold spot areas are found to be reemerged simultaneously. For example, the spatial agglomeration effects of high-value areas are further strengthened in Anding District and Huining County while a few counties or districts are found to be local low-value agglomeration rather than high-value agglomeration due to restriction factors such as industrial structure and management level. So, the trend of the spatial pattern of cold and hot spots of WRUE in the water-receiving areas is found to be “cold spot dominance–initial emergence of hot spots–hot spot strengthening” from 2010 to 2018 due to the operation of the water diversion project. As there is insufficient water resource supply before the operation of the project, it is common to find agglomeration in the low-value area. After the counties or districts obtained water from the first period project in 2015, the initial agglomeration of high-value areas is found to be formed. And the high-value agglomeration has been found to be continuously enhanced to be a spatial pattern of “high-value dominance with local low-value distribution” after the second period project in 2018. Research indicates that the benefits of the water diversion project have enhanced water supply reliability in the water-receiving areas, bolstering both the capacity and effects of industrial agglomeration in Huining County, Anding District, and Lintao County, and advancing the sustainable economic and social development of these areas. However, industrial agglomeration capacity varies distinctly across different counties and districts within the water-receiving areas. For example, in Weiyuan County, the industrial agglomeration effect has weakened since the project’s benefits took hold—a trend that may be linked to industrial transfers within the region.

3.4. Analysis of Influencing Factors of Spatial Changes in WRUE

To figure out the influencing factors of spatial changes in WRUE, a geographical detector was employed in the water-receiving areas of the Tao River Diversion Project. The larger the q value, the stronger the influence. The detection results of the q value are listed in Figure 4.

Before the operation of the water diversion (i.e., 2010–2014), the q-values for x₁₀ range from 0.609 to 0.985 while its value for x₃ rose to 0.879 in 2013. The q-value for x₅ increased to 0.689 in 2012. Their values for x₁ and x₂ fluctuated significantly, indicating the unstable impacts from natural endowments and population size. WRUE is mainly constrained by their similar natural water conditions; thus, the spatial differences in WRUE are mainly attributed to the x₃ and x₅. And the influencing factors of the nature endowments (i.e., x₁) and population size (i.e., x₂) are unstable. After the first period of operation of the water diversion project as the adjustment period (i.e., 2015–2017), the main influencing factors are x₁₀, x₃, x₅, x₆, x_7, and x₈. The q-value for x₁ dropped to 0.114 and its value for x₂ decreased to 0.132, indicating that the impacts of natural factors and the population size are weakened significantly. After water diversion, project water supply replaced natural precipitation, and the refined management reduced the influence of the population size. It can be found that the impact of natural factors decreases while the fundamental role of water consumption remains. The driving forces of x₃ and x₅ continue to strengthen. Additionally, socio-economic development factors (e.g., x₆, x₇, and x₈) are becoming more important. In the second operation period of the water diversion project (i.e., 2018–2019), the q-values for x₁₀ fell to 0.609; even its impact remains the foundation of efficiency differentiation. The q-value for x₃ rose to 0.592, and its value for x₅ increased to 0.818, indicating that industrial water conservation and industrial upgrading are the core driving forces of efficiency differentiation. The q-values for x₆, x₇, and x₈ increased significantly, and the agglomeration effect of socio-economic development continued to widen the regional efficiency gap. Although the influence of water consumption weakens, it still ranks first; the agglomeration effects of socio-economic factors such as the proportion of industrial water use, the proportion of the population with college education or above, urbanization rate, fiscal expenditure, and per capita GDP became the core drivers, while the impacts of fixed asset investment and the proportion of agricultural water use decreased.

Overall, there was a trend of shifting from natural factors to socio-economic factors. The spatial differentiation in WRUE in the water-receiving areas was affected by the quality of socio-economic development and technical management capabilities.

4. Conclusions

The WRUE in a water-receiving area has been assessed by the Super-SBM model. And its spatial and temporal variations are figured out and the key driving factors and spatial correlations are figured out. Taking the water-receiving area of the Tao River Diversion Project as a case study, the results highlight the impact of the water diversion project on the efficiency, the disparity among regions, and the shifting influence of factors over time. Significant spatial variation in WRUE has been found across the water-receiving areas from 2010 to 2019. High-efficiency areas maintain or improve their efficiencies, while low-efficiency areas show a stagnant or declining trend. The efficiency gaps between high- and low-efficiency regions became more pronounced after the water diversion. Thus, the premise that the WRUE would not decrease after the operation of the water diversion project is challenged.

From 2010 to 2019 in the case study, the total factor productivity (TFP) increases by 14.7%. The main contributors are technological progress (14.6%) and pure technical efficiency (22.7%). However, their regional disparities are notable. Substantial growths have been found in Weiyuan County and Anding District while little progress was found in Longxi County. The spatial autocorrelation of WRUE is weak as Moran’s I has positive and negative correlations over time. The global Moran’s I index increased by 0.259 from 2010 to 2018; thus, there is a strong spatial cluster. The water diversion project is a key driver for the shifting patterns from a cold spot dominance to a stronger hot spot agglomeration. The influencing factors on WRUE’s spatial differentiation are also dynamic. Before the operation of the water diversion, water consumption and education levels are the dominant factors, while the proportion of industrial water use and the urbanization rate become more and more important after the operation of the first period project in 2015. After the second period project operation, fiscal expenditure and GDP growth emerge as the key drivers, which imply a shifting trend from natural factors to socio-economic factors.

To enhance the WRUE in the water-receiving areas, a gradient water pricing system can be progressively implemented to guide efficient water usage. Meanwhile, a groundwater allocation and management mechanism that is integrated with surface water should be established. Additionally, efforts should be made to strengthen the development of regional water resource management capabilities and conduct targeted research, thereby providing systematic support for efficiency improvement [1]. High-value regions have developed an integrated water-saving technology system covering “R&D, pilot production, and promotion”, while establishing a linked monitoring platform integrating “water resources, water users, and benefits”. A combined mechanism featuring “quota management, tiered water pricing, and reward subsidies” can be implemented. Additionally, these regions adopt a “pairing assistance” model to share mature management experience and extend its impact to surrounding areas. The low-value regions, the municipal water resources departments, formulate water resource allocation plans, increase investment in basic water facilities, and promote low-cost water-saving technologies. They also strengthen the development of grassroots management teams and implement differentiated assessment and support policies. Through “capacity building and policy incentives”, improvements in WRUE are driven, ultimately achieving coordinated progress in the overall WRUE of water-receiving areas.

Our study not only enhances the understanding of WRUE dynamics in the water-receiving areas of the Tao River Diversion Project, but it can also provide many valuable insights for water resource planning.