**1. Introduction**

UNESCO (United Nations Educational, Scientific and Cultural Organization) defines the water resource as a source of water of a certain quality and quantity that is available and potentially available to meet the utilization needs of a site in the long term [1]. Water resources are the basic support for economic and social development, as well as a necessary guarantee for the construction of ecological civilization [2]. Since the 21st century, a green, coordinated, and sustainable water resource utilization model has gradually become a hot spot of concern for countries around the world [3]. The United Nations Sustainable Development Summit in 2015 released the 2030 Agenda for Sustainable Development, which identifies 17 Sustainable Development Goals (SDGs) covering economic, social, resource, and ecological dimensions [4]. It is internationally recognized that an important part of achieving SDGs is to conduct a comprehensive and in-depth exploration of water

**Citation:** Zhang, Z.; Zuo, Q.; Jiang, L.; Ma, J.; Zhao, W.; Cao, H. Dynamic Measurement of Water Use Level Based on SBM-DEA Model and Its Matching Characteristics with Economic and Social Development: A Case Study of the Yellow River Basin, China. *Water* **2022**, *14*, 399. https://doi.org/10.3390/w14030399

Academic Editor: Antonio Lo Porto

Received: 15 December 2021 Accepted: 25 January 2022 Published: 28 January 2022

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security [5], water and soil resource use efficiency [6–8], and sustainable energy use [9] in order to break the excessive dependence on energy resources for economic and social development. At present, China is facing huge pressure on water resources. The intertwining problems of water demand and supply [10], water environment pollution [11], and water ecology deterioration [12] have formed a serious water resource challenge, which seriously hinders the realization of sustainable development. In 2012, the Strictest Water Resources Management System was issued by the Chinese government [13], which issued three rules for total water use, water use efficiency, and state of water function zones. The Yellow River is called the mother river of China. It is also one of the seven significant rivers in China. The Yellow River basin is an important ecological barrier in northern China [14]. In 2019, The Chinese government promoted conservation and intensive use of water resources as an important strategy for the future development of the Yellow River basin [15]. The key way to tackle the increasingly complex water resource issues in the Yellow River Basin and even in China is to achieve efficient utilization of water resources and ensure stable social development and economic progress with minimal resource input. Thus, it is clear that quantitative research on regional water use level and exploration of the matching relationship between economic and social development and resource utilization levels are of strategic importance for the sustainable and healthy economic and social development of regions, provinces, and even countries.

Water use level is a key metric reflecting the effective exploitation, management, and utilization of water resources. As the contradiction between economic and social development and water shortage is becoming more and more prominent, many scholars have conducted comprehensive research on water use levels in recent years and gradually formed a complete theoretical and methodological system. Different research fields have different definitions of water use levels. At present, common research on water use levels can be broadly divided into two scales, macro and micro. Micro-scale studies mainly focus on the moisture utilization capacity of different crops [16,17] and farms [18], as well as agricultural irrigation efficiency. The main methods include the life cycle approach [19], water production function [20], etc. Micro-scale water use efficiency studies focus on exploring the efficiency of water and energy conversion during plant production. Moreover, in such studies, water use efficiency (WUE) is the most common indicator to characterize the level of water use. It can be simply summarized as dry matter mass produced per unit of water consumed by plant growth. The other category is macro-scale. This type of research focuses on exploring the overall water use levels of different regions and industries. This study proposes a new index, CWUI (composite water use index), to represent the level of water use. Referring to such studies, the definition of CWUI can be simply summarized as: macroscopically, the ability of a region or industry to obtain economic output through the integrated use of water and related inputs. The main methods for water use level studies at the macro scale include single-indicator assessment [21], multi-indicator integrated assessment [22], data envelopment analysis (DEA) model [23], stochastic frontier approach (SFA) model [24], and genetic projection tracing model [25], etc. Among them, the DEA model integrates the relevant knowledge of operations research, economics, and management science and can evaluate the relative effectiveness of comparable units of the same type using linear programming. Since this method does not require any assumptions, it has reflected its unique advantages in water resources level research, and a large number of high-quality research results have emerged. In terms of research scales, involving different scales includes national [26], provincial [27], and urban [28]. For example, Ibrahim et al. [26] measured the efficiency of the water-energy-land-food nexus in Organization for Economic Cooperation and Development (OECD) countries using a non-parametric benchmark ranking model derived from a DEA approach. Lu et al. [28] evaluated the spatial and temporal change characteristics of agricultural water use level and its related factors in northwest China using the combination of super-efficient DEA model. In terms of research areas, the water use level of different industries (agriculture [29], industry [30,31]) and the regional integrated water use efficiency [32] were covered. For example, Yang et al. [31], used a

DEA model to assess the water use level of the three major industries in 30 provinces in mainland China. In studies on DEA models, traditional CCR and BCC models [33], super-efficient DEA models [34], SBM-DEA models [27,30,35], Malmquist models [24,36], etc., are involved. For example, Bai et al. [36], constructed a non-radial method based on the theory of Malmquist to dynamically measure changes in water use level of the Bohai Bay urban cluster in China. In recent years, with the gradual development of the green development concept. It is worth noting that DEA models considering non-expected output have started to appear more often in resource and energy use level studies. For example, Yang et al. [30] chose a non-expected output SBM model to measure the industrial water use level in mainland China. It can be found that the DEA method was widely applied in the field of water resources. The above high-quality research results provided a solid basis for the smooth development of subsequent studies.

Economic and social development and the level of resource and energy utilization are inextricably linked, especially under the dual effect of intensifying climate change and the impact of human activities. Whether the level of resource and energy utilization can match the level of economic and social development has become an important indicator to measure the sustainable development capability of the region. With the further implementation of sustainable development policies, the relationship between the level of resource and energy use and sustainable development has gradually become a hot issue of global concern. In this context, many scholars have adopted various methods to explore the relationship between the two. The subjects of this kind of study are mainly related to energy consumption [37–39], pollution emissions [40], land resource use [41,42], etc. For example, Sarkodie et al. [38] examined the effects of energy consumption on GHG emissions using U-test estimation methods and non-additive fixed effects panel quantile regression. On World Water Day, March 22, 2021, UNESCO released the World Water Development Report 2021 [43], which focuses on "the value of water" to explain the important role of water resources in economic and social development in different dimensions. There are not many studies on the relationship between water resources utilization and economic and social development, but some scholars conducted relevant studies. For example, Sun [44] constructed a system dynamics model to study sustainable water resources utilization considering economic development, and simulated the water resources supply and demand situation from 2005 to 2020 and the changes of future supply and demand gap. The above research results have contributed value in promoting sustainable economic and social development.

After combing through the representative literature in recent years, it can be found that the important results revealed by the above-mentioned studies have greatly promoted the development of the field of water use level and the field of water resources-economic and social relations, and expanded the scope and depth of research in this field. However, there are some shortcomings. For example, most studies on water use levels still use the DEA cross-sectional model to deal with long time series panel data. This defect leads to the comparison of different decision units only within a specific year, and the evolution characteristics of water use level in time series cannot be analyzed, which reduces the reference value of the results to some extent. Meanwhile, some studies used traditional radial DEA models to measure water use levels, which failed to fully consider slack variables [45]. Finally, studies on the matching relationship between water use level and economic and social development in the Yellow River Basin are still relatively lacking.

However, the combination of SBM-DEA model and Window-DEA model can effectively solve the above problems. This study attempts to apply the DEA window analysis method to the study of water use level, combining the SBM-DEA model to explore the spatial and temporal evolution characteristics of water use level in nine provinces in the Yellow River basin. It can realize the dynamic analysis of CWUI under the premise of considering slack variables. On this basis, the Malmquist index model is used to analyze the deep-seated reasons, leading to the variation of total factor productivity of water, and the spatial matching degree calculation method based on series distance is introduced

for exploring the matching relationship between E-SDL and CWUI. This study aims to achieve the following objectives: (1) apply the SBM-DEA model combined with Window-DEA model to the study of water use level; (2) conduct dynamic evaluation of water use level in nine provinces with consideration of relaxation improvement; (3) clarify the deepseated reasons for the changes in total factor productivity of water in the nine provinces; (4) analyze the matching characteristics between the level of water utilization and the level of economic and social development in the nine provinces under different time scales.

The rest of this study is structured as follows: Part 2 introduces the four main research methods, Part 3 presents an overview of the study area and the selection of relevant indicators, and Part 4 analyzes the spatial and temporal evolution characteristics of CWUI, the changes in TFP of water, and the matching characteristics of CWUI and E-SDL. Part 5 is the conclusion and the outlook for future research.

#### **2. Methodology**
