*4.2. TFP Analysis of Water Based on Malmquist Index Model*

Based on the panel data of input-output variables of nine provinces from 2012 to 2018, the Malmquist index model was applied to measure the productivity index of nine provinces, and the total factor productivity index and its decomposition result of different years and provinces were obtained, as shown in Table 4 and Figure 4. The operation was implemented by DEAP2.1 software (Université Laval, Quebec City, Canada) [56].


**Table 4.** Malmquist Index and its decomposition (average of nine provinces), 2012–2018.

Notes: <sup>a</sup> The multi-year averages of the Malmquist index and each of its decomposition indices are geometric means.

From the results in Table 4, the multi-year average value of MI was 1.078, and MI greater than 1 indicates that the overall TFP of water of the nine provinces showed an increasing trend during the period of 2012–2018. Among them, the overall total factor productivity of water in the nine provinces declined year by year before 2016, but the declining trend gradually leveled off. Moreover, the overall total factor productivity of water has increased year by year since 2016. In order to explore the intrinsic causes of TFP changes, the results of total factor productivity decomposition were further analyzed. Moreover, the multi-year average values of all indices were less than 1, except for technical progress TC, which indicates that technical progress TC was the dominant factor driving TFP improvement. EC was greater than 1 only in 2016 and 2017, indicating that changes

in integrated technical efficiency only played a driving role in individual years. However, EC, in general, constrains the improvement of total factor productivity of water thus the industrial structure and water resources management mode need to be optimized to improve the scale efficiency and pure technical efficiency of water utilization in the nine provinces.

**Figure 4.** Multi-year average Malmquist index and its decomposition in nine provinces from 2012–2018.

As can be seen from Figure 4, the MI of Inner Mongolia, Shanxi, Shaanxi, and Shandong provinces are all higher than the nine-province average of 1.078, indicating that the water use level of these four provinces is improving faster. Among them, Inner Mongolia and Shandong provinces, because they are at the production frontier themselves, the improvement of TFP of water is entirely driven by the technological progress TC. In comparison, Shanxi and Shaanxi are driven by both technological progress TC and integrated technical efficiency change EC. The remaining five provinces have been slow to improve their TFP of water, mainly due to the constraints of the integrated technical efficiency change EC, and the distance between their water utilization levels and the production frontier surface has gradually increased. Further decomposition of EC can be found that Qinghai, Gansu, and Ningxia are mainly affected by the scale efficiency change SEC, and the scale efficiency needs to be further optimized, while Sichuan and Henan are mainly constrained by the pure technical efficiency change PEC, and need to focus on strengthening the water resources management level and optimizing the water use structure.

Comparing the Malmquist index and its decomposition results from the perspective of different regions. The comparison of upstream, midstream, and downstream provinces is shown in Figure 5. The overall productivity level of the midstream provinces is higher than that of the upstream and downstream provinces. It is not difficult to find that PEC and SEC of the upstream provinces are both at a lower level, especially the poor performance of SEC, which in turn leads to a much lower integrated technical efficiency change EC than that of the midstream provinces. Thus, the upstream provinces need to reasonably allocate water resources, optimize industrial layout, improve industrial concentration, and narrow the gap between their SEC and that of the midstream and downstream provinces. Technological progress TC is the main driving force of TFP of water in the three regions, and the difference of TC in the three regions is relatively small, with the upstream provinces even slightly higher than the downstream provinces. The production frontier of each of the three regions has moved forward significantly, indicating that the nine provinces have all invested more in scientific research in the field of efficient water utilization in recent years, effectively promoting the transformation of advanced technology into productivity [57].

**Figure 5.** Comparison of the multi-year average Malmquist index and its decomposition in the upstream, midstream, and downstream provinces.

#### *4.3. Matching Relationship between CWUI and E-SDL*

4.3.1. Analysis of the Relative Level of Economic-Social Development

Based on the quantitative index system of the relative level of economic and social development in the nine provinces in Table 2, the data of each index in the nine provinces during the period of 2012–2018 were normalized, and then all the indexes were weighted and summed up by combining the weights to obtain the quantitative characterization value of E-SDL. Arcgis10.2 software was used to map the E-SDL calculation results of the nine provinces for multiple years into a spatial distribution map, which was used to characterize the spatial and temporal distribution characteristics of the economic and social development levels of the nine provinces, as shown in Figure 6. On the time scale, the average value of E-SDL in the nine provinces showed an increasing yearly trend during the seven years, from 0.352 in 2012 to 0.657 in 2018, indicating that with the gradual implementation of the concept of sustainable and green development, the overall level of economic and social development in the nine provinces is continuously improving. Gansu, Qinghai, Sichuan, and Henan, have seen the fastest improvement in economic and social development, with E-SDL more than doubling in seven years. From the three criteria, it was found that the economic development and social harmony of the above four provinces rapidly improved in the past seven years under the premise of maintaining the steady growth of the level of ecological friendliness, thus realizing the obvious improvement of E-SDL. On the spatial scale, there were large spatial differences in the economic and social development levels of the nine provinces. In terms of the multi-year average value of E-SDL, the economic and social development level of Shandong was relatively high (E-SDL > 0.7), the E-SDLs of Inner Mongolia, Shaanxi, Henan, Sichuan, Shanxi, and Ningxia were at an intermediate level (0.4 < E-SDL < 0.6), and the economic and social development levels of Gansu and Qinghai were low (E-SDL < 0.4). The E-SDL of the nine provinces as a whole shows the spatial distribution characteristics of downstream, midstream, and upstream provinces in descending order, which is basically consistent with the regional step structure of economic and social development in the Yellow River basin [14].

**Figure 6.** Spatial and temporal distribution characteristics of E-SDL in nine provinces from 2012 to 2018.

4.3.2. Analysis of Matching Degree between CWUI and E-SDL

The spatial matching degree of the multi-year average CWUI and E-SDL of nine provinces was calculated using the spatial matching degree calculation method based on the series distance, and the results are shown in Figure 7. To further analyze the temporal change characteristics of the matching degree, the spatial matching degree of CWUI and E-SDL of the nine provinces and the upstream, midstream, and downstream provinces of the Yellow River in 2012, 2015, and 2018 were measured, and the results are listed in Table 5.

**Figure 7.** Matching characteristics of multi-year average CWUI and E-SDL in nine provinces (The red dash line can be used as an auxiliary line to identify provinces with high matching degrees).



From the results in Figure 7, the CWUI of Gansu, Sichuan, Henan, Qinghai, and Shandong matches well with the E-SDL (MD > 0.9), but the matching categories in different provinces are not exactly the same. Shandong and Henan provinces have a high level of economic and social development, and their water use level is relatively good among the nine provinces, which is a "high-high" match. Gansu and Qinghai provinces have a relatively low level of economic and social development, and their CWUI is also at the back of the nine provinces, which is a "low-low" match. The degree of matching CWUI with the E-SDL in Inner Mongolia and Shaanxi provinces is medium among the nine provinces (0.8 < MD < 0.9). The match between CWUI and E-SDL in Ningxia and Shanxi provinces is poor (MD < 0.8), and the reason for this is that Shanxi Province has a high CWUI among the nine provinces, while the level of economic and social development is relatively low, resulting in the two not matching in value. Ningxia, however, is at the bottom of the nine provinces in terms of water use level, but its economic and social development is at the middle level among the nine provinces, and it needs to focus on improving water resources utilization in the future economic and social development process. In another study on the coordination between water use and urbanization [58], the results show that there are significant differences in the synergistic effects between water use level and urbanization in different provinces in China. Moreover, the differences can be divided into three different

types of synergy, with only individual provinces showing a significant synergistic effect of urbanization level on water use. The results are similar to those of this paper, and to a certain extent, they verify the spatial variability of CWUI and E-SDL among nine provinces in the Yellow River basin.

From the results in Table 5, the matching degree of CWUI and E-SDL in Gansu Province has been increasing within the three study years of 2012, 2015, and 2018, and its MD has increased from 0.885 in 2012 to 0.990 in 2018. The matching degree of water use level and economic and social development level in Gansu Province in 2018 is the highest among the nine provinces, but it belongs to the "low-low" matching type, which still needs to improve CWUI and E-SDL comprehensively. The match between CWUI and E-SDL in Ningxia and Inner Mongolia provinces has been decreasing, with MD in Ningxia decreasing from 0.761 in 2012 to 0.729 in 2018 and MD in Inner Mongolia decreasing from 0.889 in 2012 to 0.602 in 2018. It indicates that compared with other provinces, the synergy between the level of water utilization and the improvement of economic and social development level in these two provinces is poor, and should focus on the coordinated and harmonious development of water resources utilization and economy and society. The main problem in Ningxia is the low level of water utilization, and the level of water utilization in Inner Mongolia is at a high level, but its economic and social development level is not outstanding, and it needs to pay attention to the all-round balanced development of economy, society, resources, and ecology.

The MD of the six provinces of Qinghai, Sichuan, Henan, Shaanxi, Shandong, and Shanxi showed the characteristics of first rising and then falling within three years. CWUI and E-SDL reached the best matching status in 2015. Among the six provinces mentioned above, the characteristics of MD changes can be explained in three cases. The first case is that the improvement of water use level lags behind the improvement of economic and social development level, such as Sichuan, Shaanxi, and Qinghai provinces. Sichuan's CWUI was ranked 6th in all three years 2012, 2015, and 2018, but its E-SDL improved significantly from 7th in 2012 to 4th in 2018. Shaanxi's CWUI ranked 5th in 2012 and 2018 and 4th in 2015, but its economic and social development level improved from 3rd in 2012 to 2nd in 2018. Qinghai's CWUI dropped from the 7th in 2012 to the 9th in 2018, and its E-SDL remained at the 8th for three years. The second case is that the E-SDL is rising faster, but the level of water utilization is rising slower, such as Shanxi Province. Its CWUI rose from 4th in 2012 to 2nd in 2018, but its E-SDL dropped from 5th in 2012 to 7th in 2018. The third case is that the level of water utilization and the level of economic and social development has maintained simultaneous improvement to some extent, such as Henan and Shandong. Henan's CWUI decreased from 3rd in 2012 to 4th in 2018, and its E-SDL decreased from 4th in 2012 to 5th in 2018. CWUI and E-SDL of Shandong Province have maintained 1st place in 2012, 2015, and 2018, and although there are fluctuations in MD, the fluctuations are not obvious, and the water use level and economic and social development level have maintained a relatively coordinated development. Analyzed from the perspective of different regions in the Yellow River Basin, the overall situation is that the MD of downstream provinces is higher than that of upstream provinces than that of midstream provinces. Except for the downstream provinces, the MDs of the remaining two regions showed a decreasing trend year by year during 2012, 2015, and 2018, and their economic and social development and water use level failed to achieve a harmonious and balanced improvement, and the upstream and midstream provinces of the Yellow River Basin still need to focus on the simultaneous improvement of water use level under the premise of ensuring economic and social development.

#### **5. Conclusions**

Based on the SBM-DEA model and combined with the Window-DEA model, this study measured the water use level of nine provinces in the Yellow River Basin from 2012 to 2018 and decomposed the TFP changes of water in the nine provinces using the Malmquist index model. A quantitative index system of economic and social development levels was constructed, the spatial and temporal variation characteristics of the relative levels of economic and social development in the nine provinces were analyzed, and finally the matching relationship between water use level and economic and social development levels in the nine provinces of the Yellow River Basin was explored. The results were concluded as follows:


The findings of the study clarify the characteristics of temporal changes and spatial distribution patterns of water use levels in the nine provinces of the Yellow River Basin in recent years. The key factors leading to the variation of total factor productivity of water resources in the nine provinces are also identified, and the results of the study can provide some basis for the strictest water resources management in different regions of the Yellow River Basin. In addition, this paper analyzes the adaptation characteristics between water resources utilization and economic and social development in the nine provinces, which can provide some reference for the future high-quality development layout of the Yellow River basin to a certain extent. It is also a useful exploration to carry out more complex research on the relationship between water resources utilization and economic and social development in the future.

Despite that, limitations also exist in the present study, which could be further improved. First, the SBM-DEA model cannot allow further comparison of the CWUI values of multiple effective DMUs. For example, in 2018, we learned that the CWUI of Inner Mongolia, Shanxi, and Shandong are all one, but we cannot make further comparisons of the three levels. A possible solution to this problem is to explore the applicability of more comprehensive DEA models (e.g., super-efficient SBM-DEA models) in water use

level studies. Second, the water use level involves many aspects such as resources, ecology, economy, and society, etc. Although the input-output index system of water use level constructed in this study covers as many representative indicators as possible, the extent to which it can represent the real level of water utilization still needs to be further explored. Third, this study explores the spatial matching characteristics between CWUI and E-SDL using the method of calculating spatial matching based on the series distance. However, this method cannot explore the degree of coordination of different variables on the time series. In future research, a combination of multiple coordination relationship exploration methods (e.g., Tapio decoupling model, coupling coordination degree model) can be used to comprehensively explore the adaptation relationship between CWUI and E-SDL in both time and space dimensions.

**Author Contributions:** Conceptualization, formal analysis, funding acquisition and project administration, Q.Z.; data curation, methodology, software, visualization, writing—original draft, Z.Z.; investigation, L.J. and J.M.; supervision, Q.Z. and J.M.; resources, W.Z. and H.C.; writing—review and editing, Q.Z., L.J., J.M., W.Z. and H.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Research and Development Program of China (No. 2021YFC3200201) and the Major Science and Technology Projects for Public Welfare of Henan Province (No. 201300311500).

**Data Availability Statement:** Publicly available datasets were analyzed in this study. This data can be found here: [http://www.stats.gov.cn/tjsj/ndsj/].

**Acknowledgments:** The authors are grateful to the editors and the anonymous reviewers for their insightful comments and helpful suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Jialu Li 1,2, Qiting Zuo 3,4,5,\*, Feng Feng 1,2 and Hongtao Jia 1,2**


**Abstract:** As one of the eight largest freshwater lakes in China, Wuliangsuhai Lake is an extremely rare large lake with biodiversity and environmental protection functions in one of the world's arid or semi-arid areas and it plays a pivotal role in protecting the ecological security of the Yellow River Basin. Heavy metals in sediment interstitial water, surface sediments, and sediment cores of Wuliangsuhai Lake were investigated and analyzed, and the pollution degree evaluated based on multiple assessment methods. The bioavailability of heavy metals of the surface sediments was evaluated by calculating the ratio of chemical fractions of heavy metals. The toxicity assessment of sediment interstitial water indicated that Ni, Zn, As, and Cd would not be toxic to aquatic ecosystems, however, Hg and Cr in some regions may cause acute toxicity to the benthos. The ecological assessment results of the surface sediments indicated that some areas of the lake are heavily polluted and the main polluting elements are Cd and Hg. Cd has the highest bioavailability because of its high exchangeable fraction ratio. In addition, exogenous pollution accumulated within 20 cm of the sediment cores, and then, with the increasing of the depth, the pollution degree and ecological risk decreased.

**Keywords:** heavy metals; sediment interstitial water; sediment; chemical fraction; ecological risk; Wuliangsuhai Lake
