## 4 Results
### Analysis of Urban Eco-Efficiency in Shandong Province  
#### 4.2.1 Measurement of Urban Eco-Efficiency in Shandong Province  
In terms of measuring urban ecological efficiency, the non-expected output super efficiency SBM model is used to calculate the ecological efficiency of various cities in Shandong Province through MATLAB. Figure 5 reflects the evolutionary trend of the mean eco-efficiency values in Shandong Province and each economic circle from 2014 to 2021.  
Overall, the level of urban eco-efficiency in Shandong Province is between 0.2 and 0.7, with an overall downward trend until 2020, with an average decrease of 6.4%, and an upturn in eco-efficiency in Shandong Province in 2021, with an increase of 9.6%. The average value of eco-efficiency in the study period is 0.438, which is at a lower level, and there is still much room for improvement. The temporal change characteristics of eco-efficiency in each economic circle are similar to the overall characteristics. The eco-efficiency level of the Jiaodong Economic Circle has relatively large changes, and the eco-efficiency levels of the Provincial Capital Economic Circle and Lunan Economic Circle are relatively stable.  
A comparison of eco-efficiency among the three economic circles shows that the Jiaodong Economic Circle has the highest level of eco-efficiency, the Provincial Capital Economic Circle has the middle level of eco-efficiency, and the Lunan Economic Circle has the lowest level of eco-efficiency. The Jiaodong Economic Circle is located in the coastal area of Shandong Peninsula, which has a natural advantage of opening up to the outside world, attracting high-tech industries, emerging future industries and other key areas, and high-end projects to gather in Jiaodong, and these industries help to improve the eco-efficiency level of the city, whether in terms of energy consumption, resource allocation, or pollution emissions. The Lunan Economic Circle, such as Linyi, Zaozhuang, and other cities in the economic development of the main industry, is mostly secondary industry, with high energy consumption and pollution emissions, and the level of eco-efficiency is stable. The main industries in the Lunan Economic Circle, such as Linyi and Zaozhuang, are mostly secondary industries, with high energy consumption and pollution emissions, which are not conducive to urban eco-development; the main industries in the Provincial Capital Economic Circle are diversified, including both high-tech industries such as Inspur and industrial industries such as steel, whose eco-efficiency is at a medium level.  
Figure 5: Evolution of eco-efficiency in Shandong Province, 2014–2021.  
2.2 Characteristics of the Spatial and Temporal Distribution of Urban Eco-Efficiency in Shandong Province  
To more intuitively portray the spatial and temporal differentiation characteristics of urban eco-efficiency, the spatial distribution map of eco-efficiency in 17 cities in Shandong Province (Laiwu city was not assigned to Jinan before 2019) from 2014 to 2021 was drawn using ArcGIS software 10.2 (Figure 6). As seen from the figure, the spatial distribution of eco-efficiency in Shandong Province has obvious polarization characteristics. The level of eco-efficiency in western Shandong Province is low, and the level of eco-efficiency in eastern Shandong Province is relatively high. Inland cities except Jinan and Zibo are at very low eco-efficiency levels, and the eco-efficiency level of Zibo city decreased during 2014-2021, falling to below 0.4 in 2018. After Laiwu was assigned to the administrative scope of Jinan city in 2019, the overall eco-efficiency level of Jinan city improved; the eco-efficiency level of the coastal areas also decreased during 2014-2020, and the eco-efficiency level of Yantai city also decreased. Yantai city's eco-efficiency declined by 18.5% during 2014-2016. In Weihai city, the eco-efficiency level declined by 87% during 2018-2020 and returned to higher levels in 2021.  
Figure 6: Spatial distribution pattern of eco-efficiency in Shandong Province, 2014–2021.