## 3 Results
### Complex Correlation Analysis  
From the compound correlation analysis of the yearly average NPP in relation to annual precipitation and the annual average air temperature (Figure 9), the compound correlation coefficients ranged from 0 to 0.9, with a high degree of overall correlation. Regarding spatial distribution, the complex correlation values of precipitation and temperature and the bias correlation coefficients of annual precipitation were consistent, i.e., most of the regions where the yearly average NPP showed strong correlations with annual rainfall also had relatively high complex correlation coefficients. On the contrary, the complex correlation coefficients for the areas where the influence of precipitation was weak were also small. Among them, 9.8% of regions with correlation coefficients below 0.4 suggested that the annual average NPP and the precipitation-temperature composite  
Figure 8: Partial correlation significance for annual average NPP with precipitation and annual average NPP with temperature. (**a**) Partial correlation significance for annual average NPP with precipitation, (**b**) Partial correlation significance for annual average NPP with temperature. Figure 7: The partial correlation coefficient of annual average NPP with precipitation and annual average NPP with temperature. (**a**) Partial correlation coefficient of annual average NPP with precipitation, (**b**) Partial correlation coefficient of annual average NPP with temperature. effect had low correlations in these areas, which were predominantly located in the eastern part of Changtu County, the southern part of Jinzhou City, the central and southern part of Xinmin City, and the southwestern part of Huludao City. Of the area, 31.8% had compound correlation coefficients between 0.4 and 0.6, including the western section of Changtu County, the eastern section of Kangping County, the central and southern parts of Huludao City, Jinzhou City, Xinmin City, and Faku County. Finally, 58.4% of the area had a compound correlation coefficient greater than 0.6, indicating that most regions in northwestern Liaoning contributed significantly to the compound effect of the precipitation-temperature impact on NPP at a highly correlated level. The significance test for the compound correlation relationship showed that 74% of the area in northwestern Liaoning had a significance of \(p<0.05\), indicating that the composite precipitation-temperature effect was significant. Of the area, 26.1% had a compound correlation that was not significant (\(p<0.05\)), which was primarily located in Changtu County, Xinmin City, and the southern-central part of Jinzhou City. Spatial Division of NPP Driving Factors  
The division of NPP annual mean values in different regions of northwest Liaoning by driving factors (Figure 10) reveals the following: 1 the areas in the study area where NPP changes were mainly driven by precipitation accounted for 65% of the total area, and they were concentrated in Chaoyang City, Fuxin City, Kangping County, north-central Huludao City, and northern Jinzhou City; 2 the areas driven by non-climatic factors were also relatively large in size, with an area of 26%, and they were mainly distributed in Changtu County, Xinmin City, the west side of Faku County, the south of Jinzhou City, and the southwest of Huludao City, suggesting that these areas may be more affected by human activities; 3 the areas weakly driven by air temperature and precipitation were mainly concentrated in the borders of Fuxin City with Jinzhou City and Xinmin City, the south of Kangping County, and the northeast of Faku County, with an area of 8.5%; and 4 the rest of the area was either strongly driven by precipitation and air temperature or driven by air temperature, which had areas of 0.5% and 0.3%, respectively; these were  
Figure 9: The multiple correlation coefficient and significance test results of NPP annual mean and precipitation temperature comprehensive effect. (**a**) The multiple correlation coefficient, (**b**) The significance test results.