Tests of GWR and OLS models. Table 1 indicated the test results of the OLS and GWR models for fitting the associations between the KDR and the RSEI variables. The higher adjusted R2, the smaller AICc values of the GWR models against the OLS models, indicate the goodness of the GWR models than the OLS ones. The relatively small in the values of Moran’s I (0.199–0.309) reveals the small spatial autocorrelation in the Residual Squares (Figs. 3B,D,F,H,J,L,N), indicating the random distribution in the residuals across the study area. Moreover, all the seven GWR models were statistically significant at the 0.001 level, also indicating highly goodness fitting for all the GWR models. This supports the use of the GWR model in this study.
Summary of coefficients of the GWR models. Table 2 presents parameter descriptive statistics of the GWR models. These statistics can be used to compare the coefficient changes of different variables and reveal the variation of the coefficients in the study area. specifically, the impacts of KDR on all the RSEI indicators were both positive and negative across the study region. Except the variable of LST, whose values were not between − 1 and 1, the impacts of KDR on the other variables (from large to small) were in the order of NDVI, RSEI, SI, NDBSI, IBI and LSM. Among, the average effect of KDR on the variables of NDVI, LSM and RSEI was negative, while it was positive on the variables of IBI, SI, NDBSI, and LST.
Spatial variations in the response of RSEI indicators to KDR. GWR regression coefficients were mapped at grid level in Figs. 3A, C, E, G, I, K, M. In these maps, the Jenks method was employed to classify the coefficients into five categories, with zero being artificially set as a demarcation point to distinguish the positive and negative effects.
Figure 3A, B showed that the negative relationships between the KDR and the NDVI were distributed across most of the study area. This indicated that the NDVI increased gradually as the decreasing of the KDR, whereas the rates of decreasing varied significantly across the study region. The negative correlation coefficients were noticeably higher in the south part (i.e., the green clusters), while the negative correlation coefficients were obviously lower in the extensively northern areas (i.e., the brown clusters), where is the urban central area. However, a narrow stripe (2 km or so) located close to the river, exhibited a positive correlation between the KDR and the NDVI, indicating that the NDVI increased gradually as the increasing of the KDR.
Figure 3C, D indicated that the positive relationships between the KDR and the IBI were dominantly distributed in the study area, which indicates that the IBI increased gradually as the increase of the KDR. The figure also showed that the impact of the KDR on the IBI varied significantly across the region, with the positive correlation coefficients being noticeably higher in the boundary regions (i.e., the red clusters), while being obviously lower in the extensively central and northern areas (i.e., the yellow clusters). However, a narrow stripe (2 km or so) located close to the river, was observed to be negatively correlated with the IBI, indicating that the IBI decreased gradually as the increasing of the KDR.
Figure 3E, F revealed the spatial variations in the relationships between the KDR and the SI. The figure revealed that the positive correlations between KDR and SI occupied most of the study area. The positive correlation presented a basin-like trend, with low values in the middle and high value in the surrounding of the study area. Similar to the Fig. 3A, B, there was also a narrow stripe closer to the river, indicating noticeably negative associations between the KDR and the SI, indicating that the SI decreased gradually as the increasing of the KDR.
Figure 3G, H indicated the spatial variations in the relationships between the KDR and the NDBSI. The law of the spatial distribution was similar to that of the Fig. 3C, D. The figure showed that the positive correlation prevailed over the negative correlation in the study area. The positive correlation coefficients being noticeably higher in the boundary regions (i.e., the red, brown, and yellow clusters), while being obviously lower in the extensively central and northern areas (i.e., the green clusters). Moreover, there was a narrow stripe (2 km or so) located close to the river, being observed to be negatively correlated with the NDBSI.
Figure 3I, J also indicated a similar pattern in the relationships between the KDR and the LST, with those of the KDR and the IBI (Fig. 3C, D). In Fig. 3I, J, the warm colour (i.e., red, brown, and yellow) represented positive relationship, and the cool colour (i.e., green) indicated negative relationship. Similar to Fig. 3C, D, the positive correlation prevailed over the negative correlation in the study area. The positive correlation coefficients being noticeably higher in the boundary regions (i.e., the red, brown, and yellow clusters), while being obviously lower in the extensively central and northern areas (i.e., the green clusters). Moreover, there was a narrow stripe (2 km or so) located close to the river, being observed to be negatively correlated with the LST.
Figure 3K, L revealed the spatial variations in the relationships between the KDR and the LSM. The relationships demonstrated that the negative relationship between the KDR and the LSM distributed in most of the study areas, indicating that the LSM decreased with the increase of the KDR. However, there were also quite a part of the study areas showing a positive relationship, distributing in the central area of the urban and the southern of the study area, where happened to be distributed in the negatively correlated places of the KDR and the IBI, and the KDR and the LST as well (Fig. 3C, D and I, J).
Figure 3M, N indicated the pattern of the relationships between the KDR and the RSEI, similar with those of the KDR and the NDVI (Fig. 3A, B), while opposite with those of the KDR and the SI (Fig. 3E, F). In Fig. 3M, N, the red cluster represented positive relationship, which was a narrow stripe (2 km or so) located close to the river, while the other areas were all in negative associations. Similar to Figs. 3A ,B and E, F, the negative/positive correlation coefficients were noticeably higher in the south part (i.e., the green/red clusters), while the negative/positive correlation coefficients were obviously lower in the extensively northern areas (i.e., the brown and yellow/light green clusters).
Correlation analysis between ecological indicators. To investigate the interactions between eco-environmental indicators, the Pearson correlation analysis and 2D-scatter plot were employed here. The sampling was implemented randomly using a 10⋅10 grid across the study area. It can be seen from the results of the Pearson correlation analysis (Table 3) that the SI and the RSEI values and their GWR regression coefficients have the greatest correlation among all the other pairs of variables, with the R2 as high as -0.989; while the NDVI and the RSEI also have strong positive relationships. The scatter plots also show high linear relationships between them (Fig. 4). Due to the water and soil loss in the upstream of Minjiang River, there is a lot of sediment in the river body, leading to the distribution of SI index to be different from other indexes, with the differences of the SI values between the land surface and water body are much smaller than those of the other indexes. For example, the eco-environmental indicators, such as NDVI, IBI and NDBSI, all show a binary distribution pattern between the land surface and water body.