A New Remote Sensing Index for Assessing the Spatial Heterogeneity in Urban Eco-Environmental Quality Associated Road Network

Although many prior efforts have found that road network has signicantly affect the landscape fragmentation, the spatially heterogeneous effects of road network on the urban eco-environment remain poorly understood. To understanding the coupling mechanism of road network and eco-environment, a new remote sensing based ecological index (RSEI) was proposed to calculate the eco-environment quality, and kernel density of road (KDR) was applied to measure the road network density. We proposed a spatially explicit approach (geographically weighted regression, GWR) to explore the spatial variations in the relationship between the road network and the eco-environmental quality The results of GWR models t better than those of the Ordinary Least Square (OLS) models. Among, the average effect of KDR on the variables of normalized difference vegetation index, land surface moisture and RSEI was negative, while it was positively associated with the variables of soil index, normalized differential build-up and bare soil index, index-based built-up index, and land surface temperature. From spatial perspective, the impacts of KDR on the urban boundary were generally greater than those on the city center. The spatial variation in the relationship between the road network and the eco-environment is mainly controlled by the relationship between the road network to the vegetation and the bare soil. Locally, the water body, whether a large regional river or urban inland rivers, has a great inuence on the spatial variation in the relationship between the roads and the eco-environmental variables, and it can even change the sign of the inuence.


Introduction
Roads appear as conspicuous objects in the world. O cial statistics is staggering, with 4.8 million km 2
China's mountainous areas, including hills and plateaus, cover an area of 6.636 million km 2 , accounting for 69.1% of the total land area in the country, which means these road networks might affect the eco-environment of a considerable part of the country's earth surface. Previous studies suggest that roads might affect the eco-environment of nearly 15-20% of the total land area of the United States 1 and nearly 16% of the Netherlands 2 . Similarly, it has been reported that roads might impact proximately 20% of China's land ecosystems 3 . It is projected that a further 25 million km 2 of road will be added on the earth by 2050 4 . Such rapid extension of roads may impose serious eco-environmental threats and challenges in the future. Roads are clearly something worth understanding. To effectively avoid or mitigate the negative impacts of roads, it is essential to develop a systematic research framework to fully understand the road-impacts on eco-environment and their causal mechanisms 5 .
Many of previous studies have focused on exploring landscape dynamics associated with road networks 6 . However, the landscape ecological effects on air, water, soil, and especially an integrated measure of eco-environment emanating from roads are not fully investigated 1,6,7 . Little knowledge on eco-environmental effects has been done in the heavily road sprawl zones in urban areas 8 .
Roads have a wide array of ecological effects spreading through terrestrial and aquatic ecosystems 1 . First of all, road construction has huge ecological impacts early during the land use and cover changes 9 , not only causing local habitat loss, but also increasing disturbances on surrounding landscapes 10 . Moreover, road extension may induce landscape fragmentation by cutting landscapes into pieces 6 . Speci cally, great changes in landscape structure can be observed in most cased, as decreasing size of patches (core area size), increasing number of patches (patch density), and simplifying or complexing shape of patches (patch dimension) [11][12][13] . Reed et al. 14 quanti ed fragmentation caused by roads in southeastern Wyoming with several landscape structure measures, such as number of patches, mean patch area and perimeter-related indices so on, indicating that forest fragmentation was aggravated by cutting large plaques into smaller pieces and by transforming forest interior habitat into forest edge. Reed et al. 14 also pointed out that fragmentation could be reduced by minimizing or rerouting road construction. Karlson Mörtberg 15 explored potential effects of fragmentation and disturbance of roads on landscape in Swedish, revealing a main consequence of habitat loss of road effects. Meanwhile, the destructive effects of roads on wildlife have even been reported as one of the major crises of the global biodiversity 16 . From many perspectives, the detrimental impacts of roads on nature (both terrestrial and aquatic) ecosystems have been fully explored 5,15 , however, eco-environmental impacts of road networks on urban area have gotten little attention 8 . Previous studies on the landscape effect of roads have emphasized on the spatial structure and pattern dynamics, while little analysis has been done in the eco-environmental function or quality for the urban area even with a dense road network. Wu et al. 17 also assessed the effects of a highway on landscape patterns in a town of Taiwan province. They discovered that the combination of highway construction and its subsequent urbanization had caused landscape isolation and fragmentation in the study area. Besides of the biological ecosystem, roads have a great impact on the abiotic ecosystem, such as air, water, and temperature as well 1 . For example, the direction of the road affects the ventilation of a city, which will affect the thermal eld distribution of a city.
Moreover, road motor vehicle is also one of the main sources of carbon emissions 5 . It has been reported that nearly 20% of the world's carbon dioxide (CO 2 ) emissions are generated from road tra c, the proportion is nearly 8% in China in 2015, and these emissions are increasing annually 7 . These may aggravate the deterioration of the urban eco-environment, such as the heat island effect. Severe health consequences for humans, coupled with a limited knowledge of how these landscape fragmentations caused by roads and road tra c pollutions jointly affect eco-environmental quality in urban area, highlight an urgent need to ll the knowledge gap of the couple relationship between roads and eco-environmental quality from a perspective of landscape. This will shed light on the mitigation measures for urban eco-environmental planning.
The need for sustainable planning and decision making for urban has stressed the construction of a framework to address effectively the eco-environmental quality. Among, Environmental Impact Assessment (EIA) and Strategic Environmental Assessment (SEA) are two legal frameworks to evaluate, project and mitigate adversely ecological effect of transport infrastructure; the Convention on Biological Diversity (CBD), the European Landscape Convention (ELC) and the EU Biodiversity Strategy (BS) also address the treatment of ecological impacts 10 . These analysis frameworks have been extensively employed in the studies of environmental assessment 18,19 . However, these frameworks emphasized the protection of habitat and the increasing of landscape connectivity for conserving biodiversity and ecosystem service. Moreover, these methods are only applicable to certain project or administrative division, while they are not feasible to explain the spatial distribution of ecological conditions and their changes for a region 20,21 . These problems are extremely important for propose an effective index to identify spatial variation in the eco-environmental impact of roads.
Recent advances in the availability of satellite-based datasets and remote sensing technology have provided a powerful tool to identify eco-environmental status at the pixel level with complete coverage for various ranges from local to global 22,23 .
Fuzhou City is in the southeast coast of China, which has experienced very rapid urbanization over the past three decades, with built-up area increasing more than 15 times from 22 km 2 in 1978 to 357 km 2 in 2018 32 . Urban sprawl combining with the basin-like topography make it a new "stove" in China. Therefore, these features of the city make it a particular interesting case for exploring the spatial relationships between the roads and the eco-environmental quality. At present, the utility of remote sensing indicators as a tool to identify the impacts of roads in eco-environmental quality remains a challenge since their relationships may vary across the study area (i.e., spatial non-stationarity). To our knowledge, the spatial non-stationarity in the relationships between roads and eco-environmental quality has rarely been explored. Therefore, taking Fuzhou City as a case, we employed geographically weighted regression (GWR), a local model, to explore the spatial non-stationarity in the relationships between the kernel density of road (KDR) and RSEI across the study area. The following questions were explored: 1) Do the effects of roads on RSEI and its constituent factors vary with locations across the study area? 2) Does trade-off or synergy relationships between the two regressors predominate? 3) How do their relationships distribute? Results for the above three questions will improve our knowledge on urban eco-environmental pattern and enhance improve our capability in road network and urban planning.

Materials And Methods
Study area. Fuzhou City is the capital and the largest prefecture-level city in the Fujian Province of China ( Fig. 1), which is in the west coast of the Taiwan Strait and in the lower reaches of the Minjiang River. The average annual temperature is approximately 293.9 K. The annual precipitation varies widely from 796.5 to 1 913.6 mm, with approximately one-third receiving in the May and June. The study area (Fig. 1b) is the downtown area of the city, with dense buildings and population. It has been witnessed that the eco-environmental quality has been deteriorating dramatically in the past two decades 33 . And the city becomes one of the four new furnaces in China. Consequently, the study on spatial variations in the associations between the eco-environment quality and the road networks is very necessary, and may shed a light on those of rapidly urbanization region in the world.
Data resources and pre-processing. Landsat OLI/TIRS image used in this study was acquired on 2016-06-25. The road network dataset was obtained from OpenStreetMap. The pre-processing of the Landsat image includes radiometric calibration and atmospheric correction. For detailed steps, please refer to our published literature 22,24 .
Calculation of remote sensing based ecological index. Remote sensing based ecological index (RSEI) is a synthetic index could assess a region's eco-environmental quality quickly and quantitatively, which was based on the pressure-state-response framework (PSR) using a principal components analysis (PCA) 22,24 . RSEI is capable of overcoming the weakness of most of the previous ecological indicators, which measure merely the response of the ecosystem to anthropogenic stresses causing impairment. The RSEI is composed of a couple of indicators, including the greenness, dryness, heat, and humidity, which were represented by normalized difference vegetation index (NDVI), normalized differential build-up and bare soil index (NDBSI), land surface temperature (LST) and land surface moisture (LSM), respectively. For NDBSI, which was calculated by combining soil index (SI) and index-based built-up index (IBI). All these indicators can be quickly obtained from Landsat datasets at the pixel level. The calculation formulas of these indicators and the synthesis of RSEI are detailed in the references 22,24 .
Estimation of kernel density of road. The kernel function is used to calculate the road network density (i.e., KDR) per unit area based on points to t each point to a smooth cone-shaped surface by moving windows 34 . The kernel function used was adapted from the fourth-order kernel function used to calculate the point density described in Silverman's book 35 . The search radius (bandwidth) of moving windows within which the density is calculated according to the "Silverman rule of thumb" spatial variable, which can effectively avoid spatial outliers (that is, points that are too far away from other points). The KDR map produced in the ArcGIS, in which the speci c parameter design can refer to a previously published paper 36 .
Sampling. Using ArcGIS software, a shing net of 300⋅300 m was established as sampling unit, with a total of 7,796 samples for the study area (Fig. 2). The tool of Zonal Statistics as Table was employed to summarize the average values of all rasters within each sample of the datasets of each variable, and the statistics tables for all the variables were outputted. Then, all the average values in the output tables were joined to the sample layer based on the predetermined eld. Thus, the sample layer had the attributes (i.e., the average value) of all variables at 300⋅300 m polygons, which can be used as input feature in modeling spatial relationships in ArcGIS.
Regression models. Both a global model (ordinary least squares, OLS) and a local model (GWR) were employed to examine the association between the RSEI associated indices (including NDVI, IBI, SI, NDBSI, LST, LSM, and RSEI) and KDR, respectively. The OLS models were used to detect the overall relationship between each two regressors, while the GWR models were applied to identify the spatial heterogeneity in the interactions between the two regressors across locations 32 . The regression models were simulated in the ArcGIS program. The KDR was set as independent variable, and NDVI, IBI, SI, NDBSI, LST, LSM, and RSEI were set as dependent variable in each separating model. In terms of the GWR models, the adaptive kernel type was set, and the bandwidth of the kernel was determined using the Akaike Information Criterion (AICc). The goodness of the models was evaluated using the following test indicators 32 , including the adjusted R-squared, AICc, residual squares, P-value, and Moran's I.

Results
Tests of GWR and OLS models. Table 1 indicated the test results of the OLS and GWR models for tting the associations between the KDR and the RSEI variables. The higher adjusted R 2 , 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 signi cant at the 0.001 level, also indicating highly goodness tting for all the GWR models. This supports the use of the GWR model in this study.
Summary of coe cients of the GWR models. Table 2 presents parameter descriptive statistics of the GWR models. These statistics can be used to compare the coe cient changes of different variables and reveal the variation of the coe cients in the study area. speci cally, 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 coe cients 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 coe cients into ve categories, with zero being arti cially 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 signi cantly across the study region. The negative correlation coe cients were noticeably higher in the south part (i.e., the green clusters), while the negative correlation coe cients 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 gure also showed that the impact of the KDR on the IBI varied signi cantly across the region, with the positive correlation coe cients 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 gure 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 gure showed that the positive correlation prevailed over the negative correlation in the study area. The positive correlation coe cients 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 coe cients 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 coe cients were noticeably higher in the south part (i.e., the green/red clusters), while the negative/positive correlation coe cients 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 coe cients have the greatest correlation among all the other pairs of variables, with the R 2 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.

Discussion
From the regression results, the OLS models indicated statistically signi cant relationships between KDR and the RSEI composed indicators (R 2 = 0.013 ~ 0.168, p-value = 0.05), while the GWR model showed more considerably stronger relationships from the same datasets (R 2 = 0.314 ~ 0.564, p-value = 0.001), highlighting a tendency of spatial non-stationary in the relationships ( Table 1). The main reason is that the conventional ordinary least squares regression models, assuming spatially stationary in the relationship between the regressors. Such assumption may often be untenable by ignoring the local variations of variables in each sample site, particularly in the large-scale studies based on remote sensing images [37][38][39] . Local statistical approaches (e.g., GWR), can be more appropriate than global techniques (e.g., OLS), if the relationship is spatially non-stationary 40 . GWR can capture the spatial variations in the relationship between variables, by including the spatial coordinates of the sample grids in the model. Therefore, GWR has huge potential in the studies using remote sensing data, as such data commonly have an explicit spatial character. However, the method is not a panacea, with essential issues, such as the calculation of weight matrix, in the processing of the model 38 . The weights are set to ensure the observations having more in uence on nearer locations than those further away in the estimating of the parameters. The weights depend on a spatial kernel function in a bandwidth. Previous studies have often used a xed bandwidth with a Gaussian function to assign sample plots for each regression and their spatial weights 41 . The assumption of a xed bandwidth is that the sample plots are regular and consistent in size. An adaptive bandwidth is recommended in the uneven distribution of observations, in which the kernel bandwidth is based on the rule of the Akaike information criterion (AICc) 42 . This kind of bandwidth is adaptive in size to guarantee a same number of samples including in each regression 43 . In this study, we selected adaptive bandwidths with the Gaussian spatial kernel because of the uneven distribution of data, and used Moran's I index to examine spatial autocorrelation of the GWR residuals (Fig. 3). The goodness of tting indicates effective of the local models and obviously superior to the conventional OLS models. We hope this study may again shed a new light on the potential regression or prediction analysis using remote sensing as a source data.
Upgrading and extending of road network has improve the accessibility of remote places, subsequently, triggering the sprawling of arti cial landscape, as well as the human disturbances 44 . Road network has thus become a focus of interest in landscape ecology research. Many studies have focused on the relationship between the road network and landscape ecology in a range of spatial and temporal scales 6, 45,46 . Thus, the quanti cation of the characteristics of road network and ecosystem is a priority in understanding the coupling mechanism. In terms of road network, road density is among the most commonly used index, which has been proved to be an effective indicator of road network, and associated with many eco-environmental effects 47 . However, the limitation of this classis indictor is that the value is the same in each entity, ignoring the spatial heterogeneity of road network distribution even in a homogeneous space 48 . Therefore, unlike many of studies that use road density indicator, we employ a more effective indicator (KDR) to measure road network at the pixel level 33,49 . In terms of ecological aspect, though different studies of road impact on landscape have been distinct in detail, each has inevitably measure landscape metrics (e.g., fragmentation, connectivity) for a region or an observation unit 33,50 . These landscape metrics are either patch level, landscape level, or moving window level 51 , which are relatively coarse in terms of spatial resolution. In comparison with these landscape metrics, we employed a newly proposed remote sensing based ecological index (i.e., RSEI) at the pixel level to match the measurement of road network (i.e., KDR). RSEI has been coined by Xu et al. 52 and extensively applied to quantify and detect eco-environmental changes at various scales 21,32,52 . Our previous published papers have illustrated that this index can assess the regionally eco-environmental status objectively and easily 22,32 . These support our usage of the KDR and RSEI as proxy of road network and eco-environmental status, respectively, to explore the spatial variations in their relationships.
Since spatial non-stationarity may be common for most geographical events, local information should be included in regression analyses 53 . By identifying local variation in the relationships between the KDR and RSEI (including its sub-indicators) which may be missed using a global method, the GWR model was employed in this paper to act as a spatial microscope, revealing both synergy and trade-off locations, which is more feasible for future targeted measures. Our evidence revealed that the relationships were multiple, with different symbols of coe cients coexisting and varying across locations in the study area (Fig. 3). Thus, our outputs may provide a more scienti c base for furtherly understanding of the mechanism how road network impacts on the observed RSEI values, and the variables of NDVI, IBI, SI, NDBSI, LST, LSM as well.
This was most apparent on the banks of the rivers, which contained a strip cluster showing an opposite relationship with KDR, compared with most of the study area, and the clusters varied across each variable (Fig. 3). This shows that the water body has a great in uence on the relationship between roads and the eco-environment, and is the main in uencing factor of the spatial variation of the relationship. Previous studies have revealed that the variations of the mapped coe cient values (Fig. 3) appear to connect with land cover patterns 32,38 . This is mainly because the spectral characteristics of water bodies are very different from those of other land use types, which is manifested by strong absorption in the near-infrared band, resulting in signi cant differences in the remote sensing retrieval index values of water bodies with other land types 54 . Moreover, due to the spill-over effect of high-density buildings in the urban center, the eco-environmental status of riversides is similar to that of urban centers 22 , but these riversides land use patterns are usually different with those of the urban centers, with high coverage of green places, and low density of the road network. Therefore, the relationship between the road network and the ecoenvironment in the riverside is opposite to the other area of the urban. Specially, the narrow stipe (2 km or so) located close to the river, exhibiting a positive relationship between the KDR and the NDVI/RSEI, a negative relationship between the KDR and the SI, is due to the better greened road network and the less bare lands in such new district. The narrow stripe (2 km or so) located close to the river, with negative relationship between the KDR and the NDBSI/IBI, is due to the low construction density in such High-tech Development Zone. Moreover, the negative relationship between the KDR and the LST is because that there are more wetlands in the riverside, which has a cooling effect.
It should also be noted that all the impacts of road network on the RSEI and its indicators of urban boundaries (urban-rural junctions) were greater than that of urban centers, the southern part was among the most sensitive area with the highest values of all coe cients for all the eco-environmental variables (Fig. 3). This is because the density of road network in the urban center is relatively high and therefore has a high KDR value, while the urban-rural junction is the opposite. While the values of the ecoenvironmental indicators are relatively consistence ranging from − 1 to 1, the higher the KDR value, the lower the regression coe cient is, otherwise the opposite. It is worth mentioning that the locally spatial variation in the relationships between the road network and eco-environmental indicators would have gone buried by a global regression analysis 42 . Moreover, the statistically signi cant relationships derived from the OLS models (Table 1), could lead to inappropriate and unproductive effort being directed towards discovering potential spatial variability in the relationships.

Conclusion
Both OLS and GWR models were employed to explore the spatial variations in the relationship between the road network (i.e., KDR) and the eco-environmental quality (i.e., RSEI), and the land surface parameters (i.e., NDVI, IBI, SI, NDBSI, LST, LSM) as well, with the Landsat-8 OLI/TIRS data in the megacities of Southeast China. The results show that the GWR models t better than those of the OLS models, which supports our use of the GWR approach. Both positive and negative associations between the KDR and all the eco-environmental and land surface variables coexisted across the study area. 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 SI, NDBSI, IBI, and LST.
The spatial patterns of GWR coe cients indicated that (1) The impacts of KDR on the urban boundary were generally greater than those on the city center. (2) The response of urban eco-environment and land surface feature to road network was affected greatly by water area, whether a large regional river (i.e., the Minjiang River) or urban inland rivers. Rivers may change the sign of the relationships between the road network and the variables. Because the river itself and the riverside have special land cover features, such as covered by wetland parks and low-density buildings. (3) The spatial variation in the relationship between the road network and the eco-environment is mainly controlled by the relationship between the road network and the vegetation and the relationship between the road network and the bare soil.  Tables   Table 1 Tests of the ordinary least squares (OLS) and the geographically weighted regression (GWR) models.   Table 3. Pearson correlation analysis (** indicates statistically signi cant at 0.01 level). Figure 1 Location of the study area  Scatter plots of coe cients of remote sensing based ecological index (RSEI), soil index (SI) and normalized difference vegetation index (NDVI).