Quantifying how urban landscape heterogeneity affects land surface 1 temperature: A comparison of discrete and continuous approaches

10 The present study examines the efficiency of discrete and continuous approaches to measuring 11 urban heterogeneity effects on land surface temperature (LST). In the discrete approach, landscape 12 metrics have been widely applied to quantifying the relationship between land surface temperature and 13 urban spatial patterns and have received acceptable verification from landscape ecologists but some 14 studies have shown their inaccurate results. The objective of the study is to compare landscape metrics 15 and alternative approaches to measuring urban heterogeneity effects on LST. We compared landscape 16 metrics results with nine texture-based measures, and two local spatial autocorrelation indices (local 17 Moran’s I and Gi statistics) applied to NDVI and BAI indices as a proxy of the spatial patterns of Tehran 18 vegetation and built-up classes. The statistical results showed that urban landscape heterogeneity had 19 significant impacts on the LST variations, and there was a compatibility between landscape metrics and 20 alternative measures results. Overall results showed that the less-fragmented, the more complex, larger, 21 and the higher number of patches, the lower LST. The most significant relationship was between patch 22 density (PD) and LST (r= -0.71). Higher values of PD have mostly been interpreted to show higher 23 fragmentation, but other landscape metrics and alternative measures declined this conclusion. Our study 24 demonstrated that PD was not a reliable metric and presented no information about the spatial 25 distribution of landscape elements. This study confirms alternative measures for overcoming landscape 26 metrics shortcomings in estimating the effects of landscape heterogeneity on LST variations and gives land managers and urban planners new insights into the urban design . of paved surfaces and a positive correlation between LST and patch


43
Land surface temperature (LST) of cities is warmer than suburbs due to impervious surfaces 44 and buildings Tuttle et al., 2006). This phenomenon is due to the change of 45 natural habitats into cities, parking lots, roads, and other impervious surfaces that considerably  Estimating the relationship between LST and green spaces patterns is an essential step 60 for lowering LST in a city because it is possible to reduce the city's temperature by creating 61 new green space patches. Therefore, there is an urgent need for quantifying the effects of urban 62 landscape heterogeneity on LST correctly (Cadenasso et al., 2007). In this regard, Landscape  (Shao and Wu, 2008). Therefore, the uncertainties related to the classification process of 69 continuous variables into discrete classes, have reduced the efficiency and accuracy of these 70 metrics (Dormann, 2007). Many other factors affect the accuracy and applicability of landscape 71 metrics, like data source accuracy, scale effects, and ecological interpretation (Liu et al., 2013). 72 It has also been reported that although some landscape metrics calculated differently, they are 73 highly correlated (Neel et al., 2004;Turner et al., 2001). 74 As mentioned above, the accuracy of landscape metrics is considerably related to the 75 accuracy of classified maps. The classification of urban areas that are a mixture of different 76 covers is more complicated than other land covers. Therefore, we need new methods to examine 77 urban heterogeneity correctly. One of the suggested alternative methods that can display and 78 analyze urban heterogeneity based on continuous data (e.g., NDVI) are local spatial 79 autocorrelation indices (e.g., local Moran's I and local Getis-Ord (Gi)). The Gi index in 80 measuring urban fragmentation  and quantifying the effects of spatial 81 patterns of green spaces on air temperature (Yang and Li, 2012) has shown significant ability.

82
A few studies have applied local spatial autocorrelation to estimate the relationship between  Other alternative measures are texture-based measures that, similar to local spatial 87 autocorrelation indices directly use remote sensing data as their inputs to capture landscape 88 heterogeneity. These measures quantify spatial aspects of landscapes based on the gray-level 89 co-occurrence matrix (GLCM) (Haralick and Shanmugam, 1973). Each GLCM index can 90 highlight a particular property of texture, such as smoothness or coarseness produced by the 91 uniformity or variability of image color or tone (Li and Narayanan, 2004;Park and Guldmann, 92 2020). Texture analysis methods have been used in the different remote sensing-based analysis, 93 such as analysis of urban growth (Gluch, 2002), forest cover classification (Coburn and Roberts,94 2004), habitat selection (Tuttle et al., 2006), and as a predictor of spices richness ( images. Next, we estimate the effects of urban composition and configuration on LST values 106 using landscape metrics, spatial autocorrelation indices, and texture-based measures and 107 compare the ability of these metrics in quantifying the relationship between LST and urban 108 structure elements like buildings and green spaces.  Spatial data 123 We used two Landsat image sets as initial data for deriving LST; Landsat 7 ETM + image (band   135 We used the split-window method for Landsat 8 TIRS (Sahana et al., 2016)  In this study, we applied landscape metrics to compare to local spatial autocorrelation indices   the ratio of cell size to landscape area ≤ MESH ≤ total landscape area (A) NP NP ≥ 1, without limit PD

Calculation of LST
Where N is the total pixel number, Xi and Xj are intensities in points i and j (with I≠j),

186
The local Moran's I differ from the Getis statistic in that the co-variances than the sums 187 are computed (Anselin, 1995). The local Moran's I is (Equation 7): 188 189 Vegetation indices 190 In the continuous framework, we need to use continuous indices that reflect landscape patterns Texture-based measures 202 We applied two types of texture measures to NDVI and BAI indices as input images: first and 203 second-order measures (      Table   266 7. According to   There was a significant difference between composition and configuration metrics in  The most significant correlation was between patch density (PD) and LST (-0.71), 304 apparently suggesting fragmented green space patches reduce LST. In several studies, higher 305 LST has been associated with higher PD of green spaces, which is concluded to a more

326
The earlier studies have concluded their results based on the belief that higher PD means 327 higher fragmentation. Still, our research shows that this statement is not always accurate 328 because the SPLIT (r= 0.38) metric and other aggregation metrics (CLUMPY, AI, and MESH) 329 showed that less-fragmented and clustered vegetation cover in Tehran city resulted in lower 330 LST not dispersed (Table. 7). SPLIT metric approaches 1 when the landscape; consists of a 331 single patch and increases as the focal patch type increasingly losses its area and is subdivided 332 into smaller patches (McGarigal et al., 2002). Therefore, Relationship between LST and 333 aggregation metrics like SPLIT showed that fragmented green space affects LST adversely.  The statistical relationships between Local spatial autocorrelation indices and LST maps in the 358 year 2017 are presented in Table 8. An area is interpreted as a clustered or homogeneous (high-359 value clustering or low-value clustering) when the local Moran's I is considerably higher than  (Fig 4-A and D). The negative relationship between local Moran's I of NDVI and LST (r= 364 -0.60) implies that LST values increase as values of local Moran's I decrease or, in other words, 365 clustered patterns of NDVI (green spaces) in Tehran city are cooler than heterogeneous ones.

366
This result is consistent with landscape metrics that showed homogenous patterns of green 367 space class were more correlated to LST than fragmented. For local Moran's I of BAI (r= -368 0.59) (Fig. 5), higher values belong to areas with the least vegetation cover and constitute 369 evident clusters of buildings and paved surfaces. Therefore, a positive correlation between local 370 Moran's I of BAI and LST shows that warmer places are in more clustered and more 371 homogeneous buildings parts of Tehran city. It is essential to consider that local Moran's I is 372 strongly affected by input images, meaning that high values of the input images are often 373 considered as clustered patterns (Fig. 5).    LST.

438
The lower values of homogeneity (Fig 6-D)