1. Introduction
Although urban areas occupy only a small fraction of the earth’s surface, they are home to more than half of the world’s population, a figure that is expected to increase to more than two-thirds by 2050 [
1]. The process of urbanization is accompanied by a suite of surface modifications that alter energy flows, including the replacement of soil and vegetation with impervious surfaces like concrete and asphalt, producing novel ecosystems whose dynamics are controlled by coupled human-natural systems [
2,
3,
4]. A widely recognized characteristic of urban areas is an increase in temperature relative to surrounding rural areas known as the urban heat island (UHI) effect, a consequence of anthropogenic heat, decreased albedo, increased thermal capacity, and decreased evapotranspiration [
5,
6]. The lack of vegetated surfaces contributes heavily to UHIs through the increased partitioning of incoming solar radiation into sensible rather than latent heat flux [
7,
8]. Additionally, the increased runoff associated with impervious surfaces decreases the amount of moisture available for evapotranspiration [
9]. The surface UHI (SUHI) is defined for the urban land surface, and is measured by remote sensing instruments as upwelling thermal radiance [
3]. The spatial distribution of SUHIs is a manifestation of the surface energy balance and is consequently strongly dependent on the presence or absence of vegetation [
6,
8,
10], with vegetated areas being potentially 2–8 °C cooler than surrounding areas [
9].
Urban areas magnify the warming effects of climate change, with studies showing urban temperatures to be increasing at approximately double the rate of average global warming [
11]. Global mean temperature is projected to warm by at least 1.5 °C by the end of the 21st century and both the frequency and intensity of heatwaves are expected to increase, amplifying risk for people, economies, and the environment in urban areas without sufficient infrastructure, including green space networks [
1,
12]. Extreme heat events are the leading cause of weather-related mortality in the U.S. [
13] and during the European heatwave of 2003, somewhere between 22,000 and 45,000 people died of heat-related illness [
14]. Models show that anthropogenic forcing was a significant factor in this occurrence and it is projected that the likelihood of such extreme heat events will increase by 100% by 2050 [
15]. With a greater proportion of the global population living in urban areas, more people will be exposed to the risks associated with heat stress, causing not only increased mortality but also widespread economic and environmental disruption and increased energy demand [
2,
12].
The pattern of urban green space influences the distribution and magnitude of land surface temperature (LST) through its effects on energy flows in urban areas [
16,
17] and can be controlled through urban planning [
11,
18]. Pattern comprises composition—the variety and abundance of land cover types—and configuration, their arrangement and distribution [
19]. Urban landscapes are composed of many different land cover types, and vegetated cover and impervious surface are the two most important factors in SUHI formation [
20]. Urban green space has a consistently positive effect on SUHI mitigation [
7,
17,
21,
22,
23,
24], however, the effects of green space configuration, especially when controlling for the effects of landscape composition, are more complicated and less well understood [
16].
Landscape ecology provides a powerful paradigm for the integration of environmental science and sustainability through the design of the built environment [
25], as well as the tools necessary to characterize the urban environment and quantitatively relate it to biophysical processes [
6]. Landscape metrics are indices that were created by landscape ecologists to quantify the pattern of land cover within a landscape based on the fundamental idea that environmental pattern influences ecological process [
19]. Landscape metrics are especially well suited to describing urban areas because the basic land cover classes are well defined and the landscape structure is fairly static; they can also facilitate information exchange between scientists and planners by providing a language common across these disciplines [
26].
While there has been recent interest in relating the configuration of urban green space to SUHIs using landscape metrics [
16,
17,
22,
24,
27,
28,
29], these studies produce inconsistent and sometimes contradictory results. Li et al. [
22] found that, given a set quantity of green space, dispersed, rather than clustered, configurations more effectively mitigate SUHIs. Likewise, Stone and Rodgers Stone and Rodgers [
30] found that dispersed rather than clustered distributions of neighborhood street trees can more significantly influence LSTs than the total number of trees. Zhou et al. [
16] reported negative relationships between LST and edge density and shape complexity and no significant relationship between mean patch size and LST. More recently, Li et al. [
28] found that configuration had a stronger correlation with LST than composition. Li et al. [
27] and Chen and Yu [
24] found that larger vegetated patches more effectively lowered LST. In contrast to Li et al. [
22] and Stone and Rodgers [
30], Chen and Yu [
24] and Estoque et al. [
29] found that clustered rather than dispersed green space more effectively lowered LST.
Urban areas are complex systems characterized by heterogeneity and nonlinear relationships between structure and function across both spatial and temporal scales, increasing the difficulty of modeling urban environments [
4,
6,
10,
31,
32,
33]. The characteristic scale of a phenomenon is the spatial and temporal scale at which it predominantly operates, and if it is not matched by the scale of observation, the phenomenon may not be properly observed [
33]. The relationships between pattern and process are often scale-dependent, and as the scale of observation changes, a phenomenon may manifest in different ways [
33,
34]. Additionally, the quantification of the pattern is scale-dependent; what is dispersed in a small area may be clustered when considered within a larger extent [
33]. Thus, when using landscape metrics the scale at which they are calculated must represent the scale of the biophysical phenomenon under consideration or the results of modeling the relationship between pattern and process have little meaning [
19].
Understanding how the pattern of urban green space affects the surface-energy balance and the variability of LST requires that the analytical extent represent the characteristic spatial scale of LST-green space interaction. However, in several studies the spatial scale at which landscape metrics were calculated were census tracts [
27,
28] whose borders have little to do with microclimatic interactions and are variable from tract to tract, with Li et al. [
28] using only a sample of census tracts that were primarily single-family residential. Zhou et al. [
16], Chen and Yu [
24], and Grafius et al. [
31] calculated metrics for variably-sized patches based on urban land heterogeneity, the standard deviation of LST, and urban land-cover classes respectively. However, because changing the spatial scale of landscape pattern analysis can have strong effects on landscape metric values, comparison of landscape pattern should either be based on the same extent or explicitly deal with the scale dependence of pattern to be meaningful [
35]. While Li et al. [
22] calculated metrics within 2 km extents, Maimaitiyiming et al. [
17] within a 500 m moving extent, and Estoque et al. [
29] within 3 km extents, none of these studies give biophysical justification for their choice of extent. Although Zhou et al. [
36] and Guo et al. [
37] quantified landscape pattern at a variety of scales, there is no indication that the calculation extents reflect the characteristic scales of LST-green space interaction. While all of these studies investigate the relationship between green space pattern and LST, none do so for biophysically-derived extents.
Urbanization is a multi-scale process and therefore requires multi-scale information to observe relevant patterns [
33,
35,
38]. Wavelet analysis is an inherently multi-scale method for identifying the characteristic scales of landscape structure [
35]. Wavelet transforms provide the ability to examine the spatial pattern of LST across scales and to determine the scale at which features make the greatest contributions to the overall LST signal, known as the dominant length scale [
39,
40]. The dominant length scale for LST represents the spatial scale that contributes the most variance to the total LST signal at a given location and is, therefore, the scale at which pattern should be quantified in order to examine the impacts of green space pattern on LST production.
The purpose of this study is to provide a robust methodology for analyzing urban landscape patterns at biophysically-relevant extents and to investigate the relationship between green space configuration and LST. We quantified landscape patterns using high-resolution land cover data at the dominant length scales of LST production. The ultimate goal of this analysis is to provide parsimonious statistical results that can help to guide urban land-use decisions to ensure heat resilience in the context of climate change.