> TGRS-2010-00524.R2 < 1

Modeling Urban Heat Islands and Their Relationship with Impervious Surface and Vegetation Abundance by Using ASTER Images

Qihao Weng, Member, IEEE, Umamaheshwaran Rajasekar, Xuefei Hu

Abstract—An important issue in urban thermal remote sensing sensed TIR data can provide a continuous and simultaneous is how to use pixel-based measurements of land surface view of a whole city, which is of prime importance for detailed temperature (LST) to characterize and quantify the urban heat investigation of urban surface climate. However, it should be island (UHI) observed at the meso- and macro-scales. noted that LSTs and air temperatures can be very different, Characterization and modeling of UHIs must consider the especially in summer daytime with clear skies and high solar inherent spatial non-stationarity within land surface variables. This study extended a kernel convolution modeling method for loading. LSTs show much larger spatial variability associated two-dimensional LST imagery to characterize and model the UHI with the properties of the surface, whereas air temperatures are in Indianapolis, U.S.A., as a Gaussian process. To understand the much less variable due to mixing of heat by the atmosphere. UHI pattern over the space and time, four ASTER images of Among the majority of the existing literature in remote sensing, different seasons / years were acquired and analyzed. there is confusion between LST patterns and UHIs. Nichol Furthermore, we employed linear spectral mixture analysis to suggested that the concept of a “satellite derived” heat island is extract sub-pixel urban biophysical variables (i.e., green largely an artifact of low spatial resolution imagery used, and vegetation/GV and impervious surface/IS), and developed new the term “surface temperature patterns” is more meaningful indices of greenness and imperviousness based on the convoluted than surface heat island [2]. The UHI was first defined in terms images of GV and IS fractions. These indices were proposed to show the contrast in the urban-rural biophysical environmental of air temperatures to represent the difference between warmer conditions. Results indicate that the UHI intensity possessed a urban compared to cooler rural areas, but sufficient care must stronger correlation with both greenness and imperviousness be taken to defining the urban and rural surfaces chosen for the indices than with GV and IS abundance. Because this study comparison [3]. The definition of UHI has since been adapted utilized a smoothing kernel to characterize the local variability of to looking at spatial patterns of surface temperature using urban biophysical parameters including LST, characterized UHIs remote sensing [4]; however, there were different opinions can therefore be examined as a scale-dependent process. To this about what constitute the representative “urban” and “rural” end, we categorized the smoothing parameters into three groups, surfaces. An appropriate rural reference should be from a corresponding to the three scales suitable to studying the urban representative land cover type typical of non-urban thermal landscape at the micro-scale, meso-scale, and regional scale, respectively. The identified scales can then be matched with surroundings of a city and should be from the same type of various applications in urban planning and environmental topographical setting without major elevation change. Stewart management. and Oke recently developed a classification scheme of urban land cover zones, which can be used to select representative Index Terms—ASTER imagery, green vegetation, impervious surfaces for studies of surface and air temperature heat islands surface, modeling, pattern recognition, urban heat island [5]. When imaged at high spatial resolution, the apparent UHI for surface temperatures may potentially be very large since extremely hot and cold individual surfaces (pixels) may be seen I. INTRODUCTION and measured. Therefore, what needs to be considered is an and surface temperature (LST) and emissivity data derived appropriate scale for assessing the UHI based on LSTs. It is of L from satellite thermal infrared (TIR) imagery have been great scientific significance to investigate how satellite-derived used in urban climate studies mainly for analyzing LST patterns LSTs can be utilized to characterize UHI phenomenon and to and its relationship with surface characteristics, assessing the derive UHI parameters. Few studies have focused on the urban heat island (UHI), and relating LSTs to surface energy modeling of UHI by deriving its parameters, such as magnitude fluxes for characterizing landscape properties, patterns, and / intensity, center, spatial extent, shape, and orientation, from processes [1]. Permanent meteorological station data and LST measurements. Streutker used AVHRR data to quantify moving observations using air temperatures cannot provide a the UHI of Houston, Texas, as a continuously varying synchronized view of temperature over a city. Only remotely two-dimensional Gaussian surface superimposed on a planar rural background, and to derive the UHI parameters of magnitude, spatial extent, orientation, and central location Manuscript received February 21, 2010. This work was supported by the [6]-[7]. Rajasekar and Weng applied a non-parametric model National Science Foundation under Grant BCS-0521734. by applying Fast Fourier Transformation (FFT) to MODIS Q. Weng and U. Rajasekar are with Indiana State University, Terre Haute, IN 47809, USA (phone: 812-237-2255; fax: 812-237-8029; e-mail: imagery (in 2005) for characterization of the UHI over time in [email protected]). the metropolitan Indianapolis (city of Indianapolis and eight X. Hu is with the Environmental Health, Emory University, Atlanta, GA neighboring counties) [8]. It is found that the magnitude of the 30322, USA (e-mail: [email protected]). > TGRS-2010-00524.R2 < 2

UHI varied from 1-5 °C and 1-3 °C over the daytime and Situated in the middle of the country, Indianapolis possesses nighttime images, respectively. Rajasekar and Weng further several other advantages that make it an appropriate choice. It applied a process Gaussian model to Landsat-5 (from years has a single central city, and other large urban areas in the 1985 and 1995) and Landsat-7 (from year 2000) images for the vicinity have not influenced its growth. The city is located on a city of Indianapolis to examine changes in the center and the flat plain, and is relatively symmetrical, having possibilities of spatial extent of the UHI from 1985 to 2000 [9]. Imhoff et al. expansion in all directions. Like most American cities, utilized impervious surface area from the USGS NLCD 2001 Indianapolis is increasing in population and in area. It is one of dataset and LST data from MODIS averaged over three annual the three major cities in the Midwest having an annual cycles (2003-2005) to assess the UHI skin temperature population growth rate over 5%. The areal expansion is through magnitude and its relationship to development intensity, size, encroachment into the adjacent agricultural and nonurban land. and ecological setting for 38 of the most populous cities in the As a result, a new metropolitan area of nine counties (Marion, continental United States [10]. Their results show that the UHI Hamilton, Johnson, Madison, Hancock, Shelby, Boone, magnitude increases with city size and is seasonally Hendricks, Morgan) is forming, comprised of approximately asymmetric with a 4.3 °C temperature difference in summer 9,100 sq. km. in area and 1.6 million population in 2000. and 1.3 °C in winter. In spite of these research efforts, Certain decision-making forces have encouraged some sectors characterizing and modeling UHIs across various spatial scales of the Metropolitan Indianapolis (especially towards north, in the urban areas, especially estimation of UHI intensity / northeast, northwest, south, and more recently towards magnitude based on multi-temporal and multi-resolution TIR southwest) to expand faster than others. Detecting its urban imagery remains a promising research direction given the expansion and the relationship to UHI development is increased interest among the urban climate and the significant to mitigate its effect, and also provides important environment science communities. insights into the city’s future urban planning and environmental Another important issue in urban thermal remote sensing is management. how to deepen the understanding of the relationship between the reception/loss of radiation and urban surface characteristics. 86 # 19'30" W 85 # 56'30"W There has been a tendency to use thematic land use and land cover (LULC) data for simple correlation between LST and 39 # 55'30" N I-65 I-465 LULC types [11]. The relationship between LST and I-465 # vegetation indices (e.g., NDVI) has been extensively Townships PIKE WASHINGTON LAWRENCE Rivers documented [12], and shows a negative correlation. Recent Major Roads studies have used impervious surface (IS) area [13]-[15], which

# is positively correlated with LST, and has the advantage of less I-465 I-70 seasonal variability. Most recent advances include the CENTER WARREN development of sub-pixel quantitative surface descriptors for WAYNE assessing the interplay between urban material fabric and I-70 thermal behavior [16], and employing the landscape ecology # I-465 approach to identify the operational scales across urban thermal DECATUR PERRY FRANKLIN landscapes [17]-[18]. However, few published works have

# related sub-pixel biophysical descriptors to the UHI I-65 N 39 # 38'00" N parameters, derived from the optical and TIR data of satellite W E images respectively. 9 0 9 18 Kilometers S This research develops a modeling approach to characterize Fig. 1. Study area - City of Indianapolis, Indiana, USA UHI phenomenon at various spatial scales, and to derive UHI intensity so as to relate it to remotely sensed biophysical The primary remote sensing data used in this research include parameters. Four ASTER images over the city of Indianapolis Advanced Spaceborne Thermal Emission and Reflection were used for the analysis. These images were acquired in Radiometer (ASTER) [19] and US Geological Survey’s Digital different seasons/years, so we can examine the applicability of Raster Graphic imagery. ASTER images were acquired on Oct. the modeling approach for multi-temporal satellite images. 3, 2000 (12:00:51 eastern standard time), June 16, 2001 Specific objectives of this research are three-fold: (1) to (11:55:29), April 5, 2004 (11:46:39), and Oct. 13, 2006 characterize the spatial patterns of UHIs and to estimate UHI (11:40:01). Although we were approved by JPL NASA to intensity by using LSTs; (2) to develop greenness and acquire four images annually for the study area, clouds and imperviousness indices based on convoluted spectrally other weather conditions have prevented us to get a quality unmixed green vegetation (GV) and IS fractions; and (3) to image every season. These selected images are the best investigate the relationship between the UHI intensity and the available ones, which we intend to use for examination of the indices of greenness and imperviousness. seasonal variability of urban landscape and the effect of urban growth on the UHI. The local times of satellite overpasses were II. DATA all between 11:40 AM and 12:01 PM. Satellite detection of The City of Indianapolis, located in Marion County, Indiana UHIs using TIR sensors has demonstrated that the UHI has been chosen as the area of study (Fig. 1). With over 0.8 intensity reaches the greatest in the daytime and in the warm million population, the city is the nation’s twelfth largest one. > TGRS-2010-00524.R2 < 3 season and least at the nighttime – the opposite to the UHI space, which are assumed to represent the purest pixels in the results based on the measurement of air temperatures [20]. image [28]. The LSMA approach requires that the number of ASTER data, including the level 1B registered radiance at endmembers derived should not exceed the number of the the sensor and the level 2 surface reflectance, kinetic image bands plus one. Theoretically speaking, ten endmembers temperature and emissivity data, were obtained. The theoretical may be developed with the nine VNIR and SWIR bands of an basis and computation algorithm for surface reflectance ASTER image. However, high correlation between certain products have been reported by Thome et al. [21]. The bands (especially between the six SWIR bands) limits the usage algorithm for converting ASTER thermal infrared of a large number of endmembers. We found that the NIR band measurements to LSTs has been reported by Gillespie et al. had very low correlation with any of the other ASTER bands, [22] and the ASTER Temperature / Emissivity Working Group indicating its independency in information. The correlation (TEWG) [23], with which surface kinetic temperature is coefficients between visible bands and between SWIR bands, determined by applying Planck’s Law using the emissivity especially between SWIR 5-9 bands, were frequently greater values from the Temperature-Emissivity Separation (TES) than 0.97. The principal component analysis result indicated algorithm. LST values calculated using this procedure are that the first four components accounted for 99.98% of the expected to have an absolute accuracy of 1-4 K and relative overall variance. This suggests that a maximum of five accuracy of 0.3 K, and surface emissivity values an absolute endmembers may be developed in this study. accuracy of 0.05-0.1, and relative accuracy of 0.005 [23]. Endmembers were initially identified from the ASTER Separated single bands of VNIR, SWIR, and TIR data were images in reference to high-resolution aerial photographs. Four first stacked into one set. An image-to-image registration was types of endmembers were selected: green vegetation, soils conducted. The ASTER images were georectified to Universal (including dry soil and dark soil), low albedo (asphalt, water, Transverse Mercator (UTM) projection with NAD27 Clarke etc.), and high albedo surfaces (concrete, sand, etc.). 1866 Zone 16, by using 1:24000 Digital Raster Graphic (DRG) Vegetation was selected from the areas of dense grass and maps as the reference data. Approximately 40-50 ground pasture. Different types of impervious surfaces were selected control points were chosen for each image. The images were from building roofs, airport runway, highway intersections, etc. re-sampled to the spatial resolution of 15 m with the Soils were selected from bare grounds in agricultural lands. nearest-neighbor resampling algorithm. The root mean square Next, these initial endmembers were compared with those error (RMSE) for the geocorrection was all less than 0.3 pixel. endmembers selected from the image scatter plots. The An improved image based dark object subtraction model has endmembers with similar spectra located at the extreme proved effective and was applied to reduce the atmospheric vertices of the scatter plots were finally selected. To find best effects [24]-[25]. quality of fraction images for estimation of impervious surfaces, different combinations of endmembers were examined and compared. Visualization of fraction images, III. METHODOLOGY analysis of fractional spectral properties of representative land cover types, and assessment of error images were conducted to A. Linear Spectral Mixture Analysis determine which combination provided the best fractions for Linear spectral mixture analysis (LSMA) is regarded as a each image. The criteria for selecting the most suitable fraction physically based image processing technique that supports images were based on: (1) high-quality fraction images for the repeatable and accurate extraction of quantitative sub-pixel urban landscape, (2) relatively low error, and (3) the distinction information [26]-[28]. It assumes that the spectrum measured among typical LULC types in the study area. A constrained by a sensor is a linear combination of the spectra of all least-squares solution was applied to unmix the nine VNIR and components within the pixel [27], [29]. Because of its SWIR bands of ASTER images into fraction images. Fig. 2 effectiveness in handling the spectral mixture problem, LSMA shows fraction image of green vegetation and impervious has been widely used in estimation of vegetation cover surface at the four dates. [30]-[32], in land cover classification and change detection [33]-[34], and in urban studies [35]-[36]. In this study, LSMA was employed to develop green vegetation, soil, and impervious surface fraction images. A constrained least-squares solution [26] was applied to unmix the nine VNIR and SWIR bands of ASTER imagery into fraction images, including high albedo, low albedo, vegetation, and soil fractions. With the LSMA approach, the selection of appropriate endmembers is a key for successful development of high-quality fraction images. In previous studies, many methods have been developed for endmember selection [37]. Image-based endmembers are well accepted, because image Fig. 2. Fraction images of green vegetation (first row) and impervious surface endmembers can be easily obtained from the image feature (second row) at the four imaging dates, derived from linear spectral mixture space. Moreover, no calibration is needed between selected analysis. Fraction value ranges from 0 to 1. Brighter tone is associated with endmembers and the spectra measured. Image endmembers are more abundance of green vegetation/impervious surface. frequently derived from the extremes of the image feature > TGRS-2010-00524.R2 < 4

B. Estimation of Impervious Surfaces dividing the area of impervious surface by the sampling area. Impervious surface was estimated based on the relationship The root-mean-square-error (RMSE) was then computed to between the reflectance of two endmembers (high- and low- indicate the accuracy of impervious surface estimation as albedo) and the reflectance of the impervious areas. By follows: examining the relationships between impervious surfaces and the four endmembers, Wu and Murray found that impervious N (Iˆ − I )2 surfaces were located on or near the line connecting the low ∑ i i RMSE = i=1 (2) albedo and high albedo endmembers in the feature space [35]. N An estimation procedure was thus developed based on this relationship by combining the fractions of high albedo and low ˆ albedo endmembers. The IS image can be computed as: Where I i is the estimated impervious surface fraction for

sample i; I i is the impervious surface proportion computed R = f R + f R + e (1) imp,b low low,b high high,b b from DOQQ; and N is the number of samples. The computational result indicates that these impervious surface maps yielded RMSE of 16.3% (October 3, 2000), 17% (June Where Rimp,b is the reflectance spectra of impervious surfaces 16, 2001), 20.2% (April 5, 2004), and 24.6% (October 13, for band b, f low and f high are the fractions of low albedo and 2006), respectively. high albedo, respectively, Rlow,b and Rhigh,b are the reflectance C. Kernel Convolution spectra of low albedo and high albedo for band b, and eb is the unmodeled residual. The fitness of this two-endmember linear A kernel convolution model implementing Gaussian spectral mixture model has been demonstrated by Wu and bi-variate function was employed to characterize LST, GV, and Murray for the central business district of Columbus, Ohio, IS data patterns. Higdon explained this process convolution for USA. We tested this model in the central part of the study area, a single dimensional process and made suggestions for its the central business district (CBD) of Indianapolis, and found extension to two or three dimensions [40]. The kernel an excellent fit with mean RMSE value of less than 0.02 for all convolution results in smoothened data surfaces showing the images. Following the Wu and Murray’s method [35], four IS spatial patterns of LST, GV, and IS across scales. We have images were computed. written a computer program for this task using the language R. Due to spectral confusion, non-impervious materials of both In order to understand how the kernel convolution works, we low reflectance (e.g., water and shades) and high reflectance first need to know the definitions of kernel and convolution, (e.g., sand and dry soils) may be contained in the low- and and then the process convolution, which was extended in this high-albedo image fractions. These non-impervious materials study to model LST, GV, and IS as a 2-dimensional Gaussian should be removed to improve the quality of impervious process. surface maps. Lu and Weng used LST to develop an image Kernel smoothing refers to a general class of techniques for mask to remove those materials, because there was a non-parametric estimation of functions. The kernel is a smooth temperature difference between impervious surfaces and positive function k(x, h) which peaks at zero and decreases non-impervious surfaces [38]. It is found that the method was monotonically as x increases in size. The smoothing parameter fairly effective to remove non-impervious pixels. In this h controls the width of the kernel function and hence the degree research, we extended this method by using LST and LULC of smoothing applied to the data [41]. One can define the kernel maps and their various combinations as image masks for as a function k that for all x, h ∈ X satisfies [42]: refining IS images. These image masks were built based on the relationship of individual LULC type with the abundance of k (x, h) = (φ (x) , φ (h)) (3) impervious surfaces and their significance in the maximum, minimum, and mean LSTs. In particular, the maximum and where φ is a mapping from X to an (inner product) feature space mean temperatures of non-impervious covers (such as water, F. agricultural land, and forestland) and the minimum temperature of impervious covers (such as urban/built-up land) were tested φ : x → φ (x) ∈ F (4) for their effectiveness as image masks [39]. The second row of Fig. 2 shows the resultant four impervious surface images. The degree of smoothing (i.e., the extent of standard deviation For the accuracy assessment of impervious surface images, a of the Gaussian distribution) to be performed by the kernel is a total of 400 samples were selected using a stratified random function defined by its bandwidth h. The value of h increases as sampling scheme. The size of each sample equaled to 6 by 6 the degree of smoothing increases and vice versa. pixels, which had the ground dimension of 90m by 90m. For The convolution of f and g could be written as f * g. It is each sample, the boundary of impervious surface polygons was defined as the integral of the product of the two functions after digitized on the corresponding DOQQ (Digital Ortho Quarter one is reversed and shifted. Quadrangles) using ArcGIS. The alignment of DOQQ with ASTER images was ensured to be very precise with registration (f * g) (t) = ∫ f (τ) g (t - τ) dt (5) error of smaller than 0.001 pixel. After the digitization, the proportion of impervious surface area was computed by > TGRS-2010-00524.R2 < 5

If X and Y are two independent variables with probability The smoothing kernel or the parameter, as described in the densities f and g, then the probability density of the sum X + Y is Equation (10), defines the degree of smoothing and is a crucial given by the convolution f * g. For discrete functions, one can parameter in the kernel convolution modeling. The degree of use a discrete version of the convolution. It is given below by smoothing is inversely proportional to the smoothing kernel. In Equation (6): other words, as the value of the smoothing kernel decreases, the degree of smoothing over the spatial domain increases. When ∑ (6) the degree of smoothing reached the maximum value of one, a kernel-convoluted image was formed; whose values were A Gaussian process over Rd is to take the independent and equivalent to the mean of the original image. When the degree identically distributed Gaussian random variables on a lattice in of smoothing was minimum (i.e., zero smoothing), the final Rd and convolve them with a kernel. The process involves kernel convoluted image would be the same as that of the successive increase in the density of the lattice by a factor of original image. two in each dimension and reduces the variance of the variates by a factor of 2d, leading to a continuous Gaussian white noise d process over R . A Gaussian white noise is a white noise with IV. RESULTS normal distribution. The convolution of this process can be d A. UHI Intensity across Spatial Scales equivalently defined by using some covariogram in R . The process of convolution gives very similar results to defining a By changing the smoothing parameter from 0.05 to 1.0, with process by the covariogram. an incremental rate of 0.05, the kernel convolution modeling Let y(1,1),…, y(i,j) (where y is a two dimensional matrix of resulted in 20 convoluted maps for each LST, GV, and IS (1,1),…,(i,j)) be data recorded over the two dimensional spatial image. Fig. 3 shows the convoluted LST maps with the T locations s(1,1),…,s(i,j) in S, a spatial process z = (z(1,1),…,z(i,j)) , smoothing parameter ranging from 0.05 to 0.9 in the four dates. T 2 We further computed the magnitude (intensity) of UHI by and Gaussian white noise ε = (ε(1,1),…, ε(i,j)) with variance σ ε. The spatial method represents the data as the sum of an overall subtracting the minimum temperature value from the maximum mean µ. temperature value of each convoluted image. Table 1 shows the UHI intensity value at each smoothing level. An examination of y = s + z + ε (7) data distribution pinpointed two breaks at the smoothing level of 0.2 and 0.5. When the smoothing parameter ranged from where the elements of z are the restriction of the spatial process 0.05 to 0.2, the UHI intensity mostly reached 6 K, peaking around 14 K. Fig. 3 shows that the thermal landscapes of all z(s) to the two dimensional data locations s(1,1),…,s(i,j). z(s) is defined to be a mean zero Gaussian process. Rather than dates exhibited scattered hot spots to as few as four. These specifying z(s) through its covariance function, it is determined types of landscapes would be suitable for studies at the by the latent process x(s) and the smoothing kernel k(s). The micro-scale level. The term “surface temperature patterns” is latent process x(s) is restricted to be non-zero at the two more meaningful here than surface UHI. The information on micro-scale LST patterns may be useful for zoning dimensional spatial sites ω ,…, ω , also in S and define x = (1,1) (a,b) considerations in the process of city planning and (x ,…,x )T where xω = x(ω )and p = (1,1),…,(a,b). Each x (1,1) (a,b) p p p environmental management at the relevant geographical scale. is then modeled as independent variable and draws from a 2 For the purpose of comparison, Table 1 also lists the N(0,σ ω) distribution. The resulting continuous Gaussian minimum-maximum temperature differences for the original process is then: LST images, which have values from 15.7 K to 18.3K. It has been suggested that the UHI magnitude computed by using , ∑, (8) single pixel comparison method was strongly influenced by localized extreme temperatures and tended to be several times where k(.-ωp) is a kernel centered at ωp. This gives a linear higher than the Gaussian magnitude [6]. When the smoothing model: parameter ranged from 0.25 to 0.5, the UHI intensity yielded a value from 3 K to 6 K, subject to the seasonality. Two to four y = µl(i,j) + Kx + ε (9) hot spots can be identified from each image, with the largest hot spot in the city center corresponding to its central business th where l(i,j) is the (i,j) vector of l’s. The elements of K are given district. These hot spots can be directly linked to the by: biophysical structure of the city and the structure of the urban atmosphere, and are thus suitable for studies at the meso-scale

Kpq = k(sp - ωq) xq (10) (i.e., the city scale). These types of studies would provide valuable information for city planning, especially for 2 transportation, large infrastructures, and clustered development x ~ N(0, σ xl(a,b)) (11) (e.g., leap-frog development). Fig. 3 shows that the hot spots and identified at this scale appeared to associate with major infrastructures and urban clusters in the city (e.g., major 2 transportation network, CBD, commercial/industrial cluster, ε ~ N(0, σ xl(i,j)) (12) etc.). By setting the smoothing parameter in the range of 0.55 to 1.0, the kernel convolution modeling yielded consistently > TGRS-2010-00524.R2 < 6 single-hot spot thermal landscape pattern. This kind of spatial effect of urban development on the UHI pattern, since the two pattern is essentially in agreement with the conventional images were acquired at nearly anniversary dates. At the definition of UHI, which reveals the difference between the micro-scale, we may not be able to visualize much difference in urban and the rural temperatures of a specific city. It should be the thermal pattern. However, at the meso- and macro-scale, the noted that the conventional definition of UHI being referred to difference was noticeable. The UHI was more spread-out along is the air temperature heat island, which has shown the greatest the west-east corridor in 2000, reflecting well the layout of intensity at night [43]. Most UHI intensity values computed in historical urban development in Indianapolis. LULC changes this study ranged from 1.5 to 3.5 K, despite of over-time and especially recent urban build-ups (commercial, industrial, changes in the UHI center position, spatial extent and shape. and residential developments along the highways) in the south The studies on such UHI pattern and its dynamics would of the city in Perry Township (see Fig. 1) had elongated the contribute to understanding of urban climate. More UHI from the CBD to this newly developed area. importantly, the modeling at this macro-scale would allow for concurrent comparison of UHIs across nearby cities in the Table I UHI intensity values at each smoothing parameter level region. The information provided by such studies would be Smoothing UHI intensity (K) beneficial for regional planning and watershed management of parameter a city-region (i.e., an urban cluster). 10-3-2000 6-16-2001 4-5-2004 10-13-2006 none 18.3 15.7 16.3 15.8 0.05 12.5 9.6 11.4 14.1 0.1 9.0 8.2 8.5 6.9 0.15 7.5 7.3 7.0 5.5 0.2 6.6 6.6 6.2 5.0 0.25 6.0 6.0 5.5 4.6 0.3 5.5 5.6 5.1 4.3 0.35 5.0 5.1 4.7 3.9 0.4 4.5 4.6 4.2 3.6 0.45 4.1 4.2 3.8 3.3 0.5 3.6 3.8 3.4 3.0 0.55 3.3 3.5 3.1 2.8 0.6 2.9 3.3 2.8 2.6 0.65 2.7 3.0 2.5 2.3 .07 2.4 2.8 2.3 2.1 0.75 2.2 2.6 2.1 2.0 Fig. 3. Urban heat island pattern in Indianapolis at different spatial scales, as 0.8 2.0 2.5 2.0 1.8 revealed by the kernel convolution modeling result with the smoothing 0.85 1.9 2.3 1.8 1.6 parameter ranging from 0.05 to 0.9. 0.9 1.7 2.2 1.7 1.5 By comparing the convoluted LST maps of different dates at 0.95 1.6 2.0 1.6 1.4 the same smoothing levels, it is possible to observe the changes 1.0 1.5 1.9 1.4 1.3 in the urban thermal landscape pattern over the time. The changes in the thermal pattern reflected largely the changes in “surface” factors, including the thermal properties of surface B. Relationship between UHI Intensity, Greenness and materials, the composition and layout of LULC types, and Imperviousness anthropogenic effects related to the existence of automobiles, The urban-rural temperature disparity is largely modulated by air conditioning units, industries, and air pollution. As these the differences in environmental conditions between the urban images were acquired in different seasons (spring summer, and and rural areas. In this study, we developed a greenness and an fall) spanning several years (2000 through 2006), the variation imperviousness index to set apart the urban and the rural in the surface factors embraced the effects of seasonal change biophysical environments. Because the kernel convolution and long-term change due to urban sprawl. The UHI intensity process removed the extreme values and generated more was greatest in the summer (June 16, 2001) as far as the macro- uniform images, we adapted the mean value of each convoluted and meso-scales were concerned. This observation is consistent image of GV and IS as the base value, indicating the mean rural with the findings in previous literature [20]. environmental conditions [44]-[45]. By subtracting the mean However, at the micro-scale, the UHI intensity was strongly value from the maximum value, an index of greenness or influenced by pixels with extreme LST values. At all imperviousness for each convoluted image was computed. In smoothing levels, the UHI intensity was lowest on October 13, each imaging date, there were 20 convoluted GV and IS images. 2006. The only exception was observed at the smoothing Therefore, 20 greenness and imperviousness indices were parameter 0.05, when the UHI intensity was detected to be the calculated. greatest on October 13, 2006. This anomaly can be explained Correlation analysis was performed between the 20 UHI by the co-existence of the extreme low LST (291K) and the intensity values and the 20 greenness values, so was between extreme high LST (305K) on that date. A comparison between the 20 UHI intensity values and the 20 imperviousness values. Fig. 3(C) and 3(D) offers some useful information about the Table 2 shows the result of correlation analysis between the > TGRS-2010-00524.R2 < 7

UHI intensity and greenness, as well as between the UHI which indicated the urban-rural contrast in the abundance of intensity and imperviousness index. The significance of each GV / IS. The correlations were stronger than previous LST correlation coefficient was determined by using a one-tail indicators such as GV abundance and IS coverage explored in Student’s t-test. The UHI intensity was found highly positively the remote sensing literature. correlated with both greenness and imperviousness, regardless Various methods and algorithms have been developed for of seasonality. That is, the more contrast in the biophysical characterizing surfaces in the spatial domain. For example, conditions between the urban and the rural in respect to GV and kriging and thin plate spline models have been used IS, the more intensive the UHI would tend to be. As IS is successfully for spatial estimation, while Cellular Automaton - usually inversely related to GV cover in urban areas, a higher based models are widely used for prediction/simulation of contrast in greenness tends to associate with the larger urban LULC change. These algorithms characterize spatial difference of imperviousness. Correlation analysis was further surfaces from a global or whole map view without considering conducted between the UHI intensity values and the mean GV / the variations across the space. This failure to adapt to local IS values. Table 2 further shows that the UHI intensity was variability, or heterogeneity, in the unknown process is of negatively correlated to the mean GV value, implying that the particular importance in environmental, geophysical, and other greater abundance of GV contributed to reduce the UHI effect. spatial datasets, in which domain knowledge suggests that in This finding is in good agreement with previous studies [12]. most cases the phenomenon may be non-stationary [46]. In Furthermore, mean LST values were found to have highly remote sensing studies of UHIs, even though a single positive correlation with mean IS values, which is consistent parametric model could be defined for the analysis of a single with some recent researches [13]-[15]. However, by comparing image, it would be difficult to apply the same model to the mean IS value and the imperviousness index that we multi-temporal and multi-sensor images in order to perform a developed in this study, it is found that imperviousness was comparative analysis and thus to conduct spatio-temporal more closely correlated to the UHI intensity. Similarly, we dynamic modeling and analysis. Because the UHI effect is observed that the greenness index had a stronger correlation closely related to the composition and layout of LULC, urban with the UHI intensity than the mean GV value. growth frequently generates an important impact on the dynamics of UHI over the space and time [45], [47], [48]. The Table II. fact that urban growth is a non-stationary process over the Correlation between the UHI intensity, greenness, and imperviousness space and that factors underlying LULC change may vary from (significant at 0.05 level) place to place [49] implies that the same set of underlying Date of Image Oct 3, June April 5, Oct 13, factors may yield various effects in different cities / regions and 2000 13, 2004 2006 2001 at different geographical scales, leading to different patterns and processes of urbanization and UHI. A method / algorithm UHI intensity vs. 0.9924 0.9944 0.9573 0.9868 that can account for the spatial non-stationarity, such as the Greenness process kernel convolution model used in this study, is proper UHI intensity vs. 0.9932 0.9981 0.9822 0.8833 for UHI characterization and modeling. Imperviousness In this study, we utilized the smoothing kernel to UHI intensity vs. -0.9849 -0.9135 -0.9846 -0.9069 characterize the spatial non-stationarity in the urban thermal Mean GV values landscape and to link the UHIs with the biophysical parameters. This characterization and the linkage allow us to examine UHI Mean LST vs. 0.9744 0.9849 0.9888 0.9685 Mean IS values as a scale-dependent process. Oke suggested that there were often several linked UHIs in one city, and that each

distinguished from one another mainly by scales imposed by the biophysical structure of a given city and the structure of the V. DISCUSSION AND CONCLUSIONS urban atmosphere [50]. Each UHI is therefore required A key issue in thermal remote sensing of urban areas is how measurement arrays appropriate to the scale [50]. Most to use pixel-based LST measurements to characterize and previous literature failed to account for the existence of quantify UHIs observed at various spatial scales. This study has multiple UHIs in a city [6], [10]. By changing the smoothing employed a kernel convolution modeling method to parameter, this study was able to characterize multiple UHIs of characterize the UHI in Indianapolis as a two-dimensional various sizes (spatial extent) in Indianapolis. Further, we Gaussian process. The modeling results allowed us to analyze categorized the smoothing parameters into three groups. Each several key UHI parameters, including the intensity, center, group was found suitable to study the urban thermal landscape spatial extent, and orientation, but this study focused on the at a particular spatial scale, i.e., the micro-scale, meso-scale, UHI intensity only. Moreover, we extended our previous and regional scale, such that the identified scales can be efforts for employing LSMA to extract sub-pixel urban matched to various applications in urban planning and biophysical variables (i.e., GV and IS) [16], [39], but focused environmental management. Further studies are necessary to on the improvement of extraction quality and the comparability reconcile studies of the UHI scale (e.g., this study) and the of these variables from multi-temporal ASTER images. Finally, operational scale of LST ([12], [18], [51], [52]) in order to we developed two new indices (greenness and imperviousness) better understand urban thermal landscapes and dynamics from based on the convoluted images of GV and IS fractions. It is the remote sensing perspective. found that the UHI intensity had an extremely strong positive correlation with both greenness and imperviousness indices, > TGRS-2010-00524.R2 < 8

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Qihao Weng (M’07) was born in Fuzhou, China. He received the A.S. degree in geography from Minjiang University, China, in 1984, the M.S. degree in physical geography from South China Normal University in 1990, the M.A. degree in geography from the University of Arizona, Tucson, in 1996, and the Ph.D. degree in geography from the University of Georgia, Athens, in 1999. He is currently a professor of geography and director of the Center for Urban and Environmental Change, Indiana State University, Terre Haute. During 2008-2009, he visited NASA Marshall Space Flight Center as a senior research fellow. He is the author of more than 120 peer-reviewed journal articles and other publications. In addition, he has published four books, i.e., Urban Remote Sensing (CRC, 2006), Remote Sensing of Impervious Surfaces (CRC, 2007), Remote Sensing and GIS Integration: Theories, Methods, and Applications (McGraw-Hill, 2009), and Advances in Environmental Remote Sensing: Sensors, Algorithms and Applications (CRC, 2011). He serves as an Associate Editor of ISPRS Journal of Photogrammetry and Remote Sensing, and is the series editor for both Taylor & Francis Series in Remote Sensing Applications, and McGraw-Hill Series in GIS&T. His research focuses on remote sensing and GIS analysis of urban ecological and environmental systems, land-use and land-cover change, urbanization impacts, and human-environment interactions. Dr. Weng is a member of ASPRS, AGU, and AAG. He served as a national Director of the American Society for Photogrammetry and Remote Sensing (2007-2010). He has been the first-place recipient of the Erdas Award for Best Scientific paper in Remote Sensing (2010) and the recipient of the Robert E. Altenhofen Memorial Scholarship Award from the American Society for Photogrammetry and Remote Sensing (1999) and the Best Student-Authored Paper Award from the International Geographic Information Foundation (1998). In 2006, he received the Theodore Dreiser Distinguished Research Award from Indiana State University, the university’s highest research honor bestowed to faculty. In 2008, he was awarded a senior fellowship from NASA.

Umamaheshwaran Rajasekar received his degree in Civil Engineering and Construction Management from Center for Environmental Planning & Technology (CEPT University), Gujarat, India (2002) and MSc degree in Geoinformatics from International Institute for Geo-Information Science and Earth Observation (ITC), Enschede, The Netherlands (2005). He then worked as a GIS engineer for RMS India in the spatial modeling team (2005-06). He is currently pursuing a Ph.D. degree at Indiana State University, USA. His main research interests are in the field of spatial data mining, event modeling/ analysis, geo-databases and soft computing.