by the end of【Two-,and,Three-Dimensional,Urban,Core,Determinants,of,the,Urban,Heat,Island:,A,Statistical,Approach】

　　Abstract: There is no doubt that the UHI (urban heat island) is a mounting problem in built-up environments, due to the energy retention by surface dense building materials, leading to increased temperatures, air pollution, and energy consumption. Much of the earlier research on the UHI has used two-dimensional (2-D) information, such as land uses and the distribution of vegetation. In the case of homogeneous land uses, it is possible to predict surface temperatures with reasonable accuracy with 2-D information. However, three-dimensional (3-D) information is necessary to analyze more complex sites, including dense building clusters. In this research, 3-D building geometry information is combined with 2-D urban surface information to examine the relationship between urban characteristics and temperature. The research includes the following stages: (1) estimating urban temperature; (2) developing a 3-D city model; (3) generating geometric parameters; and (4) conducting statistical analyses using both linear and non-linear regression models. The implications of the results are discussed, providing guidelines for policies aiming to reduce the UHI.
　　Key words: Urban heat island, urban morphology, three-dimensional city model, geographic information system.
　　1. Introduction
　　While melting glaciers, sea level rise, and the flooding of coastal cities are often viewed as the most dramatic effects of global warming, increasing urban temperatures is also a mounting problem. Construction materials, such as concrete and asphalt, absorb thermal energy during daytime and release it during nighttime, leading to temperature in urban core areas higher than in surrounding suburban and rural areas. This phenomenon is called the UHI (urban heat island).
　　The UHI directly impacts urban population, by inducing heat stress and health problem and worsening air quality through the formation of tropospheric ozone. Increased temperatures lead to increased energy and electricity consumption for air conditioning. In addition, increasing water temperatures can result in ecosystem destruction.
　　The purpose of this research is to improve our understanding of how urban characteristics influence surface temperatures, using both GIS (geographical information systems) and statistical techniques, and making use of data for the urban core of the city of Columbus, Ohio. To model this relationship, both 2-D and 3-D information is used to represent the complex urban geometric structure of urban centers. Much of the earlier UHI research has used 2-D information, such as land uses delineated with satellite imagery and building ground floor boundaries produced by GIS. In the case of homogeneous land uses, this information may be sufficient to predict surface temperatures with good accuracy [1, 2]. However, 3-D information is necessary to analyze more complex sites, including dense building clusters [3, 4]. This research employs LiDAR data and techniques to generate 3-D urban geometry characteristics.
　　The remainder of the paper is organized as follows. Section 2 consists of a literature review. Section 3 presents the modeling methodology. Section 4 describes the case study area and the data used. Model estimation results are discussed in Section 5. Section 6 concludes and outlines areas for further research.
　　2. Literature Review
　　The UHI is an important environmental issue related to differentials in surface temperature created by urban development. Many cities and some of their suburbs have higher temperatures than their surroundings [5]. In general, urban impervious surfaces absorb solar heat and hold it in the absence of cold air advection, resulting from complex surface characteristics, such as high-rise buildings and their low albedo [5, 6]. This increased thermal capacity induces a difference in the micrclimates of urban and rural areas. Oke [7] has been among the first to describe the UHI. The UHI is relatively lower during summer daytime because of humidity, but it becomes higher during summer nighttime and during all days in winter [8]. Wind speed is reduced by buildings that face each other closely. Weak airflows are one of the factors influencing surface temperatures. With regard to surface characteristics, the albedo (reflectivity) is directly related to the UHI. A high albedo releases thermal energy from the surface, but a lower albedo absorbs this energy into the surface [9]. Thermal storage by surface materials is also an important factor in investigating urban energy balances. Most materials used for buildings and impervious surfaces easily store thermal energy. In contrast, a vegetative cover has much lower absorption of thermal energy, due to evapotranspiration and high albedo. Several studies have examined the implementation of statistical models aiming to understand and mitigate the UHI. These models are characterized by two categories of factors: surface characteristics and 3-D building infrastructure.
　　First, with regard to surface characteristics, land use/cover is the primary feature used in exploring the UHI. Weng [10], Chen et al. [11] and Amiri et al. [12] generate maps displaying land use/cover patterns with images captured by Landsat TM (thematic mapper) or ETM+ to analyze surface temperature characteristics of urban environments. They find that urban expansion reduces the amount of biomass, which tends to raise temperature. They use simple comparisons of land-cover changes over time. Wilson et al. [13] analyze the UHI by using the NDVI calculated from Landsat 7 ETM+ and GIS land-use data. Their simple linear regression models show that lands covered by impervious materials generate higher surface temperatures. They also explore the relationship between surface temperature, NDVI, and development density. Lower NDVI and higher development density increase surface temperature. Solecki et al. [14] concentrate on the NDVI to understand the characteristics of surface temperatures. Most studies focusing on vegetative coverage have been performed using the NDVI, which has a negative impact on surface temperature. Jenerette et al. [15] apply demographic and topographic information (i.e. population density, median income, Hispanic population, year built, elevation, and slope) to find indirect effects by using path analysis. An increase in median income tends to decrease surface temperature. However, the other variables increase surface temperature.
　　Second, 3-D geometric characteristics are directly related to building infrastructure [16]. In particular, solar radiation and canyon effects are determined by 3-D geometry. Built-up environments have relatively lower solar radiation because of the blocking of sunlight by dense buildings, whereas more sunlight reaches ground surfaces in rural areas. Despite this difference, surface temperatures in built-up environments are higher than in rural areas, because high-rise buildings trap heat within a limited ground space [5]. The SVF (sky view factor) and the H/W ratio measure of these geometric effects [17-24]. The SVF measures the amount of sky visible from a ground-level location, as projected onto a 2-D space. This projection involves two stages: (1) projection of a point from the 3-D space to a sphere, and (2) projection
　　 from the sphere to a plane. The SVF represents the ratio of visible sky to surrounding structures within a reference circle. The SVF varies between 0 and 1. If an observer cannot see the sky due to buildings and trees obstructions, SVF = 0; if the visible sky fills the whole reference circle, SVF = 1. Previous research shows that nocturnal urban temperatures are negatively correlated with the SVF [12, 25, 26]. Bottyán and Unger [17] and Unger [4] show that surface temperatures are negatively affected by the SVF.
　　The H/W (height-to-width) ratio is another representative index of street geometry [27-29]. It impacts surface temperature by isolating air flows. For example, a deep urban canyon (H/W ≈ 10) has high nocturnal temperatures at ground level, as compared to a shallow canyon. A deep urban canyon may create a comfort zone due to shading during daytime, but it does not maintain this comfort at night because of heat accumulation without airflows. The ventilation pattern determined by the H/W ratio has an impact on surface temperatures. High surface temperatures on impervious surfaces cannot be easily decreased without a low H/W ratio that induces dynamic air circulation. Enough space between buildings plays a role in creating a cooling effect. Offerle et al. [30] explore the H/W ratio for each land use, considering its mean value for CBD (central business districts), industrial, residential and rural areas. As expected, the CBD and rural areas have the highest and lowest ratios, respectively.
　　Another index of geometric characteristics is the porosity, which quantifies the 3-D open space in built-up environments [19, 31-33]. This parameter, based on building volumes, has been used to investigate dispersion of air pollution and the UHI, by linking ventilation patterns to urban roughness. Despite its applicability, it has not yet been used in statistical analyses of the UHI.
　　Other parameters have been recently explored to describe urban geometric characteristics. Compactness(C), weighted volumetric compactness (Cw), and volumetrically averaged building height, used in conjunction with building volumes and surface parameters, are relatively new surface parameters representing surface roughness. Unger [4] proposes a weighted volumetric compactness index (Cw) that expands the compactness index, and obtains R2 = 0.30 and R2 = 0.52 when regressing surface temperature to C and Cw, respectively.
　　In contrast to previous studies, this research also accounts for anthropogenic heat. Only a few studies have focused on the amount of energy consumed by buildings. Ichinose et al. [34] study seasonal and temporal changes in temperature and energy consumption, using graphical analyses.
　　Anthropogenic heat has the effect of increasing surface temperatures, but its impact is stronger in winter than in summer because of the need for space-heating. Hinkel et al. [35] investigate the relationship between the UHI intensity and natural gas use, using monthly-averaged temperatures for urban and rural areas, and find that the winter season (i.e. December, January, and February) has higher temperature differences between urban and rural areas because of increased gas consumption.
　　3. Modeling Methodology
　　A model is proposed for UHI analysis that involves the overlaying of a grid over an urban core area, with several layers of data generated from different sources(geometry, energy consumption, surface temperature, vegetation).
　　3.1 Three-Dimensional City Model
　　A 3-D city model is fundamental to represent the geometry of built-up environments. With 3-D information, the topological and geometric characteristics of urban form can be measured quantitatively and used to analyze the UHI. This research makes use of three geospatial databases: (1) LiDAR data to estimate each building height, (2) GIS building footprints to describe their ground-level
　　 boundaries and (3) a DTM (digital terrain model) to estimate terrain elevation from sea level.
　　Filtering LiDAR data is the first step to remove unnecessary data and to reduce the size of the LiDAR database. Second, dissolving GIS building footprints removes internal building boundaries and creates a unique footprint containing all parts of a given building, based on its name.
　　There are three steps in filtering LiDAR data. First, these data are filtered by type of LiDAR pulse. A LiDAR pulse may strike different objects on its way to the ground, and a portion of the pulse may return to the sensor. Because of this phenomenon, LiDAR pulses are classified as first-return pulses and multiple-return pulses. A first-return pulse would detect a concrete surface, while a multiple-return pulse would detect materials composed of several layers, such as a canopy. Multiple-return pulses are discarded, so that LiDAR data only measure man-made objects. Second, the intensity of a LiDAR pulse measures the degree of material rigidity (e.g., building roofs). This intensity is relative, varying with altitude, atmospheric conditions, directional reflectance properties, and the reflectivity of the target. In particular, the intensity of LiDAR data requires numerous trials because intensity values are relative. In this research, observations with intensity below 50 are eliminated. Most data having intensity less than 50 represent the top of a tree canopy. In contrast, building roofs generate a high intensity due to their hardened materials. Third, LiDAR data ground filtering is a critical step for distinguishing buildings from non-building objects. LiDAR data are classified into two types: ground and non-ground. Extracting non-ground LiDAR data provides the elevation of buildings as input to the DSM (digital surface model).
　　The procedure for data fusion starts with adding the filtered LiDAR data onto the digitized building footprints. The spatial joining capability of ArcGIS is used to perform this data fusion. The highest point among the LiDAR points within each dissolving building footprint is taken as the height of that building roof. A building height estimated with only LiDAR points is larger than the actual height, because this height includes also ground-level height. Excluding the influence of topography leads to the actual building height by normalizing the DSM (nDSM):
　　nDSM = DSM – DTM (1)
　　The nDSM filtering process must be performed to test for discrepancy between the height of the actual buildings and the height of the building constructed in the 3-D model. The resolution of DTM and the density of LiDAR points may cause problem. For example, the spatial resolution of DTM is 3 m × 3 m. The DTM cannot provide ground floor elevation for buildings that are smaller than this resolution. For accuracy assessment, two types of information are needed: DTM and LiDAR points. However, rasterized DTM must be converted to a regular point-based DTM, because a critical function in ArcGIS, its spatial joining capability, cannot be applied to raster-based DTM. Based on the density of LiDAR points and the regular point-based DTM, this research has evaluated the accuracy of the fusion process in three cases leading to erroneous building shapes.
　　Case 1: DSM = 0. There are several DTM points in a building footprint, but no LiDAR points for the DSM. As the DSM is set to zero, the nDSM takes a negative value. This discrepancy may be due to (a) the building footprint having been created at a time after using the LiDAR system, or (b) the building footprint being smaller than the resolution of the LiDAR system.
　　Case 2: DTM = 0. There are no DTM points on a building footprint although it includes several LiDAR points for DSM. Thus, the nDSM value is greater than the actual building height.
　　Case 3: DSM = DTM = 0. As there are no LiDAR and DTM points on the building footprint, the nDSM value is set equal to zero. This discrepancy may be due to (a) the building footprint being smaller than the resolution of the LiDAR system and (b) the density of DTM points.
　　A simple numerical assessment is implemented by
　　(2) where, x1 = number of building footprints in case 1(DSM = 0), x2 = number of building footprints in case 2(DTM = 0), x3 = number of building footprints in case 3(DSM = DTM = 0), and x4 = total number of building footprints. In the empirical application of this research, the values of these variables are: x1 = 993, x2 = 269, x3 = 180, and x4 = 37,133. Thus, the building detection accuracy is y = 96.12%. In other words, there is a 96.12% match between building footprints and buildings reconstructed with LiDAR data, which supports the method for constructing a 3-D model. In addition, it is assumed that buildings having an average height of less than 7 ft. are not surface objects impacting people and their environment. 915 building footprints were lower than 7 ft. After removing them, the total number of available building footprints in the case study area is 34,776. Therefore, 93.65% of building structures are reconstructed with spatial information.
　　3.2 Urban Geometrical Characteristics
　　Several geometry-based characteristics of high-density urban cores have been suggested as important determinants of the UHI. They are discussed below.
　　3.2.1 The H/W (Height-to-Width) Ratio
　　The H/W ratio is calculated as the ratio of a building height to the width of the street abutting the building. The problem is to identify streets between buildings, which is not easy because of lack of street information and irregular street patterns. In addition, there can be space between buildings without streets. This means that GIS street information cannot provide all the necessary information, leading to possibly imperfect results. In this research, it is proposed to focus on primary moving patterns in the four main directions(east, west, south, and north) to solve H/W ratio estimation problems [36]. This is illustrated in Fig. 1 by starting to calculate the H/W ratio from west (left) to east (right). The ratio of building’s height to the distance between buildings is first calculated. Then, the H/W ratio between buildings is similarly calculated. Conversely, the H/W ratios can be calculated when moving east (right) to west (left). Similar calculation can be done in the north (upper) to south (bottom) and south (bottom) to north (upper) directions.
　　3.2.2 SVF (Sky View Factor)
　　The spatial openness of a built environment is an important factor that decreases urban temperatures, by enhancing air circulation and wind flow. This openness is related to the effects generated by buildings. The SVF has been applied to explore spatial openness. A higher SVF produces not only more air circulation, but also less shadows during daytime, and it facilitates the release of thermal energy during nighttime. In contrast, a lower SVF obstructs cooling effects because of surrounding building structures, and generates more shadows during daytime.
　　The SVF measures the ratio of visible sky within a reference circle area on the 2-D space. It can range from 0 to 1. A higher SVF represents more open space, whereas a lower SVF is generated by densely-built environments. This research uses the Sky View Factor Extension of Arc View GIS to estimate SVF at each observation location. Building footprints and heights are required to estimate SVF. The total number of observed location is 11,067 and their separation 200
　　1 (8)
　　where, VT = volume of the area, defined as the product of the area surface by the height of its tallest building. 3.3 Anthropogenic Heat
　　Energy used for building operations may further exacerbate the UHI. Earlier research has concentrated on vehicle energy flows in analyzing the UHI. However, energy use in buildings may be a more serious problem because of emissions of air pollutants and carbon dioxide.
　　The U.S. EIA (Energy Information Administration) provides statistical data on building energy consumption. Total building floorspace is used to estimate the amount of fuel used: primary electricity, site electricity, natural gas, and fuel oil. The EIA also provides average RECS (residential energy consumption data). For commercial buildings(CBECS), it only publicly provides total energy consumptions for building floor space ranges. This research computes, for each range, the energy consumption per ft2, and then applies these ratios to the actual buildings. However, it is difficult to estimate the floorspace of actual buildings, because Franklin County does not publicly provide total floorspace and number of stories for buildings. It is therefore necessary to estimate total building floorspace in order to estimate energy consumption.
　　3.5 Surface Temperature
　　The thermal infrared band of Landsat TM has a spatial resolution1 of 120 m, and can provide urban temperature estimates. Moreover, its DN (digital number) value2 varies from 0 to 255 for recording the spectral reflectance from the earth surface. This digital number must be numerically converted to a radiometric scale to estimate urban temperatures. The numerical conversion method is provided by the USGS (U.S. Geological Survey) and has been broadly used to map temperatures. This method has been updated by the EDC (Earth Resource Observation System Data Center). Eq. (11) and Eq. (12) are used to perform this conversion.
　　Eq. (11) is the primary formula to estimate temperature, and includes two calibration constants (K1 and K2) and the spectral radiance at the sensor’s aperture (Lλ). The two constants have been defined by Landsat TM sensors. Lλ is a rescaling factor to predict
　　4. Study Area and Data
　　4.1 Study Area
　　This research focuses on a densely-built part of the City of Columbus, Ohio (Fig. 3), with an area of 17.9 square miles (46.5 km2), and including the CBD(Central Business District), the city’s economic development hub. The Scioto River and the Olentangy River flow from north to south, and merge into one channel near the CBD. There are parks and recreation places for outdoor activities in the southern part of the research area. The site also includes residential areas. Its temperature has increased by at least 5?°C since 1986.
　　In 2000, the population of the city was 711,470. A continuing population growth since 1950 has induced
　　5. Model Estimation and Results
　　5.1 Research Approach
　　Four regression analysis models are considered
　　 5.2 Multi-Scale Grid Indices
　　Multi-scale grids are used to estimate statistical models of the UHI. The use of grids reflects the geographical variations of urban temperatures and other parameters. The temperature grid data set is created by averaging temperatures over each grid unit. All other parameters are averaged out or computed over each grid unit. The size of a grid unit depends on the spatial resolution of the thermal band of Landsat TM. It should be bigger than, or equal to the resolution(120 m). Four different scales are considered: 480 m, 360 m, 240 m and 120 m.
　　5.3 Simple Regression Models
　　Simple linear and non-linear regression models are first estimated to investigate the relationships between dependent and independent variables across the scales. The dependent variable is the surface temperature captured by Landsat TM, and the independent variables are related to building geometry, street canyon, anthropogenic heat, and land cover. The linear model is expressed as:
　　T = a0 + a1X (14)
　　where, X is any of the possible independent variables.
　　The non-linear model is:
　　T = a0 + a1Xb (15)
　　where, b is the estimated exponent of X, using the Boxtid-Well transformation.
　　The results are presented in Table 3. Most of the independent variables are statistically significant at the 0.05 level. The non-linear estimates are significant at the 0.01 level. However, compactness is not statistically significant with the 240 m and 120 m grids. The results are sensitive to grid size. Smaller grids generally yield smaller R2. As expected, porosity and SVF have negative impacts on surface temperature. Increases in porosity and SVF induce more open space, which enhances active air and wind circulation. This phenomenon plays a role in decreasing surface temperature. In contrast, the HW
　　 ratio has a positive impact on surface temperature. Narrow spaces between high buildings obstruct wind flows around them, and therefore an increase in the HW ratio tends to increase the intensity of the UHI. Building size is highly positively correlated with surface temperature in the linear model. Weighted compactness better explains the UHI than compactness in the linear models. In addition, increasing energy consumption leads to increasing surface temperatures, although this effect is weak.
　　However, unexpected signs are obtained with non-linear regression models across all grid sizes in the case of building height. In addition, several independent variables (i.e. building volume, compactness, and volumetrically averaged building height) have also unexpected effects. In general, the R2 of porosity, HW ratio, and SVF are relatively higher than for other variables, which suggests that open space in built environments may be a critical factor for UHI mitigation. Higher energy consumption increases surface temperature in the linear models. The impact depends on the size of the grid. The smaller the grid size the lower the R2 for the energy consumption models.
　　5.4 Multiple Regression Models
　　Multiple regression models are used to explain the relationship between surface temperature and several variables. Correlation matrices are generated and analyzed to reduce multi-collinearity problems. Variables having low correlations (less than 0.7) with others are selected to estimate the models[41].
　　In order to efficiently estimate comprehensive models, the independent variables are grouped into five categories: 3D building geometry, 3D building density, 3D spatial openness, 2D surface characteristics, and energy consumption. Variables having a small number of shaded correlation coefficients are selected to develop multiple regression models.
　　Tables 4-7 present the estimation results for the multiple regression models over the four grids. Most of the independent variables are statistically significant at the 0.1 level. For 3-D building geometry, compactness is predominantly used to estimate the models. Simple regression models indicate that weighted compactness yields higher R2 than compactness, as Unger [4] found. However, compactness was more useful in multiple regression models. With the 240 m grid, building height is representative of 3-D building geometry. For 3-D spatial openness, total SVF is negatively associated with surface temperature, while the total HW ratio is positively related to it. As expected, more spatial openness is a way to mitigate the UHI. The coefficients of total electricity have negative signs. Porosity and NDVI strongly affect the UHI.
　　The non-linear models using the Boxtid-Well transformation have higher R2 than the linear models.
　　 An elasticity analysis has been also carried out to better understand the impacts of the independent variables. The elasticity ε is defined as the ratio of the percentage change in the dependent variable to a 1-percent change in the independent variable (Table 8).
　　In all cases, porosity strongly affects surface temperature, which decreases by 1.8%, 3.4%, 2.2%, and 1.3% for a 10-percent increase in porosity. Urban plans that consider extending open spaces and restricting the building-to-land ratio can mitigate the UHI by increasing porosity, although it is difficult to increase open spaces in highly developed urban
　　6. Conclusions
　　This research has presented statistical models explaining UHI effects by using not only 2-D surface characteristics, but also 3-D urban geometric characteristics derived with LiDAR data and GIS building footprints. Both linear and non-linear regression models have been used to investigate the relationships between surface temperature and the explanatory variables. In particular, the Boxtid-Well transformation was applied to develop non-linear models.
　　In the case of the simple regression models, most coefficients reflect the expected influence on surface temperature. First, the variables related to 3-D building geometry tend to increase temperature. The R2 varies between 0.06 and 0.44. Among 3-D building geometry variables, a building ground floor and its surface have strong impacts on temperature. Second, energy consumption also has a positive effect on the UHI, but this effect is small. Third, higher SVF, porosity, and NDVI play a role in decreasing surface temperature.
　　In the case of the multiple regression models, the focus has been on non-linear estimation. A representative variable is drawn from five categories of surface characteristics, using correlations to reduce collinearity problems. The multiple regression models explain about 50% of the variability in temperatures. Porosity and NDVI are the most important features to mitigate the UHI. The results provide guidelines for environmental policy. Developing green open spaces and constructing building roof gardens and vertical
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