Theor. Appl. Climatol. 75, 233–243 (2003) DOI 10.1007/s00704-003-0735-7

Department of Climatology and Landscape Ecology, University of Szeged, Szeged, Hungary

A multiple linear statistical model for estimating the mean maximum urban heat island Z. Bottya´n and J. Unger With 9 Figures Received September 26, 2002; revised February 25, 2003; accepted March 22, 2003 Published online July 30, 2003 # Springer-Verlag 2003

Summary

1. Introduction

This study examines the spatial and quantitative influence of urban factors on the surface air temperature field of the medium-sized of Szeged, Hungary, using mobile measurements under different weather conditions in the periods of March 1999–February 2000 and April–October 2002. Efforts have been concentrated on the development of the urban heat island (UHI) in its peak development during the diurnal cycle. Tasks included: (1) determination of spatial distribution of mean maximum UHI intensity and some urban surface parameters (built-up and water surface ratios, sky view factor, building height) using the standard Kriging procedure, as well as (2) development of a statistical model in the so-called heating and non-heating seasons using the above mentioned parameters and their areal extensions. In both seasons the spatial distribution of the mean maximum UHI intensity fields had a concentric shape with some local irregularities. The intensity reaches more than 2.1 C (heating season) and 3.1 C (non-heating season) in the centre of the city. For both seasons statistical model equations were determined by means of stepwise multiple linear regression analysis. As the measured and calculated mean maximum UHI intensity patterns show, there is a clear connection between the spatial distribution of the urban thermal excess and the examined land-use parameters, so these parameters play an important role in the evolution of the strong UHI intensity field. From the above mentioned parameters the sky-view factor and the building height were the most determining factors which are in line with the urban surface energy balance. Therefore in the future, using our model it will be possible to predict mean maximum UHI intensity in other cities, which have landuse features similar to Szeged.

The mainly artifical surface of the city, anthropogenic heat emission and air pollution modify the urban atmosphere. The modification effect of urbanization on local climate is most obvious in the case of temperature, which is the socalled urban heat island (UHI) phenomenon or urban heat archipelago if the structure is multicellar. Its intensity has a distinguished diurnal cycle with a strongest development in the first part of the night, in general 3–5 hours after the sunset. The simulation of real factors and physical processes generating this temperature-increasing effect is extremely difficult as it includes the surface geometry and materials as well as artificial production of heat and air pollution. Statistical modeling may provide useful quantitative information about the structure as well as the spatial and temporal features of the maximum UHI intensity by employing different urban surface parameters (e.g. Outcalt, 1972; Oke, 1981, 1988; Park, 1986, 1987; Kuttler et al., 1996; Matzarakis et al., 1998). In our case these parameters are: built-up ratio, water surface ratio, sky view factor and building height. The selection of these parameters is based on their role in smallscale climatevariations (Oke, 1987; Golany, 1996).

234

Z. Bottya´n and J. Unger

This paper reports on effects of the urban surface factors on the patterns of quantitative differences between the urban-rural temperature in the heating and non-heating half years. 2. Study area, parameters and methods 2.1 Study area The study city, Szeged, is in the south-eastern part of Hungary on a wide flat flood plain (Fig. 1). This environmental situation makes Szeged a good case for the study of the urban climate. Its regional climate is temperate warm characterized by a rather uniform annual distribution of precipitation. Within an administration district of 281 km2 live 160,000 inhabitants. The base of the city structure is a boulevardavenue system and several land-use types are present. Two seasonal half years can be clearly

distinguished from the point of view of city dwellers: the heating (from October until April) and the non-heating (from April until October) seasons. Urbanized areas occupy about 25–30 km2, therefore our examination concentrated on the central parts of the large administration district (Fig. 1). Other parts of the city, having village and rural characteristics, are not included. This area was divided into two sectors and subdivided further into 500 m 500 m squares, so it contains 107 cells (26.75 km2) altogether. The grid network itself was established by quartering the 1 km 1 km square network of the Unified National Mapping System (in Hungarian: EOTR) developed for the topographical maps on Hungary (Unger et al., 2000; Unger et al., 2001a, 2001b). At present, investigation of the six southern and the four western cells of the original study area are omitted because of the lack in the data set of

Fig. 1. Location of Szeged in Hungary and main land-use types of the city (a: border of the study area, b: agricultural and open land, c: industrial area, d: 1–2 storey detached houses, e: 5–11 storey apartment buildings, f: historical city core with 3–5 storey buildings, g: circle dike)

A multiple linear statistical model for estimating the mean maximum UHI

one parameter (building height, see Chapter 2.5.), so the present study uses lower cells, altogether 97 cells covering an area of 24.25 km2 (see e.g. Fig. 3). 2.2 Temperature (maximum UHI intensity) The spatial distribution of the surface air temperature is based on mobile observations during the period of March 1999 to February 2000. The UHI intensity (namely T, the temperature difference between urban and rural areas) was measured at every cell, on fixed return routes once a week. Altogether 48 traverses were taken, 24 in the northern, and another 24 in the southern sector. This frequency of car traverses provided sufficient information on different weather conditions, except for rain. The study area was divided into two sectors because of the large number of cells. Return routes, 75 km and 68 km long in the northern and southern sectors, respectively, were needed to make time-based corrections and the measurements took about 3 hours. The reference time, namely the likely time of the occurrence of the strongest UHI, was 4 hours after sunset, this value based on earlier measurements. Consequently, we can assign one temperature value to every cell in the northern sector or in the southern sector in a given measuring night. The determination of the urban-rural air temperature differences (UHI intensity) of cells was based on the reference to the temperature of the westernmost cell of the original study area (Fig. 1), which was regarded as a rural one because of its location outside of the city. Moreover, the synoptic weather station of the Hungarian Meteorological Service is located there, too. The 107 (and now 97) points that cover the urban parts provide an appropriate basis to interpolate isolines using the standard Kriging procedure, which is a geostatistical gridding method. Therefore the isotherms give us a detailed picture on the average thermal field within the city at the time of the strongest effects of urban factors in both study periods. 2.3 Built-up and water surface ratio The ratios of the built-up (B) and water surface (W) by cells were determined by a vector and

235

raster-based GIS database combined with remote sensing analysis of SPOT XS images. The digital satellite image was rectified to the EOTR using 1:10,000 scale maps. The nearest-neighbour method of resampling was employed, resulting in a root mean square value of less than 1 pixel. Since the resolution of the image was 20 m 20 m, small urban units could be assessed independently of their official (larger scale) landuse classification. The Normalised Difference Vegetation Index (NDVI) was calculated from the pixel values in the bands of infrared and red. The NDVI values are between 1 and þ1, indicating the effect of green space in the units of 20 m 20 m. Built-up, water, vegetated surfaces were distinguished according to their NDVI values. In the Szeged region the occurrence of non-vegetated (bare) areas is negligible, namely each free place is covered by some vegetation (e.g. garden and cultivated plants, trees, grass, bushes, weeds). The ratios (to total cell area) of these land-use types for each grid element were determined using cross-tabulation. 2.4 Sky view factor The built-up ratio does not completely describe the characteristics of an urban surface, because the vertical dimensions of buildings are generally not well represented by satellite images. In the cities the narrow streets and high buildings create deep canyons and this vertical geometry plays an important role in development of UHI. Namely, the heat transport and the outgoing long wave radiation decrease because of the more moderated turbulence and the more increased obstruction of the sky. According to the previous paragraph, it was necessary to determine the representative openness of the cell surfaces quantitatively. In our work we used the sky view factor (SVF, in this study it is marked shortly by S) which is a dimensionless measure and is between 0 and 1. These values represent totally obstructed and free spaces, respectively (Oke, 1981, 1988). There are several methods to determine the SVF using, among others, theodolite, fish-eye lens camera (Oke, 1981; B€arring and Mattsson, 1985; Park, 1987), digital camera or automatic canopy analyzer (Grimmond et al., 1999).

Z. Bottya´n and J. Unger

236

Fig. 2. Geometry of an unsymmetric canyon flanked by buildings with a measuring point not at the centre of the floor

We have measured two angles (1 and 2) perpendicular to the axis of the streets in both directions using a 1.5 m high theodolite. From these data wall view factors can be calculated to the left side (WVFW1) and to the right side (WVFW2) as well (Oke, 1981). The measuring points are not always coincident with the midpoint of the distance between the buildings in the left and right hand side (Fig. 2). The calculation of S is based on Oke’s (1988) results (for explanation of symbols see Fig. 2): WVFW1 ¼ ð1 cos 1 Þ=2 where 1 ¼ tan 1 ðH1 =W1 Þ; WVFW2 ¼ ð1 cos 2 Þ=2 where 2 ¼ tan 1 ðH2 =W2 Þ: S ¼ 1ðWVFW1 þ WVFW2 Þ: In order to determine S values by cells the same long canyons (measuring routes) were used as for the temperature sampling. 532 points were surveyed by theodolite and the distance between the points were 125 m on average in line again with the temperature sampling, then the S data were also averaged by cells. Because of technical difficulties we did not have any measurement points in junctions so the average S values are probably a bit smaller than the real ones. Besides, if there were parks, forests or water surface in one direction from the measurement point we have assigned 0 as an angle value at that direction, because it is difficult to determine S values modified by the vegetation and the results

are not unambiguous (Yamashita et al., 1986). The significance of the obtained data set is the fact that it almost represents the total urban area. Earlier investigations were limited to the centre or only one part of the cities and used far smaller numbers of measurements (Parry, 1967; Oke, 1981, 1988; Johnson, 1985; Yamashita et al., 1986; Park, 1987; Eliasson, 1996; Grimmond et al., 1999). Since some areas with different land-use features can produce almost equal S data (narrow street with low buildings versus wide street with high buildings), S values alone do not describe sufficiently the vertical geometry of cities. Therefore, it is important to have quantitative information on the vertical size of a canyon because it plays significant role in the energy budget of an urban surface.

2.5 Building height According to Section 2.4. we had to find a suitable procedure to determine the exact vertical dimension of a canyon. The angles between the horizontal plane and the highest points of the canyon sides seen from the measurement points are available at each point. In addition, if we have the distances of the walls from the measuring point (W1 and W2, see Fig. 2) we can apply a simple formula to calculate wall heights (H1 and H2), taking the instrument height of 1.5 m into account: H1 ¼ tan 1 W1 þ 1:5 m H2 ¼ tan 2 W2 þ 1:5 m It was not possible to measure the width of the streets in the course of survey, but these values can be determined by means of aerial photographs concerning any part of the street. After digitizing these images, we made an orthophoto of Szeged by means of Ortho Base tool of the ERDAS IMAGINE GIS software (Barsi, 2000) and the measurement points were also precisely marked on it. This orthophoto is already suitable to determine distances of the walls (W1 and W2) from the measurement points in every cell. Because the aerial photographs do not cover completely the study area, these distances are not available for six and four cells in the southern and western parts of Szeged, respectively.

A multiple linear statistical model for estimating the mean maximum UHI

More details about the study area, its subdivision, the temperature measurements and determination of different land-use ratios can be found in recently published papers of Unger (1999), Unger et al. (2000) and Unger et al. (2001a and 2001b).

2.6 Building method of the statistical model In the course of determination of model equations we used the mean maximum value of UHI intensity (T) in both seasons and the earlier mentioned basic parameters, such as: mean sky view factor (S), mean building height (H) in m, ratios of built-up surface (B) and water surface (W) as a percentage by cells. Since these parameters change rapidly with the increasing distance from the city centre we applied the exponentially distance weighted spatial means of the mentioned land-use parameters for our model. The distance scale of the weight should be derived from the transport scale of heat in the urban canopy. Our statistical model have determined this scale from the measured parameter values. In compliance with the model we determined a set of predictors concerning all four basic urban parameters in the following way: *

*

*

*

*

Parameter value in the grid cell (S, H, B, W) with i2 þ j2 ¼ 0, Mean parameter value of all grid cells (S1, H1, B1, W1) with 0

Department of Climatology and Landscape Ecology, University of Szeged, Szeged, Hungary

A multiple linear statistical model for estimating the mean maximum urban heat island Z. Bottya´n and J. Unger With 9 Figures Received September 26, 2002; revised February 25, 2003; accepted March 22, 2003 Published online July 30, 2003 # Springer-Verlag 2003

Summary

1. Introduction

This study examines the spatial and quantitative influence of urban factors on the surface air temperature field of the medium-sized of Szeged, Hungary, using mobile measurements under different weather conditions in the periods of March 1999–February 2000 and April–October 2002. Efforts have been concentrated on the development of the urban heat island (UHI) in its peak development during the diurnal cycle. Tasks included: (1) determination of spatial distribution of mean maximum UHI intensity and some urban surface parameters (built-up and water surface ratios, sky view factor, building height) using the standard Kriging procedure, as well as (2) development of a statistical model in the so-called heating and non-heating seasons using the above mentioned parameters and their areal extensions. In both seasons the spatial distribution of the mean maximum UHI intensity fields had a concentric shape with some local irregularities. The intensity reaches more than 2.1 C (heating season) and 3.1 C (non-heating season) in the centre of the city. For both seasons statistical model equations were determined by means of stepwise multiple linear regression analysis. As the measured and calculated mean maximum UHI intensity patterns show, there is a clear connection between the spatial distribution of the urban thermal excess and the examined land-use parameters, so these parameters play an important role in the evolution of the strong UHI intensity field. From the above mentioned parameters the sky-view factor and the building height were the most determining factors which are in line with the urban surface energy balance. Therefore in the future, using our model it will be possible to predict mean maximum UHI intensity in other cities, which have landuse features similar to Szeged.

The mainly artifical surface of the city, anthropogenic heat emission and air pollution modify the urban atmosphere. The modification effect of urbanization on local climate is most obvious in the case of temperature, which is the socalled urban heat island (UHI) phenomenon or urban heat archipelago if the structure is multicellar. Its intensity has a distinguished diurnal cycle with a strongest development in the first part of the night, in general 3–5 hours after the sunset. The simulation of real factors and physical processes generating this temperature-increasing effect is extremely difficult as it includes the surface geometry and materials as well as artificial production of heat and air pollution. Statistical modeling may provide useful quantitative information about the structure as well as the spatial and temporal features of the maximum UHI intensity by employing different urban surface parameters (e.g. Outcalt, 1972; Oke, 1981, 1988; Park, 1986, 1987; Kuttler et al., 1996; Matzarakis et al., 1998). In our case these parameters are: built-up ratio, water surface ratio, sky view factor and building height. The selection of these parameters is based on their role in smallscale climatevariations (Oke, 1987; Golany, 1996).

234

Z. Bottya´n and J. Unger

This paper reports on effects of the urban surface factors on the patterns of quantitative differences between the urban-rural temperature in the heating and non-heating half years. 2. Study area, parameters and methods 2.1 Study area The study city, Szeged, is in the south-eastern part of Hungary on a wide flat flood plain (Fig. 1). This environmental situation makes Szeged a good case for the study of the urban climate. Its regional climate is temperate warm characterized by a rather uniform annual distribution of precipitation. Within an administration district of 281 km2 live 160,000 inhabitants. The base of the city structure is a boulevardavenue system and several land-use types are present. Two seasonal half years can be clearly

distinguished from the point of view of city dwellers: the heating (from October until April) and the non-heating (from April until October) seasons. Urbanized areas occupy about 25–30 km2, therefore our examination concentrated on the central parts of the large administration district (Fig. 1). Other parts of the city, having village and rural characteristics, are not included. This area was divided into two sectors and subdivided further into 500 m 500 m squares, so it contains 107 cells (26.75 km2) altogether. The grid network itself was established by quartering the 1 km 1 km square network of the Unified National Mapping System (in Hungarian: EOTR) developed for the topographical maps on Hungary (Unger et al., 2000; Unger et al., 2001a, 2001b). At present, investigation of the six southern and the four western cells of the original study area are omitted because of the lack in the data set of

Fig. 1. Location of Szeged in Hungary and main land-use types of the city (a: border of the study area, b: agricultural and open land, c: industrial area, d: 1–2 storey detached houses, e: 5–11 storey apartment buildings, f: historical city core with 3–5 storey buildings, g: circle dike)

A multiple linear statistical model for estimating the mean maximum UHI

one parameter (building height, see Chapter 2.5.), so the present study uses lower cells, altogether 97 cells covering an area of 24.25 km2 (see e.g. Fig. 3). 2.2 Temperature (maximum UHI intensity) The spatial distribution of the surface air temperature is based on mobile observations during the period of March 1999 to February 2000. The UHI intensity (namely T, the temperature difference between urban and rural areas) was measured at every cell, on fixed return routes once a week. Altogether 48 traverses were taken, 24 in the northern, and another 24 in the southern sector. This frequency of car traverses provided sufficient information on different weather conditions, except for rain. The study area was divided into two sectors because of the large number of cells. Return routes, 75 km and 68 km long in the northern and southern sectors, respectively, were needed to make time-based corrections and the measurements took about 3 hours. The reference time, namely the likely time of the occurrence of the strongest UHI, was 4 hours after sunset, this value based on earlier measurements. Consequently, we can assign one temperature value to every cell in the northern sector or in the southern sector in a given measuring night. The determination of the urban-rural air temperature differences (UHI intensity) of cells was based on the reference to the temperature of the westernmost cell of the original study area (Fig. 1), which was regarded as a rural one because of its location outside of the city. Moreover, the synoptic weather station of the Hungarian Meteorological Service is located there, too. The 107 (and now 97) points that cover the urban parts provide an appropriate basis to interpolate isolines using the standard Kriging procedure, which is a geostatistical gridding method. Therefore the isotherms give us a detailed picture on the average thermal field within the city at the time of the strongest effects of urban factors in both study periods. 2.3 Built-up and water surface ratio The ratios of the built-up (B) and water surface (W) by cells were determined by a vector and

235

raster-based GIS database combined with remote sensing analysis of SPOT XS images. The digital satellite image was rectified to the EOTR using 1:10,000 scale maps. The nearest-neighbour method of resampling was employed, resulting in a root mean square value of less than 1 pixel. Since the resolution of the image was 20 m 20 m, small urban units could be assessed independently of their official (larger scale) landuse classification. The Normalised Difference Vegetation Index (NDVI) was calculated from the pixel values in the bands of infrared and red. The NDVI values are between 1 and þ1, indicating the effect of green space in the units of 20 m 20 m. Built-up, water, vegetated surfaces were distinguished according to their NDVI values. In the Szeged region the occurrence of non-vegetated (bare) areas is negligible, namely each free place is covered by some vegetation (e.g. garden and cultivated plants, trees, grass, bushes, weeds). The ratios (to total cell area) of these land-use types for each grid element were determined using cross-tabulation. 2.4 Sky view factor The built-up ratio does not completely describe the characteristics of an urban surface, because the vertical dimensions of buildings are generally not well represented by satellite images. In the cities the narrow streets and high buildings create deep canyons and this vertical geometry plays an important role in development of UHI. Namely, the heat transport and the outgoing long wave radiation decrease because of the more moderated turbulence and the more increased obstruction of the sky. According to the previous paragraph, it was necessary to determine the representative openness of the cell surfaces quantitatively. In our work we used the sky view factor (SVF, in this study it is marked shortly by S) which is a dimensionless measure and is between 0 and 1. These values represent totally obstructed and free spaces, respectively (Oke, 1981, 1988). There are several methods to determine the SVF using, among others, theodolite, fish-eye lens camera (Oke, 1981; B€arring and Mattsson, 1985; Park, 1987), digital camera or automatic canopy analyzer (Grimmond et al., 1999).

Z. Bottya´n and J. Unger

236

Fig. 2. Geometry of an unsymmetric canyon flanked by buildings with a measuring point not at the centre of the floor

We have measured two angles (1 and 2) perpendicular to the axis of the streets in both directions using a 1.5 m high theodolite. From these data wall view factors can be calculated to the left side (WVFW1) and to the right side (WVFW2) as well (Oke, 1981). The measuring points are not always coincident with the midpoint of the distance between the buildings in the left and right hand side (Fig. 2). The calculation of S is based on Oke’s (1988) results (for explanation of symbols see Fig. 2): WVFW1 ¼ ð1 cos 1 Þ=2 where 1 ¼ tan 1 ðH1 =W1 Þ; WVFW2 ¼ ð1 cos 2 Þ=2 where 2 ¼ tan 1 ðH2 =W2 Þ: S ¼ 1ðWVFW1 þ WVFW2 Þ: In order to determine S values by cells the same long canyons (measuring routes) were used as for the temperature sampling. 532 points were surveyed by theodolite and the distance between the points were 125 m on average in line again with the temperature sampling, then the S data were also averaged by cells. Because of technical difficulties we did not have any measurement points in junctions so the average S values are probably a bit smaller than the real ones. Besides, if there were parks, forests or water surface in one direction from the measurement point we have assigned 0 as an angle value at that direction, because it is difficult to determine S values modified by the vegetation and the results

are not unambiguous (Yamashita et al., 1986). The significance of the obtained data set is the fact that it almost represents the total urban area. Earlier investigations were limited to the centre or only one part of the cities and used far smaller numbers of measurements (Parry, 1967; Oke, 1981, 1988; Johnson, 1985; Yamashita et al., 1986; Park, 1987; Eliasson, 1996; Grimmond et al., 1999). Since some areas with different land-use features can produce almost equal S data (narrow street with low buildings versus wide street with high buildings), S values alone do not describe sufficiently the vertical geometry of cities. Therefore, it is important to have quantitative information on the vertical size of a canyon because it plays significant role in the energy budget of an urban surface.

2.5 Building height According to Section 2.4. we had to find a suitable procedure to determine the exact vertical dimension of a canyon. The angles between the horizontal plane and the highest points of the canyon sides seen from the measurement points are available at each point. In addition, if we have the distances of the walls from the measuring point (W1 and W2, see Fig. 2) we can apply a simple formula to calculate wall heights (H1 and H2), taking the instrument height of 1.5 m into account: H1 ¼ tan 1 W1 þ 1:5 m H2 ¼ tan 2 W2 þ 1:5 m It was not possible to measure the width of the streets in the course of survey, but these values can be determined by means of aerial photographs concerning any part of the street. After digitizing these images, we made an orthophoto of Szeged by means of Ortho Base tool of the ERDAS IMAGINE GIS software (Barsi, 2000) and the measurement points were also precisely marked on it. This orthophoto is already suitable to determine distances of the walls (W1 and W2) from the measurement points in every cell. Because the aerial photographs do not cover completely the study area, these distances are not available for six and four cells in the southern and western parts of Szeged, respectively.

A multiple linear statistical model for estimating the mean maximum UHI

More details about the study area, its subdivision, the temperature measurements and determination of different land-use ratios can be found in recently published papers of Unger (1999), Unger et al. (2000) and Unger et al. (2001a and 2001b).

2.6 Building method of the statistical model In the course of determination of model equations we used the mean maximum value of UHI intensity (T) in both seasons and the earlier mentioned basic parameters, such as: mean sky view factor (S), mean building height (H) in m, ratios of built-up surface (B) and water surface (W) as a percentage by cells. Since these parameters change rapidly with the increasing distance from the city centre we applied the exponentially distance weighted spatial means of the mentioned land-use parameters for our model. The distance scale of the weight should be derived from the transport scale of heat in the urban canopy. Our statistical model have determined this scale from the measured parameter values. In compliance with the model we determined a set of predictors concerning all four basic urban parameters in the following way: *

*

*

*

*

Parameter value in the grid cell (S, H, B, W) with i2 þ j2 ¼ 0, Mean parameter value of all grid cells (S1, H1, B1, W1) with 0