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´nand 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
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 measure- ments 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 2.1C (heating season) and 3.1C (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 param- eters, 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 land- use features similar to Szeged.
1. Introduction
The mainly artifical surface of the city, anthro- pogenic heat emission and air pollution modify the urban atmosphere. The modification effect of urbanization on local climate is most obvi- ous in the case of temperature, which is the so- called urban heat island (UHI) phenomenon or urban heat archipelago if the structure is multi- cellar. 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 sur- face geometry and materials as well as artificial production of heat and air pollution. Statistical modeling may provide useful quantitative infor- mation 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 param- eters are: built-up ratio, water surface ratio, sky view factor and building height. The selection of these parameters is based on their role in small- scale climate variations (Oke, 1987; Golany, 1996).
This paper reports on effects of the urban sur- face factors on the patterns of quantitative differ- ences 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 distri- bution of precipitation. Within an administra- tion district of 281 km2 live 160,000 inhabitants.
The base of the city structure is a boulevard- avenue 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 m500 m squares, so it contains 107 cells (26.75 km2) altogether. The grid net- work itself was established by quartering the 1 km1 km square network of the Unified Na- tional 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: his- torical city core with 3–5 storey buildings, g: circle dike)
one parameter (building height, see Chapter 2.5.), so the present study uses lower cells, alto- gether 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 tem- perature is based on mobile observations during the period of March 1999 to February 2000. The UHI intensity (namely T, the temperature dif- ference between urban and rural areas) was mea- sured 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 sec- tor. This frequency of car traverses provided sufficient information on different weather con- ditions, 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 measure- ments 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. Conse- quently, we can assign one temperature value to every cell in the northern sector or in the south- ern 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. More- over, the synoptic weather station of the Hungar- ian 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. There- fore 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
raster-based GIS database combined with remote sensing analysis of SPOT XS images. The digital satellite image was rectified to the EOTR us- ing 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 m20 m, small urban units could be assessed independently of their official (larger scale) land- use 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 m20 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 cov- ered by some vegetation (e.g. garden and culti- vated 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, be- cause 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 out- going 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 open- ness 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€aarring and Mattsson, 1985; Park, 1987), digital camera or automatic canopy anal- yzer (Grimmond et al., 1999).
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 mid- point of the distance between the buildings in the left and right hand side (Fig. 2). The calcula- tion of S is based on Oke’s (1988) results (for explanation of symbols see Fig. 2):
WVFW1¼ ð1cos1Þ=2
where 1¼tan1ðH1=W1Þ;
WVFW2¼ ð1cos2Þ=2
where 2¼tan1ðH2=W2Þ:
S¼1ðWVFW1þWVFW2Þ:
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 sur- face 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 fea- tures 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. There- fore, it is important to have quantitative informa- tion 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 suit- able 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 (W1and 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:
H1¼tan1W1þ1:5 m H2¼tan2W2þ1:5 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 photo- graphs 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 (W1and 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.
Fig. 2. Geometry of an unsymmetric canyon flanked by buildings with a measuring point not at the centre of the floor
More details about the study area, its subdivi- sion, the temperature measurements and determi- nation 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 equa- tions we used the mean maximum value of UHI intensity (T) in both seasons and the ear- lier mentioned basic parameters, such as: mean sky view factor (S), mean building height (H) in m, ratios of built-up surface (B) and water sur- face (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 deter- mined 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 i2þj2 ¼0,
* Mean parameter value of all grid cells (S1, H1, B1, W1) with 0<i2þj2<22,
* Mean parameter value of all grid cells (S2, H2, B2, W2) with 22<i2þj2<42,
* Mean parameter value of all grid cells (S3, H3, B3, W3) with 42<i2þj2<82,
* Mean parameter value of all grid cells (S4, H4, B4, W4) with 82<i2þj2<162.
Here i and j are cell indices in the two dimen- sions, and i and j are the differences of grid cell indices with respect to a given cell. These zones cover the entire model (investigated) area of Szeged. After that we had 16 predictors to build our linear statistical model. This procedure creates the right conditions for applying our model to predict the UHI intensity over other cities which have different sizes and a non- concentric shape.
The chosen model building method was the stepwise multiple linear regression. The applied implementation of this procedure can be found in the SPSS 9 computer statistics software. A com- prehensive discussion of the mathematical back- ground of the method is found in Miller (2002).
Predictors were entered or removed from the model depending on the significance of the F value of 0.05 and 0.1, respectively. Under these conditions two linear statistical model equations were determined for both the heating and non- heating season, separately, because there is a very noticeable difference between the magni- tudes of UHI intensity fields in these seasons.
3. Results and discussion
3.1 Spatial characteristics of urban parameters with special regard to mean maximum UHI
In both (heating and non-heating) seasons the shape of the UHI patterns are almost concentric and the temperature values increase from the out- skirts towards the inner urban areas (Fig. 3). In the non-heating season, the greatest intensity (3.18C) is found in the central grid cell and the mean maximum UHI value of higher than 2C covers about 37% of the investigated area.
In the heating season the highest value of the UHI intensity (2.12C) occurs in the central grid cell, too, but the significant differences (more than 2C) covers only about 2% of the total area (Unger et al., 2000).
The spatial distribution of the built-up ratio over the city has also a concentric shape- decreasing from the central urban areas to the outwards (Fig. 4). The highest built-up ratio values are concentrated in the middle and the north-eastern parts of the city. The maximum values are higher than 96%. The River Tisza with its environment has a low built-up ratio and of course a high water surface ratio which can be clearly recognized with its east-to-south curve in the south-eastern part of the study area (Fig. 5).
Apart from this, the extension of water surfaces is negligible, instead of some small and shallow recreational lakes (ponds) in the western part of the city.
The sky view factor pattern is also very com- plicated because of the significant variability
of the building height and width of the streets (Fig. 6). Accordingly, this parameter field does not form an entirely circular structure and its extreme values are not located in the centre.
There are three parts of the city where the S values are very low, so this parameter influences the outgoing longwave radiation there consider- ably. These areas have the values of lower than 0.8 and in the centre of the city they are lower than 0.7.
The highest buildings are located in the north- eastern part of the city with the maximum values of about 20 m (Fig. 7). There is another area in the southern central region where the buildings are higher than 15 m. Generally, the average building height is higher than 10 m in the study area.
Towards the north-eastern part of the city the isotherms are considerably streched (Fig. 3). This can be explained by the influence of the large
Fig. 4. Spatial distribution of the ratio of the built-up area to the total area (in percent) by cells in Szeged
Fig. 5. Spatial distribution of the ratio of the water surface to the total area (in percent) by cells in Szeged
Fig. 3. Spatial distribution of the measured mean max. UHI intensity (C) during the non-heating season (April 16–
October 15) and the heating season (October 16–April 15) in Szeged
housing estates with tall concrete buildings located mainly in this neighbourhood of the city so this area has the built-up ratio higher than 75%, the building height higher than 15 m, but the sky view factor is less than 0.85. The second irregularity is caused by the cooling influence of the River Tisza that flows through the city (Fig. 5). Along the river the isotherms are a bit withdrawn towards the city centre. The third area with significant anomaly can be found in the western part of the city where the urban surface
geometry changes abruptly along a westbound transect (which starts at the centre). This region is characterized by S values higher than 0.95, building heights lower than 7 m and built-up ratio of about 25%.
As we mentioned above, there are some essen- tial deviations in the concentric shapes of the UHI intensity field, and the most important one extends from the north-eastern to the south- western part of the city. It can also be observed, that spatial distributions of urban land-use factors have a similar irregularity in the same direction.
On the other hand, the central urban area – which has the highest UHI intensity in both seasons – has the lowest S values and the highest built-up ratio. Therefore, these parameters may play an important role in the evolution of the strong UHI intensity field over the city.
3.2 Statistical model equations
As the results show, in both seasons the order of significance of the applied parameters is the same but in the heating season the role of them is more pronounced than in the non-heating one. The model equation has six predictors in the non- heating season and seven parameters in the heating one (Table 1). As it can be seen the S1 predictor is the most important one among all of them but B1 and W1 factors play also significant role in both seasons.
The two 6- and 7-variable models (bold setting in Table 1) indicate a very strong linear connec- tion between the mean maximum UHI intensity and the applied land-use parameters. The abso- lute values of the multiple correlation coefficients (r) between the maximum UHI intensity and the studied parameters are 0.895 and 0.919 in the heating and non-heating seasons, respectively, so they are significant at 0.1% level. This means that these four parametes and their aerial exten- sions are able to explain 80.1% and 84.5% of the above mentioned relationship in both studied pe- riods. The standard errors of the estimates are 0.203 and 0.251 in the heating and non-heating half year, respectively. The confidence intervals of the calculated regression coefficients and their standard errors can be found in Table 2.
We have used these two model equations to determine the spatial distribution of the UHI intensity patterns over the area studied
Fig. 6. Spatial distribution of the average sky view factor values by cells in Szeged
Fig. 7. Spatial distribution of the average building height (in m) by cells in Szeged
concerning heating and non-heating periods as well. The measured and calculated T values are presented with the help of isotherms (Fig. 3 and Fig. 8). It can be seen that there is a consid- erable similarity between the measured and pre- dicted UHI intensity fields in both seasons but some differences can be detected too. As it can be observed on the Fig. 8 the calculated T fields have also the same significant irregularities in Szeged.
We compared the results of the model to an independent UHI intensity data set which was measured during the non-heating half year in 2002. The study area and the mobile sampling method were the same as the earlier cases, except that we used two cars to make temperature mea- surements at the same time in the two sectors, altogether 18 times. According to the Fig. 9 the measured UHI intensity pattern is similar to the earlier mentioned one (Fig. 3) but the maximum
Table 2. The values of the significance, coefficients, standard errors and 95% confidence intervals of the applied urban surface parameters of our models in the two studied periods in Szeged (n¼97)
Period Param. Signif. Coeff. Std.
error
95% Confidence interval
Lower Upper
bound bound
April 16–October 15 S1 0.000 4.140 0.727 5.594 2.686
(non-heating season) H 0.000 0.029 0.006 0.017 0.041
B1 0.000 0.016 0.004 0.008 0.024
W1 0.000 0.032 0.007 0.046 0.018
W 0.000 0.012 0.003 0.006 0.018
B 0.000 0.007 0.002 0.003 0.011
Const. 0.000 3.703 0.827 2.049 5.357
October 16–April 15 S1 0.000 2.712 0.613 3.938 1.486
(heating season) S 0.017 1.049 0.430 1.909 0.189
B1 0.006 0.008 0.003 0.002 0.014
W1 0.022 0.013 0.006 0.001 0.025
H 0.033 0.013 0.006 0.001 0.025
W 0.001 0.009 0.003 0.003 0.015
B 0.005 0.004 0.001 0.002 0.006
Const. 0.000 3.673 0.730 2.213 5.133
Table 1. Values of the stepwise correlation of maximum UHI intensity (T) and urban surface parameters by grid cells and their significance levels in the two studied periods in Szeged (n¼97)
Period Parameter entered Multiple Multiple r2 Sign. level
jrj r2
April 16–October 15 S1 0.806 0.649 0.000 0.1%
(non-heating season) S1, H 0.845 0.714 0.065 0.1%
S1, H, B1 0.863 0.744 0.030 0.1%
S1, H, B1, W1 0.902 0.814 0.070 0.1%
S1, H, B1, W1, W 0.907 0.822 0.008 0.1%
S1, H, B1, W1, W, B 0.919 0.845 0.023 0.1%
October 16–April 15 S1 0.791 0.626 0.000 0.1%
(heating season) S1, S 0.837 0.701 0.075 0.1%
S1, S, B1 0.853 0.727 0.026 0.1%
S1, S, B1, W1 0.867 0.752 0.025 0.1%
S1, S, B1, W1, H 0.879 0.772 0.020 0.1%
S1, S, B1, W1, H, W 0.884 0.782 0.010 0.1%
S1, S, B1, W1, H, W, B 0.895 0.801 0.019 0.1%
UHI intensity value is smaller by about 0.5C.
After that we calculated the spatial distribution of the difference between the measured indepen- dent UHI intensity values and the predicted ones by our model (Fig. 9). There is also a similarity between the measured and the predicted UHI intensity fields in the non-heating season but we can find three important areas where the abso- lute UHI intensity anomaly is between 0.4C and 0.6C. In the north-eastern and the southern parts of the city the predicted values are higher than
the measured ones (negative anomaly). At the western border of the investigated area the pre- dicted values are lower than the measured ones (positive anomaly). However, these areas occupy only a minor part of the study area (about 5.5 cells, 1.4 km2, 6% of the total area). The areas characterized by the differences lower than 0.2C are significantly greater, they cover alto- gether 55 cells (about 13,75 km2, 57%).
Fig. 8. Spatial distribution of the predicted mean max. UHI intensity (C) during the non-heating season (April 16–
October 15) and the heating season (October 16–April 15) in Szeged
Fig. 9. Spatial distribution of the measured mean max.
UHI intensity (C) during the non-heating season (April 16–October 15) in 2002 and spatial distribution of the dif- ference of the measured and predicted mean max. UHI intensity (C) during this season in Szeged
As a consequence, it can be stated, that our model described the spatial distribution of the real UHI intensity field in the investigated area rather correctly. On the basis of our results, we may apply this model building procedure to pre- dict the UHI intensity for other cities which have different size and even non-concentric shape.
Besides we also intend to employ the same land-use characteristics used in this study and additional meteorological parameters to predict the spatial and temporal distribution of the max- imum UHI intensity on the days characterised by any kind of weather conditions at any time of the year. Although adding meteorological predictors increase the complexity of the model, it can give us a useful tool for the prediction of the tempera- ture field in advance for several hours and as a consequence for the prediction of the pattern of energy consumption inside the city. With full knowledge of the spatial and temporal distribu- tion of the predicted maximum UHI intensity field over the city we can forecast and plan the energy demand, particularly in cold and warm periods of the year with special regard to the extreme heating and cooling terms.
4. Conclusions
In this study we have estimated the spatial dis- tribution of the mean UHI intensity with the help of urban surface parameters in two half-year per- iods in Szeged, Hungary. The following conclu- sions are reached from the analysis presented:
(i) The spatial distribution of the UHI intensity patterns have almost concentric shapes and the temperature values decrease from the central urban areas towards the outskirts in both study periods. On the other hand, there are irregularities caused by the areal distri- bution of buildings and water surfaces having different structural and material properties, respectively.
(ii) On the basis of our statistical analysis we have proved a strong linear relationship between the mean maximum UHI intensity and the studied urban parameters like sky view factor (S), building height (H), built- up ratio (B), water surface ratio (W) and areal extended versions of these predictors (e.g. S1, H1) in both seasons. With the help
of the obtained model equations we are able to produce the UHI intensity fields which are very similar to the measured ones in the investigated city.
(iii) Generally, our model has described the spa- tial distribution of the real UHI intensity field over the study area rather correctly, because the areas characterized by the differences lower than 0.2C cover the overwhelming parts of the city (57%).
Nevertheless, there are some important – but not significant – differences between the predicted and measured UHI fields which are caused by some possible errors in the temperature samplings, the low num- ber of studied parameters and the consid- erable irregularities of the urban surface geometry.
(iv) This model building procedure used to pre- dict the UHI intensity may be applicable for other cities which have different size and even non-concentric shape, but for the true validation it is necessary to have complete databases of the measured UHI intensities for those cities.
(v) The presented statistical estimation serves a reliable basis for the development of our model to predict this temperature field in time and space with the help of some addi- tional meteorological parameters.
Acknowledgements
The authors are grateful to anonymous reviewers for provid- ing valuable comments on this study. The authors wish to give special thanks to Z. S€uumeghy for preparation of Figs. 1 and 2 and to the students (P. Purnhauser, E. Robotka and Z. Zboray) who took part in the measurement campaigns and in the data pre-processing. This research was supported by the grant of the Hungarian Scientific Research Fund (OTKA T=034161).
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Authors’ address: Zsolt Bottya´n (e-mail: zbottyan@mail.
externet.hu) and Ja´nos Unger, Department of Climatology and Landscape Ecology, University of Szeged, P.O. Box 653, 6701 Szeged, Hungary.
