Theor. Appl. Climatol. (2009) 95: 111–123DOI 10.1007/s00704-007-0362-9Printed in The Netherlands

1 Department of Climatology and Landscape Ecology, University of Szeged, Szeged, Hungary2 Urban Climate Group, Physical Geography, G€ooteborg University, G€ooteborg, Sweden

Computing continuous sky view factors using 3D urbanraster and vector databases: comparison and applicationto urban climate

T. Gal1, F. Lindberg2, J. Unger1

With 13 Figures

Received 28 December 2006; Accepted 17 September 2007; Published online 8 January 2008# Springer-Verlag 2008

Summary

The use of high resolution 3D urban raster and vectordatabases in urban climatology is presented. It applies twodifferent methods to the calculation of continuous sky viewfactors (SVF), compares their values and considers theirusefulness and limitations in urban climate studies. It showsand evaluates the relationship between urban geometry,quantified by SVF, and intra-urban nocturnal temperaturevariations using areal means in the whole urban area ofSzeged, a city located in southeast Hungary. Results fromthe vector and raster models shows similar SVF values(r2¼ 0.9827). The usefulness of using areal means in SVF-temperature relations is confirmed. The vector and the ras-ter approaches to the derivation of areal means of SVF areboth shown to be powerful tools to obtain a general pictureof the geometrical conditions of an urban environment.

1. Introduction

Urban areas exhibit striking and continuing man-made changes in land-use, especially surfaceproperties such as their materials and geometricform. As a consequence, urban environments mod-ify the surface energy and water balance which

often results in higher nocturnal urban tempera-tures compared to their more natural surround-ings (urban heat island – UHI, �T). Differentheat islands can be distinguished: beneath thesurface, at the surface, in the urban canopy layer(UCL) and the urban boundary layer (Oke 1982).As in the case here, the UHI is typically pre-sented as a temperature difference between theair within the UCL (extends from the groundup to about mean roof level) and that measuredin a rural area outside the settlement at similarheights. Generally, its strongest developmentoccurs at night when the heat, stored in the day-time, is released more slowly than the rural areaand therefore does not cool off as fast (Landsberg1981; Oke 1987).

Nocturnal cooling processes are primarilyforced by outgoing long wave radiation. In cities,narrow streets and high buildings create deep can-yons. This 3D geometrical configuration plays animportant role in regulating long-wave radiativeheat loss. Due to the fact that only a smaller partof the sky is seen from the surface (because ofthe horizontal and vertical unevenness of the sur-face elements), the nocturnal long wave radiationloss is more restricted here than in rural areas.

Correspondence: Tamas Gal, Department of Climatology and

Landscape Ecology, University of Szeged, PO Box 653, 6701

Szeged, Hungary, e-mail: tgal@geo.u-szeged.hu

Therefore, urban geometry is one importantfactor contributing to intra-urban temperature var-iations below roof level (e.g. Oke 1981; Eliasson1996). The sky view factor (SVF) is often usedto describe the urban geometry but also othermeasures are also used e.g. height-to-width ratio(Goh and Chang 1999) and frontal area index(Grimmond and Oke 1999). By definition, SVFis the ratio of the radiation received (or emitted)by a planar surface to the radiation emitted (orreceived) by the entire hemispheric environment(Watson and Johnson 1987). It is a dimensionlessmeasure between zero and one, representing totallyobstructed and free spaces, respectively (Oke1988). It is expected that a region of a city witha smaller SVF should cool off more slowly sincethe sky is obstructed by buildings and the long-wave radiation tend to be trapped in the UCL.

Of course, other factors also contribute to thedevelopment of the UHI (built-up or paved arearatio, heat released by human activity, etc. seee.g. Oke (1987)). But the focus of this investiga-tion is on urban surface geometry – UHI rela-tionship using one of the most useful measureof surface geometry, the SVF as earlier studieshave shown (e.g. Oke 1981; Svensson 2004).

Modern GIS-based 3D models of cities opennew possibilities to describe and develop mea-sures of geometry applicable in urban climateresearch (e.g. Ratti and Richens 1999). Ratti(2001) utilizes high resolution raster DEMs forcomputing images of continuous sky view fac-tors. His SVF-model has been validated and hasgenerated accurate results (Brown et al. 2001;Lindberg 2005).

A comprehensive literature review of SVF-temperature variations within urban areas byUnger (2004) showed that results from previousstudies can be rather contradictory, especially ifcomparisons are based on a few element pairsmeasured at selected sites within the city. Unger(2004, 2007) suggests that further studies shouldfocus on comparison between areal means ofboth geometry and temperature variations.

The overall purpose of the present study is toconsider the application of high resolution 3Durban raster and vector databases in urban cli-matology. The specific objectives are (1) to pres-ent and apply two different methods to calculateSVFs, both based on urban 3D models; (2) tocompare the two methods and consider their lim-itations and potentials in urban climate studies;(3) to study and evaluate the relationship betweenurban geometry as quantified by SVF and intra-urban nocturnal temperature variations using ar-eal means for the whole urban area of Szeged,Hungary.

2. Study area and temperature measurements

Szeged (46� N, 20� E) is a city located in south-east Hungary, in the southern part of the GreatHungarian Plain at 79 m above sea level on a flatplain (Fig. 1). According to Trewartha’s classifi-cation Szeged belongs to the climatic type D.1(continental climate with longer warm season),similarly to the predominant part of the country(Unger 1996). While the administrative area ofSzeged is 281 km2, the urbanized area is onlyaround 30 km2. The avenue-boulevard structure

Fig. 1. Location of Szeged inEurope and in Hungary, as wellas the grid network in Szeged:(a) open area, (b) built-up area,(c) border of the investigated ar-ea, (d, e) measurement routes

112 T. Gal et al.

of the town was built to follow the axis of theriver Tisza. There are no other water bodies inthe vicinity of the city. The population was about160,000 in the investigated years (2002–2003).

In order to determine the spatial variation oftemperature in the city the study area was dividedinto two sectors and subdivided further into500 m� 500 m cells (Fig. 1). It consists of 107cells covering the urban and suburban parts ofSzeged (26.75 km2). The outlying parts of thecity, characterized by villages and rural features,are not included in the grid, with the exception offour cells on the western side of the area. Thislatter part is necessary to determine urban-ruraltemperature contrasts and it is not included in theinvestigated area (103 cells).

According to Oke (2004) the circle of influ-ence on a screen level (�1.5 m) temperature isthought to have a radius of about 0.5 km typical-ly, but this is likely to depend upon the buildingdensity. So the 500 m mesh is reasonable to sim-ulate night temperatures in urban canopies.

Mobile temperature measurements were madeat night by two cars in two sectors at the sametime during a one-year period (April 2002 –March 2003), altogether 35 times approximatelywith 10-day frequency (Unger 2006). In studyingUHI, the quantity of interest is frequently not theabsolute urban temperature, but the differencebetween the urban and rural areas. The possibili-ty of errors due to inter-sensor differences isthereby removed (Streutker 2003).

On the basis of previous studies, data collec-tion was carried out in such a way that observa-tions took place around the expected time ofmaximum development of the UHI, about 4 h af-ter sunset based on previous research (e.g. Oke1981) and on earlier measurements in Szeged(e.g. Unger et al. 2001). After averaging the 15–20 measurement values in each grid cell, timeadjustments were applied back to a referencetime. The approach assumed an approximatelylinear change in air temperature with time (whichwas checked against continuous records at theautomatic weather station at the University ofSzeged).

Due to the size of the study area as well as thelength of the measurement routes, the area wasdivided into 2 sectors. Routes were designed sothat all cells were traversed at least once on theway out and back (Fig. 1). It took about 3 h to

obtain measurements on the outward and inwardtraverse legs and were conducted in all weatherconditions, except for rain. The cars reached theturning point at the reference time (4 h after sun-set). The temperature observations were carriedout by an automatic radiation-shielded sensorconnected to a digital data logger that sampledevery 10 s. In order to diminish the thermal dis-turbance due to the car, the sensor was attachedto a bar extending 0.6 m ahead of the car at theheight of 1.45 m above the ground. Due to theneed for efficient ventilation and to obtain a highdensity of data, the speed of the car was 20 to30 km h�1 hence data were gathered from every55 to 83 m travelled. Measurements were takenafter the peak traffic hours had passed so stop-pages due to red lights or other barriers were sel-dom: data taken when the car was stopped forthe any reason was later deleted from the data-base. Height-dependent temperature correctionsare not an issue because the area is essentiallyflat (<8 m elevation difference).

�T values were determined by referring cellaverages (Tcell) to the temperature average of thewesternmost cell (Tcell(W)) of the study area, lo-cated in countryside:

�T ¼ Tcell � TcellðWÞ

The westernmost cell consists of agricultural land,mainly fields of non-irrigated wheat, sunflowersand maize, which are representative of the ruralsurroundings of Szeged (Fig. 1).

3. Methods: 3D building database, SVFcalculations

The creation of the applied 3D building databasefor Szeged was based on local municipality dataof building footprints and aerial photographs todetermine individual building heights. To cross-check, theodolite measurements of heights wereconducted giving the mean ratio of the differ-ences compared to the database was about 5%.The database covers the whole study area andconsists of more than 22,000 buildings. Smallbuildings are difficult to determine from the aerialphotographs, and further their heat absorption andemission are negligible. Thus, buildings smallerthan 15 m2 were excluded from the database.The Digital Elevation Model (DEM) for Szegedrepresents a bare surface with a small vertical

Computing continuous sky view factors using 3D urban raster and vector databases 113

variation of the surface (75.5–83 m a.s.l.). Bothvector and raster data are in the Unified NationalProjection (EOV in Hungarian). The creation ofthe database is described in detail in Unger (2006,2007).

Our assessment of the strength of the SVF-UHI relationship is almost the same if the SVFcalculation is based at screen- or ground level(Unger 2007). Here, SVF calculations refer topoints at ground level.

3.1 SVF calculation using an urban vectordatabase

The 3D building database is a model of the realworld. It represents a simplified view of the ur-ban surface made up of flat-roofed buildings on-ly. Further the walls of any given building havethe same height.

The projection of every building on the skyis managed like the projection of their walls vis-ible from a given surface point and polygong(x) is the border of the visible sky (Fig. 2a).After dividing the hemisphere equally into slicesby rotation angle �, ‘rectangles’ are drawn whoseheights are equal to the g(x) values in the middlepoints of the intervals.

SVF values for a common geometric arrange-ments are given by Oke (1987). For the case ofa regular basin, where � is the elevation anglefrom the centre to the wall, the SVF value is(referring to the basin centre): SVFbasin¼ cos2�.So the view factor (VF) of a basin with an ele-vation angle � is VFbasin¼ 1� cos2�¼ sin2�,therefore the view factor for a slice (S) with awidth of � (Fig. 2b) can be written as:

VFS ¼ sin2� � ð�=360Þ

The algorithm draws a line by the angle �from the selected point and along that line itsearches a single building which obstructs thelargest part from the sky at that direction. Thatis, which building has the largest elevation angle� within a certain distance at that direction. Theaccuracy of the algorithm depends on the magni-tude of the rotation angle (�). Smaller � anglesresult in more accurate estimation of SVF (givenhere as SVFv – i.e. SVF computed by vectorbased method) but require longer computationtime. The length of the lines is set by the user.After calculating the VF values by slices they areadded and the sum is subtracted from 1 to get theSVFv.

ESRI ArcView 3.2 software (www.esri.com)has a built-in object-oriented language (Avenue)appropriate for our purpose. The software is pro-grammable so that every element is accessible(Souza et al. 2003). Our application is compiledfrom 9 scripts (graphical surface, control of theparameters, calculation of SVFv, etc.). Figure 3schematically illustrates the developed algo-rithm. Values for two parameters have to be se-lected: (i) the radius of the area around the sitewhere the algorithm takes into account theheights and positions of the building, and (ii)the interval of the rotation angle (�) which deter-mines the density of the target lines starting fromthe site. In our case a radius of 200 m and a rota-tion angle of 1� seemed appropriate (details inUnger 2007).

The SVFv was determined in a point networkthat covers the entire investigated area. The ele-vation of points was derived from a DEM cov-ering the study area. To select optimal pointresolution the precision of the database and the

Fig. 2. (a) Polygon g(x) as the border of the visible sky and division of the overlying hemisphere under g(x) into equal slicesby angle � (heights are equal to the g(x) values in the middle points of the intervals), (b) a slice of a ‘width’ of � (S) of a basinwith an elevation angle �

114 T. Gal et al.

necessary computing time must be considered.We found a 5 m resolution is appropriate to ob-tain continuous spatial distribution of the SVFv

and to reveal the main characteristics of the dis-tribution. Application of this resolution resultedin a total of 1,030,000 points in the 103 studycells.

After all individual values of SVFv were de-rived, cell averages were computed. For this,points overlapped by the buildings were deletedfrom the point network so that the relationshipbetween the SVFv and the thermal characteristicsof the urban canopy layer could be examined(Fig. 4). Thus, inclusion of SVFv values of thesepoints in the calculation of cell averages wouldbe inappropriate. After the deletion, altogether897,188 points were left in the investigated area.The number of point was different (ranging be-

tween 6171 and 9900) in cells depending on thetotal footprint area of the buildings. The SVFv

calculation was run for this point network onthe ground surface. It needed one day to computethe SVFv values for one cell. Therefore compu-tation for the complete study area took severaldays, but not more than two weeks, if more thanone computer was utilized. The outcome is apoint shape file containing SVFv values at groundlevel, distributed throughout the city of Szeged.

Figure 5 shows the spatial distribution of theSVFv values for selected areas representing dif-ferent built-up types in Szeged. This figure illus-trates the small-scale spatial variation of theSVFv. The values are relatively low in the citycentre, because of the narrow streets and smallcourtyards. In some parts of this area the valuescan reach about 0.1 and the highest values (�0.8)

Fig. 3. Schematic descriptionof the algorithm for the SVFcalculation using a vector data-base

Computing continuous sky view factors using 3D urban raster and vector databases 115

occur in parks (Fig. 5a). In the residential area,with mainly detached houses, the lowest SVFv

values are adjacent to the houses with minimum

values of about 0.5 and there are open placeswhere the SVFv values are almost 1 (Fig. 5b).In the area with large apartment blocks the build-ing density is relatively low but the SVFv ofabout 0.6 covers a significant part of this cell.This is the effect of the sparse but high buildings(Fig. 5c). In industrial districts the buildings cov-er large areas but they are not very high, so SVFv

values lower than 1 are found only near thebuildings (Fig. 5d).

3.2 SVF calculation using a raster DEM

Raster DEMs used in this type of studies can berelatively easy derived from a local governmentalvector database (Lindberg 2007). Since munici-pality raw data is mainly used for planning pur-poses both spatial accuracy and precision is highwhich makes it possible to produce a detailedraster image. Some spatial information is alwayslost in the vector-raster conversion but the overallquality of the final DEM is satisfying (Fig. 6).The quality of the raster model depends onthe chosen pixel size of the model and how de-

Fig. 4. A small part of the study area with (a) the buildingfootprints and (b) the SVF measurement points at 5 m reso-lution for the vector based method

Fig. 5. Spatial distribution of SVFv in some selected typical cells in Szeged and their averages

116 T. Gal et al.

tailed is the input vector-based information.Here we use a spatial resolution of 2 m for theraster DEM. Thus, a 1 m error is added in thevector-raster conversion. Clark Labs IDRISIKilimanjaro# was used for the vector-raster con-version (www.clarklabs.org). By using a spatialresolution of 2 m, 7,562,500 pixels were used inthe calculations.

A shadow casting algorithm developed byRatti and Richens (1999) underlies our GIS-anal-ysis. It is used to calculate shadow patterns on araster image. The algorithm is fairly straightfor-ward: the altitude and azimuth of a distant light

source (the Sun) is used as input informationtogether with the raster DEM (Fig. 7, left). Twobasic image processing operations are includedin the algorithm; (1) translation of the DEM ina given direction, and (2) reduction of buildingheights based on solar altitude. The approachtaken is to compute ‘shadow volumes’ as a newDEM, that is, the upper surface of the atmospher-ic volume that is in shadow. First, three com-ponents of the vector pointing towards the Sunare defined based on solar altitude and azimuth.Then the opposite vector is used for further cal-culations. The largest of the x and y components

Fig. 7. Left: A section of theurban DEM of Szeged (pixelresolution 1 m). Right: Shadowpatterns with a solar altitude of25� and an azimuth angle of135� (southeast)

Fig. 6. The raster DEM converted from a3D vector database covering the city ofSzeged used in the current study (pixel re-solution¼ 2 m)

Computing continuous sky view factors using 3D urban raster and vector databases 117

are scaled so that the movement is equal to thepixel size of the DEM and the z component isused as a subtraction value for the translatedDEM. If the DEM is translated by the x and ycomponents and at the same time a reduction inheight by the z component is made, part of theshadow volume is produced. By continuing trans-lating and lowering by multiplies of the vectorand taking the maximum of this volume with thatpreviously calculated, the whole shadow volumeis built up as a new DEM. The process is stoppedwhen all levels are zero or translation has shiftedthe volume right off the image. To reduce theshadow volume to an actual map of shadows onthe roofs and ground the original DEM is sub-tracted from the shadow volume and a Booleanimage is produced where pixels with a negativeor zero value are those exposed to sunlight andgiven a new value of 1, and positive values are inshade and given a new value of 0 (Fig. 7, right).For a more detailed description of the shadowcasting algorithm, see Ratti (2001) and Rattiand Richens (2004).

By using the shadow casting algorithm it ispossible to calculate SVF (given here as SVFr –i.e. SVF computed by the raster based method)for all pixels in a DEM by generating 1000 shad-ow maps where solar altitude and azimuth arerandomly chosen for each separate shadow map.To get correct SVFr values, generated shadowimages with computed vectors based on artifi-cially large solar altitudes must have a higherweighted coefficient than a point closer to thehorizon, according to heat transfer theory. Thisis done by using the sum of the cosine weightedelemental solid angles in the whole hemisphere.The SVFr images are the average of the 1000different shadow images produced. The shadowcasting algorithm was validated by comparisonbetween extracted values from a DEM and SVFvalues derived from hemispheric photographs inG€ooteborg with very satisfactory results (Lindberg2005).

Investigating the spatial distribution of theSVFr values for selected areas representing dif-ferent built-up types in Szeged (Fig. 8), we get,

Fig. 8. Spatial distribution of SVFr in some selected typical cells in Szeged and their averages

118 T. Gal et al.

very similar pictures to the corresponding onesin Fig. 5.

4. Results of calculations

4.1 Spatial distributions of SVF valuesand comparison of methods

As a first step, we compare the calculated SVFvalues to the ones of the analytical method givenby Oke (1987) for two idealized cases: (i) aninfinitely-long canyon flanked by two parallelbuildings of equal height (canyon width 20 m,building height 12 m) where the SVF calculationwas done for the mid-point between the build-ings, and (ii) a circular basin with walls of equalheight (radius 10 m, wall height 12 m) where theSVF calculation was done for the centre point.The analytical computation used these equations(Oke 1987) is:

SVFcanyon ¼ cos2� and SVFbasin ¼ cos �

where, � is the elevation angle from the centre tothe wall.

As a second step, we calculated the SVF valueswith both of the methods for two idealized cases.

The first is an infinitely-long canyon (in the cal-culation we used two 3 km long, 20 m wide and12 m high buildings separated by a 20 m street).The second is a circular basin (in the calculationwe used one circular 10 m high building with a20 m wide space around the centre). Table 1 showsthe vector method gives almost the same valuesas the analytical, while the raster method givesslightly larger values than the analytically com-puted value, but the difference is negligible.

Figure 9 shows the spatial distribution ofthe cell averages of SVF calculated by the vectorand raster based methods. The cell averages ofSVFv and SVFr range between 0.616–0.999 and0.641–0.999, respectively, in the study area ofSzeged. It is generally true that cells located nearthe city border have high mean SVF values andcells near the centre have low values. However,among the sampled cells there are cells with lowSVF values at the city border because of the largehousing estates where high rise buildings are lo-cated (see also Fig. 5). In order to compare thecell averages of the two SVF methods, SVF dif-ferences were calculated for each cell: �SVF ¼SVFv � SVFr (Fig. 10). In most cases the differ-ences are negative i.e. the SVFr values are largerthan SVFv. However, absolute values of the dif-ferences are less than 0.005 in one third of thestudy area. The largest deviation between the twomethods is �0.037 and differences range from�0.025 to �0.037 in only 15% of the area. Incells where �SVF differences are greater than�0.02 the built-up ratio is usually greater than58% (Unger et al. 2001). From the city centretowards the suburbs the built-up ratio decreasesas do �SVF values.

Table 1. Result of comparison between SVFv, SVFr and theSVF value using an analytic calculation for two idealizedcases

SVF in aninfinitely-long canyon

SVF in acircular basin

SVFr 0.6543 0.4170SVFv 0.6402 0.4086SVFanalytic 0.6402 0.4098

Fig. 9. Spatial distribution of(a) SVFv (cell averages by vec-tor based method) and (b) SVFr

(cell averages by raster basedmethod), as well as the annualmean of �T [�C] (April 2002–March 2003) in Szeged

Computing continuous sky view factors using 3D urban raster and vector databases 119

Figure 11 shows the regression line and thecorrelation between the cell averages by raster(SVFr) and vector (SVFv) based calculation.The deviation is minimal and the coefficient ofdetermination (r2) is 0.9827. The point of inter-section of the regression line with the y axis is atthe origin. The slope coefficient of SVFv is a bitlarger than 1 (�1.012) which confirms that dif-ferences between the two methods are small andmostly negative, i.e. SVFr values are slightlylarger than the corresponding SVFv values.

This slight difference can be explained in thefollowing way. As we earlier mentioned, there issome tendency in the difference between the ras-

ter and vector based methods depending on thelocation of the cells within the urban area. In thecentral (densely built-up) areas the average SVFr

values are higher than the corresponding SVFv

values. The possible reason for this lies in differ-ences between the raster and vector based calcu-lations (Fig. 12). In most cases the smallest SVFvalues can be found near the walls of buildings.Applying the vector based method we includethis small individual SVFv value in the calcula-tion of the cell average. On the other hand, withthe raster based method the SVFr value at a pointwhich is closer to the wall than half the pixelresolution cannot be calculated because the cen-tre of the pixel overlaps the building (the SVFr

value should refer to the roof) so it is not includ-ed in the pixels used to calculate the cell average.In areas where the built-up ratio is high this situ-ation is frequently encountered so differences be-tween the two SVF cell averages are larger.

There are two other factors causing cell av-erages of SVFr to be slightly higher than cellaverages of SVFv at high values of averageSVF. Firstly, ground elevation is included in theraster DEM which could increase SVFr in certainareas to a small extent. Secondly, the vectormethod only includes buildings within a distanceof less than 200 m from the point of SVFcalculation. If buildings outside that proximitywere included, increased hemispheric obstructionwould have resulted in smaller SVFv. The shad-ow casting algorithm used in the raster methodhas no such horizontal limitation except for theboundaries of the DEM itself. The reason whythe difference between SVFr and SVFv is higher

Fig. 10. Spatial distribution of the difference betweenthe SVF values of cells calculated by the applied meth-ods: �SVF ¼ SVFv � SVFr (a: 0.005>�SVF ��0.005; b:�0.005>�SVF ��0.015; c: �0.015>�SVF ��0.025; d:�0.025>�SVF ��0.037)

Fig. 11. Relationship between the cell averages of SVFcalculated by the applied methods in Szeged (n¼ 103)

Fig. 12. The different approaches of the raster and vectorbased method (a: SVF measurement point, b: centre of thepixel)

120 T. Gal et al.

in the cells with high built-up areas is becausethe mean height of the buildings is usually higherin those cells.

4.2 Limitations, possibilities

Local municipality data can be very suitable inthe production of a high resolution DEM of ur-ban geometry. One limitation is that the con-version from vector to raster format results inloss of information, another limitation is data ac-cessibility. Datasets that include building heightsare still rare.

The advantage of using raster images insteadof vector data is the possibility to examine largerareas (e.g. cities) because geometric calculationsare faster. The computation time of the shadowcasting algorithm increases quadratically as thenumber of pixels increases. Hence, if large areasare to be studied image resolution must be de-creased to speed up the computation. The com-putation time of the SVFr image covering Szeged(n¼ 7,562,500) was 38 h of a regular PC whereasit takes 12 days with the vector based method.Lindberg (2005) shows that in the city centre ofG€ooteborg (mean canyon width¼ 7 m) pixel sizecan be increased to approximately half the can-yon width i.e. 4 metres without any appreciableloss of information and therefore computationaltime is decreased.

5. Application – UHI-SVF relationshipin Szeged

First, we examine the spatial distribution of an-nual mean �T calculated from the 35 nights ofmeasurement (see Sect. 2). The effects of differ-ent weather conditions (more or less favourablefor heat island development) are amalgamated inthese �T averages. Figure 9 shows the most ob-vious feature of the yearly UHI pattern is thealmost concentric shape of the isotherms. Highest�T values are found in the centre (>2.5 �C) andthe mean �T ranges between 0.74 and 2.72 �Cwithin the study area. A deviation from thisshape occurs in the north-eastern part of the city,where the isotherms stretch towards the suburbs.This can be explained by the effect of the largehousing estates with high concrete buildings thatare mainly located there. A second irregularitymay be due to the cooling influence of river

Tisza. Along the river isotherms are drawn backa bit towards the centre (see also Fig. 1). Thethird irregularity can be found in the western partof the city, where large open (green) areas arelocated (see also Fig. 1).

Secondly, we examine the relationship be-tween the intra-urban variations of SVF and�T. Low SVF values occur together with highUHI intensities in the central parts and vice versain the suburbs (Fig. 9). The ‘‘toes’’ of the iso-therms (e.g. in the north-eastern part of the area)are in line with the drop of the SVF. Since thereare no significant differences in the magnitudesand in the intra-urban variations of SVFv andSVFr (Fig. 9a and b) these interpretations applyto sets.

In order to demonstrate the above mentionedrelationship, linear regression is used, where theapplied parameters (as cell averages) are the fol-lowing:

(i) independent variable: sky view factor (SVFv

or SVFr),(ii) dependent variable: annual mean UHI inten-

sity (�Tyear).

There is a strong linear connection betweenSVFv and �Tyear in the studied urban area(Fig. 13). According to the statistical measures,about 63% of the intra-urban variations of tem-perature excess can be explained by variations ofSVF. The relation is inverse (i.e. negative) at the1% level of significance (n¼ 103). ApplyingSVFr as the independent variable gives very sim-ilar results (Table 2). This is about a 15–20%)improvement in explanation compared to earlierwork in Szeged (Table 2). In the first of theearlier studies the SVF was determined by an

Fig. 13. Relationship between the SVFv and �Tyear inSzeged (n¼ 103)

Computing continuous sky view factors using 3D urban raster and vector databases 121

analytical (surveying) method (referred to asSVFs(route)) in which two elevation angles to thetop of the buildings were measured normal to theaxis of streets in both directions at points alongthe measurement route at 125 m intervals in thesame study area (Bottyan and Unger 2003; Unger2004). In the second study the SVF was deter-mined by the vector based method (referred to asSVFv(route)) used in the present study, but the cal-culations were applied at points along the sameroute in 20 m intervals (Unger 2007).

6. Conclusions

Two different methods to derive continuousimages of SVF covering large urban areas areexamined. The first method utilizes a vectorbased algorithm whereas the second one com-putes SVF using a high resolution raster DEM.The spatial data consists of 3D building struc-tures and ground elevation. Relationship betweenurban geometry, quantified by SVF, and varia-tions of intra-urban nocturnal air temperatureare also investigated. Results show that:

(i) Both methods result in very similar valuesfor urban geometry.

(ii) By using the vector based method smallSVFv values (e.g. at the points closer to wallsthan half the pixel resolution) can be includ-ed in the calculation of the cell average.When averaging SVF over a large area (e.g.500 by 500 m) an insignificant overestima-tion occurs using the raster based method.

(iii) The raster based method is significantly fas-ter than the vector based method.

The study utilized a large number of are-al means of SVF and �T. Values were re-lated to a large sample area and based onnumerous measurements. Measured temper-ature values at sites might show large vari-

ations because of the influence of micro-variations of the immediate environments.Moreover, these values can be affected byadvective effects from a wider environment(source area). Therefore, the applied areasextended over several blocks in the city.

(iv) In clarifying the SVF-UHI relationship theusefulness of the suggestion by Unger(2004, 2007) of applying areal means is con-firmed. In accord with previous work theresults in Szeged confirm that urban surfacegeometry (described by SVF) is a significantdetermining factor of the air temperaturedistribution inside the city. Both the vectorand the raster approaches of deriving arealmeans of SVF are shown to be powerfulways to obtain a general picture of the geo-metric conditions for relatively large urbanenvironments.

Acknowledgements

This research was supported by the Hungarian ScientificResearch Fund (OTKA T=049573) and by FORMAS, theSwedish Research Council for Environment, AgriculturalSciences and Spatial Planning. Helpful comments fromanonymous reviewers are acknowledged. Special thanks toTim Oke for his additional comments and clarifying editorialwork on the manuscript.

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Raster based �Tyear¼�4.76� SVFþ 6.03 �0.795 0.6320 1 Current study

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