a. Building-height data collection

Building-height data collection took about three months for the three city areas. Planar dimensions of the buildings were available from 1:2000 scale planar maps stored in digital form. All buildings on the map were checked and identified on site. Building footprints were in some cases inaccurate and were corrected by measuring them on site. Building heights were measured from the ground level from two sides when possible. Building-height data were measured using a distance meter Leica DISTO mounted on a tripod at ground level, positioned 2–3 m from the building façade. This instrument is a laser diode consisting of a laser pulse of known frequency split into a reference beam and a measurement beam by a system of mirrors. Because of the delay time between the reference ray and the external trajectory of the ray of measurement, the difference of phase between these two signals is proportional to the distance between the distance meter and the reflecting surface. To make use of the full nominal accuracy of the instrument (2 mm) we placed it in front of each building facade and performed sets of three auxiliary measurements. Figure 2 shows the typical instrument setup with the three auxiliary measurements. The figure also shows photographs of one of the street canyons and the DISTO instrument. As the laser measuring points have to be on a straight line in a vertical plane, the use of the tripod avoids the possibility of shaky measurements. The second auxiliary measurement must be made perpendicular to the desired length. This can be done by using a bubble level allowing for a simple horizontal leveling of the instrument as the distance meter is provided with a magnetic support for attaching accessories. The estimated building height is the result of the three measurements combined through their squared, triangle geometrical relationships.

While the distance meter has a resolution of 2 mm, the laser dot resolution can be up to few centimeters for each set of measurements. Errors introduced by the operator can be significant for very tall buildings as some difficulties may arise in performing the auxiliary measurement along a vertical plane (label 1 in Fig. 2). The instrumental errors are always negligible in comparison with those introduced by the operator. To minimize them, the distance meter was equipped with a telescopic viewfinder with fourfold magnification.

By performing some tests on building of known height we estimated that, for building heights less than 40–50 m, errors associated with the overall building height measurement are less than 1 m. Such measurement errors were considered acceptable for our research purposes.

For the representation of buildings on the map, some approximations were made:

• a porch inside a group of buildings was not represented;

• sparse trees, walls, roof overhangs, turrets of staircases at the top of some buildings, buildings under construction, etc., were neglected;

• over the whole study area, the road level was assumed to be horizontal;

• the representation of the dome of a church was also approximated. It was drawn as a cylinder of the diameter of the dome, but of smaller height to simulate a cylinder of similar volume;

• the trees of the Public Gardens were represented by a square plan shape with a constant height equal to the average tree height.

b. Construction of the DEMs

The construction of the actual DEMs consisted in displaying individual building heights on the original planar maps and in forming new vector layers where the basic units to be mapped were structures of different heights. Every building is described by a 2D polygon with specific attributes corresponding to its footprint and rooftop elevation. DEMs of the three study areas were manipulated using ESRI ArcView GIS 3.2 tools to convert them into a raster image, that is, in a form appropriate for the application of image processing techniques. Figure 3 shows the various phases of the DEM construction from the aerial photograph to the DEM in raster form. The intermediate phases consist of using planar building maps in digital form, editing building footprints if necessary with CAD software, adding building-height measurements to them and representing the maps as a vector DEMs. Once the DEMs are in raster form they can be analyzed using image processing techniques.

In this study we compute urban morphometric parameters (explained in the next section) by using previously developed computer programs and by developing new ones within Matlab’s Image Processing Toolbox in which images were represented as square matrices and pixels were coded using 8 bits (though higher resolutions could be used in principle).

In the vector to raster transformation, care should be taken in choosing the appropriate correspondence between image pixel and building height. This was done by using a grayscale so that each pixel has a level of gray proportional to the building height. For 8-bit images this corresponds to 256 levels of gray. Each image has its own scale so that the value 255, displayed as white on a raster structure, is assigned to the road level (0 m) and the 0 value corresponding to the black color is assigned to the maximum building height. Typically, if building-height accuracy is 1 m, not all 256 values of gray are used because buildings normally are shorter than 255 m. Instead, particular shades are used for a given building height in such a way to minimize the errors arising from the conversion from the grayscale to the building height. The choice of the shade interval can be made according to the building-height distribution histogram as done in remote sensing data representations. This way of assigning the pixel level makes full use of the range of gray shades and more clearly represents building heights.

A further point to make concerns the choice of the pixel size (this is separate from the issue above). One of the problems related to the DEM construction in a raster form, obtained as a data conversion from vector structures, is that the pixel size should be small enough not to affect the positional accuracy of building footprints. This could be solved following general rules adopted in digital photogrammetry. On the other hand, the size of the pixel should not affect the values of the morphometric parameters to be calculated. From the theoretical point of view, one should choose the pixel size that satisfies both requirements and which is the lower of the two. However, in the context of this work, it is sufficient that the choice of the pixel size is made only in relation to the calculation of the morphometric parameters without taking into account the problem of the positional accuracy. This is further addressed below.

c. Estimation of morphometric parameters for three areas

The originally derived DEMs for the three areas Le1, Le2, and Le3 were analyzed to calculate building statistics as well as several building morphometric parameters. In particular, λ_p, λ_f , and z_H (the average height weighted with building frontal area) are calculated as

View Expanded

View Expanded

View Expanded

where H_i and A_p,i are respectively the height and the planar area of the ith building, while A_f,i(θ) is its frontal area perpendicular to the wind direction θ. The A_T is the total site planar area, λ_f represents the total area of buildings projected into the plane normal to the incoming wind direction and is a function of orientation. For a given wind direction, λ_f is smaller if the wind angle is oblique, rather than perpendicular, to the front face of the building. That is, A_f,i is multiplied by a sin(θ) function dependent on wind angle relative to that building face.

In addition, we calculated four other statistical parameters: the average building height and its standard deviation, and the average building height weighted with the planar area and its standard deviation. The last two, more meaningful from the fluid dynamics point of view, are defined as

View Expanded

View Expanded

Starting from these parameters, we computed the zero-plane displacement height z_d and roughness length z₀ using the equations derived by Macdonald et al. (1998):

View Expanded

View Expanded

with α = 4.43, β = 1.0, κ = 0.4, and C_D ∼ 1.

As discussed previously, the particular technique used to derive those building morphological parameters requires an assessment of the influence of image resolution on the results. This is particularly relevant when using those parameters within urban dispersion models. One may find that an error of 10% on the calculated parameters is acceptable given the large approximations usually made in those models. More importantly, one may find that a variation of 10% in the value of the building morphological parameters is irrelevant from the fluid dynamics point of view. This needs to be evaluated through detailed numerical flow simulations.

As described in the previous subsection, the construction and analysis of DEMs consists of converting vector data into a raster image and then storing this image in a specific format. This format should be chosen in such a way to avoid, or at least minimize, loss of information relevant for urban morphometry analyses. For the same reason, image spatial resolution is important, also because it can affect the edge detection occurring in several algorithms; for example, those related to λ_p and λ_f calculations. As a consequence, it is appropriate to investigate how the image storage format may affect results before interpreting them. Indeed, even when DEM analysis by image processing techniques has been carried out (i.e., Ratti et al. 2006), a suitable sensitivity analysis has not always been done. We performed several tests on many building arrangements of different complexity to investigate how specific image formats, such as TIFF, BMP, JPEG, and GIF, as well as the image spatial resolution influence the accuracy of the calculated parameters. Details on the various tests and specific results of the sensitivity analyses are reported in the appendix. In general, all formats except JPEG do not influence results but the image resolution does. The way image resolution affects the calculation accuracy is rather complex, because it depends on the specific building arrangements, shape, and orientation. The various tests performed suggest that to minimize errors, the original DEMs should be rotated in such a way as to get most of the building facades aligned with the external raster frame. This procedure allows us to reduce the effect of changing the intrinsic positional regularity of the pixels.

The sensitivity analysis shows that the accuracy of the λ_p parameter improves with increasing image resolution. This does not happen for all other parameters, which, instead, do not behave linearly with image resolution and appear to be more dependent on the specific building arrangement rather than the image resolution. To identify a general rule for handling errors due to image resolution, it is reasonable to adopt the criterion of choosing that image resolution that does not affect the value of λ_p. Errors on the other building morphology parameters are then calculated on the basis of the chosen image resolution. Table 1 summarizes the errors related to all calculated parameters for the case when λ_p agrees with its theoretical value, at least within the first two significant digits. The errors can be large on both roughness length and displacement height. We anticipate that errors are more significant for cities that tend to have irregular building arrangements and orientations as it is typically the case of southern European/Mediterranean cities.

a. Southern European DEMs: General description

Figure 6 shows DEMs in grayscale for the three areas of Lecce. We reiterate that each image has its own scale and that black corresponds to the maximum building or tree height in that specific area (32 m for Le1 and 28 m for the other two). To facilitate the interpretation of these images, building distribution histograms are shown for the three areas in Fig. 7, with and without the trees of the Le3 area. To more clearly emphasize the natural breakdown of building distribution in each neighborhood, a height interval of 3 m, which is typical for each storey in Lecce, was chosen. Focusing on the building height distribution only, without trees, it can be seen that Le1 is the most uniform among the three areas, with a similar number of short and tall buildings. Le2 has the highest number of short buildings and few tall buildings. Le3 is characterized by buildings of intermediate height. Overall, this area has a bell-shape building-height distribution around a mean value of 10–12 m, corresponding to three to four stories. This distribution is altered substantially by the trees. Trees act as additional obstacles to the flow, and therefore, they have been included in the basic building height statistics and, most importantly, in the derivation of fluid dynamics parameters as discussed in the next sections.

b. Southern European cities versus northern European and North American cities: First analysis

DEMs shown in Fig. 6 have been analyzed using the image processing technique to derive the morphometric parameters that have been illustrated in detail in section 3 and 4. Summarized in Fig. 8, the results are compared with those of existing DEMs of parts of three northern European and two North American cities, which have been recalculated with the exception of Los Angeles, for which we used values from Burian et al. (2002), directly. From Fig. 8 we observe a substantial difference among the five urban morphometry datasets. European cities have an average building height H of 12–20 m and σ/H values typically between 0.3 and 0.4. On the contrary, the North American cities have a much larger range for both parameters. For European cities the planar area index λ_p is around 0.40, a reflection of their typical layout with buildings close to each other and narrow streets. For the two North American cities λ_p is considerably smaller. This might not be the case for all North American cities because such cities as Boston (Massachusetts), New York (New York), Chicago (Illinois), and others have a much larger λ_p (Burian et al. 2007) more similar to European cities. Differences are larger for the λ_f parameter: it is the largest for Lecce (∼0.5), smaller (∼0.3) for northern European cities, and the smallest (∼0.25) for the two cities in North America.

An additional way to derive building shape information is by looking at polar diagrams of λ_f variation with wind direction θ. As an example, Fig. 9 reports λ_f(θ) for Le2, Toulouse, and Salt Lake City, chosen to represent the three geographic regions (southern Europe, northern Europe, and North America) investigated in this study. The first two cities have a circular symmetry, with λ_f(θ) almost constant with wind direction, while Le2 has an increase in the north–south direction because most building facades are oriented east to west. In addition to the particular shape of λ_f with orientation, the plot immediately shows the comparative difference in frontal area densities among the cities investigated. It further emphasizes the higher building densities of European cities with respect to the ones in North America.

As previously discussed, we also calculated H, the average building height, and z_H, the building-height weighted with the building frontal area. As pointed out by Ratti et al. (2002), z_H is the parameter that, in principle, should be used in the calculation of the aerodynamic roughness. This is because it explicitly accounts for some features of building shape, synthesizes the overall resistance to the wind, and, in this respect, is fluid dynamical relevant. By comparing the two building-height averages for the DEMs, we see that z_H is slightly smaller than H for Le1 and Le2, and typically larger for all DEMs analyzed. The difference between the two building-height averages is much larger for the two North American cities, with respect to the other DEMs. This is a first indication that the overall building frontal area of the European cities investigated here is smaller than that of the two North American cities. This also indicates buildings which are wider rather than taller in these European cities. The difference between H and z_H is reflected in the derived zero-plane displacement height, z_d, and the roughness length z₀, calculated with Eqs. (6) and (7). First of all, z_d and z₀ calculated with z_H in place of H are not significantly different for the European cities. The difference ranges from about 3% for Toulouse and London to 9% for Berlin. Instead, significant differences are observed for the DEMs of the two North American cities for which the use of z_H instead of H in the z₀ calculation leads to an increment of about 46% for Salt Lake City and 68% for Los Angeles. This and the z₀ results for Lecce are consistent with Ratti et al. (2000) in that, although the use of z_H in Macdonald’s formulas is generally appropriate, it is not adequate for the North American cities analyzed here. The reason for this is that Macdonald’s formulas have been derived for cubic building arrays. They tend to underestimate z₀ for real cities, because those formulas do not take into account building-height variability. The use of z_H is appropriate for cities characterized by relatively large λ_p values. If λ_p is very small, as in downtown areas of American cities, the use of z_H is not required. This is confirmed by the agreement between the z₀ value for downtown Los Angeles, obtained by Ratti et al. (2002), using H and independently calculated by Burian et al. (2002). In general, the size of the northern European and Lecce sites (400 m × 400 m), used in this study, would not be large enough to perform a z₀ calculation; however, this simplification can be accepted as these sites may be considered representative of larger urban areas with similar morphometric characteristics or neighborhoods with similar lambda parameters. It should be pointed out that even though the roughness length, calculated solely on the basis of geometric considerations, might be important in the derivation of some flow characteristics in urban environment applications, the use of z₀ is questionable. In general, the use of z₀ in urban flow and dispersion models should be avoided or limited. Its determination is controversial because of the intrinsic difficulty linked to limited fetch, typical in urban areas, which prevents the flow to be in equilibrium with the changing surface (Belcher et al. 2003). It is important to bear in mind that the derivation of z₀ based on geometrical considerations only, is a first estimate, but its aerodynamic properties need to be evaluated on a case by case basis. Additionally, doubts remain about the suitability of Macdonald’s formulas for z₀ in complex geometries. For this and other reasons, it is worth investigating other building morphometry parameters that can replace, among others, the use of z₀ in urban flow and dispersion models, as well as in urban representations within mesoscale models. Obviously, the choice of a particular set of building statistical parameters depends upon the specific application. In the following, we show how λ_p, and λ_f as a function of elevation, are suitable for representing a city or neighborhoods in urban canopy models and mesoscale flow models. Obviously, other choices to represent a city based on morphometric parameters can be made. For example, one may use lookup tables of building and vegetation descriptors, including fractional weights of small versus tall buildings, vegetative fraction, etc., as well as their spatial variations. In this context it is important to include intracity variations among neighborhoods through the variation of the lambda descriptors. An alternative way to describe a city is in terms of its population density and distribution. This might be used to derive anthropogenic heat fluxes within the city. Studies in this direction have been initiated by several research teams (Ching et al. 2009) with a focus on cities in North America. Studies on city’s morphology and city’s categorization based on the building distribution and other parameters in Europe and in other continents are isolated and far from being comprehensive.

c. Southern European cities versus northern European and North American cities: Further analysis

As discussed in the previous sections, lambda parameters λ_p, and λ_f , as a function of elevation, can be used directly in flow and dispersion models as recently done by Di Sabatino et al. (2008) and Solazzo et al. (2010, manuscript submitted to Bound.-Layer Meteor.). Even though the building statistics of city’s portions illustrated in this study is too limited to allow any generalization, we argue that the direct comparison of lambda parameters can be used to infer city building structure (wider or taller buildings) when detailed building data are not available. Also λ_f(z) and λ_p(z) synthesize the vertical distribution of a city. This is separate from having detailed building geometry. Specific information about building arrangements within urban areas or neighborhoods as well as building shapes can be derived directly from the analysis of λ_f(z) profiles as shown in Fig. 10. We reiterate that λ_f(z) describes the variation of the frontal area density with height, which illustrates the resistance to the wind at various heights. This has direct implications on drag force calculations at various heights. Looking at Fig. 10, we observe a spike close to the origin, due to the presence of tall buildings. This spike is very pronounced for the North American cities that typically have skyscrapers in their central business district. It is less evident for cities in northern Europe, and absent for Lecce, where building heights show little variation. Again, any generalization should be avoided because those features reflect those of the datasets analyzed. However, some broad indications of the different city configurations in the three geographic regions considered can be extracted based on Fig. 10. There is an indication of larger packing densities in Lecce with wide and low buildings. Note that all the profiles for λ_f(z) are calculated for winds from the north. This particular orientation was chosen as winds blow primarily from this direction. The results may be easily extended to other wind directions. Similar curves are obtained for λ_p(z) profiles as shown in Fig. 11.

If we focus on the three Lecce areas, we see that the λ_f(z) profile for Le1 has a slightly different curvature than Le2 and Le3 profiles, which, in turn, are more markedly discontinuous. This is of interest for investigation of intracity variations of the lambda parameters, considering that Le1 and Le2 are adjacent areas. Similar considerations can be made from λ_p(z) profiles. Overall, profiles are more similar among the European cities than those for Los Angeles and Salt Lake City. This may be an indication of common features among the European cities, which are generally more compact and less regular than the ones in North America. Other observations can be made from the derived statistical parameters keeping in mind that all datasets with the exception of Le2 include building heights only without trees or vegetation, and therefore some care should be paid in using the results directly.

d. Toward a synthetic representation of a city

The choice of a particular set of building statistical parameters to represent a city depends upon the specific application, which needs to be evaluated before using. For flow and dispersion modeling applications, as well as for mesoscale modeling, it is useful to describe an urban area or a neighborhood through a small set of parameters rather than explicitly include all buildings.

On the basis of λ_f(z) and λ_p(z) parameters, we can argue that different flow patterns may be expected within a city. Also, pollution dilution potential of a given city is linked to city’s breathability a result of the combined effect of flow transport and entrainment within the city (Buccolieri et al. 2010). This is expected to be dependent on λ(z) parameters, their spatial distribution (intracity variation) and the vertical building height variability (e.g., σ/H values). The following arguments clarify the previous statements. We explain how λ_p and λ_f parameters, as well as λ_f(z) and λ_p(z) can be used to extract information about the building distribution of a city, and the average shape of the “city’s building envelop.” The purpose is to show how a combination of those lambda parameters can be used to capture the important geometric features of a city, which in turn influences flow patterns within urban areas or within specific neighborhoods. First we consider λ_f and λ_p, then we extend the analysis to λ_f(z) and λ_p(z).

One way of extracting information about building shape is by direct evaluation of the λ_p to λ_f ratio given by

View Expanded

where B is an average value between the width and the depth of buildings (see Fig. 4) and the overbar indicates the average over all azimuths. It shows that the combination of both lambda parameters can be used to determine whether a city has grown more horizontally or vertically. Based on the λ_f and λ_p values in Fig. 8, these ratios indicate that northern European cities and Salt Lake City are characterized by buildings with heights smaller than breadths (ratios between 1.3 and 2) whereas buildings in southern European cities and Los Angeles, have heights larger than, or comparable to, their breadths (ratios between 0.7 and 0.9). Additional information on the average building shape can be derived from these ratios as follows.

One may start by considering the ith building of height H_i, depth L_i, and width W_i. Here, W_i always denotes the horizontal dimension of the building façade facing the incoming wind, while L_i is the other horizontal dimension. Its planar area A_p,i is L_iW_i. For simplicity, we assume that the ith building is positioned in such a way that the building frontal area is just A_f,i(θ) = H_iW_i. This simplification is not too restrictive, because one can always find a wind direction θ for which most of buildings have a facade in the direction perpendicular to the wind. Then, replacing A_p,i and A_f,i with the respective λ_p and λ_f definitions given by Eqs. (1) and (2) yields

View Expanded

where H_W and L_W are the average building height and the average depth of buildings weighted by their width, respectively. Similarly, if we considered the direction perpendicular to θ, that is, , the frontal area is H_iL_i and, therefore,

View Expanded

Consequently, the comparison of these ratios indicates approximately whether the buildings have square or rectangular footprints. By applying the above reasoning to all cities studied, we conclude that both northern European cities and Salt Lake City have mainly short rectangular buildings, while southern European cities and Los Angeles have mainly cubelike buildings. Even though some care should be taken in adopting this reasoning, because the averaging process might lead to wrong conclusions on the actual building shape, the specific result can be interpreted as the “average shape of the neighborhood building envelop” relevant to the flow. This needs to be appropriately assessed by detailed flow calculations using for instance CFD models.

Other observations can be made from the analysis of λ_f(z) and λ_p(z) profiles shown in Fig. 10 and Fig. 11 as discussed earlier. For example, it is clear that small values of both λ_f(z) and λ_p(z) indicate a low density of buildings with heights equal to or larger than z. To highlight similarities and differences of the cities investigated, Figs. 12a,b show λ_f(z) and λ_p(z) profiles normalized with their corresponding value at the ground level versus elevation. The latter has been normalized with H_max, the maximum building height. This choice is not arbitrary but it is relevant fluid dynamically as recently proven by Xie et al. (2008) who have shown that the tallest buildings within a neighborhood area have a dominant effect on the overall drag exerted on the flow. The normalization with H_max represents a way of showing how a city’s neighborhood is “seen” by the wind, facilitating the comparison with other cities and highlighting features that are common or not common between them. Looking at the figures, the difference between U.S. and European cities is apparent. The former have almost the same profile, while the European cities are characterized by a large spectrum of profiles. Although, once again any generalization should be avoided, this suggests that these European cities have different architectural features, while the two U.S. cities have similar ones. In Fig. 12a, three layers can be identified: the first layer for z/H_max < 0.2, the second one for 0.2 < z/H_max ≤ 0.6, and the last one for z/H_max > 0.6. Near the ground, λ_f(z) is almost constant for European cities, while for U.S. cities, this is the layer where λ_f(z) varies the most. In the intermediate layer, the behavior of λ_f(z) for European and U.S. cities is reversed. Finally, at the highest elevations λ_f(z) is constant for both U.S. and northern European cities. Here, only Lecce shows a different shape; that is, λ_f(z) keeps on varying. Since λ_p(z) profiles show the same features of λ_f(z) profiles, we can derive important information about the vertical structure of the cities. The two U.S. cities can be thought of as having two main types of buildings: high-rise and very short buildings. However, the spike of the profiles near the origin shows that the majority of buildings belong to the second category, and only a few high-rise buildings are present. An opposite configuration appears for the southern European city, whose profiles confirm the presence of a considerable number of buildings distributed within a relatively large range of heights. The northern European cities can be located between these two limits. London has a profile more similar to that found for two U.S. cities, because of the spike near the origin and the presence of a spectrum of λ_f values in a restricted range of low z values. The Toulouse profile shows a similar shape, but is shifted up, slightly. This fact, and a larger value of λ_f near the origin, suggests a slightly larger number of tall buildings. Finally, Berlin is characterized by a very low variability of λ_f and λ_p, indicative of the most homogenous city among all those investigated.

We further observe that all European cities have almost the same values of H and σ/H, but different shapes of λ_f(z) profiles. More explicitly λ_f(z) coupled with λ_p(z), incorporates the information contained in σ/H, and provides a description of building height spatial variability more like the real spatial configuration of a city. The U.S. cities are characterized by very large values of σ/H, suggesting large building-height variability. However, lambda profiles show that these cities are rather homogeneous, despite the large σ/H, the result of having few high-rise buildings.

The estimation of λ_p and λ_f parameters and the analysis of their profiles versus elevation, suggest how to represent a city in a compact and effective way. The two North American cities have a sparse (low values of λ_p and λ_f) canopy of two building heights: tall buildings (cubelike shape for both), and short (compared their respective H_max) buildings (narrow for Los Angeles and wide for Salt Like City). Southern European cities have a dense canopy made up of tall (compared to their respective H_max) cubelike buildings. An intermediate configuration can be hypothesized for the northern European cities. For example, most buildings in Berlin have similar heights, with tall and wide buildings characterized by a low value of λ_p. For city configurations like this, it becomes difficult to conjecture a possible wind regime and its implication for city breathability. This case requires a quantitative evaluation of the building effects on flow and consequently on dispersion characteristics. The presence of a low spatial building-height variability (a negative effect with respect to city breathability) and a low value of built-up area index (positive effect) needs to be assessed to establish which one is the most dominant by using, for example, CFD models. Furthermore intracity variability of morphometry is expected to be relevant in this context. Cities are made up of different neighborhoods and the “physical neighborhood” might be identified by its lambda parameters. Possibly, cities may be better categorized by the types and distribution of neighborhoods.

The analysis presented in this paper has only hinted on the possibility of including the effect on the flow due to intracity variations of the morphometric parameters. This is strictly dependent on the definition one adopts for the neighborhoods. Once this is done the lambda categorization presented here can be used as a framework to interpret the overall effect of the city on the flow. This aspect is expected to be especially relevant for large cities (including megacities), which typically incorporate many land-use types and require additional investigations. This is left to future research.