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  • 1. The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010 On the effects of complex urban geometries in mesocale modelling Adil Rasheeda, Darren Robinsona, Djamel Lakehal b a EPFL ENAC, Lausanne, Switzerland ( b ASCOMP GmbH, Zurich, Switzerland ( ABSTRACT: Urban parameterizations that are developed can be applied to only those urban geometries which can be represented by a regular array of cubes. However, in a real city we tend to encoun- ter complex geometries which do not obviously match such simplified ones. Yet all of the urban parameterizations thus far developed share the assumption that a city is made up either of a regu- lar array of cubes or of infinitely long canopies. The inputs to these models which include street width, building width, building density and a statistical representation of the building heights, are generally obtained through quantitative field surveys or qualitative estimates. But in performing this geometric abstraction there is no way to ensure that the total built surfaces and volumes of the simplified geometry match those of the actual city, or more importantly that the energy and momentum exchanges are equivalent. We aim here to test the hypothesis that cities can be accu- rately represented by a regular array of cubes or canopies. For this we investigate, for a particular scenario, the effects of urban complexity on the spatially averaged drag forces and shortwave rad- iation exchange. We propose a new approach for fitting an array of cubes to any realistic geome- try, so that new or existing urban parameterization schemes can be used with confidence. 1 INTRODUCTION Climate has a direct impact on cities’ energy flows due to the space conditioning (heating, cooling) needs of the buildings accommodated. This impact may be reinforced due to climate change and to the (so-called) urban heat island (UHI) effect. The corresponding changes in ener- gy demands alter greenhouse gas emissions so that there is a feedback loop. To be able to simu- late cities’ metabolism with reasonable accuracy it is thus important to have good models of the urban climate. But this is complicated by the diverse scales involved. The climate in a city, for example, will be affected not only by the buildings within the urban canopy (the size of a few meters) but also by large topographical features such as nearby water bodies or mountains (the size of a few kilometers). Unfortunately, it is not possible to satisfactorily resolve all of these scales in a computationally tractable way using a single model. It is because of this that we use a mesoscale model having a resolution of say 1 km and a domain having a size of up to a few hun- dred of kilometers. The impact of bigger scales is then forced through the boundary conditions using results from a Global model while the subgrid scales are parameterized. Such parameteriza- tions are generally comprised of an Urban Canopy Model and a Building Energy Model. It is well established that urban structures can modify the local climate: they present drag forces and generate turbulent wake diffusion and decrease wind speed Roth (2000). Furthermore buildings produce an intense shear layer at the top of an urban canopy, where mean kinetic ener- gy is transformed into turbulent kinetic energy. The thermo-physical and hygroscopic properties of urban structures are such that these tend to be rather dry, so that evaporation-transpiration is
  • 2. The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010 relatively weak. Radiation-absorption in street canyons and heat storage in buildings may also modify the radiative and energy budget, causing a city to be on average warmer than the sur- rounding areas. Due to differences in heat capacity urban and rural temperature differences tend to reach maxima during the night and minima during the day. Many parameterizations have been developed to account for these effects. However these assume a city to be comprised of a regular array of parallelepipeds. In this paper we try to investigate the importance of this assumption and we suggest a procedure for fitting real complex urban geometries to simplified equivalents to im- prove the predictive accuracy of urban climate models, the details of which can be found in Ra- sheed et al., (2010). 2 MODELLING BACKGROUND To accurately model the physics of the urban canopy, new concepts in surface modeling have been developed. These models aim to solve the surface energy balance (SEB) for a realistic 3D urban canopy. They share in common the following characteristics in their construction: (i) 3D building shapes that offer drag to air flow, (ii) separate treatment of roof, wall and street surfaces from energetic point of view, and (iii) radiative interactions between streets and walls. These models consist of horizontal and vertical representations of the urban structures. The vertical sur- faces represent building walls and the horizontal surfaces represent streets and roofs. Since, a clear distinction between these surfaces is made it is very convenient to assign different values of thermo-physical parameters to these surfaces and to model them differently. Such simple models use a highly simplified approach to compute complex radiation exchanges like in the work of Noiah (2000) which is based on view factors between the different surfaces or facets comprising the surfaces. Solar reflections and occlusions to sun and the (normally isotropic) sky are also ex- plicitly resolved. Surface temperatures, energy exchanges with the surrounding and energy sto- rage in the built material is computed via solving a set of one dimensional conduction equation for different types of surfaces. These models are broadly classified into two major categories: Single Layer Urban Canopy Models like the Town Energy Balance (TEB) model of Masson (2000) and Multilayer Urban Canopy Model like that of Martilli et. al (2002). Almost all multi- layer urban canopy models (e.g. Kondo, 2005; Martilli, 2002) are mathematically represented by: ∂u ∂  ∂u  =  k zm  + Qu ∂t ∂x  ∂z  ∂v ∂  ∂v  =  k zm  + Qv (1) ∂t ∂x  ∂z  ∂θ ∂  ∂θ  =  k zθ  + Qθ ∂t ∂x  ∂z  where u and v are the horizontal velocity components and θ is the potential temperature and t is time. The basic assumption here is that a city is represented by a regular array of cubes (Figure 1), and the terms k zm , k zθ , Qu , Qv , Qθ represent the effects of drag, shear and other sources which are parameterized in terms of the parameters B1, B2, W1, W2 and street orientation. The term Qθ represents the energy exchange with the buildings, which depends on the surface tempera- tures of the wall, ground and roof. The thermo-physical properties of the materials are generally quite different and hence a differential heating of these surfaces may lead to very different source terms. This differential heating can be caused due to the different amount of radiation incident on these different surfaces and the canopy velocity which in turn will be affected by the drag force.
  • 3. The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010 3 TESTING THE HYPOTHESIS All canopy models need as inputs: street width & orientation, building width, building density and a statistical representation of building heights which are generally obtained through quantita- tive field survey (which are very slow and time consuming to perform) or qualitative estimates. But in performing this geometric abstraction there is no way to ensure that the total built surfaces and volumes of the simplified geometry match those of the actual city or more importantly that the energy and momentum exchanges are equivalent. In this section we aim to test the central hy- pothesis that cities can be accurately represented by a regular array of parallelepipeds. For the purpose we investigate, for a particular scenario, the effects of complexity in urban geometry on the spatially averaged drag forces and short wave radiation exchanges with different surfaces (roofs, ground, and walls). For radiation exchange we use a Simplified Radiosity Algorithm (SRA) (Robinson and Stone 2004), while for drag computation we employ the Immersed Surface Technique (IST) (Labois et al., 2010). Table 1: Geometric characteristics of built surfaces in the domain of interest Horizontal built area (Roofs) 144,000m2 Vertical built area (Walls) 432,000m2 Horizontal built area (Ground) 606,000m2 Building Height 15m Total Built Volume 2,160,000m3 Table 2: Building plan area fraction and wall area fraction Ar (m2) At (m2) Aw (m2) Lp Lw Long Canopies 150,000 750,000 159,000 0.200 0.21 Simple cuboid 1 144,000 750,000 432,000 0.192 0.57 Simple cuboid 2 144,180 750,000 450,360 0.192 0.60 Real morphology 144,000 750,000 432,000 0.192 0.57 3.1 Test set-up Figure 1: Computational domain. We chose a part of the city of Basel (Switzerland), which has a dimension of 1000m by 750m. A good approximation of the real geometry is sketched and it is assumed that all the buildings have a uniform height of 15m. Many of the buildings in this part of Basel have been constructed to this maximum height, although they do not necessarily all have flat roofs. However, our objec-
  • 4. The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010 tive here is not to attempt to reproduce reality. Rather it is to test whether a simplified abstract re- presentation of urban geometry can be used to reproduce similar energy and momentum ex- change to its real (complex) counterpart. For this, a simplification of the third dimension of the geometry should not undermine the relevance of our study. The total built vertical and horizontal surface areas are presented in Table 1. Three simplified representations are also considered. These we refer to as long canopies, simple cuboids 1, and simple cuboids 2. The long canopies representation of the city consists of ten rows of terraced buildings each of dimension 500m × 30m, with an interspacing of 67m, as shown in Figure 2. Simple cuboids 1 consists of 20 × 18, cuboids each of dimension 20m × 20m × 15m and aligned in a regular array with a spacing of 30m in the stream wise direction and 20m in the span wise direction (Figure 2). Similarly, the simple cuboids 2 representation consists of 20×18 cuboids of size 26.7m × 15m × 15m aligned in a regular array with a spacing of 23.3m in the x direction and 25m in the y direction (Figure 2). Figure 2: Surface tesselization of geometries. For clarity we present in Table 2 some associated geometric quantities; the building plan area fraction and the building wall area fraction. It should be noted that the building plan area fraction for all the representations under consideration are similar, at about 0.2. However, the wall area fraction for the long canopy is different compared to other representations. The intention here is to show that even when the built volume and roof area are kept equal, the vertical wall area can differ and have a severe impact on radiation exchange and air flow. In reality even basic quanti- ties like the built volume are hardly conserved. Thus by ensuring the equivalence of these quanti- ties we focus on testing the underlying hypothesis that real geometries can be modeled with rea- sonable accuracy by simplified, rather than on errors in geometric (survey) abstraction.
  • 5. The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010 Table 3: Space averaged drag (Fx, Fy) and shear forces (Sx,Sy) - Fx (N) Fy (N) Sx (N) Sy (N) Fx+Sx (N) Fy+Sy (N) Complex 8207 157 985 2.5 9194 160 Long Canopies 14093 38.52 1424 1.95 15507 40.5 Simple cuboids 1 4931 -46 754 1.3 5658 -45 Simple cuboids 2 2911 -35 665 -3 3577 -38 3.2 Radiation modeling Figure 3: Comparison of the amount of shortwave radiation incident on roof (left) and wall (right) surfaces every hour for the four cases The magnitude of incident irradiation varies with the type of surfaces (wall, roof and ground; due to differences in surface tilt, orientation and occlusion). This tends to result in different sur- face temperatures, which in turn affects the quantity of energy exchanged with the surroundings. To better understand this problem we investigate in this section the differences in incident irrad- iation for our simplified geometries of equivalent volume. For radiation computation, the surfaces in each of the representations are tessellated into smaller surfaces (Figure 2). This simulation was conducted for the 7th of January. All domains of the same size will have the same quantity of so- lar radiation entering them. For mesoscale modeling the correct calculation of the distribution of the radiation amongst the wall, roof and ground surfaces is very important, as this determines the total absorption of radiation within our domain and the corresponding energy that is transferred to the adjacent air. Variations in the spatial distribution of absorbed solar energy may also modify momentum transfers. From Figure 3 we reach the following observations: • Roofs: Since the horizontal roof surface areas in all the representations are the same and all the buildings are of the same height we observe that the amount of radiation absorbed dur- ing the whole day is similar, as expected. • Ground: In the particular case of long canopies the ground receives more solar radiation than either of the cuboids layouts, as views to the sun and sky are relatively unobstructed. In the complex representation these views are relatively obstructed so that the radiation in- cident on the ground decreases. In the case of the two cuboids representations views are even further obstructed, so that even less solar radiation is incident on the ground. • For walls: The two simplified cuboids representations receive more shortwave radiation than the complex and long canopy representations. This is due to an increased reflected contribution and an increased south facing surface area. Thus, for this particular day, the walls in the simplified representation will be warmer than in the complex one. The opposite will be true for the ground surfaces. This will result in different surface temperatures for the walls and ground with a corresponding influence on surface energy exchanges.
  • 6. The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010 Figure 4: Velocity field at 5.6m above the ground level 4 COMPUTATIONAL FLUID DYNAMICS For the CFD simulations the geometrical representation is the same as for the radiation calcula- tions. However, the domain has been extended at all four boundaries by an additional 200m, to allow the inflow to develop before encountering urban structures. The domain is discretized into 175 × 175 × 40 cells. For the complex geometry two more simulations were conducted using 150x150x40 and 225x225x60 cells for grid independence; for subsequent simulations a grid of 175 × 175 × 40 was used. An inlet boundary condition with a 1m/s velocity in the flow direction is imposed. Wall boundary conditions were specified where required. The turbulence model used is the standard k − ε model; with a 2nd-order convection scheme used velocities. A precondi- tioned (multigrid) GMRES pressure scheme is used for the pressure field. The flow is converged in steady state with convergence criteria of E-5 for velocities and kinetic energy and E-3 for dis- sipation. All the simulations presented in this section are for a neutral atmosphere. In Figure 4 we present the velocity field for all four geometric representations at a height of 5.6m above the ground plane. The more complex representation is characterized by the formation of large vortic- es in the inter-building spaces. There is also a tendency for the flow to be deflected in the span- wise direction, due to the irregular orientation of the buildings. Long canopies strongly retard the flow, which tends to stagnate within the canopies. Within the other simplified representations, vortices are formed on the leeward side of the cuboids, which are small and well isolated from each other. Also, because these obstructions are non-continuous the fluid motion remains essen- tially unidirectional in the streamwise direction. These observations are also evident from the magnitude of the spatially averaged drag forces presented in Table 4.
  • 7. The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010 5 CONCEPT OF EQUIVALENT CITY Figure 5: Complex geometry reduced to its equivalent simplified form From the previous section it appears to be clear that the form and layout of buildings of similar total volume has important implications for the imposed drag forces and the distribution of ab- sorbed radiant energy, which might lead to differential heating of surfaces and hence to differ- ences in the total energy exchange with the surrounding air. It is thus important to identify an ar- rangement of a simplified geometry (as used in urban parameterization scheme) for which these two quantities (drag and shortwave radiation absorption) are roughly equivalent to those expe- rienced by the corresponding real geometry. For this purpose we introduce a new technique for fitting such an equivalent simplified geometry. In this we define an equivalent geometry as “that geometry which has the same built volume, horizontal and vertical built area, offers the same drag and absorbs the same shortwave radiation on vertical and horizontal surfaces as the com- plex/real representation”. To find the equivalent geometry a digitalized 3-D representation is sketched and parsed to the solver, which then identifies the corresponding equivalent geometry. The constraints are that the total built surface area and volume of the geometries are equivalent: Scomplex = S simplified ; and Vcomplex = Vsimplified (2) where S stands for vertical or horizontal surface area and V stands for total built volume. The ob- jective functions to be minimized are: wall wall ground ground f1 = Radiationcomplex − Radiationsimplified ; f 2 = Radiationcomplex − Radiationsimplified (3) f 3 = Drag complex − Drag simplified Figure 6: Shortwave radiation incident on different surfaces for ground and wall surfaces
  • 8. The Fifth International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA May 23-27, 2010 After several iterations we have identified a geometry which satisfies our definition of ”equiva- lent geometry” (Figure 5) for our case study of Basel. We can see from Table 5 that the drag forces for both geometric models are comparable. Although the forces in the spanwise direction do differ, their magnitudes compared to the streamwise forces are negligible. Furthermore, from Figure 6 we see that the profiles of radiation incident on the ground and wall surfaces for the complex and equivalent representations are now precisely superimposed. The radiation incident on the roof surfaces is not presented: it is proportional to the horizontal roof surface areas, which are identical for both representations. Each cube in the equivalent representation has a dimension of 26.7m×15m×15m. The West-East street width is 23.3m and it is aligned at an angle of 30 de- grees to the east, while the South-North street width is 25m and is aligned o the other street. Table 4: Drag, shear and total forces - Fx (N) Fy (N) Sx (N) Sy (N) Fx+Sx (N) Fy+Sy (N) Complex 8207 157 985 2.5 9194 160 Equivalent 7731 -346 894 5.8 8625 -340 6 CONCLUSION A new algorithm has been developed and tested for fitting equivalent urban canopy geometry to any real complex geometry, based on minimizing the error in drag force and absorbed radiation. This new method may be used to calibrate the geometric inputs to any urban canopy model in a rigorous way. It should be noted that in this work we have sketched the geometry of the complex city using Google earth images and then extruded them to a particular height based on field mea- surement. However, the algorithm which is explained in this paper can handle non-uniformity in building height so that with 3-D laser scanned geometries becoming more and more accessible could in principle further improve the accuracy of our equivalent representation. We have fo- cused on these two for reasons of parsimony, but further work would be warranted to confirm or otherwise this hypothesis and in the latter case to select alternative or additional parameters. Fi- nally, a process of manual trial and error has thus far been employed in fitting our simplified geometries by minimizing differences in drag and radiation predictions. Subject to computational constraints the use of evolutionary algorithms would be more appropriate, enabling the available parameter space to be further explored. 7 REFERENCES Kondo H, Genchi Y, Kikegawa Y, Ohashi Y, Yoshikado H. and Komiyama H. 2005. Development of a multi-layer urban canopy model for the analysis of energy consumption in a big city. BLM 116:395-421 Labois M., C., Narayanan and D. Lakehal, 2010. A New CFD approach for urban flow and pollution dispersion si- mulation. In Proc. CWE10, Chapel Hill, NC, USA, May 23-27 (this volume). Martilli A, Clappier, A. and Rotach M., 2002. An urban surface exchange parameterization for mesoscale models. Boundary Layer Meteorology 104:261-304 Masson, V., 2000. A physically-based scheme for the urban energy budget in atmospheric models. BLM 94:357-397 Noihan, J., 1981. A model for the net total radiation flux at the surfaces of a building. Building & Env. 16, 259-266 Rasheed, A., Robinson, D., A, Clappier, C. Narayanan and Lakehal, D., 2010. Representing Complex Geometries in Mesoscale Modeling. (in press) J. of Climatology. Robinson, D. and Stone, A., 2005. Solar radiation modeling in the urban context. Solar Energy, 77(3):295-309 Rotach, M (2001), Urban scale dispersion modelling using a Lagrangian Particle dispersion model, BLM 99:379-410 Roth, M., 2000. Review of atmospheric turbulence over cities. Quart J Roy Meteor Soc 126: 941-990