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  1. 1. The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan DEVELOPMENT OF A NEW URBAN CANOPY MODEL Adil Rasheed*, Darren Robinson*, Alain Clappier** *Solar Energy and Building Physics Lab, EPFL, Switzerland; **Soil and Air Pollution Lab., EPFL, Switzerland Abstract The effects of urban structures on the atmosphere are studied using mesoscale models having a resolution ranging from a few meters to a few kilometers. Because of such a coarse resolution additional urban parameterizations are required to simulate the effects of the subgrid scales (buildings and canyons). This is accomplished using an Urban Canopy Model. In this paper, results from Large Eddy Simulations are used for validating a new 1-D Urban Canopy Model. The model assumes a periodic occurrence of buildings and accounts for the street width, building width, building density, height and street orientation. To ensure the models applicability to real complex (non periodic) forms we also introduce a new method of deriving an equivalent (simplified periodic) city. Key words: Urban Canopy Model, Complex Urban Geometry 1. INTRODUCTION Mesoscales models are used to understand the heat and momentum exchanges between the air flowing through a city and the urban elements from which they are composed. However, with a resolution of a few hundreds of meters or a few kilometers, these models are not capable of resolving the effects of these urban elements. So, these effects are parameterized and simulated using an Urban Canopy Model. But, all such canopy models assume a city to be made up of a regular array of cubes or infinitely long canopies. The inputs to these models are street width, building width, building density, a statistical representation of the building heights and street orientation. These inputs are generally estimated or obtained through field surveys, which are a very slow and time consuming process. There is also no guarantee that the total built surfaces and volumes of the simplified city will match that of the actual city. Also there is no scientific justification for choosing a particular set of input parameters. To address this shortfall we present not only an improved 1-D model but also a methodology to represent a complex city with an equivalent simple city consisting of a regular array of cubes which will be compatible with any UCM. Such an equivalent city will have the same built surfaces and volume and similar drag and radiative characteristics compared to the complex one. 2. URBAN CANOPY MODEL In developing our Urban Canopy Model we first conducted LES over an array of cubes. The spatially averaged quantities were investigated and it was observed that the dispersive fluxes behave in a strange manner. They exhibit behaviour which is similar to that of turbulent fluxes for widely placed cubes but which is opposite for closely packed cubes. Thus it was concluded that for sufficiently wide streets they could be modeled in the same way as the turbulent fluxes. When we combine them and assume periodicity, the Navier Stokes Equation takes on the following form (which is a one dimensional equation in the vertical direction with a variable diffusivity after the modification prescribed by Kondo [1]). Figure 1: Geometries handled in the UCM ∂u 1 ∂ ⎛ = ⎜ K zu Λ ∂u ⎞ 2 ⎟ − a1Cd u u + v 2 … (1) ∂v = 1 ∂ ⎛ K zv Λ ∂v ⎞ − a2Cd v u 2 + v 2 ⎜ ⎟ …(2) ∂t Λ ∂zc ⎝ ∂zc ⎠ ∂ tΛ∂ zc ⎝∂ zc ⎠ The drag forces offered by the rectangular cuboids have been taken to be proportional to the square of the local velocity field and the turbulent and dispersive fluxes (which arise due to spatial averaging) have been combined (because they are similar for B/W > 1). At the lower boundary both the horizontal velocity components are taken as zero. The upper boundary condition is applied at 3.4 times the height of the cube. Constant values are applied at the upper end by the MM. B1 Pb ( z ) B2 Pb ( z ) a1 = a2 = ( B1 + W1 )( B2 + W2 ) − B1 B2 Pb ( z ) ...(3) ( B1 + W1 )( B2 + W2 ) − B1 B2 Pb ( z ) ..(4)
  2. 2. The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan ⎛ B1 B2 ⎞ Λ = 1− ⎜ ⎟ Pb ( z ) ⎝ ( B1 + W1 )( B2 + W2 ) ⎠ ...(5) Where B1, B2, W1,W2 are explained in Figure 1. Also 2 2 ⎛ ∂u ⎞ ⎛ ∂v ⎞ S m 2 3/ K zu = K zv = L2 ⎜ ⎟ +⎜ ⎟ ⎝ ∂zc ⎠ ⎝ ∂zc ⎠ C ...(6) A complete derivation of the expression for Kz can be found in Gambo [2]. The length scale L is given by Watanabe and Kondo [3] and was derived from considerations of a forest canopy: 2κ 3 caz L ( zc ) = (1 − exp(−η ) ) η= ca ...(7) 2κ 2 ; ...(8) and above the canopy we use an interpolation formula after Blackadar [4]: κ zc L ( zc ) ≤ κz 1+ L0 ...(9) which interpolates between two limits L ~ kz , at z = 0 and L=L o as L → ∞ . In this study we have used a value of Lo = 70m. The solution to the above equations gives the vertical profile of the involved quantities, which can be used to compute the heat and momentum sink / source terms. Below we present the solution of the equations given above for two different configurations B/H=3 & 2 (B1=B2=B, W1=W2=H) (a) (b) Figure 2: Comparision between the predictions by the 1-D Column Model and LES data (a)B/H=3(b)B/H=2 One can clearly see from Figure 2 that the model reproduces the LES results very well. The inflection point in the velocity profile is also captured and the retardation of flow due to building (z/H<1) results in an accelerated flow above the buildings (z/H>1). 3. EQUIVALENCE OF A COMPLEX CITY The model presented in the last section suffers from the fact that it can represent only a city consisting of a regular array of cubes. However, in reality city geometries are highly complex and somewhat randomly aligned. Here we present a methodology to simplify these complex geometries into an equivalent geometry which will be compatible with the canopy model presented in this paper as well as with other urban canopy models in use. The algorithm to find the equivalent city consists of the following steps: Algorithm: Step 1. Sketch the complex geometry of a city using a sketching tool. Step 2. Compute the total built volume and horizontal and vertical built surfaces. Step 3. Compute the total solar radiation incident on each surface (roofs, walls and grounds). Step 4. Compute the drag forces and spatially averaged velocity profiles. Step 5. Using the built volume and surfaces generate a simplified geometry consisting of a regular array of blocks with B1,B2, W1,W2 and street orientation. Step 6. Compute the solar radiation incident on the surfaces of this new geometry as well as the drag and spatially averaged velocity profile. Step 7. Check whether the characteristics of the simplified representation are within acceptable limits to the complex geometry
  3. 3. The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan If yes, then use this simplified representation in the mesoscale model. If not then go to step 5 and repeat the whole process with different values of B1, B2, W1, W2 and street orientation. 4. SIMULATIONS AND RESULTS The simplified radiosity algorithm and immersed boundary technique have already been briefly described in [??]. Using these models, identifying the equivalent geometry is an iterative process. Because of the constraints on the length of this paper we restrict ourselves to presenting the comparison between the complex geometry and the equivalent geometry, which closely reproduces the radiative and flow characteristics of the former. The geometric characteristics for both the representations are presented in Table 1. The flow domain and the numerics of the simulations are the same as those described in [5]. The mesh and flow domain is shown in Figure 3. Table 1: Geometric characteristic of the built surfaces in the domain Horizontal built area (Roofs) 144000 m2 Building Height 15 m Vertical built ares (Walls) 432000m2 Total Built Volume 2160000 m3 Ground area (Ground) 606000 m2 Figure 3: Mesh for complex and equivalent representations Figure 4: Velocity field in the complex and equivalent representation of the buildings Table 2: Drag, shear and total spanwise forces experienced by the built structures Fx Fy Sx Sy Fx+Sx Fy+Sy Complex 8207 157 985 2.5 9194 160 Equivalent 7731 -346 894 5.8 8625 -340 One can clearly see from the Table 2 that the streamwise 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. Figure 5 also shows that the space averaged velocity profiles are almost identical. Figure 5: Space averaged velocity profile
  4. 4. The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan Figure 6: Incident shortwave radiation on the walls and roofs Figure 6 presents a comparison (of the radiation incident on the ground and wall surfaces) for the complex and equivalent representations. Note that the irradiance profiles are precisely superimposed. The radiation incident on the roof surfaces has not been presented but this identical to the horizontal roof surface area which is the same for both representations. (a) (b) Figure 7: (a) Complex Geometry (b) Equivalent Geometry The equivalent representation of the complex geometry is shown in Figure 7(b). Each cube in the equivalent representation has a dimension of 26.7mX15mX15m (Width X Bredth X Height). The West-East street width is 23.3m and it is aligned at an angle of 30 degrees to the east, while the South-North street width is 25m and is aligned orthogonal to the other street. 5. CONCLUSION A new Urban Canopy Model has been presented in this paper and the results from the model are validated against the LES results. A methodology to reduce any complex geometry to its equivalent simplified representation has been presented and demonstrated by a real life example. A combination of these two approaches will result in improved mesoscale prediction. 6. REFERENCES [1] 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: Structure of the urban canopy model and its basic performance. Boundary-Layer Meteorology, 116:395{42 [2] Gambo, K. (1978). Notes on the turbulence closure model for atmospheric boundary layers. Journal of the Meteorological Society of Japan, 56:466{480. [3] Watanabe, T. and Kondo, J. (1990). The influence of the canopy structure and density upon te mixing length within and above vegetation. Journal of Meteorological Society of Japan, 68:227{235} [4] Blackadar, A. (1968). The vertical distribution of wind and turbulent exchange in neutral atmosphere. Jounal of Geophysics, 4:3085{3102 [5] Rasheed,A., Robinson, D., Narayanan, C. and Lakehal, D., (2009) On the effects of Complex Urban Geometries on Mesoscale Modelling, ICUC-7, Yokohama, Japan