The Building Effect Parameterization BEP (Martilli 2002) accounts for the three- dimensional nature of urban surfaces and treats the buildings as sources and sinks of heat, moisture and momentum. By impacting the thermodynamic structure of the urban roughness sub-layer in the lower part of the urban boundary layer, the BEP allows a direct interaction with the PBL. The effects of horizontal and vertical surfaces on the turbulent kinetic energy (TKE), potential temperature (Ɵ) and momentum are also covered by this model by allowing a high vertical resolution close to the ground. For these simulations, the internal temperature of the buildings is assumed to be constant (Chen 2011
In the BEP, a city consists of a combination of different urban classes. Each class is characterized by an arrangement of buildings of the same canyon width but with a distribution of different heights h according to a certain probability. The length of the street canyon is thereby consistent with the horizontal grid size.
The urban structure however is defined on a grid different from the mesoscale model to provide the greatest flexibility in calculating sub-scale processes. Areas of urban surface types are defined with regard to the total horizontal and vertical surface area. The crucial effects of urban surfaces on atmospheric dynamics are computed as follows (Martilli 2002):
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a) Effects on airflow
The presence of horizontal surfaces like roofs and the ground induce a consequent loss of momentum due to the generation of a frictional force. This term is similar to the mesoscale model, with the exception that it is vertically distributed from the ground up to the highest building. Moreover, it is proportional to the fractional area of the horizontal surfaces existent in the cell. In general, momentum fluxes are produced due to the presence of vertical surfaces of the buildings (Martilli 2002).
Momentum
The turbulent flux of momentum due to horizontal surfaces is calculated for every model level in the urban canopy using the Monin-Obukhov Similarity Theory (MOST). The flux at level U on the urban scale is thus computed using the wind speed and air temperature at some level M calculated at the mesoscale model grid. The roughness length is represented by the roughness of the specific surface types (roof or canyon floor). Buildings induce pressure and drag forces on the flow which is used accordingly to parameterise the exchange of momentum on vertical structures (walls). This approach can be compared with modelling the impact of vegetative canopies on the flow. All forces explained above occur orthogonal to the direction of the street canyon and have components against the horizontal wind direction. The exact equations are presented in Raupach (1991) for horizontal and in Louis (1979) for vertical surfaces. For an overall explanation and calculation within the BEP model, refer to equations (13) and (14) presented in Martilli (2002). Changing some features of the building geometry can modify relevant parameters which results in an alteration of modelled momentum fluxes
Temperature
The turbulent fluxes of sensible heat from the roof and canyon floor are mainly calculated from the gradient between the air and surface temperature and described accurately by equation (15) in Martilli (2002) with reference to Louis (1979).
Temperature fluxes from the wall are also a function of the gradient between the air and wall temperatures and calculated from the sensible heat coefficient as a function of the wind speed between the buildings (calculated by an urban canopy budget model in Arnfield and Grimmond (1998) using a formulation by Clarke (2001)). The temperature of
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roofs, walls and streets are computed by solving a heat diffusion equation for several levels in the materials whereas surface-specific energy budgets are computed. Details of this calculation are given in the appendix of Martilli (2002).
By increasing the surface albedo by using light façades and roof colours, or urban greening, one can significantly impact the temperature fluxes within the urban canopy.
Turbulent kinetic energy
In urban areas, the conversion of mean energy into turbulent kinetic energy is increased by the presence of buildings. In the BEP, this aspect is calculated by the impact of the surface at the lowest level in the shear and buoyant production terms of the turbulent kinetic energy (TKE). The considerations are similar with those of momentum fluxes, but since the effect is considered to be volumetric, the terms of the MOST-equation are multiplied by a reference volume above the surface (Martilli 2002).
b) Computation of urban terms
In urban areas, the general energy conservation equations are modified by an extra term DA, where A can be any variable like temperature, wind speed or TKE. This extra term is
generated by fluxes due to interactions between buildings and the airflow. It can be simplified by the following equation:
𝐷𝐴 = 𝐹𝑎𝐻𝑉+𝐹𝑎𝐴 𝑉, (6.6)
with V being the volume of air in a grid cell and FaHand FaV the average of the fluxes computed on the urban grid due to the presence of buildings and interpolated to the grid of the mesoscale model (Martilli 2002).
c) Modification of the turbulent length scale
In order to estimate the dissipation of TKE, the parameter of the turbulent length scale l is introduced. In general, the term turbulent length scale defines a physical variable describing the size of the large energy-containing eddies in a turbulent flow. The presence of a building generates vortices which are of the order of the building’s height. Whereas lower levels are influenced by both high and small buildings, higher buildings are predominantly affected by self-induced eddies. Consequently, the myriad of buildings
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Detailed information about all terms and equations used in the BEP model are given in Martilli (2002) and a short user’s manual is given in Martilli et al. (2009).
6.2 Setting up WRF for real data application