A complete physically-based Town Energy Budget scheme for atmospheric models

    An urban surface model for atmospheric meso-scale models is presented. A generalization of local canyon geometry is defined instead of the usual bare soil formulation currently used to represent cities in atmospheric models. This allows refinement of the radiative budgets as well as momentum, heat and conduction fluxes. This scheme is aimed to be as general as possible, in order to represent any city in the world, for any time or weather condition (heat island cooling by night, urban wake, water evaporation after rainfall and snow effects.

    The Town Energy Budget (TEB) scheme is built following the canyon approach, generalized in order to represent larger horizontal scales. The physics treated by the scheme are relatively complete. Due to the complex shape of the city surface, not one but three energy budgets are considered: one for the roofs, one for the roads, and one for the walls. Orientation effects are averaged for roads and walls. Up to two energy budgets are added for snow when it is present on roofs or roads. Some of the physics were derived from the literature (long wave radiation or thermal conduction through the surfaces), since they are classically assumed to estimate building temperature in conditions without feedback towards atmosphere (during night with calm wind). However, most parts of the physics need an original approach (short wave radiation, thermodynamical and anthropogenic flux treatment, rain and snow), since they occur when interaction with the atmosphere is strong.

a.) Context

   The Town Energy Budget model is aimed to simulate the surface exchange turbulent fluxes with the atmosphere at the surface of a meso-scale atmospheric model, when it is covered by buildings, roads, or any artificial material.

    It must be considered as a part of the surface parameterization set of the atmospheric model. The fluxes should be computed for each surface type by the appropriate scheme, and then averaged in the atmospheric model grid mesh, in respect to the proportion occupied by each type. For example, a partition should be: (1) sea; (2) inland water; (3) natural and cultivated terrestrial surface; (4) towns. The following fluxes will be calculated: latent and sensible heat fluxes W m^-2, and momentum fluxes along the axes of the model m^2 s^-2.

b.) Town geometry description

    Numerous fine-scale studies on buildings climatology exist throughout the world. In those, several individual buildings are usually present, in order to study their radiative interaction, the wind channeling effects, or the building isolation. The canyon concept developped by city climatologists (e.g. Oke 1987) takes place into such frames: it considers a single road, bordered by facing buildings. These studies are, at best, forced by atmospheric data (radiation, wind above the roofs), but are not in interaction with it.

    The TEB model is aimed to parameterize the town-atmosphere dynamical and thermodynamical interactions. It works for meso-scale atmospheric models (grid mesh larger than few hundreds of meters). Then, spatial averaging of the town characteristics as well as its effect on the atmosphere, is necessary. The individual shapes of each building are no longer taken into account. The TEB geometry is based on the canyon hypothesis. However, a single canyon would be to restrictive at the considered horizontal scale.

    We therefore use the following original city representation

1. the buildings have the same height and width (in the model mesh).

2. they are located along identical roads, the length of which is considered far greater than their width. The air contained between two facing buildings is then a canyon.

3. any road orientations is possible, and all of them exist with the same probability. This hypothesis allows to compute averaged forcings for road and wall surfaces. In other words, when the canyon orientation appears in a formula (with respect to the sun or the wind directions), it is averaged on 360 degrees. In this way, no discretization is performed on orientation, leading to a relatively simple scheme.

c.) Physical phenomena handled by the Town Energy Budget scheme

    The physics treated by the scheme are relatively complete. Due to the complex shape of the city surface, not one but three energy budgets are considered: one for the roofs, one for the roads, and one for the walls. Orientations effects are averaged for roads and walls. Up to two energy budgets are added for snow when it is present on roofs or roads.

    Some of the physics were found in the state of art (long wave radiation or thermal conduction through the surfaces), since they are classically assumed to estimate building temperature in conditions whitout retro-action towards atmosphere (during night with calm wind). Because the roof heights are supposed to be uniform, this also allows to use some classical approch for the fluxes characteristics above the roof level. These physics (listed hereafter) are not original in themselves, but so is their application to an averaged city geometry:

• trapping of long-wave radiation by the canyon surfaces, with one re-emission taken into account [Johnson et al. (1991) formulation].
• The explicit conduction fluxes inside the buildings and road allow to take into account the layer-type struture of these surfaces (e.g. insulation layers) with the minimum of approximation.
• the effect of stability within the urban rouhgness boundary layer and the boundary layer above it (by use of friction coefficients and aerodynamical resistances).
• the momentum fluxes are computed for the entire urban cover, with a roughness length formulation and the stability coefficients of Mascart et al. (1995).
• the turbulent heat fluxes for the roofs are recovered from classical boundary layer laws. Nevertheless, the humidity flux needs a special treatment, because of the waterproof surface.

    However, the most part of the physics needed an original approach (short wave radiation, thermodynamical and anthropogenic fluxes treatment, rain and snow), since they occured when interaction with the atmosphere are strong. Liquid or solid precipitation phenomena are rarely adressed in the litterature (an exception is Grimmond and Oke (1991), except for sewer system and hydrology considerations.