Coupling the Town Energy Balance with the urban radiation model SPARTACUS-Urban and evaluation with a Monte-Carlo-based reference model
Authors: Schoetter Robert , Hogan Robin , Caliot Cyril , Masson Valéry 
Published: July 2024

Radiative exchange in the complex 3-D urban geometry is a crucial physical process for the urban heat island, building energy consumption, and outdoor human thermal comfort. Urban canopy models calculate radiative exchange by simplifying both urban morphology (e.g. by an infinitely-long street canyon or a regular array of square blocs) and radiative transfer physics. Radiative exchanges are usually calculated with the radiosity method assuming that there is vacuum in the urban canopy layer and that urban materials have a broadband Lambertian reflectivity. This introduces systematic biases, since uniform radiosity on surfaces is assumed and because the distribution of wall-to-wall and ground-to-wall distances corresponds to the simplified morphologies and is therefore systematically different to the one in real districts. Furthermore, it is difficult to take into account a variety of building height, urban vegetation with complex shape, and physical processes like specular reflections by windows, spectral materials, and interaction of radiation with air, aerosols, or clouds in the urban canopy layer. The urban radiation model SPARTACUS-Urban is based on a more realistic hypothesis of urban morphology (exponential distribution of wall-to-wall and ground-to-wall distances), and tree geometry (cylinders). It solves radiative transfer with the Discrete Ordinate Method. This allows to take into account more complex urban geometry and the mentioned physical processes. The urban canopy model Town Energy Balance (TEB) is coupled with SPARTACUS-Urban and the new TEB-SPARTACUS is available in the open-source land surface model SURFEXv9.0. TEB-SPARTACUS keeps the geometrical simplicity of the original TEB, which is that there is no variety of building and tree height at grid point scale. The TEB-SPARTACUS results for the direct and diffuse solar, and the terrestrial urban radiation budget are evaluated for procedurally-generated urban morphologies mimicking the Local Climate Zones (LCZ). Evaluation is made by comparison with results of the newly-developed Monte-Carlo-based reference model HTRDR-Urban. HTRDR-Urban can produce reference results of radiative flux densities in complex urban geometries, including spectral and specular materials, trees with individual leaves, and the participating atmosphere. It is shown that TEB-SPARTACUS improves the solar and terrestrial urban radiation budget for all LCZ, the improvement of radiative observables can be up to 10% of the downwelling solar radiation. A considerable improvement is found for the partitioning between the direct solar radiation absorbed by the walls and the ground. This might help to improve the simulated building energy consumption, and outdoor human thermal comfort. TEB-SPARTACUS also simulates better the impact of trees on the urban radiation budget since it better represents the tree edges. Therefore, TEB-SPARTACUS could help to improve the simulated evapotranspiration or CO2 uptake by urban trees.