A practical approach to compute short-wave irradiance interacting with subgrid-scale buildings

A numerical approach for the calculation of short-wave irradiances at the ground as well as the walls and roofs of buildings in an environment with unresolved built-up is presented. In this radiative parameterization scheme the properties of the unresolved built-up are assigned to settlement types which are characterized by mean values of the volume density of the buildings and their wall area density. Therefore it is named wall area approach. In the vertical direction the range of building heights may be subdivided into several layers. In the case of non-uniform building heights the shadowing of the lower roofs by the taller buildings is taken into account. The method includes the approximate calculation of sky view and sun view factors. For an idealized building arrangement it is shown that the obtained approximate factors are in good agreement with exact calculations just as for the comparison of the calculated and measured effective albedo values. For arrangements with isolated single buildings the presented wall area approach yields a better agreement with the observations than similar methods where the unresolved built-up is characterized by the aspect ratio of a representative street canyon (aspect ratio approach). In the limiting case where the built-up is well represented by an ensemble of idealized street canyons both approaches become equivalent. The presented short-wave radiation scheme is part of the microscale atmospheric model MUKLIMO_3 where it contributes to the calculation of surface temperatures on the basis of energy-flux equilibrium conditions.