Calculation of aggregated albedo in rectangular solid geometry on environmental interfaces

Abstract

© 2010 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. The albedo of the interface has always been an important parameter for the evaluation of the radiation fluxes in environmental studies. The practical problem arises if the surface is a heterogeneous one. Various approaches to calculate the aggregated albedo have been developed. Our previous research demonstrated the existence of a geometrical effect when different parts of the interface have different heights. We have offered the general approach for the calculation of the flux that is lost due to the absorption on the vertical lateral boundaries. The multiple scattering effect and the dependence of the albedo on the zenithal angle of the incident radiation were disregarded. In the case of simple geometries we derived analytically the expressions for this loss coefficient, which, for some ideal urban geometries, coincides with Oke’s sky-view factor. The aim of this chapter is an elaboration of this effect for more complex geometry, which does not allow analytic solutions. Therefore, it was necessary to develop an efficient numerical procedure, in this case the so-called ray-tracing Monte Carlo approach. It was first tested for known analytical solutions. As the next step, it was incorporated into one land surface scheme (LAPS), and then an example of central geometry was considered for: (i) a two-patch grid cell with a square geometrical distribution and (ii) different heights of its parts. Simulations were done for several patch areas, with different heights (“propagating building”). Various surface types were considered. The derived value for the albedo was compared with the result of the conventional approach. Changes in albedo lead to a significant change in partitioning of the energy at the environmental interface. The most remarkable changes were in values of sensible and latent heat fluxes, as well as the surface temperature. The values of effective surface temperature were calculated using the LAPS parameterisation scheme and then compared to the values obtained with a conventional parameterisation of the albedo.