Modelling of flux exchanges between heterogeneous surfaces and atmosphere
In numerical models of atmospheric flow it is necessary to consider the properties of boundary-layer flow as averaged over the grid cell of the model. “Flux aggregation” is the process by which an effective horizontal average or aggregate of turbulent fluxes is formed over heterogeneous surfaces. The aggregated flux differs from spatial average of equilibrium fluxes in an area, due to nonlinear advective enhancement associated with local advection across surface transitions. Aggregated fluxes can be related to vertical profiles only above the blending height. The concept of so-called blending height has become frequently used approach to the parameterization of areally averaged fluxes over heterogeneous surfaces. There are three approaches commonly taken for calculating the transfer of momentum, heat and moisture from a grid cell comprised of heterogeneous surfaces. They are: (a) “parameter aggregation”, where grid cell mean parameters such as roughness length, albedo, leaf area index, stomatal resistance, soil conductivity, etc., are derived in a manner which attempts to incorporate in the best way the combined non-linear effects of each of different relatively homogeneous subregions (“tiles”) over the grid cell; (b) “flux aggregation”, where the fluxes are averaged over the grid cell, using a weighted average with the weights determined by the area covered by each tile; and (c) a combination of the “flux aggregation” and “parameter aggregation” methods. However, if large differences exist in the heterogeneity of the surfaces over the grid cell, then a combined method has to be applied. In “parameter aggregation” and “flux aggregation”, numerical modellers usually either use the dominant type for the grid cell or make a simple linear average to determine grid cell averages of certain parameters. Both these methods lead to uncertainties in the parameterization of boundary layer processes when heterogeneities exist over the grid cell. In this chapter we describe: (1) the concept of the blending height, (2) an approach for aggregation of aerodynamic surface parameters, (3) an approach for aggregation of albedo and (4) a combined method for calculating the surface temperature and water vapour pressure over heterogeneous surface.