THE BULK AERODYNAMIC FORMULATION OVER HETEROGENEOUS SURFACES

This interpretative literature survey examines problems with applicati on of the bulk aerodynamic method to spatially averaged fluxes over he terogeneous surfaces. This task is approached by tying together concep ts from a diverse range of recent studies on subgrid parameterization, the roughness sublayer, the roll of large ''inactive'' boundary-layer eddies, internal boundary-layer growth, the equilibrium sublayer, foo tprint theory and the blending height. Although these concepts are not completely compatible, qualitative scaling arguments based on these c oncepts lead to a tentative unified picture of the qualitative influen ce of surface heterogeneity for a wide spectrum of spatial scales. Gen eralization of the velocity scale is considered to account for nonvani shing heat and moisture fluxes in the limit of vanishing time-averaged wind speed and to account for the influence of subgrid mesoscale moti ons on the grid-averaged turbulent flux. The bulk aerodynamic relation ship for the heat flux usually employs the surface radiation temperatu re or, equivalently, the temperature from the modelled surface energy budget. The corresponding thermal roughness length is quite variable a nd its dependence on available parameters is predictable only in speci al cases. An effective transfer coefficient to relate the spatially av eraged surface fluxes to spatially averaged air-ground differences of temperature and other scalars can be most clearly defined when the ble nding height occurs below the reference level (observational level or first model level). This condition is satisfied only for surface heter ogeneity occurring over horizontal scales up to a few times the bounda ry-layer depth, depending on the stability and height of the reference level. For surface heterogeneity on larger scales (small mesoscale), an effective transfer coefficient for the spatially averaged flow must be defined, for which predictive schemes are unavailable. For surface variations on large mesoscales, homogeneous subareas may be maintaine d where traditional similarity theory is locally applicable. Surface v ariations on these scales may generate thermally-driven mesoscale moti ons.