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The bulk aerodynamic formulation over heterogeneous surfaces

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Abstract

This interpretative literature survey examines problems with application of the bulk aerodynamic method to spatially averaged fluxes over heterogeneous surfaces. This task is approached by tying together concepts 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, footprint theory and the blending height. Although these concepts are not completely compatible, qualitative scaling arguments based on these concepts lead to a tentative unified picture of the qualitative influence of surface heterogeneity for a wide spectrum of spatial scales.

Generalization of the velocity scale is considered to account for nonvanishing heat and moisture fluxes in the limit of vanishing time-averaged wind speed and to account for the influence of subgrid mesoscale motions on the grid-averaged turbulent flux. The bulk aerodynamic relationship for the heat flux usually employs the surface radiation temperature or, equivalently, the temperature from the modelled surface energy budget. The corresponding thermal roughness length is quite variable and its dependence on available parameters is predictable only in special cases.

An effective transfer coefficient to relate the spatially averaged surface fluxes to spatially averaged air-ground differences of temperature and other scalars can be most clearly defined when the blending height occurs below the reference level (observational level or first model level). This condition is satisfied only for surface heterogeneity occurring over horizontal scales up to a few times the boundary-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 maintained where traditional similarity theory is locally applicable. Surface variations on these scales may generate thermally-driven mesoscale motions.

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Mahrt, L. The bulk aerodynamic formulation over heterogeneous surfaces. Boundary-Layer Meteorol 78, 87–119 (1996). https://doi.org/10.1007/BF00122488

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