Estimation of areally-averaged surface fluxes

The concept of blending height is used to estimate areally averaged surface fluxes of momentum and heat in a stratified, horizontally inhomogeneous surface-layer flow. This concept is based on the assumption that at sufficiently large heights above a heterogeneous surface, subsequent surface modifications will not be recognizable in the flow individually, but overall flux and mean profiles will represent the surface condition of a large area. The height at which the flow becomes approximately independent of horizontal position is called blending height according to Wieringa (1986).Here, it is proposed to classify the ground surface in a surface-layer grid box of a larger-scale model into several land-use categories. Surface momentum and heat fluxes should be estimated for each category at the blending height. The grid-averaged surface fluxes are to be obtained by the average of surface fluxes on each land-use surface weighted by its fractional area. The postulate of computing the surface fluxes at the blending height leads to a new formulation of turbulent transfer coefficients.The proposed parameterization has been tested by employing a small-scale numerical model as a surface-layer grid box of a hypothesized larger-scale model. Several quite different flow configurations have been studied in order to investigate the performance of the new parameterization. Generally, the relative errors of estimated averaged surface fluxes are found to be well within ±10%.