Flux Footprints Over an Undulating Surface

Abstract

The flux footprint probability distribution (FPD) functions for near-surface receptors over an idealised undulating surface are evaluated using a backward Lagrangian stochastic model. The wind and turbulence fields employed to drive the stochastic model are derived from large-eddy simulations, in which the horizontal wind aligns with the surface-elevation-varying direction. The flux FPD for a receptor is affected by flow divergence or convergence, and varies with the receptor’s location. The widest crosswind-integrated FPD (CIFPD) curve with the smallest peak value appears when the receptor is located in the crest area, while the narrowest CIFPD curve with the largest peak value appears when the receptor is located in the windward area. Experiments are designed to highlight the impact of the horizontal homogeneity assumption on the estimation of the FPD. When the receptor is located in the area with surface-wind convergence, the peak value of the CIFPD is larger than its counterpart under assumed horizontally homogeneous flow conditions, with the peak position being closer to the receptor. The case is reversed when the receptor is located in the area with surface-wind divergence. Similar results are obtained when the CIFPD derived from an analytical footprint model (developed under the assumption of horizontally homogeneous flow conditions) is compared with that from the stochastic model over the undulating surface. The analytical model fails to simulate the CIFPD in the local downwind area under weak wind conditions due to the longitudinal wind fluctuation not being considered.