Flux footprints over a hilly surface : a case study ( Research Note )

The flux footprint probability distribution (FPD) for the near-surface receptor over a series of sinusoidal hills is evaluated using a backward Lagrangian stochastic (LS) model. The wind and turbulence fields derived from large-eddy simulations under unstable conditions, in which the synoptic wind aligns with the surface-elevation-varying direction, are used to drive the LS model. The characteristics of the crosswind-integrated FPD (CIFPD) vary with the location of the receptor over the hilly surface. The widest CIFPD with the smallest peak value appears when the receptor is located in the crest area, while the narrowest CIFPD with the largest peak value appears in the wind convergent area. The peak value of CIFPD in the convergent area is larger than its counterpart derived from the experiment in which a flat surface and horizontally-homogeneous wind and turbulence fields are assumed, with the peak position being closer to the receptor. The case, however, is reversed for the divergent area. Horizontal heterogeneity in turbulence affects the magnitude of the peak and width of the CIFPD, compared with their counterparts over the flat surface, but has less impact on the peak location than that in the mean flow. Similar results are obtained when the CIFPD derived from an analytical footprint model is compared with that from the LS model over the hills. The analytical model fails to simulate CIFPD in the downwind area under weak wind conditions due to the longitudinal wind fluctuation not being considered.