Flux Footprints Over a Forested Hill Derived From a Lagrangian Particle Model Coupled Into a Large‐Eddy Simulation Model

Abstract Flux footprints are widely used in the study of turbulent flux measurements. Most of the existing footprint models assume horizontal homogeneity. However, as more and more flux towers are established over complex terrain, it is necessary to advance our understanding of footprints over complex terrain. Here we use a Lagrangian particle model coupled into a large‐eddy simulation model to investigate footprints over an idealized 2‐dimensional forested hill. Coordinate rotation, which is similar to that performed in real eddy‐covariance measurement, is considered in the calculation of footprints. For detectors over the upwind slope, their footprints are generally larger than the footprints of the detectors over the upwind flat ground. For detectors over the separation point, which is slightly downwind of the hill crest, their footprints extend both in the upwind and downwind directions. For detectors over the downwind slope and away from the separation point, their footprints also extend to the downwind direction, provided that the sources are released at the lower half of the canopy. This substantial downwind extension is in contrast to the conventional viewpoint. It is found that the footprints for the whole soil‐canopy system can be calculated by assuming that the canopy source/sink occurs at the single layer with the strongest source/sink. Compared to the footprints calculated with coordinate rotation, footprints calculated without coordinate rotation extend much farther upwind for detectors over the upwind slope, and have opposite signs for detectors over the downwind slope. Plain Language Summary Flux footprints help determine where the measured flux comes from. Existing footprint models are developed for horizontally homogeneous terrain. However, footprint models are also needed over complex terrain. We use particle trajectories predicted by an advanced flow model to calculate the footprints over a forested hill in a way that closely mimics the real flux measurement process. We find that the footprints are substantially different from those predicted by existing models. When the measurements are performed over the downwind slope, the footprints predicted by us extend substantially in the downwind direction while those predicted by existing models hardly extend in the downwind direction. Our results suggest that the existing footprint models need to be improved before being applied over complex terrain. Key Points Footprints over a forested hill cannot be predicted by analytical models Footprints of the whole soil‐canopy system can be derived from those of two layers Coordinate rotation should be performed when calculating footprints