Boundary-layer flow within and above a forest canopy of variable density

An analytical model is developed for flow within and above a forest canopy with a slowly varying canopy density. Results are compared with existing analytical models for flow over a surface with slowly varying roughness length, and also with numerical simulations. The results show that the analytical solution is successful in capturing the behaviour of the flow for small and slowly changing variations in canopy density. Previous models which only vary the roughness length and neglect changes in displacement height fail to capture the near-surface flow accurately. Including changes in displacement height as well as roughness length changes gives results closer to those obtained with the full canopy model, but even then the flow induced in the canopy leads to significant differences. The analytical model also highlights the sensitivity of the results to the parametrization of the vertical component of the turbulent stress tensor, τ . For shorter wavelength variations in the canopy density, the analytical model breaks down as the more rapid changes in density induce larger flow perturbations which lead to increased flow into and out of the canopy. This kind of idealised analytical study provides important insights into the role of canopy heterogeneities on boundary-layer flow. This is important both for understanding near-surface winds and transport, and also for parametrizing the effects of surface heterogeneities in large-scale weather and climate models.