Atmospheric boundary-layer flow over heterogeneous surfaces is a multi-scale problem that is impossible to “resolve” by any wind simulation; every level of computational grid refinement brings a new level of surface detail. Therefore, even the most advanced flow model depends upon subgrid-scale parameterisations often derived using idealised assumptions.

The logarithmic velocity profile (the “log-law”) is an analytical solution derived from assumptions of horizontal homogeneity, and it relates the surface “roughness length” to the near-ground wind speed. However, the premise of subgrid-scale homogeneity is often violated for flows over hilly terrain. Mesoscale models, as an example, have grid resolutions of several kilometres and therefore have considerable subgrid-scale surface variability. Still, due to the lack of alternatives, we may want to apply the log-law for complex terrain, even if it is outside its validation region.

One way to apply the log-law in complex terrain is to assume that the log-law accurately describes the areal-mean wind speed at some height above the hills (the displacement height). This dis-placed logarithmic velocity profile is characterised by an “effective” roughness length representing the drag exerted by the unresolved terrain below. But how valid is the dis-placed log law, and how do we determine the effective roughness length?

In a recent paper, Kelly and Cavar (2023) investigate these questions by analysing high-resolution CFD simulations of several complex terrains. They first show that the horizontally averaged flow above the displacement height follows the logarithmic profile. Secondly, they demonstrate that the standard deviation of the terrain slope correlates well with the effective roughness length, and thirdly provide mathematical formulations for estimating its value.

Kelly, Mark, and Dalibor Cavar. 2023. “Effective Roughness and Displaced Mean Flow over Complex Terrain.” Boundary-Layer Meteorology 186 (1): 93–123. https://doi.org/10.1007/s10546-022-00748-z.