A New Formulation and Code to Compute Aerodynamic Roughness Length for Gridded Geometry—Tested on Lidar-Derived Snow Surfaces

The roughness of the Earth’s surface dictates the nature of air flow across it. Detailed meteorological data that are necessary to access the aerodynamic roughness ((Formula presented.)) are not widely collected and, as such, the geometry of a surface can be used to estimate (Formula presented.). Here, we present a novel formulation, and the corresponding computer code, to compute (Formula presented.) based on the Lettau (1969) geometric approach. The new code produces a mean (Formula presented.), as well as a histogram of all (Formula presented.) values for each individual roughness element (e.g., 10 s of thousand for the 1000 × 1000 grids) discretized using watersheds, as well as directional (Formula presented.) diagrams, which can be matches with the wind rose for the location. The formulation includes two parameters that may optionally be applied to smooth the surface before calculating (Formula presented.). By calculating (Formula presented.) as a function of these two parameters, we demonstrate the sensitivity of the (Formula presented.) value to these parameter choices. Since a large portion of the Earth’s surface is snow covered during some parts of the year, and the roughness of the snow surface varies over the snow season and over space, we apply the code to three snow surface datasets. Each surface is during a different phases of the snowpack. Each surface is evaluated at two resolutions). These surfaces are: fresh snow accumulation (1 m² at 1 and 10 mm), peak accumulation (1 km² at 1 and 10 m) and ablation sun cups (25 m² at 5 and 50 mm).