Estimates of surface roughness length in heterogeneous under‐ice boundary layers

Measurements obtained in the under‐ice ocean boundary layer by two autonomous buoys deployed in 2004 and 2005 are used to estimate the roughness length z 0 of the underside morphology of Arctic Ocean pack ice. Two techniques are used to estimate z 0 . The first uses an extension of the law of the wall and directly measured turbulent shear stress and velocity at a single point near the ice‐ocean interface. The second uses a one‐dimensional numerical boundary layer model that is matched to measured velocity profiles in the outer part of the boundary layer with z 0 as an adjustable parameter. The stress‐based estimates are sensitive to local morphological features, and the effect of nearby ice ridge keels on the roughness estimates is evident. Averaged over flow direction there is a significant difference in floe roughness between the 2004 and 2005 deployments. Velocity‐profile‐based z 0 estimates are more uniform with direction than the stress‐based estimates, and the average value of the profile‐based estimates lies within the range of the stress‐based estimates. Averaged over flow direction, both techniques yield z 0 estimates of about 100 mm for the 2005 data set. A central question is how to best estimate a z 0 that can be applied to an individual grid cell in large‐scale numerical models. The profile‐based estimates are promising in this regard because they are less affected by local morphology than stress‐based measurements, which must be made fairly close to the interface in order to be interpretable using a framework based on the law of the wall.