Inferring Katabatic Jet Height from Cospectral Analysis of Turbulence

Katabatic winds strongly influence turbulent heat fluxes over glaciers, yet the turbulent length scales governing these fluxes remain poorly understood. The height of the wind speed maximum ( \(hⱼₑₜ\) ) has been proposed as a relevant turbulent length scale for some katabatic flows, while scaling based on distance from the surface (law-of-the-wall scaling) may apply when \(hⱼₑₜ\) exceeds the Obukhov length ( \( \) ). However, these relations remain underexplored for glacier surfaces and katabatic flows more broadly. In this study, we use cospectral analysis of near-surface eddy covariance measurements and kite-borne wind profiles from a glacier site to identify dominant turbulent length scales and assess their relation with \(hⱼₑₜ\) . We introduce a filtering method to remove non-turbulent contributions — such as internal gravity waves — from the cospectra, improving the reliability of length scale detection. For comparison, we investigate tower-based data from a non-glacierized site with deep katabatic flows. Our results reveal a one-to-one relation between the streamwise temperature flux length scale ( \(LuT\) ) and the smaller of \(hⱼₑₜ\) and \( \) , defining two regimes: \(hⱼₑₜ\) –scaling and \( \) –scaling, with \(hⱼₑₜ\) –scaling dominant at the glacier site. This relation indicates that it may be possible to detect katabatic jet height from near-surface observations from a single sensor. Neither site exhibited classical boundary layer scaling: turbulent mixing lengths scaled with distance from \(hⱼₑₜ\) rather than height above the surface. These findings challenge conventional turbulence scaling assumptions for katabatic flows.