Adapting tilt corrections and the governing flow equations for steep, fully three-dimensional, mountainous terrain

In recent studies of atmospheric turbulent surface exchange in complex terrain, questions arise concerning velocity-sensor tilt corrections and the governing flow equations for coordinate systems aligned with steep slopes. The standard planar-fit method, a popular tilt-correction technique, must be modified when applied to complex mountainous terrain. The ramifications of these adaptations have not previously been fully explored. Here, we carefully evaluate the impacts of the selection of sector size (the range of flow angles admitted for analysis) and planar-fit averaging time. We offer a methodology for determining an optimized sector-wise planar fit (SPF), and evaluate the sensitivity of momentum fluxes to varying these SPF input parameters. Additionally, we clarify discrepancies in the governing flow equations for slope-aligned coordinate systems that arise in the buoyancy terms due to the gravitational vector no longer acting along a coordinate axis. New adaptions to the momentum equations and turbulence kinetic energy budget equation allow for the proper treatment of the buoyancy terms for purely upslope or downslope flows, and for slope flows having a cross-slope component. Field data show that new terms in the slope-aligned forms of the governing flow equations can be significant and should not be omitted. Since the optimized SPF and the proper alignment of buoyancy terms in the governing flow equations both affect turbulent fluxes, these results hold implications for similarity theory or budget analyses for which accurate flux estimates are important.