Adapting Tilt Corrections and the Governing Flow Equations for Steep, Fully Three-Dimensional, Mountainous Terrain

Abstract

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 B Holly J. Oldroyd

Exchange Processes in the Atmospheric Boundary Layer Over Mountainous Terrain

“…For instance, the definition of the most appropriate coordinate system (slope-normal vs. vertical third coordinate-especially for the heat flux) and the associated post-processing of turbulence data (in terms of anemometer tilt correction) has triggered some discussion [58,67], but no agreement within the scientific community has yet been reached. While it is clear that post-processing matters and that it can substantially affect the estimation of turbulent fluxes and variances [16,58,68], no convincing arguments have been put forward yet that support the superiority of any of the possible options (e.g., tilt correction using double rotation or any of the various versions of planar-fit rotation) over the others.…”

Turbulent Mechanical Energy Budget in Stably Stratified Baroclinic Flows over Sloping Terrain

“…parallel to the gravity-force vector. However, use of this system to analyze flows over slopes is rather inconvenient, and so hereafter we use a Cartesian coordinate frame (x 1 , x 2 , x 3 ), termed the 'slope coordinates', with its x 3 axis perpendicular to the terrain, and the (x 1 , x 2 ) plane tangent to the slope; the x 1 axis orientation may still be freely chosen, e.g., streamwise, downslope/upslope, or eastward (see discussion in Oldroyd et al 2016a). There are two basic approaches to express the conservation equations in slope coordinates.…”

“…Recent experiments, such as the MATERHORN-X (Fernando et al 2015) and SELF-2010 (Nadeau et al 2013) field campaigns provided new information that encouraged many subsequent studies (e.g., Oldroyd et al 2014Oldroyd et al , 2016aGrachev et al 2016). One of the important aspects of this research is the turbulent exchange and turbulence structure close to the surface.…”

Evaporation from cultivated and semi-wild Sudanian Savanna in west Africa

“…We used a planar fit correction that effectively tilted measurements of the three components of the wind field perpendicular to the direction of flow, so that the vertical wind was equal to zero over 1-month averaging periods Burba, 2005;Oldroyd et al, 2015;Rebmann et al, 2012;Wilczak et al, 2001). We then performed a linear regression using the mean wind vectors to obtain a matrix that we used to adjust wind vectors and stress tensors in a new coordinate system with a z axis perpendicular to the mean streamline.…”