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.

Turbulent Transport in Complex, Alpine Environments

Holly Jayne Oldroyd

Turbulent exchanges between the atmosphere and the underlying surface transport heat, moisture, momentum and pollutants, and thus understanding them is crucial to water resource management, meteorological predictions, climate modeling, wind energy production and pollution transport modeling and mitigation. The majority of established theories and techniques used to model, predict and observe turbulent exchange assume the underlying surface is flat, uniform and homogeneous. Consequently, in mountainous regions, turbulent exchanges are difficult to model and predict because they are intrinsically linked to the underlying surface conditions and complexity. Few observational studies have focused on the vertical structure of turbulent fluxes over mountainous terrain due to practical challenges. In sum, researchers and practitioners urgently need better theories and techniques to study and model turbulent exchange in alpine environments. In this dissertation, we analyze turbulent exchange measured over a steep, alpine slope in Switzerland to make quantitative comparisons with standard flat-terrain âlawsâ and practices and develop new theories and techniques adapted to mountainous terrain. First, flux-profile relations derived from Monin-Obukhov similarity theory are widely used in a variety of models to relate the surface conditions to atmospheric variables. We show that for katabatic flow, or thermally-driven air drainage that often occurs at night over sloping terrain, these relations break down because they do not account for the strong vertical gradients in the observed turbulent fluxes. However, the measurements exhibit clear functionalities that we use to derive new, empirical flux-profile relations for katabatic flow. Our functions indicate increased turbulent mixing compared to the flat-terrain relations. Misalignment between gravity and the inclined surface helps explain these functional differences because it reduces (and even reverses over steep slopes) the typical nighttime buoyant suppression of turbulent kinetic energy, which acts vertically via gravity. We also revise the governing flow equations to properly account for this misalignment. Second, standard data treatment techniques, such as sensor tilt corrections, do not hold true over complex topography. We develop an optimized sector-wise planar fit (SPF) tilt correction to best select the SPF input parameters for any complex site, and quantify the resulting sensitivities in the momentum fluxes. Finally, we present a mechanistic study that combines measurements and the one-dimensional momentum balance. Results show that frictional and buoyant mechanisms dominate, but that drag forces from the alpine grass canopy and the modeled outer-layer pressure (for conditions with low wind speeds) are also significant. In summary, this one-dimensional model or the newly developed flux-profile relations could replace inappropriate, flat-terrain wall models in larger-scale numerical models to improve atmospheric predictions for katabatic flow regimes. Additionally, terrain appropriate sensor tilt corrections and proper alignment of buoyant forces improve turbulent flux estimates for complex and steep topography, and hence have ramifications for similarity or budget analyses that require accurate quantification of turbulent exchange.

EPFL2015

Counter-Gradient, Co-Gradient and ‘Surface-Layer' Momentum Fluxes in Nocturnal Slope Flows over Steep Alpine Terrain

Holly Jayne Oldroyd, Eric Richard Pardyjak, Marc Parlange

Generally, the more an underlying terrain deviates from being flat, uniform and homogeneous, the less that classical theories and models of the atmospheric boundary layer hold. At times this leads to high uncertainties in turbulent flux predictions, and at other times the models completely break down. Hence, to better understand, model and subsequently predict surface turbulent exchanges over non-idealized terrain, an important objective of many recent field campaigns has been to investigate the near-surface turbulence structure. We present observations of momentum fluxes in nocturnal slope flows over steep (35.5 degree), alpine terrain in Val Ferret, Switzerland. Under clear-sky conditions, we observe two distinct flow regimes with mean winds directed down the slope: (1) buoyancy-driven, ‘katabatic flow', for which an elevated velocity maximum (katabatic jet peak) is observed and (2) ‘downslope winds', for which larger-scale forcing prevents formation of a katabatic jet. In downslope wind cases, the velocity profile is quite similar to a logarithmic profile often observed over flat terrain, and the corresponding momentum fluxes roughly resemble a constant-flux surface-layer. In stark contrast, the velocity profiles in the katabatic regime exhibit a jet-like shape. The katabatic jet strongly modulates the corresponding momentum fluxes, which show steep gradients over the shallow katabatic layer and typically change sign near the jet peak as the velocity gradients change sign. However, frequently a counter-gradient momentum flux is observed near the jet peak (and at times at higher levels), suggesting significant non-local turbulent transport within the katabatic jet layer. We compare and contrast this behavior with katabatic flow theories and observational studies over shallow-angle slopes, and use budget and co-spectral analyses to better understand the non-local transport dynamics. In addition, we show that as a consequence of the counter-gradient momentum fluxes, even local stability can be difficult to characterize because a counter-gradient momentum flux represent a sink in the shear term of turbulence kinetic energy budget equation. These results have broad implications for stability-based modeling of katabatic flows.

2016

Turbulent Transport in Complex, Alpine Environments

Holly Jayne Oldroyd

EPFL2015

Counter-Gradient, Co-Gradient and ‘Surface-Layer' Momentum Fluxes in Nocturnal Slope Flows over Steep Alpine Terrain

Holly Jayne Oldroyd, Eric Richard Pardyjak, Marc Parlange

2016