Effects of Horizontal Geometrical Spreading on the Parameterization of Orographic Gravity Wave Drag. Part I: Numerical Transform Solutions

Abstract

Numerical transform solutions for hydrostatic gravity waves generated by both uniform and sheared flow over elliptical obstacles are used to quantify effects of horizontal geometrical spreading on amplitude evolution with height. Both vertical displacement and steepness amplitudes are considered because of their close connections to drag parameterizations in weather and climate models. Novel diagnostics quantify the location and value of the largest wavefield amplitudes most likely to break at each altitude. These horizontal locations do not stray far from the obstacle peak even at high altitudes. Resulting vertical profiles of wave amplitude are normalized to remove density and refraction effects, thereby quantifying the horizontal geometrical spreading contribution, currently absent from parameterizations. Horizontal geometrical spreading produces monotonic amplitude decreases with height through wave-action conservation as waves propagate into progressively larger horizontal areas. Accumulated amplitude reductions are appreciable for all but the most quasi-two-dimensional obstacles with long axes orthogonal to the flow, and even these are impacted appreciably if the obstacle is rotated by more than 208-308. Profiles are insensitive to the obstacle's functional form but vary strongly in response to changes in its horizontal aspect ratio. Responses to background winds are captured by a vertical coordinate transformation that remaps profiles to a universal form for a given obstacle. These results show that horizontal geometrical spreading has comparable or larger effects on wave amplitudes as the refraction of vertical wavenumbers and thus is important for accurate parameterizations of wave breaking and drag.

Impacts of Horizontal Propagation of Orographic Gravity Waves on the Wave Drag in the Stratosphere and Lower Mesosphere

“…As revealed by the notable difference between OGWD_H and OGWD_V (e.g., Figure ), the horizontal propagation of mountain waves has a great influence on the mountain wave drag. In accordance with Eckermann et al () and X17, the horizontal propagation of mountain waves can reduce the local wave amplitude with height. Therefore, mountain waves in the X17 scheme are prone to break at higher altitudes than in the LM97 scheme.…”

Spatial and temporal variability in MLT turbulence inferred from in situ and ground-based observations during the WADIS-1 sounding rocket campaign

“…Since the pioneering work of Lindzen (1981) followed by modeling efforts (see, e.g., Holton, 1982;Fritts and Alexander, 2003;Eckermann et al, 2015b, a) and experimental evidences (e.g., Goldberg et al, 2004Goldberg et al, , 2006, it is now understood that the thermal structure and circulation pattern of the mesosphere/lower thermosphere (MLT) region is essentially determined by dynamic processes. The latter include gravity waves, tides, their interaction with each other and with the background atmosphere, generally summarized by terms wave-wave and wave-mean flow interaction.…”

Directional Absorption of Parameterized Mountain Waves and Its Influence on the Wave Momentum Transport in the Northern Hemisphere

“…In the LM97 scheme mountain‐wave breaking tends to take place at lower height (see the OGWD immediately above the tropopause in Figure a) than in the other two schemes (Figures c and e). This is attributed to the horizontal propagation of mountain waves which reduces the wave amplitude and pushes wave breaking to higher altitudes (Eckermann et al, ). For instance, the wintertime OGWD is suppressed (enhanced) in the lower stratosphere (middle to upper stratosphere and lower mesosphere) in the X17 scheme when compared to the LM97 scheme (Figure a), consistent with the results of Xu, Shu, and Wang ().…”