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Ronald B. Smith and Christopher G. Kruse

predict this wave drag using regional environmental parameters. The development of wave drag theory for complex terrain has a long history. Wurtele (1957) , Crapper (1962) , Blumen and McGregor (1976) , and Smith (1980) examined mountain waves from ideally shaped isolated hills using linear theory. Phillips (1984) derived the wave drag on a smooth elliptical hill at various angles to the wind vector. He developed the idea of “transverse drag”: the component of wave drag perpendicular to the

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Christopher G. Kruse and Ronald B. Smith

state and small-scale perturbations. The third step takes pointwise products of the perturbation quantities to form quadratic diagnostic quantities (e.g., momentum flux). The last step involves low-pass spatial filtering to smooth the field and reduce noise, effectively “regionalizing” the diagnostics. These steps are described in the following subsections. Note that limited area models often make use of map projections leading to nonuniform grids on the earth. In the presented WRF simulations, the

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David C. Fritts, Ronald B. Smith, Michael J. Taylor, James D. Doyle, Stephen D. Eckermann, Andreas Dörnbrack, Markus Rapp, Bifford P. Williams, P.-Dominique Pautet, Katrina Bossert, Neal R. Criddle, Carolyn A. Reynolds, P. Alex Reinecke, Michael Uddstrom, Michael J. Revell, Richard Turner, Bernd Kaifler, Johannes S. Wagner, Tyler Mixa, Christopher G. Kruse, Alison D. Nugent, Campbell D. Watson, Sonja Gisinger, Steven M. Smith, Ruth S. Lieberman, Brian Laughman, James J. Moore, William O. Brown, Julie A. Haggerty, Alison Rockwell, Gregory J. Stossmeister, Steven F. Williams, Gonzalo Hernandez, Damian J. Murphy, Andrew R. Klekociuk, Iain M. Reid, and Jun Ma

). Research goals motivating the DEEPWAVE measurement program are summarized in Table 1 . To achieve our research goals, DEEPWAVE needed to sample regions having large horizontal extents because of large horizontal GW propagation distances for some GW sources. DEEPWAVE accomplished this goal through airborne and ground-based (GB) measurements that together provided sensitivity to multiple GW sources and their propagation to, and effects at, higher altitudes. DEEPWAVE was performed over and around the GW

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Stephen D. Eckermann, Dave Broutman, Jun Ma, James D. Doyle, Pierre-Dominique Pautet, Michael J. Taylor, Katrina Bossert, Bifford P. Williams, David C. Fritts, and Ronald B. Smith

1. Introduction The Deep Propagating Gravity Wave Experiment (DEEPWAVE) was a field measurement campaign to observe the end-to-end dynamics of gravity waves—generation, propagation, breakdown, and effects on large-scale circulations—at altitudes from the ground to ~100 km. The primary observational platform was the National Science Foundation (NSF)/National Center for Atmospheric Research (NCAR) Gulfstream V research aircraft (NGV: Laursen et al. 2006 ), which for DEEPWAVE was equipped with a

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Christopher G. Kruse and Ronald B. Smith

simulations of the atmospheric general circulation at nearly all levels (e.g., Holton 1983 ; Garcia and Solomon 1985 ; McLandress 1998 ; Palmer et al. 1986 ; McFarlane 1987 ), demonstrating the importance of MW momentum deposition. This deposition is important regionally as well (e.g., Lott and Miller 1997 ; Chen et al. 2007 ). Conventionally, MW parameterizations make use of steady, linear theory, where the ambient environment is horizontally homogeneous and both the environment and the waves

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Stephen D. Eckermann, James D. Doyle, P. Alex Reinecke, Carolyn A. Reynolds, Ronald B. Smith, David C. Fritts, and Andreas Dörnbrack

is seeded by subwavelength instabilities that form at unstable wave phases ( Andreassen et al. 1998 ). Current weather and climate models typically run at horizontal gridpoint resolutions of ~10–100 km, approaching a so-called gray zone (e.g., Vosper et al. 2016 ) where long-wavelength gravity waves are resolved explicitly, but the net drag effects of smaller-scale waves on the resolved flow require parameterization ( Kim et al. 2003 ). Despite decades of research, vigorous debate persists about

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Ronald B. Smith and Christopher G. Kruse

. Fritts , 1990 : Further study of terrain effects on the mesoscale spectrum of atmospheric motions . J. Atmos. Sci. , 47 , 979 – 987 , doi: 10.1175/1520-0469(1990)047<0979:FSOTEO>2.0.CO;2 . 10.1175/1520-0469(1990)047<0979:FSOTEO>2.0.CO;2 Korup , O. , J. Schmidt , and M. J. McSaveny , 2005 : Regional relief characteristics and denudation pattern of the western Southern Alps . Geomorphology , 71 , 402 – 423 , doi: 10.1016/j.geomorph.2005.04.013 . 10.1016/j.geomorph.2005.04.013 Kruse

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Ronald B. Smith, Alison D. Nugent, Christopher G. Kruse, David C. Fritts, James D. Doyle, Steven D. Eckermann, Michael J. Taylor, Andreas Dörnbrack, M. Uddstrom, William Cooper, Pavel Romashkin, Jorgen Jensen, and Stuart Beaton

current state of knowledge of gravity waves fluxes around the world is nicely reviewed by Geller at al. (2013) . They emphasize that satellites and global models are unable to resolve the short wavelength components of the gravity wave spectrum. In addition, wave parameterization schemes are oversimplified and differ from model to model. As a result, there are significant differences and uncertainties in regional wave momentum flux (MF) estimates. In the Southern Hemisphere winter, for example, the

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Sonja Gisinger, Andreas Dörnbrack, Vivien Matthias, James D. Doyle, Stephen D. Eckermann, Benedikt Ehard, Lars Hoffmann, Bernd Kaifler, Christopher G. Kruse, and Markus Rapp

coefficients r (valid for Ri ≫ ¼) from ECMWF 6-hourly operational analyses (stars) and 24-h running means (solid lines) using an averaged stratospheric value of N (gray) and N MAX taken in the UTLS (black). (b) The 3-hourly regional vertical energy fluxes over SI computed from WRF constrained by MERRA2 initial conditions at 4- (gray) and 12-km (black) altitude. Arrows mark the GW events, when the reflection coefficient is close to or larger than 0.5 and the EF z at 12 km is reduced by 47%–77% (red

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