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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

numerical simulation and NCEP GFS = National Centers for Environmental Prediction Global Forecast System. MOTIVATIONS. GWs, or buoyancy waves, for which the restoring force is due to negatively (positively) buoyant air for upward (downward) displacements, play major roles in atmospheric dynamics, spanning a wide range of spatial and temporal scales. Vertical and horizontal wavelengths, λ z and λ h , respectively, for vertically propagating GWs are dictated by their sources and propagation conditions

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Benedikt Ehard, Peggy Achtert, Andreas Dörnbrack, Sonja Gisinger, Jörg Gumbel, Mikhail Khaplanov, Markus Rapp, and Johannes Wagner

. 2006 ), radars (e.g., Stober et al. 2013 ), airglow imagers (e.g., Suzuki et al. 2010 ), noctilucent cloud images (e.g., Pautet et al. 2011 ), satellite measurements (e.g., Alexander et al. 2008 ), radiosonde soundings (e.g., Dörnbrack et al. 1999 ; Zhang and Yi 2005 ), and rocket soundings (e.g., Rapp et al. 2004 ). However, these instruments are limited to particular altitude ranges and are only sensitive to a distinct part of the gravity wave spectrum ( Gardner and Taylor 1998 ; Preusse

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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

1. Introduction Gravity waves are ubiquitous features of the atmosphere. Although their major sources are tropospheric, some of these waves propagate into the stratosphere, mesosphere, and thermosphere where, in response to density decreases with height, amplitudes increase, leading to progressively larger impacts. Growth of amplitudes with height, for example, leads to wave breaking and deposition of energy and momentum into the flow as dynamical heating and body forcing, respectively

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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

value problem with “switch on” of surface forcing at t = 0. Since each harmonic ( k , l ) has an associated group propagation time to reach a given height z , then imposing a fixed cutoff time limit t prop ( k , l , z c ) = t c and solving numerically for z in (7) yields a spectrum of corresponding cutoff altitudes z c ( k , l , t c ). We can use this result to approximate the time-dependent wave field solution X ( x , y , z , t ) at time t = t c using the inverse Fourier

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Benjamin Witschas, Stephan Rahm, Andreas Dörnbrack, Johannes Wagner, and Markus Rapp

1. Introduction Internal waves are waves that oscillate within a stratified fluid. If the fluid is considered to be the atmosphere and the restoring force of vertical displaced air parcels is provided by buoyancy, such waves are called internal gravity waves or just gravity waves (GWs). GWs are ubiquitous in the atmosphere and their impact on the vertical transport and exchange of energy and momentum between the troposphere and the middle atmosphere is well known ( Fritts and Alexander 2003

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Qingfang Jiang, James D. Doyle, Stephen D. Eckermann, and Bifford P. Williams

Mellor and Yamada (1974) and Thompson and Burk (1991) . The surface heat and momentum fluxes are computed following Louis (1979) and Louis et al. (1982) . The gridscale evolution of the moist processes is explicitly predicted from budget equations for cloud water, cloud ice, rainwater, snowflakes, and water vapor ( Rutledge and Hobbs 1983 ), and the subgrid-scale moist convective processes are parameterized using an approach based on Kain and Fritsch (1993) . A δ -four-stream approximation is

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