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Christopher G. Kruse, Ronald B. Smith, and Stephen D. Eckermann

and high-resolution modeling. Acknowledgments This work was supported by the National Science Foundation (NSF-AGS-1338655) and the Chief of Naval Research (PE-61153N). High-performance computing was performed on the Yellowstone supercomputer (ark:/85065/d7wd3xhc) with support provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation. We would like to acknowledge Andreas Dörnbrack for providing the ECMWF analyses, Johannes Wagner for

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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

width of the airglow emission profile I ( z ). Since I ( z ) extends to altitudes above 90 km, accurate numerical evaluation of (15) requires an accurate model of T ′( x , y , z ′, t c ) throughout the MLT, whereas our linear solutions begin to break down near 78 km (see Fig. 7 ). To gauge the effects more simply, we instead apply the spectral filter S AG ( m ) in (17) as an additional filter function multiplier S when inverting the Fourier solution using (3) at z = 78 km for t

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Christopher G. Kruse and Ronald B. Smith

and decelerate the flow from an initial profile. A pseudomomentum diagnostic is used to estimate nondissipative decelerations within these solutions. The linear FR model is also used to estimate linear nondissipative decelerations and to understand how finite forcing duration influences the evolution of a spectrum of MWs with a spectrum of vertical group velocities. Finally, dissipative decelerations by the LSP model are quantitatively evaluated against those in the WRF solutions. 2. Background

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Stephen D. Eckermann, Jun Ma, Karl W. Hoppel, David D. Kuhl, Douglas R. Allen, James A. Doyle, Kevin C. Viner, Benjamin C. Ruston, Nancy L. Baker, Steven D. Swadley, Timothy R. Whitcomb, Carolyn A. Reynolds, Liang Xu, N. Kaifler, B. Kaifler, Iain M. Reid, Damian J. Murphy, and Peter T. Love

the forecast model as a nonlinear operator M , such that forecast states where the index n denotes discrete successive forecast times and , then linearizing M around the background trajectory yields where is the tangent linear form of the forecast model (TLM) at . The current NAVGEM TLM and adjoint use a linearized Eulerian spectral core ( Rosmond 1997 ); a new TLM based on a linearized SISL core is currently being evaluated. Given an error covariance matrix for the background

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

et al. 2009 ). Therefore, various instruments and measurement techniques must be combined to cover the different altitude ranges and to obtain a comprehensive picture of the gravity wave spectrum (e.g., Bossert et al. 2014 ; Goldberg et al. 2004 ; Takahashi et al. 2014 ). Furthermore, complementary linear theory or numerical modeling is a necessary prerequisite to understand the characteristics and propagation properties of the observed gravity waves. The approach of the Role of the Middle

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Christopher G. Kruse and Ronald B. Smith

models and observations. Acknowledgments This work was supported by the National Science Foundation under Grant NSF-AGS-1338655. High-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) was provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation. We would like to acknowledge Andreas Dörnbrack for providing the ECMWF grids to force the WRF simulations, Johannes Wagner for assistance with WRF and ECMWF grids, and Simon Vosper

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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

.1002/qj.49711951110 . 10.1002/qj.49711951110 Skamarock , W. C. , 2004 : Evaluating mesoscale NWP models using kinetic energy spectra . Mon. Wea. Rev. , 132 , 3019 – 3032 , https://doi.org/10.1175/MWR2830.1 . 10.1175/MWR2830.1 Smith , R. B. , and Coauthors , 2016 : Stratospheric gravity wave fluxes and scales during DEEPWAVE . J. Atmos. Sci. , 73 , 2851 – 2869 , https://doi.org/10.1175/JAS-D-15-0324.1 . 10.1175/JAS-D-15-0324.1 Vosper , S. B. , A. R. Brown , and S. Webster , 2016

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

Holton 1968 ; Fels and Lindzen 1974 ; Lindzen 1981 ; Fritts and Alexander 2003 ). Over the past decade or two, MWs entering the stratosphere have received increasing attention because of new observations from emerging remote sensing tools ( Fritts et al. 2016 ; Pautet et al. 2016 ) and advances in numerical weather prediction models that allow for the use of deep domains ( Kruse and Smith 2015 ). In the high-latitude Southern Hemisphere during austral winter and spring, significant wave activity

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

, B. , P. Achtert , A. Dörnbrack , S. Gisinger , J. Gumbel , M. Khaplanov , M. Rapp , and J. Wagner , 2016 : Combination of lidar and model data for studying deep gravity wave propagation . Mon. Wea. Rev. , 144 , 77 – 98 , doi: 10.1175/MWR-D-14-00405.1 . 10.1175/MWR-D-14-00405.1 Frehlich , R. , 2001a : Errors for space-based Doppler lidar wind measurements: Definition, performance, and verification . J. Atmos. Oceanic Technol. , 18 , 1749 – 1772 , doi: 10

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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

1. Introduction The overarching objectives of the Deep Propagating Gravity Wave Experiment (DEEPWAVE; see appendix A for a list of key acronyms used in this paper) were to observe, model, understand, and predict the deep vertical propagation of internal gravity waves from the troposphere to the lower thermosphere and to study their impacts on the atmospheric momentum and energy budget ( Fritts et al. 2016 ). Convection, fronts, flow over mountains, and spontaneous adjustments occurring at the

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