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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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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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