• Alexander, M., and T. Dunkerton, 1999: A spectral parameterization of mean-flow forcing due to breaking gravity waves. J. Atmos. Phys., 56, 41674182, https://doi.org/10.1175/1520-0469(1999)056<4167:ASPOMF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Baldwin, M. P., D. B. Stephenson, D. W. J. Thompson, T. J. Dunkerton, A. J. Charlton, and A. O’Neill, 2003: Stratospheric memory and skill of extended-range weather forecasts. Science, 301, 636640, https://doi.org/10.1126/science.1087143.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Barton, C. A., J. P. McCormack, S. D. Eckermann, and K. W. Hoppel, 2019: Optimization of gravity wave source parameters for improved seasonal prediction of the quasi-biennial oscillation. J. Atmos. Sci., 76, 29412962, https://doi.org/10.1175/JAS-D-19-0077.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Beres, J. H., M. J. Alexander, and J. R. Holton, 2004: A method of specifying the gravity wave spectrum above convection based on latent heating properties and background wind. J. Atmos. Sci., 61, 324337, https://doi.org/10.1175/1520-0469(2004)061<0324:AMOSTG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bonavita, M., L. Isaksen, and E. Hólm, 2012: On the use of EDA background error variances in the ECMWF 4D-Var. ECMWF Tech Memo. 664, 33 pp., https://www.ecmwf.int/en/elibrary/8272-use-eda-background-error-variances-ecmwf-4d-var.

    • Crossref
    • Export Citation
  • Buehner, M., P. L. Houtekamer, C. Charette, H. L. Mitchell, and B. He, 2010: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part II: One-month experiments with real observations. Mon. Wea. Rev., 138, 15671586, https://doi.org/10.1175/2009MWR3158.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Charlton, A. J., A. O’Neill, A. C. Massacand, and W. A. Lahoz, 2004: Sensitivity of tropospheric forecasts to stratospheric initial conditions. Quart. J. Roy. Meteor. Soc., 130, 17711792, https://doi.org/10.1256/qj.03.167.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Charron, M., and E. Manzini, 2002: Gravity waves from fronts: Parameterization and middle atmosphere response in a general circulation model. J. Atmos. Sci., 59, 923941, https://doi.org/10.1175/1520-0469(2002)059<0923:GWFFPA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Clayton, A. M., A. C. Lorenc, and D. M. Barker, 2013: Operational implementation of a hybrid ensemble/4D-VAR global data assimilation system at the Met Office. Quart. J. Roy. Meteor. Soc., 139, 14451461, https://doi.org/10.1002/qj.2054.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Coy, L., S. D. Eckermann, K. W. Hoppel, and F. Sassi, 2011: Mesospheric precursors to the major stratospheric sudden warming of 2009: Validation and dynamical attribution using a ground-to-edge-of-space data assimilation system. J. Adv. Model. Earth Syst., 3, M10002, https://doi.org/10.1029/2011MS000067.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Daley, R., 1991: Statistical interpolation: Multivariate. Atmospheric Data Analysis, Cambridge University Press, 150–185.

  • Daley, R., and E. Barker, 2001: NAVDAS Source Book 2001. Naval Research Laboratory, 163 pp., https://apps.dtic.mil/sti/pdfs/ADA396883.pdf.

  • Davis, R. N., Y.-W. Chen, S. Miyahara, and N. J. Mitchell, 2012: The climatology, propagation and excitation of ultra-fast Kelvin waves as observed by meteor radar, Aura MLS, TRMM and in the Kyushu‐GCM. Atmos. Chem. Phys., 12, 18651879, https://doi.org/10.5194/acp-12-1865-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • de la Cámara, A., and F. Lott, 2015: A parameterization of gravity waves emitted by fronts and jets. Geophys. Res. Lett., 42, 20712078, https://doi.org/10.1002/2015GL063298.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • DelSole, T., and X. Yang, 2010: State parameter estimation in stochastic dynamical models. Physica D, 239, 17811788, https://doi.org/10.1016/j.physd.2010.06.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Domeisen, D. I. V., C. I. Garfinkel, and A. H. Butler, 2019: The teleconnection of El Niño Southern Oscillation to the stratosphere. Rev. Geophys., 57, 547, https://doi.org/10.1029/2018RG000596.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dowdy, A. J., R. A. Vincent, D. J. Murphy, M. Tsutsumi, D. M. Riggin, and M. J. Jarvis, 2004: The large-scale dynamics of the mesosphere-lower thermosphere during the Southern Hemisphere stratospheric warming of 2002. Geophys. Res. Lett., 31, L14102, https://doi.org/10.1029/2004GL020282.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eckermann, S. D., 2011: Explicitly stochastic parameterization of nonorographic gravity wave drag. J. Atmos. Sci., 68, 17491765, https://doi.org/10.1175/2011JAS3684.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eckermann, S. D., and Coauthors, 2009: High-altitude data assimilation system for the northern summer mesosphere season of 2007. J. Atmos. Sol.-Terr. Phys., 71, 531551, https://doi.org/10.1016/j.jastp.2008.09.036.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eckermann, S. D., and Coauthors, 2018: High-altitude (0–100 km) global atmospheric reanalysis system: Description and application to the 2014 austral winter of the Deep Propagating Gravity-Wave Experiment (DEEPWAVE). Mon. Wea. Rev., 146, 26392666, https://doi.org/10.1175/MWR-D-17-0386.1.

    • Search Google Scholar
    • Export Citation
  • Garcia, R. R., D. R. Marsh, D. E. Kinnison, B. A. Boville, and F. Sassi, 2007: Simulation of secular trends in the middle atmosphere, 1950–2003. J. Geophys. Res., 112, D09301, https://doi.org/10.1029/2006JD007485.

    • Search Google Scholar
    • Export Citation
  • Garfinkel, C. I., and L. D. Oman, 2018: Effect of gravity waves from small islands in the Southern Ocean on the Southern Hemisphere atmospheric circulation. J. Geophys. Res. Atmos., 123, 15521561, https://doi.org/10.1002/2017JD027576.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goncharenko, L. P., J. L. Chau, H.-L. Liu, and A. J. Coster, 2010: Unexpected connections between the stratosphere and ionosphere. Geophys. Res. Lett., 37, L10101, https://doi.org/10.1029/2010GL043125.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gong, J., M. A. Geller, and L. Wang, 2008: Source spectra information derived from U.S. high‐resolution radiosonde data. J. Geophys. Res., 113, D10106, https://doi.org/10.1029/2007JD009252.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hansen, J. A., and C. Penland, 2007: On stochastic parameter estimation using data assimilation. Physica D, 230, 8898, https://doi.org/10.1016/j.physd.2006.11.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hayashi, Y., D. G. Golder, and J. D. Mahlman, 1984: Stratospheric and mesospheric Kelvin waves simulated by the GFDL “SKYHI” general circulation model. J. Atmos. Sci., 41, 19711984, https://doi.org/10.1175/1520-0469(1984)041<1971:SAMKWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hogan, T. F., and Coauthors, 2014: The Navy Global Environmental Model. Oceanography, 27, 116125, https://doi.org/10.5670/oceanog.2014.73.

  • Holt, L. A., M. J. Alexander, L. Coy, A. Molod, W. Putman, and S. Pawson, 2016: Tropical waves and the quasi-biennial oscillation in a 7-km global climate simulation. J. Atmos. Sci., 73, 37713783, https://doi.org/10.1175/JAS-D-15-0350.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hoppel, K. W., S. D. Eckermann, L. Coy, G. E. Nedoluha, D. R. Allen, S. D. Swadley, and N. L. Baker, 2013: Evaluation of SSMIS upper atmosphere sounding channels for high-altitude data assimilation. Mon. Wea. Rev., 141, 33143330, https://doi.org/10.1175/MWR-D-13-00003.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ineson, S., and A. A. Scaife, 2009: The role of the stratosphere in the European climate response to El Niño. Nat. Geosci., 2, 3236, https://doi.org/10.1038/ngeo381.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jewtoukoff, V., A. Hertzog, R. Plougonven, A. de la Camara, and F. Lott, 2015: Comparison of gravity waves in the Southern Hemisphere derived from balloon observations and the ECMWF analyses. J. Atmos. Sci., 72, 34493468, https://doi.org/10.1175/JAS-D-14-0324.1.

    • Search Google Scholar
    • Export Citation
  • Jung, T., and J. Barkmeijer, 2006: Sensitivity of the tropospheric circulation to changes in the strength of the stratospheric polar vortex. Mon. Wea. Rev., 134, 21912207, https://doi.org/10.1175/MWR3178.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kiehl, J. T., J. J. Hack, G. D. Bonan, B. A. Boville, B. P. Brieglab, D. L. Williamson, and P. J. Rasch, 1996: Description of the NCAR Community Climate Model (CCM3). NCAR Tech. Note NCAR/TN-4201STR, 152 pp., http://www.cgd.ucar.edu/cms/ccm3/TN-420/.

  • Kim, Y.-J., S. D. Eckermann, and H.-Y. Chun, 2003: An overview of the past, present, and future of gravity-wave drag parameterization for numerical climate and weather prediction models. Atmos.–Ocean, 41, 6598, https://doi.org/10.3137/ao.410105.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuhl, D. D., T. E. Rosmond, C. H. Bishop, J. McLay, and N. L. Baker, 2013: Comparison of hybrid ensemble/4DVAR and 4DVAR within the NAVDAS-AR data assimilation framework. Mon. Wea. Rev., 141, 27402758, https://doi.org/10.1175/MWR-D-12-00182.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, H.-L., J. M. McInerney, S. Santos, P. H. Lauritzen, M. A. Taylor, and N. M. Pedatella, 2014: Gravity waves simulated by high-resolution Whole Atmosphere Community Climate Model. Geophys. Res. Lett., 41, 91069112, https://doi.org/10.1002/2014GL062468.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Livesey, N. J., and Coauthors, 2020: Version 4.2x Level 2 and 3 data quality and description document. Jet Propulsion Laboratory Doc. JPL D-33509 Rev. E, 174 pp., accessed 25 May 2021, https://mls.jpl.nasa.gov/data/v4-2_data_quality_document.pdf.

  • Long, D. J., D. R. Jackson, and J. Thuburn, 2014: Offline estimates and tuning of mesospheric gravity-wave forcing using Met Office analyses. Quart. J. Roy. Meteor. Soc., 140, 10251038, https://doi.org/10.1002/qj.2168.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McCormack, J. P., S. D. Eckermann, and T. F. Hogan, 2015: Generation of a quasi-biennial oscillation in an NWP model using a stochastic gravity wave drag parameterization. Mon. Wea. Rev., 143, 21212147, https://doi.org/10.1175/MWR-D-14-00208.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McFarlane, N. A., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44, 17751800, https://doi.org/10.1175/1520-0469(1987)044<1775:TEOOEG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McLandress, C., T. G. Shepherd, S. Polavarapu, and S. R. Beagley, 2012: Is missing orographic gravity wave drag near 60°S the case of the stratospheric zonal winds biases in chemistry–climate models? J. Atmos. Sci., 69, 802818, https://doi.org/10.1175/JAS-D-11-0159.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McLay, J. G., C. H. Bishop, and C. A. Reynolds, 2008: Evaluation of the ensemble transform analysis perturbation scheme at NRL. Mon. Wea. Rev., 136, 10931108, https://doi.org/10.1175/2007MWR2010.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Medvedev, A. S., and G. P. Klaassen, 2000: Parameterization of gravity wave momentum deposition based on nonlinear wave interactions: Basic formulation and sensitivity tests. J. Atmos. Sol.-Terr. Phys., 62, 10151033, https://doi.org/10.1016/S1364-6826(00)00067-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miyoshi, Y., and H. Fujiwara, 2006: Excitation mechanism of intraseasonal oscillation in the equatorial mesosphere and lower thermosphere. J. Geophys. Res., 111, D14108, https://doi.org/10.1029/2005JD006993.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moorthi, S., H.-L. Pan, and P. Caplan, 2001: Changes to the 2001 NCEP Operational MRF/AVN Global Analysis/Forecast System. National Weather Service Office of Meteorology, Tech. Procedures Bull. 484, 14 pp., accessed 5 April 2021, https://rda.ucar.edu/datasets/ds093.0/docs/484.pdf.

  • Palmer, T. N., G. J. Shutts, and R. Swinbank, 1986: Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parameterization. Quart. J. Roy. Meteor. Soc., 112, 10011039, https://doi.org/10.1002/qj.49711247406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pramitha, M., K. Kishore Kumar, M. Venat Ratnam, M. Praveen, and S. Vijaya Bhaskara Rao, 2020: Gravity wave source spectra appropriation for mesosphere lower thermosphere using meteor radar observations and GROGAT model simulations. Geophys. Res. Lett., 47, e2020GL089390, https://doi.org/10.1029/2020GL089390.

    • Crossref
    • Export Citation
  • Preusse, P., M. Ern, P. Bechtold, S. D. Eckermann, S. Kalisch, Q. T. Trinh, and M. Riese, 2014: Characteristics of gravity waves resolved by ECMWF. Atmos. Chem. Phys., 14, 10 48310 508, https://doi.org/10.5194/acp-14-10483-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pulido, M., 2014: A simple technique to infer the missing gravity wave drag in the middle atmosphere using a general circulation model: Potential vorticity budget. J. Atmos. Sci., 71, 683696, https://doi.org/10.1175/JAS-D-13-0198.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pulido, M., and J. Thuburn, 2005: Gravity wave drag estimation from global analyses using variational data assimilation principles. I: Theory and implementation. Quart. J. Roy. Meteor. Soc., 131, 18211840, https://doi.org/10.1256/qj.04.116.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pulido, M., and J. Thuburn, 2006: Gravity wave drag estimation from global analyses using variational data assimilation principles. II: A case-study. Quart. J. Roy. Meteor. Soc., 132, 15271543, https://doi.org/10.1256/qj.05.43.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pulido, M., and J. Thuburn, 2008: The seasonal cycle of gravity wave drag in the middle atmosphere. J. Climate, 21, 46644679, https://doi.org/10.1175/2008JCLI2006.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pulido, M., S. Polavarapu, T. Shepherd, and J. Thuburn, 2012: Estimation of optimal gravity wave parameters for climate models using data assimilation. Quart. J. Roy. Meteor. Soc., 138, 298309, https://doi.org/10.1002/qj.932.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Remsberg, E. E., and Coauthors, 2008: Assessment of the quality of the version 1.07 temperature-versus-pressure profiles of the middle atmosphere from TIMED/SAMBER. J. Geophys. Res., 113, D17101, https://doi.org/10.1029/2008JD010013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Richter, J. H., F. Sassi, and R. R. Garcia, 2010: Toward a physically based gravity wave source parameterization in a general circulation model. J. Atmos. Sci., 67, 136156, https://doi.org/10.1175/2009JAS3112.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roff, G., D. W. J. Thompson, and H. Hendon, 2011: Does increasing model stratospheric resolution improve extended-range forecast skill? Geophys. Res. Lett., 38, L05809, https://doi.org/10.1029/2010GL046515.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosmond, T., and L. Xu, 2006: Development of NAVDAS-AR: Non-linear formulation and outer loop tests. Tellus, 58A, 4558, https://doi.org/10.1111/j.1600-0870.2006.00148.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ruiz, J. J., M. Pulido, and Y. Moyoshi, 2013: Estimating model parameters with ensemble-based data assimilation: A review. J. Meteor. Soc. Japan, 91, 7999, https://doi.org/10.2151/jmsj.2013-201.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sato, K., S. Watanabe, Y. Kawatani, Y. Tomikawa, K. Miyazaki, and M. Takahashi, 2009: On the origins of mesospheric gravity waves. Geophys. Res. Lett., 36, L19801, https://doi.org/10.1029/2009GL039908.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sato, K., S. Tateno, S. Watanabe, and Y. Kawatani, 2012: Gravity wave characteristics in the Southern Hemisphere revealed by a high-resolution middle-atmosphere general circulation model. J. Atmos. Sci., 69, 13781396, https://doi.org/10.1175/JAS-D-11-0101.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Satterfield, E. A., D. Hodyss, D. D. Kuhl, and C. H. Bishop, 2018: Observation-informed generalized hybrid error covariance models. Mon. Wea. Rev., 146, 36053622, https://doi.org/10.1175/MWR-D-18-0016.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scheffler, G., and M. Pulido, 2017: Estimation of gravity-wave parameters to alleviate the delay in the Antarctic vortex breakup in general circulation models. Quart. J. Roy. Meteor. Soc., 143, 21572167, https://doi.org/10.1002/qj.3074.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schroeder, S., P. Preusse, M. Ern, and M. Riese, 2009: Gravity waves resolved in ECMWF and measured by SABER. Geophys. Res. Lett., 36, L10805, https://doi.org/10.1029/2008GL037054.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schwartz, M. J., and Coauthors, 2008: Validation of the Aura Microwave Limb Sounder temperature and geopotential height measurements. J. Geophys. Res., 113, D15S11, https://doi.org/10.1029/2007JD008783.

    • Search Google Scholar
    • Export Citation
  • Scinocca, J. F., 2003: An accurate spectral nonorographic gravity wave drag parameterization for general circulation models. J. Atmos. Sci., 60, 667682, https://doi.org/10.1175/1520-0469(2003)060<0667:AASNGW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scinocca, J. F., and B. R. Sutherland, 2010: Self-acceleration in the parameterization of orographic gravity wave drag. J. Atmos. Sci., 67, 25372546, https://doi.org/10.1175/2010JAS3358.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scinocca, J. F., N. A. McFarland, M. Lazare, J. Li, and D. Plummer, 2008: The CCCma third generation AGCM and its extension into the middle atmosphere. Atmos. Chem. Phys., 8, 70557074, https://doi.org/10.5194/acp-8-7055-2008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shaw, T. A., M. Sigmond, T. G. Shepherd, and J. F. Scinocca, 2009: Sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization. J. Climate, 22, 27262742, https://doi.org/10.1175/2009JCLI2688.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shepherd, T. G., 2000: The middle atmosphere. J. Atmos. Sol.-Terr. Phys., 62, 15871601, https://doi.org/10.1016/S1364-6826(00)00114-0.

  • Shutts, G. J., and S. B. Vosper, 2011: Stratospheric gravity waves revealed in NWP model forecasts. Quart. J. Roy. Meteor. Soc., 137, 303–317, https://doi.org/10.1002/qj.763.

    • Crossref
    • Export Citation
  • Song, I.-S., and H.-Y. Chun, 2005: Momentum flux spectrum of convectively forced internal gravity waves and its application to gravity wave drag parameterization. Part I: Theory. J. Atmos. Sci., 62, 107124, https://doi.org/10.1175/JAS-3363.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stephan, C. C., C. Strube, D. Klocke, M. Ern, L. Hoffmann, P. Preusse, and H. Schmidt, 2019a: Gravity waves in global high-resolution simulations with explicit and parameterized convection. J. Geophys. Res. Atmos., 124, 44464459, https://doi.org/10.1029/2018JD030073.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stephan, C. C., C. Strube, D. Klocke, M. Ern, L. Hoffmann, P. Preusse, and H. Schmidt, 2019b: Intercomparison of gravity waves in global convection-permitting models. J. Atmos. Sci., 76, 27392759, https://doi.org/10.1175/JAS-D-19-0040.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Swadley, S., G. Poe, W. Bell, Y. Hong, D. B. Kunkee, I. S. McDermid, and T. Leblanc, 2008: Analysis and characterization of the SSMIS upper atmosphere sounding channel measurements. IEEE Trans. Geosci. Remote Sens., 46, 962983, https://doi.org/10.1109/TGRS.2008.916980.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tandeo, P., M. Pulido, and F. Lott, 2015: Offline parameter estimation using EnKF and maximum likelihood error covariance estimates: Application to a subgrid-scale orography parametrization. Quart. J. Roy. Meteor. Soc., 141, 383395, https://doi.org/10.1002/qj.2357.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tandeo, P., P. Ailliot, M. Bocquet, A. Carrassi, T. Miyoshi, M. Pulido, and Y. Zhen, 2020: A review of innovation-based methods to jointly estimate model and observation error covariance matrices in ensemble data assimilation. Mon. Wea. Rev., 148, 39733994, https://doi.org/10.1175/MWR-D-19-0240.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, D. W. J., M. P. Baldwin, and J. M. Wallace, 2002: Stratospheric connection to Northern Hemisphere wintertime weather: Implications for prediction. J. Climate, 15, 14211428, https://doi.org/10.1175/1520-0442(2002)015<1421:SCTNHW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vosper, S. B., A. R. Brown, and S. Webster, 2016: Orographic drag on islands in the NWP mountain grey zone. Quart. J. Roy. Meteor. Soc., 142, 31283137, https://doi.org/10.1002/qj.2894.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, H., T. J. Fuller-Rowell, R. A. Akmaev, M. Hu, D. T. Kleist, and M. D. Iredell, 2011: First simulations with a whole atmosphere data assimilation and forecast system: The January 2009 major sudden stratospheric warming. J. Geophys. Res., 116, A12321, https://doi.org/10.1029/2011JA017081.

    • Search Google Scholar
    • Export Citation
  • Watanabe, S., K. Sato, Y. Kawatani, and M. Takahashi, 2015: Vertical resolution dependence of gravity wave momentum flux simulated by an atmospheric general circulation model. Geosci. Model Dev., 8, 16371644, https://doi.org/10.5194/gmd-8-1637-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Webster, S., A. R. Brown, D. R. Cameron, and C. P. Jones, 2003: Improvements to the representation of orography in the Met Office Unified Model. Quart. J. Roy. Meteor. Soc., 129, 19892010, https://doi.org/10.1256/qj.02.133.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xu, L., T. Rosmond, and R. Daley, 2005: Development of NAVDAS-AR: Formulation and initial tests of the linear problem. Tellus, 57A, 546559, https://doi.org/10.3402/tellusa.v57i4.14710.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, X. S., and T. Delsole, 2009: Using the ensemble Kalman filter to estimate multiplicative model parameters. Tellus, 61A, 601609, https://doi.org/10.1111/j.1600-0870.2009.00407.x.

    • Search Google Scholar
    • Export Citation
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Ensemble-Based Gravity Wave Parameter Retrieval for Numerical Weather Prediction

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  • 1 aRemote Sensing Division, U.S. Naval Research Laboratory, Washington, D.C.
  • | 2 bSpace Science Division, U.S. Naval Research Laboratory, Washington, D.C.
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Abstract

Gravity wave (GW) momentum and energy deposition are large components of the momentum and heat budgets of the stratosphere and mesosphere, affecting predictability across scales. Since weather and climate models cannot resolve the entire GW spectrum, GW parameterizations are required. Tuning these parameterizations is time-consuming and must be repeated whenever model configurations are changed. We introduce a self-tuning approach, called GW parameter retrieval (GWPR), applied when the model is coupled to a data assimilation (DA) system. A key component of GWPR is a linearized model of the sensitivity of model wind and temperature to the GW parameters, which is calculated using an ensemble of nonlinear forecasts with perturbed parameters. GWPR calculates optimal parameters using an adaptive grid search that reduces DA analysis increments via a cost-function minimization. We test GWPR within the Navy Global Environmental Model (NAVGEM) using three latitude-dependent GW parameters: peak momentum flux, phase-speed width of the Gaussian source spectrum, and phase-speed weighting relative to the source-level wind. Compared to a baseline experiment with fixed parameters, GWPR reduces analysis increments and improves 5-day mesospheric forecasts. Relative to the baseline, retrieved parameters reveal enhanced source-level fluxes and westward shift of the wave spectrum in the winter extratropics, which we relate to seasonal variations in frontogenesis. The GWPR reduces stratospheric increments near 60°S during austral winter, compensating for excessive baseline nonorographic GW drag. Tropical sensitivity is weaker due to significant absorption of GW in the stratosphere, resulting in less confidence in tropical GWPR values.

Corresponding author: D. R. Allen, douglas.allen@nrl.navy.mil

Abstract

Gravity wave (GW) momentum and energy deposition are large components of the momentum and heat budgets of the stratosphere and mesosphere, affecting predictability across scales. Since weather and climate models cannot resolve the entire GW spectrum, GW parameterizations are required. Tuning these parameterizations is time-consuming and must be repeated whenever model configurations are changed. We introduce a self-tuning approach, called GW parameter retrieval (GWPR), applied when the model is coupled to a data assimilation (DA) system. A key component of GWPR is a linearized model of the sensitivity of model wind and temperature to the GW parameters, which is calculated using an ensemble of nonlinear forecasts with perturbed parameters. GWPR calculates optimal parameters using an adaptive grid search that reduces DA analysis increments via a cost-function minimization. We test GWPR within the Navy Global Environmental Model (NAVGEM) using three latitude-dependent GW parameters: peak momentum flux, phase-speed width of the Gaussian source spectrum, and phase-speed weighting relative to the source-level wind. Compared to a baseline experiment with fixed parameters, GWPR reduces analysis increments and improves 5-day mesospheric forecasts. Relative to the baseline, retrieved parameters reveal enhanced source-level fluxes and westward shift of the wave spectrum in the winter extratropics, which we relate to seasonal variations in frontogenesis. The GWPR reduces stratospheric increments near 60°S during austral winter, compensating for excessive baseline nonorographic GW drag. Tropical sensitivity is weaker due to significant absorption of GW in the stratosphere, resulting in less confidence in tropical GWPR values.

Corresponding author: D. R. Allen, douglas.allen@nrl.navy.mil
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