Articles | Volume 23, issue 11
https://doi.org/10.5194/acp-23-6145-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/acp-23-6145-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
06 Jun 2023
Research article |
| 06 Jun 2023
| 06 Jun 2023
Variations in global zonal wind from 18 to 100 km due to solar activity and the quasi-biennial oscillation and El Niño–Southern Oscillation during 2002–2019
Institute of Electromagnetic Wave, School of Physics, Henan Normal
University, Xinxiang, 453000, China
State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, 100190, China
Jiyao Xu
CORRESPONDING AUTHOR
State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, 100190, China
School of Astronomy and Space Science, University of the Chinese Academy of Science, Beijing, 100049, China
Physics Department, Catholic University of America, Washington, DC
20064, USA
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Vania F. Andrioli
State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, 100190, China
Heliophysics, Planetary Science and Aeronomy Division, National Institute for Space Research (INPE), São José dos Campos, São Paulo, Brazil
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Xiao Liu, Jiyao Xu, Jia Yue, Yangkun Liu, and Vania F. Andrioli
EGUsphere, https://doi.org/10.5194/egusphere-2024-396, https://doi.org/10.5194/egusphere-2024-396, 2024
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The disagreement of long-term trends of the high latitude mesosphere temperature should be elucidated using one coherent measurement over a long period. Using the advantages of SABER measurements at high latitudes and binning the data based on yaw cycle, we focus on long-term trends of the mean temperature and mesopause at the high latitude MLT region, which has been rarely studied through observations but is more sensitive to dynamic changes.
Qinzeng Li, Jiyao Xu, Aditya Riadi Gusman, Hanli Liu, Wei Yuan, Weijun Liu, Yajun Zhu, and Xiao Liu
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The 2022 Hunga Tonga-Hunga Ha’apai (HTHH) volcano eruption not only triggered broad spectrum atmospheric waves, but also generated unusual tsunamis which can generate AGWs. Multi-group of strong atmospheric waves were observed in the far-field area of the 2022 HTHH volcano eruption in the upper atmosphere by a ground-based airglow network. The AGWs caused by tsunamis can propagate to the mesopause region, and there is a good match between atmospheric waves and tsunamis.
Qinzeng Li, Jiyao Xu, Hanli Liu, Xiao Liu, and Wei Yuan
Atmos. Chem. Phys., 22, 12077–12091, https://doi.org/10.5194/acp-22-12077-2022, https://doi.org/10.5194/acp-22-12077-2022, 2022
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We use ground-based airglow network observations, reanalysis data, and satellite observations to explore the propagation process of concentric gravity waves (CGWs) excited by a typhoon between the troposphere, stratosphere, mesosphere, and thermosphere. We find that CGWs in the mesosphere are generated directly by the typhoon but the CGW observed in the thermosphere may be excited by CGW dissipation in the mesosphere, rather than directly excited by a typhoon and propagated to the thermosphere.
Xiao Liu, Jiyao Xu, Jia Yue, You Yu, Paulo P. Batista, Vania F. Andrioli, Zhengkuan Liu, Tao Yuan, Chi Wang, Ziming Zou, Guozhu Li, and James M. Russell III
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Based on the gradient balance wind theory and the SABER observations, a dataset of monthly mean zonal wind has been developed at heights of 18–100 km and latitudes of 50° Sndash;50° N from 2002 to 2019. The dataset agrees with the zonal wind from models (MERRA2, UARP, HWM14) and observations by meteor radar and lidar at seven stations. The dataset can be used to study seasonal and interannual variations and can serve as a background for wave studies of tides and planetary waves.
Xiao Liu, Jiyao Xu, Jia Yue, and Hanli Liu
Atmos. Chem. Phys., 20, 14437–14456, https://doi.org/10.5194/acp-20-14437-2020, https://doi.org/10.5194/acp-20-14437-2020, 2020
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Large wind shears in the mesosphere and lower thermosphere are recognized as a common phenomenon. Simulation and ground-based observations show that the main contributor of large wind shears is gravity waves. We present a method of deriving wind shears induced by gravity waves according to the linear theory and using the global temperature observations by SABER (Sounding of the Atmosphere using Broadband Emission Radiometry). Our results agree well with observations and model simulations.
Gunter Stober, Sharon L. Vadas, Erich Becker, Alan Liu, Alexander Kozlovsky, Diego Janches, Zishun Qiao, Witali Krochin, Guochun Shi, Wen Yi, Jie Zeng, Peter Brown, Denis Vida, Neil Hindley, Christoph Jacobi, Damian Murphy, Ricardo Buriti, Vania Andrioli, Paulo Batista, John Marino, Scott Palo, Denise Thorsen, Masaki Tsutsumi, Njål Gulbrandsen, Satonori Nozawa, Mark Lester, Kathrin Baumgarten, Johan Kero, Evgenia Belova, Nicholas Mitchell, Tracy Moffat-Griffin, and Na Li
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On 15 January 2022, the Hunga Tonga-Hunga Ha‘apai volcano exploded in a vigorous eruption, causing many atmospheric phenomena reaching from the surface up to space. In this study, we investigate how the mesospheric winds were affected by the volcanogenic gravity waves and estimated their propagation direction and speed. The interplay between model and observations permits us to gain new insights into the vertical coupling through atmospheric gravity waves.
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The 2022 Hunga Tonga-Hunga Ha’apai (HTHH) volcano eruption not only triggered broad spectrum atmospheric waves, but also generated unusual tsunamis which can generate AGWs. Multi-group of strong atmospheric waves were observed in the far-field area of the 2022 HTHH volcano eruption in the upper atmosphere by a ground-based airglow network. The AGWs caused by tsunamis can propagate to the mesopause region, and there is a good match between atmospheric waves and tsunamis.
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Ann. Geophys., 41, 209–224, https://doi.org/10.5194/angeo-41-209-2023, https://doi.org/10.5194/angeo-41-209-2023, 2023
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In the terrestrial ionosphere, sporadic (metallic) layers are formed. The formation of these layers are related to the action of atmospheric waves. These waves, also named tides, are due to the absorption of solar radiation in the atmosphere. We investigated the role of the tides with 8 h period in the formation of the sporadic layers. The study was conducted using ionosonde and meteor radar data, as well as computing simulations. The 8 h tides intensified the density of the sporadic layers.
Qinzeng Li, Jiyao Xu, Hanli Liu, Xiao Liu, and Wei Yuan
Atmos. Chem. Phys., 22, 12077–12091, https://doi.org/10.5194/acp-22-12077-2022, https://doi.org/10.5194/acp-22-12077-2022, 2022
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Yetao Cen, Chengyun Yang, Tao Li, James M. Russell III, and Xiankang Dou
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The MLT DW1 amplitude is suppressed during El Niño winters in both satellite observation and SD-WACCM simulations. The suppressed Hough mode (1, 1) in the tropopause region propagates vertically to the MLT region, leading to decreased DW1 amplitude. The latitudinal zonal wind shear anomalies during El Niño winters would narrow the waveguide and prevent the vertical propagation of DW1. The gravity wave drag excited by ENSO-induced anomalous convection could also modulate the MLT DW1 amplitude.
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Based on the gradient balance wind theory and the SABER observations, a dataset of monthly mean zonal wind has been developed at heights of 18–100 km and latitudes of 50° Sndash;50° N from 2002 to 2019. The dataset agrees with the zonal wind from models (MERRA2, UARP, HWM14) and observations by meteor radar and lidar at seven stations. The dataset can be used to study seasonal and interannual variations and can serve as a background for wave studies of tides and planetary waves.
Zhaohai He, Jiyao Xu, Ilan Roth, Chi Wang, and Lei Dai
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Xiao Liu, Jiyao Xu, Jia Yue, and Hanli Liu
Atmos. Chem. Phys., 20, 14437–14456, https://doi.org/10.5194/acp-20-14437-2020, https://doi.org/10.5194/acp-20-14437-2020, 2020
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Pingping Rong, Jia Yue, James M. Russell III, David E. Siskind, and Cora E. Randall
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Q. Gan, J. Yue, L. C. Chang, W. B. Wang, S. D. Zhang, and J. Du
Ann. Geophys., 33, 913–922, https://doi.org/10.5194/angeo-33-913-2015, https://doi.org/10.5194/angeo-33-913-2015, 2015
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The 6.5-day traveling planetary wave is able to impact the ionosphere/thermosphere via a dissipation mechanism. Ionospheric TEC and thermosphere O/N2 exhibit an apparent decrease as the result of extra meridional circulation induced by 6.5-day wave dissipation. Our work suggests that the modulation of E-dynamo is not the unique pathway through which planetary waves substantially influence the IT system.
X. Liu, J. Xu, H.-L. Liu, J. Yue, and W. Yuan
Ann. Geophys., 32, 543–552, https://doi.org/10.5194/angeo-32-543-2014, https://doi.org/10.5194/angeo-32-543-2014, 2014
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Subject: Dynamics | Research Activity: Field Measurements | Altitude Range: Mesosphere | Science Focus: Physics (physical properties and processes)
Radar observations of winds, waves and tides in the mesosphere and lower thermosphere over South Georgia island (54° S, 36° W) and comparison with WACCM simulations
Simultaneous in situ measurements of small-scale structures in neutral, plasma, and atomic oxygen densities during the WADIS sounding rocket project
Mesospheric anomalous diffusion during noctilucent cloud scenarios
Thermal structure of the mesopause region during the WADIS-2 rocket campaign
On the origin of the mesospheric quasi-stationary planetary waves in the unusual Arctic winter 2015/2016
Influence of geomagnetic activity on mesopause temperature over Yakutia
Quasi-12 h inertia–gravity waves in the lower mesosphere observed by the PANSY radar at Syowa Station (39.6° E, 69.0° S)
Change in turbopause altitude at 52 and 70° N
High-resolution observations of the near-surface wind field over an isolated mountain and in a steep river canyon
Characteristics and sources of gravity waves observed in noctilucent cloud over Norway
Observation of a mesospheric front in a thermal-doppler duct over King George Island, Antarctica
The role of the QBO in the inter-hemispheric coupling of summer mesospheric temperatures
Neil P. Hindley, Nicholas J. Mitchell, Neil Cobbett, Anne K. Smith, Dave C. Fritts, Diego Janches, Corwin J. Wright, and Tracy Moffat-Griffin
Atmos. Chem. Phys., 22, 9435–9459, https://doi.org/10.5194/acp-22-9435-2022, https://doi.org/10.5194/acp-22-9435-2022, 2022
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We present observations of winds in the mesosphere and lower thermosphere (MLT) from a recently installed meteor radar on the remote island of South Georgia (54° S, 36° W). We characterise mean winds, tides, planetary waves, and gravity waves in the MLT at this location and compare our measured winds with a leading climate model. We find that the observed wintertime winds are unexpectedly reversed from model predictions, probably because of missing impacts of secondary gravity waves in the model.
Boris Strelnikov, Martin Eberhart, Martin Friedrich, Jonas Hedin, Mikhail Khaplanov, Gerd Baumgarten, Bifford P. Williams, Tristan Staszak, Heiner Asmus, Irina Strelnikova, Ralph Latteck, Mykhaylo Grygalashvyly, Franz-Josef Lübken, Josef Höffner, Raimund Wörl, Jörg Gumbel, Stefan Löhle, Stefanos Fasoulas, Markus Rapp, Aroh Barjatya, Michael J. Taylor, and Pierre-Dominique Pautet
Atmos. Chem. Phys., 19, 11443–11460, https://doi.org/10.5194/acp-19-11443-2019, https://doi.org/10.5194/acp-19-11443-2019, 2019
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Sounding rockets are the only means of measuring small-scale structures (i.e., spatial scales of kilometers to centimeters) in the Earth's middle atmosphere (50–120 km). We present and analyze brand-new high-resolution measurements of atomic oxygen (O) concentration together with high-resolution measurements of ionospheric plasma and neutral air parameters. We found a new behavior of the O inside turbulent layers, which might be essential to adequately model weather and climate.
Fazlul I. Laskar, Gunter Stober, Jens Fiedler, Meers M. Oppenheim, Jorge L. Chau, Duggirala Pallamraju, Nicholas M. Pedatella, Masaki Tsutsumi, and Toralf Renkwitz
Atmos. Chem. Phys., 19, 5259–5267, https://doi.org/10.5194/acp-19-5259-2019, https://doi.org/10.5194/acp-19-5259-2019, 2019
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Meteor radars are used to track and estimate the fading time of meteor trails. In this investigation, it is observed that the diffusion time estimated from such trail fading time is anomalously higher during noctilucent clouds (NLC) than that in its absence. We propose that NLC particles absorb background electrons and thus modify the background electrodynamics, leading to such an anomaly.
Raimund Wörl, Boris Strelnikov, Timo P. Viehl, Josef Höffner, Pierre-Dominique Pautet, Michael J. Taylor, Yucheng Zhao, and Franz-Josef Lübken
Atmos. Chem. Phys., 19, 77–88, https://doi.org/10.5194/acp-19-77-2019, https://doi.org/10.5194/acp-19-77-2019, 2019
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Simultaneous temperature measurements during the WADIS-2 rocket campaign are used to investigate the thermal structure of the mesopause region. Vertically and horizontally resolved in situ and remote measurements are in good agreement and show dominating long-term and large-scale waves with periods of 24 h and higher tidal harmonics. Only a few gravity waves with periods shorter than 6 h and small amplitudes are there.
Vivien Matthias and Manfred Ern
Atmos. Chem. Phys., 18, 4803–4815, https://doi.org/10.5194/acp-18-4803-2018, https://doi.org/10.5194/acp-18-4803-2018, 2018
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The aim of this study is to find the origin of mesospheric stationary planetary wave (SPW) in the subtropics and in mid and polar latitudes in mid winter 2015/2016. Our results based on observations show that upward propagating SPW and in situ generated SPWs by longitudinally variable gravity wave drag and by instabilities can be responsible for the occurrence of mesospheric SPWs and that they can act at the same time, which confirms earlier model studies.
Galina Gavrilyeva and Petr Ammosov
Atmos. Chem. Phys., 18, 3363–3367, https://doi.org/10.5194/acp-18-3363-2018, https://doi.org/10.5194/acp-18-3363-2018, 2018
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The study of the response of the upper atmosphere to changes in solar and geomagnetic activity is an important contribution to the study of the Earth's climate. Measurements showed that the change in the atmospheric temperature at an altitude of 87 km above Yakutia lags behind the maximum solar radiation by 2 years and correlates with a change in geomagnetic activity. The winter temperature is higher in the years of the geomagnetic activity maximum than in the years of the minimum.
Ryosuke Shibuya, Kaoru Sato, Masaki Tsutsumi, Toru Sato, Yoshihiro Tomikawa, Koji Nishimura, and Masashi Kohma
Atmos. Chem. Phys., 17, 6455–6476, https://doi.org/10.5194/acp-17-6455-2017, https://doi.org/10.5194/acp-17-6455-2017, 2017
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The first observations made by a complete PANSY radar system (Program of the Antarctic Syowa MST/IS radar) installed at Syowa Station were successfully performed from 16 to 24 March 2015. Over this period, quasi-12 h period disturbances in the mesosphere at heights of 70 to 80 km were observed. Combining the observational data and numerical simulation outputs, we found that quasi-12 h disturbances are due to large-scale inertia–gravity waves, not to semi-diurnal migrating tides.
Chris M. Hall, Silje E. Holmen, Chris E. Meek, Alan H. Manson, and Satonori Nozawa
Atmos. Chem. Phys., 16, 2299–2308, https://doi.org/10.5194/acp-16-2299-2016, https://doi.org/10.5194/acp-16-2299-2016, 2016
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Turbulent energy dissipation rates are calculated using MF-radar signals from 70 and 52° N for the period 2001–2014 inclusive, and they are used to estimate turbopause altitudes. A positive trend in turbopause altitude is identified for 70° N in summer, but not in winter and not at 52° N. The turbopause altitude change between 2001 and 2014 can be used to hypothesize a corresponding change in atomic oxygen concentration.
B. W. Butler, N. S. Wagenbrenner, J. M. Forthofer, B. K. Lamb, K. S. Shannon, D. Finn, R. M. Eckman, K. Clawson, L. Bradshaw, P. Sopko, S. Beard, D. Jimenez, C. Wold, and M. Vosburgh
Atmos. Chem. Phys., 15, 3785–3801, https://doi.org/10.5194/acp-15-3785-2015, https://doi.org/10.5194/acp-15-3785-2015, 2015
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Interest in numerical wind models continues to increase, especially for models that can simulate winds at relatively high spatial resolution (~100m). However, limited observational data exist for evaluation of model predictive performance. This study presents high-resolution surface wind data sets collected from an isolated mountain and a steep river canyon. The data are available to the public at http://www.firemodels.org/index.php/windninja-introduction/windninja-publications.
T. D. Demissie, P. J. Espy, N. H. Kleinknecht, M. Hatlen, N. Kaifler, and G. Baumgarten
Atmos. Chem. Phys., 14, 12133–12142, https://doi.org/10.5194/acp-14-12133-2014, https://doi.org/10.5194/acp-14-12133-2014, 2014
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Summertime gravity waves detected in noctilucent clouds (NLCs) between 64◦ and 74◦N are found to have a similar climatology to those observed between 60◦ and 64◦N, and their direction of propagation is to the north and northeast as observed south of 64◦N. However, a unique population of fast, short wavelength waves propagating towards the SW is observed in the NLC. The sources of the prominent wave structures observed in the NLC are likely to be from waves propagating from near the tropopause.
J. V. Bageston, C. M. Wrasse, P. P. Batista, R. E. Hibbins, D. C Fritts, D. Gobbi, and V. F. Andrioli
Atmos. Chem. Phys., 11, 12137–12147, https://doi.org/10.5194/acp-11-12137-2011, https://doi.org/10.5194/acp-11-12137-2011, 2011
P. J. Espy, S. Ochoa Fernández, P. Forkman, D. Murtagh, and J. Stegman
Atmos. Chem. Phys., 11, 495–502, https://doi.org/10.5194/acp-11-495-2011, https://doi.org/10.5194/acp-11-495-2011, 2011
Cited articles
Baldwin, M. P. and O'Sullivan, D.: Stratospheric Effects of ENSO-Related Tropospheric Circulation Anomalies, J. Climate, 8, 649–667, https://doi.org/10.1175/1520-0442(1995)008<0649:SEOERT>2.0.CO;2, 1995.
Baldwin, M. P., Gray, L. J., Dunkerton, T. J., Hamilton, K., Haynes, P. H.,
Randel, W. J., Holton, J. R., Alexander, M. J., Hirota, I., Horinouchi, T.,
Jones, D. B. A., Kinnersley, J. S., Marquardt, C., Sato, K., and Takahashi,
M.: The quasi-biennial oscillation, Rev. Geophys., 39, 179–229,
https://doi.org/10.1029/1999RG000073, 2001.
Baldwin, M. P., Ayarzagüena, B., Birner, T., Butchart, N., Butler, A.
H., Charlton-Perez, A. J., Domeisen, D. I. V., Garfinkel, C. I., Garny, H.,
Gerber, E. P., Hegglin, M. I., Langematz, U., and Pedatella, N. M.: Sudden
Stratospheric Warmings, Rev. Geophys., 59, e2020RG000708,
https://doi.org/10.1029/2020RG000708, 2021 (data available at: https://www.geo.fu-berlin.de/en/met/ag/strat/produkte/qbo/, last access: March 2022).
Beig, G., Keckhut, P., Lowe, R. P., Roble, R. G., Mlynczak, M. G., Scheer,
J., Fomichev, V. I., Offermann, D., French, W. J. R., Shepherd, M. G.,
Semenov, A. I., Remsberg, E. E., She, C. Y., Lübken, F. J., Bremer, J.,
Clemesha, B. R., Stegman, J., Sigernes, F., and Fadnavis, S.: Review of
mesospheric temperature trends, Rev. Geophys., 41, 1015, https://doi.org/10.1029/2002RG000121, 2003.
Beig, G., Scheer, J., Mlynczak, M. G., and Keckhut, P.: Overview of the
temperature response in the mesosphere and lower thermosphere to solar
activity, Rev. Geophys., 46, RG3002, https://doi.org/10.1029/2007RG000236, 2008.
Burrage, M. D., Vincent, R. A., Mayr, H. G., Skinner, W. R., Arnold, N. F.,
and Hays, P. B.: Long-term variability in the equatorial middle atmosphere
zonal wind, J. Geophys. Res.-Atmos., 101, 12847–12854,
https://doi.org/10.1029/96JD00575, 1996.
Butler, A. H., Seidel, D. J., Hardiman, S. C., Butchart, N., Birner, T., and
Match, A.: Defining sudden stratospheric warmings, B. Am. Meteorol. Soc.,
96, 1913–1928, https://doi.org/10.1175/BAMS-D-13-00173.1, 2015.
Cai, B., Xu, Q. C., Hu, X., Cheng, X., Yang, J. F., and Li, W.: Analysis of
the correlation between horizontal wind and 11-year solar activity over
Langfang, China, Earth Planet. Phys., 5, 270–279,
https://doi.org/10.26464/epp2021029, 2021.
Coy, L., Wargan, K., Molod, A. M., McCarty, W. R., and Pawson, S.: Structure
and dynamics of the quasi-biennial oscillation in MERRA-2, J. Climate, 29,
5339–5354, https://doi.org/10.1175/JCLI-D-15-0809.1, 2016.
Delisi, D. P. and Dunkerton, T. J.: Seasonal variation of the semiannual oscillation, J. Atmos. Sci., 45, 2772–2787,
https://doi.org/10.1175/1520-0469(1988)045<2772:SVOTSO>2.0.CO;2, 1988.
Domeisen, D. I. V., Garfinkel, C. I., and Butler, A. H.: The teleconnection
of El Niño Southern Oscillation to the stratosphere, Rev. Geophys., 57,
5–47, https://doi.org/10.1029/2018RG000596, 2019.
Dunkerton, T. J.: Theory of the mesopause semiannual oscillation, J. Atmos.
Sci., 39, 2681–2690, https://doi.org/10.1175/1520-0469(1982)039<2681:TOTMSO>2.0.CO;2, 1982.
Emmert, J. T., Stevens, M. H., Bernath, P. F., Drob, D. P., and Boone, C.
D.: Observations of increasing carbon dioxide concentration in Earth's
thermosphere, Nat. Geosci., 5, 868–871, https://doi.org/10.1038/ngeo1626, 2012.
Ern, M., Diallo, M., Preusse, P., Mlynczak, M. G., Schwartz, M. J., Wu, Q., and Riese, M.: The semiannual oscillation (SAO) in the tropical middle atmosphere and its gravity wave driving in reanalyses and satellite observations, Atmos. Chem. Phys., 21, 13763–13795, https://doi.org/10.5194/acp-21-13763-2021, 2021.
Eswaraiah, S., Kim, Y. H., Hong, J., Kim, J. H., Ratnam, M. V., Chandran,
A., Rao, S. V. B., and Riggin, D.: Mesospheric signatures observed during
2010 minor stratospheric warming at King Sejong Station (62∘ S,
59∘ W), J. Atmos. Sol.-Terr. Phy., 140, 55–64,
https://doi.org/10.1016/j.jastp.2016.02.007, 2016.
Fleming, E. L., Chandra, S., Barnett, J. J., and Corney, M.: Zonal mean
temperature, pressure, zonal wind and geopotential height as functions of
latitude, Adv. Sp. Res., 10, 11–59, https://doi.org/10.1016/0273-1177(90)90386-E, 1990.
Garcia, R. R., Dunkerton, T. J., Lieberman, R. S., and Vincent, R. A.:
Climatology of the semiannual oscillation of the tropical middle atmosphere,
J. Geophys. Res.-Atmos., 102, 26019–26032, https://doi.org/10.1029/97jd00207, 1997.
Garcia, R. R., Yue, J., and Russell, J. M.: Middle atmosphere temperature
trends in the twentieth and twenty-first centuries simulated with the Whole
Atmosphere Community Climate Model (WACCM), J. Geophys. Res.-Space, 124,
7984–7993, https://doi.org/10.1029/2019JA026909, 2019.
Gelaro, R., McCarty, W., Suárez, M. J., Todling, R., Molod, A., Takacs,
L., Randles, C. A., Darmenov, A., Bosilovich, M. G., Reichle, R., Wargan,
K., Coy, L., Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A.,
da Silva, A. M., Gu, W., Kim, G. K., Koster, R., Lucchesi, R., Merkova, D.,
Nielsen, J. E., Partyka, G., Pawson, S., Putman, W., Rienecker, M.,
Schubert, S. D., Sienkiewicz, M., and Zhao, B.: The modern-era retrospective
analysis for research and applications, version 2 (MERRA-2), J. Climate, 30,
5419–5454, https://doi.org/10.1175/JCLI-D-16-0758.1, 2017.
Hayashi, H., Koyama, Y., Hori, T., Tanaka, Y., Abe, S., Shinbori, A.,
Kagitani, M., Kouno, T., Yoshida, D., UeNo, S., Kaneda, N., Yoneda, M.,
Umemura, N., Tadokoro, H., and Motoba, T.: Inter-university upper atmosphere
global observation network (IUGONET), Data Sci. J., 12, 179–184,
https://doi.org/10.2481/dsj.WDS-030, 2013.
Hitchman, M. H. and Leovy, C. B.: Diurnal tide in the equatorial middle atmosphere as seen in LIMS temperatures, J. Atmos. Sci., 42, 557–561,
https://doi.org/10.1175/1520-0469(1985)042<0557:DTITEM>2.0.CO;2, 1985.
Hitchman, M. H. and Leovy, C. B.: Evolution of the zonal mean state in the equatorial middle atmosphere during October 1978–May 1979, J. Atmos. Sci.,
43, 3159–3176, https://doi.org/10.1175/1520-0469(1986)043<3159:EOTZMS>2.0.CO;2, 1986.
Keuer, D., Hoffmann, P., Singer, W., and Bremer, J.: Long-term variations of the mesospheric wind field at mid-latitudes, Ann. Geophys., 25, 1779–1790, https://doi.org/10.5194/angeo-25-1779-2007, 2007.
Kumar, K. K.: Is Mesospheric quasi-biennial oscillation ephemeral?, Geophys.
Res. Lett., 48, e2020GL091033, https://doi.org/10.1029/2020GL091033, 2021.
Kutner, M., Neter, C. N. J., and Li, W.: Applied linear statistical models,
5th edn., McGraw-Hill Irwin, Boston, 258 pp., ISBN 978-0073108742, 2004.
Laštovička, J.: A review of recent progress in trends in the upper
atmosphere, J. Atmos. Sol.-Terr. Phy., 163, 2–13,
https://doi.org/10.1016/j.jastp.2017.03.009, 2017.
Li, N., Lei, J., Huang, F., Yi, W., Chen, J., Xue, X., Gu, S., Luan, X.,
Zhong, J., Liu, F., Dou, X., Qin, Y., and Owolabi, C.: Responses of the
ionosphere and neutral winds in the mesosphere and lower thermosphere in the
Asian-Australian sector to the 2019 Southern Hemisphere Sudden Stratospheric
Warming, J. Geophys. Res.-Space, 126, e2020JA028653,
https://doi.org/10.1029/2020JA028653, 2021.
Li, T., Leblanc, T., McDermid, I. S., Keckhut, P., Hauchecorne, A., and Dou,
X.: Middle atmosphere temperature trend and solar cycle revealed by
long-term Rayleigh lidar observations, J. Geophys. Res.-Atmos., 116, 1–11, https://doi.org/10.1029/2010JD015275, 2011.
Li, T., Liu, A. Z., Lu, X., Li, Z., Franke, S. J., Swenson, G. R., and Dou,
X.: Meteor-radar observed mesospheric semi-annual oscillation (SAO) and
quasi-biennial oscillation (QBO) over Maui, Hawaii, J. Geophys. Res.-Atmos.,
117, D05130, https://doi.org/10.1029/2011JD016123, 2012.
Li, T., Calvo, N., Yue, J., Dou, X., Russell, J. M., Mlynczak, M. G., She,
C. Y., and Xue, X.: Influence of El Niño-Southern oscillation in the
mesosphere, Geophys. Res. Lett., 40, 3292–3296, https://doi.org/10.1002/grl.50598, 2013.
Li, T., Calvo, N., Yue, J., Russell, J. M., Smith, A. K., Mlynczak, M. G.,
Chandran, A., Dou, X., and Liu, A. Z.: Southern Hemisphere summer mesopause
responses to El Niño-Southern Oscillation, J. Climate, 29, 6319–6328,
https://doi.org/10.1175/JCLI-D-15-0816.1, 2016.
Lin, J. and Qian, T.: Impacts of the ENSO lifecycle on stratospheric ozone
and temperature, Geophys. Res. Lett., 46, 10646–10658,
https://doi.org/10.1029/2019GL083697, 2019.
Liu, X., Yue, J., Xu, J., Garcia, R. R., Russell, J. M., Mlynczak, M., Wu,
D. L., and Nakamura, T.: Variations of global gravity waves derived from 14
years of SABER temperature observations, J. Geophys. Res.-Atmos., 122,
6231–6249, https://doi.org/10.1002/2017JD026604, 2017.
Liu, X., Xu, J., Yue, J., Yu, Y., Batista, P. P., Andrioli, V. F., Liu, Z., Yuan, T., Wang, C., Zou, Z., Li, G., and Russell III, J. M.: Global balanced wind derived from SABER temperature and pressure observations and its validations, Earth Syst. Sci. Data, 13, 5643–5661, https://doi.org/10.5194/essd-13-5643-2021, 2021a.
Liu, X., Xu, J., Yue, J., Yu, Y., Batista, P. P., Andrioli, V. F., Liu, Z., Yuan, T., Wang, C., Zou, Z., Li, G., and Russell III, J. M.: Global Balanced Wind Derived from SABER Temperature and Pressure Observations and its Validations, V1, sadr [data set], https://doi.org/10.12176/01.99.00574, 2021b.
Liu, X., Xu, J., Yue, J., and Kogure, M.: Persistent layers of enhanced
gravity wave dissipation in the upper mesosphere revealed from SABER
observations, Geophys. Res. Lett., 49, 1–11,
https://doi.org/10.1029/2021GL097038, 2022.
Lübken, F. J., Baumgarten, G., Fiedler, J., Gerding, M., Höffner,
J., and Berger, U.: Seasonal and latitudinal variation of noctilucent cloud
altitudes, Geophys. Res. Lett., 35, 1–4, https://doi.org/10.1029/2007GL032281, 2008.
Manney, G. L. and Hegglin, M. I.: Seasonal and regional variations of
long-term changes in upper-tropospheric jets from reanalyses, J. Climate, 31,
423–448, https://doi.org/10.1175/JCLI-D-17-0303.1, 2018.
Manzini, E., Giorgetta, M. A., Esch, M., Kornblueh, L., and Roeckner, E.:
The influence of sea surface temperatures on the northern winter
stratosphere: ensemble simulations with the MAECHAM5 model, J. Climate, 19,
3863–3881, https://doi.org/10.1175/JCLI3826.1, 2006.
Matsumoto, N., Shinbori, A., Riggin, D. M., and Tsuda, T.: Measurement of momentum flux using two meteor radars in Indonesia, Ann. Geophys., 34, 369–377, https://doi.org/10.5194/angeo-34-369-2016, 2016.
Mitchell, D. M., Gray, L. J., Fujiwara, M., Hibino, T., Anstey, J. A.,
Ebisuzaki, W., Harada, Y., Long, C., Misios, S., Stott, P. A., and Tan, D.:
Signatures of naturally induced variability in the atmosphere using multiple
reanalysis datasets, Q. J. Roy. Meteor. Soc., 141, 2011–2031,
https://doi.org/10.1002/qj.2492, 2015.
Mlynczak, M. G., Hunt, L. A., Garcia, R. R., Harvey, V. L., Marshall, B. T.,
Yue, J., Mertens, C. J., and Russell, J. M.: Cooling and contraction of the mesosphere and lower thermosphere from 2002 to 2021, J. Geophys. Res.-Atmos., 127, e2022JD036767, https://doi.org/10.1029/2022JD036767, 2022.
Molod, A., Takacs, L., Suarez, M., and Bacmeister, J.: Development of the GEOS-5 atmospheric general circulation model: evolution from MERRA to MERRA2, Geosci. Model Dev., 8, 1339–1356, https://doi.org/10.5194/gmd-8-1339-2015, 2015 (data avaialble at: http://disc.sci.gsfc.nasa.gov/mdisc, last access: March 2022).
Mudelsee, M.: Trend analysis of climate time series: A review of methods,
Earth-Sci. Rev., 190, 310–322, https://doi.org/10.1016/j.earscirev.2018.12.005, 2019.
Polvani, L. M. and Waugh, D. W.: Upward wave activity flux as a precursor to
extreme stratospheric events and subsequent anomalous surface weather
regimes, J. Climate, 17, 3548–3554,
https://doi.org/10.1175/1520-0442(2004)017<3548:UWAFAA>2.0.CO;2, 2004.
Qian, L., Jacobi, C., and McInerney, J.: Trends and solar irradiance effects in the mesosphere, J. Geophys. Res.-Space, 124, 1343–1360,
https://doi.org/10.1029/2018JA026367, 2019.
Ramesh, K., Smith, A. K., Garcia, R. R., Marsh, D. R., Sridharan, S., and
Kishore Kumar, K.: Long-term variability and tendencies in middle atmosphere
temperature and zonal wind from WACCM6 simulations during 1850–2014, J.
Geophys. Res.-Atmos., 125, e2020JD033579, https://doi.org/10.1029/2020JD033579, 2020.
Randel, W. J.: The Evaluation of Winds from geopotential height data in the
stratosphere, J. Atmos. Sci., 44, 3097–3120,
https://doi.org/10.1175/1520-0469(1987)044<3097:TEOWFG>2.0.CO;2, 1987.
Randel, W. J. and Cobb, J. B.: Coherent variations of monthly mean total
ozone and lower stratospheric temperature, J. Geophys. Res., 99, 5433,
https://doi.org/10.1029/93JD03454, 1994.
Randel, W. J., Udelhofen, P., Fleming, E., Geller, M., Gelman, M., Hamilton,
K., Karoly, D., Ortland, D., Pawson, S., Swinbank, R., Wu, F., Baldwin, M.,
Chanin, M.-L., Keckhut, P., Labitzke, K., Remsberg, E., Simmons, A., and Wu,
D.: The SPARC intercomparison of middle-atmosphere climatologies, J. Climate,
17, 986–1003, https://doi.org/10.1175/1520-0442(2004)017<0986:TSIOMC>2.0.CO;2, 2004.
Randel, W. J., Garcia, R. R., Calvo, N., and Marsh, D.: ENSO influence on
zonal mean temperature and ozone in the tropical lower stratosphere,
Geophys. Res. Lett., 36, L15822, https://doi.org/10.1029/2009GL039343, 2009.
Randel, W. J., Polvani, L., Wu, F., Kinnison, D. E., Zou, C. Z., and Mears,
C.: Troposphere-stratosphere temperature trends derived from satellite data
compared with ensemble simulations from WACCM, J. Geophys. Res.-Atmos., 122,
9651–9667, https://doi.org/10.1002/2017JD027158, 2017.
Rao, J., Garfinkel, C. I., White, I. P., and Schwartz, C.: The southern
hemisphere minor sudden stratospheric warming in September 2019 and its
predictions in S2S models, J. Geophys. Res.-Atmos., 125, e2020JD032723,
https://doi.org/10.1029/2020JD032723, 2020.
Ray, E. A., Alexander, M. J., and Holton, J. R.: An analysis of the
structure and forcing of the equatorial semiannual oscillation in zonal
wind, J. Geophys. Res.-Atmos., 103, 1759–1774,
https://doi.org/10.1029/97JD02679, 1998.
Russell III, J. M., Mlynczak, M. G., Gordley, L. L., Tansock Jr., J. J.,
and Esplin, R. W.: Overview of the SABER experiment and preliminary
calibration results, in: Optical Spectroscopic Techniques and
Instrumentation for Atmospheric and Space Research III, SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 20 October 1999, Denver, CO, USA, Space Dynamics Lab Publications, 277–288, https://doi.org/10.1117/12.366382, 1999.
She, C., Berger, U., Yan, Z., Yuan, T., Lübken, F.-J., Krueger, D. A.,
and Hu, X.: Solar response and long-term trend of midlatitude mesopause
region temperature based on 28 Years (1990–2017) of Na lidar observations,
J. Geophys. Res.-Space, 124, 7140–7156, https://doi.org/10.1029/2019JA026759, 2019.
Smith, A. K., Garcia, R. R., Moss, A. C., and Mitchell, N. J.: The
semiannual oscillation of the tropical zonal wind in the middle atmosphere
derived from satellite geopotential height retrievals, J. Atmos. Sci., 74,
2413–2425, https://doi.org/10.1175/JAS-D-17-0067.1, 2017.
Souleymane, S., Madonna, F., Rosoldi, M., Tramutola, E., Gagliardi, S.,
Proto, M., and Pappalardo, G.: Sensitivity of trends to estimation methods
and quantification of subsampling effects in global radiosounding
temperature and humidity time series, Int. J. Climatol., 41, E1992–E2014,
https://doi.org/10.1002/joc.6827, 2021.
Sridharan, S., Tsuda, T., and Gurubaran, S.: Radar observations of long-term
variability of mesosphere and lower thermosphere winds over Tirunelveli
(8.7∘ N, 77.8∘ E), J. Geophys. Res.-Atmos., 112, D23105,
https://doi.org/10.1029/2007JD008669, 2007.
Swinbank, R. and Ortland, D. A.: Compilation of wind data for the Upper
Atmosphere Research Satellite (UARS) Reference Atmosphere Project, J.
Geophys. Res., 108, 4615, https://doi.org/10.1029/2002jd003135, 2003.
Taguchi, M.: Observed connection of the stratospheric quasi-biennial
oscillation with El Niño–Southern Oscillation in radiosonde data, J.
Geophys. Res., 115, D18120, https://doi.org/10.1029/2010JD014325, 2010.
Tapping, K. F.: The 10.7 cm solar radio flux (F10.7), Sp. Weather, 11,
394–406, https://doi.org/10.1002/swe.20064, 2013 (data available at: https://spdf.gsfc.nasa.gov/pub/data/omni/, last access: March 2022).
Venkat Ratnam, M., Kishore Kumar, G., Venkateswara Rao, N., Krishna Murthy,
B. V., Laštovička, J., and Qian, L.: Evidence of long-term change in
zonal wind in the tropical lower mesosphere: Observations and model
simulations, Geophys. Res. Lett., 40, 397–401,
https://doi.org/10.1002/grl.50158, 2013.
Venkat Ratnam, M., Akhil Raj, S. T., and Qian, L.: Long-term trends in the
low-latitude middle atmosphere temperature and winds: observations and
WACCM-X model smulations, J. Geophys. Res.-Space, 124, 7320–7331,
https://doi.org/10.1029/2019JA026928, 2019.
Venkateswara Rao, N., Tsuda, T., Riggin, D. M., Gurubaran, S., Reid, I. M.,
and Vincent, R. A.: Long-term variability of mean winds in the mesosphere
and lower thermosphere at low latitudes, J. Geophys. Res.-Space, 117,
1–16, https://doi.org/10.1029/2012JA017850, 2012.
Wolter, K. and Timlin, M. S.: El Niño/Southern Oscillation behaviour
since 1871 as diagnosed in an extended multivariate ENSO index (MEI.ext),
Int. J. Climatol., 31, 1074–1087, https://doi.org/10.1002/joc.2336, 2011.
Xu, J., Liu, H.-L., Yuan, W., Smith, A. K., Roble, R. G., Mertens, C. J.,
Russell, J. M., and Mlynczak, M. G.: Mesopause structure from Thermosphere,
Ionosphere, Mesosphere, Energetics, and Dynamics (TIMED)/Sounding of the
Atmosphere Using Broadband Emission Radiometry (SABER) observations, J.
Geophys. Res., 112, D09102, https://doi.org/10.1029/2006JD007711, 2007.
Xu, J., Smith, A. K., Liu, H.-L., Yuan, W., Wu, Q., Jiang, G., Mlynczak, M.
G., and Russell, J. M.: Estimation of the equivalent Rayleigh friction in
mesosphere/lower thermosphere region from the migrating diurnal tides
observed by TIMED, J. Geophys. Res., 114, D23103,
https://doi.org/10.1029/2009JD012209, 2009a.
Xu, J., Smith, A. K., Liu, H. L., Yuan, W., Wu, Q., Jiang, G., Mlynczak, M.
G., Russell, J. M., and Franke, S. J.: Seasonal and quasi-biennial
variations in the migrating diurnal tide observed by Thermosphere,
Ionosphere, Mesosphere, Energetics and Dynamics (TIMED), J. Geophys. Res.-Atmos., 114, 1–16, https://doi.org/10.1029/2008jd011298, 2009b.
Yuan, T., Solomon, S. C., She, C.-Y., Krueger, D. A., and Liu, H.-L.: The
long-term trends of nocturnal mesopause temperature and altitude revealed by
Na lidar observations between 1990 and 2018 at Midlatitude, J. Geophys. Res.-Atmos., 124, 5970–5980, https://doi.org/10.1029/2018JD029828, 2019.
Yue, J., Russell, J., Jian, Y., Rezac, L., Garcia, R., López-Puertas,
M., and Mlynczak, M. G.: Increasing carbon dioxide concentration in the
upper atmosphere observed by SABER, Geophys. Res. Lett., 42, 7194–7199,
https://doi.org/10.1002/2015GL064696, 2015.
Yue, J., Russell, J., Gan, Q., Wang, T., Rong, P., Garcia, R., and Mlynczak,
M.: Increasing water vapor in the stratosphere and mesosphere after 2002,
Geophys. Res. Lett., 46, 13452–13460, https://doi.org/10.1029/2019GL084973,
2019a.
Yue, J., Li, T., Qian, L., Lastovicka, J., and Zhang, S.: Introduction to
special issue on “long-term changes and trends in the middle and upper
atmosphere”, J. Geophys. Res.-Space, 124, 10360–10364,
https://doi.org/10.1029/2019JA027462, 2019b.
Zhang, S., Cnossen, I., Laštovička, J., Elias, A. G., Yue, X.,
Jacobi, C., Yue, J., Wang, W., Qian, L., and Goncharenko, L.: Long-term
geospace climate monitoring, Front. Astron. Sp. Sci., 10, 1–5,
https://doi.org/10.3389/fspas.2023.1139230, 2023.
Zhang, T., Hoell, A., Perlwitz, J., Eischeid, J., Murray, D., Hoerling, M.,
and Hamill, T. M.: Towards probabilistic multivariate ENSO monitoring,
Geophys. Res. Lett., 46, 10532–10540, https://doi.org/10.1029/2019GL083946, 2019 (data available at: https://www.psl.noaa.gov/enso/mei/, last access: March 2022).
Short summary
Winds are important in characterizing atmospheric dynamics and coupling. However, it is difficult to directly measure the global winds from the stratosphere to the lower thermosphere. We developed a global zonal wind dataset according to the gradient wind theory and SABER and meteor radar observations. Using the dataset, we studied the intra-annual, inter-annual, and long-term variations. This is helpful to understand the variations and coupling of the stratosphere to the lower thermosphere.
Winds are important in characterizing atmospheric dynamics and coupling. However, it is...
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