Articles | Volume 17, issue 2
https://doi.org/10.5194/amt-17-783-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/amt-17-783-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Assessing atmospheric gravity wave spectra in the presence of observational gaps
Department Optical Soundings and Sounding Rockets, Leibniz Institute of Atmospheric Physics, Kühlungsborn, Germany
Irina Strelnikova
Department Optical Soundings and Sounding Rockets, Leibniz Institute of Atmospheric Physics, Kühlungsborn, Germany
Department Optical Soundings and Sounding Rockets, Leibniz Institute of Atmospheric Physics, Kühlungsborn, Germany
Gerd Baumgarten
Department Optical Soundings and Sounding Rockets, Leibniz Institute of Atmospheric Physics, Kühlungsborn, Germany
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We recorded atmospheric waves over seven years with a lidar in northern Norway, analysing temperature and wind from 35 to 60 km altitude. This yielded the first long-term picture of how wave energy varies with height and season at this location. Winter carried up to ten times more energy than summer, and the balance shifted with wavelength and frequency. Energy patterns often diverged from textbook slopes. These findings refine our view of the upper atmosphere at high latitudes.
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We recorded atmospheric waves over seven years with a lidar in northern Norway, analysing temperature and wind from 35 to 60 km altitude. This yielded the first long-term picture of how wave energy varies with height and season at this location. Winter carried up to ten times more energy than summer, and the balance shifted with wavelength and frequency. Energy patterns often diverged from textbook slopes. These findings refine our view of the upper atmosphere at high latitudes.
Jens Fiedler, Gerd Baumgarten, Michael Gerding, Torsten Köpnick, Reik Ostermann, and Bernd Kaifler
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We developed a system for frequency control and monitoring of pulsed high-power lasers. It works in real-time, controls the laser cavity length, and performs a spectral analyzes of each individual laser pulse. The motivation for this work was to improve the retrieval of Doppler winds measured by lidar in the middle atmosphere by taking the frequency stability of the lidar transmitter into account.
Natalie Kaifler, Bernd Kaifler, Markus Rapp, Guiping Liu, Diego Janches, Gerd Baumgarten, and Jose-Luis Hormaechea
Atmos. Chem. Phys., 24, 14029–14044, https://doi.org/10.5194/acp-24-14029-2024, https://doi.org/10.5194/acp-24-14029-2024, 2024
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Noctilucent clouds (NLCs) are silvery clouds that can be viewed during twilight and indicate atmospheric conditions like temperature and water vapor in the upper mesosphere. High-resolution measurements from a remote sensing laser instrument provide NLC height, brightness, and occurrence rate since 2017. Most observations occur in the morning hours, likely caused by strong tidal winds, and NLC ice particles are thus transported from elsewhere to the observing location in the Southern Hemisphere.
Jens Fiedler and Gerd Baumgarten
Atmos. Meas. Tech., 17, 5841–5859, https://doi.org/10.5194/amt-17-5841-2024, https://doi.org/10.5194/amt-17-5841-2024, 2024
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This article describes the current status of a lidar installed at ALOMAR in northern Norway. It has investigated the Arctic middle atmosphere on a climatological basis for 30 years. We discuss major upgrades of the system implemented during recent years, including methods for reliable remote operation of this complex lidar. We also show examples that illustrate the performance of the lidar during measurements at different altitude ranges and timescales.
Michael Gerding, Robin Wing, Eframir Franco-Diaz, Gerd Baumgarten, Jens Fiedler, Torsten Köpnick, and Reik Ostermann
Atmos. Meas. Tech., 17, 2789–2809, https://doi.org/10.5194/amt-17-2789-2024, https://doi.org/10.5194/amt-17-2789-2024, 2024
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This paper describes a new lidar system developed in Germany intended to study wind and temperature at night in the middle atmosphere. The paper explains how we have set up the system to work automatically and gives technical details for anyone who wants to build a similar system. We present a case study showing temperatures and winds at different altitudes. In a future article, we will present how we process the data and deal with uncertainties.
Thorben H. Mense, Josef Höffner, Gerd Baumgarten, Ronald Eixmann, Jan Froh, Alsu Mauer, Alexander Munk, Robin Wing, and Franz-Josef Lübken
Atmos. Meas. Tech., 17, 1665–1677, https://doi.org/10.5194/amt-17-1665-2024, https://doi.org/10.5194/amt-17-1665-2024, 2024
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A novel lidar system with five beams measured horizontal and vertical winds together, reaching altitudes up to 25 km. Developed in Germany, it revealed accurate horizontal wind data compared to forecasts, but vertical wind estimates differed. The lidar's capability to detect small-scale wind patterns was highlighted, advancing atmospheric research.
Eframir Franco-Diaz, Michael Gerding, Laura Holt, Irina Strelnikova, Robin Wing, Gerd Baumgarten, and Franz-Josef Lübken
Atmos. Chem. Phys., 24, 1543–1558, https://doi.org/10.5194/acp-24-1543-2024, https://doi.org/10.5194/acp-24-1543-2024, 2024
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We use satellite, lidar, and ECMWF data to study storm-related waves that propagate above Kühlungsborn, Germany, during summer. Although these events occur in roughly half of the years of the satellite data we analyzed, we focus our study on two case study years (2014 and 2015). These events could contribute significantly to middle atmospheric circulation and are not accounted for in weather and climate models.
Juliana Jaen, Toralf Renkwitz, Huixin Liu, Christoph Jacobi, Robin Wing, Aleš Kuchař, Masaki Tsutsumi, Njål Gulbrandsen, and Jorge L. Chau
Atmos. Chem. Phys., 23, 14871–14887, https://doi.org/10.5194/acp-23-14871-2023, https://doi.org/10.5194/acp-23-14871-2023, 2023
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Investigation of winds is important to understand atmospheric dynamics. In the summer mesosphere and lower thermosphere, there are three main wind flows: the mesospheric westward, the mesopause southward (equatorward), and the lower-thermospheric eastward wind. Combining almost 2 decades of measurements from different radars, we study the trend, their interannual oscillations, and the effects of the geomagnetic activity over these wind maxima.
Ashique Vellalassery, Gerd Baumgarten, Mykhaylo Grygalashvyly, and Franz-Josef Lübken
Ann. Geophys., 41, 289–300, https://doi.org/10.5194/angeo-41-289-2023, https://doi.org/10.5194/angeo-41-289-2023, 2023
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The solar cycle affects the H2O concentration in the upper mesosphere mainly in two ways: directly through photolysis and, at the time and place of NLC formation, indirectly through temperature changes. The H2O–Lyman-α response is modified by NLC formation, resulting in a positive response at the ice formation region (due to the temperature change effect on the ice formation rate) and a negative response at the sublimation zone (due to the photolysis effect).
Mathieu Ratynski, Sergey Khaykin, Alain Hauchecorne, Robin Wing, Jean-Pierre Cammas, Yann Hello, and Philippe Keckhut
Atmos. Meas. Tech., 16, 997–1016, https://doi.org/10.5194/amt-16-997-2023, https://doi.org/10.5194/amt-16-997-2023, 2023
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Aeolus is the first spaceborne wind lidar providing global wind measurements since 2018. This study offers a comprehensive analysis of Aeolus instrument performance, using ground-based wind lidars and meteorological radiosondes, at tropical and mid-latitudes sites. The analysis allows assessing the long-term evolution of the satellite's performance for more than 3 years. The results will help further elaborate the understanding of the error sources and the behavior of the Doppler wind lidar.
Anna Lange, Gerd Baumgarten, Alexei Rozanov, and Christian von Savigny
Ann. Geophys., 40, 407–419, https://doi.org/10.5194/angeo-40-407-2022, https://doi.org/10.5194/angeo-40-407-2022, 2022
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We investigate the influence of different parameters on the colour of noctilucent clouds (highest clouds in the atmosphere), using radiative transfer calculations. We determined the effect of the particle size, optical depth, single scattering/multiple scattering and ozone. For sufficiently large optical depth and for specific viewing geometries, ozone plays only a minor role in the blueish colour of noctilucent clouds (new result).
Robin Wing, Sophie Godin-Beekmann, Wolfgang Steinbrecht, Thomas J. McGee, John T. Sullivan, Sergey Khaykin, Grant Sumnicht, and Laurence Twigg
Atmos. Meas. Tech., 14, 3773–3794, https://doi.org/10.5194/amt-14-3773-2021, https://doi.org/10.5194/amt-14-3773-2021, 2021
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This paper is a validation study of the newly installed ozone and temperature lidar at Hohenpeißenberg, Germany. As part of the Network for the Detection of Atmospheric Composition Change (NDACC), lidar stations are routinely compared against a travelling reference lidar operated by NASA. We have also attempted to assess potential biases in the reference lidar by comparing the results of this validation campaign with a previous campaign at the Observatoire de Haute-Provence, France.
Graeme Marlton, Andrew Charlton-Perez, Giles Harrison, Inna Polichtchouk, Alain Hauchecorne, Philippe Keckhut, Robin Wing, Thierry Leblanc, and Wolfgang Steinbrecht
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A network of Rayleigh lidars have been used to infer the upper-stratosphere temperature bias in ECMWF ERA-5 and ERA-Interim reanalyses during 1990–2017. Results show that ERA-Interim exhibits a cold bias of −3 to −4 K between 10 and 1 hPa. Comparisons with ERA-5 found a smaller bias of 1 K which varies between cold and warm between 10 and 3 hPa, indicating a good thermal representation of the atmosphere to 3 hPa. These biases must be accounted for in stratospheric studies using these reanalyses.
Robin Wing, Wolfgang Steinbrecht, Sophie Godin-Beekmann, Thomas J. McGee, John T. Sullivan, Grant Sumnicht, Gérard Ancellet, Alain Hauchecorne, Sergey Khaykin, and Philippe Keckhut
Atmos. Meas. Tech., 13, 5621–5642, https://doi.org/10.5194/amt-13-5621-2020, https://doi.org/10.5194/amt-13-5621-2020, 2020
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A lidar intercomparison campaign was conducted over a period of 28 nights at Observatoire de Haute-Provence (OHP) in 2017 and 2018. The objective is to validate the ozone and temperature profiles at OHP to ensure the quality of data submitted to the NDACC database remains high. A mobile reference lidar operated by NASA was transported to OHP and operated concurrently with the French lidars. Agreement for ozone was better than 5 % between 20 and 40 km, and temperatures were equal within 3 K.
Cited articles
Alexander, M., Tsuda, T., and Vincent, R. N.: Latitudinal Variations Observed in Gravity Waves with Short Vertical Wavelengths, J. Atmos. Sci., 59, 1394–1404, https://doi.org/10.1175/1520-0469(2002)059<1394:LVOIGW>2.0.CO;2, 2002. a
Axford, D.: Spectral analysis of an aircraft observation of gravity waves, Q. J. Roy. Meteor. Soc., 97, 313–321, https://doi.org/10.1002/qj.49709741306, 1971. a
Babu, P. and Stoica, P.: Spectral analysis of nonuniformly sampled data – a review, Digit. Signal Process., 20, 359–378, https://doi.org/10.1016/j.dsp.2009.06.019, 2010. a
Beldon, C. L. and Mitchell, N. J.: Gravity wave–tidal interactions in the mesosphere and lower thermosphere over Rothera, Antarctica (68∘ S, 68∘ W), J. Geophys. Res., 115, D18101, https://doi.org/10.1029/2009jd013617, 2010. a
Beres, J., Garcia, R. R., Boville, B. A., and Sassi, F.: Implementation of a gravity wave source spectrum parameterization dependent on the properties of convection in the Whole Atmosphere Community Climate Model (WACCM), J. Geophys. Res., 110, D10108, https://doi.org/10.1029/2004jd005504, 2005. a
Bieber, J. W., Chen, J., Matthaeus, W. H., Smith, C. W., and Pomerantz, M. A.: Long-term variations of interplanetary magnetic field spectra with implications for cosmic ray modulation, J. Geophys. Res., 98, 3585–3603, https://doi.org/10.1029/92ja02566, 1993. a
Billah, K. Y. R. and Shinozuka, M.: Numerical method for colored-noise generation and its application to a bistable system, Phys. Rev. A, 42, 7492–7495, https://doi.org/10.1103/PhysRevA.42.7492, 1990. a
Blackman, R. B. and Tukey, J. W.: The measurement of power spectra from the point of view of communications engineering – Part I, Bell Syst. Tech. J., 37, 185–282, https://doi.org/10.1002/j.1538-7305.1958.tb03874.x, 1958. a
Brown, T. M. and Christensen-Dalsgaard, J.: A technique for estimating complicated power spectra from time series with gaps, Astrophys. J., 349, 667, https://doi.org/10.1086/168354, 1990. a
Clauset, A., Shalizi, C. R., and Newman, M.: Power-law distributions in empirical data, Siam Rev., 51, 661–703, https://doi.org/10.1137/070710111, 2009. a
Cooley, J. and Tukey, J. W.: An algorithm for the machine calculation of complex Fourier series, Math. Comput., 19, 297–301, https://doi.org/10.1090/s0025-5718-1965-0178586-1, 1965. a, b
Crowley, G. and Williams, P.: Observations of the source and propagation of atmospheric gravity waves, Nature, 328, 231–233, https://doi.org/10.1038/328231a0, 1987. a
Dewan, E. M. and Good, R. E.: Saturation and the “universal” spectrum for vertical profiles of horizontal scalar winds in the atmosphere, J. Geophys. Res., 91, 2742, https://doi.org/10.1029/jd091id02p02742, 1986. a, b, c
Dewan, E. M. and Grossbard, N.: Power spectral artifacts in published balloon data and implications regarding saturated gravity wave theories, J. Geophys. Res., 105, 4667–4683, https://doi.org/10.1029/1999jd901108, 2000. a, b, c
Duvall, T. L. and Harvey, J. T.: Solar Doppler shifts: sources of continuous spectra, Springer, https://doi.org/10.1007/978-94-009-4608-8_11, 1986. a
Eckermann, S. D. and Hocking, W. K.: Effect of superposition on measurements of atmospheric gravity waves: A cautionary note and some reinterpretations, J. Geophys. Res., 94, 6333, https://doi.org/10.1029/jd094id05p06333, 1989. a, b
Ern, M., Trinh, Q. T., Preusse, P., Gille, J. C., Mlynczak, M. G., Russell III, J. M., and Riese, M.: GRACILE: a comprehensive climatology of atmospheric gravity wave parameters based on satellite limb soundings, Earth Syst. Sci. Data, 10, 857–892, https://doi.org/10.5194/essd-10-857-2018, 2018. a
Eyer, L. and Bartholdi, P.: Variable stars: Which Nyquist frequency?, Astron. Astrophys. Sup., 135, 1–3, https://doi.org/10.1051/aas:1999102, 1999. a
Ferraz-Mello, S.: Estimation of Periods from Unequally Spaced Observations, Astron. J., 86, 619, https://doi.org/10.1086/112924, 1981. a
Fritts, D. C.: A review of gravity wave saturation processes, effects, and variability in the middle atmosphere, Pure Appl. Geophys., 130, 343–371, https://doi.org/10.1007/bf00874464, 1989. a
Fritts, D. C. and Alexander, M.: Gravity wave dynamics and effects in the middle atmosphere, Rev. Geophys., 41, 1003, https://doi.org/10.1029/2001rg000106, 2003. a
Fritts, D. C. and VanZandt, T. E.: Spectral Estimates of gravity wave energy and momentum fluxes. Part I: Energy dissipation, acceleration, and constraints, J. Atmos. Sci., 50, 3685–3694, https://doi.org/10.1175/1520-0469(1993)050<3685:SEOGWE>2.0.CO;2, 1993. a
Fritts, D. C., Tsuda, T., Sato, T., Fukao, S., and Kato, S.: Observational evidence of a saturated gravity wave spectrum in the troposphere and lower stratosphere, J. Atmos. Sci., 45, 1741–1759, https://doi.org/10.1175/1520-0469(1988)045<1741:OEOASG>2.0.CO;2, 1988. a
Gardner, C. S., Tao, X., and Papen, G. C.: Simultaneous lidar observations of vertical wind, temperature, and density profiles in the upper mesophere: Evidence for nonseparability of atmospheric perturbation spectra, Geophys. Res. Lett., 22, 2877–2880, https://doi.org/10.1029/95gl02783, 1995. a, b, c, d, e, f, g, h
Gerding, M., Höffner, J., Lautenbach, J., Rauthe, M., and Lübken, F.-J.: Seasonal variation of nocturnal temperatures between 1 and 105 km altitude at 54∘ N observed by lidar, Atmos. Chem. Phys., 8, 7465–7482, https://doi.org/10.5194/acp-8-7465-2008, 2008. a
Guharay, A. and Sekar, R.: Seasonal characteristics of gravity waves in the middle atmosphere over Gadanki using Rayleigh lidar observations, J. Atmos. Sol.-Terr. Phy., 73, 1762–1770, https://doi.org/10.1016/j.jastp.2011.04.013, 2011. a, b, c
Haar, A.: On the theory of orthogonal function systems, Math. Ann., 69, 331–371, 1910. a
Hall, C. M. and Aso, T.: Mesospheric velocities and buoyancy subrange spectral slopes determined over Svalbard by ESR, Geophys. Res. Lett., 26, 1685–1688, https://doi.org/10.1029/1999gl900340, 1999. a, b, c, d
Hamilton, K.: The role of parameterized drag in a troposphere-stratosphere-mesosphere general circulation model, Springer, https://doi.org/10.1007/978-3-642-60654-0_23, 1997. a
He, Y., Sheng, Z., and He, M.: Spectral Analysis of Gravity Waves from Near Space High-Resolution Balloon Data in Northwest China, Atmosphere, 11, 133, https://doi.org/10.3390/atmos11020133, 2020. a
Hébert, R.: RScaling (1.0.0), Zenodo, https://doi.org/10.5281/zenodo.5037581, 2021. a
Hébert, R., Rehfeld, K., and Laepple, T.: Comparing estimation techniques for temporal scaling in palaeoclimate time series, Nonlin. Processes Geophys., 28, 311–328, https://doi.org/10.5194/npg-28-311-2021, 2021. a
Hertzog, A. and Vial, F.: A study of the dynamics of the equatorial lower stratosphere by use of ultra-long-duration balloons: 2. Gravity waves, J. Geophys. Res., 106, 22745–22761, https://doi.org/10.1029/2000jd000242, 2001. a, b
Hines, C. O.: Internal atmospheric gravity waves at ionospheric heights, Can. J. Phys., 38, 1441–1481, https://doi.org/10.1139/p60-150, 1960. a
Hines, C. O.: The Saturation of Gravity Waves in the Middle Atmosphere. Part II: Development Of Doppler-Spread Theory, J. Atmos. Sci., 48, 1361–1379, https://doi.org/10.1175/1520-0469(1991)048<1361:TSOGWI>2.0.CO;2, 1991. a, b, c, d
Holton, J. M.: The influence of gravity wave breaking on the general circulation of the middle atmosphere, J. Atmos. Sci., 40, 2497–2507, https://doi.org/10.1175/1520-0469(1983)040<2497:TIOGWB>2.0.CO;2, 1983. a
Horne, J. H. and Baliunas, S. L.: A prescription for period analysis of unevenly sampled time series, Astrophys. J., 302, 757, https://doi.org/10.1086/164037, 1986. a, b
Houbolt, J. C., Steiner, R., and Pratt, K. G.: Dynamic response of airplanes to atmospheric turbulence including flight data on input and response, vol. 199, National Aeronautics and Space Administration, https://hdl.handle.net/2027/uiug.30112106585620 (last access: 25 January 2024), 1964. a
Houchi, K., Stoffelen, A., Marseille, G.-J., and De Kloe, J.: Comparison of wind and wind shear climatologies derived from high-resolution radiosondes and the ECMWF model, J. Geophys. Res., 115, D22123, https://doi.org/10.1029/2009jd013196, 2010. a
Kirchner, J. W.: Aliasing in noise spectra: Origins, consequences, and remedies, Phys. Rev. E, 71, 066110, https://doi.org/10.1103/PhysRevE.71.066110, 2005. a
Lepot, M., Aubin, J.-B., and Clemens, F.: Interpolation in Time Series: An introductive overview of existing methods, their performance criteria and uncertainty assessment, Water, 9, 796, https://doi.org/10.3390/w9100796, 2017. a
Lindgren, E., Sheshadri, A., Podglajen, A., and Carver, R. W.: Seasonal and latitudinal variability of the gravity wave spectrum in the lower stratosphere, J. Geophys. Res.-Atmos., 125, e2020JD03285, https://doi.org/10.1029/2020jd032850, 2020. a
Lindzen, R. S.: Turbulence and stress owing to gravity wave and tidal breakdown, J. Geophys. Res., 86, 9707, https://doi.org/10.1029/jc086ic10p09707, 1981. a
Liu, H., McInerney, J., Santos, S. A., Lauritzen, P. H., Taylor, M. J., and Pedatella, N.: Gravity waves simulated by high-resolution Whole Atmosphere Community Climate Model, Geophys. Res. Lett., 41, 9106–9112, https://doi.org/10.1002/2014gl062468, 2014. a
Lomb, N. R.: Least-squares frequency analysis of unequally spaced data, Astrophys. Space Sci., 39, 447–462, https://doi.org/10.1007/bf00648343, 1976. a
Lovejoy, S.: A voyage through scales, a missing quadrillion and why the climate is not what you expect, Clim. Dynam., 44, 3187–3210, https://doi.org/10.1007/s00382-014-2324-0, 2014. a, b
Lovejoy, S. and Schertzer, D.: Haar wavelets, fluctuations and structure functions: convenient choices for geophysics, Nonlin. Processes Geophys., 19, 513–527, https://doi.org/10.5194/npg-19-513-2012, 2012. a, b, c
Maekawa, Y., Fukao, S., Sato, T., Kato, S., and Woodman, R. F.: Internal inertia–gravity waves in the tropical lower stratosphere observed by the Arecibo Radar, J. Atmos. Sci., 41, 2359–2367, https://doi.org/10.1175/1520-0469(1984)041<2359:IIWITT>2.0.CO;2, 1984. a, b
Marinna, A. M., Alfredo, L. A., and Christopher, R. S.: Using the Lomb-Scargle method for wave statistics from gappy time series, IEEE Conference Proceedings, 2019, 1–9, https://doi.org/10.1109/CWTM43797.2019.8955285, 2019. a
Meisel, D. D.: Fourier transforms of data sampled at unequal observational intervals, Astron. J., 83, 538, https://doi.org/10.1086/112233, 1978. a
Mossad, M.: GapWaveSpectra (1.0.0), Zenodo [code], https://doi.org/10.5281/zenodo.8136556, 2023. a, b
Munteanu, C., Negrea, C., Echim, M., and Mursula, K.: Effect of data gaps: comparison of different spectral analysis methods, Ann. Geophys., 34, 437–449, https://doi.org/10.5194/angeo-34-437-2016, 2016. a, b
Muraoka, Y., Sugiyama, T., Kawahira, K., Sato, T., Tsuda, T., Fukao, S., and Kato, S.: Cause of a monochromatic inertia-gravity wave breaking observed by the MU radar, Geophys. Res. Lett., 15, 1349–1352, https://doi.org/10.1029/gl015i012p01349, 1988. a
Narendra Babu, A., Kishore Kumar, K., Kishore Kumar, G., Venkat Ratnam, M., Vijaya Bhaskara Rao, S., and Narayana Rao, D.: Long-term MST radar observations of vertical wave number spectra of gravity waves in the tropical troposphere over Gadanki (13.5∘ N, 79.2∘ E): comparison with model spectra, Ann. Geophys., 26, 1671–1680, https://doi.org/10.5194/angeo-26-1671-2008, 2008. a
Nastrom, G. D., Van Zandt, T. E., and Warnock, J. M.: Vertical wavenumber spectra of wind and temperature from high-resolution balloon soundings over Illinois, J. Geophys. Res., 102, 6685–6701, https://doi.org/10.1029/96jd03784, 1997. a
Pichon, A. L., Assink, J., Heinrich, P., Blanc, E., Charlton-Perez, A., Lee, C. S., Keckhut, P., Hauchecorne, A., Rüfenacht, R., Kämpfer, N., Drob, D. P., Smets, P., Evers, L., Ceranna, L., Pilger, C., Ross, O. A., and Claud, C.: Comparison of co-located independent ground-based middle atmospheric wind and temperature measurements with numerical weather prediction models, J. Geophys. Res.-Atmos., 120, 8318–8331, https://doi.org/10.1002/2015jd023273, 2015. a
Pinel, J. and Lovejoy, S.: Atmospheric waves as scaling, turbulent phenomena, Atmos. Chem. Phys., 14, 3195–3210, https://doi.org/10.5194/acp-14-3195-2014, 2014. a
Podglajen, A., Hertzog, A., Plougonven, R., and Legras, B.: Lagrangian temperature and vertical velocity fluctuations due to gravity waves in the lower stratosphere, Geophys. Res. Lett., 43, 3543–3553, https://doi.org/10.1002/2016gl068148, 2016. a
Qing, H., Zhou, C., Zhao, Z., Chen, G., Ni, B., Gu, X., Yang, G., and Zhang, Y.: A statistical study of inertia gravity waves in the troposphere based on the measurements of Wuhan Atmosphere Radio Exploration (WARE) radar, J. Geophys. Res.-Atmos., 119, 3701–3714, https://doi.org/10.1002/2013jd020684, 2014. a, b
Rao, N. K., Ratnam, M. V., Vedavathi, C., Tsuda, T., Murthy, B. V. K., Sathishkumar, S., Gurubaran, S., Kumar, K. S., Subrahmanyam, K. V., and Rao, S. V.: Seasonal, inter-annual and solar cycle variability of the quasi two day wave in the low-latitude mesosphere and lower thermosphere, J. Atmos. Sol.-Terr. Phy., 152–153, 20–29, https://doi.org/10.1016/j.jastp.2016.11.005, 2017. a
Rice, S. O.: Mathematical analysis of random noise, Bell Syst. Tech. J., 23, 282–332, https://doi.org/10.1002/j.1538-7305.1944.tb00874.x, 1944. a
Rigling, B. D.: Application of temporal gap filling to natural power law spectrums, IEEE Geosci. Remote S., 9, 624–628, https://doi.org/10.1109/lgrs.2011.2177062, 2012. a
Roberts, D. A., Lehar, J., and Dreher, J.: Time Series Analysis with Clean – Part One – Derivation of a Spectrum, Astron. J., 93, 968, https://doi.org/10.1086/114383, 1987. a
Scargle, J. D.: Studies in astronomical time series analysis. II – Statistical aspects of spectral analysis of unevenly spaced data, Astrophys. J., 263, 835, https://doi.org/10.1086/160554, 1982. a, b, c
Schulz, M. and Mudelsee, M.: REDFIT: estimating red-noise spectra directly from unevenly spaced paleoclimatic time series, Comput. Geosci., 28, 421–426, https://doi.org/10.1016/s0098-3004(01)00044-9, 2002. a
Schulz, M. and Stattegger, K.: Spectrum: spectral analysis of unevenly spaced paleoclimatic time series, Comput. Geosci., 23, 929–945, https://doi.org/10.1016/s0098-3004(97)00087-3, 1997. a, b
Schuster, A.: On the investigation of hidden periodicities with application to a supposed 26 d period of meteorological phenomena, J. Geophys. Res., 3, 13, https://doi.org/10.1029/tm003i001p00013, 1898. a
Shibata, T., Ichimori, S., Narikiyo, T., and Maeda, M.: Spectral analysis of vertical temperature profiles observed by a lidar in the upper stratosphere and the lower mesosphere, J. Meteorol. Soc. Jpn. Ser. II, 66, 1001–1005, https://doi.org/10.2151/jmsj1965.66.6_1001, 1988. a
Shinozuka, M.: Simulation of Multivariate and Multidimensional Random Processes, J. Acoust. Soc. Am., 49, 357–368, https://doi.org/10.1121/1.1912338, 2005. a
Sica, R. J. and Russell, A. G.: How many waves are in the gravity wave spectrum?, Geophys. Res. Lett., 26, 3617–3620, https://doi.org/10.1029/1999gl003683, 1999. a, b
Smith, A. M.: Global Dynamics of the MLT, Surv. Geophys., 33, 1177–1230, https://doi.org/10.1007/s10712-012-9196-9, 2012. a
Smith, S. M., Fritts, D. C., and VanZandt, T. E.: Evidence for a saturated spectrum of atmospheric gravity waves, J. Atmos. Sci., 44, 1404–1410, https://doi.org/10.1175/1520-0469(1987)044<1404:EFASSO>2.0.CO;2, 1987. a, b, c
Song, I.-S. and Chun, H.-Y.: A Lagrangian Spectral Parameterization of Gravity Wave Drag Induced by Cumulus Convection, J. Atmos. Sci., 65, 1204–1224, https://doi.org/10.1175/2007jas2369.1, 2008. a
Swenson, G. R., Haque, R., Yang, W., and Gardner, C. S.: Momentum and energy fluxes of monochromatic gravity waves observed by an OH imager at Starfire Optical Range, New Mexico, J. Geophys. Res., 104, 6067–6080, https://doi.org/10.1029/1998jd200080, 1999. a
Vanderplas, J.: Understanding the lomb–scargle periodogram, Astrophys. J. Suppl. S., 236, 16, https://doi.org/10.3847/1538-4365/aab766, 2018. a, b
VanZandt, T.: A universal spectrum of buoyancy waves in the atmosphere, Geophys. Res. Lett., 9, 575–578, https://doi.org/10.1029/gl009i005p00575, 1982. a, b
Vio, R., Andreani, P., and Biggs, A. D.: Unevenly-sampled signals: a general formalism for the Lomb-Scargle periodogram, Astron. Astrophys., 519, A85, https://doi.org/10.1051/0004-6361/201014079, 2010. a
Weinstock, J.: Nonlinear Theory of Gravity Waves: Momentum Deposition, Generalized Rayleigh Friction, and Diffusion, J. Atmos. Sci., 39, 1698–1710, https://doi.org/10.1175/1520-0469(1982)039<1698:NTOGWM>2.0.CO;2, 1982. a
Weinstock, J.: Saturated and unsaturated spectra of gravity waves and scale-dependent diffusion, J. Atmos. Sci., 47, 2211–2226, https://doi.org/10.1175/1520-0469(1990)047<2211:SAUSOG>2.0.CO;2, 1990. a, b, c, d
Zhan, Q., Manson, A. H., and Meek, C.: The impact of gaps and spectral methods on the spectral slope of the middle atmospheric wind, J. Atmos. Terr. Phys., 58, 1329–1336, https://doi.org/10.1016/0021-9169(95)00159-x, 1996. a
Zhang, S., Huang, C., Huang, K., Gong, Y., Chen, G., Gan, Q., and Zhang, Y.: Latitudinal and seasonal variations of vertical wave number spectra of three-dimensional winds revealed by radiosonde observations, J. Geophys. Res.-Atmos., 122, 13174–13190, https://doi.org/10.1002/2017jd027602, 2017. a, b, c, d
Zhang, S. D., Huang, C., and Yi, F.: Radiosonde observations of vertical wave number spectra for gravity waves in the lower atmosphere over Central China, Ann. Geophys., 24, 3257–3265, https://doi.org/10.5194/angeo-24-3257-2006, 2006. a, b, c
Zhang, S.-N., Peterson, R. N., Wiens, R. H., and Shepherd, G. G.: Gravity waves from O2 nightglow during the AIDA '89 campaign I: emission rate/temperature observations, J. Atmos. Terr. Phys., 55, 355–375, https://doi.org/10.1016/0021-9169(93)90074-9, 1993. a
Zhu, X.: A new theory of the saturated gravity wave spectrum for the middle atmosphere, J. Atmos. Sci., 51, 3615–3626, https://doi.org/10.1175/1520-0469(1994)051<3615:ANTOTS>2.0.CO;2, 1994. a, b
Short summary
This numerical study addresses observational gaps' impact on atmospheric gravity wave spectra. Three methods, fast Fourier transform (FFT), generalized Lomb–Scargle periodogram (GLS), and Haar structure function (HSF), were tested on synthetic data. HSF is best for spectra with negative slopes. GLS excels for flat and positive slopes and identifying dominant frequencies. Accurately estimating these aspects is crucial for understanding gravity wave dynamics and energy transfer in the atmosphere.
This numerical study addresses observational gaps' impact on atmospheric gravity wave spectra....