Abstract
A methodology for diagnosis of free and convectively coupled equatorial waves (CCEWs) is reviewed and illustrated for Kelvin and mixed Rossby–gravity (MRG) waves. The method is based on prefiltering of the geopotential and horizontal wind, using three-dimensional normal mode functions of the adiabatic linearized equations of a resting atmosphere, followed by space–time power and cross-spectral analysis applied to the normal-mode-filtered fields and the outgoing long-wave radiation (OLR) to identify spectral regions of coherence. The methodology is applied to geopotential and horizontal wind fields produced by European Centre for Medium-Range Weather Forecasts interim reanalysis and OLR data produced by the National Oceanic and Atmospheric Administration. The same type of data simulated by two climate models that participated in the fifth phase of the climate model intercomparison project are also used. Overall, simulation of free and CCEWs was achieved by the models with moderate success. Kelvin and MRG waves were identified in the space–time spectral domains, using both observationally based and climate model datasets. Other nonequatorial waves, classified as tropical depression and extratropical storm track activity, along with the Madden–Julian oscillation were also observed. However, significant deviations were also evident in the models, which may help identification of deficiencies in the models’ simulation schemes for some physical processes. Therefore, this diagnosis method should be a useful procedure for climate model validation and model benchmarking.
Similar content being viewed by others
References
Allen MR, Smith LA (1996) Monte Carlo SSA: deteting irregular oscilations in the presence of coloured noise. J Clim 9:3373–3404
Andrews DG, Holton JR, Leovy CB (1987) Middle atmosphere dynamics. Academic Press, London
Castanheira JM, Marques CAF (2015) Convectively coupled equatorial waves diagnosis using 3-D normal modes. Q J R Meteorol Soc 141:2776–2792. https://doi.org/10.1002/qj.2563
Castanheira JM, DaCamara CC, Rocha A (1999) Numerical solutions of the vertical structure equation and associated energetics. Tellus 51A:337–348
Cohn SE, Dee DP (1989) An analysis of the vertical structure equation for arbitrary thermal profiles. Q J R Meteorol Soc 115:143–171
Dee DP, Uppala SM, Simmons AJ, Berrisford P, Poli P, Kobayashi S, Andrae U, Balmaseda MA, Balsamo G, Bauer P, Bechtold P, Beljaars ACM, van de Berg L, Bidlot J, Bormann N, Delsol C, Dragani R, Fuentes M, Geer AJ, Haimberger L, Healy SB, Hersbach H, Hólm EV, Isaksen L, Kållberg P, Köhler M, Matricardi M, McNally AP, Monge-Sanz BM, Morcrette JJ, Park BK, Peubey C, de Rosnay P, Tavolato C, Thépaut JN, Vitart F (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137:553–597. https://doi.org/10.1002/qj.828
Dias J, Kiladis GN (2014) Influence of the basic state zonal flow on convectively coupled equatorial waves. Geophys Res Lett 41:6904–6913. https://doi.org/10.1002/2014GL061476
Fulton SR, Schubert WH (1985) Vertical normal modes transforms: theory and application. Mon Weather Rev 113:647–657
Gehne M, Kleeman R (2012) Spectral analysis of tropical atmospheric dynamical variables using a linear shallow-water modal decomposition. J Atmos Sci 69:2300–2316
Hall NMJ, Kiladis GN, Thorncroft CD (2006) Three-dimensional structure and dynamics of african easterly waves. Part II: dynamical modes. J Atmos Sci 63:2231–2245
Hayashi Y (1971) A Generalized method of resolving disturbances into progressive and retrogressive waves by space Fourier and time cross-spectral analyses. J Meteorol Soc Jpn 49:125–128
Hayashi Y (1982) Space-time spectral analysis and its applications to atmospheric waves. J Meteorol Soc Jpn 60:451–465
Hendon HH, Wheeler M (2008) Some space-time spectral analyses of tropical convection and planetary-scale waves. J Atmos Sci 65:2936–2948
Hough SS (1898) On the application of harmonic analysis to the dynamical theory of the tides Part II. On the general integration of laplaces tidal equations. Phil Trans Roy Soc Lond A191:139–185
Hung MP, Lin JL, Wang W, Kim D, Shinoda T, Weaver SJ (2013) MJO and convectively coupled equatorial waves simulated by CMIP5 climate models. J Clim 26:6185–6214
Jones PW (1999) First- and second-order conservative remapping schemes for grids in spherical coordinates. Mon Weather Rev 127:2204–2210
Kasahara A (1976) Normal modes of ultralong waves in the atmosphere. Mon Weather Rev 104:669–690
Kasahara A (1977) Numerical integration of the global barotropic primitive equations with hough harmonic expansions. J Atmos Sci 34:687–701
Kasahara A (1984) The linear response of a stratified global atmosphere to tropical thermal forcing. J Atmos Sci 41:2217–2237
Kasahara A, Puri K (1981) Spectral representation of three-dimensional global data by expansion in normal mode functions. Mon Wea Rev 109:37–51
Kiladis GN, Thorncroft CD, Hall NMJ (2006) Three dimensional structure and dynamics of African easterly waves. Part I: observations. J Atmos Sci 63:2212–2230. https://doi.org/10.1175/JAS3741.1
Kiladis GN, Wheeler MC, Haertel PT, Straub KH, Roundy PE (2009) Convectively coupled equatorial waves. Rev Geophys 47:RG2003. https://doi.org/10.1029/2008RG000266
Liebmann B, Smith CA (1996) Description of a complete (interpolated) outgoing longwave radiation dataset. Bull Am Meteorol Soc 77:1275–1277
Lin JL, Kiladis GN, Mapes BE, Weickmann KM, Sperber KR, Lin W, Wheeler MC, Schubert SD, Genio AD, Donner LJ, Emori S, Gueremy JF, Hourdin F, Rasch PJ, Roeckner E, Scinocca JF (2006) Tropical intraseasonal variability in 14 IPCC AR4 climate models. Part I: convective signals. J Clim 19:2665–2690. https://doi.org/10.1175/JCLI3735.1
Longuet-Higgins MS (1968) The eigenfunctions of Laplaces tidal equations over a sphere. Philos Trans R Soc Lond A262:511–607
Madden R, Julian P (1994) Observations of the 40–50 day tropical oscillation: a review. Mon Weather Rev 122:814–837
Marques CAF, Castanheira JM (2012) A detailed normal mode energetics of the general circulation of the atmosphere. J Atmos Sci 69(9):2718–2732
Matsuno T (1966) Quasi-geostrophic motions in the equatorial area. J Meteorol Soc Jpn 44:25–43
Ogrosky HR, Stechmann SN (2016) Identifying convectively coupled equatorial waves using theoretical wave eigenvectors. Mon Weather Rev 144:2235–2264. https://doi.org/10.1175/MWR-D-15-0292.1
Roundy PE, Frank WM (2004) A climatology of waves in the equatorial region. J Atmos Sci 61:2105–2132
Roundy PE, Schreck CJ III (2009) A combined wave-number-frequency and time-extended EOF approach for tracking the progress of modes of large-scale organized tropical convection. Q J R Meteorol Soc 135:161–173
Sneddon IN (1972) The use of integral transforms. McGraw-Hill, New York, p 539
Swarztrauber PN, Kasahara A (1985) The vector harmonic analysis of Laplaces tidal equations. SIAM J Sci Stat Comput 6:464–491
Takayabu YN (1994a) Large-scale cloud disturbances associated with equatorial waves. Part I: spectral features of the cloud disturbances. J Meteorol Soc Jpn 72:433–449
Takayabu YN (1994b) Large-scale cloud disturbances associated with equatorial waves. Part II: westward-propagating inertio-gravity waves. J Meteorol Soc Jpn 72:451–465
Tanaka HL (1985) Global energetics analysis by expansion into three-dimensional normal-mode functions during the FGGE winter. J Meteorol Soc Jpn 63:180–200
Taylor KE, Stouffer RJ, Meehl GA (2012) An overview of CMIP5 and the experiment design. Bull Am Meteorol Soc 93:485–498
Trenberth KE, Berry JC, Buja LE (1993) Vertical interpolation and truncation of model-coordinate data. Technical Note. NCAR/TN-396+STR, NCAR, p 54
von Storch H, Zwiers FW (2003) Statistical analysis in climate research. Cambridge University Press, Cambridge
Wheeler M, Kiladis GN (1999) Convectively coupled equatorial waves: analysis of clouds and temperature in the wavenumber-frequency domain. J Atmos Sci 56:374–399
Wheeler M, Kiladis GN, Webster PJ (2000) Large-scale dynamical fields associated with convectively coupled equatorial waves. J Atmos Sci 57:613–640
Yang GY, Hoskins B, Slingo J (2003) Convectively coupled equatorial waves: a new methodology for identifying wave structures in observational data. J Atmos Sci 60:1637–1654
Yang GY, Hoskins B, Slingo J (2007a) Convectively coupled equatorial waves. Part I: horizontal and vertical structures. J Atmos Sci 64:3406–3423
Yang GY, Hoskins B, Slingo J (2007b) Convectively coupled equatorial waves. Part II: propagation characteristics. J Atmos Sci 64:3424–3437
Yang GY, Hoskins B, Slingo J (2007c) Convectively coupled equatorial waves. Part III: synthesis structures and their forcing and evolution. J Atmos Sci 64:3438–3451
Acknowledgements
This work was supported by the National Foundation for Science and Technology (FCT) within project CLICURB (EXLC/AAG-MAA/0383/2012). C.A.F.M. was supported by the FCT under grant SFRH/BPD/76232/2011. We are grateful to the Beijing Climate Center and to the Max Planck Institute for Meteorology for providing the atmospheric datasets used in this study. The CMIP5 datasets were obtained from its data portal at http://pcmdi9.llnl.gov/. ERA interim data were obtained from the ECMWF data server. Interpolated OLR data were provided by the NOAA/OAR/ESRL PSD, Boulder, CO, USA, from their website at http://www.esrl.noaa.gov/psd/.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Marques, C.A.F., Castanheira, J.M. Diagnosis of Free and Convectively Coupled Equatorial Waves. Math Geosci 50, 585–606 (2018). https://doi.org/10.1007/s11004-018-9729-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-018-9729-y