Mathematical Geosciences

, Volume 50, Issue 5, pp 585–606 | Cite as

Diagnosis of Free and Convectively Coupled Equatorial Waves

  • Carlos A. F. Marques
  • José M. Castanheira
Special Issue


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.


Convectively coupled equatorial waves Hough functions Vertical normal modes Kelvin wave Mixed Rossby–gravity wave 



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 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


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Copyright information

© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  1. 1.CESAM and Department of PhysicsUniversity of AveiroAveiroPortugal

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