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3D Modal Variability and Energy Transformations on the Sphere

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Part of the Mathematics of Planet Earth book series (MPE, volume 8)

Abstract

The three-dimensional (3D) normal-mode function (NMF) decomposition is derived in the system with pressure as the vertical coordinate followed by the applications of NMFs to atmospheric variability and energetics. Energy generation and transfers are analyzed in modal space. It is demonstrated that 3D NMF decomposition filters inertia-gravity waves even outside the tropics. Energy decomposition into the Rossby and inertia-gravity components shows that modern analysis data have the Rossby wave energy spectrum obeying a k−3 law, where k is the zonal wavenumber. The energy spectrum of inertia-gravity modes follows a k−5/3 law at smaller synoptic scales which are well resolved by analyses whereas the analyses still lack variability at mesoscale. The energy spectrum of the Rossby modes obeys the 2 power of the eigen frequency for the barotropic mode, as expected from the Rossby wave saturation theory. A clear energy peak at the spherical Rhines scale separates the nonlinear turbulent regime from the linear wave regime. Scale-dependent diagnostics of climate model biases is derived in relation to spatio-temporal variability of the models in comparison with reanalysis data.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Center for Computational SciencesUniversity of TsukubaTsukubaJapan
  2. 2.Meteorological InstituteUniversität HamburgHamburgGermany

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