Linear Stability of Moist Convecting Atmospheres. Part I: From Linear Response Functions to a Simple Model and Applications to Convectively Coupled Waves
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Linear Stability of Moist Convecting Atmospheres. Part I: From Linear Response Functions to a Simple Model and Applications to Convectively Coupled Waves

  • 2018

  • By Kuang, Zhiming
  • Source: Journal of the Atmospheric Sciences, 75(9), 2889-2907
Filetype[PDF-3.12 MB]


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Details:

  • Journal Title:
    Journal of the Atmospheric Sciences
  • Personal Author:
    Kuang, Zhiming
  • NOAA Program & Office:
    OAR (Oceanic and Atmospheric Research)
  • Description:
    A procedure is presented to systematically construct simple models for the linear stability of moist convecting atmospheres. First, linear response functions of a cumulus ensemble constructed from cloud-system-resolving models are coupled with matrices expressing two-dimensional large-scale linear wave dynamics. For a radiative–convective equilibrium reference state, this model gives two branches of unstable modes: a propagating convectively coupled wave branch and a stationary branch related to storage of column-integrated moist static energy (MSE). The stationary branch is unstable only when radiative feedback is included, while the convectively coupled wave branch is less affected by radiative feedback. With a modular order-reduction procedure from control theory, the linear-response-function-based model is reduced to a system of six ordinary differential equations while still capturing the essential features of the unstable modes (eigenvalues and structures). The six-dimensional system is then split into a slow and a fast manifold. The slow manifold (again, reflecting column MSE storage) is essential for the stationary mode but not for the convectively coupled waves. The fast manifold is then transformed into a form similar to that of prior simple models of convectively coupled waves, thus placing those models and the insights derived from them on a firmer footing. The procedure also better quantifies the parameters of such simple models and allows the stability difference between different reference states to be better understood.
  • Keywords:
  • Source:
    Journal of the Atmospheric Sciences, 75(9), 2889-2907
  • DOI:
  • ISSN:
    0022-4928;1520-0469;
  • Format:
    PDF
  • Publisher:
    American Meteorological Society
  • Document Type:
    Journal Article
  • Funding:
    Grant no. NA17OAR4310260
  • Rights Information:
    Other
  • Compliance:
    Library
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