Quasi-Equilibrium and Weak Temperature Gradient Balances in an Equatorial Beta-Plane Model

Fiaz Ahmed aDepartment of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, California

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J. David Neelin aDepartment of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, California

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Ángel F. Adames bDepartment of Climate and Space Science and Engineering, University of Michigan, Ann Arbor, Michigan

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Abstract

Convective quasi-equilibrium (QE) and weak temperature gradient (WTG) balances are frequently employed to study the tropical atmosphere. This study uses linearized equatorial beta-plane solutions to examine the relevant regimes for these balances. Wave solutions are characterized by moisture–temperature ratio (qT ratio) and dominant thermodynamic balances. An empirically constrained precipitation closure assigns different sensitivities of convection to temperature (ε t ) and moisture (ε q ). Longwave equatorial Kelvin and Rossby waves tend toward the QE balance with qT ratios of ε t :ε q that can be ~1–3. Departures from strict QE, essential to both precipitation and wave dynamics, grow with wavenumber. The propagating QE modes have reduced phase speeds because of the effective gross moist stability m eff, with a further reduction when ε t > 0. Moisture modes obeying the WTG balance and with large qT ratios (>10) emerge in the shortwave regime; these modes exist with both Kelvin and Rossby wave meridional structures. In the υ = 0 case, long propagating gravity waves are absent and only emerge beyond a cutoff wavenumber. Two bifurcations in the wave solutions are identified and used to locate the spatial scales for QE–WTG transition and gravity wave emergence. These scales are governed by the competition between the convection and gravity wave adjustment times and are modulated by m eff. Near-zero values of m eff shift the QE–WTG transition wavenumber toward zero. Continuous transitions replace the bifurcations when m eff < 0 or moisture advection/WISHE mechanisms are included, but the wavenumber-dependent QE and WTG balances remain qualitatively unaltered. Rapidly decaying convective/gravity wave modes adjust to the slowly evolving QE/WTG state in the longwave/shortwave regimes, respectively.

Current affiliation: Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, Wisconsin.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JAS-D-20-0184.s1.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Fiaz Ahmed, fiaz@ucla.edu

Abstract

Convective quasi-equilibrium (QE) and weak temperature gradient (WTG) balances are frequently employed to study the tropical atmosphere. This study uses linearized equatorial beta-plane solutions to examine the relevant regimes for these balances. Wave solutions are characterized by moisture–temperature ratio (qT ratio) and dominant thermodynamic balances. An empirically constrained precipitation closure assigns different sensitivities of convection to temperature (ε t ) and moisture (ε q ). Longwave equatorial Kelvin and Rossby waves tend toward the QE balance with qT ratios of ε t :ε q that can be ~1–3. Departures from strict QE, essential to both precipitation and wave dynamics, grow with wavenumber. The propagating QE modes have reduced phase speeds because of the effective gross moist stability m eff, with a further reduction when ε t > 0. Moisture modes obeying the WTG balance and with large qT ratios (>10) emerge in the shortwave regime; these modes exist with both Kelvin and Rossby wave meridional structures. In the υ = 0 case, long propagating gravity waves are absent and only emerge beyond a cutoff wavenumber. Two bifurcations in the wave solutions are identified and used to locate the spatial scales for QE–WTG transition and gravity wave emergence. These scales are governed by the competition between the convection and gravity wave adjustment times and are modulated by m eff. Near-zero values of m eff shift the QE–WTG transition wavenumber toward zero. Continuous transitions replace the bifurcations when m eff < 0 or moisture advection/WISHE mechanisms are included, but the wavenumber-dependent QE and WTG balances remain qualitatively unaltered. Rapidly decaying convective/gravity wave modes adjust to the slowly evolving QE/WTG state in the longwave/shortwave regimes, respectively.

Current affiliation: Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, Wisconsin.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JAS-D-20-0184.s1.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Fiaz Ahmed, fiaz@ucla.edu

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