• Bergman, J. W., , and P. D. Sardeshmukh, 2004: Dynamic stabilization of atmospheric single column models. J. Climate,17, 1004–1021, doi:10.1175/1520-0442(2004)017<1004:DSOASC>2.0.CO;2.

  • Blossey, P. N., , C. S. Bretherton, , and M. C. Wyant, 2009: Subtropical low cloud response to a warmer climate in a superparameterized climate model. Part II: Column modeling with a cloud resolving model. J. Adv. Model. Earth Syst., 1 (3), doi:10.3894/JAMES.2009.1.8.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., , and P. K. Smolarkiewicz, 1989: Gravity waves, compensating subsidence and detrainment around cumulus clouds. J. Atmos. Sci.,46, 740–759, doi:10.1175/1520-0469(1989)046<0740:GWCSAD>2.0.CO;2.

  • Daleu, C. L., , S. J. Woolnough, , and R. S. Plant, 2012: Cloud-resolving model simulations with one- and two-way couplings via the weak temperature gradient approximation. J. Atmos. Sci., 69, 36833699, doi:10.1175/JAS-D-12-058.1.

    • Search Google Scholar
    • Export Citation
  • Hack, J. J., , and J. A. Pedretti, 2000: Assessment of solution uncertainties in single-column modeling frameworks. J. Climate,13, 352–365, doi:10.1175/1520-0442(2000)013<0352:AOSUIS>2.0.CO;2.

  • Holton, J., 1973: A one-dimensional cumulus model including pressure perturbations. Mon. Wea. Rev.,101, 201–205, doi:10.1175/1520-0493(1973)101<0201:AOCMIP>2.3.CO;2.

  • Kuang, Z., 2008: Modeling the interaction between cumulus convection and linear gravity waves using a limited-domain cloud system–resolving model. J. Atmos. Sci., 65, 576591, doi:10.1175/2007JAS2399.1.

    • Search Google Scholar
    • Export Citation
  • Kuang, Z., 2011: The wavelength dependence of the gross moist stability and the scale selection in the instability of column-integrated moist static energy. J. Atmos. Sci., 68, 6174, doi:10.1175/2010JAS3591.1.

    • Search Google Scholar
    • Export Citation
  • Mapes, B., 1993: Gregarious tropical convection. J. Atmos. Sci.,50, 2026–2037, doi:10.1175/1520-0469(1993)050<2026:GTC>2.0.CO;2.

  • Mapes, B., 1997: Equilibrium vs. activation control of large-scale variations of tropical deep convection. The Physics and Parameterization of Moist Atmospheric Convection, Springer, 321–356.

  • Mapes, B., 2004: Sensitivities of cumulus-ensemble rainfall in a cloud-resolving model with parameterized large-scale dynamics. J. Atmos. Sci.,61, 2308–2317, doi:10.1175/1520-0469(2004)061<2308:SOCRIA>2.0.CO;2.

  • Mapes, B., , P. Ciesielski, , and R. Johnson, 2003: Sampling errors in rawinsonde-array budgets. J. Atmos. Sci.,60, 2697–2714, doi:10.1175/1520-0469(2003)060<2697:SEIRB>2.0.CO;2.

  • Nilsson, J., , and K. Emanuel, 1999: Equilibrium atmospheres of a two-column radiative–convective model. Quart. J. Roy. Meteor. Soc., 125,22392264, doi:10.1002/qj.49712555814.

    • Search Google Scholar
    • Export Citation
  • Randall, D., , K. Xu, , R. Somerville, , and S. Iacobellis, 1996: Single-column models and cloud ensemble models as links between observations and climate models. J. Climate, 9, 1683–1697, doi:10.1175/1520-0442(1996)009<1683:SCMACE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., , and X. Zeng, 2000: Instability and large-scale circulations in a two-column model of the tropical troposphere. Quart. J. Roy. Meteor. Soc., 126,31173135, doi:10.1002/qj.49712657007.

    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., , and X. Zeng, 2005: Modelling tropical atmospheric convection in the context of the weak temperature gradient approximation. Quart. J. Roy. Meteor. Soc., 131, 13011320, doi:10.1256/qj.03.97.

    • Search Google Scholar
    • Export Citation
  • Roads, J., , S. Chen, , M. Kanamitsu, , and H. Juang, 1998: Vertical structure of humidity and temperature budget residuals over the Mississippi River basin. J. Geophys. Res., 103, 3741–3759, doi:10.1029/97JD02759.

    • Search Google Scholar
    • Export Citation
  • Romps, D. M., 2012a: Numerical tests of the weak pressure gradient approximation. J. Atmos. Sci., 69, 28462856, doi:10.1175/JAS-D-11-0337.1.

    • Search Google Scholar
    • Export Citation
  • Romps, D. M., 2012b: Weak pressure gradient approximation and its analytical solutions. J. Atmos. Sci., 69, 28352845, doi:10.1175/JAS-D-11-0336.1.

    • Search Google Scholar
    • Export Citation
  • Romps, D. M., 2014: Rayleigh damping in the free troposphere. J. Atmos. Sci., 71, 553565, doi:10.1175/JAS-D-13-062.1.

  • Sessions, S. L., , S. Sugaya, , D. J. Raymond, , and A. H. Sobel, 2010: Multiple equilibria in a cloud-resolving model using the weak temperature gradient approximation. J. Geophys. Res.,115, D12110, doi:10.1029/2009JD013376.

  • Sobel, A., , and C. Bretherton, 2000: Modeling tropical precipitation in a single column. J. Climate,13, 4378–4392, doi:10.1175/1520-0442(2000)013<4378:MTPIAS>2.0.CO;2.

  • Wang, S., , and A. H. Sobel, 2011: Response of convection to relative sea surface temperature: Cloud-resolving simulations in two and three dimensions. J. Geophys. Res., 116, D11119, doi:10.1029/2010JD015347.

    • Search Google Scholar
    • Export Citation
  • Wang, S., , and A. H. Sobel, 2012: Impact of imposed drying on deep convection in a cloud-resolving model. J. Geophys. Res., 117, D02112, doi:10.1029/2011JD016847.

    • Search Google Scholar
    • Export Citation
  • Wang, S., , A. H. Sobel, , and Z. Kuang, 2013: Cloud-resolving simulation of TOGA-COARE using parameterized large-scale dynamics. J. Geophys. Res. Atmos.,118, 6290–6301, doi:10.1002/jgrd.50510.

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An Improved Weak Pressure Gradient Scheme for Single-Column Modeling

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  • 1 Department of Earth and Planetary Science, University of California, Berkeley, and Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California
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Abstract

A new formulation of the weak pressure gradient approximation (WPG) is introduced for parameterizing large-scale dynamics in limited-domain atmospheric models. This new WPG is developed in the context of the one-dimensional, linearized, damped, shallow-water equations and then extended to Boussinesq and compressible fluids. Unlike previous supradomain-scale parameterizations, this formulation of WPG correctly reproduces both steady-state solutions and first baroclinic gravity waves. In so doing, this scheme eliminates the undesirable gravity wave resonance in previous versions of WPG. In addition, this scheme can be extended to accurately model the emission of gravity waves with arbitrary vertical wavenumber.

Corresponding author address: Jacob P. Edman, Department of Earth and Planetary Science, 449 McCone Hall, University of California, Berkeley, Berkeley, CA 94720. E-mail: jedman@berkeley.edu

Abstract

A new formulation of the weak pressure gradient approximation (WPG) is introduced for parameterizing large-scale dynamics in limited-domain atmospheric models. This new WPG is developed in the context of the one-dimensional, linearized, damped, shallow-water equations and then extended to Boussinesq and compressible fluids. Unlike previous supradomain-scale parameterizations, this formulation of WPG correctly reproduces both steady-state solutions and first baroclinic gravity waves. In so doing, this scheme eliminates the undesirable gravity wave resonance in previous versions of WPG. In addition, this scheme can be extended to accurately model the emission of gravity waves with arbitrary vertical wavenumber.

Corresponding author address: Jacob P. Edman, Department of Earth and Planetary Science, 449 McCone Hall, University of California, Berkeley, Berkeley, CA 94720. E-mail: jedman@berkeley.edu
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