Convective quasi–equilibrium
Yano, J.-I. and Plant, R. S. Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1029/2011RG000378 Abstract/SummaryThe concept of convective quasi–equilibrium (CQE) is a key ingredient in order to understand the role of deep moist convection in the atmosphere. It has been used as a guiding principle to develop almost all convective parameterizations and provides a basic theoretical framework for large–scale tropical dynamics. The CQE concept as originally proposed by Arakawa and Schubert [1974] is systematically reviewed from wider perspectives. Various interpretations and extensions of Arakawa and Schubert’s CQE are considered in terms of both a thermodynamic analogy and as a dynamical balance. The thermodynamic interpretations can be more emphatically embraced as a homeostasis. The dynamic balance interpretations can be best understood by analogy with the slow manifold. Various criticisms of CQE can be avoided by taking the dynamic balance interpretation. Possible limits of CQE are also discussed, including the importance of triggering in many convective situations, as well as the possible self–organized criticality of tropical convection. However, the most intriguing aspect of the CQE concept is that, in spite of many observational tests supporting and interpreting it in many different senses, it has 1never been established in a robust manner based on a systematic analysis of the cloud–work function budget by observations as was originally defined.
\bibitem{}
Adkins, C. J. (1983),
{\it Equilibrium Thermodynamics},
3rd Ed.,
Cambridge University Press.
%, 285pp.
\bibitem{}
Andrews, F. C. (1963),
{\it Equilibrium Statistical Mechanics},
John Wiley \& Sons.
%,206pp.
\bibitem{}
Arakawa, A. (1969),
Parameterization of cumulus convection.
In: Proceedings of the WMO/IUGG Symposium on Numerical Weather
Prediction, Tokyo, 26 Nov.--4 Dec., 1968,
Japan Meteor. Agency, IV, 8, 1--6.
\bibitem{}
Arakawa., A. (2004),
The cumulus parameterization problem: Past, present, and future.
{\it J. Climate,} \textit{17}, 2493--2525.
\bibitem{}
Arakawa, A., and W. H. Schubert (1974),
Interaction of a cumulus cloud ensemble with the large-scale environment,
Part I.
{\it J. Atmos. Sci.,} \textit{31}, 674--701.
\bibitem{}
Bak, P., C. Tang, and K. Wiesenfeld (1987),
Self-organized criticality: An explanation of the $1/f$ noise.
{\it Phys. Rev. Lett.,} \textit{59}, 381--384.
\bibitem{}
Ball, M. A., and R. S. Plant (2008), Comparison of stochastic parameterization approaches in a single-column model.
{\it Phil. Trans. Roy. Soc. A,} \textit{366}, 2605-2623.
\bibitem{}
Bechtold, P., E. Bazile, F. Guichard, P. Mascart, and E. Richard (2001),
A mass-flux convection scheme for regional and global models.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{127}, 869 --889.
\bibitem{}
Bechtold, P. (2009),
Convection parameterization. In: Proceedings of the
ECMWF Seminar on Parameterization of Subgrid Physical Processes, 1--4
September 2008, Reading, UK
\par
%\url{
http://www.ecmwf.int/publications/library/ecpublications/\_pdf/seminar/2008/Bechtold.pdf
%}
%\parindent=-20pt
\bibitem{}
Betts, A. K. (1986),
A new convective adjustment scheme. Part I: Observational and theoretical
basis. {\it Quart. J. Roy. Meteor. Soc.,} \textit{112}, 677--691.
%\bibitem{}
%Betts, A. K., and M. J. Miller (1986), A new convective adjustment
%scheme. Part II: Single column tests using GATE wave, BOMEX, ATEX and
%arctic air--mass data sets. {\it Quart. J. Roy. Meteor. Soc.,} \textit{112}, 693--709.
\bibitem{}
Bihlo, A. (2010),
Symmetry methods in the atmospheric sciences.
PhD thesis, University of Vienna.
\bibitem{}
Blyth, A. M., W. A. Cooper, and J. B. Jensen (1988),
A study of the source of entrained air in Montana cumuli.
{\it J. Atmos. Sci.,} \textit{45}, 3944--3964.
%\bibitem{}
%Bowler, N. E., A. Arribas, K. R. Mylne, K. B. Robertson, and
%S. E. Beare (2008), The MOGREPS short-range ensemble prediction system.
%{\it Quart. J. Roy. Meteor. Soc.,} \textit{134}, 703--722.
\bibitem{}
Cannon, W. B. (1929), Organization for physiological homeostasis.
{\it Physiol. Rev.,} \textit{9}, 399--431.
\bibitem{}
Cannon, W. B. (1932), {\it The Wisdom of the Body}, W. W. Norton,
Inc., New York.
\bibitem{}
Carnot, S. (1824),
Reflections on the motive power of fire, and on machines fitted to develop
that power. Reprinted in Mendoza, E. (ed.): {\it Reflections on the Motive
Power of Fire}, Dover Publications, New York (1960), 3--59.
\bibitem{}
Chandler, D. (1987),
{\it Introduction to Modern Statistical Mechanics},
Oxford University Press.
%272pp
\bibitem{}
Charney, J. G. (1963),
A note on large--scale motions in the tropics.
{\it J. Atmos. Sci.,} \textit{20}, 607--609.
\bibitem{}
Charney, J. G. (1971),
Geostrophic turbulence, {\it J. Atmos. Sci.,} \textit{28}, 1087--1095.
\bibitem{}
Clapeyron, E. (1834),
Memoir on the motive power of heat. Reprinted in Mendoza, E. (ed.):
{\it Reflections on the Motive Power of Fire}, Dover Publications, New York (1960), 73--105.
\bibitem{}
Clauset, A., C. R. Shalizi and M. E. J. Newman (2009),
Power-law distributions in empirical data.
{\it SIAM Review} \textit{51}, 661--703.
\bibitem{}
Cohen, B. G., and G. C. Craig (2006),
Fluctuations in an equilibrium convective ensemble. Part II:
Numerical experiments.
{\it J. Atmos. Sci.,} \textit{63}, 2005--2015.
\bibitem{}
Cox, S. M., and Roberts, A. J. (1994),
Initialization and the quasi-geostrophic slow manifold.
{\it Preprint}, arXiv:nlin/0303011v1.
\bibitem{}
Craig, G. C., and B. G. Cohen (2006),
Fluctuations in an equilibrium convective ensemble. Part I),
Theoretical formulation.
{\it J. Atmos. Sci.,} \textit{63}, 1996--2004.
\bibitem{}
Davoudi, J., N. A. McFarlane, T. Birner (2010),
Fluctuation of mass flux in a cloud-resolving simulation with interactive radiation.
{\it J. Atmos. Sci.,} \textit{67}, 400--418.
\bibitem{}
Davies, L., R. S. Plant, and S. H. Debyshire (2009),
A simple model of convection with memory.
{\it J. Geophys. Res.,} \textit{114}(D17202), doc:10.1029/2008JD011653.
\bibitem{}
Davies, L., R. S. Plant, and S. H. Derbyshire (2012),
Departures from convective equilibrium with a rapidly-varying surface forcing.
Submitted to: \textit{Quart. J. Roy. Met. Soc.}
\bibitem{}
Delayen, K., and J.-I. Yano (2009),
Is asymptotic non--divergence of the large--scale tropical atmosphere
consistent with equatorial wave theories?
{\it Tellus} \textit{61A}, 491--497.
\bibitem{}
de Rooy, W. C. de, P. Bechtold, K. Froehlich, C. Hohenegger, H. J. J. Jonker,
D. Mironov, A. P. Siebesma, J. Teixeira and J.-I. Yano (2012),
Entrainment and detrainment in cumulus convection: an overview
{\it Quart. J. Roy. Meteor. Soc.,} in press, DOI: 10.1002/qj.1959.
\bibitem{}
Donner, L. J. (1993),
A cumulus parameterization including mass fluxes, vertical momentum dynamics,
and mesoscale effects.
{\it J. Atmos. Sci.,} \textit{60}, 137--151.
\bibitem{}
Donner, L. J., and V. T. Phillips (2003),
Boundary layer control on convective available
potential energy:
Implications for cumulus parameterization. {\it J. Geophys. Res.,} \textit{108}{D22},
doi:10.1029/2003JD03773.
\bibitem{}
Emanuel, K. A. (1994), {\it Atmospheric Convection}, Oxford University
Press.
%, 580pp.
\bibitem{}
Emanuel, K. (2000),
Quasi--equilibrium thinking.
In: {\it General Circulation Model Development}
(D. A. Randall, Ed.), Elsevier, Ch.~8, 225--255.
\bibitem{}
Emanuel, K. A. (2007).
Quasi--equilibrium dynamics of the tropical atmosphere.
In: {\it The Global Circulation of the Atmosphere}
(T. Schneider and A. H. Sobel, Eds.), Princeton University Press,
Ch.~7, 186--218.
\bibitem{}
Emanuel, K. A., J. D. Neelin, and C. S. Bretherton (1994),
On large--scale circulation in convective atmospheres.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{120}, 1111--1143.
\bibitem{}
Feller, W. (1968),
{\it An Introduction to Probability Theory and Its Applications},
Vol. 1, 3rd Ed., John Wiley and Sons.
%, 509pp.
\bibitem{}
Fierro, A. O., R. F. Rogers, F. D. Marks, D. S. Nolan
(2009), The impact of horizontal grid spacing on the microphysical and
kinematic structures of strong tropical cyclones simulated with the
WRF-ARW model. {\it Mon. Wea. Rev.,} \textit{137}, 3717--3743.
\bibitem{}
Fierro, A. O., E. J. Zipser, M. A. LeMone, J. M. Straka, J.
(Malkus) Simpson (2012), Tropical oceanic hot towers: Need they be
undilute to transport energy from the boundary layer to the upper
troposphere effectively? An answer based on trajectory analysis of a
simulation of a TOGA COARE convective system. {\it J. Atmos. Sci.,} \textit{69},
195--213.
\bibitem{}
Fletcher, J. K., and C. S. Bretherton (2010),
Evaluating boundary layer--based mass flux closures using cloud--resolving
model simulations of deep convection.
{\it J. Atmos. Sci.,} \textit{67}, 2212--2225.
\bibitem{}
Ford, R. (1994),
Gravity wave radiation from vortex trains in rotating shallow water.
{\it J. Fluid Mech.,} \textit{281}, 81--118.
\bibitem{}
Ford, R., M. E. McIntyre, and W. A. Norton (2000),
Balance and the slow quasimanifold: Some explicit results.
{\it J. Atmos. Sci.,} \textit{57}, 1236--1254.
\bibitem{}
Fraedrich, K., and J. L. McBride (1989),
The physical mechanism of CISK and the free-ride balance.
{\it J. Atmos. Sci.,} \textit{46}, 2642--2648.
\bibitem{}
Fritsch, J. M., and C. F. Chappell (1980),
Numerical prediction of convectively driven mesoscale pressure systems.
Part i: convective parameterization.
{\it J. Atmos. Sci.,} \textit{37}, 1722--1733.
\bibitem{}
Gill, A. E. (1980),
Some simple solutions for heat-induced tropical circulation.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{449}, 447--462.
\bibitem{}
Goldstein, H., C. Poole, and J. Safko (2002),
{\it Classical Mechanics}, 3rd Ed.
Addison Wesley, San Francisco.
%, 638pp.
\bibitem{}
Gombosi, T. I. (1994),
{\it Gaskinetic theory.}
Cambridge University Press.
%, 297pp.
\bibitem{}
Grabowski, W. W. (2003), Impact of cloud microphysics on
convective--radiative quasi--equilibrium revealed by cloud-resolving
convection parameterization.
{\it J. Climate,} \textit{16}, 3463--3475.
%\bibitem{}
%Gray, M. E. B., and G. J. Shutts (2002), A stochastic scheme for
%representing convectively generated vorticity sources in general
%circulation models. APR Turbulence and Diffusion Note 285, Met
%Office, UK.
\bibitem{}
Gregory, D., and P. R. Rowntree (1990),
A mass flux convection scheme with representation of cloud ensemble characteristics and stability-dependent closure.
{\it Mon. Wea. Rev.,} \textit{118}, 1483--1506.
\bibitem{}
Gregory, D., J.--J. Morcrette, C. Jacob, A. C. M. Beljaars, and T. Stockdale
(2000),
Revision of convection, radiation and cloud schemes in the ECMWF Integrated Forecast System.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{126}, 1685--1710.
\bibitem{}
Greenspan, H. P. (1968),
{\it The Theory of Rotating Fluids}.
Cambridge University Press, New York.
%, xii + 328 pp
\bibitem{}
Groenemeijer, A. P., and G. C. Craig (2012),
Ensemble forecasting with a stochastic convective parametrization based on equilibrium statistics.
\textit{Atmos. Chem. Phys.,} \textit{12}, 4555-4565.
\bibitem{}
Guichard F., J. C. Petch, J. L. Redelsperger, P. Bechtold,
J.--P. Chaboureau, S. Cheinet, W. Grabowski, H. Grenier, C. G. Jones,
M. Kohler, J.--M. Piriou, R. Tailleux, M. Tomasini (2004),
Modelling the diurnal cycle of deep precipitating convection over land
with cloud-resolving models and single-column models.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{604}, 3139--3172.
\bibitem{}
Guha, P. (2007).
Metriplectic structure, Leibniz dynamics and dissipative systems.
{\it J. Math. Anal. Appl.,}, {\bf 326}, 121-136.
\bibitem{}
Heus, T., and H. J. J. Jonker (2008),
Subsiding shells around shallow cumulus clouds.
{\it J. Atmos. Sci.,} \textit{65}, 1003-1018.
\bibitem{}
Hepburn, B. S. (2007),
Equilibrium and explanation in 18th century mechanics.
PhD thesis, University of Pittsburgh.
\bibitem{}
Hildebrandt, S. and Tromba, A. (1996),
{\it The Parsimonious Universe: Shape and Form in the Natural World}.
Springer-Verlag, New York.
%, 353pp.
\bibitem{}
Hohenegger, C., and C. S. Bretherton (2011),
Simulating deep convection with a shallow convection scheme.
{\it Atmos. Chem. Phys.,} \textit{11}, 10389--10406.
\bibitem{}
Holloway, C. E., and J. D. Neelin (2007),
The convective cold top and quasi--equilibrium.
{\it J. Atmos. Sci.,} \textit{64}, 1467--1487.
\bibitem{}
Holloway, C. E., and J. D. Neelin (2009),
Moisture vertical structure, column water vapor, and tropical deep convection.
{\it J. Atmos. Sci.,} \textit{66}, 1665--1683.
\bibitem{}
Holloway, C. E., and J. D. Neelin (2010),
Temporal relations of column water vapor and tropical precipitation.
{\it J. Atmos. Sci.,} \textit{67}, 1091--1105.
\bibitem{}
Holloway, C. E., S. J. Woolnough and G. M. S. Lister (2012),
Precipitation distributions for explicit versus parameterized convection in a large-domain high-resolution tropical case study.
To appear in: {\it Quart. J. Roy. Meteor. Soc.}, doi: 10.1002/qj.1903
\bibitem{}
Jensen, H. J. (1998),
{\it Self-organized criticality.}
Cambridge University Press.
\bibitem{}
Jones, T. R., and Randall, D. A. (2011),
Quantifying the limits of convective parameterizations.
{\it J. Geophys. Res.,} \textit{116}(D08210), doi:10.102910/2010JD014913.
\bibitem{}
Kain, J. S., and J. M. Fritsch (1990),
A one-dimensional entraining/detraining plume model and its application in convective parameterization.
{\it J. Atmos. Sci.,} \textit{47}, 2784--2802.
\bibitem{}
Kain, J. S., and J. M. Fritsch (1992),
The role of the convective ``trigger function'' in numerical forecasts
of mesoscale convective systems.
{\it Meteorol. Atmos. Phys.,} \textit{49}, 93--106.
\bibitem{}
Khouider, B., Biello, J. A. and Majda, A. J. (2010),
A stochastic multicloud model for tropical convection.
{\it Comm. Math. Sci.,} \textit{8}, 187--216.
\bibitem{}
Kondepudi, D., and I. Prigogine (1998),
{\it Modern Thermodynamics:
From Heat Engines to Dissipative Structures},
John Wiley \& Sons.
%,486pp.
\bibitem{}
Kuang, Z. (2011),
The wavelength dependence of the gross moist stability and the scale
selection in the instability of column-integrated moist static energy.
{\it J. Atmos. Sci.,} \textit{68}, 61--74.
\bibitem{}
Kuang, Z., and C. S. Bretherton (2006),
A mass--flux scheme view of a high--resolution
simulation of a transition from shallow to deep cumulus convection.
{\it J. Atmos. Sci.,} \textit{63}, 3421--3436.
\bibitem{}
Kuo, H. L. (1974),
Further studies of the parameterization of the influence of cumulus clouds on the large-scale flow.
{\it J. Atmos. Sci.,} \textit{31}, 1232-�1240.
\bibitem{}
Lander, J. L., and B. J. Hoskins (1997),
Believable scales and parameterizations in a spectral transform model.
{\it Mon. Wea. Rev.,} \textit{125}, 292--303.
\bibitem{}
Landau, L. D., and Lifshitz, E. M. (1980),
{\it Statistical Physics Part 1},
3rd Ed.,
Course of Theoretical Physics Volume 5,
Elsevier.
%,544pp.
\bibitem{}
Leith, C. E. (1980),
Nonlinear normal mode initialization and quasi--geostrophic theory.
{\it J. Atmos. Sci.,} \textit{37}, 958--968.
\bibitem{}
Levine, J. (1959),
Spherical vortex theory of bubble--like motion in cumulus clouds.
{\it J. Meteor.,} \textit{16}, 653--662.
\bibitem{}
Lighthill, M. J. (1952),
On sound generated aerodynamically. I. General theory.
{\it Proc. Roy. Soc. Lond.,} \textit{A211}, 564--587.
\bibitem{}
Lighthill, M. J. (1954),
On sound generated aerodynamically. II. Turbulence as a source of sound.
{\it Proc. Roy. Soc. Lond.,} \textit{A222}, 1--32.
\bibitem{}
Lintner, B. R., C. E. Holloway, and J. D. Neelin (2011),
Column water vapor statistics and their relationship to deep convection, vertical
and horizontal circulation, and the moisture structure of Nauru.
{\it J. Climate,} \textit{24}, 5454--5466.
\bibitem{}
Liu, P., M. Satoh, B. Wang, H. Fudeyasu, T. Nasuno, T. Li, H. Miura, H. Taniguchi, H. Masunaga, X. Fu and H, Annamalai (2009),
An MJO simulated by the NICAM at 14- and 7-km resolutions.
{\it Mon. Wea. Rev.,} \textit{137}, 3254--3268.
\bibitem{}
Lord, S. J. (1982), Interaction of a cumulus cloud ensemble with the
large-scale environment. Part III: Semi-prognostic test of the
Arakawa-Schubert cumulus parameterization.
{\it J. Atmos. Sci.,} \textit{39}, 88--103.
\bibitem{}
Lord, S. J., and A. Arakawa (1980),
Interaction of a cumulus cloud ensemble with the large-scale environment,
Part II.
{\it J. Atmos. Sci.,} \textit{37}, 2677--2692.
\bibitem{}
Lord, S. J., W. C. Chao and A. Arakawa (1982),
Interaction of a cumulus cloud ensemble with the large-scale environment,
Part IV.
{\it J. Atmos. Sci.,} \textit{39}, 104--113.
\bibitem{}
Lorenz, E. N. (1986),
On the existence of a slow manifold.
{\it J. Atmos. Sci.,} \textit{43}, 1547--1557.
\bibitem{}
Lorenz, E. N. (1992),
The slow manifold --- What is it?
{\it J. Atmos. Sci.,} \textit{49}, 2449--2451.
\bibitem{}
Lovejoy, S. (1982),
Area--perimeter relation for rain and cloud areas.
{\it Science}, {\it 216}, 185--187.
\bibitem{}
Lovejoy, S., and D. Schertzer (2010),
Towards a new synthesis for atmospheric dynamics: Space--time cascades.
\textit{Atmos. Res.,}\textit{96}, 1--52.
\bibitem{}
Lovelock, J. E., and L. Margulis (1974),
Atmospheric homeostasis by and for biosphere - Gaia hypothesis.
\textit{Tellus,} \textit{26}, 2--10.
\bibitem{}
Ludlam, F. H., and R. S. Scorer (1953),
Convection in the atmosphere.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{79}, 317--341.
\bibitem{}
Majda, A. J. and B. Khouider (2002),
Stochastic and mesoscopic models for tropical convection.
\textit{Proc. Nat. Acad. Sci.,}\textit{99}, 1123--1128.
\bibitem{}
Manabe, S., and R. F. Strickler (1964),
Thermal equilibrium of the atmosphere with a convective adjustment.
{\it J. Atmos. Sci.,} \textit{21}, 361--385.
\bibitem{}
Manabe, S., J. S. Smagorinsky, and R. F. Strickler (1965),
Simulated climatology of a general circulation model with a hydrological cycle.
{\it Mon. Wea. Rev.,} \textit{93}, 769--798.
\bibitem{}
Mapes, B. E. (1997), Equilibrium vs. activation controls on
large--scale variations of tropical deep convection.
In: {\it the Physics and Parameterization of Moist Atmospheric Convection},
(R. K. Smith, Ed.), %%% 498pp.
NATO ASI, Kloster Seeon, Kluwer Academic Publishers, Dordrecht,
321--358.
\bibitem{}
Mapes, B. E. (1998),
The large--scale part of tropical mesoscale convective system circulations:
A linear vertical spectrum band model.
{\it J. Met. Soc. Japan} \textit{76}, 29--55.
\bibitem{}
Mapes, B. E. (2000),
Convective inhibition, subgrid-scale triggering energy, and stratiform
instability in a toy tropical wave model.
{\it J. Atmos. Sci.,} \textit{57}, 1515--1535
\bibitem{}
McKane, A. J., and T. J. Newman (2005),
Predator-prey cycles from resonant amplification of demographic stochasticity.
{\it Phys. Rev. Lett.,} \textit{94}, 218102.
\bibitem{}
McIntyre, M. (2001),
Balance, potential-vorticity inversion, Lighthill radiation and the slow quasimanifold.
In: Proceedings of the IUTAM/IUGG/Royal Irish Academy Symposium on Advances in Mathematical Modelling of Atmosphere and Ocean Dynamics, Limerick, Ireland, (P. F. Hodnett, Ed.), 45--68. Kluwer Academic Publishers.
\bibitem{}
M{\"o}ller, F., and S. Manabe (1961),
{\"U}ber das Strahlungsgleichgewicht in der Atmosph{\"a}re.
{\it Z. Meteor.,} \textit{15}, 3--8.
\bibitem{}
Moncrieff, M. W. (1981),
A theory of organized steady convection and its transport properties.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{107}, 29--50.
\bibitem{}
Moncrieff, M. W. (1992),
Organized convective systems: Archetypal dynamical models, mass and momentum
flux theory, and parametrization.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{118}, 819--850.
\bibitem{}
Moorthi, S., and M. J. Suarez (1992), Relaxed Arakawa-Schubert. A
parameterization of moist convection for general circulation models.
{\it Mon. Wea. Rev.,} \textit{120}, 978--1002.
\bibitem{}
Neelin, J. D. (1997),
Implications of convective quasi--equilibrium for the large--scale flow.
In: {\it the Physics and Parameterization of Moist Atmospheric Convection},
(R. K. Smith, Ed.), %%% 498pp.
NATO ASI, Kloster Seeon, Kluwer Academic Publishers, Dordrecht,
413--446.
\bibitem{}
Neelin, J. D., and I. M. Held (1987),
Modeling tropical convergence based on the moist static energy budget.
{\it Mon. Wea. Rev.,} \textit{115} 3--12
\bibitem{}
Neelin, J. D., and J.-Y. Yu (1994), Modes of tropical variability
under convective adjustment and the Madden--Julian
oscillation. Part I: Analytical theory.
{\it J. Atmos. Sci.,} \textit{51}, 1876--1894.
\bibitem{}
Neelin, J. D., and N. Zeng (2000), The first quasi-equilibrium tropical
circulation model--formulation.
{\it J. Atmos. Sci} \textit{57}, 1741--1766.
\bibitem{}
Neelin, J. D., O. Peters, J. W.--B. Lin, K. Hales,
and C. E. Holloway (2008),
Rethinking convective quasi--equilibrium:
Observational constraints for stochastic convective schemes
in climate models.
{\it Phil. Trans. Roy. Soc.,} \textit{A366}, 2581--2604.
\bibitem{}
Neelin, J. D., O. Peters, and K. Hales (2009),
The transition to strong convection.
{\it J. Atmos. Sci.,} \textit{66}, 2367--2384.
\bibitem{}
Ooyama, K. V. (1982),
Conceptual evolution of the theory and modeling of the tropical cyclone,
{\it J. Met. Soc. Japan} \textit{60}, 369--380.
\bibitem{}
Pan, D.-M., and D. A. Randall (1998),
A cumulus parameterization with prognostic closure,
{\it Quart. J. Roy. Meteor. Soc.,} \textit{124}, 949--981.
\bibitem{}
Parodi, A., and K. Emanuel (2009),
A theory for buoyancy and velocity scales in deep moist convection.
{\it J. Atmos. Sci.,} \textit{66}, 3449--3463.
\bibitem{}
Peters, O., and D. Neelin (2006), Critical phenomena in atmospheric
precipitation. {\it Nature Phys.,} \textit{2}, 393--396.
%doi:10.1038/Nphys314
\bibitem{}
Peters, O., C. Hertlein, and K. Christensen (2002), A complexity view
of rainfall.
{\it Phys. Rev. Lett.,} \textit{88}, 018701, doi:10.1103/PhysRevLett.88.018701
\bibitem{}
Peters, O., J. D. Neelin, and S. W. Nesbitt (2009),
Mesoscale convective systems and critical clusters.
{\it J. Atmos. Sci.,} \textit{66}, 2913--2924.
\bibitem{}
Peters, O., A. Deluca, A. Corral, J. D. Neelin, and C E Holloway (2010),
Universality of rain event size distributions.
{\it J. Stat. Mech. Theor. Exp.,} \textit{P11030}. doi:10.1088/1742-5468/2010/11/P11030
\bibitem{}
Planck, M. (1922),
{\it Treatise on Thermodynamics.} 7th edition. Translation by Ogg, A. (1926),
3rd edition translated from the seventh German edition. Dover Publications,
New York.
\bibitem{}
Plant, R. S. and G. C. Craig (2008),
A stochastic parameterization for deep convection based on equilibrium statistics.
{\it J. Atmos. Sci.,} \textit{65}, 87--105.
\bibitem{}
Plant, R. S. (2009),
Statistical properties of cloud lifecycles in cloud-resolving models.
{\it Atmos. Chem. Phys.,} \textit{9}, 2195--2205.
\bibitem{}
Plant, R. S. (2010),
A review of the theoretical basis for bulk mass flux convective parameterization.
{\it Atmos. Chem. Phys.,} \textit{10}, 3529--3544.
\bibitem{}
Plant R. S. (2012),
A new modelling framework for statistical cumulus dynamics.
{\it Phil. Trans. Roy. Soc.,} \textit{A370}, 1041--1060.
\bibitem{}
Plant, R. S., and J.-I. Yano (2011),
Comment on ``An ensemble cumulus convection parameterisation with
explicit cloud treatment'' by T. M. Wagner and H.-F. Graf.
{\it J. Atmos. Sci.,} \textit{68}, 1541--1544.
\bibitem{}
Posselt, D. J., S. van den Heever, G. Stephens, and M. R. Igel, (2012),
Changes in the interaction between tropical convection, radiation, and the large-scale circulation in a warming environment.
\textit{J. Climate,} \textit{25}, 557--571.
\bibitem{}
Randall, D. A., and D.-M. Pan (1993),
Implementation of the Arakawa-Schubert cumulus parameterization with a
prognostic closure. In: {\it The Representation of Cumulus
Convection in Numerical Models},
(Emanuel, K. A., and D. J. Raymond, Eds.),
Meteorological Monographs No. 46, Amer. Meteor. Soc.,
137--144.
\bibitem{}
Randall, D. A., D.--M. Pan, P. Ding, and D. G. Gripe (1997),
Quasi-equilibrium.
In: {\it the Physics and Parameterization of Moist Atmospheric Convection},
(R. K. Smith, Ed.), %%% 498pp.
NATO ASI, Kloster Seeon, Kluwer Academic Publishers, Dordrecht,
359--385.
\bibitem{}
Raymond, D. J. (1995), Regulation of moist convection over the warm
tropical oceans. {\it J. Atmos. Sci.,} \textit{52}, 3945--3959.
\bibitem{}
Raymond, D. J., and M. J. Herman (2011),
Convective quasi-equilibrium reconsidered.
{\it J. Adv. Model. Earth Syst.,} \textit{3}, Art. 2011MS000079, 14 pp, doi:10.1029/2011MS000079.
\bibitem{}
Raymond, D. J., S. L. Sessions, and Z. Fuchs (2007),
A theory for the spinup of tropical depressions.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{133}, 1743--1754.
\bibitem{}
Raymond, D. J., S. Sessions, A. Sobel and Z. Fuchs (2009), The
mechanics of gross moist stability. {\it J. Adv. Model. Earth Syst.,}
\textit{1}, Art. \#9, 20 pp., doi:10.3894/JAMES.2009.1.9
\bibitem{}
Ring, D. (2009),
Non--linear wave interactions in rotating stratified fluid flows.
PhD Dissertation, John Hopkins University.
\bibitem{}
Roff, G. L., and J.-I. Yano (2002),
Tropical convective variability in the CAPE phase space.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{128}, 2317--2333.
\bibitem{}
Rogers, R.F., and J. M. Fritsch (1996),
A general framework for convective triggering functions.
{\it Mon. Wea. Rev.,}\textit{124}, 2438--2452.
\bibitem{}
Romps, D. M., and Z. Kuang (2010),
Do undiluted convective plumes exist in the upper tropical troposphere?
{\it J. Atmos. Sci.,} \textit{67}, 468--484.
\bibitem{}
Romps, D. M., and Z. Kuang (2011),
A transilient matrix for moist convection.
{\it J. Atmos. Sci.,} \textit{68}, 2009--2025.
\bibitem{}
Rossby, G.-G. (1938),
On the mutual adjustment of pressure and velocity distribution in certain simple current systems. II. {\it J. Mar. Res.,} \textit{1}, 239--263.
\bibitem{}
Sahany, S., J. D. Neelin, K. Hales, and R. Neale (2012),
Temperature--moisture dependence of the deep convective transition as a
constraint on entrainment in climate models.
{\it J. Atmos. Sci.,} \textit{69}, 1340--1358.
\bibitem{}
Salmon, R. (1998),
{\it Lectures on Geophysical Fluid Dynamics}.
Oxford University Press.
%, 383pp.
\bibitem{}
Scorer, R. S., and F. H. Ludlam (1953),
Bubble theory of penetrative convection.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{79}, 94--103.
\bibitem{}
Schubert, W. H. (2000),
A retrospective view of Arakawa's ideas on cumulus parameterization.
In: {\it General Circulation Model Development}
(D. Randall, Ed.), Elsevier, Ch.~6, 181--198.
\bibitem{}
Sessions, S. L., Sugaya, S., Raymond, D. J., and Sobel, A. H. (2010),
Multiple equilibria in a cloud-resolving model using the weak temperature
gradient approximation.
{\it J. Geophys. Res.,} \textit{115}(D12110),
doi.10.1029/2009JD013376.
\bibitem{}
Shutts, G. J. and Gray, M. E. B. (1999),
Numerical simulations of convective equilibrium under prescribed forcing.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{125} 2767--2787.
\bibitem{}
Shutts, G. J. and Palmer, T. N. (2007),
Convective forcing fluctuations in a cloud-resolving model: Relevance to the
stochastic parameterization problem.
{\it J. Climate,} \textit{20}, 187--202.
\bibitem{}
Sobel, A. H., J. Nilsson, and L. M. Polvani (2001), The weak temperature
gradient approximation and balanced tropical moisture
waves. {\it J. Atmos. Sci.,} \textit{58}, 3650--3665.
\bibitem{}
Sol{\'e}, R. V., and J. Bascompte (2006),
{\it Self--Organization in Complex Ecosystems}.
Princeton University Press.
%, 371pp.
\bibitem{}
Stanley, H. E. (1972), {\it Introduction to Phase Transition and
Critical Phenomena}. Oxford University Press.
\bibitem{}
Stephens, G. L., S. van den Heever, and L. Pakula (2008),
Radiative--convective feedbacks in idealized states of
radiative--convective equilibrium.
{\it J. Atmos. Sci.,} \textit{65}, 3899--3916.
\bibitem{}
Sud, Y. C., W. C. Chao, and G. K. Walker, (1991),
Contribution to the implementation of the Arakawa--Schubert cumulus
parameterization in the GLA GCM.
{\it J. Atmos. Sci.},\textit{48}, 1573--1586.
\bibitem{}
Sui, C. H., K. M. Lau, W. K. Tao, and J. Simpson (1994),
The tropical water and energy cycles in a cumulus ensemble model. Part I: Equilibrium climate.
{\it J. Atmos. Sci.,} \textit{51}, 711--728.
\bibitem{}
Tuck, A.
{\it Atmospheric turbulence: A molecular dynamics perspective},
Oxford University Press.
\bibitem{}
van Kampen, N. G. (1985),
Elimination of fast variables.
{\it Phys. Rep.,} \textit{124}, 71--160.
\bibitem{}
van Kampen, N. G. (2007),
{\it Stochastic Processes in Physics and Chemistry}, 3rd Ed.,
Elsevier.
%, 463pp.
\bibitem{}
Wagner, T. M. (2010),
A dynamical convective cloud field model and the effects of aerosols.
PhD thesis, University of Cambridge.
\bibitem{}
Wilson, G. K. (1983),
The renormalization group and critical phenomena.
{\it Rev. Mod. Phys.,} \textit{55}, 583--600.
\bibitem{}
Xu, K.-M., A. Arakawa, and S. K. Krueger (1992),
The macroscopic behavior of cumulus ensembles simulated by a cumulus ensemble
model.
{\it J. Atmos. Sci.,} \textit{49}, 2402--2420.
\bibitem{}
Xu, K.-M., and K. A. Emanuel (1989),
Is the tropical atmosphere conditionally unstable?
{\it Mon. Wea. Rev.,} \textit{117}, 1471--1479.
\bibitem{}
Yanai, M. S., S. Esbensen and J. H. Chu (1973),
Determination of bulk properties of tropical cloud clusters from large--scale heat and
moisture budgets.
{\it J. Atmos. Sci.,} \textit{30}, 611--627.
\bibitem{}
Yano, J.-I. (1999), Scale--separation and quasi--equilibrium principles
in Arakawa and Schubert's cumulus parameterization.
{\it J. Atmos. Sci.,} \textit{56}, 3821--3823.
\bibitem{}
Yano, J.-I. (2001),
Residual cumulus parameterization.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{127}, 1261--1276.
\bibitem{}
Yano, J.-I. (2003),
The cumulus parameterization problem in the context of MJO simulations.
In: Proceedings for the MJO workshop, ECMWF, 2--5 November 2003,
115--127.
http://www.ecmwf.int/publications/library/do/references/list/17124
\bibitem{}
Yano, J.--I. (2011),
Interactive comment on ``Simulating deep
convection with a shallow convection scheme'' by
C. Hohenegger and C. S. Bretherton.
{Atmos. Chem. Phys. Discuss.,}{11}, C2411--C2425.
%{Atmos. Chem. Phys.,}{11}, 10389--10406.
\bibitem{}
Yano, J. I., and Y. Takeuchi (1987),
The self-similarity of horizontal cloud pattern in the intertropical
convergence zone,
{\it J. Met. Soc. Japan} \textit{65}, 661-667.
\bibitem{}
Yano, J.-I., M. W. Moncrieff, and J. C. McWilliams (1998),
Linear stability
and single--column analyses of several cumulus parameterization
categories in a shallow--water model.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{124} 983--1005.
\bibitem{}
Yano, J.-I., W. W. Grabowski, G. L. Roff, and B. E. Mapes (2000),
Asymptotic approaches to convective quasi--equilibrium.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{126}, 1861--1887.
\bibitem{}
Yano, J.-I., K. Fraedrich, and R. Blender (2001),
Tropical convective variability as $1/f$--noise.
{\it J. Climate,} \textit{14}, 3608--3616.
\bibitem{}
Yano, J.-I., R. Blender, C. Zhang, and K. Fraedrich (2004),
$1/f$ noise and pulse--like events in the tropical atmospheric surface
variabilities. {\it Quart. J. Roy. Meteor. Soc.,} \textit{300},
1697--1721.
\bibitem{}
Yano, J.-I., and M. Bonazzola (2009),
Scale analysis for the large-scale tropical atmospheric dynamics.
{\it J. Atmos. Sci.,} \textit{66}, 159--172.
\bibitem{}
Yano, J.-I., J.--P. Chaboureau, and F. Guichard (2005),
A generalization of CAPE into potential--energy convertibility.
{\it Quart. J. Roy. Meteor. Soc.,} \textit{131}, 861--875.
\bibitem{}
Yano, J.-I., S. Mulet, and M. Bonazzola (2009),
Tropical large--scale circulations: Asymptotically nondivergent?
\textit{Tellus,} \textit{61A}, 417--427.
\bibitem{}
Yano, J.-I., and R. S. Plant (2012a),
Finite departure from convective quasi-equilibrium: Periodic cycle and discharge-recharge mechanism.
\textit{Quart. J. Roy. Meteor. Soc.,} \textit{128}, 626--637.
\bibitem{}
Yano, J.-I., and R. S. Plant (2012b),
Interactions between shallow and deep convection
under a finite departure from convective quasi--equilibrium.
\textit{J. Atmos. Sci.}, accepted.
\bibitem{}
Yano, J.--I., H.-F. Graf, and F. Spineanu (2012a), Meeting report:
Theoretical and operational implications of atmospheric convective
organization.
\textit{Bull. Amer. Meteor. Soc.,}, \textit{93}, ES39-ES41,
doi: http://dx.doi.org/10.1175/BAMS-D-11-00178.1
\bibitem{}
Yano, J.--I., C. Liu, and M. W. Moncrieff (2012b),
Atmospheric convective organization: homeostasis or criticality?
accepted to \textit{J. Atmos. Sci.,}.
\bibitem{}
Yeomans, J. (1992), {\it Statistical Mechanics of Phase Transitions},
Oxford University Press.
\bibitem{}
Yu, J-Y., and J. D. Neelin (1994), Modes of tropical variability under
convective adjustment and the Madden--Julian oscillation. Part II:
Numerical results. \textit{ J. Atmos. Sci.,} \textit{51}, 1895--1914.
\bibitem{}
Zagar, N., J. Tribbia, J. L. Anderson, and K. Raeder (2009),
Uncertainties of estimates of inertia--gravity energy in the
atmosphere. Part I: Intercomparison of four analysis systems. \textit{Mon. Wea. Rev.,} \textit{137}, 3837--3857.
\bibitem{}
Zhang, G. (2002), Convective quasi--equilibrium in midlatitude
continental environment and its effect on convective
parameterization. \textit{J. Geophys. Res.,} \textit{107}(D14), doi:10.1029/2001JD001005.
\bibitem{}
Zhang, G. (2003), Convective
quasi--equilibrium in the tropical western Pacific. Comparison
with midlatitude continental environment. \textit{ J. Geophys. Res.,}
\textit{108} (D19), doc.10.1029/2003/JD003520.
\bibitem{}
Zhang, G. J. (2009),
Effects of entrainment on convective available potential energy and
closure assumptions in convection parameterization.
\textit{J. Geophys. Res.,}
\textit{114}, D07109, doc.10.1029/2008/JD010976.
\bibitem{}
Zhang, G. J., and N. A. McFarlane (1995),
Sensitivity of climate simulations to the parameterization of cumulus
convection in the Canadian Climate Centre General Circulation Model.
\textit{Atmos.--Ocean,} \textit{33}, 407--446.
\bibitem{}
Zimmer, M., Craig, G. C., Wernli, H. and Keil, C. (2011),
Classification of precipitation events with a convective response
timescale.
\textit{Geophys. Res. Lett.,} \textit{38}, L05802, doi:10.1029/2010GL046199. University Staff: Request a correction | Centaur Editors: Update this record |
University of Reading
CentAUR: Central Archive at the University of Reading
Accessibility navigation
Convective quasi–equilibrium
Yano, J.-I. and Plant, R. S. Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1029/2011RG000378 Abstract/SummaryThe concept of convective quasi–equilibrium (CQE) is a key ingredient in order to understand the role of deep moist convection in the atmosphere. It has been used as a guiding principle to develop almost all convective parameterizations and provides a basic theoretical framework for large–scale tropical dynamics. The CQE concept as originally proposed by Arakawa and Schubert [1974] is systematically reviewed from wider perspectives. Various interpretations and extensions of Arakawa and Schubert’s CQE are considered in terms of both a thermodynamic analogy and as a dynamical balance. The thermodynamic interpretations can be more emphatically embraced as a homeostasis. The dynamic balance interpretations can be best understood by analogy with the slow manifold. Various criticisms of CQE can be avoided by taking the dynamic balance interpretation. Possible limits of CQE are also discussed, including the importance of triggering in many convective situations, as well as the possible self–organized criticality of tropical convection. However, the most intriguing aspect of the CQE concept is that, in spite of many observational tests supporting and interpreting it in many different senses, it has 1never been established in a robust manner based on a systematic analysis of the cloud–work function budget by observations as was originally defined.
Altmetric Related URLs Deposit Details References University Staff: Request a correction | Centaur Editors: Update this record |
Lists
Lists
