Why does Arakawa and Schubert's convective quasi-equilibrium closure not work? Mathematical analysis and implications

Downloads

Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large564 scale environment, Part I. J. Atmos. Sci., 31, 674–701. 565 Bechtold, P., N. Semane, P. Lopez, J.-P. Chaboureau, A. Beljaars, N. Bormann, 2014: Repre566 senting equilibrium and non-equilibrium convection in large-scale models. J. Atmos. Sci., 71, 567 734–753. 568 Deardorff, J. W., 1980: Cloud top entrainment instability. J. Atmos. Sci., 37, 131–147. 569 de Rooy, Wim C., Bechtold, P., Frohlich, K., Hohenegger, C., Jonker H., Mironov, D., Pier 570 Siebesma, A., Teixeira, J., and Yano, J.-I., 2013: Entrainment and detrainment in cumulus convec571 tion: an overview. Quart. J. Roy. Meteor. Soc., 139, 1–19, DOI: 10.1002/qj.1959. 572 Donner, L. J. and V. T. Phillips, 2003: Boundary layer control on convective available po573 tential energy: implications for cumulus parameterization, J. Geophys. Res., 108, 4701, 574 doi:10.1029/2003JD003773. 575 Fraedrich, K., and J. L. McBride, 1989: The physical mechanism of CISK and the free-ride bal576 ance. J. Atmos. Sci., 46, 2642–2648. 577 Fulton, S. R., and W. H. Schubert, 1985: Vertical normal mode transforms: Theory and applica578 tion. Mon. Wea. Rev., 113, 647–658. 579 Hack, J. J., W. H. Schubert, and P. L. Silva Dias, 1984: A spectral cumulus parameterization for 580 use in numerical models of tropical atmosphere. Mon. Wea. Rev., 112, 704–716. 581 Houze, R. A., Jr., and A. K. Betts, 1981: Convection in GATE, Rev. Geophys. Space Phys., 19, 582 541–576. 583 Jordan, C. L., 1958: Mean sounding for the West Indies area. J. Meteor., 15, 91–97. 28 584 Kasahara, A., and K. Puri, 1981: Spectral representation of three–dimensional global data by 585 expansion in normal mode functions. Mon. Wea. Rev., 109, 37–51. 586 Lord, S. J., 1982: Interaction of a cumulus cloud ensemble with the large-scale environment. Part 587 III: Semi-prognostic test of the Arakawa-Schubert cumulus parameterization. J. Atmos. Sci., 39, 588 88–103. 589 Lord, S. J., and A. Arakawa, 1980: Interaction of a cumulus cloud ensemble with the large-scale 590 environment, Part II. J. Atmos. Sci., 37, 2677–2692. 591 Lord, S. J., W. C. Chao and A. Arakawa, 1982: Interaction of a cumulus cloud ensemble with the 592 large-scale environment, Part IV. J. Atmos. Sci., 39, 104–113. 593 Mapes, B. E.: 1997: Equilibrium vs. activation controls on large–scale variations of tropical deep 594 convection, in: The Physics and Parameterization of Moist Atmospheric Convection, R. K. Smith 595 (Ed.), NATO ASI, Kloster Seeon, Kluwer Academic Publishers, Dordrecht, 321–358. 596 Moorthi, S., and M. J. Suarez, 1992: Relaxed Arakawa-Schubert. A parameterization of moist 597 convection for general circulation models. Mon. Wea. Rev., 120, 978–1002. 598 Pan, D.-M., and D. A. Randall, 1998: A cumulus parameterization with prognostic closure, Quart. 599 J. Roy. Meteor. Soc., 124, 949–981. 600 Plant, R. S., and J.-I. Yano (Eds), 2015: Parameterization of Atmospheric Convec601 tion, Volumes I and II, World Scientific, Singapore, Imperial College Press, London 602 http://www.worldscientific.com/worldscibooks/10.1142/p1005 603 Randall, D. A., 1980: Conditional instability of the first kind upside down. J. Atmos. Sci., 37, 604 125–130. 29 605 Sobel, A. H., J. Nilsson, and L. M. Polvani, 2001: The weak temperature gradient approximation 606 and balanced tropical moisture waves. J. Atmos. Sci., 58, 3650–3665. 607 Yano, J.-I., 2001: Residual cumulus parameterization. Quart. J. Roy. Meteor. Soc., 127, 1261– 608 1276. 609 Yano, J.-I., 2014a: Basic Convective Element: Bubble or Plume?: A Historical Review. Atmos. 610 Phys. Chem., 14, 7019–7030, doi:10.5194/acp-14-7019-2014 611 Yano, J.-I., 2014b: Fromulation structure of mass-flux convection parameterization. Dyn. Atmos. 612 Ocean, 67, 1–28. http://dx.doi.org/10.1016/j.dynatmoce.2014.04.002 613 Yano, J.-I., 2015: Thermodynamic effects of convection under the mass–flux formulation, in: 614 Parameterization of Atmospheric Convection, Volume I (R. S. Plant and J. I. Yano, Eds.), World 615 Scientific, Imperial College Press, 227–248. 616 Yano, J. I., 2016: Subgrid–Scale Physical Parameterization in Atmospheric Modelling: How 617 Can We Make it Consistent? J. Phys. A: Math. Theor., 49, 284001 doi:10.1088/1751- 618 8113/49/28/284001. 619 Yano, J.-I., and R. S. Plant, 2012a: Convective quasi–equilibrium. Rev. Geophys., 50, RG4004, 620 doi:10.1029/2011RG000378. 621 Yano, J.-I., and R. S. Plant, 2012b: Interactions between shallow and deep convection under a 622 finite departure from convective quasi–equilibrium. J. Atmos. Sci., 69, 3463–3470. 623 Yano, J.-I., and R. S. Plant, 2012c: Finite Departure from Convective Quasi-Equilibrium: Periodic 624 Cycle and Discharge-Recharge Mechanism. Quart. J. Roy. Meteor. Soc., 138, 626–637. 625 Yano, J.-I., and R. S. Plant, 2016: Generalized Convective Quasi-Equilibrium Principle. Dyn. 626 Atmos. Ocean., 73, 10–33. 30 627 Yano, J.-I., J.–P. Chaboureau, and F. Guichard, 2005a: A generalization of CAPE into potential– 628 energy convertibility. Quart. J. Roy. Meteor. Soc., 131, 861–875. 629 Yano, J.-I., J.-L. Redelsperger, F. Guichard, and P. Bechtold, 2005b: Mode decomposition as a 630 methodology for developing convective-scale representations in global models. Quart. J. Roy. 631 Meteor. Soc., 131, 2313–2336. 632 Yano J.-I., M. Bister, Z. Fuchs, L. Gerard, V. Phillips, S. Barkidija, and J. M. Piriou, 2013: Phe633 nomenology of convection-parameterization closure, Atmos. Phys. Chem., 13, 4111–4131. 634 Zhang, G. J., 2002: Convective quasi-equilibrium in midlatitude continental environment and its 635 effect on convective parameterization, J. Geophys. Res., 107, 4220, doi:10.1029/2001JD001005. 636 Zhang, G. J., 2003: The concept of convective quasi–equilibrium in the tropical western Pa637 cific: Comparison with midlatitude continental environment. J. Geophys. Res., 108, 4592, 638 doi:10.1029/2003JD003520.