Abstract
We review bulk representations of tropical and subtropical maritime atmospheric boundary layers. Three types of bulk representations are studied in detail: stratocumulus topped mixed layers, trade-wind layers, and sub-cloud mixed layers. Through the development of a consistent description of these disparate regimes, connections among their varied representations are emphasized, as well as their relation to regions of deeper convection. New results relating to the equilibrium mass flux and cloud fraction in the trade winds; the ability of bulk models to represent qualitatively major cloud regimes; and the relationship amongst different bulk representations of the surface layer are presented. Throughout we emphasize the identification of consistent and physically based mixing and cloud regime rules for use in intermediate complexity models of the tropical climate, which in turn can be used to study cloud and dynamical interactions on larger scales.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ahlgrimm M., Randall D.A. (2006): Diagnosing monthly mean boundary layer properties from re-analysis data using a bulk boundary layer model. J. Atmos. Sci. 63, 998–1012
Albrecht B.A., Betts A.K., Schubert W.H., Cox S.K. (1979): A model of the thermodynamic structure of the trade-wind boundary layer. Part I: Theoretical formulation and sensitivity tests. J. Atmos. Sci. 36, 90–98
Arakawa A., Schubert W.S. (1974): Interaction of a cumulus cloud ensemble with the large-scale environment. Part I. J. Atmos. Sci. 31, 674–701
Bellon G., Stevens B. (2005): On bulk models of shallow cumulus convection. J. Atmos. Sci. 62, 3286–3302
Betts A.K. (2976): Modeling subcloud layer structure and interaction with a shallow cumulus layer. J. Atmos. Sci. 33, 2363–2382
Betts A.K., Albrecht B.A. (1987): Conserved variable analysis of boundarylayer thermodynamic structure over the tropical oceans. J. Atmos. Sci. 44, 83–99
Betts A.K., Ridgway W. (1989): Climatic equilibrium of the atmospheric convective boundary layer over a tropical ocean. J. Atmos. Sci. 46, 2621–2641
Bretherton C.S. (1993): Understanding Albrecht’s model of trade cumulus cloud fields. J. Atmos. Sci. 50, 2264–2283
Bretherton C.S., Wyant M.C. (1997): Moisture transport, lower tropospheric stability, and decoupling of cloud-topped boundary layers. J. Atmos. Sci. 54, 148–167
Cuijpers J., Duynkerke P.G. (1993): Large-eddy simulation of trade-wind cumulus clouds. J. Atmos. Sci. 50, 3894–3908
Deardorff J.W. (1970): Convective velocity and temperaure scales for the unstable planetary boundary layer and for Rayleigh convection. J. Atmos. Sci. 27, 1211–1213
Deardorff J.W. (1972): Parameterization of the planetary boundary layer for use in general circulation models. Mon. Wea. Rev. 100, 93–106
Deardorff J.W. (1980): Cloud top entrainment instability. J. Atmos. Sci. 37, 131–147
Emanuel K.A. (1993): The effect of convective response timeon WISHE modes. J. Atmos. Sci. 50, 1763–1765
Fairall C.W., Bradley E.F., Hare J.E., Grachev A., Edson J. (2003): Bulk parameterization of air-sea fluxes: Updates and verification for the COARE algorithm. J. Climate 16, 571–591
Klein S.A., Hartmann D.L. (1993): The seasonal cycle of low stratiform clouds. J. Climate 6, 1587–1606
Kraus E.B. (1963): The diurnal precipitation change over the sea. J. Atmos. Sci. 20, 551–556
Lewellen D.C., Lewellen W. (1998): Large-eddy boundary layer entrainment. J. Atmos. Sci. 55, 2645–2665
Lilly D.K. (1968): Models of cloud topped mixed layers under a strong inversion. Q. J. R. Meteor. Soc. 94, 292–309
Lindzen R.S., Nigam S. (1987): On the role of sea surface temperature gradients in forcing low-level winds and convergence in the tropics. J. Atmos. Sci. 44, 2440–2458
Lock A. (2000): The numerical representation of entrainment in parameterizations of boundary layer turbulent mixing. Mon. Wea. Rev. 129, 1148–1163
Lock A.P. (1998): The parameterization of entrainment in cloudy boundary layers. Q. J. R. Meteor. Soc. 124, 2729–2753
Lock A.P., MacVean M.K. (1999): A parametrization of entrainment driven by surface heating and cloud-top cooling. Q. J. R. Meteor. Soc. 125, 271–299
McGauley M., Zhang C., Bond N.A. (2004): Large-scale characteristics of the atmospheric boundary layer in the eastern Pacific cold tongue ITCZ region. J. Climate 17, 3907–3920
Miller R.L. (1997): Tropical thermostats and low cloud cover. J. Climate 10, 409–440
Moeng C.H. (2000): Entrainment rate, cloud fraction and liquid water path of PBL stratocumulus clouds. J. Atmos. Sci. 57, 3627–3643
Moeng C.H., Sullivan P.P., Stevens B. (1999): Including radiative effects in an entrainment-rate formula for buoyancy driven PBLs. J. Atmos. Sci. 56, 1031–1049
Neggers R.A., Siebesma A.P., Lenderink G. (2004): An evaluation of mass flux closures for diurnal cycles of shallow cumulus. Mon. Wea. Rev. 132, 2525–2538
Neggers, R.A., Stevens, B., Neelin, J.D.: A simple equilibrium model for shallow cumulus topped mixed layers. Theor. Comput. Fluid Dynam. (2006) (in press)
Nicholls S., LeMone M.A. (1980): The fair weather boundary layer in GATE: the relationship of subcloud fluxes and structure to the distribution and enhancement of cumulus cloud. J. Atmos. Sci. 37, 2051–2067
Park S., Leovy C.B., Rozendaal M.A. (2004): A new heuristic lagrangian marine boundary layer cloud model. J. Atmos. Sci. 61, 3002–3024
Randall D.A. (1980): Conditional instability of the first kind upside-down. J. Atmos. Sci. 37, 125–130
Randall D.A., Suarez M.J. (1984): On the dynamics of stratocumulus formation and dissipation. J. Atmos. Sci. 41, 3052–3057
Raymond D.J. (1995): Regulation of moist convection over the west Pacific warm pool. J. Atmos. Sci. 52, 3945–3959
Riehl H., Yeh C., Malkus J.S., LaSeur N.E. (1951): The North-East Trade of the Pacific Ocean. Q. J. R. Meteor. Soc. 77, 598–626
Schlichting H. (1979): Boundary Layer Theory, 7th edn. McGraw–Hill, New York
Schubert W.H., Wakefield J.S., Steiner E.J., Cox S.K. (1979): Marine tratocumulus convection. Part I: Governing equations and horizontally homogeneous solutions. J. Atmos. Sci. 36, 1286–1307
Schubert W.H., Wakefield J.S., Steiner E.J., Cox S.K. (1979): Marine stratocumulus convection. Part II: Horizontally inhomogeneous solutions. J. Atmos. Sci. 36, 1308–1324
Siebesma, A.P.: Shallow convection. In: Plate, E.J., Fedorovich, E.E., Viegas, D.X., Wyngaard, J.C. (eds.) Buoyant Convection in Geophysical Flows, C, vol. 513, pp. 441–486. Kluwer, Dordrecht (1998)
Siebesma A.P., Brown C.S.B.A., Chlond A., Cuxart J., Duynkerke P., Jiang H., Khairoutdinov M., Lewellen D., Moeng C.H., Sanchez E., Stevens B., Steven D.E. (2003): A large-eddy simulation study of shallow cumulus convection. J. Atmos. Sci. 60, 1201–1219
Stevens B. (2000): Cloud transitions and decoupling in shear-free stratocumulus-topped boundary layers. Geophy. Res. Lett. 27, 2557–2560
Stevens B. (2002): Entrainment in stratocumulus mixed layers. Q. J. R. Meteor. Soc. 128, 2663–2690
Stevens B., Ackerman A.A., Albrecht B.A., Brown A.R., Chlond Cuxart J., Duynkerke P.G., Lewellen D.C., MacVean M.K., Neggers R., Sanchez E., Siebesma A.P., Stevens D.E. (2001): Simulations of trade-wind cumuli under a strong inversion. J. Atmos. Sci. 58, 1870–1891
Stevens, B., Beljaars, A., Bordoni, S., Holloway, C., Köhler, M., Savic-Jovcic, S.K.V., Zhang, Y.: On the sturcture of the lower troposphere: July 2001 near 120W and 30N. Mon. Wea. Rev. (2006) (in press)
Stevens B., Duan J., McWilliams J.C., Münnich M., Neelin J.D. (2002): Entrainment, Rayleigh friction and boundary layer winds over the tropical Pacific. J. Climate 15, 30–44
Stevens B., Lenschow D.H., Ian Faloona C.H.M., Lilly D.K., Blomquist B., Vali G., Bandy A., Campos T., Gerber H., Haimov S., Morley B., Thorton D. (2003): On entrainment in nocturnal marine stratocumulus. Q. J. R. Meteor. Soc. 129, 3469–3492
Stevens B., Moeng C.H., Ackerman A.S., Bretherton C.S., Chlond A., de Roode S., Edwards J., Golaz J.C., Jiang H., Khairoutdinov M., Kirkpatrick M.P., Lewellen D.C., Lock A., Müller F., Stevens D.E., Whelan E., Zhu P. (2005): Evaluation of large-eddy simulations via observations of nocturnal marine stratocumulus. Mon. Wea. Rev. 133, 1443–1462
Uppala S.M., Kållberg P.W., Simmons A.J., Andrae U., daCosta Bechtold V., Fiorino M., Gibson J.K., Haseler J., Hernandez A., Kelly G.A., Li X., Onogi K., Saarinen S., Sokka N., Allan R.P., Anderson A., Arpe K., Balmaseda M.A., Beljaars A.C.M., van de Berg L., Bidlot J., Bormann N., Caires S., Dethof A., Dragasovac M., Fisher M., Fuentes M., Hagemann S., Holm E., Hoskings B., Isaksen L., Janssen P.A.E.M., McNally A.P., Mahfouf J.F., Jenne R., Morcrette J.M., Raynor N.A., Saunders R.W., Simon P., Sterl A., Trenberth K.E., Untch A., Vasiljevic D., Viterbo P., Woolen J. (2005): The ERA-40 re-analysis. Q. J. R. Meteor. Soc. 131, 2961–3012
Wood R., Bretheron C.S. (2004): Boundary layer depth, entrainment and decoupling in the cloud-capped subtropical and tropical marine boundary layer. J. Climate 17, 3576–3588
Zhang Y., Stevens B., Ghil M. (2005): On the diurnal cycle and susceptibility to aerosol concentration in a stratocumulus-topped mixed layer. Q. J. R. Meteor. Soc. 131, 1567–1584
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by R. Klein
Rights and permissions
About this article
Cite this article
Stevens, B. Bulk boundary-layer concepts for simplified models of tropical dynamics. Theor. Comput. Fluid Dyn. 20, 279–304 (2006). https://doi.org/10.1007/s00162-006-0032-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00162-006-0032-z