• Ball, F. K., 1960: Control of inversion height by surface heating. Quart. J. Roy. Meteor. Soc., 86 , 483494.

  • Batchvarova, E., and S-E. Gryning, 1991: Applied model for the growth of the daytime mixed layer. Bound.-Layer Meteor., 56 , 261274.

  • Batchvarova, E., and S-E. Gryning, 1994: An applied model for the height of the daytime mixed layer and the entrainment zone. Bound.-Layer Meteor., 71 , 311323.

    • Search Google Scholar
    • Export Citation
  • Betts, A. K., 1973: Non-precipitating cumulus convection and its parameterization. Quart. J. Roy. Meteor. Soc., 99 , 178196.

  • Betts, A. K., 1974: Reply to comment on the paper “Non-precipitating cumulus convection and its parameterization.”. Quart. J. Roy. Meteor. Soc., 100 , 469471.

    • Search Google Scholar
    • Export Citation
  • Boers, R., E. W. Eloranta, and R. L. Coulter, 1984: Lidar observations of mixed layer dynamics: Tests of parameterized entrainment models of mixed layer growth rate. J. Climate Appl. Meteor., 23 , 247266.

    • Search Google Scholar
    • Export Citation
  • Carson, D. J., 1973: The development of dry inversion-capped convectively unstable boundary layer. Quart. J. Roy. Meteor. Soc., 99 , 450467.

    • Search Google Scholar
    • Export Citation
  • Conzemius, R., and E. Fedorovich, 2006a: Dynamics of sheared convective boundary layer entrainment. Part I: Methodological background and large eddy simulations. J. Atmos. Sci., 63 , 11511178.

    • Search Google Scholar
    • Export Citation
  • Conzemius, R., and E. Fedorovich, 2006b: Dynamics of sheared convective boundary layer entrainment. Part II: Evaluation of bulk model predictions of entrainment flux. J. Atmos. Sci., 63 , 11791199.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1970: Convective velocity and temperature scales for the unstable planetary boundary layer and for Raleigh convection. J. Atmos. Sci., 27 , 12111213.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1979: Prediction of convective mixed-layer entrainment for realistic capping inversion structure. J. Atmos. Sci., 36 , 424436.

    • Search Google Scholar
    • Export Citation
  • Driedonks, A. G. M., 1982: Models and observations of the growth of the atmospheric boundary layer. Bound.-Layer Meteor., 23 , 283306.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., 1995: Modeling the atmospheric convective boundary layer within a zero-order jump approach: An extended theoretical framework. J. Appl. Meteor., 34 , 19161928.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., 1998: Bulk models of the atmospheric convective boundary layer. Buoyant Convection in Geophysical Flows, E. J. Plate et al., Eds., Kluwer, 265–290.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., and D. V. Mironov, 1995: A model for a shear-free convective boundary layer with parameterized capping inversion structure. J. Atmos. Sci., 52 , 8395.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., R. Conzemius, and D. Mironov, 2004a: Convective entrainment into a shear-free, linearly stratified atmosphere: Bulk models reevaluated through large eddy simulations. J. Atmos. Sci., 61 , 281295.

    • Search Google Scholar
    • Export Citation
  • Fedorovich, E., R. Conzemius, and A. M. Shapiro, 2004b: Nonstationarity of convective boundary layer growth in a heterogeneously stratified, shear-free atmosphere. Preprints, 16th Symp. on Boundary Layers and Turbulence, Portland, ME, Amer. Meteor. Soc., CD-ROM, 7.9.

  • García, J. A., M. L. Cancillo, and J. L. Cano, 2002: A case study of the morning evolution of the convective boundary layer depth. J. Appl. Meteor., 41 , 10531059.

    • Search Google Scholar
    • Export Citation
  • Garratt, J. R., 1992: The Atmospheric Boundary Layer. Cambridge University Press, 316 pp.

  • Haltiner, G. J., and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology. 2d ed. John Wiley and Sons, 477 pp.

  • Kiemle, C., M. Kaestner, and G. Ehret, 1995: The convective boundary layer structure from lidar and radiosonde measurements during the EFEDA ’91 campaign. J. Atmos. Oceanic Technol., 12 , 771782.

    • Search Google Scholar
    • Export Citation
  • Kim, S-W., S-U. Park, and C-H. Moeng, 2003: Entrainment processes in the convective boundary layer with varying wind shear. Bound.-Layer Meteor., 108 , 221245.

    • Search Google Scholar
    • Export Citation
  • Kim, S-W., S-U. Park, D. Pino, and J. V-G. de Arellano, 2006: Parameterization of entrainment in a sheared convective boundary layer using a first-order jump model. Bound.-Layer Meteor., 120 , 455475.

    • Search Google Scholar
    • Export Citation
  • Lenschow, D. H., 1970: Airplane measurements of planetary boundary layer structure. J. Appl. Meteor., 9 , 874884.

  • Lenschow, D. H., 1974: Model of the height variation of the turbulence kinetic energy budget in the unstable planetary boundary layer. J. Atmos. Sci., 31 , 465474.

    • Search Google Scholar
    • Export Citation
  • Lewellen, D. C., and W. S. Lewellen, 1998: Large-eddy boundary layer entrainment. J. Atmos. Sci., 55 , 26452665.

  • Lewellen, D. C., and W. S. Lewellen, 2000: Boundary layer entrainment for different capping conditions. Preprints, 14th Symp. on Boundary Layers and Turbulence, Aspen, CO, Amer. Meteor. Soc., 80–83.

  • Lilly, D. K., 1968: Models of cloud-topped mixed layers under a strong inversion. Quart. J. Roy. Meteor. Soc., 94 , 292309.

  • Lilly, D. K., 2002a: Entrainment into mixed layers. Part I: Sharp-edged and smooth-edged tops. J. Atmos. Sci., 59 , 33403352.

  • Lilly, D. K., 2002b: Entrainment into mixed layers. Part II: A new closure. J. Atmos. Sci., 59 , 33533361.

  • Mahrt, L., and D. H. Lenschow, 1976: Growth dynamics of the convectively mixed layer. J. Atmos. Sci., 33 , 4151.

  • Otte, M. J., and J. C. Wyngaard, 2001: Stably stratified interfacial-layer turbulence from large eddy simulation. J. Atmos. Sci., 58 , 34243442.

    • Search Google Scholar
    • Export Citation
  • Pino, D., J. V-G. de Arellano, and P. J. Duynkerke, 2003: The contribution of shear to the evolution of a convective boundary layer. J. Atmos. Sci., 60 , 19131926.

    • Search Google Scholar
    • Export Citation
  • Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992: Numerical Recipes in Fortran 77. 2d ed. Cambridge University Press, 933 pp.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 1996a: Numerical study of penetrative and “solid lid” nonpenetrative convective boundary layers. J. Atmos. Sci., 53 , 101112.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 1996b: Effects cause by varying the strength of the capping inversion based on a large eddy simulation model of the shear-free convective boundary layer. J. Atmos. Sci., 53 , 20152024.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 2004: Large-eddy simulation of the baroclinic mixed layer. Bound.-Layer Meteor., 112 , 5780.

  • Stull, R. B., 1973: Inversion rise model based on penetrative convection. J. Atmos. Sci., 30 , 10921099.

  • Stull, R. B., 1976a: The energetics of entrainment across a density interface. J. Atmos. Sci., 33 , 12601267.

  • Stull, R. B., 1976b: Internal gravity waves generated by penetrative convection. J. Atmos. Sci., 33 , 12791286.

  • Stull, R. B., 1976c: Mixed-layer depth model based on turbulent energetics. J. Atmos. Sci., 33 , 12681278.

  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 670 pp.

  • Sullivan, P., C-H. Moeng, B. Stevens, D. H. Lenschow, and S. D. Mayor, 1998: Structure of the entrainment zone capping the convective atmospheric boundary layer. J. Atmos. Sci., 55 , 30423064.

    • Search Google Scholar
    • Export Citation
  • Tennekes, H., 1973: A model for the dynamics of the inversion above a convective boundary layer. J. Atmos. Sci., 30 , 558567.

  • Tennekes, H., and A. G. M. Driedonks, 1981: Basic entrainment equations for the atmospheric boundary layer. Bound.-Layer Meteor., 20 , 515531.

    • Search Google Scholar
    • Export Citation
  • VanZanten, M. C., P. G. Duynkerke, and J. W. M. Cuijpers, 1999: Entrainment parameterization in convective boundary layers. J. Atmos. Sci., 56 , 813828.

    • Search Google Scholar
    • Export Citation
  • Zeman, O., and H. Tennekes, 1977: Parameterization of the turbulent energy budget at the top of the daytime atmospheric boundary layer. J. Atmos. Sci., 34 , 111123.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., 1991: Turbulent Penetrative Convection. Avebury Technical, 179 pp.

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Bulk Models of the Sheared Convective Boundary Layer: Evaluation through Large Eddy Simulations

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  • 1 School of Meteorology, University of Oklahoma, Norman, Oklahoma, Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado, and Windlogics, Inc., Grand Rapids, Minnesota
  • | 2 School of Meteorology, University of Oklahoma, Norman, Oklahoma
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Abstract

A set of first-order model (FOM) equations, describing the sheared convective boundary layer (CBL) evolution, is derived. The model output is compared with predictions of the zero-order bulk model (ZOM) for the same CBL type. Large eddy simulation (LES) data are employed to test both models. The results show an advantage of the FOM over the ZOM in the prediction of entrainment, but in many CBL cases, the predictions by the two models are fairly close. Despite its relative simplicity, the ZOM is able to quantify the effects of shear production and dissipation in an integral sense—as long as the constants describing the integral dissipation of shear- and buoyancy-produced turbulence kinetic energy (TKE) are prescribed appropriately and the shear is weak enough that the denominator of the ZOM entrainment equation does not approach zero, causing a numerical instability in the solutions. Overall, the FOM better predicts the entrainment rate due to its ability to avoid this instability. Also, the FOM in a more physically consistent manner reproduces the sheared CBL entrainment zone, whose depth is controlled by a balance among shear generation, buoyancy consumption, and dissipation of TKE. Such balance is manifested by nearly constant values of Richardson numbers observed in the entrainment zone of simulated sheared CBLs. Conducted model tests support the conclusion that the surface shear generation of TKE and its corresponding dissipation, as well as the nonstationary terms, can be omitted from the integral TKE balance equation.

Corresponding author address: Robert Conzemius, Windlogics, Inc., 201 NW 4th St., Grand Rapids, MN 55744. Email: robert.conzemius@att.net

Abstract

A set of first-order model (FOM) equations, describing the sheared convective boundary layer (CBL) evolution, is derived. The model output is compared with predictions of the zero-order bulk model (ZOM) for the same CBL type. Large eddy simulation (LES) data are employed to test both models. The results show an advantage of the FOM over the ZOM in the prediction of entrainment, but in many CBL cases, the predictions by the two models are fairly close. Despite its relative simplicity, the ZOM is able to quantify the effects of shear production and dissipation in an integral sense—as long as the constants describing the integral dissipation of shear- and buoyancy-produced turbulence kinetic energy (TKE) are prescribed appropriately and the shear is weak enough that the denominator of the ZOM entrainment equation does not approach zero, causing a numerical instability in the solutions. Overall, the FOM better predicts the entrainment rate due to its ability to avoid this instability. Also, the FOM in a more physically consistent manner reproduces the sheared CBL entrainment zone, whose depth is controlled by a balance among shear generation, buoyancy consumption, and dissipation of TKE. Such balance is manifested by nearly constant values of Richardson numbers observed in the entrainment zone of simulated sheared CBLs. Conducted model tests support the conclusion that the surface shear generation of TKE and its corresponding dissipation, as well as the nonstationary terms, can be omitted from the integral TKE balance equation.

Corresponding author address: Robert Conzemius, Windlogics, Inc., 201 NW 4th St., Grand Rapids, MN 55744. Email: robert.conzemius@att.net

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