• Abgrall, R., and S. Karni, 2001: Computations of compressible multifluids. J. Comput. Phys., 169, 594623, https://doi.org/10.1006/jcph.2000.6685.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Allaire, G., S. Clerc, and S. Kokh, 2002: A five-equation model for the simulation of interfaces between compressible fluids. J. Comput. Phys., 181, 577616, https://doi.org/10.1006/jcph.2002.7143.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Arakawa, A., 2004: The cumulus parameterization problem: Past, present, and future. J. Climate, 17, 24932525, https://doi.org/10.1175/1520-0442(2004)017<2493:RATCPP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, part I. J. Atmos. Sci., 31, 674701, https://doi.org/10.1175/1520-0469(1974)031<0674:IOACCE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Arakawa, A., and C.-M. Wu, 2013: A unified representation of deep moist convection in numerical modeling of the atmosphere. Part I. J. Atmos. Sci., 70, 19771992, https://doi.org/10.1175/JAS-D-12-0330.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bannon, P. R., 2002: Theoretical foundations for models of moist convection. J. Atmos. Sci., 59, 19671982, https://doi.org/10.1175/1520-0469(2002)059<1967:TFFMOM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bogenschutz, P. A., A. Gettelman, H. Morrison, V. E. Larson, C. Craig, and D. P. Schanen, 2013: Higher-order turbulence closure and its impact on climate simulations in the Community Atmosphere Model. J. Climate, 26, 96559676, https://doi.org/10.1175/JCLI-D-13-00075.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chaouat, B., and R. Schiestel, 2013: Partially integrated transport modeling for turbulence simulation with variable filters. Phys. Fluids, 25, 125102, https://doi.org/10.1063/1.4833235.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Couvreux, F., F. Hourdin, and C. Rio, 2010: Resolved versus parameterized boundary-layer plumes. Part I: A parameterization-oriented conditional sampling in large-eddy simulations. Bound.-Layer Meteor., 134, 441458, https://doi.org/10.1007/s10546-009-9456-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cullen, M. J. P., D. Salmond, and N. Wedi, 2001: Interaction of parametrised processes with resolved dynamics. Proc. Key Issues in the Parametrization of Subgrid Physical Processes Workshop, Reading, United Kingdom, ECMWF, 127–149.

  • Cushman-Roisin, B., 1982: A theory of convection: Modelling by two buoyant interacting fluids. Geophys. Astrophys. Fluid Dyn., 19, 3559, https://doi.org/10.1080/03091928208208946.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davies, T., A. Staniforth, N. Wood, and J. Thuburn, 2003: Validity of anelastic and other equation sets as inferred from normal-mode analysis. Quart. J. Roy. Meteor. Soc., 129, 27612775, https://doi.org/10.1256/qj.02.1951.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • de Rooy, W. C., and et al. , 2013: Entrainment and detrainment in cumulus convection: An overview. Quart. J. Roy. Meteor. Soc., 139, 119, https://doi.org/10.1002/qj.1959.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dopazo, C., 1977: On conditioned averages for intermittent turbulent flows. J. Fluid Mech., 81, 433438, https://doi.org/10.1017/S0022112077002158.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Drew, D. A., 1983: Mathematical modeling of two-phase flow. Annu. Rev. Fluid Mech., 15, 261291, https://doi.org/10.1146/annurev.fl.15.010183.001401.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fureby, C., and G. Tabor, 1997: Mathematical and physical constraints on large-eddy simulations. Theor. Comput. Fluid Dyn., 9, 85102, https://doi.org/10.1007/s001620050034.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garrick, D. P., M. Owkes, and J. D. Regele, 2017: A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension. J. Comput. Phys., 339, 4667, https://doi.org/10.1016/j.jcp.2017.03.007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gerard, L., J.-M. Piriou, R. Brožková, J.-F. Geleyn, and D. Banciu, 2009: Cloud and precipitation parameterization in a meso-gamma-scale operational weather prediction model. Mon. Wea. Rev., 137, 39603977, https://doi.org/10.1175/2009MWR2750.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Germano, M., 1992: Turbulence: The filtering approach. J. Fluid Mech., 238, 325336, https://doi.org/10.1017/S0022112092001733.

  • Germano, M., U. Piomelli, P. Moin, and W. H. Cabot, 1991: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids, 3, 17601765, https://doi.org/10.1063/1.857955.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Golaz, J.-C., 2002: A PDF-based model for boundary layer clouds. Part I: Method and model description. J. Atmos. Sci., 59, 35403551, https://doi.org/10.1175/1520-0469(2002)059<3540:APBMFB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., and P. Smolarkiewicz, 1999: CRCP: A cloud resolving convection parameterization for modeling the tropical convecting atmosphere. Physica D, 133, 171178, https://doi.org/10.1016/S0167-2789(99)00104-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grandpeix, J.-Y., and J.-P. Lafore, 2010: A density current parameterization coupled with Emanuel’s convection scheme. Part I: The models. J. Atmos. Sci., 67, 881897, https://doi.org/10.1175/2009JAS3044.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregory, D., and P. R. Rowntree, 1990: A mass flux convection scheme with representation of cloud ensemble characteristics and stability-dependent closure. Mon. Wea. Rev., 118, 14831506, https://doi.org/10.1175/1520-0493(1990)118<1483:AMFCSW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grell, G. A., and S. Freitas, 2014: A scale and aerosol aware stochastic convective parameterization for weather and air quality modeling. Atmos. Chem. Phys., 14, 52335250, https://doi.org/10.5194/acp-14-5233-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holloway, C. E., and et al. , 2014: Understanding and representing convection across scales: Recommendations from the meeting held at Dartington Hall, Devon, UK, 28–30 January 2013. Atmos. Sci. Lett., 15, 348353, https://doi.org/10.1002/asl2.508.

    • Search Google Scholar
    • Export Citation
  • Holton, J. R., 2004: An Introduction to Dynamic Meteorology. 4th ed. Academic Press, 535 pp.

  • Holtslag, A. A. M., and B. A. Boville, 1993: Local versus nonlocal boundary-layer diffusion in a global climate model. J. Climate, 6, 18251842, https://doi.org/10.1175/1520-0442(1993)006<1825:LVNBLD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jackson, R., 1997: Locally averaged equations of motion for a mixture of identical spherical particles in a Newtonian fluid. Chem. Eng. Sci., 52, 24572469, https://doi.org/10.1016/S0009-2509(97)00065-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jakob, C., and A. P. Siebesma, 2003: A new subcloud model for mass-flux convection schemes: Influence on triggering, updraft properties, and model climate. Mon. Wea. Rev., 131, 27652778, https://doi.org/10.1175/1520-0493(2003)131<2765:ANSMFM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kain, J. S., 2004: The Kain–Fritsch convective parameterization: An update. J. Appl. Meteor., 43, 170181, https://doi.org/10.1175/1520-0450(2004)043<0170:TKCPAU>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 341 pp.

    • Crossref
    • Export Citation
  • Keane, R. J., and R. S. Plant, 2012: Large-scale length and time-scales for use with stochastic convective parametrization. Quart. J. Roy. Meteor. Soc., 138, 11501164, https://doi.org/10.1002/qj.992.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kim, D., J.-S. Kug, I.-S. Kang, F.-F. Jin, and A. T. Wittenberg, 2008: Tropical Pacific impacts of convective momentum transport in the SNU coupled GCM. Climate Dyn., 31, 213226, https://doi.org/10.1007/s00382-007-0348-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Krueger, S. K., 2001: Current issues in cumulus parameterization. Proc. Key Issues in the Parametrization of Subgrid Physical Processes Workshop, Reading, United Kingdom, ECMWF, 25–51.

  • Kuell, V., and A. Bott, 2008: A hybrid convection scheme for use in non-hydrostatic numerical weather prediction models. Meteor. Z., 17, 775783, https://doi.org/10.1127/0941-2948/2008/0342.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuell, V., A. Gassmann, and A. Bott, 2007: Towards a new hybrid cumulus parametrization scheme for use in non-hydrostatic weather prediction models. Quart. J. Roy. Meteor. Soc., 133, 479490, https://doi.org/10.1002/qj.28.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lance, M., and J. Bataille, 1991: Turbulence in the liquid phase of a uniform bubbly air–water flow. J. Fluid Mech., 222, 95118, https://doi.org/10.1017/S0022112091001015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lappen, C.-L., and D. A. Randall, 2001: Toward a unified parameterization of the boundary layer and moist convection. Part I: A new type of mass-flux model. J. Atmos. Sci., 58, 20212036, https://doi.org/10.1175/1520-0469(2001)058<2021:TAUPOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leonard, A., 1975: Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys., 18, 237248, https://doi.org/10.1016/S0065-2687(08)60464-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Libby, P. A., 1975: On the prediction of intermittent turbulent flows. J. Fluid Mech., 68, 273295, https://doi.org/10.1017/S0022112075000808.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Louis, J.-F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor., 17, 187202, https://doi.org/10.1007/BF00117978.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problem. Rev. Geophys. Space Phys., 20, 851875, https://doi.org/10.1029/RG020i004p00851.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mote, P., and A. O’Neill, Eds., 2000: Numerical Modeling of the Global Atmosphere in the Climate System. NATO Science Series C, Vol. 550, Kluwer Academic, 517 pp.

    • Crossref
    • Export Citation
  • Neggers, R. A. J., M. Köhler, and A. C. M. Beljaars, 2009: A dual mass flux framework for boundary layer convection. Part I: Transport. J. Atmos. Sci., 66, 14651487, https://doi.org/10.1175/2008JAS2635.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park, S., 2014: A unified convection scheme (UNICON). Part I: Formulation. J. Atmos. Sci., 71, 39023930, https://doi.org/10.1175/JAS-D-13-0233.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Plant, R. S., and G. C. Craig, 2008: A stochastic parameterization for deep convection based on equilibrium statistics. J. Atmos. Sci., 65, 87105, https://doi.org/10.1175/2007JAS2263.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pope, S. B., 2000: Turbulent Flows. Cambridge University Press, 802 pp.

    • Crossref
    • Export Citation
  • Rafique, M., P. Chen, and M. P. Duduković, 2004: Computational modeling of gas-liquid flow in bubble columns. Rev. Chem. Eng., 20, 225375, https://doi.org/10.1515/REVCE.2004.20.3-4.225.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Randall, D. A., Ed., 2000: General Circulation Model Development: Past, Present, and Future. International Geophysics Series, Vol. 70, Academic Press, 807 pp.

    • Crossref
    • Export Citation
  • Randall, D. A., M. Kairoutdinov, A. Arakawa, and W. Grabowski, 2003: Breaking the cloud-parameterization deadlock. Bull. Amer. Meteor. Soc., 84, 15471564, https://doi.org/10.1175/BAMS-84-11-1547.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., 2013: Sources and sinks of entropy in the atmosphere. J. Adv. Model. Earth Syst., 5, 755763, https://doi.org/10.1002/jame.20050.

  • Rio, C., F. Hourdin, F. Couvreux, and A. Jam, 2010: Resolved versus parametrized boundary-layer plumes. Part II: Continuous formulations of mixing rates for mass flux schemes. Bound.-Layer Meteor., 135, 469483, https://doi.org/10.1007/s10546-010-9478-z.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Romps, D. M., 2015: MSE minus CAPE is the true conserved variable for an adiabatically lifted parcel. J. Atmos. Sci., 72, 36393646, https://doi.org/10.1175/JAS-D-15-0054.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Romps, D. M., and A. B. Charn, 2015: Sticky thermals: Evidence for a dominant balance between buoyancy and drag in cloud updrafts. J. Atmos. Sci., 72, 28902901, https://doi.org/10.1175/JAS-D-15-0042.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sherwood, S. C., D. Hernández-Deckers, M. Colin, and F. Robinson, 2013: Slippery thermals and the cumulus entrainment paradox. J. Atmos. Sci., 70, 24262442, https://doi.org/10.1175/JAS-D-12-0220.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Siebesma, A. P., P. M. M. Soares, and J. Teixeira, 2007: A combined eddy-diffusivity mass-flux approach for the convective boundary layer. J. Atmos. Sci., 64, 12301248, https://doi.org/10.1175/JAS3888.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smagorinsky, J., 1963: General circulation experiments with the primitive equations. Mon. Wea. Rev., 91, 99165, https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Soares, P. M. M., P. M. A. Miranda, A. P. Siebesma, and J. Teixeira, 2004: An eddy-diffusivity/mass-flux parametrization for dry and shallow cumulus convection. Quart. J. Roy. Meteor. Soc., 130, 33653383, https://doi.org/10.1256/qj.03.223.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Städtke, H., 2006: Gasdynamic Aspects of Two-Phase Flow: Hyperbolicity, Wave Propagation Phenomena, and Related Numerical Methods. Wiley, 288 pp.

    • Crossref
    • Export Citation
  • Storer, R. L., B. M. Griffin, J. Höft, J. K. Weber, E. Raut, V. E. Larson, M. Wang, and P. J. Rasch, 2015: Parameterizing deep convection using the assumed probability density function method. Geosci. Model Dev., 8, 119, https://doi.org/10.5194/gmd-8-1-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Wea. Rev., 117, 17791800, https://doi.org/10.1175/1520-0493(1989)117<1779:ACMFSF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vallis, G. K., 2017: Atmospheric and Oceanic Fluid Dynamics. 2nd ed. Cambridge University Press, 946 pp.

    • Crossref
    • Export Citation
  • Weller, H. G., 2005: Derivation, modelling and solution of the conditionally averaged two-phase flow equations. OpenFOAM Tech. Rep., 29 pp.

  • Williamson, D. L., 2008: Convergence of aqua-planet simulations with increasing resolution in the Community Atmospheric Model, version 3. Tellus, 60A, 848862, https://doi.org/10.1111/j.1600-0870.2008.00339.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wood, N., and et al. , 2014: An inherently mass-conserving semi-implicit semi-Lagrangian discretization of the deep-atmosphere global nonhydrostatic equations. Quart. J. Roy. Meteor. Soc., 140, 15051520, https://doi.org/10.1002/qj.2235.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wyngaard, J. C., and C.-H. Moeng, 1992: Parameterizing turbulent diffusion through the joint probability density. Bound.-Layer Meteor., 60, 113, https://doi.org/10.1007/BF00122059.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yano, J.-I., 2012: Mass-flux subgrid-scale parameterization in analogy with multi-component flows: A formulation towards scale independence. Geosci. Model Dev., 5, 14251440, https://doi.org/10.5194/gmd-5-1425-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yano, J.-I., 2014: Formulation structure of the mass-flux convection parameterization. Dyn. Atmos. Oceans, 67, 128, https://doi.org/10.1016/j.dynatmoce.2014.04.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yano, J.-I., 2016: Subgrid-scale physical parameterization in atmospheric modeling: How can we make it consistent? J. Phys., 49A, 284001, https://doi.org/10.1088/1751-8113/49/28/284001.

    • Search Google Scholar
    • Export Citation
  • Yano, J.-I., P. Bénard, F. Couvreux, and A. Lahellec, 2010: NAM-SCA: A nonhydrostatic anelastic model with segmentally constant approximation. Mon. Wea. Rev., 138, 19571974, https://doi.org/10.1175/2009MWR2997.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yeo, K., and D. M. Romps, 2013: Measurement of convective entrainment using Lagrangian particles. J. Atmos. Sci., 70, 266277, https://doi.org/10.1175/JAS-D-12-0144.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, D. Z., and A. Prosperetti, 1997: Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions. Int. J. Multiphase Flow, 23, 425453, https://doi.org/10.1016/S0301-9322(96)00080-8.

    • Crossref
    • Search Google Scholar
    • Export Citation
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A Framework for Convection and Boundary Layer Parameterization Derived from Conditional Filtering

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  • 1 University of Exeter, Exeter, United Kingdom
  • | 2 University of Reading, Reading, United Kingdom
  • | 3 University of Exeter, Exeter, United Kingdom
  • | 4 Met Office, Exeter, United Kingdom
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Abstract

A new theoretical framework is derived for parameterization of subgrid physical processes in atmospheric models; the application to parameterization of convection and boundary layer fluxes is a particular focus. The derivation is based on conditional filtering, which uses a set of quasi-Lagrangian labels to pick out different regions of the fluid, such as convective updrafts and environment, before applying a spatial filter. This results in a set of coupled prognostic equations for the different fluid components, including subfilter-scale flux terms and entrainment/detrainment terms. The framework can accommodate different types of approaches to parameterization, such as local turbulence approaches and mass flux approaches. It provides a natural way to distinguish between local and nonlocal transport processes and makes a clearer conceptual link to schemes based on coherent structures such as convective plumes or thermals than the straightforward application of a filter without the quasi-Lagrangian labels. The framework should facilitate the unification of different approaches to parameterization by highlighting the different approximations made and by helping to ensure that budgets of energy, entropy, and momentum are handled consistently and without double counting. The framework also points to various ways in which traditional parameterizations might be extended, for example, by including additional prognostic variables. One possibility is to allow the large-scale dynamics of all the fluid components to be handled by the dynamical core. This has the potential to improve several aspects of convection–dynamics coupling, such as dynamical memory, the location of compensating subsidence, and the propagation of convection to neighboring grid columns.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: John Thuburn, j.thuburn@exeter.ac.uk

Abstract

A new theoretical framework is derived for parameterization of subgrid physical processes in atmospheric models; the application to parameterization of convection and boundary layer fluxes is a particular focus. The derivation is based on conditional filtering, which uses a set of quasi-Lagrangian labels to pick out different regions of the fluid, such as convective updrafts and environment, before applying a spatial filter. This results in a set of coupled prognostic equations for the different fluid components, including subfilter-scale flux terms and entrainment/detrainment terms. The framework can accommodate different types of approaches to parameterization, such as local turbulence approaches and mass flux approaches. It provides a natural way to distinguish between local and nonlocal transport processes and makes a clearer conceptual link to schemes based on coherent structures such as convective plumes or thermals than the straightforward application of a filter without the quasi-Lagrangian labels. The framework should facilitate the unification of different approaches to parameterization by highlighting the different approximations made and by helping to ensure that budgets of energy, entropy, and momentum are handled consistently and without double counting. The framework also points to various ways in which traditional parameterizations might be extended, for example, by including additional prognostic variables. One possibility is to allow the large-scale dynamics of all the fluid components to be handled by the dynamical core. This has the potential to improve several aspects of convection–dynamics coupling, such as dynamical memory, the location of compensating subsidence, and the propagation of convection to neighboring grid columns.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: John Thuburn, j.thuburn@exeter.ac.uk
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