Editorial Type:
Article
Article Type:
Research Article

Bulk Convergence of Cloud-Resolving Simulations of Moist Convection over Complex Terrain

Wolfgang Langhans Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland

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Juerg Schmidli Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland

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Christoph Schär Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland

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Print Publication:
01 Jul 2012
DOI:
https://doi.org/10.1175/JAS-D-11-0252.1
Page(s):
2207–2228
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Abstract

The explicit treatment of moist convection in cloud-resolving models with kilometer-scale horizontal resolution is increasingly used for atmospheric research and numerical weather prediction purposes. However, several previous studies have implicitly questioned the physical validity of this approach, as the accurate representation of the structure and evolution of moist convective phenomena requires considerably higher resolution. Unlike these studies, which focused on single convective systems, here the convergence of bulk properties of an ensemble of moist convective cells in kilometer-scale simulations is considered.

To address the convergence, the authors focus on the bulk net heating and moistening in a large control volume, the associated vertical fluxes, and the diurnal evolution of regionally averaged precipitation. Besides numerical convergence, “physical” convergence (Reynolds number increases with resolution) is addressed for two conceptually different subgrid-mixing approaches (1D mesoscale and 3D LES). Simulations are conducted for a 9-day period of diurnal summer convection over the Alps, using a large computational domain with grid spacings of 4.4, 2.2, 1.1, and 0.55 km and grid-independent topography.

Results show that for the model and episode considered, the simulated bulk properties and vertical fluxes converge numerically toward the 0.55-km solution. In terms of bulk effects, differences between the simulations are surprisingly small, even within the physical convergence framework that exhibits a sensitivity of the small-scale dynamics and ensuing convective structures to the horizontal resolution. Despite some sensitivities related to the applied turbulence closure, the results support the feasibility of kilometer-scale models to appropriately represent the bulk feedbacks between moist convection and the larger-scale flow.

Additional affiliation: Centre for Climate Systems Modeling (C2SM), Zurich, Switzerland.

Corresponding author address: Wolfgang Langhans, Institute for Atmospheric and Climate Science, Universitätstrasse 16, 8092 Zurich, Switzerland. E-mail: wolfgang.langhans@env.ethz.ch

Abstract

The explicit treatment of moist convection in cloud-resolving models with kilometer-scale horizontal resolution is increasingly used for atmospheric research and numerical weather prediction purposes. However, several previous studies have implicitly questioned the physical validity of this approach, as the accurate representation of the structure and evolution of moist convective phenomena requires considerably higher resolution. Unlike these studies, which focused on single convective systems, here the convergence of bulk properties of an ensemble of moist convective cells in kilometer-scale simulations is considered.

To address the convergence, the authors focus on the bulk net heating and moistening in a large control volume, the associated vertical fluxes, and the diurnal evolution of regionally averaged precipitation. Besides numerical convergence, “physical” convergence (Reynolds number increases with resolution) is addressed for two conceptually different subgrid-mixing approaches (1D mesoscale and 3D LES). Simulations are conducted for a 9-day period of diurnal summer convection over the Alps, using a large computational domain with grid spacings of 4.4, 2.2, 1.1, and 0.55 km and grid-independent topography.

Results show that for the model and episode considered, the simulated bulk properties and vertical fluxes converge numerically toward the 0.55-km solution. In terms of bulk effects, differences between the simulations are surprisingly small, even within the physical convergence framework that exhibits a sensitivity of the small-scale dynamics and ensuing convective structures to the horizontal resolution. Despite some sensitivities related to the applied turbulence closure, the results support the feasibility of kilometer-scale models to appropriately represent the bulk feedbacks between moist convection and the larger-scale flow.

Additional affiliation: Centre for Climate Systems Modeling (C2SM), Zurich, Switzerland.

Corresponding author address: Wolfgang Langhans, Institute for Atmospheric and Climate Science, Universitätstrasse 16, 8092 Zurich, Switzerland. E-mail: wolfgang.langhans@env.ethz.ch
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  • Baldauf, M., A. Seifert, J. Förstner, D. Majewski, M. Raschendorfer, and T. Reinhardt, 2011: Operational convective-scale numerical weather prediction with the COSMO model: Description and sensitivities. Mon. Wea. Rev., 139, 3887–3905.

    • Search Google Scholar
    • Export Citation

  • Blackadar, A. K., 1962: The vertical distribution of wind and turbulent exchange in a neutral atmosphere. J. Geophys. Res., 67, 3095–3102.

    • Search Google Scholar
    • Export Citation

  • Boer, G. J., and B. Denis, 1997: Numerical convergence of the dynamics of a GCM. Climate Dyn., 13, 359–374.

  • Bott, A., 1989: A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes. Mon. Wea. Rev., 117, 1006–1015.

    • Search Google Scholar
    • Export Citation

  • Bryan, G. H., J. C. Wyngaard, and J. M. Fritsch, 2003: Resolution requirements for simulations of deep moist convection. Mon. Wea. Rev., 131, 2394–2416.

    • Search Google Scholar
    • Export Citation

  • Cheng, A., and K.-M. Xu, 2006: Simulation of shallow cumuli and their transition to deep convective clouds by cloud-resolving models with different third-order turbulence closures. Quart. J. Roy. Meteor. Soc., 132, 359–382.

    • Search Google Scholar
    • Export Citation

  • Craig, G. C., and A. Dörnbrack, 2008: Entrainment in cumulus clouds: What resolution is cloud-resolving? J. Atmos. Sci., 65, 3978–3988.

    • Search Google Scholar
    • Export Citation

  • Cullen, M. J. P., and A. R. Brown, 2009: Large eddy simulation of the atmosphere on various scales. Philos. Trans. Roy. Soc. London, 367, 2947–2956.

    • Search Google Scholar
    • Export Citation

  • Doms, G., and J. Förstner, 2004: Development of a kilometer-scale NWP-system: LMK. COSMO Newsletter, No. 4, 159–167. [Available online at http://www.cosmo-model.org/content/model/documentation/newsLetters/default.htm.]

  • Durran, D. R., and J. B. Klemp, 1982a: The effects of moisture on trapped mountain lee waves. J. Atmos. Sci., 39, 2490–2506.

  • Durran, D. R., and J. B. Klemp, 1982b: On the effects of moisture on the Brunt–Väisälä frequency. J. Atmos. Sci., 39, 2152–2158.

  • Fiori, E., A. Parodi, and F. Siccardi, 2010: Turbulence closure parameterization and grid spacing effects in simulated supercell storms. J. Atmos. Sci., 67, 3870–3890.

    • Search Google Scholar
    • Export Citation

  • Fuhrer, O., and C. Schär, 2005: Embedded cellular convection in moist flow past topography. J. Atmos. Sci., 62, 2810–2828.

  • Grabowski, W. W., 2001: Coupling cloud processes with the large-scale dynamics using the Cloud-Resolving Convection Parameterization (CRCP). J. Atmos. Sci., 58, 978–997.

    • Search Google Scholar
    • Export Citation

  • Grell, G. A., L. Schade, R. Knoche, A. Pfeiffer, and J. Egger, 2000: Nonhydrostatic climate simulations of precipitation over complex terrain. J. Geophys. Res., 105, 29 595–29 608.

    • Search Google Scholar
    • Export Citation

  • Heise, E., M. Lange, B. Ritter, and R. Schrodin, 2003: Improvement and validation of the multi-layer soil model. COSMO Newsletter, No. 3, 198–203. [Available online at http://www.cosmo-model.org/content/model/documentation/newsLetters/default.htm.]

  • Hohenegger, C., P. Brockhaus, and C. Schär, 2008a: Towards climate simulations at cloud-resolving scales. Meteor. Z., 17, 383–394.

  • Hohenegger, C., A. Walser, W. Langhans, and C. Schär, 2008b: Cloud-resolving ensemble simulations of the August 2005 Alpine flood. Quart. J. Roy. Meteor. Soc., 134, 889–904.

    • Search Google Scholar
    • Export Citation

  • Jäger, E. B., I. Anders, D. Lüthi, B. Rockel, C. Schär, and S. I. Seneviratne, 2008: Analysis of ERA40-driven CLM simulations for Europe. Meteor. Z., 17, 349–367.

    • Search Google Scholar
    • Export Citation

  • Khairoutdinov, M. F., and D. A. Randall, 2001: A cloud resolving model as a cloud parameterization in the NCAR Community Climate System Model: Preliminary results. Geophys. Res. Lett., 28, 3617–3620.

    • Search Google Scholar
    • Export Citation

  • Khairoutdinov, M. F., S. K. Krueger, C.-H. Moeng, P. A. Bogenschutz, and D. A. Randall, 2009: Large-eddy simulation of maritime deep tropical convection. J. Adv. Model. Earth Syst., 1, 15, doi:10.3894/JAMES.2009.1.15.

    • Search Google Scholar
    • Export Citation

  • Klemp, J., and R. Wilhelmson, 1978: Simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 1070–1096.

  • Langhans, W., O. Fuhrer, and J. Schmidli, 2012a: Description and application of a budget-diagnosis tool in COSMO. COSMO Newsletter, No. 12, 43–51. [Available online at http://www.cosmo-model.org/content/model/documentation/newsLetters/default.htm.]

  • Langhans, W., J. Schmidli, and C. Schär, 2012b: Mesoscale impacts of explicit numerical diffusion in a convection-permitting model. Mon. Wea. Rev., 140, 226–244.

    • Search Google Scholar
    • Export Citation

  • Lax, P. D., and R. D. Richtmyer, 1956: Survey of the stability of linear finite difference equations. Commun. Pure Appl. Math., 9, 267–293.

    • Search Google Scholar
    • Export Citation

  • Lean, H. W., P. A. Clark, M. Dixon, N. M. Roberts, A. Fitch, R. Forbes, and C. Halliwell, 2008: Characteristics of high-resolution versions of the Met Office Unified Model for forecasting convection over the United Kingdom. Mon. Wea. Rev., 136, 3408–3424.

    • Search Google Scholar
    • Export Citation

  • Lilly, D. K., 1962: On the numerical simulations of buoyant convection. Tellus, 14, 148–172.

  • Lugauer, M., and P. Winkler, 2005: Thermal circulation in South Bavaria—Climatology and synoptic aspects. Meteor. Z., 14, 15–30.

  • Mason, P. J., 1994: Large-eddy simulation: A critical review of the technique. Quart. J. Roy. Meteor. Soc., 120, 1–26.

  • Mason, P. J., and R. I. Sykes, 1982: A two-dimensional numerical study of horizontal roll vortices in an inversion capped planetary boundary layer. Quart. J. Roy. Meteor. Soc., 108, 801–823.

    • Search Google Scholar
    • Export Citation

  • Mason, P. J., and N. S. Callen, 1986: On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow. J. Fluid Mech., 162, 439–462.

    • Search Google Scholar
    • Export Citation

  • Mason, P. J., and A. R. Brown, 1999: On subgrid models and filter operations in large eddy simulations. J. Atmos. Sci., 56, 2101–2114.

    • Search Google Scholar
    • Export Citation

  • Mellor, G. L., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20, 851–875.

    • Search Google Scholar
    • Export Citation

  • MeteoSchweiz, cited 2006: Juli 2006: Klimatologisch ein extremer Monat. [Available online at http://www.meteoschweiz.admin.ch/web/de/wetter/wetterereignisse/juli_2006_erste_bilanz.html.]

  • Moeng, C.-H., P. P. Sullivan, M. F. Khairoutdinov, and D. A. Randall, 2010: A mixed scheme for subgrid-scale fluxes in cloud-resolving models. J. Atmos. Sci., 67, 3692–3705.

    • Search Google Scholar
    • Export Citation

  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer, 710 pp.

  • Petch, J. C., A. R. Brown, and M. E. B. Gray, 2002: The impact of horizontal resolution on the simulations of convective development over land. Quart. J. Roy. Meteor. Soc., 128, 2031–2044.

    • Search Google Scholar
    • Export Citation

  • Pope, S. B., 2000: Turbulent Flows. Cambridge University Press, 770 pp.

  • Raschendorfer, M., 2001: The new turbulence parameterization of LM. COSMO Newsletter, No. 1, 90–98. [Available online at http://www.cosmo-model.org/content/model/documentation/newsLetters/default.htm.]

  • Raymond, W. H., 1988: High-order low-pass implicit tangent filters for use in finite area calculations. Mon. Wea. Rev., 116, 2132–2141.

    • Search Google Scholar
    • Export Citation

  • Reinhardt, T., and A. Seifert, 2006: A three-category ice-scheme for LMK. COSMO Newsletter, No. 6, 115–120. [Available online at http://www.cosmo-model.org/content/model/documentation/newsLetters/default.htm.]

  • Richard, E., A. Buzzi, and G. Zängl, 2007: Quantitative precipitation forecasting in the Alps: The advances achieved by the Mesoscale Alpine Programme. Quart. J. Roy. Meteor. Soc., 133, 831–846.

    • Search Google Scholar
    • Export Citation

  • Ritter, B., and J. F. Geleyn, 1992: A comprehensive radiation scheme for numerical weather prediction models with potential applications in climate simulations. Mon. Wea. Rev., 120, 303–325.

    • Search Google Scholar
    • Export Citation

  • Rosinger, E. E., 1980: Stability and convergence for non-linear difference schemes are equivalent. IMA J. Appl. Math., 26, 143–149.

  • Schlemmer, L., C. Hohenegger, J. Schmidli, C. S. Bretherton, and C. Schär, 2011: An idealized cloud-resolving framework for the study of midlatitude diurnal convection over land. Mon. Wea. Rev., 68, 1041–1057.

    • Search Google Scholar
    • Export Citation

  • Schmidli, J., and R. Rotunno, 2010: Mechanisms of along-valley winds and heat exchange over mountainous terrain. J. Atmos. Sci., 67, 3033–3047.

    • Search Google Scholar
    • Export Citation

  • Schwartz, C. S., and Coauthors, 2009: Next-day convection-allowing WRF model guidance: A second look at 2-km versus 4-km grid spacing. Mon. Wea. Rev., 137, 3351–3372.

    • Search Google Scholar
    • Export Citation

  • Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132, 3019–3032.

  • Smagorinsky, J., 1963: General circulation experiments with the primitive equations. Mon. Wea. Rev., 91, 99–164.

  • Steppeler, J., G. Doms, U. Schättler, H. W. Bitzer, A. Gassmann, U. Damrath, and G. Gregoric, 2003: Meso-gamma scale forecasts using the nonhydrostatic model LM. Meteor. Atmos. Phys., 82, 75–96.

    • Search Google Scholar
    • Export Citation

  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

  • Takemi, T., and R. Rotunno, 2003: The effects of subgrid model mixing and numerical filtering in simulations of mesoscale cloud systems. Mon. Wea. Rev., 131, 2085–2101; Corrigendum, 133, 339–341.

    • Search Google Scholar
    • Export Citation

  • Weinbrecht, S., and P. J. Mason, 2008: Stochastic backscatter for cloud-resolving models. Part I: Implementation and testing in a dry convective boundary layer. J. Atmos. Sci., 65, 123–139.

    • Search Google Scholar
    • Export Citation

  • Weisman, M. L., W. C. Skamarock, and J. B. Klemp, 1997: The resolution dependence of explicitly modeled convective systems. Mon. Wea. Rev., 125, 527–548.

    • Search Google Scholar
    • Export Citation

  • Weissmann, M., F. J. Braun, L. Ganter, G. J. Mayr, S. Rahm, and O. Reitebuch, 2005: The Alpine mountain–plain circulation: Airborne Doppler lidar measurements and numerical simulations. Mon. Wea. Rev., 133, 3095–3109.

    • Search Google Scholar
    • Export Citation

  • Weusthoff, T., F. Ament, M. Arpagaus, and M. W. Rotach, 2010: Assessing the benefits of convection-permitting models by neighborhood verification: Examples from MAP D-PHASE. Mon. Wea. Rev., 138, 3418–3433.

    • Search Google Scholar
    • Export Citation

  • Wicker, L. J., and W. C. Skamarock, 2002: Time-splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130, 2088–2097.

    • Search Google Scholar
    • Export Citation

  • Wyngaard, J. C., 2004: Toward numerical modeling in the “Terra Incognita.” J. Atmos. Sci., 61, 1816–1826.

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