Impacts of Numerical Advection Schemes and Turbulence Modeling on Gray-Zone Simulation of a Squall Line

Jianan Chen Hong Kong University of Science and Technology, Hong Kong, China

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Xiaoming Shi Hong Kong University of Science and Technology, Hong Kong, China
Center for Ocean Research in Hong Kong and Macau, Hong Kong University of Science and Technology, Hong Kong, China

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Abstract

With increasing computational power, atmospheric simulations have approached the gray-zone resolutions, where energetic turbulent eddies are partly resolved. The representation of turbulence in the gray zone is challenging and sensitive to the choices of turbulence models and numerical advection schemes. Numerical advection schemes are typically designed with numerical dissipation to suppress small-scale numerical oscillations. However, at gray-zone resolutions, the numerical dissipation can damp both numerical and physical oscillations. In this study, we first evaluate the impact of advection schemes on the simulation of an idealized squall line at two gray-zone resolutions (1 and 4 km). We found that at the 4-km resolution, the numerical dissipation from advection schemes can be unfavorable because it damps convective cells greatly and weakens the front-to-rear flow, producing an underestimated convective precipitation maximum and excessive stratiform precipitation. At the 1-km resolution, the numerical dissipation is essential because, without it, excessive spurious numerical oscillations disrupt the squall-line structure. The dynamic reconstruction model (DRM) of turbulence is designed to model both forward- and backscatter having the potential to counter the effect of numerical dissipation from the advection schemes. Our findings demonstrate that DRM enhances squall-line simulations at the 4-km resolution, improving both the squall-line structure and precipitation distribution. However, at the 1-km resolution, DRM fails to improve simulation accuracy, likely due to its influence on triggering spurious convections.

Significance Statement

This work investigates the effects of numerical mixing arising from numerical advection schemes and physical mixing from turbulence schemes on an organized deep convective system in the gray zone. The numerical mixing is found to be critical in shaping the deep convective system structure and the corresponding precipitation distribution. Meanwhile, the role of numerical mixing varies with gray-zone resolutions. The numerical mixing is necessary when it primarily acts on spurious numerical oscillations but unfavorable when it mainly acts on physical convections. Turbulence schemes that allow backscatter can reduce the impact of numerical mixing, which helps improve the accuracy of simulations at certain gray-zone resolutions.

© 2025 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xiaoming Shi, shixm@ust.hk

Abstract

With increasing computational power, atmospheric simulations have approached the gray-zone resolutions, where energetic turbulent eddies are partly resolved. The representation of turbulence in the gray zone is challenging and sensitive to the choices of turbulence models and numerical advection schemes. Numerical advection schemes are typically designed with numerical dissipation to suppress small-scale numerical oscillations. However, at gray-zone resolutions, the numerical dissipation can damp both numerical and physical oscillations. In this study, we first evaluate the impact of advection schemes on the simulation of an idealized squall line at two gray-zone resolutions (1 and 4 km). We found that at the 4-km resolution, the numerical dissipation from advection schemes can be unfavorable because it damps convective cells greatly and weakens the front-to-rear flow, producing an underestimated convective precipitation maximum and excessive stratiform precipitation. At the 1-km resolution, the numerical dissipation is essential because, without it, excessive spurious numerical oscillations disrupt the squall-line structure. The dynamic reconstruction model (DRM) of turbulence is designed to model both forward- and backscatter having the potential to counter the effect of numerical dissipation from the advection schemes. Our findings demonstrate that DRM enhances squall-line simulations at the 4-km resolution, improving both the squall-line structure and precipitation distribution. However, at the 1-km resolution, DRM fails to improve simulation accuracy, likely due to its influence on triggering spurious convections.

Significance Statement

This work investigates the effects of numerical mixing arising from numerical advection schemes and physical mixing from turbulence schemes on an organized deep convective system in the gray zone. The numerical mixing is found to be critical in shaping the deep convective system structure and the corresponding precipitation distribution. Meanwhile, the role of numerical mixing varies with gray-zone resolutions. The numerical mixing is necessary when it primarily acts on spurious numerical oscillations but unfavorable when it mainly acts on physical convections. Turbulence schemes that allow backscatter can reduce the impact of numerical mixing, which helps improve the accuracy of simulations at certain gray-zone resolutions.

© 2025 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xiaoming Shi, shixm@ust.hk

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  • Arakawa, A., and V. R. Lamb, 1977: Computational design of the basic dynamical processes of the UCLA general circulation model. General Circulation Models of the Atmosphere, J. Chang, Ed., Methods in Computational Physics: Advances in Research and Applications, Vol. 17, Elsevier, 173265.

    • Search Google Scholar
    • Export Citation
  • Beare, R. J., 2014: A length scale defining partially-resolved boundary-layer turbulence simulations. Bound.-Layer Meteor., 151, 3955, https://doi.org/10.1007/s10546-013-9881-3.

    • Search Google Scholar
    • Export Citation
  • Borges, R., M. Carmona, B. Costa, and W. S. Don, 2008: An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws. J. Comput. Phys., 227, 31913211, https://doi.org/10.1016/j.jcp.2007.11.038.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., 2005: Spurious convective organization in simulated squall lines owing to moist absolutely unstable layers. Mon. Wea. Rev., 133, 19781997, https://doi.org/10.1175/MWR2952.1.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., 2012: Effects of surface exchange coefficients and turbulence length scales on the intensity and structure of numerically simulated hurricanes. Mon. Wea. Rev., 140, 11251143, https://doi.org/10.1175/MWR-D-11-00231.1.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and J. M. Fritsch, 2002: A benchmark simulation for moist nonhydrostatic numerical models. Mon. Wea. Rev., 130, 29172928, https://doi.org/10.1175/1520-0493(2002)130<2917:ABSFMN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and H. Morrison, 2012: Sensitivity of a simulated squall line to horizontal resolution and parameterization of microphysics. Mon. Wea. Rev., 140, 202225, https://doi.org/10.1175/MWR-D-11-00046.1.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and R. Rotunno, 2014: Gravity currents in confined channels with environmental shear. J. Atmos. Sci., 71, 11211142, https://doi.org/10.1175/JAS-D-13-0157.1.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., J. C. Wyngaard, and J. M. Fritsch, 2003: Resolution requirements for the simulation of deep moist convection. Mon. Wea. Rev., 131, 23942416, https://doi.org/10.1175/1520-0493(2003)131<2394:RRFTSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., J. C. Knievel, and M. D. Parker, 2006: A multimodel assessment of RKW theory’s relevance to squall-line characteristics. Mon. Wea. Rev., 134, 27722792, https://doi.org/10.1175/MWR3226.1.

    • Search Google Scholar
    • Export Citation
  • Chow, F. K., R. L. Street, M. Xue, and J. H. Ferziger, 2005: Explicit filtering and reconstruction turbulence modeling for large-eddy simulation of neutral boundary layer flow. J. Atmos. Sci., 62, 20582077, https://doi.org/10.1175/JAS3456.1.

    • Search Google Scholar
    • Export Citation
  • Chow, F. K., C. Schär, N. Ban, K. A. Lundquist, L. Schlemmer, and X. Shi, 2019: Crossing multiple gray zones in the transition from mesoscale to microscale simulation over complex terrain. Atmosphere, 10, 274, https://doi.org/10.3390/atmos10050274.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1980: Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound.-Layer Meteor., 18, 495527, https://doi.org/10.1007/BF00119502.

    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 2010: Numerical Methods for Fluid Dynamics: With Applications to Geophysics. Texts in Applied Mathematics, Vol. 32, Springer Science & Business Media, 532 pp.

    • Search Google Scholar
    • Export Citation
  • Gullbrand, J., and F. K. Chow, 2003: The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering. J. Fluid Mech., 495, 323341, https://doi.org/10.1017/S0022112003006268.

    • Search Google Scholar
    • Export Citation
  • Honnert, R., and Coauthors, 2020: The atmospheric boundary layer and the “gray zone” of turbulence: A critical review. J. Geophys. Res. Atmos., 125, e2019JD030317, https://doi.org/10.1029/2019JD030317.

    • Search Google Scholar
    • Export Citation
  • Jiang, G.-S., and C.-W. Shu, 1996: Efficient implementation of weighted ENO schemes. J. Comput. Phys., 126, 202228, https://doi.org/10.1006/jcph.1996.0130.

    • Search Google Scholar
    • Export Citation
  • Knievel, J. C., G. H. Bryan, and J. P. Hacker, 2007: Explicit numerical diffusion in the WRF model. Mon. Wea. Rev., 135, 38083824, https://doi.org/10.1175/2007MWR2100.1.

    • Search Google Scholar
    • Export Citation
  • Kosović, B., D. Muñoz-Esparza, and J. A. Sauer, 2016: Improving spectral resolution of finite difference schemes for multiscale modeling applications using numerical weather prediction model. 22nd Symp. on Boundary Layers and Turbulence, Salt Lake City, UT, Amer. Meteor. Soc., 3B.5, https://ams.confex.com/ams/32AgF22BLT3BG/webprogram/Paper295892.html.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., A. Crook, J. C. Knievel, and J. Dudhia, 2005: Sensitivity of the WRF model to advection and diffusion schemes for simulation of heavy rainfall along the Baiu Front. SOLA, 1, 177180, https://doi.org/10.2151/sola.2005-046.

    • Search Google Scholar
    • Export Citation
  • Lai, K. T., and M. L. Waite, 2020: Resolution dependence and subfilter-scale motions in idealized squall-line simulations. Mon. Wea. Rev., 148, 30593078, https://doi.org/10.1175/MWR-D-19-0330.1.

    • Search Google Scholar
    • Export Citation
  • LeMone, M. A., and E. J. Zipser, 1980: Cumulonimbus vertical velocity events in gate. Part I: Diameter, intensity and mass flux. J. Atmos. Sci., 37, 24442457, https://doi.org/10.1175/1520-0469(1980)037<2444:CVVEIG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Moeng, C.-H., 1984: A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci., 41, 20522062, https://doi.org/10.1175/1520-0469(1984)041<2052:ALESMF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Morrison, H., G. Thompson, and V. Tatarskii, 2009: Impact of cloud microphysics on the development of trailing stratiform precipitation in a simulated squall line: Comparison of one- and two-moment schemes. Mon. Wea. Rev., 137, 9911007, https://doi.org/10.1175/2008MWR2556.1.

    • Search Google Scholar
    • Export Citation
  • Parodi, A., and S. Tanelli, 2010: Influence of turbulence parameterizations on high-resolution numerical modeling of tropical convection observed during the TC4 field campaign. J. Geophys. Res., 115, D00J14, https://doi.org/10.1029/2009JD013302.

    • Search Google Scholar
    • Export Citation
  • Pressel, K. G., C. M. Kaul, T. Schneider, Z. Tan, and S. Mishra, 2015: Large-eddy simulation in an anelastic framework with closed water and entropy balances. J. Adv. Model. Earth Syst., 7, 14251456, https://doi.org/10.1002/2015MS000496.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., J. B. Klemp, and M. L. Weisman, 1988: A theory for strong, long-lived squall lines. J. Atmos. Sci., 45, 463–485, https://doi.org/10.1175/1520-0469(1988)045<0463:ATFSLL>2.0.CO;2.

  • Shi, X., F. K. Chow, R. L. Street, and G. H. Bryan, 2018a: An evaluation of LES turbulence models for scalar mixing in the stratocumulus-capped boundary layer. J. Atmos. Sci., 75, 14991507, https://doi.org/10.1175/JAS-D-17-0392.1.

    • Search Google Scholar
    • Export Citation
  • Shi, X., H. L. Hagen, F. K. Chow, G. H. Bryan, and R. L. Street, 2018b: Large-eddy simulation of the stratocumulus-capped boundary layer with explicit filtering and reconstruction turbulence modeling. J. Atmos. Sci., 75, 611637, https://doi.org/10.1175/JAS-D-17-0162.1.

    • Search Google Scholar
    • Export Citation
  • Shi, X., F. K. Chow, R. L. Street, and G. H. Bryan, 2019: Key elements of turbulence closures for simulating deep convection at kilometer-scale resolution. J. Adv. Model. Earth Syst., 11, 818838, https://doi.org/10.1029/2018MS001446.

    • Search Google Scholar
    • Export Citation
  • Shin, H. H., and S.-Y. Hong, 2015: Representation of the subgrid-scale turbulent transport in convective boundary layers at gray-zone resolutions. Mon. Wea. Rev., 143, 250271, https://doi.org/10.1175/MWR-D-14-00116.1.

    • Search Google Scholar
    • Export Citation
  • Simon, J. S., B. Zhou, J. D. Mirocha, and F. K. Chow, 2019: Explicit filtering and reconstruction to reduce grid dependence in convective boundary layer simulations using WRF-LES. Mon. Wea. Rev., 147, 18051821, https://doi.org/10.1175/MWR-D-18-0205.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132, 30193032, https://doi.org/10.1175/MWR2830.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.

    • Search Google Scholar
    • Export Citation
  • Stolz, S., and N. A. Adams, 1999: An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids, 11, 16991701, https://doi.org/10.1063/1.869867.

    • Search Google Scholar
    • Export Citation
  • Sun, S., B. Zhou, M. Xue, and K. Zhu, 2021: Scale-similarity subgrid-scale turbulence closure for supercell simulations at kilometer-scale resolutions: Comparison against a large-eddy simulation. J. Atmos. Sci., 78, 417437, https://doi.org/10.1175/JAS-D-20-0187.1.

    • Search Google Scholar
    • Export Citation
  • 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, 20852101, https://doi.org/10.1175/1520-0493(2003)131<2085:TEOSMM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wang, A., Y. Pan, and P. M. Markowski, 2021: The influence of WENO schemes on large-eddy simulations of a neutral atmospheric boundary layer. J. Atmos. Sci., 78, 36133628, https://doi.org/10.1175/JAS-D-21-0033.1.

    • Search Google Scholar
    • Export Citation
  • Weisman, M. L., and R. Rotunno, 2004: “A theory for strong long-lived squall lines” revisited. J. Atmos. Sci., 61, 361382, https://doi.org/10.1175/1520-0469(2004)061<0361:ATFSLS>2.0.CO;2.

    • 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, 527548, https://doi.org/10.1175/1520-0493(1997)125<0527:TRDOEM>2.0.CO;2.

    • 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, 20882097, https://doi.org/10.1175/1520-0493(2002)130<2088:TSMFEM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wong, V. C., and D. K. Lilly, 1994: A comparison of two dynamic subgrid closure methods for turbulent thermal convection. Phys. Fluids, 6, 10161023, https://doi.org/10.1063/1.868335.

    • Search Google Scholar
    • Export Citation
  • Xu, X., C. Sun, C. Lu, Y. Liu, G. J. Zhang, and Q. Chen, 2021: Factors affecting entrainment rate in deep convective clouds and parameterizations. J. Geophys. Res. Atmos., 126, e2021JD034881, https://doi.org/10.1029/2021JD034881.

    • Search Google Scholar
    • Export Citation
  • Xue, M., 2000: High-order monotonic numerical diffusion and smoothing. Mon. Wea. Rev., 128, 28532864, https://doi.org/10.1175/1520-0493(2000)128<2853:HOMNDA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
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