Univariate Flux Partition Functions for Planetary Boundary Layer Schemes at Gray Zone Resolutions

Mengjuan Liu aKey Laboratory for Mesoscale Severe Weather, Ministry of Education, Nanjing University, Nanjing, China
bSchool of Atmospheric Sciences, Nanjing University, Nanjing, China
cShanghai Typhoon Institute, China Meteorological Administration, Shanghai, China
dAsia-Pacific Typhoon Collaborative Research Center, Shanghai, China

Search for other papers by Mengjuan Liu in
Current site
Google Scholar
PubMed
Close
,
Wei Huang cShanghai Typhoon Institute, China Meteorological Administration, Shanghai, China

Search for other papers by Wei Huang in
Current site
Google Scholar
PubMed
Close
,
Hai Chu eShanghai Central Meteorological Observatory, Shanghai, China

Search for other papers by Hai Chu in
Current site
Google Scholar
PubMed
Close
, and
Bowen Zhou aKey Laboratory for Mesoscale Severe Weather, Ministry of Education, Nanjing University, Nanjing, China
bSchool of Atmospheric Sciences, Nanjing University, Nanjing, China

Search for other papers by Bowen Zhou in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

When the horizontal grid spacing of a numerical weather prediction model approaches kilometer scale, the so-called gray zone range, turbulent fluxes in the convective boundary layer (CBL) are partially resolved and partially subgrid scale (SGS). Knowledge of the partition between resolved and SGS turbulent fluxes is key to building scale-adaptive planetary boundary layer (PBL) schemes that are capable of regulating the SGS fluxes with varying grid spacing. However, flux partition depends not only on horizontal grid spacing, but also on local height, bulk stability of the boundary layer, and the particular turbulent flux. Such multivariate functions are difficult to construct analytically, so their implementations in scale-adaptive PBL schemes always involve certain levels of approximation that can lead to inaccuracies. This study introduces a physically based perspective for the flux partition functions that greatly simplifies their implementation with high accuracy. By introducing an appropriate scaling length λ that accounts for both height and bulk stability dependencies, the dimensionality of the partition functions is reduced to a single dimensionless group. Based on the analysis of a comprehensive large-eddy simulation dataset of the CBL, it is further shown that λ’s height and bulk stability dependencies can be separately represented by a similarity length scale and a stability coefficient. The resulting univariate partition functions are incorporated into a traditional first-order PBL scheme as a proof of concept. Our results show that the augmented scheme well-reproduces the SGS fluxes at gray zone resolutions.

Significance Statement

Flux partition functions are a key component in most scale-adaptive planetary boundary layer (PBL) schemes developed for kilometer- and subkilometer-resolution numerical weather prediction models. They regulate the parameterized turbulent fluxes as a function of horizontal grid spacing, while they also depend on height and atmospheric stability. Such multivariate dependencies forbid simple analytical expressions, and as a result, partition functions implemented in scale-adaptive PBL schemes are generally simplified at the cost of accuracy in previous works. This study investigates the possibility of constructing partition functions that are both accurate and easy to parameterize. Utilizing a physically based length scale, univariate partition functions are built, evaluated, and put into a conventional PBL scheme to improve the gray zone turbulence parameterization.

© 2024 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: Bowen Zhou, zhoubowen@nju.edu.cn

Abstract

When the horizontal grid spacing of a numerical weather prediction model approaches kilometer scale, the so-called gray zone range, turbulent fluxes in the convective boundary layer (CBL) are partially resolved and partially subgrid scale (SGS). Knowledge of the partition between resolved and SGS turbulent fluxes is key to building scale-adaptive planetary boundary layer (PBL) schemes that are capable of regulating the SGS fluxes with varying grid spacing. However, flux partition depends not only on horizontal grid spacing, but also on local height, bulk stability of the boundary layer, and the particular turbulent flux. Such multivariate functions are difficult to construct analytically, so their implementations in scale-adaptive PBL schemes always involve certain levels of approximation that can lead to inaccuracies. This study introduces a physically based perspective for the flux partition functions that greatly simplifies their implementation with high accuracy. By introducing an appropriate scaling length λ that accounts for both height and bulk stability dependencies, the dimensionality of the partition functions is reduced to a single dimensionless group. Based on the analysis of a comprehensive large-eddy simulation dataset of the CBL, it is further shown that λ’s height and bulk stability dependencies can be separately represented by a similarity length scale and a stability coefficient. The resulting univariate partition functions are incorporated into a traditional first-order PBL scheme as a proof of concept. Our results show that the augmented scheme well-reproduces the SGS fluxes at gray zone resolutions.

Significance Statement

Flux partition functions are a key component in most scale-adaptive planetary boundary layer (PBL) schemes developed for kilometer- and subkilometer-resolution numerical weather prediction models. They regulate the parameterized turbulent fluxes as a function of horizontal grid spacing, while they also depend on height and atmospheric stability. Such multivariate dependencies forbid simple analytical expressions, and as a result, partition functions implemented in scale-adaptive PBL schemes are generally simplified at the cost of accuracy in previous works. This study investigates the possibility of constructing partition functions that are both accurate and easy to parameterize. Utilizing a physically based length scale, univariate partition functions are built, evaluated, and put into a conventional PBL scheme to improve the gray zone turbulence parameterization.

© 2024 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: Bowen Zhou, zhoubowen@nju.edu.cn
Save
  • 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, 38873905, https://doi.org/10.1175/MWR-D-10-05013.1.

    • Search Google Scholar
    • Export Citation
  • Benjamin, S. G., and Coauthors, 2016: A North American hourly assimilation and model forecast cycle: The Rapid Refresh. Mon. Wea. Rev., 144, 16691694, https://doi.org/10.1175/MWR-D-15-0242.1.

    • Search Google Scholar
    • Export Citation
  • Boutle, I. A., J. E. J. Eyre, and A. P. Lock, 2014: Seamless stratocumulus simulation across the turbulent gray zone. Mon. Wea. Rev., 142, 16551668, https://doi.org/10.1175/MWR-D-13-00229.1.

    • Search Google Scholar
    • Export Citation
  • Caughey, S. J., and S. G. Palmer, 1979: Some aspects of turbulence structure through the depth of the convective boundary layer. Quart. J. Roy. Meteor. Soc., 105, 811827, https://doi.org/10.1002/qj.49710544606.

    • Search Google Scholar
    • Export Citation
  • Clark, P., N. Roberts, H. Lean, S. P. Ballard, and C. Charlton-Perez, 2016: Convection-permitting models: A step-change in rainfall forecasting. Meteor. Appl., 23, 165181, https://doi.org/10.1002/met.1538.

    • Search Google Scholar
    • Export Citation
  • Clark, P., C. E. Halliwell, and D. L. A. Flack, 2021: A physically based stochastic boundary layer perturbation scheme. Part I: Formulation and evaluation in a convection-permitting model. J. Atmos. Sci., 78, 727746, https://doi.org/10.1175/JAS-D-19-0291.1.

    • Search Google Scholar
    • Export Citation
  • de Roode, S. R., P. G. Duynkerke, and H. J. J. Jonker, 2004: Large-eddy simulation: How large is large enough? J. Atmos. Sci., 61, 403421, https://doi.org/10.1175/1520-0469(2004)061<0403:LSHLIL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Efstathiou, G. A., and R. J. Beare, 2015: Quantifying and improving sub-grid diffusion in the boundary-layer grey zone. Quart. J. Roy. Meteor. Soc., 141, 30063017, https://doi.org/10.1002/qj.2585.

    • Search Google Scholar
    • Export Citation
  • Efstathiou, G. A., and R. S. Plant, 2019: A dynamic extension of the pragmatic blending scheme for scale-dependent sub-grid mixing. Quart. J. Roy. Meteor. Soc., 145, 884892, https://doi.org/10.1002/qj.3445.

    • Search Google Scholar
    • Export Citation
  • Garcia, J. R., and J. P. Mellado, 2014: The two-layer structure of the entrainment zone in the convective boundary layer. J. Atmos. Sci., 71, 19351955, https://doi.org/10.1175/JAS-D-13-0148.1.

    • Search Google Scholar
    • Export Citation
  • Haghshenas, A., and J. P. Mellado, 2019: Characterization of wind-shear effects on entrainment in a convective boundary layer. J. Fluid Mech., 858, 145183, https://doi.org/10.1017/jfm.2018.761.

    • Search Google Scholar
    • Export Citation
  • Hirt, M., S. Rasp, U. Blahak, and G. C. Craig, 2019: Stochastic parameterization of processes leading to convective initiation in kilometer-scale models. Mon. Wea. Rev., 147, 39173934, https://doi.org/10.1175/mwr-d-19-0060.1.

    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., and H.-L. Pan, 1996: Nonlocal boundary layer vertical diffusion in a medium-range forecast model. Mon. Wea. Rev., 124, 23222339, https://doi.org/10.1175/1520-0493(1996)124<2322:NBLVDI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, https://doi.org/10.1175/MWR3199.1.

    • Search Google Scholar
    • Export Citation
  • Honnert, R., V. Masson, and F. Couvreux, 2011: A diagnostic for evaluating the representation of turbulence in atmospheric models at the kilometric scale. J. Atmos. Sci., 68, 31123131, https://doi.org/10.1175/JAS-D-11-061.1.

    • 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
  • Ito, J., H. Niino, M. Nakanishi, and C.-H. Moeng, 2015: An extension of the Mellor-Yamada model to the terra incognita zone for dry convective mixed layers in the free convection regime. Bound.-Layer Meteor., 157, 2343, https://doi.org/10.1007/s10546-015-0045-5.

    • Search Google Scholar
    • Export Citation
  • Jayaraman, B., and J. G. Brasseur, 2021: Transition in atmospheric boundary layer turbulence structure from neutral to convective, and large-scale rolls. J. Fluid Mech., 913, A42, https://doi.org/10.1017/jfm.2021.3.

    • Search Google Scholar
    • Export Citation
  • Juliano, T. W., B. Kosović, P. A. Jiménez, M. Eghdami, S. E. Haupt, and A. Martilli, 2022: “Gray zone” simulations using a three-dimensional planetary boundary layer parameterization in the Weather Research and Forecasting Model. Mon. Wea. Rev., 150, 15851619, https://doi.org/10.1175/MWR-D-21-0164.1.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., and J. J. Finnigan, 1994: Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, 289 pp.

  • Kurowski, M. J., and J. Teixeira, 2018: A scale-adaptive turbulent kinetic energy closure for the dry convective boundary layer. J. Atmos. Sci., 75, 675690, https://doi.org/10.1175/JAS-D-16-0296.1.

    • Search Google Scholar
    • Export Citation
  • Lenschow, D. H., and P. L. Stephens, 1980: The role of thermals in the convective boundary layer. Bound.-Layer Meteor., 19, 509532, https://doi.org/10.1007/BF00122351.

    • Search Google Scholar
    • Export Citation
  • Liu, M., and B. Zhou, 2022: Variations of subgrid-scale turbulent fluxes in the dry convective boundary layer at gray zone resolutions. J. Atmos. Sci., 79, 32453261, https://doi.org/10.1175/JAS-D-22-0085.1.

    • Search Google Scholar
    • Export Citation
  • McNaughton, K. G., R. J. Clement, and J. B. Moncrieff, 2007: Scaling properties of velocity and temperature spectra above the surface friction layer in a convective atmospheric boundary layer. Nonlinear Processes Geophys., 14, 257271, https://doi.org/10.5194/npg-14-257-2007.

    • 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
  • Moeng, C.-H., and P. P. Sullivan, 1994: A comparison of shear- and buoyancy-driven planetary boundary layer flows. J. Atmos. Sci., 51, 9991022, https://doi.org/10.1175/1520-0469(1994)051<0999:ACOSAB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Moeng, C.-H., M. A. LeMone, M. F. Khairoutdinov, S. K. Krueger, P. A. Bogenschutz, and D. A. Randall, 2009: The tropical marine boundary layer under a deep convection system: A large-eddy simulation study. J. Adv. Model. Earth Syst., 1 (4), https://doi.org/10.3894/JAMES.2009.1.16.

    • Search Google Scholar
    • Export Citation
  • Nakanishi, M., and H. Niino, 2009: Development of an improved turbulence closure model for the atmospheric boundary layer. J. Meteor. Soc. Japan, 87, 895912, https://doi.org/10.2151/jmsj.87.895.

    • Search Google Scholar
    • Export Citation
  • Oncley, S. P., C. A. Friehe, J. C. Larue, J. A. Businger, E. C. Itsweire, and S. S. Chang, 1996: Surface-layer fluxes, profiles, and turbulence measurements over uniform terrain under near-neutral conditions. J. Atmos. Sci., 53, 10291044, https://doi.org/10.1175/1520-0469(1996)053<1029:SLFPAT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Pino, D., H. J. J. Jonker, J. V.-G. Arellano, and A. Dosio, 2006: Role of shear and the inversion strength during sunset turbulence over land: Characteristic length scales. Bound.-Layer Meteor., 121, 537556, https://doi.org/10.1007/s10546-006-9080-6.

    • Search Google Scholar
    • Export Citation
  • Salesky, S. T., M. Chamecki, and E. Bou-Zeid, 2017: On the nature of the transition between roll and cellular organization in the convective boundary layer. Bound.-Layer Meteor., 163, 4168, https://doi.org/10.1007/s10546-016-0220-3.

    • Search Google Scholar
    • Export Citation
  • Senel, C. B., O. Temel, S. Porchetta, D. Muñoz-Esparza, and J. van Beeck, 2019: A new planetary boundary layer scheme based on LES: Application to the XPIA campaign. J. Adv. Model. Earth Syst., 11, 26552679, https://doi.org/10.1029/2018MS001580.

    • Search Google Scholar
    • Export Citation
  • Senel, C. B., O. Temel, D. Muñoz-Esparza, A. Parente, and J. van Beeck, 2020: Gray zone partitioning functions and parameterization of turbulence fluxes in the convective atmospheric boundary layer. J. Geophys. Res. Atmos., 125, e2020JD033581, https://doi.org/10.1029/2020JD033581.

    • Search Google Scholar
    • Export Citation
  • Shin, H. H., and S.-Y. Hong, 2013: Analysis of resolved and parameterized vertical transports in convective boundary layers at gray-zone resolutions. J. Atmos. Sci., 70, 32483261, https://doi.org/10.1175/JAS-D-12-0290.1.

    • 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
  • Skamarock, W. C., and Coauthors, 2019: A description of the Advanced Research WRF Model version 4. NCAR Tech. Note NCAR/TN-556+STR, 145 pp., https://doi.org/10.5065/1dfh-6p97.

  • Townsend, A. A. R., 1976: The Structure of Turbulent Shear Flow. Cambridge University Press, 429 pp.

  • Wang, Y., X. Cheng, J. Fei, and B. Zhou, 2022: Modeling the shallow cumulus-topped boundary layer at gray zone resolutions. J. Atmos. Sci., 79, 24352451, https://doi.org/10.1175/JAS-D-21-0339.1.

    • Search Google Scholar
    • Export Citation
  • Wei, W., X. Peng, Y. Lin, J. Li, G. Zhang, Y. Yang, and J. Long, 2022: Extension and evaluation of University of Washington moist turbulence scheme to gray-zone scales. J. Adv. Model. Earth Syst., 14, e2021MS002978, https://doi.org/10.1029/2021MS002978.

    • Search Google Scholar
    • Export Citation
  • Wyngaard, J. C., 2004: Toward numerical modeling in the “terra incognita.” J. Atmos. Sci., 61, 18161826, https://doi.org/10.1175/1520-0469(2004)061<1816:Tnmitt>2.0.Co;2.

    • Search Google Scholar
    • Export Citation
  • Xue, M., K. K. Droegemeier, and V. Wong, 2000: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification. Meteor. Atmos. Phys., 75, 161193, https://doi.org/10.1007/s007030070003.

    • Search Google Scholar
    • Export Citation
  • Xue, M., and Coauthors, 2001: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction tool. Part II: Model physics and applications. Meteor. Atmos. Phys., 76, 143165, https://doi.org/10.1007/s007030170027.

    • Search Google Scholar
    • Export Citation
  • Zhang, X., J. W. Bao, B. D. Chen, and E. D. Grell, 2018: A three-dimensional scale-adaptive turbulent kinetic energy scheme in the WRF-ARW model. Mon. Wea. Rev., 146, 20232045, https://doi.org/10.1175/mwr-d-17-0356.1.

    • Search Google Scholar
    • Export Citation
  • Zhou, B., S. Sun, J. Sun, and K. Zhu, 2019: The universality of the normalized vertical velocity variance in contrast to the horizontal velocity variance in the convective boundary layer. J. Atmos. Sci., 76, 14371456, https://doi.org/10.1175/JAS-D-18-0325.1.

    • Search Google Scholar
    • Export Citation
  • Zhou, B., Y. Li, and S. Miao, 2021: A scale-adaptive turbulence model for the dry convective boundary layer. J. Atmos. Sci., 78, 17151733, https://doi.org/10.1175/JAS-D-20-0240.1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 433 433 46
Full Text Views 101 101 9
PDF Downloads 139 139 12