• Ahmed, F., and J. D. Neelin, 2018: Reverse engineering the tropical precipitation–buoyancy relationship. J. Atmos. Sci., 75, 15871608, https://doi.org/10.1175/JAS-D-17-0333.1.

    • 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
  • Browning, K. A., 1963: The growth of large hail within a steady updraught. Quart. J. Roy. Meteor. Soc., 89, 490506, https://doi.org/10.1002/qj.49708938206.

    • Crossref
    • 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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bunkers, M. J., B. A. Klimowski, R. L. Thompson, and M. L. Weisman, 2000: Predicting supercell motion using a new hodograph technique. Wea. Forecasting, 15, 6179, https://doi.org/10.1175/1520-0434(2000)015<0061:PSMUAN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Coffer, B. E., and M. D. Parker, 2015: Impacts of increasing low-level shear on supercells during the early evening transition. Mon. Wea. Rev., 143, 19451969, https://doi.org/10.1175/MWR-D-14-00328.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cotton, W. R., 1975: On parameterization of turbulent transport in cumulus clouds. J. Atmos. Sci., 32, 548564, https://doi.org/10.1175/1520-0469(1975)032<0548:OPOTTI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 2002: Linear and nonlinear propagation of supercell storms. J. Atmos. Sci., 59, 31783205, https://doi.org/10.1175/1520-0469(2003)059<3178:LANPOS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 2003: An expression for effective buoyancy in surroundings with horizontal density gradients. J. Atmos. Sci., 60, 29222925, https://doi.org/10.1175/1520-0469(2003)060<2922:AEFEBI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • De Roode, S. R., A. P. Siebesma, H. J. Jonker, and Y. De Voog, 2012: Parameterization of the vertical velocity equation for shallow cumulus clouds. Mon. Wea. Rev., 140, 24242436, https://doi.org/10.1175/MWR-D-11-00277.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doswell, C. A., III, and P. M. Markowski, 2004: Is buoyancy a relative quantity? Mon. Wea. Rev., 132, 853863, https://doi.org/10.1175/1520-0493(2004)132<0853:IBARQ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doswell, C. A., III, H. E. Brooks, and R. A. Maddox, 1996: Flash flood forecasting: An ingredients-based methodology. Wea. Forecasting, 11, 560581, https://doi.org/10.1175/1520-0434(1996)011<0560:FFFAIB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1994: Atmospheric Convection. Oxford University Press, 588 pp.

  • Gallus, W. A. J., N. A. Snook, and E. V. Johnson, 2008: Spring and summer severe weather reports over the Midwest as a function of convective mode: A preliminary study. Wea. Forecasting, 23, 101113, https://doi.org/10.1175/2007WAF2006120.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hannah, W. M., 2017: Entrainment versus dilution in tropical deep convection. J. Atmos. Sci., 74, 37253747, https://doi.org/10.1175/JAS-D-16-0169.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hernandez-Deckers, D., and S. C. Sherwood, 2016: A numerical investigation of cumulus thermals. J. Atmos. Sci., 73, 41174136, https://doi.org/10.1175/JAS-D-15-0385.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hernandez-Deckers, D., and S. C. Sherwood, 2018: On the role of entrainment in the fate of cumulus thermals. J. Atmos. Sci., 75, 39113924, https://doi.org/10.1175/JAS-D-18-0077.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holloway, C. E., and J. D. Neelin, 2009: Moisture vertical structure, column water vapor, and tropical deep convection. J. Atmos. Sci., 66, 16651683, https://doi.org/10.1175/2008JAS2806.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Johari, H., 1992: Mixing in thermals with and without buoyancy reversal. J. Atmos. Sci., 49, 14121426, https://doi.org/10.1175/1520-0469(1992)049<1412:MITWAW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kyle, T. G., W. R. Sand, and D. J. Musil, 1976: Fitting measurements of thunderstorm updraft properties to model profiles. Mon. Wea. Rev., 104, 611617, https://doi.org/10.1175/1520-0493(1976)104<0611:FMOTUP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lecoanet, D., and N. Jeevanjee, 2019: Entrainment in resolved, dry thermals. J. Atmos. Sci., 76, 37853801, https://doi.org/10.1175/JAS-D-18-0320.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mapes, B. E., and R. Neale, 2011: Parameterizing convective organization to escape the entrainment dilemma. J. Adv. Model. Earth Sys., 3, M06004, https://doi.org/10.1029/2011ms000042.

    • Search Google Scholar
    • Export Citation
  • Marion, G. R., and R. Trapp, 2019: The dynamical coupling of convective updrafts, downdrafts, and cold pools in simulated supercell thunderstorms. J. Geophys. Res. Atmos, 124, 664683, https://doi.org/10.1029/2018JD029055.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McCaul, E. W., and M. L. Weisman, 1996: Simulations of shallow supercell storms in landfalling hurricane environments. Mon. Wea. Rev., 124, 408429, https://doi.org/10.1175/1520-0493(1996)124<0408:SOSSSI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., and M. J. Miller, 1976: The dynamics and simulation of tropical cumulonimbus and squall lines. Quart. J. Roy. Meteor. Soc., 102, 373394, https://doi.org/10.1002/qj.49710243208.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., 2016a: Impacts of updraft size and dimensionality on the perturbation pressure and vertical velocity in cumulus convection. Part I: Simple, generalized analytic solutions. J. Atmos. Sci., 73, 14411454, https://doi.org/10.1175/JAS-D-15-0040.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., 2016b: Impacts of updraft size and dimensionality on the perturbation pressure and vertical velocity in cumulus convection. Part II: Comparison of theoretical and numerical solutions and fully dynamical simulations. J. Atmos. Sci., 73, 14551480, https://doi.org/10.1175/JAS-D-15-0041.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., 2017: An analytic description of the structure and evolution of growing deep cumulus updrafts. J. Atmos. Sci., 74, 809834, https://doi.org/10.1175/JAS-D-16-0234.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., and J. M. Peters, 2018: Theoretical expressions for the ascent rate of moist convective thermals. J. Atmos. Sci., 75, 16991719, https://doi.org/10.1175/JAS-D-17-0295.1.

    • Crossref
    • 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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., J. M. Peters, W. M. Hannah, A. C. Varble, and S. E. Giangrande, 2020: Thermal chains and entrainment in cumulus updrafts: Part I: Theoretical description. J. Atmos. Sci., 77, 36373660, https://doi.org/10.1175/JAS-D-19-0243.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morton, B. R., 1957: Buoyant plumes in a moist atmosphere. J. Fluid Mech., 2, 127144, https://doi.org/10.1017/S0022112057000038.

  • Morton, B. R., G. Taylor, and J. S. Turner, 1956: Turbulent gravitational convection from maintained and instantaneous sources. Proc. Roy. Soc. London, 234A, 123, https://doi.org/10.1098/RSPA.1956.0011.

    • Search Google Scholar
    • Export Citation
  • Naylor, J., and M. S. Gilmore, 2012: Convective initiation in an idealized cloud model using an updraft nudging technique. Mon. Wea. Rev., 140, 36993705, https://doi.org/10.1175/MWR-D-12-00163.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nowotarski, C. J., J. M. Peters, and J. P. Mulholland, 2020: Evaluating the effective inflow layer of simulated supercell updrafts. Mon. Wea. Rev., 148, 35073532, https://doi.org/10.1175/MWR-D-20-0013.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peters, J. M., 2016: The impact of effective buoyancy and dynamic pressure forcing on vertical velocities within two-dimensional updrafts. J. Atmos. Sci., 73, 45314551, https://doi.org/10.1175/JAS-D-16-0016.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peters, J. M., C. Nowotarski, and H. Morrison, 2019: The role of vertical wind shear in modulating maximum supercell updraft velocities. J. Atmos. Sci., 76, 31693189, https://doi.org/10.1175/JAS-D-19-0096.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peters, J. M., H. Morrison, W. M. Hannah, A. C. Varble, and S. E. Giangrande, 2020a: Thermal chains and entrainment in cumulus updrafts. Part II: Analysis of idealized simulations. J. Atmos. Sci., 77, 36613681, https://doi.org/10.1175/JAS-D-19-0244.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peters, J. M., C. Nowotarski, and G. Mullendore, 2020b: Are supercells resistant to entrainment because of their rotation? J. Atmos. Sci., 77, 14751495, https://doi.org/10.1175/JAS-D-19-0316.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Romps, D. M., 2010: A direct measure of entrainment. J. Atmos. Sci., 67, 19081927, https://doi.org/10.1175/2010JAS3371.1.

  • Romps, D. M., 2016: The stochastic parcel model: A deterministic parameterization of stochastically entraining convection. J. Adv. Model. Earth Syst., 8, 319344, https://doi.org/10.1002/2015MS000537.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Romps, D. M., and Z. Kuang, 2010: Nature versus nurture in shallow convection. J. Atmos. Sci., 67, 16551666, https://doi.org/10.1175/2009JAS3307.1.

    • 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
  • Rotunno, R., and J. B. Klemp, 1982: The influence of the shear-induced pressure gradient on thunderstorm motion. Mon. Wea. Rev., 110, 136151, https://doi.org/10.1175/1520-0493(1982)110<0136:TIOTSI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rotunno, R., and J. B. Klemp, 1985: On the rotation and propagation of simulated supercell thunderstorms. J. Atmos. Sci., 42, 271292, https://doi.org/10.1175/1520-0469(1985)042<0271:OTRAPO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scorer, R. S., 1957: Experiments on convection of isolated masses in buoyant fluid. J. Fluid Mech., 2, 583594, https://doi.org/10.1017/S0022112057000397.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sherwood, S. C., D. Hernandez-Deckers, and M. Colin, 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., and et al. , 2003: A large eddy simulation intercomparison study of shallow cumulus convection. J. Atmos. Sci., 60, 12011219, https://doi.org/10.1175/1520-0469(2003)60<1201:ALESIS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simpson, J., and V. Wiggert, 1969: Models of precipitating cumulus towers. Mon. Wea. Rev., 97, 471489, https://doi.org/10.1175/1520-0493(1969)097<0471:MOPCT>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, B. T., R. L. Thompson, J. S. Grams, C. Broyles, and H. E. Brooks, 2012: Convective modes for significant severe thunderstorms in the contiguous United States. Part I: Storm classification and climatology. Wea. Forecasting, 27, 11141135, https://doi.org/10.1175/WAF-D-11-00115.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tarshish, N., N. Jeevanjee, and D. Lecoanet, 2018: Buoyant motion of a turbulent thermal. J. Atmos. Sci., 75, 32333244, https://doi.org/10.1175/JAS-D-17-0371.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, R. L., R. Edwards, J. A. Hart, K. L. Elmore, and P. Markowski, 2003: Close proximity soundings within supercell environments obtained from the Rapid Update Cycle. Wea. Forecasting, 18, 12431261, https://doi.org/10.1175/1520-0434(2003)018<1243:CPSWSE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, R. L., C. M. Mead, and R. Edwards, 2007: Effective storm-relative helicity and bulk shear in supercell thunderstorm environments. Wea. Forecasting, 22, 102115, https://doi.org/10.1175/WAF969.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, R. L., B. T. Smith, J. S. Grams, A. R. Dean, and C. Broyles, 2012: Convective modes for significant severe thunderstorms in the contiguous United States. Part II: Supercell and QLCS tornado environments. Wea. Forecasting, 27, 11361154, https://doi.org/10.1175/WAF-D-11-00116.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tian, Y., Z. Kuang, M. S. Singh, and J. Nie, 2019: The vertical momentum budget of shallow cumulus convection: Insights from a Lagrangian perspective. J. Adv. Model. Earth Syst., 11, 113126, https://doi.org/10.1029/2018MS001451.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tochimoto, E., K. Sueeki, and H. Niino, 2019: Entraining cape for better assessment of tornado outbreak potential in the warm sector of extratropical cyclones. Mon. Wea. Rev., 147, 913930, https://doi.org/10.1175/MWR-D-18-0137.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Trapp, R. J., G. R. Marion, and S. W. Nesbitt, 2017: The regulation of tornado intensity by updraft width. J. Atmos. Sci., 74, 41994211, https://doi.org/10.1175/JAS-D-16-0331.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Warner, J., 1970: On steady-state one-dimensional models of cumulus convection. J. Atmos. Sci., 27, 10351040, https://doi.org/10.1175/1520-0469(1970)027<1035:OSSODM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Warren, R. A., H. Richter, H. A. Ramsay, S. T. Siems, and M. J. Manton, 2017: Impact of variations in upper-level shear on simulated supercells. Mon. Wea. Rev., 145, 26592681, https://doi.org/10.1175/MWR-D-16-0412.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weisman, M. L., and J. B. Klemp, 1982: The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon. Wea. Rev., 110, 504520, https://doi.org/10.1175/1520-0493(1982)110<0504:TDONSC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weisman, M. L., and J. B. Klemp, 1984: The structure and classification of numerically simulated convective storms in directionally varying wind shears. Mon. Wea. Rev., 112, 24792498, https://doi.org/10.1175/1520-0493(1984)112<2479:TSACON>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weisman, M. L., and R. Rotunno, 2000: The use of vertical wind shear versus helicity in interpreting supercell dynamics. J. Atmos. Sci., 57, 14521472, https://doi.org/10.1175/1520-0469(2000)057<1452:TUOVWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G. J., 2009: Effects of entrainment on convective available potential energy and closure assumptions in convection parameterization. J. Geophys. Res., 114, D07109, https://doi.org/10.1029/2008JD010976.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G. J., and N. A. McFarlane, 1991: Convective stabilization in midlatitudes. Mon. Wea. Rev., 119, 19151928, https://doi.org/10.1175/1520-0493(1991)119<1915:CSIM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G. J., and N. A. McFarlane, 1995: Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian Climate Center general-circulation model. Atmos.–Ocean, 33, 407446, https://doi.org/10.1080/07055900.1995.9649539.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, M., and P. H. Austin, 2003: Episodic mixing and buoyancy-sorting representations of shallow convection: A diagnostic study. J. Atmos. Sci., 60, 892912, https://doi.org/10.1175/1520-0469(2003)060<0892:EMABSR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
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A Formula for the Maximum Vertical Velocity in Supercell Updrafts

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  • 1 Department of Meteorology, Naval Postgraduate School, Monterey, California
  • | 2 National Center for Atmospheric Research, Boulder, Colorado
  • | 3 Climate Change Research Centre, University of New South Wales, Sydney, New South Wales, Australia
  • | 4 Australian Research Council Centre for Excellence in Climate System Science, University of New South Wales, Sydney, New South Wales, Australia
  • | 5 Department of Atmospheric Sciences, Texas A&M University, College Station, Texas
  • | 6 NOAA/NWS/NCEP/Storm Prediction Center, Norman, Oklahoma
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Abstract

In supercell environments, previous authors have shown strong connections between the vertical wind shear magnitude, updraft width, and entrainment. Based on these results, it is hypothesized that the influences of entrainment-driven dilution on buoyancy and maximum updraft vertical velocity w in supercell environments are a predictable function of the vertical wind shear profile. It is also hypothesized that the influences of pressure perturbation forces on maximum updraft w are small because of a nearly complete offset between upward dynamic pressure forces and downward buoyant pressure forces. To address these hypotheses, we derive a formula for the maximum updraft w that incorporates the effects of entrainment-driven dilution on buoyancy but neglects pressure gradient forces. Solutions to this formula are compared with output from previous numerical simulations. This formula substantially improves predictions of maximum updraft w over past CAPE-derived formulas for maximum updraft w, which supports the first hypothesis. Furthermore, integrated vertical accelerations along trajectories show substantial offsets between dynamic and buoyant pressure forces, supporting the second hypothesis. It is argued that the new formula should be used in addition to CAPE-derived measures for w in forecast and research applications when accurate diagnosis of updraft speed is required.

© 2020 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: J. Peters, jmpeters@nps.edu

Abstract

In supercell environments, previous authors have shown strong connections between the vertical wind shear magnitude, updraft width, and entrainment. Based on these results, it is hypothesized that the influences of entrainment-driven dilution on buoyancy and maximum updraft vertical velocity w in supercell environments are a predictable function of the vertical wind shear profile. It is also hypothesized that the influences of pressure perturbation forces on maximum updraft w are small because of a nearly complete offset between upward dynamic pressure forces and downward buoyant pressure forces. To address these hypotheses, we derive a formula for the maximum updraft w that incorporates the effects of entrainment-driven dilution on buoyancy but neglects pressure gradient forces. Solutions to this formula are compared with output from previous numerical simulations. This formula substantially improves predictions of maximum updraft w over past CAPE-derived formulas for maximum updraft w, which supports the first hypothesis. Furthermore, integrated vertical accelerations along trajectories show substantial offsets between dynamic and buoyant pressure forces, supporting the second hypothesis. It is argued that the new formula should be used in addition to CAPE-derived measures for w in forecast and research applications when accurate diagnosis of updraft speed is required.

© 2020 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: J. Peters, jmpeters@nps.edu
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