• Bryan, G. H., , and J. M. Fritsch, 2000: Moist absolute instability: The sixth static stability state. Bull. Amer. Meteor. Soc., 81, 12071230.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., , and M. D. Parker, 2010: Observations of a squall line and its near environment using high-frequency rawinsonde launches during VORTEX2. Mon. Wea. Rev., 138, 40764097.

    • 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.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Chou, M.-D., 1990: Parameterization for the absorption of solar radiation by O2 and CO2 with application to climate studies. J. Climate, 3, 209217.

    • Search Google Scholar
    • Export Citation
  • Chou, M.-D., 1992: A solar radiation model for climate studies. J. Atmos. Sci., 49, 762772.

  • Chou, M.-D., , M. J. Suarez, , C.-H. Ho, , M. M.-H. Yan, , and K.-T. Lee, 1998: Parameterizations for cloud overlapping and shortwave single scattering properties for use in general circulation and cloud ensemble models. J. Climate, 11, 202214.

    • Search Google Scholar
    • Export Citation
  • Chou, M.-D., , K.-T. Lee, , S.-C. Tsay, , and Q. Fu, 1999: Parameterization for cloud longwave scattering for use in atmospheric models. J. Climate, 12, 159169.

    • Search Google Scholar
    • Export Citation
  • Coniglio, M. C., , and D. J. Stensrud, 2001: Simulation of a progressive derecho using composite initial conditions. Mon. Wea. Rev., 129, 15931616.

    • Search Google Scholar
    • Export Citation
  • Coniglio, M. C., , D. J. Stensrud, , and M. B. Richman, 2004: An observational study of derecho-producing convective systems. Wea. Forecasting, 19, 320337.

    • Search Google Scholar
    • Export Citation
  • Coniglio, M. C., , D. J. Stensrud, , and L. J. Wicker, 2006: Effects of upper-level shear on the structure and maintenance of strong quasi-linear mesoscale convective systems. J. Atmos. Sci., 63, 12311252.

    • Search Google Scholar
    • Export Citation
  • Coniglio, M. C., , S. F. Corfidi, , and J. S. Kain, 2012: Views on applying RKW theory: An illustration using the 8 May 2009 derecho-producing convective system. Mon. Wea. Rev., 140, 10231043.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R. P., , R. J. Trapp, , and H. B. Bluestein, 2001: Tornadoes and tornadic storms. Severe Convective Storms, Meteor. Monogr., No. 50, Amer. Meteor. Soc., 167–221.

  • Dawson, D. T., II, , M. Xue, , J. A. Milbrandt, , and M. K. Yau, 2010: Comparison of evaporation and cold pool development between single-moment and multimoment bulk microphysics schemes in idealized simulations of tornadic thunderstorms. Mon. Wea. Rev., 138, 11521171.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1972: Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci., 29, 91115.

  • Doswell, C. A., III, , and D. W. Burgess, 1993: Tornadoes and tornadic storms: A review of conceptual models. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., Vol. 79, Amer. Geophys. Union, 161–172.

  • Evans, J. S., , and C. A. Doswell III, 2001: Examination of derecho environments using proximity soundings. Wea. Forecasting, 16, 329342.

    • Search Google Scholar
    • Export Citation
  • Fovell, R. G., 2002: Upstream influence of numerically simulated squall-line storms. Quart. J. Roy. Meteor. Soc., 128, 893912.

  • Frame, J. W., , and P. M. Markowski, 2010: Numerical simulations of radiative cooling beneath the anvils of supercell thunderstorms. Mon. Wea. Rev., 138, 30243047.

    • Search Google Scholar
    • Export Citation
  • Frame, J. W., , P. M. Markowski, , and J. Petters, 2008: The dynamical influences of cloud shading on simulated supercell thunderstorms. Preprints, 24th Conf. on Severe Local Storms, Savannah, GA, Amer. Meteor. Soc., 17B.1. [Available online at https://ams.confex.com/ams/24SLS/techprogram/paper_141832.htm.]

  • Frame, J. W., , J. L. Petters, , P. M. Markowski, , and J. Y. Harrington, 2009: An application of the tilted independent pixel approximation to cumulonimbus environments. Atmos. Res., 91, 127136.

    • Search Google Scholar
    • Export Citation
  • Gilmore, M. S., , J. M. Straka, , and E. N. Rasmussen, 2004a: Precipitation and evolution sensitivity in simulated deep convective storms: Comparisons between liquid-only and simple ice and liquid phase microphysics. Mon. Wea. Rev., 132, 18971916.

    • Search Google Scholar
    • Export Citation
  • Gilmore, M. S., , J. M. Straka, , and E. N. Rasmussen, 2004b: Precipitation uncertainty due to variations in precipitation particle parameters within a simple microphysics scheme. Mon. Wea. Rev., 132, 26102627.

    • Search Google Scholar
    • Export Citation
  • Houze, R. A., Jr., 2004: Mesoscale convective systems. Rev. Geophys., 42, 143.

  • James, R. P., , P. M. Markowski, , and J. M. Fritsch, 2006: Bow echo sensitivity to low-level moisture. Mon. Wea. Rev., 134, 950964.

  • Klemp, J. B., , and R. Rotunno, 1983: A study of the tornadic region within a supercell thunderstorm. J. Atmos. Sci., 40, 359377.

  • Markowski, P. M., , and J. Y. Harrington, 2005: A simulation of a supercell thunderstorm with emulated radiative cooling beneath the anvil. J. Atmos. Sci., 62, 26072617.

    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., , E. N. Rasmussen, , J. M. Straka, , and D. C. Dowell, 1998: Observations of low-level baroclinity generated by anvil shadows. Mon. Wea. Rev., 126, 29592971.

    • Search Google Scholar
    • Export Citation
  • Morrison, H., , and J. Milbrandt, 2011: Comparison of two-moment bulk microphysics schemes in idealized supercell thunderstorm simulations. Mon. Wea. Rev., 139, 11031130.

    • Search Google Scholar
    • Export Citation
  • Noilhan, J., , and S. Planton, 1989: A simple parameterization of land surface processes for meteorological models. Mon. Wea. Rev., 117, 536549.

    • Search Google Scholar
    • Export Citation
  • Nowotarski, C., , P. Markowski, , Y. Richardson, , and G. Bryan, 2011: Interactions between simulated supercell thunderstorms and dry boundary layer convection. Preprints, 14th Conf. on Mesoscale Processes, Los Angeles, CA, Amer. Meteor. Soc., 7.3. [Available online at https://ams.confex.com/ams/14Meso15ARAM/techprogram/paper_190799.htm.]

  • Orlanski, I., 1976: A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys., 21, 251269.

  • Parker, M. D., 2008: Response of simulated squall lines to low-level cooling. J. Atmos. Sci., 65, 13231341.

  • Parker, M. D., , and R. H. Johnson, 2000: Organizational modes of midlatitude mesoscale convective systems. Mon. Wea. Rev., 128, 34133436.

    • Search Google Scholar
    • Export Citation
  • Parker, M. D., , and R. H. Johnson, 2004: Structure and dynamics of quasi-2D mesoscale convective systems. J. Atmos. Sci., 61, 545567.

  • Pleim, J. E., , and A. Xiu, 1995: Development and testing of a surface flux and planetary boundary layer model for application in mesoscale models. J. Appl. Meteor., 34, 1632.

    • Search Google Scholar
    • Export Citation
  • Rosenfeld, D., and Coauthors, 2011: Glaciation temperatures of convective clouds ingesting desert dust, air pollution and smoke from forest fire. Geophys. Res. Lett., 38, L21804, doi:10.1029/2011GL049423.

    • 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.

    • 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, 463485.

  • Schultz, P., 1995: An explicit cloud physics parameterization for operational numerical weather prediction. Mon. Wea. Rev., 123, 33313343.

    • Search Google Scholar
    • Export Citation
  • Seigel, R. B., , and S. C. van den Heever, 2012: Dust lofting and ingestion by supercell storms. J. Atmos. Sci., 69, 14531473.

  • Stensrud, D. J., , M. C. Coniglio, , R. Davies-Jones, , and J. Evans, 2005: Comments on “‘A theory for strong, long-lived squall lines’ revisited.” J. Atmos. Sci., 62, 29892996.

    • Search Google Scholar
    • Export Citation
  • Storer, R. L., , S. C. van den Heever, , and G. L. Stephens, 2010: Modeling aerosol impacts on convective storms in different environments. J. Atmos. Sci., 67, 39043915.

    • Search Google Scholar
    • Export Citation
  • Sun, W.-Y., , and C.-Z. Chang, 1986: Diffusion model for a convective layer. Part I: Numerical simulation of a convective boundary layer. J. Climate Appl. Meteor., 25, 14451453.

    • Search Google Scholar
    • Export Citation
  • Tao, W.-K., , S. Lang, , J. Simpson, , C.-H. Sui, , B. Ferrier, , and M.-D. Chou, 1996: Mechanisms of cloud radiation interaction in the tropics and midlatitudes. J. Atmos. Sci., 53, 26242651.

    • Search Google Scholar
    • Export Citation
  • Trapp, R. J., , and M. L. Weisman, 2003: Low-level mesovortices within squall lines and bow echoes. Part II: Their genesis and implications. Mon. Wea. Rev., 131, 28042823.

    • Search Google Scholar
    • Export Citation
  • Van Weverberg, K., , A. M. Vogelmann, , H. Morrison, , and J. Milbrandt, 2012: Sensitivity of idealized squall line simulations to the level of complexity used in two-moment bulk microphysics schemes. Mon. Wea. Rev., 140, 18831907.

    • Search Google Scholar
    • Export Citation
  • Varnai, T., , and R. Davies, 1999: Effects of cloud heterogeneities on shortwave radiation: Comparison of cloud-top variability and internal heterogeneity. J. Atmos. Sci., 56, 42064224.

    • Search Google Scholar
    • Export Citation
  • Wapler, K., , and B. Meyer, 2008: A fast three-dimensional approximation for the calculation of surface irradiance in large-eddy simulation models. J. Appl. Meteor. Climatol., 47, 30613071.

    • Search Google Scholar
    • Export Citation
  • Weisman, M. L., 1992: The role of convectively generated rear-inflow jets in the evolution of long-lived mesoconvective systems. J. Atmos. Sci., 49, 18261847.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Weisman, M. L., , and C. A. Davis, 1998: Mechanisms for the generation of mesoscale vortices within quasi-linear convective systems. J. Atmos. Sci., 55, 26032622.

    • 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.

  • Weisman, M. L., , and R. Rotunno, 2005: Reply. J. Atmos. Sci., 62, 29973002.

  • Weisman, M. L., , W. C. Skamarock, , and J. B. Klemp, 1997: The resolution dependence of explicitly modeled convective systems. Mon. Wea. Rev., 125, 527548.

    • Search Google Scholar
    • Export Citation
  • Xue, M., , K. K. Droegemeier, , V. Wong, , A. Shapiro, , and K. Brewster, 1995: ARPS version 4.0 user’s guide. Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, OK, 380 pp.

  • Xue, M., , K. K. Droegemeier, , and V. Wong, 2000: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction tool. Part I: Model dynamics and verification. Meteor. Atmos. Phys., 75, 161193.

    • 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, 143166.

    • Search Google Scholar
    • Export Citation
  • Xue, M., , D.-H. Wang, , J.-D. Gao, , K. Brewster, , and K. K. Droegemeier, 2003: The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation. Meteor. Atmos. Phys., 82, 139170.

    • Search Google Scholar
    • Export Citation
  • Ziegler, C. L., , E. R. Mansell, , J. M. Straka, , D. R. MacGorman, , and D. W. Burgess, 2010: The impact of spatial variations of low-level stability on the life cycle of a simulated supercell storm. Mon. Wea. Rev., 138, 17381766.

    • Search Google Scholar
    • Export Citation
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    (a) The 1200 LST sounding used to initialize the numerical simulations. The dashed curve represents the path of a parcel lifted dry adiabatically from the surface to its saturation point and pseudoadiabatically thereafter. (b)–(e) Zoomed view of the soundings at 1200, 1400, 1600, and 1900 LST (1800, 2000, 2200, and 0100 UTC) in the sunny environment well east of the convection (x = 1100 km) in the CONTROL-EAST simulation. The evolution is similar in the other simulations.

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    (a) The vertical wind profiles used to initialize the EAST and WEST simulations. Markers are placed along each simulated profile at every grid level. (b) The low-level vertical wind profiles at 1400 LST (2000 UTC; t = 2 h) in the sunny environment well east of the convection (x = 1100 km) in the CONTROL-EAST and CONTROL-WEST simulations (the wind profiles in the far-field environment in the SHADING simulations are practically identical).

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    (a) Time series of latitudinally averaged 5-m air temperature (°C) at x = 300 km in the SHADING-EAST simulation with and without the optical thickness of the anvil being artificially enhanced, and in the sunny far-field environment well east of the convection (x = 1100 km). Anvil shading begins at 1400 LST (2000 UTC) and the gust front arrives at 1715 LST (2315 UTC). The time series of 3-m air temperature observed at Cherokee, Oklahoma, in the 15 May 2009 squall line case documented by BP10 also is overlaid (cf. their Fig. 5a). Anvil shading began at 2145 UTC and the gust front arrived at 2320 UTC. (b) Time series of latitudinally averaged shortwave radiation (W m2) for the same numerical simulation and at the same locations as in (a). As in (a), the time series obtained at Cherokee on 15 May 2009 also is shown (cf. BP10’s Fig. 5e). (c) Vertical profiles of latitudinally averaged potential temperature (K) at 1700 LST (2300 UTC) at x = 300 km (just ahead of the gust front), and in the sunny far-field environment well east of the convection (x = 1100 km), for the same numerical simulations as in (a) and (b). Markers are placed along each simulated profile at every grid level. The profiles obtained from soundings documented by BP10 also are shown at approximately the same times, approximately 20 km ahead of the gust front of the 15 May 2009 squall line, and in the sunny far-field environment (these are the soundings identified by BP10 as S4 and S1, respectively). (d) Visible satellite image at 2139 UTC 15 May 2009 showing the location of Cherokee relative to the squall line documented by BP10 (after BP10’s Fig. 6).

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    The prognosed cloud ice qi passed to the radiative transfer subroutines was artificially augmented. The augmentation was designed to increase the optical thickness of the thin cirrus in the model in order to obtain a reduction in shortwave radiation and low-level cooling that better agrees with the shortwave radiation attenuation and cooling observed beneath the anvils of midlatitude convective storms in past studies. The solid line shows as a function of qi; the dashed line is . The units of both variables are kg kg−1.

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    Horizontal cross sections of total hydrometeor mixing ratio qh (rain, hail, and snow) at z = 1 km (color shading; see legend) and select vertical velocity contours (black; the 10, 30, and 50 m s−1 isotachs are shown) at z = 7.5 km in the CONTROL and SHADING simulations initialized with the EAST and WEST vertical wind profiles at t = 5 h [1700 LST (2300 UTC)]. The θ′ = −4 K isentrope at the lowest grid level also is shown (white dashed line); it indicates the approximate location of the gust front. Axis labels indicate the x and y coordinates in kilometers.

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    (a),(b) Vertical cross sections of meridionally averaged total hydrometeor mixing ratio qh (rain, hail, and snow; color shading) at t = 5 h [1700 LST (2300 UTC)] in the CONTROL and SHADING simulations with the EAST environmental wind profile. The white contour encloses the meridionally averaged cloud boundary. The region enclosed by the black box is shown in (c) and (d). Axis labels indicate the x and z coordinates in kilometers. (c),(d) Zoomed view of the region outlined in (a),(b), showing meridionally averaged potential temperature perturbation θ′ (color shading) and select isotachs of meridionally averaged vertical velocity w and system-relative zonal wind usr. Potential temperature perturbations are defined relative to the meridionally averaged potential temperature at the eastern boundary of the model domain. The w contours are black and shown for w = 2, 4, 6, 8, … m s−1; the usr contours are white and shown for usr = 0, 2, 4, 6, 8, … m s−1 (though only below 8 km; i.e., the contouring of usr is suppressed in the anvil region in the interest of figure clarity). Axis labels indicate the x and z coordinates in kilometers.

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    As in Fig. 6, but for the CONTROL and SHADING simulations with the WEST environmental wind profile.

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    (a),(b) Hovmöller diagram of meridionally averaged potential temperature θ at z = 5 m (the lowest scalar grid level). Axis labels indicate time (ordinate) and the x coordinate (km; abscissa). Note that the color scale is nonlinear, with increased resolution for θ > 300 K in order to emphasize the cooling owing to the anvil shading. The meridionally averaged cloud boundary at z = 10 km is indicate with the white line. The filled circles indicate the locations of the vertical profiles shown in Fig. 10. (c),(d) As in (a)–(b), but TKE at z = 300 m is shown.

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    As in Fig. 8, but for the CONTROL and SHADING simulations with the WEST environmental wind profile. The filled circles indicate the locations of the vertical profiles shown in Fig. 11.

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    Vertical profiles of (a) meridionally averaged potential temperature θ (K) and (b) meridionally averaged zonal wind u (m s−1) in the lowest 2500 m at t = 5 h [1700 LST (2300 UTC)] in the CONTROL (black) and SHADING (gray) simulations with the EAST environmental wind profile. Profiles are shown (left to right) 10, 50, 100, and 150 km east of the gust front. Black (gray) square markers indicate the zonal wind at the lowest grid level (z = 5 m) in the CONTROL (SHADING) simulation (without the markers it is difficult to see the differences in the wind profiles near the surface). The locations of the vertical θ and u profiles are indicated with filled circles in Fig. 8.

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    As in Fig. 10, but for the CONTROL and SHADING simulations with the WEST environmental wind profile. The locations of the profiles are indicated with filled circles in Fig. 9.

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    Time series of the w = 10 m s−1 isosurface volume for the CONTROL and SHADING simulations with the (a) EAST and (b) WEST environmental wind profiles.

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    Net positive area (CAPE − CIN) of the inflow soundings east of the gust front for the CONTROL and SHADING simulations with the (a) EAST and (b) WEST environmental wind profiles at t = 5 h [1700 LST (2300 UTC)]. The net positive area was computed by lifting an air parcel from the surface dry adiabatically to its saturation point and pseudoadiabatically thereafter.

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    (a),(c) Evolution of the cold pool parameter c (solid traces) and 0–2.5-km bulk environmental vertical wind shear Δu (dashed traces) for 1300–1900 LST (1900–0100 UTC), or t = 1–7 h (the first hour is not shown because c is influenced by the initial cold block rather than a precipitating convective system during this early time period), in the CONTROL (black) and SHADING (gray) simulations using the EAST and WEST environmental wind profiles, respectively. See section 3 for details regarding how c and Δu were computed. (b),(d) The quantity cu in the same time period in the simulations using the EAST and WEST environmental wind profiles, respectively.

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    Meridionally and vertically averaged (a)–(c) meridional vorticity 〈η〉, (d)–(f) meridional baroclinic vorticity generation 〈−∂B/∂x〉, (g)–(i) meridional vorticity tendency owing to turbulent mixing 〈j · × F〉, and (j)–(l) 〈−∂B/∂x〉 + 〈 j · × F 〉 at t = 5 h [1700 LST (2300 UTC)] east of the gust front for the CONTROL and SHADING simulations initialized with the EAST environmental wind profile. (left to right) Vertically averaged quantities in the 0–2.5-km, 0–1-km, and 1–2.5-km layers.

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    As in Fig. 15, but for the simulations initialized with the WEST environmental wind profile.

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    Zonally averaged 〈−∂B/∂x〉 (unshaded bars), 〈 j · × F 〉 (shaded bars), and 〈−∂B/∂x〉 + 〈 j · × F 〉 (striped bars) at t = 5 h [1700 LST (2300 UTC)] in the CONTROL (black) and SHADING (gray) simulations initialized with the (a)–(c) EAST and (d)–(f) WEST environmental wind profiles. The horizontal averages are from within the region of anvil shading; that is, from within the region 0–210 km east of the gust front in (a)–(c) and 0–160 km east of the gust front in (d)–(f), per the vertical dashed lines in Figs. 15 and 16 that indicate the locations where shading begins. (left to right) The 0–2.5-km, 0–1-km, and 1–2.5-km layers.

  • View in gallery

    (a) Zonal variation in meridionally averaged shortwave radiation in the CONTROL-EAST, SHADING-EAST, and INFLOWSHADING-EAST simulations at 1700 LST (t = 5 h). (b) As in Fig. 6d, but for the INFLOWSHADING-EAST simulation at 1700 LST (t = 5 h). (c) As in Fig. 14a, but the traces of c and Δu from Fig. 14a are gray, and c and Δu in the INFLOWSHADING-EAST simulation are indicated using the black solid and dashed curves, respectively. (d) As in Fig. 14b, but the traces of cu from Fig. 14b are gray, and cu in the INFLOWSHADING-EAST simulation [cf. (c)] is indicated with a black curve.

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    (a) Schematic illustration of the effects of anvil shading on the environmental vertical shear (horizontal vorticity) in the 0–2.5-km layer owing to baroclinic vorticity generation. The squall line is moving toward the east (right). (b),(c) As in (a), but for changes in the environmental vertical shear (horizontal vorticity) in the 0–2.5-km layer owing to decreased vertical mixing. Both (b) easterly and (c) westerly near-surface wind (and wind shear) scenarios are shown.

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A Numerical Simulation Study of the Effects of Anvil Shading on Quasi-Linear Convective Systems

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  • 1 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania
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Abstract

Numerical simulations are used to investigate how the attenuation of solar radiation by the intervening cumulonimbus cloud, particularly its large anvil, affects the structure, intensity, and evolution of quasi-linear convective systems and the sensitivity of the effects of this “anvil shading” to the ambient wind profile. Shading of the pre-gust-front inflow environment (as opposed to shading of the cold pool) has the most important impact on the convective systems. The magnitude of the low-level cooling, associated baroclinicity, and stabilization of the pre-gust-front environment due to anvil shading generally increases as the duration of the shading increases. Thus, for a given leading anvil length, a slow-moving convective system tends to be affected more by anvil shading than does a fast-moving convective system. Differences in the forward speeds of the convective systems simulated in this study are largely attributable to differences in the mean environmental wind speed over the depth of the troposphere.

Anvil shading reduces the buoyancy realized by the air parcels that ascend through the updrafts. As a result, anvil shading contributes to weaker updrafts relative to control simulations in which clouds are transparent to solar radiation. Anvil shading also affects the convective systems by modifying the low-level (nominally 0–2.5 km AGL) vertical wind shear in the pre-gust-front environment. The shear modifications affect the slope of the updraft region and system-relative rear-to-front flow, and the sign of the modifications is sensitive to the ground-relative vertical wind profile in the far-field environment. The vertical wind shear changes are brought about by baroclinic vorticity generation associated with the horizontal buoyancy gradient that develops in the shaded boundary layer (which makes the pre-gust-front, low-level vertical wind shear less westerly) and by a reduction of the vertical mixing of momentum due to the near-surface (nominally 0–300 m AGL) stabilization that accompanies the shading-induced cooling. The reduced mixing makes the pre-gust-front, low-level vertical shear more (less) westerly if the ambient, near-surface wind and wind shear are westerly (easterly).

Corresponding author address: Dr. Paul Markowski, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: pmarkowski@psu.edu

Abstract

Numerical simulations are used to investigate how the attenuation of solar radiation by the intervening cumulonimbus cloud, particularly its large anvil, affects the structure, intensity, and evolution of quasi-linear convective systems and the sensitivity of the effects of this “anvil shading” to the ambient wind profile. Shading of the pre-gust-front inflow environment (as opposed to shading of the cold pool) has the most important impact on the convective systems. The magnitude of the low-level cooling, associated baroclinicity, and stabilization of the pre-gust-front environment due to anvil shading generally increases as the duration of the shading increases. Thus, for a given leading anvil length, a slow-moving convective system tends to be affected more by anvil shading than does a fast-moving convective system. Differences in the forward speeds of the convective systems simulated in this study are largely attributable to differences in the mean environmental wind speed over the depth of the troposphere.

Anvil shading reduces the buoyancy realized by the air parcels that ascend through the updrafts. As a result, anvil shading contributes to weaker updrafts relative to control simulations in which clouds are transparent to solar radiation. Anvil shading also affects the convective systems by modifying the low-level (nominally 0–2.5 km AGL) vertical wind shear in the pre-gust-front environment. The shear modifications affect the slope of the updraft region and system-relative rear-to-front flow, and the sign of the modifications is sensitive to the ground-relative vertical wind profile in the far-field environment. The vertical wind shear changes are brought about by baroclinic vorticity generation associated with the horizontal buoyancy gradient that develops in the shaded boundary layer (which makes the pre-gust-front, low-level vertical wind shear less westerly) and by a reduction of the vertical mixing of momentum due to the near-surface (nominally 0–300 m AGL) stabilization that accompanies the shading-induced cooling. The reduced mixing makes the pre-gust-front, low-level vertical shear more (less) westerly if the ambient, near-surface wind and wind shear are westerly (easterly).

Corresponding author address: Dr. Paul Markowski, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: pmarkowski@psu.edu

1. Introduction

Serendipitous observations obtained from soundings launched within the shadows cast by the anvils of long-lived convective storms, which occasionally can extend for hundreds of kilometers downstream, have revealed low-level cooling and stabilization owing to the attenuation of solar radiation (e.g., Markowski et al. 1998; Bryan and Parker 2010, hereafter BP10). Near-surface air can cool by several degrees Celsius, and the superadiabatic surface layer that typifies the sunny far field is stabilized beneath the anvil. The present study is part of an ongoing numerical investigation into the dynamical effects of the low-level cooling and stabilization on the convective storms. Radiative transfer effects are usually excluded from numerical simulation studies designed to investigate “leading order” dynamical processes in storms (e.g., supercell rotation and propagation, squall line maintenance). Lengthy reviews of the topic have been written by Markowski and Harrington (2005) and Frame and Markowski (2010).

The first numerical studies designed to examine the dynamical effects of anvil shading on convective storms and their environments focused on supercells, because of their long, optically thick anvils; their longevity; and the potential importance of environmental vorticity modifications (Markowski and Harrington 2005; Frame et al. 2008, 2009; Frame and Markowski 2010). A mesocyclone is one of the defining characteristics of a supercell (e.g., Doswell and Burgess 1993), and the vertical vorticity of a mesocyclone results from the tilting of horizontal vorticity in the inflow (Davies-Jones et al. 2001). Our research was initially motivated by the possibility that a horizontal temperature gradient along the edge of a cloud shadow might be capable of generating significant horizontal vorticity baroclinically (Markowski et al. 1998). What we found instead was that the primary effect of the low-level cooling was an increase in the low-level shear within the cloud shadow due to the low-level stabilization and reduction in vertical mixing (Frame et al. 2008). Depending on the orientation of the enhanced low-level shear relative to the orientation of the storm’s gust fronts, the gust-front updrafts and storm-relative motion of the gust fronts could be altered (Rotunno et al. 1988, hereafter RKW88). For example, in the case of ambient low-level vertical wind shear having an easterly component, the eastward-moving rear-flank gust front of a simulated supercell had a strong tendency to accelerate and undercut the midlevel updraft when anvil shading reduced vertical mixing and enhanced the easterly component of the shear at low levels. Another aspect of the supercell simulations that included anvil shading was that the forward-flank baroclinic zone became more diffuse (i.e., the horizontal buoyancy gradient weakened). The forward-flank baroclinic zone has been shown to be an important source of horizontal vorticity, and ultimately the circulation of the low-level mesocyclone in simulated supercells (Klemp and Rotunno 1983; Rotunno and Klemp 1985). The weakening of this baroclinicity generally led to weaker low-level mesocyclones (in terms of both vertical vorticity and circulation) in simulations in which anvil shading was included.

The present study extends the prior work of Markowski and Harrington (2005) and Frame and Markowski (2010) to larger-scale convective systems—specifically, the quasi-linear, multicellular variety that is sustained by the nearly continuous generation of new cells by the downshear gust front. Both the strength of the cold pool and magnitude of the environmental wind shear—equal to the magnitude of the environmental horizontal vorticity if the environment has no horizontal gradients of vertical velocity—especially at low levels, influence the structure and evolution of such gust-front-driven squall lines (e.g., RKW88). The cold pool and pre-gust-front vertical shear both potentially could be influenced by anvil shading. Most squall lines possess extensive trailing regions of cloudiness and precipitation [e.g., Houze (2004) and references therein]. Moreover, significant shading can occur ahead of a squall line when the leading anvil is significant (e.g., BP10). The present study uses a suite of three-dimensional numerical simulations to address the following questions:

  • What are the bulk differences in the structure, intensity, and evolution of squall lines that are simulated with and without the effects of anvil shading, and how do the differences depend on the environmental wind profile?
  • What processes attributable to anvil shading modify the vertical wind shear ahead of the gust front, and to what degree does anvil shading influence the cold pool?

The design of the numerical simulation experiments is described in section 2. The results are presented in section 3 and discussed in section 4. Concluding remarks appear in section 5.

2. Methods

a. Model and domain configuration

The simulations were run using the Advanced Regional Prediction System (ARPS), version 5.1.5 (Xue et al. 1995, 2000, 2001, 2003), developed by the Center for Analysis and Prediction of Storms (CAPS) and the University of Oklahoma. The computational grid is centered at −100° longitude and 36° latitude (the western Oklahoma border). The grid has a uniform horizontal spacing of 1 km within a 1200–1400 km × 60 km × 18 km domain, with 75 levels in the vertical. The vertical grid is stretched, with a minimum spacing of 10 m at the lowest scalar level (z = 5 m) and a maximum spacing of 497 m at the top boundary. The simulations span 7 h from 1800–0100 UTC (1200–1900 LST) on 20 May (sunset occurs at 0140 UTC). The large (small) time step is 3 s (0.5 s).

A translating grid cannot easily be employed while also including radiative effects. Therefore, the cross-line dimension of the domain has to be relatively large—large enough to accommodate the eastward motion of the convective system over the relatively long 7-h simulations, as well as a long (~200 km) leading anvil. The cross-line dimension is smallest (1200 km) in the simulations in which the convection has the slowest eastward motion (the simulations having the slowest environmental mean wind speed), and largest (1400 km) in the simulations in which the convection has the fastest eastward motion (the simulations having the fastest environmental mean wind speed).

Open radiative boundary conditions are specified along the western and eastern sides of the domain following Orlanski (1976). The relaxation coefficient (Xue et al. 1995, 161–162) is set to zero in order to avoid generating artificial gradients of momentum, heat, and moisture near the west and east boundaries. A periodic boundary condition is applied along the northern and southern sides of the domain. A rigid lid exists at the top of the domain, and a Rayleigh sponge layer occupies the uppermost 5 km of the domain in order to damp vertically propagating gravity waves. Despite the duration of the simulations, the Coriolis force is excluded in order to keep the study as simple as possible. Though the Coriolis acceleration is known to influence the development of meso-β-scale bookend vortices (e.g., Weisman and Davis 1998) and meso-γ-scale gust-front vortices (Trapp and Weisman 2003), our focus is on the two-dimensional structure of the convective systems. Bookend vortices are precluded by the periodic boundary conditions along the northern and southern boundaries, and gust-front vortices are virtually nonexistent, presumably because two-dimensionality is so strongly favored by the two-dimensional environmental wind profile and initiation mechanism (to be explained below).

The simulations use the microphysics parameterization of Schultz (1995), which includes five categories of condensate: liquid cloud water, cloud ice, rain, snow, and hail/graupel. Radiative transfer processes are parameterized using the National Aeronautics and Space Administration (NASA) Goddard Cumulus Ensemble radiative transfer model (Chou 1990, 1992; Tao et al. 1996; Chou et al. 1998, 1999). To capture the effects of shortwave radiation along a slantwise path based on a varying zenith angle, the tilted independent pixel approximation (TIPA; Varnai and Davies 1999) is employed, following Frame et al. (2009)1 and Frame and Markowski (2010).

Eddy viscosities are determined from the prognosed turbulent kinetic energy (TKE) and a mixing length scale (Deardorff 1972), with the vertical mixing length scale being dependent on the boundary layer depth following the approach of Sun and Chang (1986). In the ARPS implementation, the boundary layer depth is determined from the height at which a parcel lifted from the surface layer becomes neutrally buoyant. The boundary layer evolution in the simulations conducted herein (1-km horizontal grid spacing) compares well with the evolution in supplemental simulations conducted in a smaller domain (20 km × 20 km) with a 100-m horizontal grid spacing, in which dry convective motions are explicitly resolved (not shown; storms were not initiated in these simulations).

Surface fluxes are computed using bulk aerodynamic formulae, with stability-dependent surface drag coefficients and predicted surface volumetric water content and temperature. The soil model is a two-layer force restore model adapted from Noilhan and Planton (1989). Additional details appear in Table 1 and in Frame and Markowski (2010).

Table 1.

Physical and computational parameters used in the numerical simulations.

Table 1.

b. Simulation design

The simulations are initialized at 1200 LST with a horizontally homogeneous environment characterized by the thermodynamic profile shown in Fig. 1a, which is a modified version of the idealized sounding used by Weisman and Klemp (1982). The sounding is typical of that found on the U.S. Great Plains on a day that supports the development of convective storms, though the midtropospheric relative humidity is higher than that usually observed on proximity soundings obtained in Great Plains severe storm environments.2 At 1200 LST, the environment has a convective available potential energy (CAPE) of 2342 J kg−1 and convective inhibition (CIN) of 49 J kg−1.3 Over the first few hours of the simulation, the boundary layer warms and deepens, CAPE increases, and CIN decreases (Figs. 1b–d).

Fig. 1.
Fig. 1.

(a) The 1200 LST sounding used to initialize the numerical simulations. The dashed curve represents the path of a parcel lifted dry adiabatically from the surface to its saturation point and pseudoadiabatically thereafter. (b)–(e) Zoomed view of the soundings at 1200, 1400, 1600, and 1900 LST (1800, 2000, 2200, and 0100 UTC) in the sunny environment well east of the convection (x = 1100 km) in the CONTROL-EAST simulation. The evolution is similar in the other simulations.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Two environmental wind profiles are used (Fig. 2a). Both profiles contain relatively strong westerly wind shear in the 0–2.5-km and 7.5–10-km layers. The low-level westerly shear in the environment is associated with northward-pointing horizontal vorticity that opposes the southward-pointing horizontal vorticity baroclinically generated within the leading portion of cold pool of the convective system. The opposing vorticity orientations are known to promote a strong gust-front updraft (e.g., RKW88), which benefits the maintenance of the convective system, given that the system’s maintenance relies on the repeated initiation of new cells by the gust front. The shear at upper levels lengthens the anvil in the downstream direction, thereby increasing the area of the low-level inflow that is shaded.

Fig. 2.
Fig. 2.

(a) The vertical wind profiles used to initialize the EAST and WEST simulations. Markers are placed along each simulated profile at every grid level. (b) The low-level vertical wind profiles at 1400 LST (2000 UTC; t = 2 h) in the sunny environment well east of the convection (x = 1100 km) in the CONTROL-EAST and CONTROL-WEST simulations (the wind profiles in the far-field environment in the SHADING simulations are practically identical).

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Vertical mixing within the boundary layer rapidly modifies the initial wind profiles at low levels. Most of the modification occurs within the first 30 min of the simulation. The initial low-level wind profiles were chosen based on trial and error such that, after modification by vertical mixing, the bulk low-level (westerly) wind shear would be approximately the same in each simulation. By 1400 LST, both environmental wind profiles are characterized by a zonal wind differential of approximately 15 m s−1 over the lowest 2.5 km (Fig. 2b); however, the two environments are characterized by different near-surface (nominally the lowest 300 m) winds and wind shear. One environment is characterized by easterly surface winds of approximately 5 m s−1, in addition to easterly near-surface wind shear. The other environment is characterized by westerly surface winds of approximately 5 m s−1 and westerly near-surface wind shear.

Though it would be possible to mitigate some of the evolution of the environmental wind profile (particularly the decrease in westerly vertical wind shear in time evident in Fig. 2b) by imposing large-scale meridional baroclinicity and the Coriolis force (i.e., the presence of a westerly base state thermal wind would better maintain westerly vertical wind shear despite the vertical mixing), introducing a meridional horizontal temperature gradient introduces meridional CAPE and CIN gradients, thereby complicating the interpretation of the results. Moreover, open (rather than periodic) north and south lateral boundary conditions would be required; thus, the domain would have to be greatly enlarged in its meridional dimension.

A pair of simulations was run for each of the two environments. In one set of simulations, hydrometeors are transparent to shortwave radiation; that is, there is no shading of the surface by the intervening clouds and precipitation. In the other set of simulations, hydrometeors attenuate shortwave radiation. The simulations are hereafter designated as CONTROL and SHADING simulations, respectively. Moreover, the two environments are identified as EAST and WEST; the labels describe the surface winds and near-surface shear as being easterly and westerly, respectively. For example, CONTROL-EAST refers to the simulation without anvil shading in which the environment is characterized by easterly surface winds and near-surface shear.

Convection is initiated by introducing an infinitely long (in the meridional dimension), 2.5-km-deep cold pool in the westernmost 30 km of the domain at t = 0, similar to the approach of Weisman et al. (1997) and Parker and Johnson (2004). The cold pool has a surface potential temperature (θ) perturbation of −12 K, and the amplitude of the θ perturbation decreases linearly with height, vanishing at 2.5 km. Additional, random 0.1-K θ perturbations are added to the easternmost 10 km of the cold pool in order to force the simulated storms to develop modest three-dimensional structure (convection initiation itself is difficult without introducing the random perturbations). The reason for resorting to such a strong “forcing” for convection initiation is that sustained convection is unable to develop in the model by introducing an infinitely long line thermal (e.g., RKW88) or a line of warm bubbles (even moistened warm bubbles; e.g., James et al. 2006). A stronger forcing is needed than in typical idealized thunderstorm simulations because of the relatively large CIN at the initial time. The large CIN (and associated strong capping inversion) are necessary at the initial time so that subsequent boundary layer warming can be accommodated over the course of the afternoon hours. With a weaker capping inversion and less CIN at the initial time, unrealistic moist absolutely unstable layers (MAULs; Bryan and Fritsch 2000) develop in the far-field environment at the top of the boundary layer. New convective storms are initiated in the regions containing the MAULs, and the development of such extraneous storms complicates the analysis we wish to pursue herein. It is worth noting that the cold pool is quickly modified by the warming underlying ground, such that there is little evidence of it after an hour has elapsed. Thus, the idealized convection initiation method employed herein probably best emulates initiation by a weakening cold front (one that might be said by forecasters to be “washing out”).

c. Artificial enhancement of the anvil ice concentration and optical thickness

In comparing the low-level cooling observed within regions shaded by actual storms to the cooling occurring within the regions shaded by simulated storms, we have found a significant warm bias (i.e., insufficient cooling) in simulations, both in the case of squall lines as well as supercells (Frame and Markowski 2010). For example, Fig. 3 compares the evolution of near-surface temperature and shortwave radiation in a simulation of a slow-moving squall line (SHADING-EAST) to observations obtained ahead of a similarly slow-moving squall line in a similar high-CAPE environment documented by BP10. The squall line investigated by BP10 also happened to occur in a similar geographical area and at roughly the same time of day and year (the late afternoon of 15 May 2009) as the simulated squall line. Despite the duration of pre-gust-front anvil shading in the simulation being roughly twice as long as in the observed case (~3 h versus ~1.5 h; Figs. 3a,b), which was a consequence of a longer anvil in the simulation rather than a slower storm motion, the amplitude of the observed near-surface cooling (at Cherokee, Oklahoma) was ~4 K (gray trace in Fig. 3a), compared with ~1 K in the simulation (dashed trace in Fig. 3a). The vertically integrated cooling in the boundary layer and near-surface static stability also are substantially smaller in the simulation compared with the 15 May 2009 case (cf. the black dashed and gray dashed–dotted profiles in Fig. 3c).

Fig. 3.
Fig. 3.

(a) Time series of latitudinally averaged 5-m air temperature (°C) at x = 300 km in the SHADING-EAST simulation with and without the optical thickness of the anvil being artificially enhanced, and in the sunny far-field environment well east of the convection (x = 1100 km). Anvil shading begins at 1400 LST (2000 UTC) and the gust front arrives at 1715 LST (2315 UTC). The time series of 3-m air temperature observed at Cherokee, Oklahoma, in the 15 May 2009 squall line case documented by BP10 also is overlaid (cf. their Fig. 5a). Anvil shading began at 2145 UTC and the gust front arrived at 2320 UTC. (b) Time series of latitudinally averaged shortwave radiation (W m2) for the same numerical simulation and at the same locations as in (a). As in (a), the time series obtained at Cherokee on 15 May 2009 also is shown (cf. BP10’s Fig. 5e). (c) Vertical profiles of latitudinally averaged potential temperature (K) at 1700 LST (2300 UTC) at x = 300 km (just ahead of the gust front), and in the sunny far-field environment well east of the convection (x = 1100 km), for the same numerical simulations as in (a) and (b). Markers are placed along each simulated profile at every grid level. The profiles obtained from soundings documented by BP10 also are shown at approximately the same times, approximately 20 km ahead of the gust front of the 15 May 2009 squall line, and in the sunny far-field environment (these are the soundings identified by BP10 as S4 and S1, respectively). (d) Visible satellite image at 2139 UTC 15 May 2009 showing the location of Cherokee relative to the squall line documented by BP10 (after BP10’s Fig. 6).

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

To obtain a more realistic evolution of the vertical temperature profiles in regions of anvil shading, the optical thickness of the thin cirrus is artificially increased in the SHADING simulations discussed hereafter. The cloud ice mixing ratio passed to the radiative transfer parameterization is enhanced relative to the prognosed cloud ice qi for small cloud ice mixing ratios via (Fig. 4)
e1
The enhancement of cloud ice specified by (1) increases the cloud ice mixing ratio of the optically thin portions of the anvil to ~1.5 g kg−1 (Fig. 4), which corresponds to an ice concentration of ~0.5 g m−3. The modification of the cloud ice concentration only affects the radiation calculations; that is, the model prognostic equation for cloud ice is unmodified. Though deficiencies in the microphysics parameterization, radiation parameterization, soil model, surface flux parameterization, and mixing length parameterization all can contribute to an unrealistic evolution of the vertical temperature profile within the region shaded by the anvil (e.g., the remaining differences between the evolution of temperature in the observations and simulation with enhanced-anvil ice evident in Figs. 3a,c would seem to imply a shortcoming in the soil model, surface flux parameterization, and/or mixing length parameterization), we believe that a modification of the microphysical aspects of the anvil is most justified given the well-known shortcomings of microphysical parameterizations (e.g., Gilmore et al. 2004a,b; Dawson et al. 2010; Morrison and Milbrandt 2011; Bryan and Morrison 2012; Van Weverberg et al. 2012).
Fig. 4.
Fig. 4.

The prognosed cloud ice qi passed to the radiative transfer subroutines was artificially augmented. The augmentation was designed to increase the optical thickness of the thin cirrus in the model in order to obtain a reduction in shortwave radiation and low-level cooling that better agrees with the shortwave radiation attenuation and cooling observed beneath the anvils of midlatitude convective storms in past studies. The solid line shows as a function of qi; the dashed line is . The units of both variables are kg kg−1.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

The evolution of low-level temperature and shortwave radiation in the SHADING-EAST simulation using the modification described above also is shown in Fig. 3 (dashed–dotted traces). The attenuation of shortwave radiation in this simulation better matches the 15 May 2009 observations. For example, at the onset of shading near 1400 LST in the simulation, the shortwave radiation almost immediately drops ~600 W m−2 (from ~900 to ~300 W m−2; dashed–dotted trace in Fig. 3b), which is similar in amplitude and timing to the observations at Cherokee near 1600 LST (gray trace in Fig. 3b). The drop in shortwave radiation in the simulation with artificially enhanced-anvil ice also compares well with the radiation observations documented by Markowski et al. (1998; their Fig. 9 also reveals a ~600 W m−2 drop in two different cases). In the simulation without the artificially enhanced-anvil ice, the attenuation of shortwave radiation is considerably smaller (the maximum deficit relative to the far field is ~400 W m−2) and occurs more gradually (dashed trace in Fig. 3b). The near-surface cooling amplitude is increased to ~3 K in the simulation with the enhanced-anvil ice (Fig. 3a). Though this is still smaller than the amplitude of the near-surface cooling observed at Cherokee in the 15 May 2009 case, and the cooling rate is still much slower in the enhanced-anvil simulation than in the Cherokee observations as well (per the differences in the slopes of the black dashed–dotted and gray solid traces in Fig. 3a), the vertically integrated cooling and low-level static stability in the enhanced-anvil simulation are a much better fit to the observations than in the simulation without the augmented anvil ice (black and gray dashed–dotted profiles in Fig. 3c). [Note that the preshading sounding at Cherokee (solid gray profile in Fig. 3c) reveals a stronger and shallower near-surface superadiabatic layer than in the simulation (solid black profile in Fig. 3c). Not only does the loss of this superadiabatic layer account for ~0.5 K of the total ~4-K temperature drop at Cherokee from 2200 to 2320 UTC (Fig. 3a), but we speculate that the loss of this layer with the onset of anvil shading is responsible for the much more rapid cooling rate at Cherokee than in the simulation (cf. the gray trace in Fig. 3a in the 2200–2230 UTC period with the black dashed–dotted trace from 2000 to 2030 UTC—that is, in the first 30 min of anvil shading).]

3. Results

a. Overview of the characteristics and evolution of the simulated squall lines and their environments

The structure and evolution of the simulated squall lines are summarized by horizontal and vertical cross sections at select but representative times (Figs. 57) and by way of Hovmöller diagrams (Figs. 8 and 9). Despite the considerable amount of upper-level westerly wind shear, all of the simulated squall lines look more like the trailing stratiform rather than the leading stratiform variety documented by Parker and Johnson (2000); that is, though there is an extensive leading anvil in each case (Figs. 6a,b, 7a,b, 8, and 9), the heaviest precipitation mostly trails the updrafts (Fig. 5), and the updrafts themselves slope rearward with height (Figs. 6c,d and 7c,d). Owing to the differences in mean wind speeds among the environments, the squall lines in the EAST environments have the slowest eastward motion (~12 m s−1 from t = 2 to 7 h), and the squall lines in the WEST environments have the fastest eastward motion (~28 m s−1 from t = 2 to 7 h).

Fig. 5.
Fig. 5.

Horizontal cross sections of total hydrometeor mixing ratio qh (rain, hail, and snow) at z = 1 km (color shading; see legend) and select vertical velocity contours (black; the 10, 30, and 50 m s−1 isotachs are shown) at z = 7.5 km in the CONTROL and SHADING simulations initialized with the EAST and WEST vertical wind profiles at t = 5 h [1700 LST (2300 UTC)]. The θ′ = −4 K isentrope at the lowest grid level also is shown (white dashed line); it indicates the approximate location of the gust front. Axis labels indicate the x and y coordinates in kilometers.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Fig. 6.
Fig. 6.

(a),(b) Vertical cross sections of meridionally averaged total hydrometeor mixing ratio qh (rain, hail, and snow; color shading) at t = 5 h [1700 LST (2300 UTC)] in the CONTROL and SHADING simulations with the EAST environmental wind profile. The white contour encloses the meridionally averaged cloud boundary. The region enclosed by the black box is shown in (c) and (d). Axis labels indicate the x and z coordinates in kilometers. (c),(d) Zoomed view of the region outlined in (a),(b), showing meridionally averaged potential temperature perturbation θ′ (color shading) and select isotachs of meridionally averaged vertical velocity w and system-relative zonal wind usr. Potential temperature perturbations are defined relative to the meridionally averaged potential temperature at the eastern boundary of the model domain. The w contours are black and shown for w = 2, 4, 6, 8, … m s−1; the usr contours are white and shown for usr = 0, 2, 4, 6, 8, … m s−1 (though only below 8 km; i.e., the contouring of usr is suppressed in the anvil region in the interest of figure clarity). Axis labels indicate the x and z coordinates in kilometers.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Fig. 7.
Fig. 7.

As in Fig. 6, but for the CONTROL and SHADING simulations with the WEST environmental wind profile.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Fig. 8.
Fig. 8.

(a),(b) Hovmöller diagram of meridionally averaged potential temperature θ at z = 5 m (the lowest scalar grid level). Axis labels indicate time (ordinate) and the x coordinate (km; abscissa). Note that the color scale is nonlinear, with increased resolution for θ > 300 K in order to emphasize the cooling owing to the anvil shading. The meridionally averaged cloud boundary at z = 10 km is indicate with the white line. The filled circles indicate the locations of the vertical profiles shown in Fig. 10. (c),(d) As in (a)–(b), but TKE at z = 300 m is shown.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Fig. 9.
Fig. 9.

As in Fig. 8, but for the CONTROL and SHADING simulations with the WEST environmental wind profile. The filled circles indicate the locations of the vertical profiles shown in Fig. 11.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

The amplitude of the low-level cooling in the pre-gust-front environment owing to anvil shading is largest in the SHADING-EAST simulation. In this simulation, the maximum θ deficit beneath the anvil, relative to the sunny, far-upstream environment (and relative to environment in the CONTROL-EAST simulation) occurs near 1700 LST (t = 5 h), at which time the θ deficit just ahead of the gust front is ~3 K (301 K versus 304 K in the SHADING-EAST versus CONTROL-EAST simulations, respectively; Figs. 8a,b and 10a). The low-level cooling is maximized at approximately the same time in the SHADING-WEST simulation, but the amplitude of the cooling is only ~1 K in this simulation (Figs. 9a,b and 11a). The amplitude of the cooling is larger in the SHADING-EAST simulation because the duration of anvil shading is longest in this simulation owing to the slow system motion.

Fig. 10.
Fig. 10.

Vertical profiles of (a) meridionally averaged potential temperature θ (K) and (b) meridionally averaged zonal wind u (m s−1) in the lowest 2500 m at t = 5 h [1700 LST (2300 UTC)] in the CONTROL (black) and SHADING (gray) simulations with the EAST environmental wind profile. Profiles are shown (left to right) 10, 50, 100, and 150 km east of the gust front. Black (gray) square markers indicate the zonal wind at the lowest grid level (z = 5 m) in the CONTROL (SHADING) simulation (without the markers it is difficult to see the differences in the wind profiles near the surface). The locations of the vertical θ and u profiles are indicated with filled circles in Fig. 8.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for the CONTROL and SHADING simulations with the WEST environmental wind profile. The locations of the profiles are indicated with filled circles in Fig. 9.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Low-level cooling is evident as far east as 200 km east of the gust front in the SHADING-EAST simulation (Figs. 8b and 9b) and up to 100 km east of the gust front in the SHADING-WEST simulation (Figs. 10a and 11a). In the SHADING-EAST simulation, though the amplitude of the cooling is decidedly largest in the lowest 300 m (where the static stability also is largest), significant cooling occurs throughout the depth of the boundary layer (Fig. 10a), although the boundary layer remains roughly neutrally stratified above 300 m (this portion of the boundary layer might best be regarded as a residual layer). Though the depth of cooling is likely sensitive to the parameterization of the vertical mixing length, cooling attributed to anvil shading also was observed up to an altitude of nearly 1 km in the BP10 study (Fig. 3b). The depth of the cooling in the SHADING-WEST simulation also spans the depth of the boundary layer (Fig. 11a); however, the static stability in the lowest few hundred meters is weaker in this simulation than in the SHADING-EAST simulation.

The low-level stabilization associated with the anvil shading and cooling is associated with an abrupt drop in TKE in the pre-gust-front environments of the SHADING simulations (Figs. 8c,d and 9c,d). Boundary layer TKE nearly vanishes ahead of the gust fronts in the SHADING simulations. Not surprisingly, the nearly TKE-free zone is wider in the SHADING-EAST simulation (Fig. 8d) than in the SHADING-WEST simulation (Fig. 9d). The development of horizontal temperature gradients and TKE changes in the SHADING simulations both lead to changes in the environmental wind profile relative to the CONTROL simulations (Figs. 10b and 11b). These changes will be described in detail in the following subsection.

The CONTROL-EAST squall line tends to have stronger updrafts than the SHADING-EAST squall line. The volume of the 10 m s−1 vertical velocity (w) isosurface is 5%–20% larger in the CONTROL-EAST simulations than in the SHADING-EAST from t = 3 h onward (Fig. 12a). For the WEST simulations, no clear vertical velocity differences persist for the duration of the simulation (Fig. 12b). (The temporal variation of the w = 10 m s−1 isosurface volume is much less noisy than the time series of maximum vertical velocity. The differences between the CONTROL and SHADING simulations are qualitatively similar for other w isosurfaces—e.g., 20, 30, and 40 m s−1.) The total rainfall accumulations are 1%–3% larger in the CONTROL simulations than in the respective SHADING simulations (not shown).

Fig. 12.
Fig. 12.

Time series of the w = 10 m s−1 isosurface volume for the CONTROL and SHADING simulations with the (a) EAST and (b) WEST environmental wind profiles.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

b. Analysis of the differences between the squall lines in the CONTROL and SHADING simulations

1) Net positive area

The vertical velocity differences between the CONTROL-EAST and SHADING-EAST simulations can be attributed partly to differences in the net “positive area” (i.e., the CAPE minus the CIN) between the two simulations. The low-level cooling in the pre-gust-front environment of the SHADING-EAST simulation reduces the equivalent potential temperature of the inflow, thereby increasing (decreasing) the CIN (CAPE) and decreasing the net positive area, implying a reduction in the contribution of buoyancy to the vertical velocity. For example, at 1700 LST (t = 5 h), just ahead of the gust front, the net positive area is approximately 800 J kg−1 less in the SHADING-EAST simulation than in the CONTROL-EAST simulation (Fig. 13a).4 In the SHADING-WEST simulation, the net positive area is only 150 J kg−1 less than in the CONTROL-WEST simulation owing to the shorter duration of anvil shading.

Fig. 13.
Fig. 13.

Net positive area (CAPE − CIN) of the inflow soundings east of the gust front for the CONTROL and SHADING simulations with the (a) EAST and (b) WEST environmental wind profiles at t = 5 h [1700 LST (2300 UTC)]. The net positive area was computed by lifting an air parcel from the surface dry adiabatically to its saturation point and pseudoadiabatically thereafter.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

2) The RKW88 cold pool parameter and low-level vertical shear

There are also subtle differences in the structures of the simulated squall lines that are not reflected in vertical velocity time series or rainfall accumulations. The updraft region in the SHADING-EAST simulation (Fig. 6d) is decidedly more rearward tilted than the updraft region in the CONTROL-EAST simulation (Fig. 6c). The updraft tilt in the CONTROL-WEST and SHADING-WEST simulations is similar at most times (e.g., Figs. 7c,d), though when differences are evident, the updraft in the CONTROL-WEST (not SHADING-WEST) simulation exhibits a more rearward tilt. The system-relative rear-to-front flow is stronger in the SHADING-EAST simulation than in the CONTROL-EAST simulation (Figs. 6c,d). Conversely, the system-relative rear-to-front flow is slightly stronger in the CONTROL-WEST simulation (Fig. 7c) than in the SHADING-WEST simulation (Fig. 7d).

In their “theory for strong, long-lived squall lines,” RKW88 showed that the updraft at the leading edge of a density current is approximately upright when the cold pool parameter,
e2
where B is the buoyancy and d is usually taken to be 2–3 km,5 is matched by Δu (i.e., cu = 1), where Δu is the component of the bulk vertical shear over d pointing in the direction of the dense fluid’s motion. RKW88’s theory is probably most applicable to the tilt of the gust-front updraft, as opposed to the slope of the deep ascent that spans most if not the full depth of the troposphere, given that the latter is also influenced by middle- and upper-level wind shear (e.g., Coniglio et al. 2006). However, if only the low-level wind profile is varied in a parameter-space study such as this (e.g., Fig. 2), then the ratio cu might be expected to be related to both the tilt of the gust-front updraft and slope of the deeper ascent. For example, in Weisman’s (1992) parameter-space study, the rearward tilt of the convective systems increased as cu increased, with the rearward tilt being crucial in the development of rear inflow. Our goal is not to provide yet another assessment of the applicability of RKW theory (e.g., Coniglio and Stensrud 2001; Evans and Doswell 2001; Coniglio et al. 2004, 2006; Weisman and Rotunno 2004, 2005; Stensrud et al. 2005; Bryan et al. 2006; Coniglio et al. 2012), nor do we wish to claim that cu can account for all of the differences between the CONTROL and SHADING simulations (e.g., as already mentioned, there are thermodynamic differences between the CONTROL and SHADING environments that affect updraft strength). Rather, we show below that anvil shading affects c, Δu, and cu and that the modifications of cu can explain some of the differences in squall line structure found between the CONTROL and SHADING simulations.

The vertical shear parameter Δu (Fig. 14) is measured 10 km east of the gust front over a depth d of 2.5 km, following RKW88, and meridionally averaged. The cold pool parameter c (also displayed in Fig. 14) is averaged in a swath 5–15 km west of the gust front, where the stagnation condition at the surface assumed by RKW88 is most nearly met, and then meridionally averaged. The gust front’s longitude is objectively defined as the location where the potential temperature at the lowest grid level is 4 K cooler than the far-field potential temperature 100 km inside of the eastern boundary of the domain. A smaller potential temperature deficit (sometimes θ′ = −1 or −2 K is used) cannot be used to identify the gust front because the amplitude of the near-surface cooling owing to anvil shading is ~3 K in the SHADING-EAST simulation (Fig. 10a). In the CONTROL simulations, the θ′ = −4 K and θ′ = −1 K isopleths are within a grid point of each other.

Fig. 14.
Fig. 14.

(a),(c) Evolution of the cold pool parameter c (solid traces) and 0–2.5-km bulk environmental vertical wind shear Δu (dashed traces) for 1300–1900 LST (1900–0100 UTC), or t = 1–7 h (the first hour is not shown because c is influenced by the initial cold block rather than a precipitating convective system during this early time period), in the CONTROL (black) and SHADING (gray) simulations using the EAST and WEST environmental wind profiles, respectively. See section 3 for details regarding how c and Δu were computed. (b),(d) The quantity cu in the same time period in the simulations using the EAST and WEST environmental wind profiles, respectively.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

The buoyancy appearing in (2) is evaluated relative to the properties of the air at a location 10 km east of the gust front (i.e., at the same location at which Δu is evaluated), rather than in the far field near the eastern domain boundary (i.e., where the reference state is defined in the displaying of potential temperature perturbations in Figs. 6 and 7). Though the longitude at which Δu is evaluated is fairly arbitrary, it should match the longitude of the reference state against which the negative buoyancy of the cold pool is compared in (2) in order to be consistent with the theoretical development of RKW88. It seems best to choose a longitude close enough to the gust front to capture the modifications of the environmental wind profile resulting from the anvil shading (e.g., Figs. 10b and 11b), but far enough ahead of the gust front to avoid the region where streamlines turn abruptly upward (the flow at the right boundary of RKW88’s control volume is assumed to be horizontal). Fortunately, the relative differences in cu between the CONTROL and SHADING simulations are qualitatively insensitive to the specific choice of longitude at which Δu and the reference state for the B integration in (2) are defined.

The ratio cu is considerably larger in the SHADING-EAST simulation than in the CONTROL-EAST simulation (Fig. 14b), which is consistent with the more rearward-sloping updraft region and stronger rear-to-front system-relative flow in the former simulation (Fig. 6c,d). The cu differences are due to a larger Δu in the CONTROL-EAST simulation (Fig. 14a). After 1700 LST (t = 5 h), c is virtually identical in the CONTROL-EAST and SHADING-EAST simulations, but from 1400 to 1700 LST (t = 2–5 h), c is actually larger in the CONTROL-EAST simulation (i.e., the larger Δu in this simulation is responsible for the smaller cu throughout the simulation). The cold pools of both simulations are strongest at approximately 1500 LST (t = 3 h), decrease in strength from 1500 to 1700 LST, and are roughly steady thereafter (Fig. 14a). The environmental shear decreases steadily from 1400 to 1900 LST (t = 2–7 h; Fig. 14a); Δu is 10–12 m s−1 in the pair of simulations at 1400 LST (t = 2 h) and 2–4 m s−1 by 1900 LST (t = 7 h). The differences in Δu are only ~2 m s−1 throughout the simulation, but this leads to significant differences in cu because Δu is so small (e.g., <4 m s−1 by 1900 LST in both the CONTROL-EAST and SHADING-EAST simulations). The reduced Δu in the SHADING-EAST simulation relative to the CONTROL-EAST simulation is mainly the result of weakening near-surface easterly winds (i.e., a westerly near-surface acceleration) under the anvil in the SHADING-EAST simulation (Fig. 10b). Though the 0–2.5-km shear is weaker in the SHADING-EAST simulation, the changes in this bulk measure of the wind shear mask the fact that there is an increase in easterly 0–1-km shear and westerly 1–2.5-km shear in the SHADING-EAST simulation relative to the CONTROL-EAST simulation (Fig. 10b).

Conversely, cu is generally larger (though by < 0.25 at all times) in the CONTROL-WEST simulation than in the SHADING-WEST simulation (Fig. 14d). From 1300 to 1500 LST (t = 1–3 h), the difference is attributable to larger c in the CONTROL-WEST simulation (Δu is similar in the pair of simulations during this time period; Fig. 14c). From 1500 to 1800 LST (t = 3–6 h), the difference is attributable to larger Δu in the SHADING-WEST simulation (c is similar in the pair of simulations during this time period; Fig. 14d). During this period, Δu is enhanced in the SHADING-WEST simulation relative to the CONTROL-WEST simulation, though by < 2 m s−1, by an easterly acceleration of the westerly near-surface wind (Fig. 11b). Winds in the 200–1700-m layer experience a westerly acceleration beneath the anvil in the SHADING-WEST simulation (Fig. 11b), though this acceleration does not affect the bulk shear parameter. Though the slopes of the updraft region in the pair of WEST simulations are generally similar, as mentioned earlier in this section, at times when differences are discernible, the squall line in the CONTROL-WEST simulation tends to have the more rearward-tilting updraft region. The cu differences in the 1300–1800 LST period also are consistent with the stronger system-relative front-to-rear flow in the CONTROL-WEST simulation (Figs. 7c,d).

The reasons for the changes in Δu and c are addressed in the following subsections.

3) Meridional vorticity forcings

As is evident from the results presented above, the differences in cu between CONTROL and SHADING simulations in both environments can be due to differences in either Δu or c, though differences in Δu are most often responsible for the cu differences. The evolution of Δu in the pre-gust-front environment is examined further using the anelastic governing equation for the meridional vorticity, (the RKW88 derivation is based on a balance between environmental meridional vorticity and the cold pool’s baroclinically generated meridional vorticity),
e3
where D/Dt = ∂/∂t + v· is the material derivative, v = (u, υ, w) is the velocity vector, ω = (ξ, η, ζ) is the vorticity vector, and F represents viscous forces due to turbulent mixing. The effects of computational diffusion are neglected. The j · × F term is computed as (∂Du/∂z) − (∂Dw/∂x), where Du = ∂τ11/∂x + ∂τ12/∂y + ∂τ13/∂z and Dw = ∂τ31/∂x +τ32/∂y + ∂τ33/∂z. The Reynolds stress tensor components are , , , , , and . The horizontal (vertical) turbulent mixing coefficient for momentum is Kmh (Kmv), which is obtained from the prognosed TKE via Kmh = 0.1 × (TKE)1/2lh (Kmv = 0.1 × (TKE)1/2lυ), where lh (lυ) is the horizontal (vertical) mixing length. The j · × F term is dominated by vertical turbulent mixing; that is, j · × F ≈ ∂(Kmvu/∂z)/∂z to a good approximation. We are interested in evaluating the forcings in the Lagrangian form of the vorticity equation because we are interested in why η evolves in the way that it does as the gust front is approached from the far field.

Figures 15 and 16 present meridional and vertical averages (denoted with 〈·〉) of the baroclinic term, −∂B/∂x, and the viscosity term, j · × F, in the 300 km leading up to the gust front at 1700 LST (t = 5 h) (the vertical averages are shown in the 0–1-km and 1–2.5-km layers, in addition to the 0–2.5-km layer, given the differences in the evolution of the vertical shear/horizontal vorticity in those layers). The zonal profiles at other times are qualitatively similar.

Fig. 15.
Fig. 15.

Meridionally and vertically averaged (a)–(c) meridional vorticity 〈η〉, (d)–(f) meridional baroclinic vorticity generation 〈−∂B/∂x〉, (g)–(i) meridional vorticity tendency owing to turbulent mixing 〈j · × F〉, and (j)–(l) 〈−∂B/∂x〉 + 〈 j · × F 〉 at t = 5 h [1700 LST (2300 UTC)] east of the gust front for the CONTROL and SHADING simulations initialized with the EAST environmental wind profile. (left to right) Vertically averaged quantities in the 0–2.5-km, 0–1-km, and 1–2.5-km layers.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Fig. 16.
Fig. 16.

As in Fig. 15, but for the simulations initialized with the WEST environmental wind profile.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

The sum of the baroclinic and viscosity terms is within 10% of the independently diagnosed 〈/Dt〉 at all longitudes because ω · υ is small (owing to the approximate two dimensionality of the squall lines and velocity perturbations in the environment), as are the effects of computational mixing. Zonal changes in vertically and meridionally averaged η, and therefore meridionally averaged Δu (e.g., Figs. 10b and 11b), depend on the magnitude of the forcings shown in Figs. 15 and 16, as well as the amount of time a parcel approaching the gust front experiences the forcing. The speed of the air parcels approaching the gust front does not vary much in x; thus, the magnitudes of the forcings shown in Figs. 15 and 16 give a fair sense of the importance of the forcings. Figure 17 displays the zonal averages of the forcings to facilitate comparisons of their cumulative influences.

Fig. 17.
Fig. 17.

Zonally averaged 〈−∂B/∂x〉 (unshaded bars), 〈 j · × F 〉 (shaded bars), and 〈−∂B/∂x〉 + 〈 j · × F 〉 (striped bars) at t = 5 h [1700 LST (2300 UTC)] in the CONTROL (black) and SHADING (gray) simulations initialized with the (a)–(c) EAST and (d)–(f) WEST environmental wind profiles. The horizontal averages are from within the region of anvil shading; that is, from within the region 0–210 km east of the gust front in (a)–(c) and 0–160 km east of the gust front in (d)–(f), per the vertical dashed lines in Figs. 15 and 16 that indicate the locations where shading begins. (left to right) The 0–2.5-km, 0–1-km, and 1–2.5-km layers.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

As indicated earlier, Δu was consistently smaller in the SHADING-EAST simulation than in the CONTROL-EAST simulation (Fig. 14a). The analysis of 〈η〉 at 1700 LST reveals that 〈η〉 begins decreasing approximately 170 km east of the gust front (anvil shading begins approximately 210 km east of the gust front) in the SHADING-EAST simulation in the 0–2.5-km layer (Fig. 15a). The drop is even more dramatic in the 0–1-km layer (Fig. 15b); a small increase in 〈η〉 in the 1–2.5-km layer (Fig. 15c) offsets some of the 〈η〉 decrease occurring in the lower layer. Roughly 60% of the total decrease in 〈η〉 in the 0–1-km layer (from roughly −8 × 10−3 to −12 × 10−3 s−1) within the shaded region is the result of a decrease in vertical mixing—manifest as a large negative 〈j · × F〉 term (Figs. 15h and 17b)—that accompanies the loss of the unstable surface layer (Fig. 10a). With the downward mixing of faster easterlies from aloft being effectively shut off (also note the drop in TKE evident in Fig. 8d), the surface easterly wind is slowed by surface drag, leading to an increase in the easterly (southward pointing) vertical wind shear (horizontal vorticity). Surface-layer parcels travel roughly 40 km eastward before the superadiabatic layer is lost, which is why the large drop in 〈η〉 owing to the viscosity term occurs approximately 170 km east of the gust front rather than at the location where shading begins, ~210 km east of the gust front. In the CONTROL-EAST simulation, the viscosity term is slightly positive in the 0–1-km layer, on average, within ~210 km of the gust front (Figs. 15h and 17b); that is, the viscosity term makes the negative meridional vorticity of parcels approaching the gust front in the 0–1-km layer less negative (Fig. 15b).

The remaining ~40% of the aforementioned decrease in 〈η〉 evident in the SHADING-EAST simulation in the 0–1-km layer within the shaded region is the result of baroclinic generation of southward-pointing (negative) meridional vorticity (Figs. 15e and 17b). The generation of negative meridional vorticity is attributable to the eastward-pointing horizontal buoyancy gradient at low levels resulting from the anvil shading (Fig. 8b). Although the baroclinic generation (〈−∂B/∂x〉) is an order of magnitude smaller than the viscosity term (〈j · × F〉) (cf. Figs. 15e and h), the baroclinic term is long acting, in contrast to the viscosity term. An inflow air parcel approaching the convective system from the east in the 0–1-km layer experiences persistent, albeit relatively weak, baroclinic generation of negative meridional vorticity in the shaded region leading up to the gust front. Not surprisingly, the baroclinic term is approximately zero in the 0–1-km layer in the CONTROL-EAST simulation (Figs. 15e and 17b).

In the 1–2.5-km layer, the forcing from viscosity is strongly negative in the CONTROL-EAST simulation owing to the upward mixing of negative η from the surface layer (Figs. 15i and 17c). The forcing is less negative in the SHADING-EAST simulation because the upward mixing ceases once the surface layer is stabilized. Thus, the differences in the viscosity term between the CONTROL-EAST and SHADING-EAST simulations have different signs in the 0–1-km and 1–2.5-km layers (cf. Figs. 17b,c), which leads to the term being only slightly more negative in the 0–2.5-km layer in the SHADING-EAST simulation than in the CONTROL-EAST simulation (Fig. 17a).

The zonal variation of baroclinic vorticity generation in the 1–2.5-km layer is noisy owing to temperature perturbations associated with gravity waves. Fluctuations aside, significant negative baroclinic vorticity generation is present within ~170 km of the gust front in the CONTROL-EAST simulation (Figs. 15f and 17c). The origin of the negative baroclinic generation in this layer is a broad region of mesoscale ascent well ahead of the convection, a feature referred to as a “cool, moist tongue” by Fovell (2002). Isentropes slope gently upward well ahead of the gust front, leading to an eastward-directed horizontal buoyancy gradient in the 1–2.5-km layer. Curiously, the mesoscale ascent and associated negative baroclinic vorticity generation are not as strong in the SHADING-EAST simulation. Thus, the differences in the baroclinic vorticity generation in the 1–2.5-km layer between the CONTROL-EAST and SHADING-EAST simulations partly offset the differences in baroclinic generation in the 0–1-km layer (cf. Figs. 17b and 17c). As a result, despite the strong low-level baroclinicity under the anvil of the SHADING-EAST squall line, the contribution to the differences in total vorticity forcing from differences in baroclinic generation is nearly as small as the differences in the contribution from viscosity (Fig. 17a).

Although there is less shading-induced cooling and baroclinicity in the SHADING-WEST than SHADING-EAST simulation, the cumulative negative forcing for 〈η〉 from baroclinic vorticity generation in the 0–2.5-km layer is larger in the SHADING-WEST simulation than in the SHADING-EAST simulation (cf. Figs. 15d and 16d, Figs. 17a and 17d). As was the case in the EAST simulations, an eastward-pointing buoyancy gradient in the 1–2.5-km layer due to gentle mesoscale ascent ahead of the convective system results in negative forcing for 〈η〉 in both WEST simulations in that layer (Figs. 16f and 17f), with the mesoscale ascent and baroclinic vorticity generation being slightly stronger in the SHADING-WEST simulation than in the CONTROL-WEST simulation.

Despite the effects of the baroclinicity, there is a net increase in 〈η〉 (and Δu) in the SHADING-WEST simulation relative to the CONTROL-WEST simulation in the 0–2.5-km layer as the gust front is approached from the east, though the difference is relatively small in the 0–2.5-km layer (〈η〉 is 0.5 × 10−3 s−1 larger in the SHADING-WEST simulation; Fig. 16a). In the 0–1-km layer, 〈η〉 is more than 2.5 × 10−3 s−1 larger in the SHADING-WEST simulation just ahead of the gust front (Fig. 16b). The increase in 〈η〉 in the SHADING-WEST simulation is the result of the cessation in vertical mixing—manifest as a large positive contribution to the 〈η〉 tendency from 〈j · × F〉—that occurs roughly 75 km east of the gust front (Fig. 16h; also see Fig. 17e and note the TKE change in Fig. 9b), which is approximately 85 km west of the longitude at which anvil shading begins (i.e., the unstable surface layer is not lost until inflow parcels have traveled roughly 85 km east of the edge of the anvil shadow; Fig. 11b). Once downward mixing of larger westerly momentum aloft is cut off in the SHADING-WEST simulation, the westerly near-surface winds are slowed by surface drag, thereby increasing 〈η〉 and Δu over the 0–1-km and 0–2.5-km layers.

4) Direct versus indirect effects of shading on cold pool strength

Lastly, we turn our attention to the effects of anvil shading on c. In the EAST simulations, c is smaller in the SHADING simulation in the 1400–1700 LST period, and c is similar in the SHADING and CONTROL simulations at other times (Fig. 14a). In the WEST simulations, c is smaller in the SHADING simulation in the 1300–1600 LST period, and c is similar in the SHADING and CONTROL simulations thereafter (Fig. 14c). In the SHADING simulations, c potentially could be modified (relative to the CONTROL simulations) by (i) a radiation deficit in the cold pool; (ii) cooling of the preline inflow (the buoyancy integrated in the calculation of c is defined relative to the temperature field 10 km east of the gust front, rather than relative to the far-field temperatures), as in the simulations of Parker (2008) and Ziegler et al. (2010); and (iii) changes in preline Δu accompanying the preline cooling/stabilization, with the Δu changes ultimately affecting the squall line structure and moist processes. Effects (i) and (ii) might be regarded as direct effects, with (iii) being an indirect effect.

To determine the extent to which c is influenced by (i), an additional pair of simulations (designated INFLOWSHADING-EAST and INFLOWSHADING-WEST) was run in which the pre-gust-front environment is shaded, but the clouds and hydrometeors are made to be transparent to solar radiation along paths that intersect the surface within the cold pool (Fig. 18a). Both INFLOWSHADING simulations are very similar to their respective SHADING simulations, and at most times, almost indistinguishable from their respective CONTROL simulations (only the simulation initialized with the EAST wind profile is shown in Fig. 18). This implies that the attenuation of shortwave radiation primarily influences c by modifying the inflow. This is perhaps not a surprising result, given that much of the outflow air originates above the boundary layer to the rear of squall line (these parcels would be unaffected by the shadow cast by the trailing anvil if they are above the boundary layer), overtakes the squall line from the rear, is precipitated into, and then descends to the surface. Only after reaching the surface would these parcels be able to experience the effects of the radiation deficit behind the gust front, and by that point in time, the duration of anvil shading is far less than the duration of shading beneath the leading anvil in the inflow (where parcels also travel along the surface rather than descend from aloft).

Fig. 18.
Fig. 18.

(a) Zonal variation in meridionally averaged shortwave radiation in the CONTROL-EAST, SHADING-EAST, and INFLOWSHADING-EAST simulations at 1700 LST (t = 5 h). (b) As in Fig. 6d, but for the INFLOWSHADING-EAST simulation at 1700 LST (t = 5 h). (c) As in Fig. 14a, but the traces of c and Δu from Fig. 14a are gray, and c and Δu in the INFLOWSHADING-EAST simulation are indicated using the black solid and dashed curves, respectively. (d) As in Fig. 14b, but the traces of cu from Fig. 14b are gray, and cu in the INFLOWSHADING-EAST simulation [cf. (c)] is indicated with a black curve.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

Regarding (ii), the change in c due to a change in the preline environmental temperature profile is
e4
where Δc is the change in c relative to the CONTROL simulation; is the environmental virtual potential temperature; the subscripts C and S indicate CONTROL and SHADING simulations, respectively; 〈·〉 indicates a vertical average from 0 to d (d = 2500 m); and g is the gravitational acceleration. In both the EAST and WEST pairs of simulations, is only ~0.3 K at locations 10 km east of the gust front (Figs. 10a and 10b), which is considerably less than the amplitude of the near-surface cooling, especially in the SHADING-EAST simulation. Thus, the preline cooling contributes to a drop in c of ~1 m s−1 (0.80–1.06 m s−1 in the 1300–1900 LST time period) in the SHADING simulations. The time series of c (Fig. 14a,c) imply that c is influenced both by (ii) and (iii). Effect (ii) alone cannot explain the largest differences in c between the SHADING and CONTROL simulations, which peak at ~2 m s−1, nor can (ii) account for the similarity in c in the SHADING and CONTROL simulations at other times.

4. Discussion

Overall, the differences between the CONTROL and SHADING simulations should probably be regarded as minor (i.e., at most times, the squall lines appear qualitatively similar and the differences in rainfall, maximum updraft, and maximum wind gust are typically < 10%). Nevertheless, we believe that the dynamical effects of anvil shading are worth documenting given the growing body of anvil-shading observations and increasing interest in the effects of aerosols on storms (e.g., Storer et al. 2010; Rosenfeld et al. 2011; Seigel and van den Heever 2012). Variations in aerosols can affect the microphysical and radiative properties of storms.

Additional simulations (not shown) were conducted without vertical wind shear at upper levels (e.g., vertical wind profiles similar to RKW88), which led to squall lines with shorter leading anvils and longer trailing anvils than the squall lines described in section 3. The differences between those CONTROL and SHADING simulations are smaller than those documented herein. The smaller differences are consistent with the aforementioned finding that shading of the cold pool is not as important as shading of the inflow (the shading of the cold pool is enhanced in the simulations featuring longer trailing anvils).

Section 3 exposed two main effects of anvil shading. The first is the weakening of updrafts owing to the reduction of the potential buoyancy (net positive area on a thermodynamic diagram) of the shaded inflow parcels. (Rainfall accumulations also were reduced in all of the simulations that included anvil shading, relative to the control simulations, though we did not investigate the microphysical origins of the precipitation differences.) This effect tends to increase as the forward speed of the squall line slows, because a slower speed, for a given anvil length, implies a longer period of low-level cooling beneath the anvil. Thus, this effect is sensitive to the ground-relative wind profile, with a slower mean wind yielding slower-moving squall lines and more low-level cooling of the inflow.

The second way by which anvil shading affects the squall lines, to the extent that cu has at least some bearing on squall line structure, is by altering c and Δu, though it was found that the c alterations are mainly due to Δu alterations rather than the direct effect of the shading of the cold pool. As was the case for the modifications of the net positive area of inflow parcels, the modifications of Δu also are dependent on the ambient ground-relative winds. Baroclinicity associated with the shading-induced low-level cooling (Fig. 19a) and the reduction of vertical mixing associated with near-surface stabilization beneath the anvil (Fig. 19b) can both alter Δu. The magnitude of the baroclinicity and its effect on Δu—it always reduces Δu—increases with the duration of the anvil shading for the same reason that the amplitude of the low-level, pre-gust-front cooling and reduction in positive area increase with the duration of anvil shading, as explained above. The shading-induced reduction of vertical mixing, however, can either decrease or increase Δu, depending on the ambient near-surface wind and wind shear. In the case of near-surface easterlies (westerlies), Δu is reduced (enhanced) by the reduction of vertical mixing that accompanies anvil shading.

Fig. 19.
Fig. 19.

(a) Schematic illustration of the effects of anvil shading on the environmental vertical shear (horizontal vorticity) in the 0–2.5-km layer owing to baroclinic vorticity generation. The squall line is moving toward the east (right). (b),(c) As in (a), but for changes in the environmental vertical shear (horizontal vorticity) in the 0–2.5-km layer owing to decreased vertical mixing. Both (b) easterly and (c) westerly near-surface wind (and wind shear) scenarios are shown.

Citation: Journal of the Atmospheric Sciences 70, 3; 10.1175/JAS-D-12-0123.1

The details highlighted above testify to the complexity of the response of the squall lines to anvil shading and the difficulty in generalizing the dynamical impacts. For example, it is difficult to imagine being able to anticipate the differences in mesoscale ascent ahead of the squall lines like those that led to the differences between the baroclinic forcing for Δu between the CONTROL-EAST and SHADING-EAST simulations to be comparable to the differences between the CONTROL-WEST and SHADING-WEST simulations, despite the SHADING-EAST simulation having more shading-induced low-level cooling (cf. Figs. 17a and 17d). Our hope is that we have at least identified the means by which anvil shading can influence squall lines. It is probably wise to interpret the effects only qualitatively anyway, given the artificial enhancement of the ice concentrations passed to the radiation parameterization in the SHADING simulations (section 2c), in order to better match the shading-induced, boundary layer cooling in the simulations to observations.

5. Conclusions

This numerical study investigated the effects of anvil shading on the structure, intensity, and evolution of quasi-linear convective systems and the sensitivity of the effects to the ambient wind profile. Much of the analysis focused on modifications of the cold pool and pre-gust-front vertical wind shear attributable to anvil shading, given their well-known importance to squall line structure and maintenance.

The most important conclusions can be summarized as follows:

  1. For the radiation and microphysics parameterizations used, only by artificially enhancing the ice concentration of the anvil can realistic shortwave radiation reductions and low-level air temperature deficits be obtained in the shaded, pre-gust-front environment.
  2. The magnitude of the low-level cooling, associated baroclinicity, and stabilization of the pre-gust-front environment owing to anvil shading generally increases as the duration of the shading increases (the near-surface wind speed also plays a role because of its influence on the surface sensible heat flux); thus, for a given leading anvil length, the slowest-moving convective system (i.e., the one initiated in the environment having the slowest ground-relative tropospheric mean wind, which is the profile in which low-level easterlies are present) produces the most significant low-level cooling, baroclinicity, and stabilization in the pre-gust-front environment.
  3. The principal ways by which anvil shading dynamically impacts the simulated squall lines is by
    1. reducing the equivalent potential temperature of the inflow, thereby reducing the positive area and buoyancy realized by the parcels that ascend through the updrafts (the generally weaker updrafts and less rainfall in the simulations that include anvil shading are partly the result of the reduced buoyancy), or
    2. modifying the low-level (nominally 0–2.5 km AGL) vertical wind shear in the pre-gust-front environment (the shear modifications affect the slope of the updraft region and system-relative rear-to-front flow, though the sign of the modifications is sensitive to the far-field environmental vertical wind profile).
  4. With respect to (ii) above, the low-level vertical wind shear in the shaded pre-gust-front environment can be modified by both the baroclinicity associated with the low-level cooling and the reduction or cessation of vertical mixing associated with near-surface stabilization. The disruption of vertical mixing usually has a much larger instantaneous contribution to the evolution of the vertical shear than the baroclinicity, but the latter potentially can be important given that it is long acting.

Future work might consider including a means to maintain the vertical wind shear in the far field in spite of the vertical mixing (e.g., by including large-scale, environmental baroclinicity and the Coriolis force, though these can introduce their own challenges) or finer resolution to permit the development of realistic dry convection in the ambient boundary layer (e.g., Nowotarski et al. 2011) and explore its possible effects on squall lines. It is also worth exploring ways to improve the parameterizations that affect the handling of anvil shading and its effects on the evolution of boundary layer temperature and wind profiles. It remains unclear whether our ability to faithfully simulate anvil shading’s effects is being hampered by shortcomings in the microphysics, surface physics, boundary layer, or radiation parameterizations, the soil model, or perhaps several of the above. In a future study it also might be worth exploring how the effects of anvil shading are influenced by along-line variations in the cross-line environmental wind profile (both the ground-relative winds and wind shear), which can result from both mesoscale environmental variability and three-dimensionality of the convectively induced cold pool.

Acknowledgments

We very much appreciate the reviews of earlier versions of this work provided by the other members of the lead author’s M.S. committee, Drs. Yvette Richardson and Eugene Clothiaux, and by three anonymous reviewers. We also are grateful for the consultation provided by Drs. Jeff Frame, Jerry Harrington, Matt Parker, and Sue van den Heever and for the ongoing support of the National Science Foundation (the present study was supported by NSF Grant AGS-0644533). Many of the figures were created with the help of the Grid Analysis and Display System (GrADS), developed by the Center for Ocean–Land–Atmosphere Studies. ARPS was developed by the Center for Analysis and Prediction of Storms at the University of Oklahoma.

REFERENCES

  • Bryan, G. H., , and J. M. Fritsch, 2000: Moist absolute instability: The sixth static stability state. Bull. Amer. Meteor. Soc., 81, 12071230.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., , and M. D. Parker, 2010: Observations of a squall line and its near environment using high-frequency rawinsonde launches during VORTEX2. Mon. Wea. Rev., 138, 40764097.

    • 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.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Chou, M.-D., 1990: Parameterization for the absorption of solar radiation by O2 and CO2 with application to climate studies. J. Climate, 3, 209217.

    • Search Google Scholar
    • Export Citation
  • Chou, M.-D., 1992: A solar radiation model for climate studies. J. Atmos. Sci., 49, 762772.

  • Chou, M.-D., , M. J. Suarez, , C.-H. Ho, , M. M.-H. Yan, , and K.-T. Lee, 1998: Parameterizations for cloud overlapping and shortwave single scattering properties for use in general circulation and cloud ensemble models. J. Climate, 11, 202214.

    • Search Google Scholar
    • Export Citation
  • Chou, M.-D., , K.-T. Lee, , S.-C. Tsay, , and Q. Fu, 1999: Parameterization for cloud longwave scattering for use in atmospheric models. J. Climate, 12, 159169.

    • Search Google Scholar
    • Export Citation
  • Coniglio, M. C., , and D. J. Stensrud, 2001: Simulation of a progressive derecho using composite initial conditions. Mon. Wea. Rev., 129, 15931616.

    • Search Google Scholar
    • Export Citation
  • Coniglio, M. C., , D. J. Stensrud, , and M. B. Richman, 2004: An observational study of derecho-producing convective systems. Wea. Forecasting, 19, 320337.

    • Search Google Scholar
    • Export Citation
  • Coniglio, M. C., , D. J. Stensrud, , and L. J. Wicker, 2006: Effects of upper-level shear on the structure and maintenance of strong quasi-linear mesoscale convective systems. J. Atmos. Sci., 63, 12311252.

    • Search Google Scholar
    • Export Citation
  • Coniglio, M. C., , S. F. Corfidi, , and J. S. Kain, 2012: Views on applying RKW theory: An illustration using the 8 May 2009 derecho-producing convective system. Mon. Wea. Rev., 140, 10231043.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R. P., , R. J. Trapp, , and H. B. Bluestein, 2001: Tornadoes and tornadic storms. Severe Convective Storms, Meteor. Monogr., No. 50, Amer. Meteor. Soc., 167–221.

  • Dawson, D. T., II, , M. Xue, , J. A. Milbrandt, , and M. K. Yau, 2010: Comparison of evaporation and cold pool development between single-moment and multimoment bulk microphysics schemes in idealized simulations of tornadic thunderstorms. Mon. Wea. Rev., 138, 11521171.

    • Search Google Scholar
    • Export Citation
  • Deardorff, J. W., 1972: Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci., 29, 91115.

  • Doswell, C. A., III, , and D. W. Burgess, 1993: Tornadoes and tornadic storms: A review of conceptual models. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., Vol. 79, Amer. Geophys. Union, 161–172.

  • Evans, J. S., , and C. A. Doswell III, 2001: Examination of derecho environments using proximity soundings. Wea. Forecasting, 16, 329342.

    • Search Google Scholar
    • Export Citation
  • Fovell, R. G., 2002: Upstream influence of numerically simulated squall-line storms. Quart. J. Roy. Meteor. Soc., 128, 893912.

  • Frame, J. W., , and P. M. Markowski, 2010: Numerical simulations of radiative cooling beneath the anvils of supercell thunderstorms. Mon. Wea. Rev., 138, 30243047.

    • Search Google Scholar
    • Export Citation
  • Frame, J. W., , P. M. Markowski, , and J. Petters, 2008: The dynamical influences of cloud shading on simulated supercell thunderstorms. Preprints, 24th Conf. on Severe Local Storms, Savannah, GA, Amer. Meteor. Soc., 17B.1. [Available online at https://ams.confex.com/ams/24SLS/techprogram/paper_141832.htm.]

  • Frame, J. W., , J. L. Petters, , P. M. Markowski, , and J. Y. Harrington, 2009: An application of the tilted independent pixel approximation to cumulonimbus environments. Atmos. Res., 91, 127136.

    • Search Google Scholar
    • Export Citation
  • Gilmore, M. S., , J. M. Straka, , and E. N. Rasmussen, 2004a: Precipitation and evolution sensitivity in simulated deep convective storms: Comparisons between liquid-only and simple ice and liquid phase microphysics. Mon. Wea. Rev., 132, 18971916.

    • Search Google Scholar
    • Export Citation
  • Gilmore, M. S., , J. M. Straka, , and E. N. Rasmussen, 2004b: Precipitation uncertainty due to variations in precipitation particle parameters within a simple microphysics scheme. Mon. Wea. Rev., 132, 26102627.

    • Search Google Scholar
    • Export Citation
  • Houze, R. A., Jr., 2004: Mesoscale convective systems. Rev. Geophys., 42, 143.

  • James, R. P., , P. M. Markowski, , and J. M. Fritsch, 2006: Bow echo sensitivity to low-level moisture. Mon. Wea. Rev., 134, 950964.

  • Klemp, J. B., , and R. Rotunno, 1983: A study of the tornadic region within a supercell thunderstorm. J. Atmos. Sci., 40, 359377.

  • Markowski, P. M., , and J. Y. Harrington, 2005: A simulation of a supercell thunderstorm with emulated radiative cooling beneath the anvil. J. Atmos. Sci., 62, 26072617.

    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., , E. N. Rasmussen, , J. M. Straka, , and D. C. Dowell, 1998: Observations of low-level baroclinity generated by anvil shadows. Mon. Wea. Rev., 126, 29592971.

    • Search Google Scholar
    • Export Citation
  • Morrison, H., , and J. Milbrandt, 2011: Comparison of two-moment bulk microphysics schemes in idealized supercell thunderstorm simulations. Mon. Wea. Rev., 139, 11031130.

    • Search Google Scholar
    • Export Citation
  • Noilhan, J., , and S. Planton, 1989: A simple parameterization of land surface processes for meteorological models. Mon. Wea. Rev., 117, 536549.

    • Search Google Scholar
    • Export Citation
  • Nowotarski, C., , P. Markowski, , Y. Richardson, , and G. Bryan, 2011: Interactions between simulated supercell thunderstorms and dry boundary layer convection. Preprints, 14th Conf. on Mesoscale Processes, Los Angeles, CA, Amer. Meteor. Soc., 7.3. [Available online at https://ams.confex.com/ams/14Meso15ARAM/techprogram/paper_190799.htm.]

  • Orlanski, I., 1976: A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys., 21, 251269.

  • Parker, M. D., 2008: Response of simulated squall lines to low-level cooling. J. Atmos. Sci., 65, 13231341.

  • Parker, M. D., , and R. H. Johnson, 2000: Organizational modes of midlatitude mesoscale convective systems. Mon. Wea. Rev., 128, 34133436.

    • Search Google Scholar
    • Export Citation
  • Parker, M. D., , and R. H. Johnson, 2004: Structure and dynamics of quasi-2D mesoscale convective systems. J. Atmos. Sci., 61, 545567.

  • Pleim, J. E., , and A. Xiu, 1995: Development and testing of a surface flux and planetary boundary layer model for application in mesoscale models. J. Appl. Meteor., 34, 1632.

    • Search Google Scholar
    • Export Citation
  • Rosenfeld, D., and Coauthors, 2011: Glaciation temperatures of convective clouds ingesting desert dust, air pollution and smoke from forest fire. Geophys. Res. Lett., 38, L21804, doi:10.1029/2011GL049423.

    • 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.

    • 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, 463485.

  • Schultz, P., 1995: An explicit cloud physics parameterization for operational numerical weather prediction. Mon. Wea. Rev., 123, 33313343.

    • Search Google Scholar
    • Export Citation
  • Seigel, R. B., , and S. C. van den Heever, 2012: Dust lofting and ingestion by supercell storms. J. Atmos. Sci., 69, 14531473.

  • Stensrud, D. J., , M. C. Coniglio, , R. Davies-Jones, , and J. Evans, 2005: Comments on “‘A theory for strong, long-lived squall lines’ revisited.” J. Atmos. Sci., 62, 29892996.

    • Search Google Scholar
    • Export Citation
  • Storer, R. L., , S. C. van den Heever, , and G. L. Stephens, 2010: Modeling aerosol impacts on convective storms in different environments. J. Atmos. Sci., 67, 39043915.

    • Search Google Scholar
    • Export Citation
  • Sun, W.-Y., , and C.-Z. Chang, 1986: Diffusion model for a convective layer. Part I: Numerical simulation of a convective boundary layer. J. Climate Appl. Meteor., 25, 14451453.

    • Search Google Scholar
    • Export Citation
  • Tao, W.-K., , S. Lang, , J. Simpson, , C.-H. Sui, , B. Ferrier, , and M.-D. Chou, 1996: Mechanisms of cloud radiation interaction in the tropics and midlatitudes. J. Atmos. Sci., 53, 26242651.

    • Search Google Scholar
    • Export Citation
  • Trapp, R. J., , and M. L. Weisman, 2003: Low-level mesovortices within squall lines and bow echoes. Part II: Their genesis and implications. Mon. Wea. Rev., 131, 28042823.

    • Search Google Scholar
    • Export Citation
  • Van Weverberg, K., , A. M. Vogelmann, , H. Morrison, , and J. Milbrandt, 2012: Sensitivity of idealized squall line simulations to the level of complexity used in two-moment bulk microphysics schemes. Mon. Wea. Rev., 140, 18831907.

    • Search Google Scholar
    • Export Citation
  • Varnai, T., , and R. Davies, 1999: Effects of cloud heterogeneities on shortwave radiation: Comparison of cloud-top variability and internal heterogeneity. J. Atmos. Sci., 56, 42064224.

    • Search Google Scholar
    • Export Citation
  • Wapler, K., , and B. Meyer, 2008: A fast three-dimensional approximation for the calculation of surface irradiance in large-eddy simulation models. J. Appl. Meteor. Climatol., 47, 30613071.

    • Search Google Scholar
    • Export Citation
  • Weisman, M. L., 1992: The role of convectively generated rear-inflow jets in the evolution of long-lived mesoconvective systems. J. Atmos. Sci., 49, 18261847.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Weisman, M. L., , and C. A. Davis, 1998: Mechanisms for the generation of mesoscale vortices within quasi-linear convective systems. J. Atmos. Sci., 55, 26032622.

    • 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.

  • Weisman, M. L., , and R. Rotunno, 2005: Reply. J. Atmos. Sci., 62, 29973002.

  • Weisman, M. L., , W. C. Skamarock, , and J. B. Klemp, 1997: The resolution dependence of explicitly modeled convective systems. Mon. Wea. Rev., 125, 527548.

    • Search Google Scholar
    • Export Citation
  • Xue, M., , K. K. Droegemeier, , V. Wong, , A. Shapiro, , and K. Brewster, 1995: ARPS version 4.0 user’s guide. Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, OK, 380 pp.

  • Xue, M., , K. K. Droegemeier, , and V. Wong, 2000: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction tool. Part I: Model dynamics and verification. Meteor. Atmos. Phys., 75, 161193.

    • 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, 143166.

    • Search Google Scholar
    • Export Citation
  • Xue, M., , D.-H. Wang, , J.-D. Gao, , K. Brewster, , and K. K. Droegemeier, 2003: The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation. Meteor. Atmos. Phys., 82, 139170.

    • Search Google Scholar
    • Export Citation
  • Ziegler, C. L., , E. R. Mansell, , J. M. Straka, , D. R. MacGorman, , and D. W. Burgess, 2010: The impact of spatial variations of low-level stability on the life cycle of a simulated supercell storm. Mon. Wea. Rev., 138, 17381766.

    • Search Google Scholar
    • Export Citation
2

Simulations of convective storms that are initiated in idealized ways (e.g., via a warm bubble or cold pool) in otherwise horizontally homogeneous environments, at least using a resolution similar to that used herein, typically must specify relatively moist midlevel environments in order for the convection to survive beyond its initial triggering. This issue is beyond the scope of the present paper. It is certainly possible that the effects of anvil shading documented herein are sensitive to the midlevel relative humidity.

3

The CAPE and CIN calculations include the effects of moisture on buoyancy and are based on the dry adiabatic ascent of a parcel lifted from the surface to its saturation pressure and pseudoadiabatic ascent thereafter.

4

The net positive area is ~500 J kg−1 less in the environment in the EAST simulations than in the WEST simulations at the easternmost longitude shown in Fig. 13 (i.e., 300 km east of the gust front). The net positive area differences are due to differences in the spatial distribution of compensating subsidence between the EAST and WEST simulations. The net positive area differences between the EAST and WEST simulations evident 300 km east of the gust front in Fig. 13 vanish in the very far-field environment (i.e., near the eastern boundary of the model domain).

5

In RKW88’s derivation, the upper limit of the integration of B is the depth of the density current H, not d, but this is only because the buoyancy is zero everywhere outside of the density current; d is the height at which the wind relative to the density current at the upper-left and upper-right boundaries of their control volume vanishes in the case of a vertically oriented jet at the leading edge of the density current (RKW88, p. 478). This height is a little higher than the top of the density current head, and is therefore potentially a kilometer or more higher than the depth of the dense fluid far behind the leading edge of the density current.

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