The Development of Severe Vortices within Simulated High-Shear, Low-CAPE Convection

Keith D. Sherburn Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina

Search for other papers by Keith D. Sherburn in
Current site
Google Scholar
PubMed
Close
and
Matthew D. Parker Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina

Search for other papers by Matthew D. Parker in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Environments characterized by large values of vertical wind shear and modest convective available potential energy (CAPE) are colloquially referred to as high-shear, low-CAPE (HSLC) environments. Convection within these environments represents a considerable operational forecasting challenge. Generally, it has been determined that large low-level wind shear and steep low-level lapse rates—along with synoptic-scale forcing for ascent—are common ingredients supporting severe HSLC convection. This work studies the specific processes that lead to the development of strong surface vortices in HSLC convection, particularly associated with supercells embedded within a quasi-linear convective system (QLCS), and how these processes are affected by varying low-level shear vector magnitudes and lapse rates. Analysis of a control simulation, conducted with a base state similar to a typical HSLC severe environment, reveals that the key factors in the development of a strong surface vortex in HSLC embedded supercells are (i) a strong low- to midlevel mesocyclone, and (ii) a subsequent strong low-level updraft that results from the intense, upward-pointing dynamic perturbation pressure gradient acceleration. Through a matrix of high-resolution, idealized simulations, it is determined that sufficient low-level shear vector magnitudes are necessary for the development of low- to midlevel vertical vorticity [factor (i)], while steeper low-level lapse rates provide stronger initial low-level updrafts [factor (ii)]. This work shows why increased low-level lapse rates and low-level shear vector magnitudes are important to HSLC convection on the storm scale, while also revealing similarities between surface vortexgenesis in HSLC embedded supercells and higher-CAPE supercells.

Current affiliation: National Weather Service Forecast Office, Rapid City, South Dakota.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Keith Sherburn, keith.sherburn@noaa.gov

Abstract

Environments characterized by large values of vertical wind shear and modest convective available potential energy (CAPE) are colloquially referred to as high-shear, low-CAPE (HSLC) environments. Convection within these environments represents a considerable operational forecasting challenge. Generally, it has been determined that large low-level wind shear and steep low-level lapse rates—along with synoptic-scale forcing for ascent—are common ingredients supporting severe HSLC convection. This work studies the specific processes that lead to the development of strong surface vortices in HSLC convection, particularly associated with supercells embedded within a quasi-linear convective system (QLCS), and how these processes are affected by varying low-level shear vector magnitudes and lapse rates. Analysis of a control simulation, conducted with a base state similar to a typical HSLC severe environment, reveals that the key factors in the development of a strong surface vortex in HSLC embedded supercells are (i) a strong low- to midlevel mesocyclone, and (ii) a subsequent strong low-level updraft that results from the intense, upward-pointing dynamic perturbation pressure gradient acceleration. Through a matrix of high-resolution, idealized simulations, it is determined that sufficient low-level shear vector magnitudes are necessary for the development of low- to midlevel vertical vorticity [factor (i)], while steeper low-level lapse rates provide stronger initial low-level updrafts [factor (ii)]. This work shows why increased low-level lapse rates and low-level shear vector magnitudes are important to HSLC convection on the storm scale, while also revealing similarities between surface vortexgenesis in HSLC embedded supercells and higher-CAPE supercells.

Current affiliation: National Weather Service Forecast Office, Rapid City, South Dakota.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Keith Sherburn, keith.sherburn@noaa.gov
Save
  • Adlerman, E. J., and K. K. Droegemeier, 2005: The dependence of numerically simulated cyclic mesocyclogenesis upon environmental vertical wind shear. Mon. Wea. Rev., 133, 35953623, https://doi.org/10.1175/MWR3039.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Anderson-Frey, A. K., Y. P. Richardson, A. R. Dean, R. L. Thompson, and B. T. Smith, 2016: Investigation of near-storm environments for tornado events and warnings. Wea. Forecasting, 31, 17711790, https://doi.org/10.1175/WAF-D-16-0046.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atkins, N. T., and M. St. Laurent, 2009a: Bow echo mesovortices. Part I: Processes that influence their damaging potential. Mon. Wea. Rev., 137, 14971513, https://doi.org/10.1175/2008MWR2649.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atkins, N. T., and M. St. Laurent, 2009b: Bow echo mesovortices. Part II: Their genesis. Mon. Wea. Rev., 137, 15141532, https://doi.org/10.1175/2008MWR2650.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atkins, N. T., J. M. Arnott, R. W. Przybylinski, R. A. Wolf, and B. D. Ketcham, 2004: Vortex structure and evolution within bow echoes. Part I: Single-Doppler and damage analysis of the 29 June 1998 derecho. Mon. Wea. Rev., 132, 22242242, https://doi.org/10.1175/1520-0493(2004)132<2224:VSAEWB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atkins, N. T., C. S. Bouchard, R. W. Przybylinski, R. J. Trapp, and G. Schmocker, 2005: Damaging surface wind mechanisms within the 10 June 2003 Saint Louis bow echo during BAMEX. Mon. Wea. Rev., 133, 22752296, https://doi.org/10.1175/MWR2973.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Blumberg, W. G., K. T. Halbert, T. A. Supinie, P. T. Marsh, R. L. Thompson, and J. A. Hart, 2017: SHARPpy: An open source sounding analysis toolkit for the atmospheric sciences. Bull. Amer. Meteor. Soc., 98, 16251636, https://doi.org/10.1175/BAMS-D-15-00309.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brooks, H. E., J. W. Lee, and J. P. Craven, 2003: The spatial distribution of severe thunderstorm and tornado environments from global reanalysis data. Atmos. Res., 67–68, 7394, https://doi.org/10.1016/S0169-8095(03)00045-0.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and R. Rotunno, 2009: Evaluation of an analytical model for the maximum intensity of tropical cyclones. J. Atmos. Sci., 66, 30423060, https://doi.org/10.1175/2009JAS3038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bunkers, M. J., D. A. Barber, R. L. Thompson, R. Edwards, and J. Garner, 2014: Choosing a universal mean wind for supercell motion prediction. J. Oper. Meteor., 2, 115129, https://doi.org/10.15191/nwajom.2014.0211.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Coffer, B. E., and M. D. Parker, 2017: Simulated supercells in nontornadic and tornadic VORTEX2 environments. Mon. Wea. Rev., 145, 149180, https://doi.org/10.1175/MWR-D-16-0226.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Coffer, B. E., M. D. Parker, J. M. L. Dahl, L. J. Wicker, and A. J. Clark, 2017: Volatility of tornadogenesis: An ensemble of simulated nontornadic and tornadic supercells in VORTEX2 environments. Mon. Wea. Rev., 145, 46054625, https://doi.org/10.1175/MWR-D-17-0152.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cope, A. M., 2004: An early morning mid-Atlantic severe weather episode: Short-lived tornadoes in a high-shear low-instability environment. 22nd Conf. on Severe Local Storms, Hyannis, MA, Amer. Meteor. Soc., P1.4, https://ams.confex.com/ams/11aram22sls/webprogram/Paper81834.html.

  • Dahl, J. M. L., M. D. Parker, and L. J. Wicker, 2014: Imported and storm-generated near-ground vertical vorticity in a simulated supercell. J. Atmos. Sci., 71, 30273051, https://doi.org/10.1175/JAS-D-13-0123.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davenport, C. E., and M. D. Parker, 2015: Impact of environmental heterogeneity on the dynamics of a dissipating supercell thunderstorm. Mon. Wea. Rev., 143, 42444277, https://doi.org/10.1175/MWR-D-15-0072.1.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 2015: A review of supercell and tornado dynamics. Atmos. Res., 158–159, 274291, https://doi.org/10.1016/j.atmosres.2014.04.007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., and H. Brooks, 1993: Mesocyclogenesis from a theoretical perspective. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, C. Church et al., Eds., Amer. Geophys. Union, 105–114.

    • Crossref
    • Export Citation
  • Davis, J. M., and M. D. Parker, 2014: Radar climatology of tornadic and nontornadic vortices in high-shear, low-CAPE environments in the mid-Atlantic and southeastern United States. Wea. Forecasting, 29, 828853, https://doi.org/10.1175/WAF-D-13-00127.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dawson, D. T., M. Xue, A. Shapiro, J. A. Milbrandt, and A. D. Schenkman, 2016: Sensitivity of real-data simulations of the 3 May 1999 Oklahoma City tornadic supercell and associated tornadoes to multimoment microphysics. Part II: Analysis of buoyancy and dynamic pressure forces in simulated tornado-like vortices. J. Atmos. Sci., 73, 10391061, https://doi.org/10.1175/JAS-D-15-0114.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dean, A. R., and R. S. Schneider, 2012: An examination of tornado environments, events, and impacts from 2003-2012. 26th Conf. on Severe Local Storms, Nashville, TN, Amer. Meteor. Soc., 60, https://ams.confex.com/ams/26SLS/webprogram/Paper211580.html.

  • Esterheld, J. M., and D. J. Giuliano, 2008: Discriminating between tornadic and non-tornadic supercells: A new hodograph technique. Electron. J. Severe Storms Meteor., 3 (2), http://www.ejssm.org/ojs/index.php/ejssm/article/viewArticle/33.

    • Search Google Scholar
    • Export Citation
  • Godfrey, E. S., R. J. Trapp, and H. E. Brooks, 2004: A study of the pre-storm environment of tornadic quasi-linear convective systems. 22nd Conf. on Severe Local Storms, Hyannis, MA, Amer. Meteor. Soc., 3A.5, https://ams.confex.com/ams/11aram22sls/techprogram/paper_81388.htm.

  • Hampshire, N. L., R. M. Mosier, T. M. Ryan, and D. E. Cavanaugh, 2017: Relationship of low-level instability and tornado damage rating based on observed soundings. J. Oper. Meteor., 6, 112, https://doi.org/10.15191/nwajom.2018.0601.

    • Search Google Scholar
    • Export Citation
  • King, J. R., M. D. Parker, K. D. Sherburn, and G. M. Lackmann, 2017: Rapid evolution of cool season, low CAPE severe thunderstorm environments. Wea. Forecasting, 32, 763779, https://doi.org/10.1175/WAF-D-16-0141.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., 1987: Dynamics of tornadic thunderstorms. Annu. Rev. Fluid Mech., 19, 369402, https://doi.org/10.1146/annurev.fl.19.010187.002101.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leslie, L. M., and R. K. Smith, 1978: The effect of vertical stability on tornadogenesis. J. Atmos. Sci., 35, 12811288, https://doi.org/10.1175/1520-0469(1978)035<1281:TEOVSO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mansell, E. R., C. L. Ziegler, and E. C. Bruning, 2010: Simulated electrification of a small thunderstorm with two-moment bulk microphysics. J. Atmos. Sci., 67, 171194, https://doi.org/10.1175/2009JAS2965.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., 2016: An idealized numerical simulation investigation of the effects of surface drag on the development of near-surface vertical vorticity in supercell thunderstorms. J. Atmos. Sci., 73, 43494385, https://doi.org/10.1175/JAS-D-16-0150.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., 2018: A review of the various treatments of the surface momentum flux in severe storms simulations: Assumptions, deficiencies, and alternatives. 29th Conf. on Severe Local Storms, Stowe, VT, Amer. Meteor. Soc., 7.3, https://ams.confex.com/ams/29SLS/webprogram/Paper348116.html.

  • Markowski, P. M., and G. H. Bryan, 2016: LES of laminar flow in the PBL: A potential problem for convective storm simulations. Mon. Wea. Rev., 144, 18411850, https://doi.org/10.1175/MWR-D-15-0439.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., and Y. P. Richardson, 2014: The influence of environmental low-level shear and cold pools on tornadogenesis: Insights from idealized simulations. J. Atmos. Sci., 71, 243275, https://doi.org/10.1175/JAS-D-13-0159.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., and Y. P. Richardson, 2017: Large sensitivity of near-surface vertical vorticity development to heat sink location in idealized simulations of supercell-like storms. J. Atmos. Sci., 74, 10951104, https://doi.org/10.1175/JAS-D-16-0372.1.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Okubo, A., 1970: Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences. Deep-Sea Res. Oceanogr. Abstr., 17, 445454.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Orf, L., R. Wilhelmson, B. Lee, C. Finley, and A. Houston, 2017: Evolution of a long-track violent tornado within a simulated supercell. Bull. Amer. Meteor. Soc., 98, 4568, https://doi.org/10.1175/BAMS-D-15-00073.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Parker, M. D., 2007: Simulated convective lines with parallel stratiform precipitation. Part II: Governing dynamics and associated sensitivities. J. Atmos. Sci., 64, 289313, https://doi.org/10.1175/JAS3854.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Parker, M. D., 2010: Relationship between system slope and updraft intensity in squall lines. Mon. Wea. Rev., 138, 35723578, https://doi.org/10.1175/2010MWR3441.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Parker, M. D., 2012: Impacts of lapse rates on low-level rotation in idealized storms. J. Atmos. Sci., 69, 538559, https://doi.org/10.1175/JAS-D-11-058.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Parker, M. D., 2017: How much does “backing aloft” actually impact a supercell? Wea. Forecasting, 32, 19371957, https://doi.org/10.1175/WAF-D-17-0064.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Parker, M. D., and R. H. Johnson, 2004a: Simulated convective lines with leading precipitation. Part I: Governing dynamics. J. Atmos. Sci., 61, 16371655, https://doi.org/10.1175/1520-0469(2004)061<1637:SCLWLP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Parker, M. D., and R. H. Johnson, 2004b: Structures and dynamics of quasi-2D mesoscale convective systems. J. Atmos. Sci., 61, 545567, https://doi.org/10.1175/1520-0469(2004)061<0545:SADOQM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Przybylinski, R. W., G. K. Schmocker, and Y.-J. Lin, 2000: A study of storm and vortex morphology during the “intensifying stage” of severe wind mesoscale convective systems. Preprints, 20th Conf. on Severe Local Storms, Orlando, FL, Amer. Meteor. Soc., 173176.

  • Roberts, B., M. Xue, A. D. Schenkman, and D. T. Dawson II, 2016: The role of surface drag in tornadogenesis within an idealized supercell simulation. J. Atmos. Sci., 73, 33713395, https://doi.org/10.1175/JAS-D-15-0332.1.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rotunno, R., P. M. Markowski, and G. H. Bryan, 2017: “Near ground” vertical vorticity in supercell thunderstorm models. J. Atmos. Sci., 74, 17571766, https://doi.org/10.1175/JAS-D-16-0288.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schaumann, J. S., and R. W. Przybylinski, 2012: Operational application of 0-3 km bulk shear vectors in assessing quasi linear convective system mesovortex and tornado potential. 26th Conf. on Severe Local Storms, Nashville, TN, Amer. Meteor. Soc., 142, https://ams.confex.com/ams/26SLS/webprogram/Paper212008.html.

  • Schenkman, A. D., M. Xue, and A. Shapiro, 2012: Tornadogenesis in a simulated mesovortex within a mesoscale convective system. J. Atmos. Sci., 69, 33723390, https://doi.org/10.1175/JAS-D-12-038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schenkman, A. D., M. Xue, and M. Hu, 2014: Tornadogenesis in a high-resolution simulation of the 8 May 2003 Oklahoma City supercell. J. Atmos. Sci., 71, 130154, https://doi.org/10.1175/JAS-D-13-073.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schneider, R. S., A. R. Dean, S. J. Weiss, and P. D. Bothwell, 2006: Analysis of estimated environments for 2004 and 2005 severe convective storm reports. 23rd Conf. on Severe Local Storms, St. Louis, MO, Amer. Meteor. Soc., 3.5, https://ams.confex.com/ams/23SLS/techprogram/paper_115246.htm.

  • Sherburn, K. D., and M. D. Parker, 2014: Climatology and ingredients of significant severe convection in high-shear, low-CAPE environments. Wea. Forecasting, 29, 854877, https://doi.org/10.1175/WAF-D-13-00041.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sherburn, K. D., M. D. Parker, J. R. King, and G. M. Lackmann, 2016: Composite environments of severe and nonsevere high-shear, low-CAPE convective events. Wea. Forecasting, 31, 18991927, https://doi.org/10.1175/WAF-D-16-0086.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sherburn, K. D., and Coauthors, 2019: Partnering research, education, and operations via a cool season severe weather soundings program. Bull. Amer. Meteor. Soc., 100, 307320, https://doi.org/10.1175/BAMS-D-17-0186.1.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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, https://doi.org/10.1175/1520-0493(2003)131<2804:LMWSLA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wakimoto, R. M., H. V. Murphey, A. Nester, D. P. Jorgensen, and N. T. Atkins, 2006: High winds generated by bow echoes. Part I: Overview of the Omaha bow echo 5 July 2003 storm during BAMEX. Mon. Wea. Rev., 134, 27932812, https://doi.org/10.1175/MWR3215.1.

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

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weisman, M. L., and R. J. Trapp, 2003: Low-level mesovortices within squall lines and bow echoes. Part I: Overview and dependence on environmental shear. Mon. Wea. Rev., 131, 27792803, https://doi.org/10.1175/1520-0493(2003)131<2779:LMWSLA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weiss, J., 1991: The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica D, 48, 273294, https://doi.org/10.1016/0167-2789(91)90088-Q.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wilhelmson, R. B., and Y. Ogura, 1972: The pressure perturbation and the numerical modeling of a cloud. J. Atmos. Sci., 29, 12951307, https://doi.org/10.1175/1520-0469(1972)029<1295:TPPATN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xu, X., M. Xue, and Y. Wang, 2015: The genesis of mesovortices within a real-data simulation of a bow echo system. J. Atmos. Sci., 72, 19631986, https://doi.org/10.1175/JAS-D-14-0209.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 1 0 0
Full Text Views 1295 277 49
PDF Downloads 1001 210 9