Editorial Type:
Article
Article Type:
Research Article

Impacts of Increasing Low-Level Shear on Supercells during the Early Evening Transition

Brice E. Coffer North Carolina State University, Raleigh, North Carolina

Search for other papers by Brice E. Coffer in
Current site
Google Scholar
PubMed Close
and
Matthew D. Parker North Carolina State University, Raleigh, North Carolina

Search for other papers by Matthew D. Parker in
Current site
Google Scholar
PubMed Close
Print Publication:
01 May 2015
DOI:
https://doi.org/10.1175/MWR-D-14-00328.1
Page(s):
1945–1969
Restricted access

Abstract

The dynamical response of simulated supercells to temporally increasing lower-tropospheric vertical wind shear is investigated using idealized simulations. These simulations are based upon observed soundings from two cases that underwent an early evening transition during the Second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2). Mature supercells were simulated in observed afternoon environments with moderate vertical wind shear and then compared to simulated supercells experiencing observed evening increases in lower-tropospheric shear. The primary effect of the increase in low-level shear is to establish larger values of vertical vorticity at lower altitudes in the storm’s updraft. In turn, this leads to a nonlinear increase in the updraft strength due to the enhanced dynamic pressure minimum associated with larger vorticity in the storm’s mesocyclone. This is particularly important at low levels, where it increases the storm's ability to lift cool surface air (including outflow). Trajectories launched in developing vortices show that, despite comparable buoyant accelerations, parcels experience greater vertical velocity and stretching of vertical vorticity due to increased dynamic accelerations when the low-level shear is increased. Thus, even as low-level stability gradually increases in the early evening, the supercells’ low-level updraft intensity and surface vorticity production can increase. These results are consistent with climatological observations of a supercell’s likelihood of tornadogenesis during the early evening hours.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/MWR-D-14-00328.s1.

Corresponding author address: Brice E. Coffer, Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Campus Box 8208, Raleigh, NC 27695-8208. E-mail: becoffer@ncsu.edu

Abstract

The dynamical response of simulated supercells to temporally increasing lower-tropospheric vertical wind shear is investigated using idealized simulations. These simulations are based upon observed soundings from two cases that underwent an early evening transition during the Second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2). Mature supercells were simulated in observed afternoon environments with moderate vertical wind shear and then compared to simulated supercells experiencing observed evening increases in lower-tropospheric shear. The primary effect of the increase in low-level shear is to establish larger values of vertical vorticity at lower altitudes in the storm’s updraft. In turn, this leads to a nonlinear increase in the updraft strength due to the enhanced dynamic pressure minimum associated with larger vorticity in the storm’s mesocyclone. This is particularly important at low levels, where it increases the storm's ability to lift cool surface air (including outflow). Trajectories launched in developing vortices show that, despite comparable buoyant accelerations, parcels experience greater vertical velocity and stretching of vertical vorticity due to increased dynamic accelerations when the low-level shear is increased. Thus, even as low-level stability gradually increases in the early evening, the supercells’ low-level updraft intensity and surface vorticity production can increase. These results are consistent with climatological observations of a supercell’s likelihood of tornadogenesis during the early evening hours.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/MWR-D-14-00328.s1.

Corresponding author address: Brice E. Coffer, Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Campus Box 8208, Raleigh, NC 27695-8208. E-mail: becoffer@ncsu.edu

Supplementary Materials

    • Supplemental Materials (PDF 2.45 MB)
Save
Cover Monthly Weather Review
Monthly Weather Review

  • Adlerman, E. J., K. K. Droegemeier, and R. P. Davies-Jones, 1999: A numerical simulation of cyclic mesocyclogenesis. J. Atmos. Sci., 56, 2045–2069, doi:10.1175/1520-0469(1999)056<2045:ANSOCM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Atkins, N. T., A. McGee, R. Ducharme, R. M. Wakimoto, and J. Wurman, 2012: The LaGrange Tornado during VORTEX2. Part II: Photogrammetric analysis of the tornado combined with dual-Doppler radar data. Mon. Wea. Rev., 140, 2939–2958, doi:10.1175/MWR-D-11-00285.1.

    • Search Google Scholar
    • Export Citation

  • Acevedo, O. C., and D. R. Fitzjarrald, 2001: The early evening surface-layer transition: Temporal and spatial variability. J. Atmos. Sci., 58, 2650–2667, doi:10.1175/1520-0469(2001)058<2650:TEESLT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Blackadar, A. K., 1957: Boundary layer wind maxima and their significance for the growth of nocturnal inversions. Bull. Amer. Meteor. Soc., 38, 282–290.

    • Search Google Scholar
    • Export Citation

  • Bonner, W. D., 1968: Climatology of the low level jet. Mon. Wea. Rev., 96, 833–850, doi:10.1175/1520-0493(1968)096<0833:COTLLJ>2.0.CO;2.

    • 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, 73–94, doi:10.1016/-8095(03)00045-0.

    • 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, 2917–2928, doi:10.1175/1520-0493(2002)130<2917:ABSFMN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Bunkers, M. J., B. A. Klimowski, J. W. Zeitler, R. L. Thompson, and M. L. Weisman, 2000: Predicting supercell motion using a new hodograph technique. Wea. Forecasting, 15, 61–79, doi:10.1175/1520-0434(2000)015<0061:PSMUAN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • 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, 3027–3051, doi:10.1175/JAS-D-13-0123.1.

    • Search Google Scholar
    • Export Citation

  • Davies, J. M., and A. Fischer, 2009: Environmental characteristics associated with nighttime tornadoes. Electron. J. Oper. Meteor., 10 (3), 1–29. [Available online at http://www.nwas.org/ej/2009-EJ3/.]

    • Search Google Scholar
    • Export Citation

  • Davies-Jones, R. P., 2015: A review of supercell and tornado dynamics. Atmos. Res., doi:10.1016/j.atmosres.2014.04.007, in press.

  • Davies-Jones, R. P., and H. E. Brooks, 1993: Mesocyclogenesis from a theoretical perspective. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., Vol. 79, Amer. Geophys. Union, 105–114.

  • Davies-Jones, R. P., R. J. Trapp, and H. B. Bluestein, 2001: Tornadoes and tornadic storms. Severe Convective Storms, Meteor. Monogr., No. 28, Amer. Meteor. Soc., 167–222, doi:10.1175/0065-9401-28.50.167.

  • Doswell, C. A., 1980: Synoptic-scale environments associated with High Plains severe thunderstorms. Bull. Amer. Meteor. Soc., 61, 1388–1400, doi:10.1175/1520-0477(1980)061<1388:SSEAWH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Fischer, A., and J. M. Davies, 2009: Significant nighttime tornadoes in the plains associated with relatively stable low-level conditions. Electron. J. Oper. Meteor., 10 (4), 1–33. [Available online at http://www.nwas.org/ej/2009-EJ4/.]

    • Search Google Scholar
    • Export Citation

  • Frame, J., and P. M. Markowski, 2010: Numerical simulations of radiative cooling beneath the anvils of supercell thunderstorms. Mon. Wea. Rev., 138, 3024–3047, doi:10.1175/2010MWR3177.1.

    • Search Google Scholar
    • Export Citation

  • Frame, J., and P. M. Markowski, 2013: Dynamical influences of anvil shading on simulated supercell thunderstorms. Mon. Wea. Rev., 141, 2802–2820, doi:10.1175/MWR-D-12-00146.1.

    • Search Google Scholar
    • Export Citation

  • French, A. J., and M. D. Parker, 2010: The response of simulated nocturnal convective systems to a developing low-level jet. J. Atmos. Sci., 67, 3384–3408, doi:10.1175/2010JAS3329.1.

    • Search Google Scholar
    • Export Citation

  • French, M. M., H. B. Bluestein, D. C. Dowell, L. J. Wicker, M. R. Kramar, and A. L. Pazmany, 2008: High-resolution, mobile Doppler radar observations of cyclic mesocyclogenesis in a supercell. Mon. Wea. Rev., 136, 4997–5016, doi:10.1175/2008MWR2407.1.

    • Search Google Scholar
    • Export Citation

  • Fritsch, J. M., J. D. Murphy, and J. S. Kain, 1994: Warm core vortex amplification over land. J. Atmos. Sci., 51, 1780–1807, doi:10.1175/1520-0469(1994)051<1780:WCVAOL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Kain, J. S., and Coauthors, 2008: Some practical considerations regarding horizontal resolution in the first generation of operational convection-allowing NWP. Wea. Forecasting, 23, 931–952, doi:10.1175/WAF2007106.1.

    • Search Google Scholar
    • Export Citation

  • Kis, A. K., and J. M. Straka, 2010: Nocturnal tornado climatology. Wea. Forecasting, 25, 545–561, doi:10.1175/2009WAF2222294.1.

  • Klemp, J. B., and R. B. Wilhelmson, 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 1070–1096, doi:10.1175/1520-0469(1978)035<1070:TSOTDC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Kosiba, K., J. Wurman, Y. Richardson, P. Markowski, P. Robinson, and J. Marquis, 2013: Genesis of the Goshen County, Wyoming, tornado on 5 June 2009 during VORTEX2. Mon. Wea. Rev., 141, 1157–1181, doi:10.1175/MWR-D-12-00056.1.

    • Search Google Scholar
    • Export Citation

  • Lapworth, A., 2003: Factors determining the decrease in surface wind speed following the evening transition. Quart. J. Roy. Meteor. Soc., 129, 1945–1968, doi:10.1256/qj.02.163.

    • Search Google Scholar
    • Export Citation

  • Letkewicz, C. E., A. J. French, and M. D. Parker, 2013: Base-state substitution: An idealized modeling technique for approximating environmental variability. Mon. Wea. Rev., 141, 3062–3086, doi:10.1175/MWR-D-12-00200.1.

    • Search Google Scholar
    • Export Citation

  • Lin, Y.-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 1065–1089, doi:10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Loftus, A. M., D. B. Weber, and C. A. Doswell, 2008: Parameterized mesoscale forcing mechanisms for initiating numerically simulated isolated multicellular convection. Mon. Wea. Rev., 136, 2408–2421, doi:10.1175/2007MWR2133.1.

    • Search Google Scholar
    • Export Citation

  • Maddox, R. A., 1993: Diurnal low-level wind oscillation and storm-relative helicity. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., Vol. 79, Amer. Geophys. Union, 591–598.

  • 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, 171–194, doi:10.1175/2009JAS2965.1.

    • Search Google Scholar
    • Export Citation

  • Markowski, P. M., and Y. P. Richardson, 2010: Mesoscale Meteorology in Midlatitudes. Wiley-Blackwell, 407 pp.

  • 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, 243–275, doi:10.1175/JAS-D-13-0159.1.

    • Search Google Scholar
    • Export Citation

  • Markowski, P. M., J. M. Straka, E. N. Rasmussen, and D. C. Dowell, 1998a: Observations of low-level baroclinity generated by anvil shadows. Mon. Wea. Rev., 126, 2942–2958, doi:10.1175/1520-0493(1998)126<2942:OOLLBG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Markowski, P. M., J. M. Straka, E. N. Rasmussen, and D. O. Blanchard, 1998b: Variability of storm-relative helicity during VORTEX. Mon. Wea. Rev., 126, 2959–2971, doi:10.1175/1520-0493(1998)126<2959:VOSRHD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Markowski, P. M., J. M. Straka, and E. N. Rasmussen, 2002: Direct surface thermodynamic observations within the rear-flank downdrafts of nontornadic and tornadic supercells. Mon. Wea. Rev., 130, 1692–1721, doi:10.1175/1520-0493(2002)130<1692:DSTOWT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Markowski, P. M., C. Hannon, J. Frame, E. Lancaster, A. Pietrycha, R. Edwards, and R. L. Thompson, 2003: Characteristics of vertical wind profiles near supercells obtained from the Rapid Update Cycle. Wea. Forecasting, 18, 1262–1272, doi:10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Markowski, P. M., J. M. Straka, E. N. Rasmussen, R. P. Davies-Jones, Y. Richardson, and R. J. Trapp, 2008: Vortex lines within low-level mesocyclones obtained from pseudo-dual-Doppler radar observations. Mon. Wea. Rev., 136, 3513–3535, doi:10.1175/2008MWR2315.1.

    • Search Google Scholar
    • Export Citation

  • Markowski, P. M., Y. P. Richardson, M. Majcen, J. Marquis, and J. Wurman, 2011: Characteristics of the wind field in three nontornadic low-level mesocyclones observed by the Doppler On Wheels radars. Electron. J. Severe Storms Meteor.,6 (3). [Available online at http://www.ejssm.org/ojs/index.php/ejssm/article/viewArticle/75.]

    • Search Google Scholar
    • Export Citation

  • Markowski, P. M., and Coauthors, 2012a: The pretornadic phase of the Goshen County, Wyoming, supercell of 5 June 2009 intercepted by VORTEX2. Part I: Evolution of kinematic and surface thermodynamic fields. Mon. Wea. Rev., 140, 2887–2915, doi:10.1175/MWR-D-11-00336.1.

    • Search Google Scholar
    • Export Citation

  • Markowski, P. M., and Coauthors, 2012b: The pretornadic phase of the Goshen County, Wyoming, supercell of 5 June 2009 intercepted by VORTEX2. Part II: Intensification of low-level rotation. Mon. Wea. Rev., 140, 2916–2938, doi:10.1175/MWR-D-11-00337.1.

    • Search Google Scholar
    • Export Citation

  • Marquis, J., Y. P. Richardson, P. M. Markowski, D. Dowell, and J. Wurman, 2012: Tornado maintenance investigated with high-resolution dual-Doppler and EnKF analysis. Mon. Wea. Rev., 140, 3–27, doi:10.1175/MWR-D-11-00025.1.

    • Search Google Scholar
    • Export Citation

  • Marquis, J., Y. P. Richardson, P. M. Markowski, D. Dowell, J. Wurman, K. Kosiba, P. Robinson, and G. Romine, 2014: An investigation of the Goshen County, Wyoming, tornadic supercell of 5 June 2009 using EnKF assimilation of mobile mesonet and radar observations collected during VORTEX2. Part I: Experiment design and verification of the EnKF analyses. Mon. Wea. Rev., 142, 530–554, doi:10.1175/MWR-D-13-00007.1.

    • Search Google Scholar
    • Export Citation

  • McCaul, E. W., and M. L. Weisman, 1996: Simulations of shallow supercell storms in landfalling hurricane environments. Mon. Wea. Rev., 124, 408–429, doi:10.1175/1520-0493(1996)124<0408:SOSSSI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Mead, C. M., and R. L. Thompson, 2011: Environmental characteristics associated with nocturnal significant-tornado events in the Great Plains. Electron. J. Severe Storms Meteor., 6 (6).[Available online at http://www.ejssm.org/ojs/index.php/ejssm/article/viewArticle/84.]

    • Search Google Scholar
    • Export Citation

  • Morrison, H., J. A. Curry, and V. I. Khvorostyanov, 2005: A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description. J. Atmos. Sci., 62, 1665–1677, doi:10.1175/JAS3446.1.

    • Search Google Scholar
    • Export Citation

  • Nieuwstadt, F. T. M., 1985: A model for the stationary, stable boundary layer. Turbulence and Diffusion in Stable Environments, J. C. R. Hunt, Ed., Oxford University Press, 149–179.

  • Nowotarski, C. J., P. M. Markowski, and Y. P. Richardson, 2011: The characteristics of numerically simulated supercell storms situated over statically stable boundary layers. Mon. Wea. Rev., 139, 3139–3162, doi:10.1175/MWR-D-10-05087.1.

    • Search Google Scholar
    • Export Citation

  • Nowotarski, C. J., P. M. Markowski, Y. P. Richardson, and G. H. Bryan, 2015: Supercell low-level mesocyclones in simulations with a sheared convective boundary layer. Mon. Wea. Rev., 143, 272–297, doi:10.1175/MWR-D-14-00151.1.

    • Search Google Scholar
    • Export Citation

  • Parker, M. D., 2014: Composite VORTEX2 supercell environments from near-storm soundings. Mon. Wea. Rev., 142, 508–529, doi:10.1175/MWR-D-13-00167.1.

    • Search Google Scholar
    • Export Citation

  • Richardson, Y. P., K. K. Droegemeier, and R. P. Davies-Jones, 2007: The influence of horizontal environmental variability on numerically simulated convective storms. Part I: Variations in vertical shear. Mon. Wea. Rev., 135, 3429–3455, doi:10.1175/MWR3463.1.

    • 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, 136–151, doi:10.1175/1520-0493(1982)110<0136:TIOTSI>2.0.CO;2.

    • 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, 130–154, doi:10.1175/JAS-D-13-073.1.

    • Search Google Scholar
    • Export Citation

  • Shapiro, A., and E. Fedorovich, 2010: Analytical description of a nocturnal low-level jet. Quart. J. Roy. Meteor. Soc., 136, 1255–1262, doi:10.1002/qj.628.

    • Search Google Scholar
    • Export Citation

  • Skinner, P., C. Weiss, M. French, H. Bluestein, P. Markowski, and Y. Richardson, 2014: VORTEX2 observations of a low-level mesocyclone with multiple internal real-flank downdraft momentum surges in the 18 May 2010 Dumas, Texas, supercell. Mon. Wea. Rev., 142, 2935–2960, doi:10.1175/MWR-D-13-00240.1.

    • Search Google Scholar
    • Export Citation

  • Song, J., K. Liao, R. L. Coulter, and B. M. Lesht, 2005: Climatology of the low-level jet at the southern Great Plains Atmospheric Boundary Layer Experiment site. J. Appl. Meteor., 44, 1593–1606, doi:10.1175/JAM2294.1.

    • Search Google Scholar
    • Export Citation

  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

  • Tao, W.-K., and J. Simpson, 1993: The Goddard Cumulus Ensemble Model. Part I: Model description. Terr. Atmos. Oceanic Sci., 4, 19–54.

  • Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 5095–5115, doi:10.1175/2008MWR2387.1.

    • Search Google Scholar
    • Export Citation

  • Thompson, R. L., R. Edwards, J. A. Hart, K. L. Elmore, and P. Markowski, 2003: Close proximity soundings within supercell environments obtained from the rapid update cycle. Wea. Forecasting, 18, 1243–1261, doi:10.1175/1520-0434(2003)018<1243:CPSWSE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Thompson, R. L., C. M. Mead, and R. Edwards, 2007: Effective storm-relative helicity and bulk shear in supercell thunderstorm environments. Wea. Forecasting, 22, 102–115, doi:10.1175/WAF969.1.

    • Search Google Scholar
    • Export Citation

  • Trapp, R. J., 1999: Observations of nontornadic low-level mesocyclones and attendant tornadogenesis failure during VORTEX. Mon. Wea. Rev., 127, 1693–1705, doi:10.1175/1520-0493(1999)127<1693:OONLLM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Trapp, R. J., G. J. Stumpf, and K. L. Manross, 2005: A reassessment of the precentage of tornadic mesocyclones. Wea. Forecasting, 20, 680–687, doi:10.1175/WAF864.1.

    • Search Google Scholar
    • Export Citation

  • Van de Wiel, B. J. H., A. F. Moene, G. J. Steeneveld, P. Baas, F. C. Bosveld, and A. M. Holtslag, 2010: A conceptual view on inertial oscillations and nocturnal low-level jets. J. Atmos. Sci., 67, 2679–2689, doi:10.1175/2010JAS3289.1.

    • Search Google Scholar
    • Export Citation

  • Wakimoto, R. M., N. T. Atkins, and J. Wurman, 2011: The LaGrange Tornado during VORTEX2. Part I: Photogrammetric analysis of the tornado combined with single-Doppler radar data. Mon. Wea. Rev., 139, 2233–2258, doi:10.1175/2010MWR3568.1.

    • Search Google Scholar
    • Export Citation

  • Wakimoto, R. M., P. Stauffer, W. Lee, N. T. Atkins, and J. Wurman, 2012: Finescale structure of the LaGrange, Wyoming, tornado during VORTEX2: GBVTD and photogrammetric analyses. Mon. Wea. Rev., 140, 3397–3418, doi:10.1175/MWR-D-12-00036.1.

    • 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, 1295–1307, doi:10.1175/1520-0469(1972)029<1295:TPPATN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Wilhelmson, R. B., and L. J. Wicker, 2001: Numerical modeling of severe local storms. Severe Convective Storms, Meteor. Monogr., No. 28, Amer. Meteor. Soc., 123–166, doi:10.1175/0065-9401-28.50.123.

  • Wurman, J., D. Dowell, Y. Richardson, P. Markowski, E. Rasmussen, D. Burgess, L. Wicker, and H. B. Bluestein, 2012: The Second Verification of the Origins of Rotation in Tornadoes Experiment: VORTEX2. Bull. Amer. Meteor. Soc., 93, 1147–1170, doi:10.1175/BAMS-D-11-00010.1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 3595 2060 78
PDF Downloads 1396 286 24