Editorial Type:
Article
Article Type:
Research Article

A Spectral Cumulus Parameterization Scheme Interpolating between Two Convective Updrafts with Semi-Lagrangian Calculation of Transport by Compensatory Subsidence

Hiromasa Yoshimura Meteorological Research Institute, Tsukuba, Japan

Search for other papers by Hiromasa Yoshimura in
Current site
Google Scholar
PubMed Close
,
Ryo Mizuta Meteorological Research Institute, Tsukuba, Japan

Search for other papers by Ryo Mizuta in
Current site
Google Scholar
PubMed Close
, and
Hiroyuki Murakami NOAA/Geophysical Fluid Dynamics Laboratory, Princeton University, Princeton, New Jersey

Search for other papers by Hiroyuki Murakami in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Feb 2015
DOI:
https://doi.org/10.1175/MWR-D-14-00068.1
Page(s):
597–621
Restricted access

Abstract

The authors have developed a new spectral cumulus parameterization scheme that explicitly considers an ensemble of multiple convective updrafts by interpolating in-cloud variables between two convective updrafts with large and small entrainment rates. This cumulus scheme has the advantages that the variables in entraining and detraining convective updrafts are calculated in detail layer by layer as in the Tiedtke scheme, and that a spectrum of convective updrafts with different heights due to the difference in entrainment rates is explicitly represented, as in the Arakawa–Schubert scheme. A conservative and monotonic semi-Lagrangian scheme is used for calculation of transport by convection-induced compensatory subsidence. Use of the semi-Lagrangian scheme relaxes the mass-flux limit due to the Courant–Friedrichs–Lewy (CFL) condition, and moreover ensures nonnegative natural material transport. A global atmospheric model using this cumulus scheme gives an atmospheric simulation that agrees well with the observational climatology.

Corresponding author address: Hiromasa Yoshimura, Meteorological Research Institute, 1-1 Nagamine, Tsukuba 305-0052, Japan. E-mail: hyoshimu@mri-jma.go.jp

Abstract

The authors have developed a new spectral cumulus parameterization scheme that explicitly considers an ensemble of multiple convective updrafts by interpolating in-cloud variables between two convective updrafts with large and small entrainment rates. This cumulus scheme has the advantages that the variables in entraining and detraining convective updrafts are calculated in detail layer by layer as in the Tiedtke scheme, and that a spectrum of convective updrafts with different heights due to the difference in entrainment rates is explicitly represented, as in the Arakawa–Schubert scheme. A conservative and monotonic semi-Lagrangian scheme is used for calculation of transport by convection-induced compensatory subsidence. Use of the semi-Lagrangian scheme relaxes the mass-flux limit due to the Courant–Friedrichs–Lewy (CFL) condition, and moreover ensures nonnegative natural material transport. A global atmospheric model using this cumulus scheme gives an atmospheric simulation that agrees well with the observational climatology.

Corresponding author address: Hiromasa Yoshimura, Meteorological Research Institute, 1-1 Nagamine, Tsukuba 305-0052, Japan. E-mail: hyoshimu@mri-jma.go.jp
Save
Cover Monthly Weather Review
Monthly Weather Review

  • Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. J. Atmos. Sci., 31, 674–701, doi:10.1175/1520-0469(1974)031<0674:IOACCE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Bechtold, P., M. Köhler, T. Jung, F. Doblas-Reyes, M. Leutbecher, M. Rodwell, F. Vitart, and G. Balsamo, 2008: Advances in simulating atmospheric variability with the ECMWF model: From synoptic to decadal time-scales. Quart. J. Roy. Meteor. Soc., 134, 1337–1351, doi:10.1002/qj.289.

    • Search Google Scholar
    • Export Citation

  • Betts, A. K., and M. J. Miller, 1986: A new convective adjustment scheme. Part II: Single column tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets. Quart. J. Roy. Meteor. Soc., 112, 693–709, doi:10.1002/qj.49711247308.

    • Search Google Scholar
    • Export Citation

  • Bryan, G. H., J. C. Wingaard, and J. M. Fritsch, 2003: Resolution requirements for the simulation of deep moist convection. Mon. Wea. Rev., 131, 2394–2416, doi:10.1175/1520-0493(2003)131<2394:RRFTSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Chikira, M., and M. Sugiyama, 2010: A cumulus parameterization with state-dependent entrainment rate. Part I: Description and sensitivity to temperature and humidity profiles. J. Atmos. Sci., 67, 2171–2193, doi:10.1175/2010JAS3316.1.

    • Search Google Scholar
    • Export Citation

  • Collins, W. D., 2001: Parameterization of generalized cloud overlap for radiative calculation in general circulation models. J. Atmos. Sci., 58, 3224–3242, doi:10.1175/1520-0469(2001)058<3224:POGCOF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • de Rooy, W. C., and Coauthors, 2013: Entrainment and detrainment in cumulus convection: An overview. Quart. J. Roy. Meteor. Soc., 139, 1–19, doi:10.1002/qj.1959.

    • Search Google Scholar
    • Export Citation

  • ECMWF, 2006: IFS documentation CY31r1. [Available online at http://nwmstest.ecmwf.int/research/ifsdocs/CY31r1/index.html.]

  • Eito, H., M. Murakami, C. Muroi, T. Kato, S. Hayashi, H. Kuroiwa, and M. Yoshizaki, 2010: The structure and formation mechanism of transversal cloud bands associated with the Japan-Sea polar-airmass convergence zone. J. Meteor. Soc. Japan, 88, 625–648, doi:10.2151/jmsj.2010-402.

    • Search Google Scholar
    • Export Citation

  • Emanuel, K. A., 1991: A scheme for representing cumulus convection in large-scale models. J. Atmos. Sci., 48, 2313–2335, doi:10.1175/1520-0469(1991)048<2313:ASFRCC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Endo, H., A. Kitoh, T. Ose, R. Mizuta, and S. Kusunoki, 2012: Future changes and uncertainties in Asian precipitation simulated by multi-physics and multi-sea surface temperature ensemble experiments with high-resolution Meteorological Research Institute atmospheric general circulation models (MRI-AGCMs). J. Geophys. Res., 117, D16118, doi:10.1029/2012JD017874.

    • Search Google Scholar
    • Export Citation

  • Fritsch, J. M., and C. F. Chappell, 1980: Numerical prediction of convectively driven mesoscale pressure systems. Part I: Convective parameterization. J. Atmos. Sci., 37, 1722–1733, doi:10.1175/1520-0469(1980)037<1722:NPOCDM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Gravel, S., and A. Staniforth, 1994: A mass-conserving semi-Lagrangian scheme for the shallow-water equations. Mon. Wea. Rev., 122, 243–248, doi:10.1175/1520-0493(1994)122<0243:AMCSLS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Gregory, D., and P. Rowntree, 1990: A mass flux convection scheme with representation of cloud ensemble characteristics and stability-dependent closure. Mon. Wea. Rev., 118, 1483–1506, doi:10.1175/1520-0493(1990)118<1483:AMFCSW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Gregory, D., R. Kershaw, and P. M. Inness, 1997: Parameterization of momentum transports by convection. II: Tests in single-column and general circulation models. Quart. J. Roy. Meteor. Soc., 123, 1153–1183, doi:10.1002/qj.49712354103.

    • Search Google Scholar
    • Export Citation

  • Hu, Q., 1997: A cumulus parameterization based on a cloud model of intermittently rising thermals. J. Atmos. Sci., 54, 2292–2307, doi:10.1175/1520-0469(1997)054<2292:ACPBOA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • JMA, 2007: Outline of the operational numerical weather prediction at the Japan Meteorological Agency (Appendix to WMO numerical weather prediction progress report). Japan Meteorological Agency, 194 pp. [Available online at http://www.jma.go.jp/jma/jma-eng/jma-center/nwp/outline-nwp/index.htm.]

  • Johnson, R. H., 1984: Partitioning tropical heat and moisture budgets into cumulus and mesoscale components: Implications for cumulus parameterization. Mon. Wea. Rev., 112, 1590–1601, doi:10.1175/1520-0493(1984)112<1590:PTHAMB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Johnson, R. H., and G. S. Young, 1983: Heat and moisture budgets of tropical mesoscale anvil clouds. J. Atmos. Sci., 40, 2138–2147, doi:10.1175/1520-0469(1983)040<2138:HAMBOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Kain, J. S., and J. M. Fritsch, 1990: A one-dimensional entraining/detraining plume model and its application in convective parameterization. J. Atmos. Sci., 47, 2784–2802, doi:10.1175/1520-0469(1990)047<2784:AODEPM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Kanada, S., M. Nakano, S. Hayashi, T. Kato, M. Nakamura, K. Kurihara, and A. Kitoh, 2008: Reproducibility of maximum daily precipitation amount over Japan by a high-resolution non-hydrostatic model. SOLA, 4, 105–108, doi:10.2151/sola.2008-027.

    • Search Google Scholar
    • Export Citation

  • Kawai, H., 2006: PDF cloud scheme and prognostic cloud scheme in JMA global model. CAS/JSC WGNE Research Activities in Atmospheric and Ocean Modeling, Rep. 36, Japan Meteorological Agency, 4.15–4.16. [Available online at http://www.mri-jma.go.jp/Dep/cl/cl1/members/kawai/Publications/ResActWGNE2006.pdf.]

  • Kawai, H., 2013: Improvement of a stratocumulus scheme for mid-latitude marine low clouds. CAS/JSC WGNE Research Activities in Atmospheric and Ocean Modeling, Rep. 42, Japan Meteorological Agency, 4.03–4.04. [Available online at http://www.wcrp-climate.org/WGNE/BlueBook/2013/individual-articles/04_Kawai_Hideaki_ResActWGNE2013b.pdf.]

  • Kim, D., and Coauthors, 2009: Application of MJO simulation diagnostics to climate models. J. Climate, 22, 6413–6436, doi:10.1175/2009JCLI3063.1.

    • Search Google Scholar
    • Export Citation

  • Kuell, V., and A. Bott, 2009: Application of the hybrid convection parameterization scheme HYMACS to different meteorological situations. Atmos. Res., 94, 743–753, doi:10.1016/j.atmosres.2009.04.002.

    • Search Google Scholar
    • Export Citation

  • Kuo, H. L., 1965: On formation and intensification of tropical cyclones through latent heat release by cumulus convection. J. Atmos. Sci., 22, 40–63, doi:10.1175/1520-0469(1965)022<0040:OFAIOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Kuo, H. L., 1974: Further studies of the parameterization of the influence of cumulus convection on large-scale flow. J. Atmos. Sci., 31, 1232–1240, doi:10.1175/1520-0469(1974)031<1232:FSOTPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Leary, C. A., and R. A. Houze Jr., 1979: The structure and evolution of convection in a tropical cloud cluster. J. Atmos. Sci., 36, 437–457, doi:10.1175/1520-0469(1979)036<0437:TSAEOC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Liebmann, B., and C. A. Smith, 1996: Description of a complete (interpolated) outgoing longwave radiation dataset. Bull. Amer. Meteor. Soc., 77, 1275–1277.

    • Search Google Scholar
    • Export Citation

  • Lilly, D. K., 1990: Numerical prediction of thunderstorms—Has its time come? Quart. J. Roy. Meteor. Soc., 116, 779–798, doi:10.1002/qj.49711649402.

    • Search Google Scholar
    • Export Citation

  • Lin, S.-J., and R. B. Rood, 1996: Multidimensional flux-form semi-Lagrangian transport scheme. Mon. Wea. Rev., 124, 2046–2070, doi:10.1175/1520-0493(1996)124<2046:MFFSLT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Lindzen, R. S., 1988: Some remarks on cumulus parameterization. Pure Appl. Geophys., 126, 123–135, doi:10.1007/BF00876918.

  • Loeb, N. G., B. A. Wielicki, D. R. Doelling, G. L. Smith, D. F. Keyes, S. Kato, N. M. Smith, and T. Wong, 2009: Toward optimal closure of the earth’s top-of-atmosphere radiation budget. J. Climate, 22, 748–766, doi:10.1175/2008JCLI2637.1.

    • Search Google Scholar
    • Export Citation

  • Lopez, P., and E. Moreau, 2005: A convection scheme for data assimilation: Description and initial tests. Quart. J. Roy. Meteor. Soc., 131, 409–436, doi:10.1256/qj.04.69.

    • Search Google Scholar
    • Export Citation

  • Manabe, S., and R. F. Strickler, 1964: Thermal equilibrium of the atmosphere with a convective adjustment. J. Atmos. Sci., 21, 361–385, doi:10.1175/1520-0469(1964)021<0361:TEOTAW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Mizuta, R., and Coauthors, 2006: 20-km-mesh global climate simulations using JMA-GSM model—Mean climate states. J. Meteor. Soc. Japan, 84, 165–185, doi:10.2151/jmsj.84.165.

    • Search Google Scholar
    • Export Citation

  • Mizuta, R., and Coauthors, 2012: Climate simulations using the improved MRI-AGCM with 20-km grid. J. Meteor. Soc. Japan, 90A, 233–258, doi:10.2151/jmsj.2012-A12.

    • Search Google Scholar
    • Export Citation

  • Moorthi, S., and M. J. Suarez, 1992: Relaxed Arakawa–Schubert: A parameterization of moist convection for general circulation models. Mon. Wea. Rev., 120, 978–1002, doi:10.1175/1520-0493(1992)120<0978:RASAPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Murakami, H., and Coauthors, 2012a: Future changes in tropical cyclone activity projected by the new high-resolution MRI-AGCM. J. Climate, 25, 3237–3260, doi:10.1175/JCLI-D-11-00415.1.

    • Search Google Scholar
    • Export Citation

  • Murakami, H., R. Mizuta, and E. Shindo, 2012b: Future changes in tropical cyclone activity projected by multi-physics and multi-SST ensemble experiments using the 60-km-mesh MRI-AGCM. Climate Dyn., 39, 2569–2584, doi:10.1007/s00382-011-1223-x.

    • Search Google Scholar
    • Export Citation

  • Nagasawa, R., 2012: The problem of cloud overlap in the radiation process of JMA’s global NWP model. CAS/JSC WGNE Research Activities in Atmospheric and Ocean Modeling, Rep. 42, Japan Meteorological Agency, 4.15–4.16. [Available online at http://www.wcrp-climate.org/WGNE/BlueBook/2012/individual-articles/04_Nagasawa_Ryoji_04_Ryoji_Nagasawa_cloudoverlap.pdf.]

  • Nakagawa, M., 2008: Improvement of the cumulus parameterization scheme of the operational global NWP model at JMA. CAS/JSC WGNE Research Activities in Atmospheric and Ocean Modeling, Rep. 38, Japan Meteorological Agency, 4.09–4.10. [Available online at http://www.wcrp-climate.org/WGNE/BlueBook/2008/individual-articles/04_Nakagawa_Masayuki___30330.pdf.]

  • Nober, F. J., and H.-F. Graf, 2005: A new convective cloud field model based on principles of self-organization. Atmos. Chem. Phys., 5, 2749–2759, doi:10.5194/acp-5-2749-2005.

    • Search Google Scholar
    • Export Citation

  • Nordeng, T. E., 1994: Extended versions of the convective parameterization scheme at ECMWF and their impact on the mean and transient activity of the model in the tropics. ECMWF Tech. Memo. 206, ECMWF, 41 pp.

  • Onogi, K., and Coauthors, 2007: The JRA-25 reanalysis. J. Meteor. Soc. Japan, 85, 369–432, doi:10.2151/jmsj.85.369.

  • Pan, D., and D. Randall, 1998: A cumulus parameterization with a prognostic closure. Quart. J. Roy. Meteor. Soc., 124, 949–981, doi:10.1002/qj.49712454714.

    • Search Google Scholar
    • Export Citation

  • Park, S., and C. S. Bretherton, 2009: The University of Washington shallow convection and moist turbulence schemes and their impact on climate simulations with the Community Atmosphere Model. J. Climate, 22, 3449–3469, doi:10.1175/2008JCLI2557.1.

    • Search Google Scholar
    • Export Citation

  • Posselt, D. J., S. C. van den Heever, and G. L. Stephens, 2008: Trimodal cloudiness and tropical stable layers in simulations of radiative convective equilibrium. Geophys. Res. Lett., 35, L08802, doi:10.1029/2007GL033029.

    • Search Google Scholar
    • Export Citation

  • Priestley, A., 1993: A quasi-conservative version of the semi-Lagrangian advection scheme. Mon. Wea. Rev., 121, 621–629, doi:10.1175/1520-0493(1993)121<0621:AQCVOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Raymond, D. J., and A. M. Blyth, 1986: A stochastic mixing model for nonprecipitating cumulus clouds. J. Atmos. Sci., 43, 2708–2718, doi:10.1175/1520-0469(1986)043<2708:ASMMFN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Reynolds, R. W., and T. M. Smith, 1994: Improved global sea surface temperature analysis using optimum interpolation. J. Climate, 7, 929–948, doi:10.1175/1520-0442(1994)007<0929:IGSSTA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Satoh, M., T. Matsuno, H. Tomita, H. Miura, T. Nasuno, and S. Iga, 2008: Nonhydrostatic Icosahedral Atmospheric Model (NICAM) for global cloud resolving simulations. J. Comput. Phys., 227, 3486–3514, doi:10.1016/j.jcp.2007.02.006.

    • Search Google Scholar
    • Export Citation

  • Smith, R. N. B., 1990: A scheme for prediction layer clouds and their water content in a general circulation model. Quart. J. Roy. Meteor. Soc., 116, 435–460, doi:10.1002/qj.49711649210.

    • Search Google Scholar
    • Export Citation

  • Sundqvist, H., 1978: A parameterization scheme for non-convective condensation including precipitation of cloud water content. Quart. J. Roy. Meteor. Soc., 104, 677–690, doi:10.1002/qj.49710444110.

    • Search Google Scholar
    • Export Citation

  • Taylor, K. E., 2001: Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res., 106, 7183–7192, doi:10.1029/2000JD900719.

    • Search Google Scholar
    • Export Citation

  • Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Wea. Rev., 117, 1779–1800, doi:10.1175/1520-0493(1989)117<1779:ACMFSF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Tiedtke, M., 1993: Representation of clouds in large-scale models. Mon. Wea. Rev., 121, 3040–3061, doi:10.1175/1520-0493(1993)121<3040:ROCILS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Wagner, T. M., and H. F. Graf, 2010: An ensemble cumulus convection parameterization with explicit cloud treatment. J. Atmos. Sci., 67, 3854–3869, doi:10.1175/2010JAS3485.1.

    • Search Google Scholar
    • Export Citation

  • Wheeler, M., and G. N. Kiladis, 1999: Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber–frequency domain. J. Atmos. Sci., 56, 374–399, doi:10.1175/1520-0469(1999)056<0374:CCEWAO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Wood, R., and C. S. Bretherton, 2006: On the relationship between stratiform low cloud cover and lower tropospheric stability. J. Climate, 19, 6425–6432, doi:10.1175/JCLI3988.1.

    • Search Google Scholar
    • Export Citation

  • Wu, X., and M. Yanai, 1994: Effects of vertical wind shear on the cumulus transport of momentum: Observation and parameterization. J. Atmos. Sci., 51, 1640–1660, doi:10.1175/1520-0469(1994)051<1640:EOVWSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Xiao, F., and X. Peng, 2004: A convexity preserving scheme for conservative advection transport. J. Comput. Phys., 198, 389–402, doi:10.1016/j.jcp.2004.01.013.

    • Search Google Scholar
    • Export Citation

  • Xie, P., and P. A. Arkin, 1997: Global precipitation: A 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs. Bull. Amer. Meteor. Soc., 78, 2539–2558, doi:10.1175/1520-0477(1997)078<2539:GPAYMA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Xie, S., and M. Zhang, 2000: Impact of the convective triggering function on single-column model simulations. J. Geophys. Res., 105, 14 983–14 996, doi:10.1029/2000JD900170.

    • Search Google Scholar
    • Export Citation

  • Yamasaki, M., 1975: A numerical experiment of the interaction between cumulus convection and large-scale motion. Pap. Meteor. Geophys., 26, 63–91.

    • Search Google Scholar
    • Export Citation

  • Yanai, M., S. Esbensen, and J.-H. Chu, 1973: Determination of bulk properties of tropical cloud clusters from large-scale heat and moisture budgets. J. Atmos. Sci., 30, 611–627, doi:10.1175/1520-0469(1973)030<0611:DOBPOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Yoshimura, H., and T. Matsumura, 2003: A semi-Lagrangian scheme conservative in the vertical direction. CAS/JSC WGNE Research Activities in Atmospheric and Ocean Modeling, Rep. 33, Japan Meteorological Agency, 3.19–3.20. [Available online at http://www.wcrp-climate.org/WGNE/BlueBook/2003/individual-articles/03-yoshimura.pdf.]

  • Yoshimura, H., and T. Matsumura, 2005: A two-time-level vertically-conservative semi-Lagrangian semi-implicit double Fourier series AGCM. CAS/JSC WGNE Research Activities in Atmospheric and Ocean Modeling, Rep. 35, Japan Meteorological Agency, 3.25–3.26. [Available online at http://www.wcrp-climate.org/WGNE/BlueBook/2005/individual-articles/03_Yoshimura_Hiromasa_03_yoshimura_hiromasa_2tl-dfs.pdf.]

  • Yoshimura, H., and S. Yukimoto, 2008: Development of a Simple Coupler (Scup) for Earth System Modeling. Pap. Meteor. Geophys., 59, 19–29, doi:10.2467/mripapers.59.19.

    • Search Google Scholar
    • Export Citation

  • Yukimoto, S., and Coauthors, 2011: Meteorological Research Institute-Earth System Model v1 (MRI-ESM1)—Model description. Tech. Rep. 64, Meteorological Research Institute, 88 pp.

  • Yukimoto, S., and Coauthors, 2012: A new global climate model of the Meteorological Research Institute: MRI-CGCM3—Model description and basic performance. J. Meteor. Soc. Japan, 90A, 23–64, doi:10.2151/jmsj.2012-A02.

    • Search Google Scholar
    • Export Citation

  • Zhang, G., and N. McFarlane, 1995: Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian Climate Centre general circulation model. Atmos.–Ocean, 33, 407–407, doi:10.1080/07055900.1995.9649539.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 520 158 5
PDF Downloads 333 72 3