• Barnes, E. A., and D. W. Thompson, 2014: Comparing the roles of barotropic versus baroclinic feedbacks in the atmosphere’s response to mechanical forcing. J. Atmos. Sci., 71, 177194, doi:10.1175/JAS-D-13-070.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., and P. K. Smolarkiewicz, 1989: Gravity waves, compensating subsidence and detrainment around cumulus clouds. J. Atmos. Sci., 46, 740759, doi:10.1175/1520-0469(1989)046<0740:GWCSAD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chou, M., and M. J. Suarez, 1994: An efficient thermal infrared radiation parameterization for use in general circulation models. NASA Tech. Memo. 104606, Vol. 3, 85 pp. [Available from NASA/Goddard Space Flight Center, Code 913, Greenbelt, MD 20771.]

  • Chou, M., D. P. Kratz, and W. Ridgway, 1991: Infrared radiation parameterizations in numerical climate models. J. Climate, 4, 424437, doi:10.1175/1520-0442(1991)004<0424:IRPINC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chou, M., M. J. Suarez, C. Ho, M. M. Yan, and K. Lee, 1998: Parameterizations for cloud overlapping and shortwave single-scattering properties for use in general circulation and cloud ensemble models. J. Climate, 11, 202214, doi:10.1175/1520-0442(1998)011<0202:PFCOAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Corbosiero, K. L., and J. Molinari, 2002: The effects of vertical wind shear on the distribution of convection in tropical cyclones. Mon. Wea. Rev., 130, 21102123, doi:10.1175/1520-0493(2002)130<2110:TEOVWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, S., 2007: A three-dimensional dynamic vorticity vector associated with tropical oceanic convection. J. Geophys. Res., 112, D18109, doi:10.1029/2006JD008247.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, S., F. Ping, X. Li, and W. K. Tao, 2004: A convective vorticity vector associated with tropical convection: A two-dimensional cloud-resolving modeling study. J. Geophys. Res., 109, D14106, doi:10.1029/2004JD004807.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, S., X. Cui, Y. Zhou, X. Li, and W. K. Tao, 2005: A modeling study of moist and dynamic vorticity vectors associated with two-dimensional tropical convection. J. Geophys. Res., 110, D17104, doi:10.1029/2004JD005675.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, S., X. Li, W.-K. Tao, C.-L. Shie, and S. Lang, 2007: Convective and moist vorticity vectors associated with tropical oceanic convection: A three-dimensional cloud-resolving simulation. J. Geophys. Res., 112, D01105, doi:10.1029/2006JD007179.

    • Search Google Scholar
    • Export Citation
  • George, L., and S. K. Mishra, 1993: An observational study on the energetics of the onset monsoon vortex, 1979. Quart. J. Roy. Meteor. Soc., 119, 755778, doi:10.1002/qj.49711951208.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., X. Wu, M. W. Moncrieff, and W. D. Hall, 1998: Cloud-resolving modeling of cloud systems during Phase III of GATE. Part II: Effects of resolution and the third spatial dimension. J. Atmos. Sci., 55, 32643282, doi:10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, S. C., 1995: The evolution of vortices in vertical shear. I: Initially barotropic vortices. Quart. J. Roy. Meteor. Soc., 121, 821851, doi:10.1002/qj.49712152406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Khairoutdinov, M. F., and D. A. Randall, 2003: Cloud resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties, and sensitivities. J. Atmos. Sci., 60, 607625, doi:10.1175/1520-0469(2003)060<0607:CRMOTA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., and R. B. Wilhelmson, 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 10701096, doi:10.1175/1520-0469(1978)035<1070:TSOTDC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lang, S., W. K. Tao, J. Simpson, R. Cifelli, S. Rutledge, W. Olson, and J. Halverson, 2007: Improving simulations of convective systems from TRMM LBA: Easterly and westerly regimes. J. Atmos. Sci., 64, 11411164, doi:10.1175/JAS3879.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, S., 2000: Barotropic effects on atmospheric storm tracks. J. Atmos. Sci., 57, 14201435, doi:10.1175/1520-0469(2000)057<1420:BEOAST>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, T., and X. Li, 2016a: Barotropic and baroclinic processes associated with convective development in the tropical deep convective regime. Dyn. Atmos. Oceans, 74, 5059, doi:10.1016/j.dynatmoce.2016.04.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, T., and X. Li, 2016b: Barotropic processes associated with the development of the Mei-yu precipitation system. Adv. Atmos. Sci., 33, 593598, doi:10.1007/s00376-015-5146-z.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, X., C.-H. Sui, and K.-M. Lau, 2002: Interactions between tropical convection and its environment: An energetics analysis of a 2D cloud resolving simulation. J. Atmos. Sci., 59, 17121722, doi:10.1175/1520-0469(2002)059<1712:IBTCAI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Y., E. J. Zipser, S. K. Krueger, and M. A. Zulauf, 2008: Cloud-resolving modeling of deep convection during KWAJEX. Part I: Comparison to TRMM satellite and ground-based radar observations. Mon. Wea. Rev., 136, 26992712, doi:10.1175/2007MWR2258.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mao, J., and G. Wu, 2011: Barotropic process contributing to the formation and growth of tropical cyclone Nargis. Adv. Atmos. Sci., 28, 483491, doi:10.1007/s00376-010-9190-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matsui, T., X. Zeng, W. Tao, H. Masunaga, W. S. Olson, and S. Lang, 2009: Evaluation of long-term cloud-resolving model simulations using satellite radiance observations and multifrequency satellite simulators. J. Atmos. Oceanic Technol., 26, 12611274, doi:10.1175/2008JTECHA1168.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pauluis, O., and I. M. Held, 2002: Entropy budget of an atmosphere in radiative-convective equilibrium. Part I: Maximum work and frictional dissipation. J. Atmos. Sci., 59, 125139, doi:10.1175/1520-0469(2002)059<0125:EBOAAI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peixoto, J. P., and A. H. Oort, 1992: Physics of Climate. American Institute of Physics, 520 pp.

  • Petch, J. C., P. N. Blossey, and C. S. Bretherton, 2008: Differences in the lower troposphere in two- three-dimensional cloud-resolving model simulations of deep convection. Quart. J. Roy. Meteor. Soc., 134, 19411946, doi:10.1002/qj.315.

    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., and H. Jiang, 1990: A theory for long-lived mesoscale convective systems. J. Atmos. Sci., 47, 30673077, doi:10.1175/1520-0469(1990)047<3067:ATFLLM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reasor, P. D., M. T. Montgomery, F. D. Marks Jr., and J. F. Gamache, 2000: Low-wavenumber structure and evolution of the hurricane inner core observed by airborne dual-Doppler radar. Mon. Wea. Rev., 128, 16531680, doi:10.1175/1520-0493(2000)128<1653:LWSAEO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Robe, F. R., and K. A. Emanuel, 2001: The effect of vertical wind shear on radiative-convective equilibrium states. J. Atmos. Sci., 58, 14271445, doi:10.1175/1520-0469(2001)058<1427:TEOVWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schneider, E. K., and R. S. Lindzen, 1976: A discussion of the parameterization of momentum exchange by cumulus convection. J. Geophys. Res., 81, 31583160, doi:10.1029/JC081i018p03158.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shen, X., Y. Wang, and X. Li, 2011: Effects of vertical wind shear and cloud radiative processes on responses of rainfall to the large-scale forcing during pre-summer heavy rainfall over southern China. Quart. J. Roy. Meteor. Soc., 137, 236249, doi:10.1002/qj.735.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shie, C.-L., W.-K. Tao, and J. Simpson, 2003: Simulated KWAJEX convective systems using a 2D and 3D cloud resolving model and their comparisons with radar observations. 31st Int. Conf. on Radar Meteorology, Seattle, WA, Amer. Meteor. Soc., P3A.13. [Available online at https://ams.confex.com/ams/32BC31R5C/webprogram/Paper64020.html.]

    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., S. E. Yuter, C. S. Bretherton, and G. N. Kiladis, 2004: Large-scale meteorology and deep convection during TRMM KWAJEX. Mon. Wea. Rev., 132, 422444, doi:10.1175/1520-0493(2004)132<0422:LMADCD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Soong, S., and Y. Ogura, 1980: Response of tradewind cumuli to large-scale processes. J. Atmos. Sci., 37, 20352050, doi:10.1175/1520-0469(1980)037<2035:ROTCTL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Soong, S., and W. K. Tao, 1980: Response of deep tropical cumulus clouds to mesoscale processes. J. Atmos. Sci., 37, 20162034, doi:10.1175/1520-0469(1980)037<2016:RODTCC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Soong, S., and W. K. Tao, 1984: A numerical study of the vertical transport of momentum in a tropical rainband. J. Atmos. Sci., 41, 10491061, doi:10.1175/1520-0469(1984)041<1049:ANSOTV>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stephens, G. L., V. D. H. Susan, and L. Pakula, 2008: Radiative-convective feedbacks in idealized states of radiative-convective equilibrium. J. Atmos. Sci., 65, 38993916, doi:10.1175/2008JAS2524.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sui, C. H., X. Li, M. Yang, and H. Huang, 2005: Estimation of oceanic precipitation efficiency in cloud models. J. Atmos. Sci., 62, 43584370, doi:10.1175/JAS3587.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sui, C. H., C. T. Tsay, and X. Li, 2007: Convective–stratiform rainfall separation by cloud content. J. Geophys. Res., 112, D14213, doi:10.1029/2006JD008082.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, W., and S. Soong, 1986: A study of the response of deep tropical clouds to mesoscale processes: Three-dimensional numerical experiments. J. Atmos. Sci., 43, 26532676, doi:10.1175/1520-0469(1986)043<2653:ASOTRO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, W., and J. Simpson, 1993: The Goddard cumulus ensemble model. Part I: Model description. Terr. Atmos. Oceanic Sci., 4, 3572, doi:10.3319/TAO.1993.4.1.35(A).

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, W., J. Simpson, and S. Soong, 1987: Statistical properties of a cloud ensemble: A numerical study. J. Atmos. Sci., 44, 31753187, doi:10.1175/1520-0469(1987)044<3175:SPOACE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ueno, M., 2007: Observational analysis and numerical evaluation of the effects of vertical wind shear on the rainfall asymmetry in the typhoon inner-core region. J. Meteor. Soc. Japan, 85, 115136, doi:10.2151/jmsj.85.115.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, D., X. Li, W. Tao, and Y. Wang, 2009: Effects of vertical wind shear on convective development during a landfall of severe tropical storm Bilis (2006). Atmos. Res., 94, 270275, doi:10.1016/j.atmosres.2009.06.004.

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

    • Search Google Scholar
    • Export Citation
  • Wu, X., and M. Yanai, 1994: Effects of vertical wind shear on the cumulus transport of momentum: Observations and parameterization. J. Atmos. Sci., 51, 16401660, doi:10.1175/1520-0469(1994)051<1640:EOVWSO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xu, K. M., and et al. , 2002: An intercomparison of cloud-resolving models with the Atmospheric Radiation Measurement summer 1997 intensive observation period data. Quart. J. Roy. Meteor. Soc., 128, 593624, doi:10.1256/003590002321042117.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yuter, S. E., R. A. Houze Jr., E. A. Smith, T. T. Wilheit, and E. Zipser, 2005: Physical characterization of tropical oceanic convection observed in KWAJEX. J. Appl. Meteor., 44, 385415, doi:10.1175/JAM2206.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zeng, X., and et al. , 2007: Evaluating clouds in long-term cloud-resolving model simulations with observational data. J. Atmos. Sci., 64, 41534177, doi:10.1175/2007JAS2170.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zeng, X., W. Tao, S. Lang, A. Y. Hou, M. Zhang, and J. Simpson, 2008: On the sensitivity of atmospheric ensembles to cloud microphysics in long-term cloud-resolving model simulations. J. Meteor. Soc. Japan, 86A, 4565, doi:10.2151/jmsj.86A.45.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • View in gallery

    Time–pressure cross sections of the large-scale-forcing variables in KWAJEX: (a) large-scale zonal (m s−1), (b) meridional (m s−1), (c) vertical (hPa h−1) components of velocity, (d) horizontal temperature advection (K h−1), and (e) horizontal advection of water vapor mixing ratio (g kg−1 h−1).

  • View in gallery

    Scatterplots of (a) IWP + LWP (mm) in 2D vs that in 3D CRM, (b) the mass-weighted vertically integrated perturbation kinetic energy (103 J m−2) in 2D vs that in 3D CRM, and mass-weighted vertically integrated perturbation kinetic energy vs IWP + LWP in (c) 2D CRM and (d) 3D CRM calculated using the hourly simulation data.

  • View in gallery

    Time–height distributions of domain-mean barotropic conversion (J m−2 s−1) (a) in 2D run and (b) and (c) in the 3D run. We exclude because it is negligibly small.

  • View in gallery

    Vertical profiles of (a) root-mean-squared differences (10−2 J m−2 s−1) between domain means of in the 2D run and in the 3D run (blue), in the 2D run, and in the 3D run (red), and the standard deviation of in the 2D run (black) and (b) the correlation coefficients between in the 2D run and in the 3D run (black) and in the 2D run and in the 3D run (blue).

  • View in gallery

    Scatterplots of domain-mean mass-weighted vertically integrated barotropic conversion (J m−2 s−1) in the 2D run vs (a) that in the 3D CRM, (b) that in the 3D run related to zonal winds , and (c) that in the 3D run related to meridional winds calculated using the hourly simulation data.

  • View in gallery

    Time–height distributions of (a) the imposed zonal wind gradient (; m s−1) and (b) the vertical transport of zonal momentum (; 10−2 J m−3) in the 2D run; (c) the vertical transport of zonal momentum (; 10−2 J m−3) in the 3D model; (d) the imposed meridional wind gradient (; m s−1); and (e) the vertical transport of meridional momentum (; 10−2 J m−3) in the 3D run.

  • View in gallery

    (a) Vertical profile of correlation coefficients between vertical wind shear and vertical transport of zonal momentum (blue), vertical wind shear and (red), and vertical transport of zonal momentum and (green) in the 2D run; (b) their counterparts in the 3D run; and (c) those between vertical wind shear and vertical transport of meridional momentum (blue), vertical wind shear and (red), and vertical transport of meridional momentum and (green) in the 3D run. Dashed lines denote correlation coefficients for the 99% confidence level.

  • View in gallery

    Vertical profiles of (a),(c),(e) RMSDs (10−3 Jm−3 s−1) and (b),(d),(f) correlation coefficients between the tendency of vertical transport of zonal momentum (ZT) and each term in the budget in the (a),(b) 2D and (c),(d) 3D runs and between the tendency of vertical transport of meridional momentum (MT) and each term in the budget (e),(f) in the 3D run. Dashed lines denote correlation coefficients for the 99% confidence level in (b), (d), and (f).

  • View in gallery

    Correlation coefficients of the tendency of vertical transport of zonal momentum (ZT; red) between 2D and 3D runs, and those of covariance between the zonal wind and cloud hydrometeor component of buoyancy (ZBC; black) between 2D and 3D runs. Dashed lines denote correlation coefficients for the 99% confidence level.

  • View in gallery

    Vertical profiles of barotropic conversions (BKEC; solid) and buoyancy source/sink (BS; dashed) in (a) the 2D run and (b) the 3D run. Unit is J m−2 s−1.

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The Impact of Dimensionality on Barotropic Processes during KWAJEX

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  • 1 Department of Atmospheric Sciences, School of Earth Sciences, Zhejiang University, Hangzhou, Zhejiang, China
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Abstract

In this study, the 2D and 3D cloud-resolving model simulations of the Tropical Rainfall Measuring Mission (TRMM) Kwajalein Experiment (KWAJEX) are compared to study the impact of dimensionality on barotropic processes during tropical convective development. Barotropic conversion of perturbation kinetic energy is associated with vertical transport of horizontal momentum under vertical shear of background horizontal winds. The similarities in both 2D and 3D model simulations show that 1) vertical wind shear is a necessary condition for barotropic conversion, but it does not control the barotropic conversion; 2) the evolution of barotropic conversion is related to that of the vertical transport of horizontal momentum; and 3) the tendency of vertical transport of horizontal momentum is mainly determined by the covariance between horizontal wind and the cloud hydrometeor component of buoyancy. The differences between the 2D and 3D model simulations reveal that 1) the barotropic conversion has shorter time scales and a larger contribution in the 2D model simulation than in the 3D model simulation and 2) kinetic energy is generally converted from the mean circulations to perturbation circulations in the 3D model simulation. In contrast, more kinetic energy is transferred from perturbation circulations to the mean circulations in the 2D model simulation. The same large-scale vertical velocity may account for the similarities, whereas the inclusion of meridional winds in the 3D model simulation may be responsible for the differences in barotropic conversion between the 2D and 3D model simulations.

© 2017 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: X. Li, xiaofanli@zju.edu.cn

Abstract

In this study, the 2D and 3D cloud-resolving model simulations of the Tropical Rainfall Measuring Mission (TRMM) Kwajalein Experiment (KWAJEX) are compared to study the impact of dimensionality on barotropic processes during tropical convective development. Barotropic conversion of perturbation kinetic energy is associated with vertical transport of horizontal momentum under vertical shear of background horizontal winds. The similarities in both 2D and 3D model simulations show that 1) vertical wind shear is a necessary condition for barotropic conversion, but it does not control the barotropic conversion; 2) the evolution of barotropic conversion is related to that of the vertical transport of horizontal momentum; and 3) the tendency of vertical transport of horizontal momentum is mainly determined by the covariance between horizontal wind and the cloud hydrometeor component of buoyancy. The differences between the 2D and 3D model simulations reveal that 1) the barotropic conversion has shorter time scales and a larger contribution in the 2D model simulation than in the 3D model simulation and 2) kinetic energy is generally converted from the mean circulations to perturbation circulations in the 3D model simulation. In contrast, more kinetic energy is transferred from perturbation circulations to the mean circulations in the 2D model simulation. The same large-scale vertical velocity may account for the similarities, whereas the inclusion of meridional winds in the 3D model simulation may be responsible for the differences in barotropic conversion between the 2D and 3D model simulations.

© 2017 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: X. Li, xiaofanli@zju.edu.cn

1. Introduction

The barotropic process can be described by the conversion between mean kinetic energy (background circulations) and perturbation kinetic energy (secondary circulations) through vertical transport of horizontal momentum acting on vertical shear of the mean horizontal winds (Peixoto and Oort 1992; Li et al. 2002). The kinetic energy conversion from mean background circulations to perturbation circulations may affect the structure of atmospheric circulation (Barnes and Thompson 2014) and convections. Previous studies have demonstrated that the vertical wind shear could play an important role in convective development (Klemp and Wilhelmson 1978; Raymond and Jiang 1990; Wu and Yanai 1994; Lee 2000; Reasor et al. 2000; Robe and Emanuel 2001; Corbosiero and Molinari 2002; Lang et al. 2007; Ueno 2007; Wang et al. 2009), albeit it is imposed in cloud-resolving models (CRMs). Previous studies revealed the importance of vertical transport of horizontal momentum by clouds in large-scale dynamics (Schneider and Lindzen 1976; Soong and Tao 1984). Wu and Yanai (1994) demonstrated the impacts of vertical wind shear on convection through the change in vertical transport of horizontal momentum. Vertical transport of horizontal momentum and vertical wind shear are equally important in convective development. Thus, barotropic processes may have impacts on convective development (George and Mishra 1993; Jones 1995; Mao and Wu 2011). Furthermore, recent studies showed that the barotropic conversion from the mean kinetic energy to perturbation kinetic energy plays an important role in in the budget of perturbation kinetic energy (Li and Li 2016a,b). Whereas perturbation kinetic energy could be used to quantify the intensity of secondary circulation, which is associated with dynamic instability and microphysical processes (Shen et al. 2011). From this perspective, barotropic conversion between mean kinetic energy and eddy kinetic energy could affect surface rainfall by affecting perturbation kinetic energy. For the setup of CRMs in this study, the barotropic conversion is specified by the conversion from mean kinetic energy to perturbation kinetic energy due to the imposed large-scale winds (or vertical wind shear of large-scale circulations) in the CRMs.

Li and Li (2016a,b) analyzed the budget of perturbation kinetic energy during TOGA COARE and mei-yu torrential rainfall events in mid-June 2011 using 2D CRM simulation data. Their results reveal that barotropic conversion has impacts on the change of perturbation kinetic energy. While the vertical wind shear is a necessary condition for kinetic energy conversion, the change in perturbation kinetic energy is related to the change in vertical transport of zonal momentum. They further derived a tendency equation for vertical flux of zonal momentum and showed that the tendency is associated with the zonal flux of hydrometeors (Li and Li 2016a).

Although 2D and 3D CRM simulations are similar in many aspects (Tao and Soong 1986; Tao et al. 1987; Grabowski et al. 1998; Khairoutdinov and Randall 2003; Gao et al. 2004, 2005; Sui et al. 2005; Gao 2007; Zeng et al. 2007), they may show significant differences in dynamics (Xu et al. 2002). Bretherton and Smolarkiewicz (1989) examined the nature of subsidence related to a heat source in 2D and 3D geometry and found that 2D geometry spreads the subsidence unrealistically. Gao et al. (2005) and Gao (2007) showed that tropical convection has a high correlation with the vertical and horizontal components of the dynamic vorticity vector (DVV), respectively, in 2D and 3D model frameworks, since predominant items in horizontal components of the 3D DVV are excluded from that of the 2D DVV. Zeng et al. (2007) showed that differences in buoyancy damping between 2D and 3D CRMs could lead to more vertical oscillations in the 2D model simulations than in the 3D model simulations. Petch et al. (2008) found that the use of 2D CRM simulation has a great impact on convective development, because 2D CRM simulations differ from 3D simulations in the low-level humidity structure and associated fields. Stephens et al. (2008) demonstrated differences in precipitation variability and precipitable water and upper-tropospheric condensations and cloud fractions between 2D and 3D CRM simulations. Matsui et al. (2009) found that simulations may be sensitive to the differences in the dimensionality of the cloud-resolving model.

Vertical wind shear of environmental circulations is known to be an important large-scale condition for convective development (e.g., Weisman and Klemp 1982). Compared to the 2D framework, changes in vertical wind shear due to an additional meridional wind component in the 3D framework may affect convective development through barotropic processes. Thus, the goal of this study is to investigate the impact of dimensionality on barotropic processes during the Tropical Rainfall Measuring Mission (TRMM) Kwajalein Experiment (KWAJEX). The largest rainfall events during KWAJEX were associated with disturbances in which the convection and wind signals propagated consistently (Sobel et al. 2004), which were associated with complex dynamical updrafts and downdrafts.

In this study, the data from 2D and 3D CRM simulations during the TRMM KWAJEX (Yuter et al. 2005) are utilized to analyze the impact of dimensionality on barotropic conversion of perturbation kinetic energy. The model and experimental designs are briefly described in the next section. The results are presented in section 3. Finally, a summary is given in section 4.

2. Model and experiments

The model simulation data utilized in this study come from the Mesoscale Modeling and Dynamic Group at NASA Goddard Space Flight Center (Shie et al. 2003; Matsui et al. 2009). Those 2D and 3D simulation data were simulated with the 2D and 3D Goddard Cumulus Ensemble (GCE) models, respectively. The GCE models were originally developed by Soong and Ogura (1980), Soong and Tao (1980), Tao and Soong (1986), and Tao and Simpson (1993). The models incorporate subgrid turbulence scheme (Klemp and Wilhelmson 1978), interactive solar (Chou et al. 1998) and thermal infrared (Chou et al. 1991; Chou and Suarez 1994) radiation parameterization schemes. The model dynamic core and physics in this study are similar to those used in Zeng et al. (2007) and Lang et al. (2007). Both the 2D and 3D models use periodic lateral boundaries and include five prognostic equations for mixing ratios of cloud water, raindrop, cloud ice, snow, and graupel.

The horizontal domain in the 2D model consists of 512 grid points with a horizontal grid spacing of 1 km, while the grid domain in the 3D model consists of 256 × 256 grid points with a horizontal grid spacing of 1 km. The models use 41 vertical levels with finer resolution (about 80 m) near the surface and coarser resolution (about 1000 m) in the upper levels.

Because of the small horizontal domains, large-scale circulations cannot be simulated reasonably in CRMs. Thus, large-scale forcing is imposed in CRMs during the model simulations. The large-scale forcing includes horizontally uniform vertical velocity, zonal and meridional winds and thermal and moisture advection in the 3D model, and horizontally uniform vertical velocity, zonal wind, and thermal and moisture advection in the 2D model. The large-scale forcing data are constructed from 6-hourly KWAJEX observations (Shie et al. 2003). The large-scale forcing data from the KWAJEX campaign are shown in Fig. 1. Strong easterly winds prevailed, while weak northerly and southerly winds occurred alternatively. Strong upward motions appeared mainly around 25 July, 11 August, and 3 September. The meridional velocity was imposed in the 3D CRM, but it was not imposed in the 2D CRM. Both 2D and 3D models use the two components of surface wind to compute the surface fluxes during the model integrations. The difference in surface flux computation between the 2D and 3D models is that the 2D model uses time-mean meridional winds, whereas the 3D model uses time-varying meridional winds. The 6-hourly large-scale-forcing data are linearly interpolated into 12-s data, which are imposed in the model at each time step during the model integrations.

Fig. 1.
Fig. 1.

Time–pressure cross sections of the large-scale-forcing variables in KWAJEX: (a) large-scale zonal (m s−1), (b) meridional (m s−1), (c) vertical (hPa h−1) components of velocity, (d) horizontal temperature advection (K h−1), and (e) horizontal advection of water vapor mixing ratio (g kg−1 h−1).

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

The Kwajalein Experiment field campaign was conducted from 23 July to 15 September 1999. Kwajalein Island is located at 8.44°N, 167.43°E and has an area of 15 km2, which is the largest island in Kwajalein Atoll (2200 km2). From July to September, Kwajalein Island is located around the northern edge of the western Pacific intertropical convergence zone (ITCZ). Monthly rainfall increases from north to south around this region. The simulation domain is centered at 9°N, 167°E both for 2D and 3D model simulations. Both models were integrated from 24 July to 14 September 1999 during KWAJEX. During the KWAJEX period, broad mesoscale convective systems (MCSs) moved through the KWAJEX domain during 25–26 July, 11–12 August, and 2–3 September 1999 (Sobel et al. 2004; Li et al. 2008).

Shie et al. (2003) compared domain-averaged surface rain amounts simulated from the 2D and 3D runs (the same simulation data analyzed in this study) with the observations during three KWAJEX episodes and showed that the temporal variation of both 2D- and 3D-simulated rainfall agrees fairly well with the observations in both phase and amplitude, which are consistent with those found by Gao et al. (2007), Zeng et al. (2008), and Matsui et al. (2009). Thus, their hourly simulation data from 0700 UTC 24 July to 0600 UTC 14 September 1999 are used to analyze the barotropic conversion processes in the following discussion.

3. Results

The sum of ice water path (IWP) and liquid water path (LWP) and perturbation kinetic energy from both 2D and 3D runs are first plotted in Figs. 2a and 2b. IWP and LWP are respectively defined as the sum of mass-weighted vertically integrated mixing ratios of ice and liquid hydrometeors. IWP + LWP denotes the intensity of convection (Sui et al. 2007). The perturbation kinetic energy and IWP + LWP in the 2D run are highly correlated with those in the 3D run because the modeled convection corresponds to the same large-scale vertical velocity imposed in both 2D and 3D CRMs. Since condensation and the related rainfall are associated with secondary circulations, which can be quantitatively measured by perturbation kinetic energy, we plot IWP + LWP versus mass-weighted vertically integrated perturbation kinetic energy for both 2D and 3D runs (Figs. 2c,d), which shows similar evolution and magnitudes with the linear correlation coefficients of 0.85 for the 2D run and 0.81 for the 3D run. Both correlation coefficients well exceed the critical correlation coefficient (0.073) at the 99% significant level from the Student’s t test with 1246 degrees of freedom. Thus, convection can be quantitatively measured by perturbations of kinetic energy in both 2D and 3D runs. We further calculate mass-weighted vertically integrated barotropic conversion and mass-weighted vertically integrated tendency of perturbation kinetic energy.

Fig. 2.
Fig. 2.

Scatterplots of (a) IWP + LWP (mm) in 2D vs that in 3D CRM, (b) the mass-weighted vertically integrated perturbation kinetic energy (103 J m−2) in 2D vs that in 3D CRM, and mass-weighted vertically integrated perturbation kinetic energy vs IWP + LWP in (c) 2D CRM and (d) 3D CRM calculated using the hourly simulation data.

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

Following Li et al. (2002) and Li and Li (2016b), the budget of perturbation kinetic energy is derived in the appendix. The comparison between barotropic conversion and buoyancy source shown in the appendix reveals considerable impacts on convective development. The barotropic conversion between the mean kinetic energy and perturbation kinetic energy (BKEC) in the perturbation kinetic energy budget can be written as
e1
in the 3D CRM framework and
e2
in the 2D CRM framework. The formulation of BKEC can be found in (A4b)(A4d).

Here, is excluded in the following analysis because it is negligibly small (Wang et al. 2009; Shen et al. 2011).

The barotropic conversions in the 2D run (Fig. 3a) show more negative values than those in the 3D run (Figs. 3b,c). The frequencies of the barotropic conversion in the 2D run are higher than those in the 3D run, whereas the magnitudes in the 2D run are larger than those in the 3D run. To quantitatively examine the barotropic conversion processes in both 2D and 3D runs, the root-mean-squared difference (RMSD) and correlation coefficient are calculated. The RMSD of barotropic conversion between 2D and 3D runs show similar profiles with the RMSD of barotropic conversion between 2D and 3D runs, and they are slightly larger than the standard deviation of in the 2D run (Fig. 4a). The correlation coefficients of and barotropic conversion between the 2D and 3D runs around 1–5 and 7–13 km generally do not exceed critical correlation coefficients at the 99% significant level from the Student’s t test at the 1246 degrees of freedom in the entire troposphere (Fig. 4b). We further calculate domain-mean mass-weighted vertically integrated barotropic conversion in both 2D and 3D runs. Figure 5 reveals similar magnitudes of barotropic conversion terms related to vertical shears of zonal and meridional winds in the 3D run. The magnitudes of barotropic conversion related to vertical shear of zonal winds in the 3D run (~0.4 J m−2 s−1) generally are about a half of those in the 2D run (~0.8 J m−2 s−1) (Figs. 5a,b). In the 3D run, the barotropic conversion term is always positive, preferring kinetic energy conversion from the mean circulations to perturbation circulations. In the 2D run, the barotropic conversion term has more negative values than positive values, leaning on kinetic energy transfer from perturbation circulations to the mean circulations.

Fig. 3.
Fig. 3.

Time–height distributions of domain-mean barotropic conversion (J m−2 s−1) (a) in 2D run and (b) and (c) in the 3D run. We exclude because it is negligibly small.

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

Fig. 4.
Fig. 4.

Vertical profiles of (a) root-mean-squared differences (10−2 J m−2 s−1) between domain means of in the 2D run and in the 3D run (blue), in the 2D run, and in the 3D run (red), and the standard deviation of in the 2D run (black) and (b) the correlation coefficients between in the 2D run and in the 3D run (black) and in the 2D run and in the 3D run (blue).

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

Fig. 5.
Fig. 5.

Scatterplots of domain-mean mass-weighted vertically integrated barotropic conversion (J m−2 s−1) in the 2D run vs (a) that in the 3D CRM, (b) that in the 3D run related to zonal winds , and (c) that in the 3D run related to meridional winds calculated using the hourly simulation data.

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

The impacts of dimensionality on barotropic processes have two aspects: 1) dimensional increase from 2D to 3D with the same large-scale forcing and 2) meridional winds in the 3D run. In current model setups for both 2D and 3D runs, only perturbation momentum is predicted in the current model framework, and periodic lateral boundaries are furnished. If the 2D run increases to the additional dimension but the imposed large-scale forcing stays the same, such a run has zero domain-mean meridional winds, which could lead to zero barotropic conversion related to vertical shear of meridional winds. Thus, it is expected that an increase only in dimension without a change in large-scale forcing may not change the barotropic conversion.

To further analyze the barotropic processes, vertical profiles of vertical gradient of zonal wind and vertical transport of zonal momentum are calculated. The vertical gradients of zonal wind are generally positive in the lower troposphere and above 13 km, whereas they are generally negative in the middle and upper troposphere (Fig. 6a). Since the vertical gradient of zonal wind is identical in the 2D and 3D runs, the difference in between 2D and 3D runs is associated with the differences in vertical transport of zonal momentum. The sign of vertical transport of zonal momentum changes frequently in the 2D run (Fig. 6b), while it is persistently positive in the middle and lower troposphere in the 3D run (Fig. 6c).

Fig. 6.
Fig. 6.

Time–height distributions of (a) the imposed zonal wind gradient (; m s−1) and (b) the vertical transport of zonal momentum (; 10−2 J m−3) in the 2D run; (c) the vertical transport of zonal momentum (; 10−2 J m−3) in the 3D model; (d) the imposed meridional wind gradient (; m s−1); and (e) the vertical transport of meridional momentum (; 10−2 J m−3) in the 3D run.

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

Unlike the vertical gradient of zonal wind, positive and negative values in the vertical gradients of meridional wind appear throughout the troposphere (Fig. 6d). The vertical transport of meridional momentum shows negative values sandwiched by positive values in the middle and lower troposphere (Fig. 6e), which is different from the vertical transport of zonal momentum. The frequencies of barotropic kinetic energy conversions and vertical momentum transports are similar in both 2D and 3D runs, implying the intimate relation between the barotropic kinetic energy conversions and the vertical momentum transports. This may be further demonstrated quantitatively by calculating the correlation coefficients between vertical wind shear and barotropic conversion, between vertical transport of horizontal momentum and barotropic conversion, and between vertical wind shear and vertical transport of horizontal momentum.

Both in 2D and 3D runs, the magnitudes of the correlation coefficients between and are significantly larger than those between and (Figs. 7a,b), and the magnitudes of the correlation coefficients between and are generally larger than those between and (Fig. 7c). These demonstrate that the vertical transport of horizontal momentum accounts for the change in barotropic conversion in both 2D and 3D runs. The correlation coefficients between and do not exceed the critical correlation coefficients in the 2D run, whereas those correlation coefficients between and are marginally larger than the critical correlation coefficients in the 3D run. These indicate that vertical wind shear is a necessary condition for barotropic conversion, but it does not control the vertical transport of horizontal momentum in both 2D and 3D runs.

Fig. 7.
Fig. 7.

(a) Vertical profile of correlation coefficients between vertical wind shear and vertical transport of zonal momentum (blue), vertical wind shear and (red), and vertical transport of zonal momentum and (green) in the 2D run; (b) their counterparts in the 3D run; and (c) those between vertical wind shear and vertical transport of meridional momentum (blue), vertical wind shear and (red), and vertical transport of meridional momentum and (green) in the 3D run. Dashed lines denote correlation coefficients for the 99% confidence level.

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

To further investigate physical processes that account for the variations of the vertical transport of zonal momentum, the tendency equation of is derived.

The tendency equation of the vertical transport of zonal momentum can be derived by taking (A1a) + (A1c) and model domain, which can be written as
e3
where
e3a
e3b
e3c
e3d
e3e
e3f
e3g
Equation (3) states that the tendency of vertical transport of zonal momentum (ZT) is associated with dynamic processes (ZD), processes related to interaction between wind and zonal pressure gradient (ZPG), and covariance between zonal wind and dry (ZBD), water vapor (ZBV), and cloud hydrometeor (ZBC) components of buoyancy and the zonal frictional dissipation term (ZFD). Zonal pressure gradient and wind are the largest terms compared to the other terms, but their signs are opposite, which leads to a large offset. The sum ZD + ZPG has similar magnitude to the other terms. Thus, ZD + ZPG is calculated.

In the 2D run, ZT and ZD + ZPG and ZT and ZBD have similar RMSDs in both vertical profiles and magnitudes, while their correlation coefficients have opposite signs (Figs. 8a,b). This indicates that zonal pressure gradient, wind, and zonal transport of heat are nearly canceled out. The correlation coefficient between ZT and ZBC is positive, whereas those between ZT and ZD + ZPG + ZBD and between ZT and ZBV are negative. The RMSD between ZT and ZBC is smaller than those between ZT and ZD + ZPG + ZBD and between ZT and ZBV below 6 km. Thus, the tendency of vertical transport of zonal momentum mainly corresponds to covariance between zonal wind and cloud hydrometeor component of buoyancy. This is consistent with the results from the analysis of tropical rainfall (Li and Li 2016a) and mei-yu rainfall (Li and Li 2016b) events in the 2D CRM simulations. Like those in the 2D run, the 3D run shows that the positive correlation coefficient between ZT and ZBC is larger than those between ZT and other terms in the tendency budget of vertical transport of zonal momentum (Figs. 8c,d). The RMSD between ZT and ZBC is smaller than those between ZT and other terms in the tendency budget. The major difference between the 2D and 3D runs is that the RMSDs between ZT and ZD + ZPG (ZBD) are much larger than those between ZT and other terms in the tendency budget (3) in the 2D run. However, they are slightly larger than or similar to those between ZT and other terms in the tendency budget (3) in the 3D run. The larger ZPG may account for the shorter time scales and larger magnitudes for barotropic conversion in the 2D run than in the 3D run. Furthermore, the correlation coefficient of ZT between the 2D run and 3D run generally does not exceed the critical coefficient (Fig. 9), indicating the significant differences in vertical transport of horizontal momentum between the 2D and 3D model simulations. The difference in ZT is associated with those in ZBC between 2D run and 3D runs, as shown by the statistically insignificant correlation in ZBC.

Fig. 8.
Fig. 8.

Vertical profiles of (a),(c),(e) RMSDs (10−3 Jm−3 s−1) and (b),(d),(f) correlation coefficients between the tendency of vertical transport of zonal momentum (ZT) and each term in the budget in the (a),(b) 2D and (c),(d) 3D runs and between the tendency of vertical transport of meridional momentum (MT) and each term in the budget (e),(f) in the 3D run. Dashed lines denote correlation coefficients for the 99% confidence level in (b), (d), and (f).

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

Fig. 9.
Fig. 9.

Correlation coefficients of the tendency of vertical transport of zonal momentum (ZT; red) between 2D and 3D runs, and those of covariance between the zonal wind and cloud hydrometeor component of buoyancy (ZBC; black) between 2D and 3D runs. Dashed lines denote correlation coefficients for the 99% confidence level.

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

To further investigate physical processes that account for the variations of the vertical transport of meridional momentum, the tendency equations of are derived. The tendency equation of the vertical transport of meridional momentum can be derived by taking (A1b) + (A1c) and model domain, which can be written as
e4
where
e4a
e4b
e4c
e4d
e4e
e4f
e4g
Equation (4) states that the tendency of vertical transport of meridional momentum (MT) is associated with dynamic processes (MD), processes related to the interaction between wind and meridional pressure gradient (MPG), and covariance between meridional wind and dry (MBD), water vapor (MBV), cloud hydrometeor (MBC) component of buoyancy, and meridional frictional dissipation (MFD). The positive correlation coefficient between MT and MBC is larger than those between MT and other terms in the tendency budget of vertical transport of meridional momentum (Figs. 8f). The RMSD between MT and MBC is smaller than those between MT and other terms in the tendency budget (Fig. 8e). The RMSDs and correlation coefficients between MT and other terms in the tendency budget (4) generally show similar results to those between ZT and other terms in the tendency budget (3). The analysis of barotropic conversion shows similar physical processes that are responsible for the evolution in both 2D and 3D CRMs, which may be as a result of the same large-scale vertical velocity imposed in both models.

4. Summary

The impact of dimensionality on barotropic processes is examined through the comparison in barotropic conversion of perturbation kinetic energy between 2D and 3D cloud-resolving model simulations during the Tropical Rainfall Measuring Mission (TRMM) Kwajalein Experiment (KWAJEX). The comparison shows similar evolution of barotropic conversion in both 2D and 3D model simulations. Barotropic conversion is the vertical transport of zonal momentum under vertical shear of background zonal wind in the 2D model. In the 3D model, it is the sum of vertical transport of zonal momentum under vertical shear of background zonal wind and vertical transport of meridional momentum under vertical shear of background meridional wind. The analysis of correlation coefficients in both 2D and 3D model simulations shows that the negative correlation between barotropic conversion and vertical transport of horizontal momentum is much more statistically significant than the correlation between barotropic conversion and vertical wind shear. Further, the correlation between vertical wind shear and vertical transport of horizontal momentum is marginally statistically significant. This means that the evolution of barotropic conversion is primarily associated with that of vertical transport of horizontal momentum. The examination of the tendency budget of vertical transport of horizontal momentum reveals that the tendency of vertical transport of zonal (meridional) momentum is associated with the covariance between the zonal (meridional) wind and the cloud hydrometeor component of buoyancy. The similarity may be as a result of the same large-scale vertical velocity used in both 2D and 3D model simulations.

The comparison also reveals the differences in barotropic conversion between 2D and 3D model simulations. The barotropic conversion shows shorter time scales and larger amplitudes in the 2D model simulation than in the 3D model simulation. In the 3D model simulation, the mean kinetic energy is generally converted into perturbation kinetic energy. In the 2D model simulation, the conversion from perturbation kinetic energy to mean kinetic energy occurs more frequently than does the conversion from mean kinetic energy to perturbation kinetic energy. The correlation analysis shows different evolutions of barotropic conversion processes between 2D and 3D model simulations. Those differences may stem from the inclusion of meridional winds in the 3D model simulation.

Previous studies focused on important impacts of vertical wind shear on convective development (e.g., Weisman and Klemp 1982). Our study shows that the vertical transport of horizontal momentum may account for the evolution of barotropic kinetic energy conversion under vertical wind shear of the mean circulation for both 2D and 3D flows. The inclusion of meridional flows in the 3D model simulation favors dynamic instability through the kinetic energy conversion from the mean circulations to perturbation circulations, implying the important impacts of asymmetry of horizontal flows on convective development.

In this study, the frictional dissipation terms were ignored during the budget analysis. The calculations using the data (their Fig. 10) from George and Mishra (1993) reveal that the ratio of barotropic conversions to the tendency of perturbation kinetic energy is about 32% when frictional dissipation is excluded, whereas it could increase to 67% when frictional dissipation is included. The frictional dissipation always tends to reduce energy and the associated tendency of perturbation kinetic energy, which tends to increase the relative importance of barotropic conversion in the perturbation kinetic energy budget.

Acknowledgments

The authors thank the Mesoscale Modeling and Dynamic Group at the NASA Goddard Space Flight Center for providing cloud library data, the NASA Center for Computational Sciences (NCCS) for providing the computing facility and distributing the data, and the Training Center of the Atmospheric Sciences of Zhejiang University for its support. This work was supported by the National Natural Science Foundation of China (41475039) and the National Key Basic Research and Development Project of China (2015CB953601).

APPENDIX

The Equations for the Perturbation Kinetic Energy

The governing momentum equations in the 3D cloud-resolving model can be written as
eaa1a
eab1b
eac1c
Here, u, υ, and w are zonal, meridional, and vertical components of winds, respectively; is the initial potential temperature; is potential temperature; ; ; R is the gas constant; is the specific heat of dry air at constant pressure p; p0 = 1000 hPa; is water vapor mixing ratio; is the sum of mixing ratios of cloud water, raindrops, cloud ice, snow, and graupel; and , , and are dissipation terms. An overbar represents the model domain mean, and a prime represents a perturbation from model domain mean. Superscript o is an imposed value from observations.
Taking u′ × (A1a) + υ′ × (A1b) + w′ × (A1c) in the 3D model and u′ × (A1a) + w′ × (A1c) in the 2D model and then taking the domain average, we construct the equations of perturbation kinetic energy K′ in the 3D and 2D model framework, respectively,
ea2
and
ea3
where
eaa4a
eab4b
eac4c
ead4d
eae4e
eaf4f
eag4g
eah4h
in the 3D model framework;
and
eai4i
in the 2D model framework.

Here, , and and are the heights of the bottom and the top of the model atmosphere, respectively.

In (A2)(A3), , , and are barotropic conversions between domain-mean kinetic energy and perturbation kinetic energy, respectively, through the vertical transport of zonal momentum under the vertical shear of the imposed zonal wind, the vertical transport of meridional momentum under the vertical shear of the imposed meridional wind, and the vertical transport of vertical momentum under the vertical shear of the imposed vertical velocity. The terms , , and are related to the tendency of perturbation kinetic energy through covariance between the perturbation vertical velocity and the dry, water vapor, and cloud hydrometeor components of buoyancy; and is the frictional dissipation.

Pauluis and Held (2002) found that barotropic conversion plays a role in the kinetic energy budget in a dry atmosphere, whereas it may be negligibly small in a moist atmosphere. George and Mishra (1993) showed that barotropic conversion is an important source of perturbation kinetic energy during the onset of the monsoon vortex. Our analysis reveals that the standard deviation of barotropic conversion could be up to 0.06 J m−2 s−1 around 4.5 km, which is about 40% of standard deviation of the buoyancy source in the 2D run (Fig. A1a). In the 3D run, the standard deviation of barotropic conversion could be over 50% of that of the buoyancy source near the surface, while it is about 10% of the standard deviation of the buoyancy source above 1km (Fig. A1b). This suggests that barotropic conversion is one of the important processes in the perturbation kinetic energy budget.

Fig. A1.
Fig. A1.

Vertical profiles of barotropic conversions (BKEC; solid) and buoyancy source/sink (BS; dashed) in (a) the 2D run and (b) the 3D run. Unit is J m−2 s−1.

Citation: Journal of the Atmospheric Sciences 74, 8; 10.1175/JAS-D-16-0184.1

REFERENCES

  • Barnes, E. A., and D. W. Thompson, 2014: Comparing the roles of barotropic versus baroclinic feedbacks in the atmosphere’s response to mechanical forcing. J. Atmos. Sci., 71, 177194, doi:10.1175/JAS-D-13-070.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., and P. K. Smolarkiewicz, 1989: Gravity waves, compensating subsidence and detrainment around cumulus clouds. J. Atmos. Sci., 46, 740759, doi:10.1175/1520-0469(1989)046<0740:GWCSAD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chou, M., and M. J. Suarez, 1994: An efficient thermal infrared radiation parameterization for use in general circulation models. NASA Tech. Memo. 104606, Vol. 3, 85 pp. [Available from NASA/Goddard Space Flight Center, Code 913, Greenbelt, MD 20771.]

  • Chou, M., D. P. Kratz, and W. Ridgway, 1991: Infrared radiation parameterizations in numerical climate models. J. Climate, 4, 424437, doi:10.1175/1520-0442(1991)004<0424:IRPINC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chou, M., M. J. Suarez, C. Ho, M. M. Yan, and K. Lee, 1998: Parameterizations for cloud overlapping and shortwave single-scattering properties for use in general circulation and cloud ensemble models. J. Climate, 11, 202214, doi:10.1175/1520-0442(1998)011<0202:PFCOAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Corbosiero, K. L., and J. Molinari, 2002: The effects of vertical wind shear on the distribution of convection in tropical cyclones. Mon. Wea. Rev., 130, 21102123, doi:10.1175/1520-0493(2002)130<2110:TEOVWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, S., 2007: A three-dimensional dynamic vorticity vector associated with tropical oceanic convection. J. Geophys. Res., 112, D18109, doi:10.1029/2006JD008247.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, S., F. Ping, X. Li, and W. K. Tao, 2004: A convective vorticity vector associated with tropical convection: A two-dimensional cloud-resolving modeling study. J. Geophys. Res., 109, D14106, doi:10.1029/2004JD004807.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, S., X. Cui, Y. Zhou, X. Li, and W. K. Tao, 2005: A modeling study of moist and dynamic vorticity vectors associated with two-dimensional tropical convection. J. Geophys. Res., 110, D17104, doi:10.1029/2004JD005675.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, S., X. Li, W.-K. Tao, C.-L. Shie, and S. Lang, 2007: Convective and moist vorticity vectors associated with tropical oceanic convection: A three-dimensional cloud-resolving simulation. J. Geophys. Res., 112, D01105, doi:10.1029/2006JD007179.

    • Search Google Scholar
    • Export Citation
  • George, L., and S. K. Mishra, 1993: An observational study on the energetics of the onset monsoon vortex, 1979. Quart. J. Roy. Meteor. Soc., 119, 755778, doi:10.1002/qj.49711951208.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., X. Wu, M. W. Moncrieff, and W. D. Hall, 1998: Cloud-resolving modeling of cloud systems during Phase III of GATE. Part II: Effects of resolution and the third spatial dimension. J. Atmos. Sci., 55, 32643282, doi:10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, S. C., 1995: The evolution of vortices in vertical shear. I: Initially barotropic vortices. Quart. J. Roy. Meteor. Soc., 121, 821851, doi:10.1002/qj.49712152406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Khairoutdinov, M. F., and D. A. Randall, 2003: Cloud resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties, and sensitivities. J. Atmos. Sci., 60, 607625, doi:10.1175/1520-0469(2003)060<0607:CRMOTA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., and R. B. Wilhelmson, 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 10701096, doi:10.1175/1520-0469(1978)035<1070:TSOTDC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lang, S., W. K. Tao, J. Simpson, R. Cifelli, S. Rutledge, W. Olson, and J. Halverson, 2007: Improving simulations of convective systems from TRMM LBA: Easterly and westerly regimes. J. Atmos. Sci., 64, 11411164, doi:10.1175/JAS3879.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, S., 2000: Barotropic effects on atmospheric storm tracks. J. Atmos. Sci., 57, 14201435, doi:10.1175/1520-0469(2000)057<1420:BEOAST>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, T., and X. Li, 2016a: Barotropic and baroclinic processes associated with convective development in the tropical deep convective regime. Dyn. Atmos. Oceans, 74, 5059, doi:10.1016/j.dynatmoce.2016.04.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, T., and X. Li, 2016b: Barotropic processes associated with the development of the Mei-yu precipitation system. Adv. Atmos. Sci., 33, 593598, doi:10.1007/s00376-015-5146-z.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, X., C.-H. Sui, and K.-M. Lau, 2002: Interactions between tropical convection and its environment: An energetics analysis of a 2D cloud resolving simulation. J. Atmos. Sci., 59, 17121722, doi:10.1175/1520-0469(2002)059<1712:IBTCAI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Y., E. J. Zipser, S. K. Krueger, and M. A. Zulauf, 2008: Cloud-resolving modeling of deep convection during KWAJEX. Part I: Comparison to TRMM satellite and ground-based radar observations. Mon. Wea. Rev., 136, 26992712, doi:10.1175/2007MWR2258.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mao, J., and G. Wu, 2011: Barotropic process contributing to the formation and growth of tropical cyclone Nargis. Adv. Atmos. Sci., 28, 483491, doi:10.1007/s00376-010-9190-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matsui, T., X. Zeng, W. Tao, H. Masunaga, W. S. Olson, and S. Lang, 2009: Evaluation of long-term cloud-resolving model simulations using satellite radiance observations and multifrequency satellite simulators. J. Atmos. Oceanic Technol., 26, 12611274, doi:10.1175/2008JTECHA1168.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pauluis, O., and I. M. Held, 2002: Entropy budget of an atmosphere in radiative-convective equilibrium. Part I: Maximum work and frictional dissipation. J. Atmos. Sci., 59, 125139, doi:10.1175/1520-0469(2002)059<0125:EBOAAI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peixoto, J. P., and A. H. Oort, 1992: Physics of Climate. American Institute of Physics, 520 pp.

  • Petch, J. C., P. N. Blossey, and C. S. Bretherton, 2008: Differences in the lower troposphere in two- three-dimensional cloud-resolving model simulations of deep convection. Quart. J. Roy. Meteor. Soc., 134, 19411946, doi:10.1002/qj.315.

    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., and H. Jiang, 1990: A theory for long-lived mesoscale convective systems. J. Atmos. Sci., 47, 30673077, doi:10.1175/1520-0469(1990)047<3067:ATFLLM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reasor, P. D., M. T. Montgomery, F. D. Marks Jr., and J. F. Gamache, 2000: Low-wavenumber structure and evolution of the hurricane inner core observed by airborne dual-Doppler radar. Mon. Wea. Rev., 128, 16531680, doi:10.1175/1520-0493(2000)128<1653:LWSAEO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Robe, F. R., and K. A. Emanuel, 2001: The effect of vertical wind shear on radiative-convective equilibrium states. J. Atmos. Sci., 58, 14271445, doi:10.1175/1520-0469(2001)058<1427:TEOVWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schneider, E. K., and R. S. Lindzen, 1976: A discussion of the parameterization of momentum exchange by cumulus convection. J. Geophys. Res., 81, 31583160, doi:10.1029/JC081i018p03158.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shen, X., Y. Wang, and X. Li, 2011: Effects of vertical wind shear and cloud radiative processes on responses of rainfall to the large-scale forcing during pre-summer heavy rainfall over southern China. Quart. J. Roy. Meteor. Soc., 137, 236249, doi:10.1002/qj.735.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shie, C.-L., W.-K. Tao, and J. Simpson, 2003: Simulated KWAJEX convective systems using a 2D and 3D cloud resolving model and their comparisons with radar observations. 31st Int. Conf. on Radar Meteorology, Seattle, WA, Amer. Meteor. Soc., P3A.13. [Available online at https://ams.confex.com/ams/32BC31R5C/webprogram/Paper64020.html.]

    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., S. E. Yuter, C. S. Bretherton, and G. N. Kiladis, 2004: Large-scale meteorology and deep convection during TRMM KWAJEX. Mon. Wea. Rev., 132, 422444, doi:10.1175/1520-0493(2004)132<0422:LMADCD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Soong, S., and Y. Ogura, 1980: Response of tradewind cumuli to large-scale processes. J. Atmos. Sci., 37, 20352050, doi:10.1175/1520-0469(1980)037<2035:ROTCTL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Soong, S., and W. K. Tao, 1980: Response of deep tropical cumulus clouds to mesoscale processes. J. Atmos. Sci., 37, 20162034, doi:10.1175/1520-0469(1980)037<2016:RODTCC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Soong, S., and W. K. Tao, 1984: A numerical study of the vertical transport of momentum in a tropical rainband. J. Atmos. Sci., 41, 10491061, doi:10.1175/1520-0469(1984)041<1049:ANSOTV>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stephens, G. L., V. D. H. Susan, and L. Pakula, 2008: Radiative-convective feedbacks in idealized states of radiative-convective equilibrium. J. Atmos. Sci., 65, 38993916, doi:10.1175/2008JAS2524.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sui, C. H., X. Li, M. Yang, and H. Huang, 2005: Estimation of oceanic precipitation efficiency in cloud models. J. Atmos. Sci., 62, 43584370, doi:10.1175/JAS3587.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sui, C. H., C. T. Tsay, and X. Li, 2007: Convective–stratiform rainfall separation by cloud content. J. Geophys. Res., 112, D14213, doi:10.1029/2006JD008082.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, W., and S. Soong, 1986: A study of the response of deep tropical clouds to mesoscale processes: Three-dimensional numerical experiments. J. Atmos. Sci., 43, 26532676, doi:10.1175/1520-0469(1986)043<2653:ASOTRO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, W., and J. Simpson, 1993: The Goddard cumulus ensemble model. Part I: Model description. Terr. Atmos. Oceanic Sci., 4, 3572, doi:10.3319/TAO.1993.4.1.35(A).

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, W., J. Simpson, and S. Soong, 1987: Statistical properties of a cloud ensemble: A numerical study. J. Atmos. Sci., 44, 31753187, doi:10.1175/1520-0469(1987)044<3175:SPOACE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ueno, M., 2007: Observational analysis and numerical evaluation of the effects of vertical wind shear on the rainfall asymmetry in the typhoon inner-core region. J. Meteor. Soc. Japan, 85, 115136, doi:10.2151/jmsj.85.115.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, D., X. Li, W. Tao, and Y. Wang, 2009: Effects of vertical wind shear on convective development during a landfall of severe tropical storm Bilis (2006). Atmos. Res., 94, 270275, doi:10.1016/j.atmosres.2009.06.004.

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

    • Search Google Scholar
    • Export Citation
  • Wu, X., and M. Yanai, 1994: Effects of vertical wind shear on the cumulus transport of momentum: Observations and parameterization. J. Atmos. Sci., 51, 16401660, doi:10.1175/1520-0469(1994)051<1640:EOVWSO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xu, K. M., and et al. , 2002: An intercomparison of cloud-resolving models with the Atmospheric Radiation Measurement summer 1997 intensive observation period data. Quart. J. Roy. Meteor. Soc., 128, 593624, doi:10.1256/003590002321042117.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yuter, S. E., R. A. Houze Jr., E. A. Smith, T. T. Wilheit, and E. Zipser, 2005: Physical characterization of tropical oceanic convection observed in KWAJEX. J. Appl. Meteor., 44, 385415, doi:10.1175/JAM2206.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zeng, X., and et al. , 2007: Evaluating clouds in long-term cloud-resolving model simulations with observational data. J. Atmos. Sci., 64, 41534177, doi:10.1175/2007JAS2170.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zeng, X., W. Tao, S. Lang, A. Y. Hou, M. Zhang, and J. Simpson, 2008: On the sensitivity of atmospheric ensembles to cloud microphysics in long-term cloud-resolving model simulations. J. Meteor. Soc. Japan, 86A, 4565, doi:10.2151/jmsj.86A.45.

    • Crossref
    • Search Google Scholar
    • Export Citation
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