메뉴 건너뛰기




Volumn 46, Issue 9, 2007, Pages 1480-1497

A robust numerical solution of the stochastic collection-breakup equation for warm rain

Author keywords

[No Author keywords available]

Indexed keywords

CLOUDS; COMPUTER SIMULATION; SIZE DISTRIBUTION; STOCHASTIC MODELS;

EID: 35548936856     PISSN: 15588424     EISSN: None     Source Type: Journal    
DOI: 10.1175/JAM2544.1     Document Type: Article
Times cited : (44)

References (37)
  • 1
    • 0000563725 scopus 로고
    • An analysis of cloud drop growth by collection: Part I. Double distributions
    • Berry, E. X., and R. J. Reinhardt, 1974: An analysis of cloud drop growth by collection: Part I. Double distributions. J. Atmos. Sci., 31, 1814-1824.
    • (1974) J. Atmos. Sci , vol.31 , pp. 1814-1824
    • Berry, E.X.1    Reinhardt, R.J.2
  • 2
    • 84977303603 scopus 로고
    • Empirical formulae for the terminal velocity of water drops falling through the atmosphere
    • Best, A. C., 1950: Empirical formulae for the terminal velocity of water drops falling through the atmosphere. Quart. J. Roy. Meteor. Soc., 76, 302-311.
    • (1950) Quart. J. Roy. Meteor. Soc , vol.76 , pp. 302-311
    • Best, A.C.1
  • 3
    • 0014852466 scopus 로고
    • A fast, approximative method for integrating the stochastic coalescence equation
    • Bleck, R., 1970: A fast, approximative method for integrating the stochastic coalescence equation. J. Geophys. Res., 75, 5165-5171.
    • (1970) J. Geophys. Res , vol.75 , pp. 5165-5171
    • Bleck, R.1
  • 4
    • 0032418519 scopus 로고    scopus 로고
    • A flux method for the numerical solution of the stochastic collection equation
    • Bott, A., 1998: A flux method for the numerical solution of the stochastic collection equation. J. Atmos. Sci., 55, 2284-2293.
    • (1998) J. Atmos. Sci , vol.55 , pp. 2284-2293
    • Bott, A.1
  • 5
    • 0027868804 scopus 로고
    • Analysis and parameterization of the combined coalescence, breakup, and evaporation processes
    • Brown, P. S., 1993: Analysis and parameterization of the combined coalescence, breakup, and evaporation processes. J. Atmos. Sci., 50, 2940-2951.
    • (1993) J. Atmos. Sci , vol.50 , pp. 2940-2951
    • Brown, P.S.1
  • 6
    • 0031402840 scopus 로고    scopus 로고
    • Mass conservation considerations in analytic representation of raindrop fragment distributions
    • Brown, P. S., 1997: Mass conservation considerations in analytic representation of raindrop fragment distributions. J. Atmos. Sci., 54, 1675-1687.
    • (1997) J. Atmos. Sci , vol.54 , pp. 1675-1687
    • Brown, P.S.1
  • 7
    • 0024193184 scopus 로고
    • Evolution of peaks in the spectral distribution of raindrops from warm isolated maritime clouds
    • de Beauville, C. A, R. H. Petit, G. Marion, and J. P. Lacaux, 1988: Evolution of peaks in the spectral distribution of raindrops from warm isolated maritime clouds. J. Atmos. Sci., 45, 3320-3332.
    • (1988) J. Atmos. Sci , vol.45 , pp. 3320-3332
    • de Beauville1    Petit, C.A.R.H.2    Marion, G.3    Lacaux, J.P.4
  • 8
    • 0347792644 scopus 로고
    • On the solution of the kinetic coagulation equation
    • Enukashvili, I. M., 1964: On the solution of the kinetic coagulation equation. Akad Nauk. SSSR Izv. Geofiz. Ser., 10, 944-948.
    • (1964) Akad Nauk. SSSR Izv. Geofiz. Ser , vol.10 , pp. 944-948
    • Enukashvili, I.M.1
  • 9
    • 0024229414 scopus 로고
    • Evolution of raindrop spectra. Part I: Solution to the stochastic collection/breakup equation using the method of moments
    • Feingold, G., S. Tzivion, and Z. Levin, 1988: Evolution of raindrop spectra. Part I: Solution to the stochastic collection/breakup equation using the method of moments. J. Atmos. Sci., 45, 3387-3399.
    • (1988) J. Atmos. Sci , vol.45 , pp. 3387-3399
    • Feingold, G.1    Tzivion, S.2    Levin, Z.3
  • 10
    • 33845510874 scopus 로고
    • Numerical solution of the dynamic equation for particulate systems
    • Gelbard, F., and J. H. Seinfeld, 1978: Numerical solution of the dynamic equation for particulate systems. J. Comput. Phys., 28, 357-375.
    • (1978) J. Comput. Phys , vol.28 , pp. 357-375
    • Gelbard, F.1    Seinfeld, J.H.2
  • 11
    • 0029540060 scopus 로고
    • Evolution of raindrop size distribution by coalescence, breakup, and evaporation: Theory and observations
    • Hu, Z., and R. C. Srivastava, 1995: Evolution of raindrop size distribution by coalescence, breakup, and evaporation: Theory and observations. J. Atmos. Sci., 52, 1761-1783.
    • (1995) J. Atmos. Sci , vol.52 , pp. 1761-1783
    • Hu, Z.1    Srivastava, R.C.2
  • 12
    • 0034528942 scopus 로고    scopus 로고
    • Notes on the state-of-the-art numerical modeling of cloud microphysics
    • Khain, A. P., M. Ovtchinnikov, M. Pinsky, A. Pokrovsky, and H. Krugliak, 2000: Notes on the state-of-the-art numerical modeling of cloud microphysics. Atmos. Res., 55, 159-224.
    • (2000) Atmos. Res , vol.55 , pp. 159-224
    • Khain, A.P.1    Ovtchinnikov, M.2    Pinsky, M.3    Pokrovsky, A.4    Krugliak, H.5
  • 13
    • 0000712946 scopus 로고
    • Lifetime of water drops before breaking and size distribution of fragment droplets
    • Komabayasi, M., T. Gonda, and K. Isono, 1964: Lifetime of water drops before breaking and size distribution of fragment droplets. J. Meteor. Soc. Japan, 42, 330-340.
    • (1964) J. Meteor. Soc. Japan , vol.42 , pp. 330-340
    • Komabayasi, M.1    Gonda, T.2    Isono, K.3
  • 14
    • 0001212235 scopus 로고
    • The effect of coalescence and condensation on rain formation in a cloud of finite vertical extent
    • Kovetz, A., and B. Olund, 1969: The effect of coalescence and condensation on rain formation in a cloud of finite vertical extent. J. Atmos. Sci., 26, 1060-1065.
    • (1969) J. Atmos. Sci , vol.26 , pp. 1060-1065
    • Kovetz, A.1    Olund, B.2
  • 15
    • 0030128282 scopus 로고    scopus 로고
    • On the solution of population balance equations by discretization - I. A fixed pivot technique
    • Kumar, S., and D. Ramkrishna, 1996: On the solution of population balance equations by discretization - I. A fixed pivot technique. Chem. Eng. Sci., 51, 1311-1332.
    • (1996) Chem. Eng. Sci , vol.51 , pp. 1311-1332
    • Kumar, S.1    Ramkrishna, D.2
  • 16
    • 0036565986 scopus 로고    scopus 로고
    • An investigation of the onsets of the 1999 and 2000 monsoons in central Nepal
    • Lang, J. L., and A. P. Barros, 2002: An investigation of the onsets of the 1999 and 2000 monsoons in central Nepal. Mon. Wea. Rev., 130, 1299-1316.
    • (2002) Mon. Wea. Rev , vol.130 , pp. 1299-1316
    • Lang, J.L.1    Barros, A.P.2
  • 17
    • 0017011992 scopus 로고
    • Evolution of raindrop spectra with collision-induced breakup
    • List, R., and J. R. Gillespie, 1976: Evolution of raindrop spectra with collision-induced breakup. J. Atmos. Sci., 33, 2007-2013.
    • (1976) J. Atmos. Sci , vol.33 , pp. 2007-2013
    • List, R.1    Gillespie, J.R.2
  • 18
    • 0025591268 scopus 로고
    • The role of breakup and coalescence in the three-peak equilibrium distribution of raindrops
    • List, R., and G. M. McFarquhar, 1990: The role of breakup and coalescence in the three-peak equilibrium distribution of raindrops. J. Atmos. Sci., 47, 2274-2292.
    • (1990) J. Atmos. Sci , vol.47 , pp. 2274-2292
    • List, R.1    McFarquhar, G.M.2
  • 19
    • 0001568471 scopus 로고
    • Temporal evolution of drop spectra to collisional equilibrium in steady and pulsating rain
    • List, R., N. R. Donaldson, and R. E. Stewart, 1987: Temporal evolution of drop spectra to collisional equilibrium in steady and pulsating rain. J. Atmos. Sci., 44, 362-372.
    • (1987) J. Atmos. Sci , vol.44 , pp. 362-372
    • List, R.1    Donaldson, N.R.2    Stewart, R.E.3
  • 20
    • 0016060812 scopus 로고
    • Solutions to the droplet collection equation for polynomial kernels
    • Long, A. B., 1974: Solutions to the droplet collection equation for polynomial kernels. J. Atmos. Sci., 31, 1040-1052.
    • (1974) J. Atmos. Sci , vol.31 , pp. 1040-1052
    • Long, A.B.1
  • 21
    • 0020336093 scopus 로고
    • Collision, coalescence and breakup of raindrops. Part I: Experimentally established coalescence efficiencies and fragment size distributions in breakup
    • Low, T. B., and R. List, 1982a: Collision, coalescence and breakup of raindrops. Part I: Experimentally established coalescence efficiencies and fragment size distributions in breakup. J. Atmos. Sci., 39, 1591-1606.
    • (1982) J. Atmos. Sci , vol.39 , pp. 1591-1606
    • Low, T.B.1    List, R.2
  • 22
    • 0020451767 scopus 로고
    • Collision, coalescence and breakup of raindrops. Part II: Parameterization of fragment size distributions
    • Low, T. B., and R. List, 1982b: Collision, coalescence and breakup of raindrops. Part II: Parameterization of fragment size distributions. J. Atmos. Sci., 39, 1607-1618.
    • (1982) J. Atmos. Sci , vol.39 , pp. 1607-1618
    • Low, T.B.1    List, R.2
  • 23
    • 0037155742 scopus 로고    scopus 로고
    • Efficient solution of population balance equations with discontinuities by finite elements
    • Mahoney, A. W., and D. Ramkrishna, 2002: Efficient solution of population balance equations with discontinuities by finite elements. Chem. Eng. Sci., 57, 1107-1119.
    • (2002) Chem. Eng. Sci , vol.57 , pp. 1107-1119
    • Mahoney, A.W.1    Ramkrishna, D.2
  • 24
    • 0001256212 scopus 로고
    • The distribution of raindrops with size
    • Marshall, J. S., and W. McK. Palmer, 1948: The distribution of raindrops with size. J. Atmos. Sci., 5, 165-166.
    • (1948) J. Atmos. Sci , vol.5 , pp. 165-166
    • Marshall, J.S.1    Palmer, W.M.2
  • 25
    • 2042464200 scopus 로고    scopus 로고
    • A new representation of collision-induced breakup of raindrops and its implications for the shapes of raindrop size distributions
    • McFarquhar, G. M., 2004: A new representation of collision-induced breakup of raindrops and its implications for the shapes of raindrop size distributions. J. Atmos. Sci., 61, 777-794.
    • (2004) J. Atmos. Sci , vol.61 , pp. 777-794
    • McFarquhar, G.M.1
  • 26
    • 0027798992 scopus 로고
    • The effect of curve fits for the disdrometer calibration on raindrop spectra, rainfall rate, and radar reflectivity
    • McFarquhar, G. M., and R. List, 1993: The effect of curve fits for the disdrometer calibration on raindrop spectra, rainfall rate, and radar reflectivity. J. Appl. Meteor., 32, 774-782.
    • (1993) J. Appl. Meteor , vol.32 , pp. 774-782
    • McFarquhar, G.M.1    List, R.2
  • 27
    • 0016533356 scopus 로고
    • Collision and breakup of water drops at terminal velocity
    • McTaggart-Cowan, J. D., and R. List, 1975: Collision and breakup of water drops at terminal velocity. J. Atmos. Sci., 32, 1401-1411.
    • (1975) J. Atmos. Sci , vol.32 , pp. 1401-1411
    • McTaggart-Cowan, J.D.1    List, R.2
  • 28
    • 34247489771 scopus 로고    scopus 로고
    • Exploring the use of a column model for the characterization of microphysical processes in warm rain: Results from a homogeneous rainshaft model
    • Prat, O. P., and A. P. Barros, 2007: Exploring the use of a column model for the characterization of microphysical processes in warm rain: Results from a homogeneous rainshaft model. Adv. Geosci., 10, 145-152.
    • (2007) Adv. Geosci , vol.10 , pp. 145-152
    • Prat, O.P.1    Barros, A.P.2
  • 31
    • 12144262133 scopus 로고    scopus 로고
    • Possible effects of collisional breakup on mixed-phase deep convection simulated by a spectral (bin) cloud model
    • Seifert, A., A. Khain, U. Blahak, and K. D. Beheng, 2005: Possible effects of collisional breakup on mixed-phase deep convection simulated by a spectral (bin) cloud model. J. Atmos. Sci., 62, 1917-1931.
    • (2005) J. Atmos. Sci , vol.62 , pp. 1917-1931
    • Seifert, A.1    Khain, A.2    Blahak, U.3    Beheng, K.D.4
  • 32
    • 0000712616 scopus 로고
    • Effect of irregularities in the diameter classification of raindrops by the Joss-Waldvogel disdrometer
    • Sheppard, B. E., 1990: Effect of irregularities in the diameter classification of raindrops by the Joss-Waldvogel disdrometer. J. Atmos. Oceanic Technol., 7, 180-183.
    • (1990) J. Atmos. Oceanic Technol , vol.7 , pp. 180-183
    • Sheppard, B.E.1
  • 33
    • 0015048309 scopus 로고
    • Size distribution of raindrops generated by their breakup and coalescence
    • Srivastava, R. C., 1971: Size distribution of raindrops generated by their breakup and coalescence. J. Atmos. Sci., 28, 410-415.
    • (1971) J. Atmos. Sci , vol.28 , pp. 410-415
    • Srivastava, R.C.1
  • 34
    • 34247489730 scopus 로고    scopus 로고
    • Toward elucidating the microstructure of rainfall: A survey
    • RG2003, doi:10.1029/2005RG000182
    • Testik, F. Y., and A. P. Barros, 2007: Toward elucidating the microstructure of rainfall: A survey. Rev. Geophys., 45, RG2003, doi:10.1029/2005RG000182.
    • (2007) Rev. Geophys , vol.45
    • Testik, F.Y.1    Barros, A.P.2
  • 35
    • 0023582542 scopus 로고
    • An efficient numerical solution to the stochastic collection equation
    • Tzivion, S., G. Feingold, and Z. Levin, 1987: An efficient numerical solution to the stochastic collection equation. J. Atmos. Sci., 44, 3139-3149.
    • (1987) J. Atmos. Sci , vol.44 , pp. 3139-3149
    • Tzivion, S.1    Feingold, G.2    Levin, Z.3
  • 36
    • 0022061856 scopus 로고
    • Number fluxes in equilibrium raindrop populations: A Markov chain analysis
    • Valdez, M. P., and K. C. Young, 1985: Number fluxes in equilibrium raindrop populations: A Markov chain analysis. J. Atmos. Sci., 42, 1024-1036.
    • (1985) J. Atmos. Sci , vol.42 , pp. 1024-1036
    • Valdez, M.P.1    Young, K.C.2
  • 37
    • 0024192092 scopus 로고
    • Equilibrium raindrop size distributions in tropical rain
    • Zawadzky, I., and M. de Agostinho Antonio, 1988: Equilibrium raindrop size distributions in tropical rain. J. Atmos. Sci., 45, 3452-3459.
    • (1988) J. Atmos. Sci , vol.45 , pp. 3452-3459
    • Zawadzky, I.1    de Agostinho Antonio, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.