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5 - Warm Microphysical Processes

Published online by Cambridge University Press:  22 August 2018

Alexander P. Khain  and
Mark Pinsky
Alexander P. Khain
Affiliation:
Hebrew University of Jerusalem
Mark Pinsky
Affiliation:
Hebrew University of Jerusalem
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Summary

Microphysical processes that are not related to ice formation are often referred to as warm microphysical processes. It does not mean that these processes take place at positive temperatures only. Drops of a particular kind (supercooled drops) can exist at temperatures as cold as −38°C; nevertheless their diffusional growth and collisions are considered as warm microphysical processes. The major warm microphysical processes and terms of kinetic equations describing their rates are listed in Table 5.1.1.

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Physical Processes in Clouds and Cloud Modeling , pp. 151 - 343
Publisher: Cambridge University Press
Print publication year: 2018

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References

Abdul-Razzak, H., and Ghan, S.J., 2000: A parameterization of aerosol activation 2. Multiple aerosol types. J. Geophys. Res., 105 (D5), 6837–6844.Google Scholar
Abdul-Razzak, H., Ghan, S.J., and Rivera-Carpio, C., 1998: A parameterization of aerosol activation. 1. Single aerosol type. J. Geophys. Res., 103 D6, 6123–6131.Google Scholar
Almeida, F.C., 1976: The collisional problem of cloud droplets moving in a turbulent environment-part I: A method of solution. J. Atmos. Sci., 33, 1571–1578.Google Scholar
Almeida, F.C., 1979: The collisional problem of cloud droplets moving in a turbulent environment-part II: Turbulent collision efficiencies. J. Atmos. Sci., 36, 1564–1576.Google Scholar
Alofs, D.J., and Liu, T.-H., 1981: Atmospheric measurements of CCN in the supersaturation range 0.013–0.681%. J. Atmos. Sci., 38, 2772–2778.Google Scholar
Andreae, M.O., Rosenfeld, D., Artaxo, P., Costa, A.A.. Frank, G.P., Longlo, K.M., and Silva-Dias, M.A.F., 2004: Smoking rain clouds over the Amazon. Science, 303, 1337–1342.Google Scholar
Andsager, K., Beard, K.V., and Laird, N.F., 1999: Laboratory measurements of axis ratios for large raindrops. J. Atmos. Sci., 56 (15), 2673–2683.Google Scholar
Antonia, R.A., Chambers, A.J., and Satyaprakash, B.R., 1981: Reynolds number dependence of high order moments of the streamwise turbulent velocity derivative. Bound.-Layer Meteor., 21, 159–171.Google Scholar
Arakawa, A., and Shubert, W.H., 1974: Interaction of a cumulus cloud ensemble with the large-scale environment. Part. 1. J. Atmos. Sci., 31, 674–701.Google Scholar
Arenberg, D., 1939: Turbulence as the major factor in the growth of cloud drops 1939. Bull. Amer. Meteor. Soc., 20, 444–448.Google Scholar
Ayala, O., Grabowski, W.W., and Wang, L.-P., 2007: A hybrid approach for simulating turbulent collisions of hydrodynamically interacting particles. J. Comp. Phys., 225, 51–73.Google Scholar
Ayala, O., Rosa, B., and Wang, L.-P., 2008a: Effects of turbulence on the geometric collision rate of sedimenting droplets: Part 2. Theory and parameterization. New J. Phys., 10, 099802.Google Scholar
Ayala, O., Rosa, B., Wang, L.-P., and Grabowski, W.W., 2008b: Effects of turbulence on the geometric collision rate of sedimenting droplets: Part 1. Results from direct numerical simulation. New J. Phys., 10, 075015.Google Scholar
Baker, M., Corbin, R.G., and Latham, J., 1980: The influence of entrainment on the evolution of cloud drop spectra: I. A model of inhomogeneous mixing. Quart. J. Roy. Meteor. Soc., 106, 581–598.Google Scholar
Baker, M., and Latham, J., 1979: The evolution of droplet spectra and the rate of production of embyonic raindrops in small cumulus clouds. J. Atmos. Sci., 36, 1612–1615.Google Scholar
Baker, M.B., and Latham, J., 1982: A diffusive model of the turbulent mixing of dry and cloudy air. Q. J. Royal Meteorol. Soc., 108, 871–898.Google Scholar
Barlett, J.T., and Jonas, P.R., 1972: On the dispersion of the sizes of droplets growing by condensation in turbulent clouds. Quart. J. Roy. Meteor. Soc., 98, 150–164.Google Scholar
Bar-Or, R.Z., Koren, I., Altaratz, O., and Fredj, E., 2012: Radiative properties of 322 humidified aerosols in cloudy environment. Atmos. Res., 118, 280–294.Google Scholar
Barros, A.P., Prat, O.P., Shrestha, P., and Testic, F.Y., 2008: Revisiting low and list (1982): Evaluation of raindrop collision parameterizations using laboratory observations and modeling. J. Atmos. Sci., 65, 2983–2993.Google Scholar
Beard, K.V., 1976: Terminal velocity and shape of cloud and precipitation drops aloft. J. Atmos. Sci., 33, 851–864.Google Scholar
Beard, K.V., Kubesh, R.J., and Ochs, H.T., 1991: Laboratory measurements of small raindrop distortion. Part I: Axis ratios and fall behavior. J. Atmos. Sci., 48 (5), 698–710.Google Scholar
Beard, K.V., and Ochs, H.T., 1984: Collection and coalescence efficiencies for accretion. J. Geophys. Res., 89, 7165–7169.Google Scholar
Beard, K.V., and Ochs, H.T. III, 1993: Warm-rain initiation: An overview of microphysical mechanisms. J. Appl. Meteorol., 33, 608–625.Google Scholar
Beard, K.V., and Ochs, H.T., 1995: Collisions between small precipitation drops. Part II: Formulas for coalescence, temporary coalescence, and satellites. J. Atmos. Sci., 52, 3977–3996.Google Scholar
Beard, K.V., and Pruppacher, H.R., 1971: A wind tunnel investigation of the rate of evaporation of small water drops falling at terminal velocity in air. J. Atmos. Sci., 28, 1455–1464.Google Scholar
Bedos, C., Suhre, K., and Rosset, R., 1996: Adaptation of a cloud activation scheme to a spectral-chemical aerosol model. Atmos. Res., 41, 267–279.Google Scholar
Beheng, K.D., 1994: A parameterization of warm cloud microphysical conversion processes. Atmos. Res., 33, 193–206.Google Scholar
Beheng, K.D., and Doms, G., 1986: A general formulation of collection rates of clouds and raindrops using the kinetic equation and comparison with parameterizations. Contib. Atmos. Phys., 59, 66–84.Google Scholar
Belin, F., Maurer, J., Tabeling, P., and Willaime, H., 1997: Velocity gradient distributions in fully developed turbulence: An experimental study. Phys. Fluids, 9, 3843–3850.Google Scholar
Belyaev, V.I., 1961: Drop-size distribution in a cloud during the condensation stages of development. Akad. Nauk SSSR, Izv, Geophys. Ser., 1209–1213.Google Scholar
Benmoshe, N., Pinsky, M., Pokrovsky, A., and Khain, A., 2012: Turbulent effects on microstructure and precipitation of deep convective clouds as seen from simulations with a 2-D spectral microphysics cloud model. J. Geophys. Res., 117, D06220.Google Scholar
Bera, S., Pandithurai, G., and Prabha, T.V., 2016a: Entrainment and droplet spectral characteristics in convective clouds during transition to monsoon. Atmos. Sci. Lett. 17, 286–293.Google Scholar
Bera, S., Prabha, T.V., and Grabowski, W.W., 2016b: Observations of monsoon convective cloud microphysics over India and role of entrainment-mixing. J. Geophys. Res., 121, 9767–9788.Google Scholar
Berry, E.X., and Reinhardt, R.L., 1974a: An analysis of cloud droplet growth by collection: Part I. Double distributions. J. Atmos. Sci., 31, 1814–1824.Google Scholar
Berry, E.X., and Reinhardt, R.L., 1974b: An analysis of cloud drop growth by collection: Part II. Single initial distributions. J. Atmos. Sci., 31, 1825–1831.Google Scholar
Berry, E.X., and Reinhardt, R.L., 1974c: An analysis of cloud drop growth by collection: Part III. Accretion and selfcollection. J. Atmos. Sci., 31, 2118–2126.Google Scholar
Berry, E.X., and Reinhardt, R.L., 1974d: An analysis of cloud drop growth by collection: Part IV. A new parameterization. J. Atmos. Sci., 31, 2127–2135.Google Scholar
Bleck, R., 1970: A fast approximate method for integrating the stochastic coalescence equation. J. Geophys. Res., 75, 5165–5171.Google Scholar
Blyth, A.M., Choularton, T.W., Fullarton, G., Latham, J., Mill, C.S., Smith, M.H., and Stromberg, I.M., 1980: The influence of entrainment on the evolution of cloud droplet spectra. 2. Field experiments 5 at Great Dun Fell. Q. J. Royal Meteorol. Soc., 106, 821–840.Google Scholar
Blyth, A.M., Cooper, W.A., and Jensen, J.B., 1988: A study of the source of entrained air in Montana cumuli. J. Atmos. Sci., 45, 3944–3964.Google Scholar
Boffetta, G., and Sokolov, I.M., 2002: Relative dispersion in fully developed turbulence: The Richardson’s law and intermittency corrections. Phys. Rev. Let., 88, 094501-1–094501-4.Google Scholar
Bott, A., 1989a: A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes. Mon. Wea. Rev., 117, 1006–1015.Google Scholar
Bott, A., 1989b: Reply. Mon. Wea. Rev., 117, 2633–2636.Google Scholar
Bott, A., 1998: A flux method for the numerical solution of the stochastic collection equation. J. Atmos. Sci., 55, 2284–2293.Google Scholar
Bott, A., 2000: A flux method for the numerical solution of the stochastic collection equation: Extension to two-dimensional particle distributions. J. Atmos. Sci., 57, 284–294.Google Scholar
Boucher, O., and Lohmann, U., 1995: The sulfate CCN-cloud albedo effect. A sensitivity study with 2 general circulation models. Tellus, Ser. B Chem. Phys. Meteorol., 47, 281–300.Google Scholar
Bower, K. N., and Choularton, T. W., 1988: The effects of entrainment on the growth of droplets in continental cumulus clouds. Q. J. Royal Meteorol. Soc., 114, 1411–1434.Google Scholar
Brenguier, J.-L., and Burnet, F., 1996: Experimental study of the effect of mixing on droplet spectra. Proc. 12th Int. Conf. on Clouds and Precipitation, Zurich, International Commission on Clouds and Precipitation, 67–70.Google Scholar
Brenguier, J.-L., and Chaumat, L., 2001: Droplet spectra broadening in cumulus clouds. Part I: Broadening in adiabatic cores. J. Atmos. Sci., 58, 628–641.Google Scholar
Brown, P.S., 1983: Some essential details of Bleck’s method to the collision-breakup equation. J. Clim. Appl. Meteorol., 22, 693–697.Google Scholar
Brown, P., 1986: Analysis of the low and list drop-breakup formulation. J. Climate Appl. Meteorol., 25, 313–321.Google Scholar
Burnet, F., and Brenguier, J.-L., 2007: Observational study of the entrainment-mixing process in warm convective clouds. J. Atmos. Sci., 64, 1995–2011.Google Scholar
Carpenter, R.L., Droegemeier, K.K. and Blyth, A.M., 1998: Entrainment and detrainment in numerically simulated cumulus congestus clouds. Part I: General results. J. Atmos. Sci., 55, 3417–3432.Google Scholar
Carrio, G.G., and Levi, L., 1995: On the parameterization of autoconversion. Effects of small-scale turbulent motions. Atmos. Res., 38, 21–27.Google Scholar
Carrio, G.G., and Nicolini, M., 1999: A double moment warm rain scheme: Description and test within a kinematic framework. Atmos. Res., 52, 1–16.Google Scholar
Chun, J., and Koch, D.L., 2005: Coagulation of monodisperse aerosol particles by isotropic turbulence. Phys. Fluid, 17, 27102-1–271021-5.Google Scholar
Chun, J., Koch, D.L., Rani, S.L.A. Ahluwalia, , and Collins, L.R., 2005: Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech., 536, 219–251.Google Scholar
Clark, A.D., and Kapustin, V., 2002: A Pacific aerosol survey. Part I: A decade of data on particle production, transport, evolution, and mixing in the troposphere. J. Atmos. Sci., 59, 363–382.Google Scholar
Clark, T.L., 1973: Numerical modeling of the dynamics and microphysics of warm cumulus convection. J. Atmos. Sci., 30, 857–878.Google Scholar
Cohard, J.M., and Pinty, J.P., 2000: A comprehensive two-moment warm microphysical bulk model scheme: I: Description and test. Q. J. Royal Meteorol. Soc., 126, 1815–1842.Google Scholar
Cohard, J.-M., Pinty, J.-P., and Bedos, C., 1998: Extending Twomey’s analytical estimate of nucleated cloud droplet concentrations from CCN spectra. J. Atmos. Sci., 55, 3348–3357.Google Scholar
Cooper, W.A., 1989: Effects of variable droplet growth histories on droplet size distributions. Part 1. Theory. J. Atmos. Sci., 46, 1301–1311.Google Scholar
Cooper, W.A., Bruintjes, R., and Mather, G., 1997: Calculations pertaining to hygroscopic seeding with flares. J. Appl. Meteorol., 36, 1449–1469.Google Scholar
Cooper, W.A., Lasher-Trapp, S.G., and Blyth, A.M., 2011: Initiation of coalescence in a cumulus cloud: A beneficial influence of entrainment and mixing. Atmos. Chem. Phys. Discuss., 11, 10557–10613.Google Scholar
Covert, D.S., Kapustin, V.N., Quinn, P.K., and Bates, T.S., 1992: New particle formation in the marine boundary layer. J. Geophys. Res., 97(D18), 20581–20589.Google Scholar
Damiani, R., Vali, G., and Haimov, S., 2006: The structure of thermals in cumulus from airborne dual-Doppler radar observations. J. Atmos. Sci., 63, 1432–1450.Google Scholar
Devenish, B.J., Bartello, P., Brenguier, J.-L., Collins, L.R., Grabowski, W.W., Ijzermans, R.H.A., Malinovski, S.P., Reeks, M.W., Vassilicos, J.C., Wang, L.-P., and Warhaft, Z., 2012: Droplet growth in warm turbulent clouds. Q. J. Royal Meteorol. Soc., 138, 1401–1429.Google Scholar
Devis, E.J., 2006: A history and state-of-the-art of accommodation coefficients. Atmos. Res., 82, 561–578.Google Scholar
Dinger, J.E., Howell, H.B., and Wojciechowski, T.A., 1970: On the source of composition of cloud nuclei in subsident air mass over the North Atlantic. J. Atmos. Sci., 27, 791–797.Google Scholar
Dodin, Z., and Elperin, T., 2002: On the collision rate of particles in turbulent flow with gravity. Phys. Fluid, 14, 2921–2924.Google Scholar
Duru, P., Koch, D.L., and Cohen, C., 2007: Experimental study of turbulence-induced coalescence in aerosols. Int. J. of Multiph. Flow., 33, 987–1005.Google Scholar
Elperin, T., Kleeorin, N., L’vov, V.S., Rogachevskii, I., and Sokoloff, D., 2002a: Clustering instability of the spatial distribution of inertial particles in turbulent flows. Phys. Rev., E66, 36302-1–36302-16.Google Scholar
Elperin, T., Kleeorin, N., Rogachevskii, I., 1996: Self-excitation of fluctuations of inertial particles concentration in turbulent flow. Phys. Rev. Lett., 77, 5373–5376.Google Scholar
Elperin, T., Kleeorin, N., and Rogachevskii, I., 2002b: Formation of large scale semiorginized structures in turbulent convection. Phys. Rev. E., 66, 066305, 5–10.Google Scholar
Emde, K., and Wacker, U., 1993: Comments on the relationship between aerosol spectra, equilibrium drop size spectra, and CCN spectra. Beitr. Phys. Atmosph., 66, 1–2, 157–162.Google Scholar
Enukashvily, I.M., 1980: A numerical method for integrating the kinetic equation of coalescence and breakup of cloud droplets. J. Atmos. Sci., 37, 2521–2534.Google Scholar
Erlick, C., Khain, A., Pinsky, M., and Segal, Y., 2005: The effect of turbulent velocity fluctuations on drop spectrum broadening in stratiform clouds. Atmos. Res., 75, 15–45.Google Scholar
Falkovich, G., Fouxon, A., and Stepanov, M.G., 2002: Acceleration of rain initiation by cloud turbulence. Nature, 419, 151–154.Google Scholar
Falkovich, G., and Pumir, A., 2004: Intermittent distribution of heavy particles in a turbulent flow. Phys. Fluids, 16, L47–L50.Google Scholar
Falkovich, G., and Pumir, A., 2007: Sling effect in collisions of water droplets in turbulent clouds. J. Atmos. Sci., 64, 4497–4505.Google Scholar
Fan, J., Comstock, J.M., and Ovchinnikov, M., 2010: The cloud condensational nuclei and ice nuclei effects on tropical anvil characteristics and water vapor of the tropical tropopause layer. Environ. Res. Lett. 5, doi: 10.1088/1748–9326/5/4/044005.Google Scholar
Fankhauser, J.C., Barness, G.M., Biter, C.J., Breed, D.W., and LeMone, M.A., 1983: Summary of NCAR Technical Note NCAR/TN-207+STR, p. 134. (Available from NCAR, P.O. Box 3000, Boulder, CO 80307.)Google Scholar
Feingold, G., Kreidenweis, S.M., Stevens, B., and Cotton, W.R., 1996: Numerical simulation of stratocumulus processing of cloud condensation nuclei through collision-coalescence. J. Geophys. Res., 101, 21,391–21,402.Google Scholar
Ferrier, B.S., 1994: A double-moment multiple-phase four-class bulk ice scheme. Part 1: Description. J. Atmos. Sci., 51, 249–280.Google Scholar
Ferrier, B.S., and Houze, R.A., 1989: One-dimensional time-dependent modeling of GATE cumulonimbus convection. J. Atmos. Sci., 46, 330–352.Google Scholar
Fierro, A.O., Zipser, E.J., Lemone, M.A., Straka, J.M., and Simpson, J., 2012: Tropical oceanic hot towers: Need they be undilute to transport energy from the boundary layer to the upper troposphere effectively? An answer based on trajectory analysis of a simulation of a TOGA COARE convective system. J. Atmos. Sci., 69, 195–213.Google Scholar
Flossmann, A.I., and Pruppacher, H.R., 1988: A theoretical study of the wet removal of atmospheric pollutants. Part III: The uptake, redistribution, and deposition of (NH4)2SO4 particles by a convective cloud using a two-dimensional cloud dynamics model. J. Atmos. Sci., 45, 1857–1871.Google Scholar
Fountoukis, C., and Nenes, A., 2005: Continued development of a cloud droplet formation parameterization for global clime models. J. Geophys. Res., 110, D11212.Google Scholar
Franklin, C.N., 2008: A warm rain microphysics parameterization that includes the effect of turbulence. J. Atmos. Sci., 65, 1795–1816.Google Scholar
Franklin, C.N., Vaillancourt, P.A., and Yau, M.K., 2007: Statistics and parameterizations of the effect of turbulence on the geometric collision kernel of cloud droplets. J. Atmos. Sci., 64, 938–954.Google Scholar
Franklin, C.N., Vaillancourt, P.A., Yau, M.K., and Bartello, P., 2005: Collision rates of cloud droplets in turbulent flow. J. Atmos. Sci., 62, 2451–2466.Google Scholar
Freud, E., and Rosenfeld, D., 2012: Linear relation between convective cloud drop number concentration and depth for rain initiation. J. Geophys. Res., 117, D02207.Google Scholar
Freud, E., Rosenfeld, D., Andreae, M.O., Costa, A.A., and Artaxo, P., 2008: Robust relations between CCN and the vertical evolution of cloud drop size distribution in deep convective clouds. Atmos. Chem. Phys., 8, 1661–1675.Google Scholar
Freud, E., Rosenfeld, D., Axisa, D., and Kulkarni, J.R., 2011: Resolving both entrainment-mixing and number of activated CCN in deep convective clouds. Atmos. Chem. Phys., 11, 12887–12900.Google Scholar
Fridlind, A. et al., 2004: Evidence for the predominance of mid-tropospheric aerosols as subtropical anvil cloud nuclei. Science, 304, 718–722.Google Scholar
Fung, J.C.H., 1993: Gravitational settling of particles and bubbles in homogeneous turbulence. J. Geoph. Res., 98, 20,287–20,297.Google Scholar
Fung, J.C.H., Hunt, J.C.R., Malik, N.A., and Perkins, R.J., 1992: Kinematic simulation of homogeneous turbulent flows generated by unsteady random Fourier modes. J. Fluid Mech., 236, 281–317.Google Scholar
Gerber, H., Frick, G., Jensen, J.B., and Hudson, J.G., 2008: Entrainment, mixing, and microphysics in trade-wind cumulus. J. Meteorol. Soc. Jpn., 86A, 87–106.Google Scholar
Ghan, S.J., Chuang, C.C., Easter, R.C., and Penner, J.E., 1995: A parameterization of cloud droplet nucleation. Pt. 2: Multiple aerosol types. Atmos. Res., 36, 39–54.Google Scholar
Ghan, S.J., Chuang, C.C., and Penner, J.E., 1993: A parameterization of cloud droplet nucleation. Pt.1: Single aerosol type. Atmos. Res., 30, 197–221.Google Scholar
Ghan, S.J., Hayder, A.-R., Nenes, A., Ming, Y., Xiaohong, L., Ovchinnikov, M., Shipway, B., Meskhidze, N., Xu, J., and Shi, X., 2011: Droplet nucleation: Physically-based parameterizations and comparative evaluation. J. Adv. Model. Earth Syst., 3, M10001, p. 33, DOI:10.1029/2011MS000074.Google Scholar
Gilmore, M.S., and Straka, J.M., 2008: The Berry and Reinhardt autoconversion parameterization: A digest. J. Appl. Meteorol. Climatol., 47, 375–396.Google Scholar
Giola, G., Lacorata, G., Marques Filho, E.P., Mazzino, A., and Rizza, U., 2004: Richardson’s law in large-eddy simulations of boundary-layer flows. Boundary-Layer Met., 113, 187–199.Google Scholar
Grabowski, W.W., 2006: Indirect impact of atmospheric aerosols in idealized simulations of convective–radiative quasi equilibrium. J. Climate, 19, 4664–4682.Google Scholar
Grabowski, W.W., 2007: Representation of turbulent mixing and buoyancy reversal in bulk cloud models. J. Atmos. Sci., 64, 3666–3680.Google Scholar
Grabowski, W.W., Andrejczuk, M., and Wang, L.-P., 2011: Droplet growth in a bin warm-rain scheme with Twomey CCN activation. Atmos. Res., 99, 290–301.Google Scholar
Grabowski, W.W., and Clark, T.L., 1991: Cloud-entrainment interface instability: Rising thermal calculations in two spatial dimensions. J. Atmos. Sci., 48, 527–546.Google Scholar
Grabowski, W.W., and Clark, T.L., 1993: Cloud-enviromental interface instability. Part II: Extension to three spatial dimensions. J. Atmos. Sci., 50, 555–573.Google Scholar
Grabowski, W.W., and Morrison, H., 2008: Toward the mitigation of spurious cloud-edge supersaturation in cloud models. Mon. Wea. Rev., 136, 1224–1234.Google Scholar
Grabowski, W.W., and Vaillancourt, P., 1999: Comments on “Preferential concentration of cloud droplets by turbulence: effects on the early evolution of cumulus cloud droplet spectra.” J. Atmos. Sci., 56, 1433–1436.Google Scholar
Gras, J.L., 1989: Baseline atmospheric condensation nuclei at Cape grim. J. Atmos. Chem., 11, 89–106.Google Scholar
Gras, J.L., 1990: Cloud condensation nuclei over the Southern Ocean. Geophys. Res. Lett., 17, 1565–1567.Google Scholar
Grits, B., Pinsky, M., and Khain, A., 2006: Investigation of small-scale droplet concentration inhomogeneities in a turbulent flow. Meteorol. Atmos. Phys., 92, 191–204.Google Scholar
Hall, W.D., 1980: A detailed microphysical model within a two-dimensional dynamic framework: Model description and preliminary results. J. Atmos. Sci., 37, 2486–2507.Google Scholar
Hamielec, A.E., and Johnson, A.I., 1962: Viscous flow around fluid spheres at intermediate Reynolds numbers. Can. J. Chem. Eng., April, 41–45.Google Scholar
Hegg, D.A., and Hobbs, P.V.,1992: Cloud condensation nuclei in the marine atmosphere, In N. Fukuta, P.E. Wagner (Eds.), Nucl. and Atmos. Aerosols. - Proc. 13-th Int. Conf. Nucl. Atmos. Aerosol, A. Deepak Publishing, Hampton, VA. pp. 181–192.Google Scholar
Hegg, D.A., Radke, L.F., and Hobbs, P.V., 1991: Measurements of Aitken nuclei and cloud condensation nuclei in the marine atmosphere and their relation to the DMS-cloud-climate hypothesis. J. Geophys. Res., 96, 18,727–18,733.Google Scholar
Heus, T., and Jonker, H., 2008: Subsiding shells around shallow cumulus clouds. J. Atmos. Sci., 65, 1003–1018.Google Scholar
Hill, A.A., Feingold, G., and Jiang, H., 2009: The influence of entrainment and mixing assumption on aerosol–cloud interactions in marine stratocumulus. J. Atmos. Sci., 66, 1450–1464.Google Scholar
Hill, R.J., 2002: Scaling of acceleration in locally isotropic turbulence. J. Fluid Mech., 452, 361–370.Google Scholar
Hill, T.A., and Choularton, T.W., 1986: A model of the development of the droplet spectrum in a growing cumulus cloud. Q. J. Royal Meteorol. Soc., 112, 531–554.Google Scholar
Hobbs, P.V. et al., 1978: Res. Rept. XIII, Dept. Atmos. Sci., Univ. Washington, DC.Google Scholar
Hobbs, P.V., 1993: Aerosol-cloud-climate interactions. Academic Press, p. 236.Google Scholar
Hobbs, P.V., Bowdle, D.A., and Radke, L.F., 1985: Particles in the lower troposphere over the High Plains of the United States. 1: Size distributions, elemental compositions and morphologies. J. Clim. Appl. Meteorol., 24, 1344–1356.Google Scholar
Hobbs, P.V., and Rangno, A.L., 2004: Super-large raindrops. Geophys. Res. Lett., 31, L13102, doi:10.1029/2004GL020167.Google Scholar
Hocking, L.M., and Jonas, P.R., 1970: The collision efficiency of small drops. Q. J. Royal Meteorol. Soc., 96, 722–729.Google Scholar
Hong, S.-.Y, Lim, K.-S. S., Lee, Y.-H., Ha, J.-C., Kim, H.-W., Ham, S.-J., and Dudhia, J., 2010: Evaluation of the WRF double moment 6-class microphysics scheme for precipitating convection. Advances in Meteorology, ID 707253, doi:10.1155/2010/707253.Google Scholar
Hoppel, W.A., Dinger, J.E., and Ruskin, R.E.,1973: Vertical profiles of CCN at various geographical locations. J. Atmos. Sci., 30, 1410–1420.Google Scholar
Hoppel, W.A., Fitzgerald, J.W., Frick, G.M., Larson, R.E., and Mack, E.J., 1990: Aerosol size distributions and optical properties found in the marine boundary layer over the Atlantic Ocean. J. Geophys. Res., 95, 3659–3686.Google Scholar
Hu, Z., and Srivastava, R.C., 1995: Evolution of raindrop size distribution by coalescence, breakup, and evaporation: Theory and observations. J. Atmos. Sci., 52, 1761–1783.Google Scholar
Hudson, J.G., 1984: Cloud condensation nuclei measurements within clouds. J. Climate Appl. Meteorol., 23, 42–51.Google Scholar
Hudson, J.G., and Frisbie, P.R., 1991: Cloud condensation nuclei near marine stratus. J. Geophys. Res., 96, 20,795–20,808.Google Scholar
Hudson, J.G., and Li, H., 1995: Microphysical contrasts in Atlantic stratus. J. Atmos. Sci., 52, 3031–3040.Google Scholar
Hudson, J.G., and Yum, S.S., 1997: Droplet spectral broadening in marine stratus. J. Atmos. Sci., 54, 2642–2654.Google Scholar
Hudson, J.G., and Yum, S.S., 2002: Cloud condensation nuclei spectra and polluted and clean clouds over the Indian Ocean. J. Geophys.Res., 107(D19), 8022, doi:10.1029/2001JD000829.Google Scholar
Ivanova, E.T., Kogan, Y.L., Mazin, I.P., and Permyakov, M.S., 1977: The ways of parameterization of condensation drop growth in numerical models. Izv. Atmos. Oceanic Phys., 13 (N11), 1193–1201.Google Scholar
Jaenicke, R., 1993: “Tropospheric Aerosols,” chapter in book by Aerosol-Cloud-Climate Interactions, edited by Hobbs, Peter. Academic Press, p. 236.Google Scholar
Jamerson, A.R., and Kostinski, A.B., 2000: Fluctuation properties of precipitation. Part 4: Observations of hyperfine clustering and drop size distribution structures in three-dimensional rain. J. Atmos. Sci., 57, 373–388.Google Scholar
Jarecka, D., Grabowski, W.W., and Pawlowska, H., 2009: Modeling of subgrid-scale mixing in large-eddy simulation of shallow convection. J. Atmos. Sci., 66, 2125–2133.Google Scholar
Jarecka, D., Pawlowska, H., Grabowski, W.W., and Wyszogrodzki, A.A., 2013: Modeling microphysical effects of entrainment in clouds observed during EUCAARI-IMPACT field campaign. Atmos. Chem. Phys. Discuss., 13, 1489–1526, doi:10.5194/acpd-13-1489-2013.Google Scholar
Jeffery, C.A., and Reisner, J.M., 2006: A study of cloud mixing and evolution using PDF methods. Part I: Cloud front propagation and evaporation. J. Atmos. Sci., 63, 2848–2864.Google Scholar
Jeffery, C.A., Reisner, J.M., and Andrejczuc, M., 2007: Another look at stochastic condensation for subgrid cloud modeling: Adiabatic evolution and effects. J. Atmos. Sci., 64, 3949–3969.Google Scholar
Jensen, J.B., Baker, M., 1989: A simple model of droplet spectral evolution during turbulent mixing. J. Atmos. Sci., 46, 2812–2829.Google Scholar
Jin, G., He, G.-W., and Wang, L.-P., 2010: Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence. Phys. Fluids, 22, 055106.Google Scholar
Jiusto, J.E., 1967: Aerosol and cloud microphysics measurements in Hawaii. Tellus, 19, 359–368.Google Scholar
Jiusto, J.E., and Lala, G.G., 1981: CCN-supersaturation spectra slopes (k). J. Rech. Atmos., 15, 303–311.Google Scholar
Johnson, D.B., 1993: The onset of effective coalescence growth in convective clouds. Q. J. Royal Meteorol. Soc., 119, 925–933.Google Scholar
Jonas, P.R., 1972: The collision efficiency of small drops. Q. J. Royal Meteorol. Soc., 98, 681–683.Google Scholar
Kamra, A.K., Bhalwankar, R.V., and Sathe, A.B., 1991: Spontaneous breakup of charged and uncharged water drops freely suspended in a wind tunnel. J. Geophys. Res., 96 (D9), 17,159–17,168.Google Scholar
Kato, T., 1995: A box–Lagrangian rain-drop scheme. J. Meteorol. Soc. Jpn., 73, 241–245.Google Scholar
Kerstein, A.R., 1988: Linear eddy modelling of turbulent scalar transport and mixing. Combust. Sci. Technol., 60, 391–421.Google Scholar
Kessler, E., 1969: On the distribution and continuity of water substance in atmospheric circulations. Meteorol. Monogr., 32.Google Scholar
Khain, A.P., Beheng, K.D., Heymsfield, A., Korolev, A., Krichak, S.O., Levin, Z., Pinsky, M., Phillips, V., Prabhakaran, T., Teller, A., van den Heever, S.C., and Yano, J.-I., 2015: Representation of microphysical processes in cloud resolving models: Spectral (bin) microphysics versus bulk parameterization. Rev. Geophys., 53, 247–322.Google Scholar
Khain, A.P., Benmoshe, N., and Pokrovsky, A., 2008: Factors determining the impact of aerosols on surface precipitation from clouds: An attempt of classification. J. Atmos. Sci., 65, 1721–1748.Google Scholar
Khain, A.P., Ovtchinnikov, M., Pinsky, M., Pokrovsky, A., and Krugliak, H., 2000: Notes on the state-of-the-art numerical modeling of cloud microphysics. Atmos. Res., 55, 159–224.Google Scholar
Khain, A.P., Phillips, V., Benmoshe, N., and Pokrovsky, A., 2012: The role of small soluble aerosols in the microphysics of deep maritime clouds. J. Atmos. Sci., 69, 2787–2807.Google Scholar
Khain, A.P., and Pinsky, M.B., 1995: Drops’ inertia and its contribution to turbulent coalescence in convective clouds: Part 1: Drops’ fall in the flow with random horizontal velocity. J. Atmos. Sci., 52, 196–206.Google Scholar
Khain, A., Pinsky, M., Elperin, T., Kleeorin, N., Rogachevskii, I., and Kostinski, A., 2007: Critical comments to results of investigations of drop collisions in turbulent clouds. Atmos. Res., 86, 1–20.Google Scholar
Khain, A.P., and Pokrovsky, A., 2004: Effects of atmospheric aerosols on deep convective clouds as seen from simulations using a spectral microphysics mixed-phase cumulus cloud model Part 2: Sensitivity study. J. Atmos. Sci., 61, 2983–3001.Google Scholar
Khain, A., Pokrovsky, A., Pinsky, M., Seifert, A., and Phillips, V., 2004: Effects of atmospheric aerosols on deep convective clouds as seen from simulations using a spectral microphysics mixed-phase cumulus cloud model Part 1: Model description. J. Atmos. Sci., 61, 2963–2982.Google Scholar
Khain, A., Prabha, T.V., Benmoshe, N., Pandithurai, G., and Ovchinnikov, M., 2013: The mechanism of first raindrops formation in deep convective clouds. J. Geophys. Res. Atmos., 118, 9123–9140, doi:10.1002/jgrd.50641.Google Scholar
Khain, A.P., Rosenfeld, D., and Sednev, I.L., 1993: Coastal effects in the Eastern Mediterranean as seen from experiments using a cloud ensemble model with a detailed description of warm and ice microphysical processes. Atmos. Res., 30, 295–319.Google Scholar
Khain, A.P., and Sednev, I.L., 1995: Simulation of hydrometeor size spectra evolution by water-water, ice water and ice-ice interection. Atmos. Res., 36, 107–138.Google Scholar
Khain, A.P., and Sednev, I., 1996: Simulation of precipitation formation in the Eastern Mediterranean coastal zone using a spectral microphysics cloud ensemble model. Atmos. Res., 43, 77–110.Google Scholar
Khairoutdinov, M., and Kogan, Y., 2000: A new cloud physics parameterization in a large-eddy simulation model of marine stratocumulus. Mon. Wea. Rev., 128, 229–243.Google Scholar
Kholmyansky, M., Tsinober, A., and Yorich, S., 2001: Velocity derivatives in the atmospheric surface layer at Reλ = 104. Phys. Fluids, 13, 311–314.Google Scholar
Khvorostyanov, V.I., and Curry, J.A., 1999a: Toward the theory of stochastic condensation in clouds. Part 1: A general kinetic equation. J. Atmos. Sci., 56, 3985–3996.Google Scholar
Khvorostyanov, V.I., and Curry, J.A., 1999b: Toward the theory of stochastic condensation in clouds. Part 2: Analytical solutions of the gamma-distribution type. J. Atmos. Sci., 56, 3997–4013.Google Scholar
Khvorostyanov, V.I., and Curry, J.A., 2006: Aerosol size spectra and CCN activity spectra: Reconciling the lognormal, algebraic, and power laws. J. Geophys. Res., 111, D12202.Google Scholar
Khvorostyanov, V.I., and Curry, J.A., 2008: Kinetics of cloud drop formation and its parametrization for cloud and climatemodels. J. Atmos. Sci., 65, 2784–2802.Google Scholar
Khvorostyanov, V.I., Khain, A.P., and Kogteva, E.L., 1989: A two-dimensional non stationary microphysical model of a three-phase convective cloud and evaluation of the effects of seeding by a crystallizing agent. Soviet Meteorology and Hydrology, 5, 33–45.Google Scholar
Kim, S., and Karrila, S.J., 1991: Microhydrodynamics Principles and Selected Applications. Butterworth-Heinmann, p. 507.Google Scholar
Kim, Y.J., and Boatman, J.F., 1990: Size calibration corrections for the Active Scattering Aerosol Spectrometer Probe (ASASP-100X). Aerosol Sci. Technol., 12, 665–672.Google Scholar
Kinzer, G.D., and Gann, R., 1951: The evaporation temperature and thermal relaxation time of freely falling water drops. J. Meteorol., 8, 71–83.Google Scholar
Kivekäs, N., Kerminen, V.-M., Anttila, T., Korhonen, H., Lihavainen, H., Komppula, M., and Kulmala, M., 2008: Parameterization of cloud droplet activation using a simplified treatment of the aerosol number size distribution. J. Geophys. Res., 113, D15207.Google Scholar
Klaassen, G.P., and Clark, T.L., 1985: Dynamics of the cloud environment interface and entrainment in small cumuli: Two dimensional simulations in the absence of ambient shear. J. Atmos. Sci., 42, 2621–2642.Google Scholar
Klett, J.D., and Davis, M.H., 1973: Theoretical collision efficiencies of cloud droplets at small Reynolds numbers. J. Atmos. Sci., 30, 107–117.Google Scholar
Knight, C.A., and Miller, L.J., 1998: Early radar echoes from small, warm cumulus: Bragg and hydrometeor scattering. J. Atmos. Sci., 55, 2974–2992.Google Scholar
Kocmond, W.C., 1965: Res. Rept. RM-1788-p9, p. 36, Cornell Aeronaut. Lab. Buffalo, NY.Google Scholar
Kogan, Y., 1991: The simulation of a convective cloud in a 3-D model with explicit microphysics. Part 1: Model description and sensitivity experiments. J. Atmos. Sci. 48, 1160–1189.Google Scholar
Kogan, Y.L. 2006: Large-eddy simulation of air parcels in stratocumulus clouds: Time scales and spatial variability. J. Atmos. Sci., 63, 952–967.Google Scholar
Komabayasi, M., Gond, T., and Isono, K., 1964: Lifetime of water drops before breaking and size distribution of fragment droplets. J. Meteorol. Soc. Jpn., 42, 330–340.Google Scholar
Korolev, A.V., 1995: The influence of supersaturation fluctuations on droplet size spectra formation. J. Atmos. Sci., 52, 3620–3634.Google Scholar
Korolev, A., Khain, A., Pinsky, M., and French, J., 2016: Theoretical study of mixing in liquid clouds – Part 1: Classical concept. Atmos. Chem. Phys., 16, 9235–9254.Google Scholar
Korolev, A.V., and Mazin, I.P., 2003: Supersaturation of water vapor in clouds. J. Atmos. Sci., 60, 2957–2974.Google Scholar
Korolev, A., Pinsky, M., and Khain, A., 2013: A new mechanism of droplet size distribution broadening during diffusional growth. J. Atmos. Sci., 70, 2051–2071.Google Scholar
Kostinski, A.B., and Shaw, R.A., 2001: Scale-dependent droplet clustering in turbulent clouds. J. Fluid Mech., 434, 389–398.Google Scholar
Kostinski, A.B., and Shaw, R.A., 2005: Fluctuations and luck in droplet growth by coalescence. Bull. Am. Meteorol. Soc., 86, 235–244.Google Scholar
Kovetz, A., and Olund, B., 1969: The effect of coalescence and condensation on rain formation in a cloud of finite vertical extent. J. Atmos. Sci., 26, 1060–1065.Google Scholar
Koziol, A.S., Leighton, H.G., 1996: The effect of turbulence on the collision rates of small cloud drops. J. Atmos. Sci., 53, 1910–1920.Google Scholar
Kraichnan, R.H., 1970: Diffusion by a random velocity field. Phys. Fluid, 13, 22–31.Google Scholar
Krueger, S.K., 1993: Linear eddy modeling of entrainment and mixing in stratus clouds. J. Atmos. Sci., 50, 3078–3090.Google Scholar
Krueger, S., Su, C.-W., and McMurtry, P., 1997: Modeling entrainment and fine-scale mixing in cumulus clouds. J. Atmos. Sci., 54, 2697–2712.Google Scholar
Krueger, S.K., Lehr, P.J., and Su, C.W., 2006: How entrainment and mixing scenarios affect droplet spectra in cumulus clouds. 12th Conference on Cloud Physics, and 12th Conference on Atmospheric Radiation, Madison WI, USA, July, 10–14.Google Scholar
Kubesh, R.J., and Beard, K.V., 1993: Laboratory measurements of spontaneous oscillations for moderate-size raindrops. J. Atmos. Sci., 50(8), 1089–1098.Google Scholar
Kumar, B., Bera, S., Prabhakaran, T., and Grabowski, W.W., 2016: Cloud-edge mixing: Direct numerical simulation and observations in Indian monsoon clouds. Submitted to JAMES.Google Scholar
Kumar, B., Schumacher, J., and Shaw, R.A., 2013: Cloud microphysical effects of turbulent mixing and entrainment. Theor. Comput. Fluid Dyn., 27, 361–376.Google Scholar
Kumar, B., Schumacher, J., and Shaw, R.A., 2014: Lagrangian mixing dynamics at the cloudy–clear air interface. J. Atmos. Sci., 71, 2564–2580.Google Scholar
La Porta, A., Voth, G.A., Crawford, A.M., Alexander, J., and Bodenschatz, E., 2001: Fluid particle accelerations in fully developed turbulence. Nature, 409, 1017–1019.Google Scholar
Lanotte, A.S., Seminara, A., and Toschi, F., 2009: Cloud droplet growth by condensation in homogeneous isotropic turbulence. J. Atmos. Sci., 66, 1685–1697.Google Scholar
Lasher-Trapp, S.G., Knight, C., Straka, J.M., 1998: Ultragiant aerosol growth by collection within a warm continental cumulus. AMS Conference on Cloud Physics, August 17–21, Everett, WA, pp. 494–497.Google Scholar
Latham, J., and Reed, R.L., 1977: Laboratory studies of effects of mixing on evolution of cloud droplet spectra, Q. J. Royal Meteorol. Soc., 103, 297–306.Google Scholar
Lehmann, K., Siebert, H., and Shaw, R.A., 2009: Homogeneous and inhomogeneous mixing in cumulus clouds: Dependence on local turbulence structure. J. Atmos. Sci., 66, 3641–3659.Google Scholar
Leon, D.C., French, J.R., Lasher-Trapp, S., Blyth, A.M., Abel, V., Ballard, S., Bennett, L.J., Bower, K., Brooks, B., Brown, P., Choularton, T., Clark, P., Collier, C., Crosier, J., Cui, Z., Dufton, D., Eagle, C., Flynn, M.J., Gallagher, M., Hanley, K., Huang, Y., Kitchen, M., Korolev, A., Lean, H., Liu, Z., Marsham, J., Moser, D., Nicol, J., Norton, E.G., Plummer, D., Price, J., Ricketts, H., Roberts, N., Rosenberg, P.D., Taylor, J.W., Williams, P.I., and Young, G., 2016: The Convective Precipitation Experiment (COPE): Investigating the origins of heavy precipitation in the southwestern UK. Bull. Amer. Meteor. Soc., 97, 1003–1020.Google Scholar
Levin, L.M., and Sedunov, Y.S., 1966: Stochastic condensation of drops and kinetics of cloud spectrum formation. J. Rech. Atmos., 2, 425–432.Google Scholar
Levin, Z., and Cotton, W.R. (Eds.), 2009: Aerosol Pollution Impact on Precipitation: A Scientific Review. Springer, p. 386.Google Scholar
Lewis, E.R., 2008: An examination of Kohler theory resulting in an accurate expression for the equilibrium radius ratio of a hygroscopic aerosol particle valid up to and including relative humidity 100%. J. Geoph. Res., 113, D03205.Google Scholar
Lin, C.L., and Lee, S.C., 1975: Collision efficiency of water drops in the atmosphere. J. Atmos. Sci., 32, 1412–1418.Google Scholar
Lin, Y.-L., Farley, R.D., and Orville, H.D., 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteorol., 22, 1065–1092.Google Scholar
List, R., and Gillespie, J.R., 1976: Evolution of raindrop spectra with collision-induced breakup. J. Atmos. Sci., 33, 2007–2013.Google Scholar
List, R., and McFarquhar, G.M., 1990: The role of breakup and coalescence in the three-peak equilibrium distribution of raindrops. J. Atmos. Sci., 47, 2274–2292.Google Scholar
List, R., Nissen, R., and Fung, C., 2009: Effects of pressure on collision, coalescence, and breakup of raindrops. Part II: Parameterization and spectra evolution at 50 and 100 kPa. J. Atmos. Sci., 66, 2204–2215.Google Scholar
Liu, Q., Kogan, Y., Lilly, D.K., and Khairoutdinov, M.P., 1997: Variational optimization method for calculation of cloud drop growth in Eulerian drop-size framework. J. Atmos. Sci., 54, 2493–2504.Google Scholar
Long, A., 1974: Solutions to the droplet collection equation for polynomial kernels. J. Atmos. Sci., 31, 1040–1052.Google Scholar
Low, T.B., and List, R., 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.Google Scholar
Low, T.B., and List, R., 1982b: Collision, coalescence, and breakup of raindrops. Part II: Parameterization of fragment size distributions. J. Atmos. Sci., 39, 1607–1618.Google Scholar
Lu, C., Liu, Y., Niu, S., and Endo, S., 2014: Scale dependence of entrainment-mixing mechanisms in cumulus clouds. J. Geophys. Res. Atmos., 119, 13,877–13,890.Google Scholar
Magaritz, L., Pinsky, M., and Khain, A., 2010: Effects of stratocumulus clouds on aerosols in the maritime boundary layer. Atmos. Res., 97, 498–512.Google Scholar
Magaritz, L., Pinsky, M., Krasnov, O., and Khain, A., 2009: Investigation of droplet size distributions and drizzle formation using a new trajectory ensemble model. Part 2: Lucky parcels in non-mixing limit. J. Atmos. Sci., 66, 781–805.Google Scholar
Magaritz-Ronen, L., Pinsky, M., and Khain, A., 2014: Effects of turbulent mixing on the structure and macroscopic properties of stratocumulus clouds demonstrated by a Lagrangian trajectory model. J. Atmos. Sci., 71, 1843–1862.Google Scholar
Magaritz-Ronen, L., Pinsky, M., and Khain, A., 2016a: Drizzle formation in stratocumulus clouds: Effects of turbulent mixing. Atmos. Chem. Phys., 16, 1849–1862.Google Scholar
Magaritz-Ronen, L., Pinsky, M., and Khain, A., 2016b: About the horizontal variability of effective radius in stratocumulus clouds. J. Geophys. Res., 121(16), 9640–9660.Google Scholar
Manton, M.J., 1977: The equation of motion for a small aerosol in a continuum. PAGEOPH, 115, 547–559.Google Scholar
Manton, M.J., 1979: On the broadening of a droplet distribution by turbulence near cloud base. Q. J. Royal Meteorol. Soc., 105, 899–914.Google Scholar
Marchuk, G.I., 1974: Numerical Methods in Weather Prediction. Akademic Press, p. 277.Google Scholar
Marchuk, G.I., 1980: Methods of Computational Mathematics (in Russian). Nauka Press, p. 536.Google Scholar
Martin, G.M., Johnson, D.W., and Spice, A., 1994: The measurements and parameterization of effective radius of droplets in warm stratocumulus clouds. J. Atmos. Sci., 51, 1823–1842.Google Scholar
Maxey, M.R., 1987: The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech., 174, 441–465.Google Scholar
Mazin, I.P., 1965: To the theory of formation of size spectra of particles in clouds and precipitation (in Russian). Proc. of Central Aerologic Observatory, 64, 57–70.Google Scholar
Mazin, I.P., 1967: A relationship between fluctuations of supersaturation in clouds and fluctuations of temperature and of vertical flows (in Russian). Proc. of Central Aerologic Observatory, 79, 3–8.Google Scholar
Mazin, I.P., 1968: Effect of Phase Transition on Formation of Temperature and Humidity Stratification in Clouds. Proc. Int. Conf. on Cloud Physics. Toronto, Ontario, Canada, Amer. Meteor. Soc., 132–137.Google Scholar
Mazin, I.P., Khrgian, A.K., and Imyanitov, I.M., 1989: Handbook of Clouds and Cloudy atmosphere. Gidrometeoizdat, p. 647.Google Scholar
Mazin, I.P., and Merkulovich, V.M., 2008: Stochastic condensation and its possible role in liquid cloud microstructure formation (Review). In Some Problems of Cloud Physics, Collected papers, Memorial Issue dedicated to Prof. S.M. Shmeter, Moscow, National Geophysical Committee, Russian Academy of Science, 263–295.Google Scholar
Mazin, I.P., and Shmeter, S.M., 1983: Clouds, Their Structure and Formation. Gidrometeoizdat, p. 279.Google Scholar
Mazin, I.P., and Smirnov, V.I., 1969: On the theory of cloud drop size spectrum formation by stochastic condensation. Proceed. CAO, 89, 92–94.Google Scholar
McFarquhar, G.M., 2004a: The effect of raindrop clustering on collision-induced break-up of raindrops. Q. J. Royal Meteorol. Soc., 130, 2169–2190.Google Scholar
McFarquhar, G.M., 2004b: A new representation of collision induced breakup of raindrops and its implications for the shape of raindrop size distributions. J. Atmos. Sci., 61, 777–794.Google Scholar
Mechem, D. B., and Kogan, Y.L., 2008: A bulk parameterization of giant CCN. J. Atmos. Sci., 65, 2458–2466.Google Scholar
Merkulovich, V.M., and Stepanov, A.S., 1977: Hygroscopicity effects and surface tension forces during condensational growth of cloud droplet in the presence of turbulence. Izv. Akad. Sci. USSR, Atmos. Oceanic Phys., 13, 163–171.Google Scholar
Meyers, M.P., Walko, R.L, Harrington, J.Y., and Cotton, W.R., 1997: New RAMS cloud microphysics parameterization Part 1: The single-moment scheme. Atmos. Res., 45, 3–39.Google Scholar
Milbrandt, J.A., and Yau, M.K., 2005: A multimoment bulk microphysics parameterization. Part II: A proposed three-moment closure and scheme description. J. Atmos. Sci., 62, 3065–3081.Google Scholar
Ming, Y., Ramaswamy, V., Donner, L.J., and Phillips, V.T.J., 2006: A new parameterization of cloud droplet activation applicable to general circulation models. J. Atmos. Sci., 63(4), 1348–1356, doi:10.1175/JAS3686.1.Google Scholar
Monin, A.S., and Yaglom, A.M., 1971: Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 1. MIT Press, p. 769.Google Scholar
Monin, A.S., and Yaglom, A.M., 1975: Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press, p. 874.Google Scholar
Morrison, H., Curry, J.A., and Khvorostyanov, V.I., 2005: A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description. J. Atmos. Sci., 62, 1665–1677.Google Scholar
Morrison, H., and Grabowski, W.W., 2008: Modeling supersaturation and subgrid-scale mixing with two-moment bulk warm microphysics. J. Atmos. Sci., 65, 792–812.Google Scholar
Naumann, A.K., and Seifert, A., 2016: Recirculation and growth of raindrops in simulated shallow cumulus. XVII International Conference on Clouds and Precipitation, Manchester, July 25–29, 2016, ICCP 2016 Conference Guide, p. 34.Google Scholar
Nenes, A., and Seinfeld, J.H., 2003: Parameterization of cloud droplet formation in global climate models, J. Geophys. Res., 108(D14), 4415, doi: 10.1029/2002JD002911.Google Scholar
Paluch, I.R., 1986: Mixing and the cloud droplet size spectrum: Generalizations from the CCOPE data. J. Atmos. Sci., 43, 1984–1993.Google Scholar
Paluch, I.R., and Baumgardner, D., 1989: Entrainment and fine-scale mixing in a continental convective cloud. J. Atmos. Sci., 46, 261–273.Google Scholar
Paluch, I.R., and Knight, C.A., 1984: Mixing and the evolution of cloud droplet size spectra in a vigorous continental cumulus. J. Atmos. Sci., 41, 1801–1815.Google Scholar
Paoli, R., and Shariff, K., 2009: Turbulent condensation of droplets: Direct simulation and a stochastic model. J. Atmos. Sci., 66, 723–740.Google Scholar
Pawlowska, H., Brenguier, J.L., and Burnet, F., 2000: Microphysical properties of stratocumulus clouds. Atmos. Res., 55, 15–33.Google Scholar
Phillips, V.T.J., DeMott, P.J., and Andronache, C., 2008a: An empirical parameterization of heterogeneous ice nucleation for multiple chemical species of aerosols. J. Atmos. Sci., 65, 2757–2783.Google Scholar
Phillips, V.T.J., Sherwood, S.C., Andronache, C., Bansemer, A., Conant, W.C., DeMott, P.J., Flagan, R.C., Heymsfield, A., Jonsson, H., Poellot, M., Rissman, T.A., Seinfeld, J.H., Vanreken, T., Varutbangkul, V., and Wilson, J.C., 2005: Anvil glaciation in a deep cumulus updraft over Florida simulated with an Explicit Microphysics Model. I: The impact of various nucleation processes. Q. J. Royal Meteorol. Soc., 131, 2019–2046.Google Scholar
Pinsky, M.B., and Khain, A.P., 1995: A model of homogeneous isotropic turbulence flow and its application for simulation of cloud drop tracks. Geophys. Astrophys. Fluid Dyn. 81, 33–55.Google Scholar
Pinsky, M.B., and Khain, A.P., 1996: Simulations of drops’ fall in a homogeneous isotropic turbulence flow. Atmos. Res., 40, 223–259.Google Scholar
Pinsky, M.B., and Khain, A.P., 1997a: Turbulence effects on the collision kernel. Part 1: Formation of velocity deviations of drops falling within a turbulent three-dimensional flow. Q. J. Royal Meteorol. Soc., 123, 1517–1542.Google Scholar
Pinsky, M.B., Khain, A.P., 1997b: Turbulence effects on the collision kernel. Part 2: Increase of swept volume of colliding drops. Q. J. Royal Meteorol. Soc., 123, 1543–1560.Google Scholar
Pinsky, M., and Khain, A.P., 1997c: Formation of inhomogeneity in drop concentration induced by the inertia of drops falling in a turbulent flow, and the influence of the inhomogeneity on the drop-spectrum broadening quart. J. Royal Meteorol. Soc., 123, 165–186.Google Scholar
Pinsky, M.B., and Khain, A., 2001: Fine structure of cloud drop concentration as seen from the Fast-FSSP measurements. Part 1: Method of analysis and preliminary results. J. Appl. Meteorol., 40, 1515–1537.Google Scholar
Pinsky, M., and Khain, A.P., 2002: Effects of in-cloud nucleation and turbulence on droplet spectrum formation in cumulus clouds. Q. J. Royol Meteorol. Soc., 128, 501–533.Google Scholar
Pinsky, M.B., and Khain, A.P., 2003: Fine structure of cloud droplet concentration as seen from the Fast-FSSP measurements. Part 2: Results of in-situ observations. J. Appl. Meteorol., 42, 65–73.Google Scholar
Pinsky, M.B., and Khain, A.P., 2004: Collisions of small drops in a turbulent flow. Part 2: Effects of flow accelerations. J. Atmos. Sci., 61, 1926–1939.Google Scholar
Pinsky, M.B., Khain, A.P., Grits, B., and Shapiro, M., 2006: Collisions of cloud droplets in a turbulent flow. Part 3: Relative droplet fluxes and swept volumes. J. Atmos. Sci., 63, 2123–2139.Google Scholar
Pinsky, M., Khain, A., Krugliak, H., 2008a: Collisions of cloud droplets in a turbulent flow. Part 5: Application of detailed tables of turbulent collision rate enhancement to simulation of droplet spectra evolution. J. Atmos. Sci., 65, 357–374.Google Scholar
Pinsky, M.B., Khain, A.P., and Levin, Z., 1999a: The role of the inertia of cloud drops in the evolution of the drop size spectra during drop growth by diffusion. Q. J. Royal Meteorol. Soc., 125, 553–581.Google Scholar
Pinsky, M., Khain, A., and Magaritz, L., 2010: Representing turbulent mixing of non-conservative values in Eulerian and Lagrangian cloud models. Q. J. Royal. Meteorol. Soc., 136, 1228–1242.Google Scholar
Pinsky, M.B., Khain, A.P., and Shapiro, M., 1999b: Collisions of small drops in a turbulent flow. Part I: Collision efficiency. Problem formulation and preliminary results. J. Atmos. Sci., 56, 2585–2600.Google Scholar
Pinsky, M.B., Khain, A.P., and Shapiro, M., 2000: Stochastic effects on cloud droplet hydrodynamic interaction in a turbulent flow. Atmos. Res., 53, 131–169.Google Scholar
Pinsky, M., Khain, A., Mazin, I., and Korolev, A., 2012: Analytical estimation of droplet concentration at cloud base. J. Geophys. Res., 117, D18211, doi:10.1029/2012JD017753.Google Scholar
Pinsky, M., Khain, A.P., and Shapiro, M., 2001: Collision efficiency of drops in a wide range of Reynolds numbers: Effects of pressure on spectrum evolution. J. Atmos. Sci., 58, 742–764.Google Scholar
Pinsky, M., Khain, A., and Shapiro, M., 2007: Collisions of cloud droplets in a turbulent flow. Part 4. Droplet hydrodynamic interaction. J. Atmos. Sci., 64, 2462–2482.Google Scholar
Pinsky, M., Khain, A., Korolev, A. and Magaritz-Ronen, L., 2016a: Theoretical investigation of mixing in warm clouds – Part 2: Homogeneous mixing, Atmos. Chem. Phys., 16, 9255–9272.Google Scholar
Pinsky, M., Khain, A., and Korolev, A., 2016b: Theoretical analysis of mixing in liquid clouds ? Part 3: Inhomogeneous mixing, Atmos. Chem. Phys., 16, 9273–9297.Google Scholar
Pinsky, M., Magaritz, L., Khain, A., Krasnov, O., and Sterkin, A., 2008b: Investigation of droplet size distributions and drizzle formation using a new trajectory ensemble model. Part 1: Model description and first results in a non-mixing limit. J. Atmos. Sci., 65, 2064–2086.Google Scholar
Pinsky, M., Mazin, I.P., Korolev, A., and Khain, A., 2013: Supersaturation and diffusional droplet growth in liquid clouds. J. Atmos. Sci., 70, 2778–2793.Google Scholar
Pinsky, M., Mazin, I.P., Korolev, A., and Khain, A., 2014: Supersaturation and diffusional droplet growth in liquid clouds: Polydisperse spectra. J. Geophys. Res. Atmospheres, 119, 12,872–12,887.Google Scholar
Pinsky, M., Shapiro, M., Khain, A., and Wirzberger, H., 2004: A statistical model of strains in homogeneous and isotropic turbulence. Physica D., 191, 297–313.Google Scholar
Politovich, M.K., 1993: A study of the broadening of droplet size distribution in cumuli. J. Atmos. Sci., 50, 2230–2244.Google Scholar
Politovich, M.K., and Cooper, W.A., 1988: Variability of the supersaturation in cumulus clouds. J. Atmos. Sci., 45, 1651–1664.Google Scholar
Pope, S.B., 2000: Turbulent Flows. Cambridge University Press, p. 771.Google Scholar
Prabha, T., Khain, A., Goswami, B.N., Pandithurai, G., Maheshkumar, R.S., and Kulkarni, J.R., 2011: Microphysics of pre-monsoon and monsoon clouds as seen from in-situ measurements during CAIPEEX. J. Atmos. Sci., 68, 1882–1901.Google Scholar
Prabha, V.T., Patade, S., Pandithurai, G., Khain, A., Axisa, D., PradeepKumar, P., Maheshkumar, R.S., Kulkarni, J.R., and Goswami, B.N., 2012: Spectral width of premonsoon and monsoon clouds over Indo-Gangetic valley during CAIPEEX. J. Geop. Res., 117, D20205, doi:10.1029/2011JD016837.Google Scholar
Pruppacher, H.R., and Klett, J.D., 1978: Microphysics of Clouds and Precipitation. Springer, p. 714.Google Scholar
Pruppacher, H.R., and Klett, J.D., 1997: Microphysics of Clouds and Precipitation, second edition. Kluwer Academic Publishers, p. 914.Google Scholar
Pruppacher, H.R., and Rasmussen, R., 1979: A wind tunnel investigation of the rate of evaporation of large water drops falling at terminal velocity in air. J. Atmos. Sci., 36, 1255–1260.Google Scholar
Raga, G.B., Jensen, J.B., and Baker, M.B., 1990: Characteristics of cumulus band clouds of the coast of Hawaii. J. Atmos. Sci., 47, 338–355.Google Scholar
Reade, W., and Collins, L.R., 2000: Effect of preferential concentration on turbulent collision rates. Phys. Fluids, 12, 2530–2540.Google Scholar
Reisin, T., Levin, Z. and Tzivion, S., 1996: Rain production in convective clouds as simulated in an axisymmetric model with detailed microphysics. Part 1: Description of the model. J. Atmos. Sci., 53, 497–519.Google Scholar
Reisner, J., Rassmussen, R.M., and Bruintjes, R.T., 1998: Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Q. J. Royal Meteorol. Soc., 124, 1071–1107.Google Scholar
Respondek, P.S., Flassman, A.I., Alheit, R.R., and Pruppacher, H.R., 1995: A theoretical study of the wet removal of atmospheric pollutants. Part V: The uptake, redistribution, and deposition of (NH4)2SO4 by a convective cloud containing ice. J. Atmos. Sci., 52, 2121–2132.Google Scholar
Rissler, J., Swietlicki, E., Zhou, J., Roberts, G., Andreae, M.O., Gatti, L.V., and Artaxo, P., 2004: Physical properties of the sub-micrometer aerosol over the Amazon rain forest during the wet-to-dry season transition-comparison of modelled and meaqsured CCN concentrations. Atmos. Chem. Phys. Discuss., 4, 3159–3225.Google Scholar
Rissler, J., Vestin, A., Swietlicki, E., Fisch, G., Zhou, J., Artaxo, P., and Andreae, M.O., 2006: Size distribution and hygroscopic properties of aerosol particles from dry-season biomass burning in Amazonia. Atmos. Chem. Phys., 6, 471–491, doi:10.5194/acp-6-471-2006.Google Scholar
Roesner, S., Flossmann, A.I., and Pruppacher, H.R., 1990: The effect on the evolution of the drop spectrum in clouds of the preconditioning of air by successive convective elements. Q. J. Royal Meteorol. Soc., 116, 1389–1403.Google Scholar
Rogers, R.R., 1975: An elementary parcel model with explicit condensation and supersaturation. Atmosphere, 13, 192–204.Google Scholar
Rogers, R.R, and Yau, M.K., 1996: Short Course in Cloud Physics. Butterworth-Heinemann, p. 304.Google Scholar
Rosenfeld, D., and Gutman, G., 1994: Retrieving microphysical properties near the tops of potential rain clouds by multispectral analysis of AVHRR data. Atmos. Res., 34, 259–283.Google Scholar
Saffman, P.G., Turner, J.S., 1956: On the collision of drops in turbulent clouds. J. Fluid Mech., 1, 16.Google Scholar
Saxena, V.K., and Fukuta, N., 1976: Preprints Cloud Phys. Conf., Boulder, p. 26, Am. Meteor. Soc., Boston.Google Scholar
Saxena, V.K., and Rathore, R.S., 1984: Preprints 11th Int. Conf. on Atmos. Aerosol,Condensation and Ice Nuclei, p. 292, Hungarian Meteor. Soc., Budapest.Google Scholar
Schlamp, R.J., Grover, S.N., Pruppacher, H.R., and Hamielec, A.E., 1976: A numerical investigation of the effect of electric charges and vertical external electric fields and the collision efficiency of cloud drops. J. Atmos. Sci., 33, 1747–1755.Google Scholar
Schlüter, M.H., 2006: The effects of entrainment and mixing process on the droplet size distribution in cumuli. A thesis submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Master of Science, Department of Meteorology, The University of Utah, p. 92 (MS Study).Google Scholar
Schlüter, M.H., Krueger, S.K., and Su, C.-W., 2006: The effects of entrainment and mixing on the droplet size distributions in cumuli, 12th Conference on Cloud Physics. Madison, WI, p 234.Google Scholar
Sedunov, Y.S., 1965: The fine structure of the clouds and its role in formation of the cloud droplet spectra. Izv. Acad. Sci. USSR, Atmos. Oceanic. Phys., 1, 722–731.Google Scholar
Sedunov, Y.S., 1974: Physics of Drop Formation in the Atmosphere. Wiley, p. 234.Google Scholar
Segal, Y., and Khain, A., 2006: Dependence of droplet concentration on aerosol conditions in different cloud types: Application to droplet concentration parameterization of aerosol conditions. J. Geophys. Res., 111, D15204.Google Scholar
Segal, Y., Pinsky, M., Khain, A., and Erlick, C., 2003: Theromodynamic factors influencing the bimodal spectra formation in cumulus clouds. Atmos. Res., 66, 43–64.Google Scholar
Seifert, A., and Beheng, K.D., 2001: A double-moment parameterization for simulating autoconversion, accretion and selfcollection. Atmos. Res., 59–60, 265–281.Google Scholar
Seifert, A., Khain, A., Blahak, U., and Beheng, K.D., 2005: Possible effects of collisional breakup on mixed-phase deep convection simulated by a spectral (bin) cloud model. J. Atmos. Sci., 62, 1917–1931.Google Scholar
Seifert, A., Nuijens, L., and Stevens, B., 2010: Turbulence effects on warm-rain autoconversion in precipitating shallow convection. Q. J. Royal Meteorol. Soc., 136, 1753–1762.Google Scholar
Shaw, R.A., 2003: Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech., 35, 183–227.Google Scholar
Shipway, B.J., and Abel, S.J., 2010: Analytical estimation of cloud droplet nucleation based on an underlying aerosol population. Atmos. Res., 96, 344–355.Google Scholar
Shmeter, S.M., 1987: Thermodynamics and Physics of convective clouds. Gidrometizdat, p. 288.Google Scholar
Siebert, H., Lehmann, K., and Wendisch, M., 2006: Observations of small-scale turbulence and energy dissipation rates in the cloudy boundary layer. J. Atmos. Sci., 63, 1451–1466.Google Scholar
Simmel, M., Trautmann, T., and Tetzlaff, G., 2002: Numerical solution of the stochastic collection equation – comparison of the linear discrete method with other methods. Atmos. Res., 61, 135–148.Google Scholar
Simpson, J., Helvoirt, G.V., and McCumber, M., 1982: Three-dimensional simulations of cumulus congestus clouds on GATE day 261. J. Atmos. Sci., 39, 126–145.Google Scholar
Small, J.D., and Chuang, P.Y., 2008: New observations of precipitation initiation in warm cumulus clouds. J. Atmos. Sci., 65, 2972–2982.Google Scholar
Squires, P., 1952: The growth of cloud drops by condensation. Aust. J. Sci. Res., 5, 66–86.Google Scholar
Squires, P., 1958: Penetrative downdraughts in cumuli. Tellus, 10, 381–389.Google Scholar
Srivastava, R.C., 1971: Size distribution of raindrops generated by their breakup and coalescence. J. Atmos. Sci., 28, 410–415.Google Scholar
Srivastava, R.C., 1989: Growth of cloud drops by condensation: A criticism of currently accepted theory and a new approach. J. Atmos. Sci., 46, 869–887.Google Scholar
Stein, D., Georgii, H.W., and Kramm, V., 1985: Meteor. Rundschau, 38, 15.Google Scholar
Stepanov, A.S., 1975: Condensational growth of cloud droplets in a turbulized atmosphere. Izv. Akad. Sci. USSR, Atmos. Oceanic Phys., 11, 27–42.Google Scholar
Stevens, B., et al., 2003: On entrainment rates in nocturnal maritime stratocumulus. Q. J. Royal Meteorol. Soc., 129, 3469–3492.Google Scholar
Stevens, B.G., et al., 2005: Evaluation of large-eddy simulations via observations of nocturnal marine stratocumulus. Mon. Wea. Rev., 133, 1443–1455.Google Scholar
Stevens, B., Walko, R.L., Cotton, W.R., and Feingold, G., 1996: The spurious production of cloud-edge supersaturations by Eulerian models. Mon. Wea. Rev., 124, 1034–1041.Google Scholar
Straka, J.M., and Anderson, J.R., 1993: Numerical simulations of microburst-producing storms – Some results from storms observed during COHMEX. J. Atmos. Sci., 50, 1329–1348.Google Scholar
Straka, J.M., 2009: Cloud and Precipitation Microphysics. Principles and Parameterizations. Cambridge University Press, p. 392.Google Scholar
Strapp, J.W., Leaitch, W.R., and Liu, P.S.K., 1992: Hydrated and dried aerosol-size-distribution measurements from the particle measuring system FSSP-300 probe and the deiced PCASP-100X probe. J. Atmos. Oceanic Technol., 9, 548–555.Google Scholar
Straub, W., Beheng, K.D., Seifert, A., Schlottke, J., and Weigand, B., 2010: Numerical investigation of collision-induced breakup of raindrops. Part II: Parameterizations of coalescence efficiencies and fragment size distributions. J. Atmos. Sci., 67, 576–588.Google Scholar
Su, C.-W., Krueger, S.K., McMurtry, P.A., and Austin, P.H., 1998: Linear eddy modeling of droplet spectral evolution during entrainment and mixing in cumulus clouds. Atmos. Res., 47–48, 41–58.Google Scholar
Szakáll, M., Diehl, K., Mitra, S.K., Borrmann, S., 2009: A wind tunnel study on the shape, oscillation, and internal circulation of large raindrops with sizes between 2.5 and 7.5 mm. J. Atmos. Sci., 66 (3), 755–765.Google Scholar
Szakáll, M., Mitra, S.K., Diehl, K., and Borrmann, S., 2010: Shapes and oscillations of falling raindrops. Atmos. Res., 97, 416–425.Google Scholar
Takahashi, T., 1976: Hail in axisymmetric cloud model. J. Atmos. Sci., 33, 1579–1601.Google Scholar
Telford, J.W., and Chai, S.K., 1980: A new aspect of condensation theory. Pageoph, 118, 720–742.Google Scholar
Telford, J.W., Keck, T.S., and Chai, S.K., 1984: Entrainment at cloud tops and the droplet spectra. J. Atmos. Sci., 41, 3170–3179.Google Scholar
Temam, R., 1977: Theory and Numerical Analysis of the Navier_Stokes Equations. North-Holland, p. 465.Google Scholar
Testik, F.Y., and Barros, A.P., 2007: Toward elucidating the microstructure of warm rainfall: A survey. Rev. Geophys., 45, doi:10.1029/2005RG000182.Google Scholar
Tokay, A., Chamberlain, R., and Schoenhuber, M., 2000: Laboratory and field measurements of raindrop oscillations. Phys. Chem. Earth (B), 25, 867–870.Google Scholar
Twomey, S.A., 1959a: The nuclei of natural cloud formation. part I: The chemical diffusion method and its application to atmospheric nuclei. Geofis. Pure Appl., 43, 227–242.Google Scholar
Twomey, S., 1959b: The nuclei of natural cloud formation II. The supersaturation in natural clouds and the variation of cloud droplet concentration. Pure Appl. Geophys., 43, 243–249.Google Scholar
Twomey, S., and Wojciechowski, T.A., 1969: Observations of the geographical variation of cloud nuclei. J. Atmos. Sci., 26, 684–688.Google Scholar
Tzivion, S., Feingold, G., and Levin, Z., 1987: An efficient numerical solution to the stochastic collection equation. J. Atmos. Sci., 44, 3139–3149.Google Scholar
Tzivion, S., Feingold, G., and Levin, Z., 1989: The evolution of raindrop spectra. Part 2. Collisional collection/breakup and evaporation in a rainshaft. J. Atmos. Sci., 46, 3312–3327.Google Scholar
Tzivion, S., Reisin, T.G., and Levin, Z., 1999: A numerical solution of the kinetic collection equation using high spectral grid solution: A proposed reference. J. Comput. Phys., 148, 527–544.Google Scholar
Tzivion, S., Reisin, T.G., and Levin, Z., 2001: A new formulation of the spectral multi-moment method for calculating the kinetic collection equation: More accuracy with few bins. J. Comput. Phys., 171, 418.Google Scholar
Vaillancourt, P.A., Yau, M.K., 2000: Review of particle-turbulence interactions and consequences for Cloud Physics. Bull. Am. Meteorol. Soc., 81, 285–298.Google Scholar
Vaillancourt, P.A., Yau, M.K., Bartello, P., and Grabowski, W.W., 2002: Microscopic approach to cloud droplet growth by condensation. Part 2: Turbulence, clustering, and condensational growth. J. Atmos. Sci., 59, 3421–3435.Google Scholar
Van Zanten, M.C., Stevens, B., Vali, G., and Lenschow, D.H., 2005: Observations of drizzle in nocturnal marine stratocumulus. J. Atmos. Sci., 62, 88–106.Google Scholar
Verlinde, J., and Cotton, W.R., 1993: Fitting microphysical observations of nonsteady convective clouds to a numerical model: An application of the adjoint technique of data assimilation to a kinematic model. Mon. Wea. Rev., 121, 2776–2793.Google Scholar
Verlinde, J., Flatau, P.J., and Cotton, W.R., 1990: Analytic solution to the collection growth equation: Comparison with an approximate methods and utilization in microphysics parameterization schemes. J. Atmos. Sci., 47, 2871–2880.Google Scholar
Villermaux, E., and Bossa, B., 2009: Single-drop fragmentation determines size distribution of raindrops. Nature Physics, 5, 697–702.Google Scholar
Vohl, O., Mitra, S.K., Wurzler, S., Diehl, K., and Pruppacher, H.R., 2007: Collision efficiencies empirically determined from laboratory investigations of collisional growth of small raindrops in a laminar flow field. Atmos. Res., 85, 120–125.Google Scholar
Vohl, O., Mitra, S.K., Wurzler, S.C., and Pruppacher, H.R., 1999: A wind tunnel study on the effects of turbulence on the growth of cloud drops by collision and coalescence. J. Atmos. Sci., 56 (24), 4088–4099.Google Scholar
Voloshchuk, V.M., and Sedunov, Y.S., 1977: A kinetic equation for the evolution of the droplet spectra in a turbulent medium at the condensation stage of cloud development. Sov. Meteorol. Hydrol., 3, 3–14.Google Scholar
Voth, G.A., La Porta, A., Crawford, A.M., Alexander, J., and Bodenschatz, E., 2002: Measurements of particle accelerations in fully developed turbulence. J. Fluid Mech., 469, 121–160.Google Scholar
Walko, R.L., Cotton, W.R., Meyers, M.P., and Harrington, J.Y., 1995: New RAMS cloud microphysics parameterization. Part 1: The single-moment scheme. Atmos.Res., 38, 29–62.Google Scholar
Wang, L.-P., Ayala, O., and Grabowski, W.W., 2005a: Improved formulations of the superposition method. J. Atmos. Sci., 62, 1255–1266.Google Scholar
Wang, L.-P., Ayala, O., Kasprzak, S., and Grabowski, W., 2005b: Theoretical formulation of collision rate and collision efficiency of hydrodynamically interacting cloud droplets in turbulent atmosphere. J. Atmos. Sci., 62, 2433–2450.Google Scholar
Wang, L.-P., Ayala, O., Rosa, B., and Grabowski, W., 2008: Turbulent collision efficiency of heavy particles relevant to cloud droplets. New J. Phys. 10, 075013.Google Scholar
Wang, L.-P., Franklin, C.N., Ayala, O., and Grabowski, W., 2006a: Probability distributions of angle of approach and relative velocity for colliding droplets in a turbulent flow. J. Atmos. Sci., 63, 881–900.Google Scholar
Wang, L.-P., and Grabowski, W., 2009: The role of air turbulence in warm rain initiation. Atmos. Sci. Let., 10, 1–8.Google Scholar
Wang, L.-P., and Maxey, M.R., 1993: Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech., 256, 27–68.Google Scholar
Wang, L.-P., Wexler, A.S., and Zhou, Y., 1998: Statistical mechanical descriptions of turbulent coagulation. Phys. Fluid, 10, 2647–2651.Google Scholar
Wang, L.-P., Wexler, A.S., and Zhou, Y., 2000: Statistical mechanical description and modeling of turbulent collision of inertial particles. J. Fluid Mech., 415, 117–153.Google Scholar
Wang, L.-P., Xue, Y., Ayala, O., and Grabowski, W.W., 2006b: Effects of stochastic coalescence and air turbulence on the size distribution of cloud droplets. Atmos. Res., 82, 416–432.Google Scholar
Wang, L.-P., Xue, Y., and Grabowski, W.W., 2007: A bin integral method for solving the kinetic collection equation. J. Comp. Phys., 226, 59–88.Google Scholar
Wang, P.K., and Pruppacher, H.R., 1977: Acceleration to terminal velocity of cloud and raindrops. J. Appl. Meteorol., 16, 275–280.Google Scholar
Warner, J., 1969a: The microstructure of cumulus cloud. Pt. I, General features of the droplet spectrum. J. Atmos. Sci., 26, 1049–1059.Google Scholar
Warner, J., 1969b: The microstructure of cumulus cloud. Part 2. The effect of droplet size distribution of the cloud nucleus spectrum and updraft velocity. J. Atmos. Sci., 26, 1272–1282.Google Scholar
Warner, J., 1970: The microstructure of cumulus cloud. Part 3. The nature of the updraft. J. Atmos. Sci., 27, 682–688.Google Scholar
Wex, H., Stratmann, F., Topping, D., and McFiggans, G., 2008: The Kelvin versus the Raoult Term in the Köhler Equation. J. Atmos. Sci., 65, 4004–4016.Google Scholar
Woo, S.E., and Hamielec, A.E., 1971: A numerical method of determining the rate of evaporation of small water drops falling at terminal velocity in air. J. Atmos. Sci., 28, 1448–1454.Google Scholar
Wyngaard, J.C., 2010: Turbulence in the Atmosphere. Cambridge University Press, p. 393.Google Scholar
Xue, Y., Wang, L.-P., and Grabowski, W., 2008: Growth of cloud droplets by turbulent collision?coalescence. J. Atmos. Sci., 65, 331–356.Google Scholar
Yin, Y., Levin, Z., Reisin, T., and Tzivion, S., 2000: The effects of giant cloud condensational nuclei on the development of precipitation in convective clouds: A numerical study. Atmos. Res., 53, 91–116.Google Scholar
Yin, Y., Carslaw, K.S., and Feingold, G., 2005: Vertical transport and processiong of aerosols in a mixed-phase convective cloud and the feedback on cloud development. Q. J. Royal Meteorol. Soc., 131, 221–245.Google Scholar
Zhou, Y., Wexler, A., and Wang, L., 2001: Modeling turbulent collision of bidisperse inertial particles. J. Fluid Mech., 433, 77–104.Google Scholar

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