Abade, G. C., W. W. Grabowski, and H. Pawlowska, 2018: Broadening of cloud droplet spectra through eddy hopping: Turbulent entraining parcel simulations. J. Atmos. Sci., 75, 3365−3379, https://doi.org/10.1175/JAS-D-18-0078.1. |
Ackerman, A. S., M. P. Kirkpatrick, D. E. Stevens, and O. B. Toon, 2004: The impact of humidity above stratiform clouds on indirect aerosol climate forcing. Nature, 432, 1014−1017, https://doi.org/10.1038/nature03174. |
Ackerman, A. S., and Coauthors, 2009: Large-eddy simulations of a drizzling, stratocumulus-topped marine boundary layer. Mon. Wea. Rev., 137, 1083−1110, https://doi.org/10.1175/2008MWR2582.1. |
Andrejczuk, M., W. W. Grabowski, S. P. Malinowski, and P. K. Smolarkiewicz, 2004: Numerical simulation of cloud-clear air interfacial mixing. J. Atmos. Sci., 61, 1726−1739, https://doi.org/10.1175/1520-0469(2004)061<1726:NSOCAI>2.0.CO;2. |
Albrecht, B.A., 245: Aerosols, cloud microphysics, and fractional cloudiness. Science, 1227−1230. |
Andrejczuk, M., W. W. Grabowski, S. P. Malinowski, and P. K. Smolarkiewicz, 2006: Numerical simulation of cloud-clear air interfacial mixing: Effects on cloud microphysics. J. Atmos. Sci., 63, 3204−3225, https://doi.org/10.1175/JAS3813.1. |
Andrejczuk, M., J. M. Reisner, B. Henson, M. K. Dubey, and C. A. Jeffery, 2008: The potential impacts of pollution on a nondrizzling stratus deck: Does aerosol number matter more than type. J. Geophys. Res., 113, D19204, https://doi.org/10.1029/2007JD009445. |
Andrejczuk, M., W. W. Grabowski, S. P. Malinowski, and P. K. Smolarkiewicz, 2009: Numerical simulation of cloud-clear air interfacial mixing: Homogeneous versus inhomogeneous mixing. J. Atmos. Sci., 66, 2493−2500, https://doi.org/10.1175/2009JAS2956.1. |
Andrejczuk, M., W. W. Grabowski, J. Reisner, and A. Gadian, 2010: Cloud-aerosol interactions for boundary layer stratocumulus in the Lagrangian Cloud Model. J. Geophys. Res., 115, D22214, https://doi.org/10.1029/2010JD014248. |
Ayala, O., B. Rosa, and L.-P. Wang, 2008a: Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 2. Theory and parameterization. New Journal of Physics, 10, 075016, https://doi.org/10.1088/1367-2630/10/7/075016. |
Ayala, O., B. Rosa, L.-P. Wang, and W. W. Grabowski, 2008b: Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 1. Results from direct numerical simulation. New Journal of Physics, 10, 075015, https://doi.org/10.1088/1367-2630/10/7/075015. |
Ayala, O., H. Parishani, L. Chen, B. Rosa, and L.-P. Wang, 2014: DNS of hydrodynamically interacting droplets in turbulent clouds: Parallel implementation and scalability analysis using 2D domain decomposition. Computer Physics Communications, 185, 3269−3290, https://doi.org/10.1016/j.cpc.2014.09.005. |
Baker, M. B., 1993: Variability in concentrations of CCN in the marine cloud-top boundary layer. Tellus, 45B, 458−472. |
Baker, M. B., and J. Latham, 1979: The evolution of droplet spectra and the rate of production of embryonic raindrops in small cumulus clouds. J. Atmos. Sci., 36(8), 1612−1615, https://doi.org/10.1175/1520-0469(1979)036<1612:TEODSA>2.0.CO;2. |
Baker, M. B., R. G. Corbin, and J. Latham, 1980: The influence of entrainment on the evolution of cloud droplet spectra: I. A model of inhomogeneous mixing. Quart. J. Roy. Meteor. Soc., 106(449), 581−598, https://doi.org/10.1002/qj.49710644914. |
Bartlett, J. T., and P. R. Jonas, 1972: On the dispersion of the sizes of droplets growing by condensation in turbulent clouds. Quart. J. Roy. Meteor. Soc., 98, 150−164, https://doi.org/10.1002/qj.49709841512. |
Bauer, P., B. Stevens, and W. Hazeleger, 2021: A digital twin of Earth for the green transition. Nature Climate Change, 11(2), 80−83, https://doi.org/10.1038/s41558-021-00986-y. |
Beard, K. V., and H. R. Pruppacher, 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, https://doi.org/10.1175/1520-0469(1971)028<1455:AWTIOT>2.0.CO;2. |
Beheng, K. D., 1994: A parameterization of warm cloud microphysical conversion processes. Atmospheric Research, 33, 193−206, https://doi.org/10.1016/0169-8095(94)90020-5. |
Berg, L. K., C. M. Berkowitz, J. C. Barnard, G. Senum, and S. R. Springston, 2011: Observations of the first aerosol indirect effect in shallow cumuli. Geophys. Res. Lett., 38, L03809, https://doi.org/10.1029/2010GL046047. |
Berry, E. X., 1967: Cloud droplet growth by collection. Journal of the Atmospheric Sciences, 24, 688−701, https://doi.org/10.1175/1520-0469(1967)024<0688:cdgbc>2.0.co;2. |
Berry, E. X., 1968: Modification of the warm rain process. Preprints, First National Conf. on Weather Modification, Albany, NY, Amer. Meteor. Soc., 81–88. |
Berry, E. X., and R. L. Reinhardt, 1974a: An analysis of cloud drop growth by coalescence: Part 1. Double distributions. Journal of the Atmospheric Sciences, 31, 1814−1824, https://doi.org/10.1175/1520-0469(1974)031<1814:aaocdg>2.0.co;2. |
Berry, E. X., and R. L. Reinhardt, 1974b: An analysis of cloud drop growth by coalescence: Part II. Single initial distributions. Journal of the Atmospheric Sciences, 31, 1825−1831, https://doi.org/10.1175/1520-0469(1974)031<1825:aaocdg>2.0.co;2. |
Berry, E. X., and R. L. Reinhardt, 1974c: An analysis of cloud drop growth by coalescence: Part III. Accretion and self-collection. Journal of the Atmospheric Sciences, 31, 2118−2126, https://doi.org/10.1175/1520-0469(1974)031<2118:aaocdg>2.0.co;2. |
Berry, E. X., and R. L. Reinhardt, 1974d: An analysis of cloud drop growth by collection: Part IV. A new parameterization. J. Atmos. Sci., 31, 2127−2135, https://doi.org/10.1175/1520-0469(1974)031<2127:aaocdg>2.0.co;2. |
Bleck, R., 1970: A fast, approximative method for integrating the stochastic coalescence equation. J. Geophys. Res., 75(27), 5165−5171, https://doi.org/10.1029/JC075i027p05165. |
Boucher, O., H. L. Treut, and M. B. Baker, 1995: Precipitation and radiation modeling in a general circulation model: Introduction of cloud microphysical process. J. Geophys. Res., 100D, 16 395–16 414. |
Bower, K. N., and T. W. Choularton, 1992: A parameterization of the effective radius of ice-free clouds for use in global climate models. Atmos. Res., 27, 305−339, https://doi.org/10.1016/0169-8095(92)90038-C. |
Bower, K. N., T. W. Choularton, J. Latham, J. Nelson, M. B. Baker, and J. Jensen, 1994: A parameterization of warm clouds for use in atmospheric general circulation models. J. Atmos. Sci., 51, 2722−2732, https://doi.org/10.1175/1520-0469(1994)051<2722:APOWCF>2.0.CO;2. |
Brdar, S., and A. Seifert, 2018: McSnow: A monte-carlo particle model for riming and aggregation of ice particles in a multidimensional microphysical phase space. Journal of Advances in Modeling Earth Systems, 10, 187−206, https://doi.org/10.1002/2017MS001167. |
Brandes, E. A., G. Zhang, and J. Vivekanandan, 2003: An evaluation of a drop distribution–based polarimetric radar rainfall estimator. J. Appl. Meteor., 42, 452−460. |
Brenguier, J.-L., and L. Chaumat, 2001: Droplet spectra broadening in cumulus clouds. Part I: Broadening in adiabatic cores. J. Atmos. Sci., 58, 628−641, https://doi.org/10.1175/1520-0469(2001)058<0628:DSBICC>2.0.CO;2. |
Bretherton, C. S., P. N. Blossey, and J. Uchida, 2007: Cloud droplet sedimentation, entrainment efficiency, and subtropical stratocumulus albedo. Geophys. Res. Lett., 34, L03813, https://doi.org/10.1029/2006GL027648. |
Burnet, F., and J. L. Brenguier, 2007: Observational study of the entrainment-mixing process in warm convective clouds. J. Atmos. Sci., 64(6), 1995−2011, https://doi.org/10.1175/JAS3928.1. |
Caldwell, P., and C. S. Bretherton, 2009: Large eddy simulation of the diurnal cycle in Southeast Pacific stratocumulus. J. Atmos. Sci., 66(2), 432−449, https://doi.org/10.1175/2008JAS2785.1. |
Cao, Q., and G. F. Zhang, 2009: Errors in estimating raindrop size distribution parameters employing disdrometer and simulated raindrop spectra. J. Appl. Meteor, 48, 406−424, https://doi.org/10.1175/2008JAMC2026.1. |
Cao, Q., Zhang, G., Brandes, E., Schuur, T., Ryzhkov, A., & Ikeda, K., 2008: Analysis of video disdrometer and polarimetric radar data to characterize rain microphysics in Oklahoma. Journal of Applied Meteorology and Climatology, 47(8), 2238−2255, https://doi.org/10.1175/2008jamc1732.1. |
Cao, Q., S. W. Zhang, G. L. Lei, and Y. Z. Zhang, 2022: Impact of different double-moment microphysical schemes on simulations of a bow-shaped squall line in east China. Atmosphere, 13, 667, https://doi.org/10.3390/atmos13050667. |
Celani, A., G. Falkovich, A. Mazzino, and A. Seminara, 2005: Droplet condensation in turbulence flows. Europhysics Letters, 70(6), 775−781, https://doi.org/10.1209/epl/i2005-10040-4. |
Chandrakar, K. K., H. Morrison, W. W. Grabowski, and G. H. Bryan, 2022: Comparison of Lagrangian superdroplet and Eulerian double-moment spectral microphysics schemes in large-eddy simulations of an isolated cumulus congestus cloud. J. Atmos. Sci., 79(7), 1887−1910, https://doi.org/10.1175/jas-d-21-0138.1. |
Charlson, R. J., A. S. Ackerman, F. A. M. Bender, T. L. Anderson, and Z. Y. Liu, 2007: On the climate forcing consequences of the albedo continuum between cloudy and clear air. Tellus B: Chemical and Physical Meteorology, 59, 715−727, https://doi.org/10.1111/j.1600-0889.2007.00297.x. |
Chen, J.-P., and S.-T. Liu, 2004: Physically based two-moment bulkwater parametrization for warm-cloud microphysics. Quart. J. Roy. Meteor. Soc., 130, 51−78, https://doi.org/10.1256/qj.03.41. |
Chen, J.-P., and T.-C. Tsai, 2016: Triple-moment modal parameterization for the adaptive growth habit of pristine ice crystals. J. Atmos. Sci., 73(5), 2105−2122, https://doi.org/10.1175/jas-d-15-0220.1. |
Chen, J. Y., Y. G. Liu, M. H. Zhang, and Y. R. Peng, 2016a: New understanding and quantification of the regime dependence of aerosol-cloud interaction for studying aerosol indirect effects. Geophys. Res. Lett., 43, 1780−1787, https://doi.org/10.1002/2016GL067683. |
Chen, J. Y., Y. G. Liu, M. H. Zhang, and Y. R. Peng, 2018a: Height dependency of aerosol-cloud interaction regimes. J. Geophys. Res., 123, 491−506, https://doi.org/10.1002/2017JD027431. |
Chen, J. Y., Y. G. Liu, and M. H. Zhang, 2020a: Effects of lateral entrainment mixing with entrained aerosols on cloud microphysics. Geophys. Res. Lett., 47, e2020GL087667, https://doi.org/10.1029/2020GL087667. |
Chen, S. S., P. Bartello, M. K. Yau, P. A. Vaillancourt, and K. Zwijsen, 2016b: Cloud droplet collisions in turbulent environment: Collision statistics and parameterization. J. Atmos. Sci., 73, 621−636, https://doi.org/10.1175/JAS-D-15-0203.1. |
Chen, S. S., M. K. Yau, and P. Bartello, 2018b: Turbulence effects of collision efficiency and broadening of droplet size distribution in cumulus clouds. J. Atmos. Sci., 75, 203−217, https://doi.org/10.1175/JAS-D-17-0123.1. |
Chen, S. S., M.-K. Yau, P. Bartello, and L. L. Xue, 2018c: Bridging the condensation-collision size gap: A direct numerical simulation of continuous droplet growth in turbulent cloud. Atmospheric Chemistry and Physics, 18, 7251−7262, https://doi.org/10.5194/acp-18-7251-2018. |
Chen, S. S., L. L. Xue, and M.-K. Yau, 2020b: Impact of aerosols and turbulence on cloud droplet growth: An in-cloud seeding case study using a parcel–DNS (direct numerical simulation) approach. Atmospheric Chemistry and Physics, 20, 10 111−10 124, https://doi.org/10.5194/acp-20-10111-2020. |
Chen, Y.-C., M. W. Christensen, L. Xue, A. Sorooshian, G. L. Stephens, R. M. Rasmussen, and J. H. Seinfeld, 2012: Occurrence of lower cloud albedo in ship tracks. Atmospheric Chemistry and Physics, 12(17), 8223−8235, https://doi.org/10.5194/acp-12-8223-2012. |
Ching, J., N. Riemer, and M. West, 2012: Impacts of black carbon mixing state on black carbon nucleation scavenging: Insights from a particle-resolved model. J. Geophys. Res., 117, D23209, https://doi.org/10.1029/2012JD018269. |
Chiu, J. C., C. K. Yang, Jan Van Leeuwen, G. Feingold, R. Wood, Y. Blanchard, P. F. Mei, and J. Wang, 2021: Observational constraints on warm cloud microphysical processes using machine learning and optimization techniques. Geophys. Res. Lett., 48(2), e2020GL091236, https://doi.org/10.1029/2020gl091236. |
Chosson, F., P. A. Vaillancourt, J. A. Milbrandt, M. K. Yau, and A. Zadra, 2014: Adapting two-moment microphysics schemes across model resolutions: Subgrid cloud and precipitation fraction and microphysical sub–time step. J. Atmos. Sci., 71(7), 2635−2653, https://doi.org/10.1175/jas-d-13-0367.1. |
Clark, T. L., 1973: Numerical modeling of the dynamics and microphysics of warm cumulus convection. J. Atmos. Sci., 30, 857−878, https://doi.org/10.1175/1520-0469(1973)030<0857:NMOTDA>2.0.CO;2. |
Clark, T. L., 1974: A study in cloud phase parameterization using the gamma distribution. J. Atmos. Sci., 31, 142−155, https://doi.org/10.1175/1520-0469(1974)031<0142:ASICPP>2.0.CO;2. |
Cohard, J.-M., and J.-P. Pinty, 2000: A comprehensive two-moment warm microphysical bulk scheme. I: Description and tests. Quart. J. Roy. Meteor. Soc., 126, 1815−1842, https://doi.org/10.1002/qj.49712656613. |
Cooper, W. A., 1989: Effects of variable droplet growth histories on droplet size distributions. Part I: Theory. J. Atmos. Sci., 46, 1301−1311, https://doi.org/10.1175/1520-0469(1989)046<1301:EOVDGH>2.0.CO;2. |
Cotton, W. R., and Coauthors, 1982: The Colorado State University three-dimensional cloud/mesoscale model-1982. Part II: An ice phase parameterization. Journal de Recherches Atmospheriques, 16, 295−320. |
Dawson II, D. T., E. R. Mansell, Y. Jung, L. J. Wicker, M. R. Kumjian, and M. Xue, 2014: Low-level ZDR signatures in supercell forward flanks: The role of size sorting and melting of hail. J. Atmos. Sci., 71(1), 276−299, https://doi.org/10.1175/jas-d-13-0118.1. |
De 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, https://doi.org/10.1175/1520-0469(1979)036<1564:TCPOCD>2.0.CO;2. |
de Lozar, A., and J. P. Mellado, 2013: Cloud droplets in a bulk formulation and its application to buoyancy reversal instability. Quart. J. Roy. Meteor. Soc, 140(682), 1493−1504. |
Del Genio, A. D., M. Yao, W. Kovari, and K. K. Lo, 1996: A prognostic cloud water parameterization for climate models. J. Climate, 9, 270−304. |
Deng, W., J.-M. Sun, and H.-C. Lei, 2018: Numerical investigations for the impacts of triple-moment and double-moment condensation schemes on the warm rain formation. Atmos. Ocean. Sci. Lett., 11(6), 472−480, https://doi.org/10.1080/16742834.2018.1527176. |
Desai, N., Y. G. Liu, S. Glienke, R. A. Shaw, C. S. Lu, J. Wang, and S. N. Gao, 2021: Vertical variation of turbulent entrainment mixing processes in marine stratocumulus clouds using high-resolution digital holography. J. Geophys. Res., 126(7), e2020JD033527, https://doi.org/10.1029/2020JD033527. |
Devenish, B. J., and Coauthors, 2012: Droplet growth in warm turbulent clouds. Quart. J. Roy. Meteor. Soc., 138, 1401−1429, https://doi.org/10.1002/qj.1897. |
DeVille, R. E. L., N. Riemer, and M. West, 2011: Weighted Flow Algorithms (WFA) for stochastic particle coagulation. J. Comput. Phys., 230, 8427−8451, https://doi.org/10.1016/j.jcp.2011.07.027. |
Dziekan, P., and H. Pawlowska, 2017: Stochastic coalescence in Lagrangian cloud microphysics. Atmospheric Chemistry and Physics, 17, 13 509−13 520, https://doi.org/10.5194/acp-17-13509-2017. |
Eidhammer, T., H. Morrison, A. Bansemer, A. Gettelman, and A. J. Heymsfield, 2014: Comparison of ice cloud properties simulated by the Community Atmosphere Model (CAM5) with in-situ observations. Atmos. Chem. Phys., 14, 10 103–10 118, https://doi.org/10.5194/acp-14-10103-2014. |
Eidhammer, T., H. Morrison, D. Mitchell, A. Gettelman, and E. Erfani, 2017: Improvements in global climate model microphysics using a consistent representation of ice particle properties. J. Climate, 30(2), 609−629, https://doi.org/10.1175/jcli-d-16-0050.1. |
Ekman, A. M. L., A. Engstrom, and A. Soderberg, 2011: Impact of two-way aerosol-cloud interaction and changes in aerosol size distribution on simulated aerosol-induced deep convective cloud sensitivity. J. Atmos. Sci., 68, 685−698, https://doi.org/10.1175/2010JAS3651.1. |
Endo, S., A. M. Fridlind, W. Lin, A. M. Vogelmann, T. Toto, A. S. Ackerman, G. M. McFarquhar, R. C. Jackson, and Y. Liu, 2015: Continental Boundary Layer Cloud Processes. Part II: Large Eddy Simulations of Cumulus Clouds and Evaluation with In-Situ and Ground-Based Observations. J. Geophys. Res. Atmos, 120, 59936014, https://doi.org/10.1002/2014JD022525. |
Erfani, E., and D. L. Mitchell, 2016: Developing and bounding ice particle mass- and area-dimension expressions for use in atmospheric models and remote sensing. Atmospheric Chemistry and Physics, 16(7), 4379−4400, https://doi.org/10.5194/acp-16-4379-2016. |
Fan, J. W., L. R. Leung, Z. Q. Li, H. Morrison, Y. Qian, Y. Zhou, and H. Chen, 2012: Aerosol impacts on clouds and precipitation in southeast China−Results from bin and bulk microphysics for the 2008 AMF-China field campaign. Journal of Geophysical Research, 117, D00K36, https://doi.org/10.1029/2011JD016537. |
Feingold, G., S. Tzivion, and Z. Leviv, 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, https://doi.org/10.1175/1520-0469(1988)045<3387:EORSPI>2.0.CO;2. |
Feingold, G., W. R. Cotton, S. M. Kreidenweis, and J. T. Davis, 1999: The impact of giant cloud condensation nuclei on drizzle formation in stratocumulus: Implications for cloud radiative properties. J. Atmos. Sci., 56, 4100−4117, https://doi.org/10.1175/1520-0469(1999)056<4100:TIOGCC>2.0.CO;2. |
Ferrier, B. S., 1994: A double-moment multiple-phase four-class bulk ice scheme. Part I: Description. J. Atmos. Sci., 51, 249−280, https://doi.org/10.1175/1520-0469(1994)051<0249:ADMMPF>2.0.CO;2. |
Fouquart, Y., J. C. Buriez, and H. Herman, 1989: The influence of boundary layer clouds on radiation, A review. Atmos. Res., 23, 203−228, https://doi.org/10.1016/0169-8095(89)90019-7. |
Franklin, C. N., P. A. Vaillancourt, M. K. Yau, and P. Bartello, 2005: Collision rates of cloud droplets in turbulent flow. J. Atmos. Sci., 62, 2451−2466, https://doi.org/10.1175/JAS3493.1. |
Franklin, C. N., P. A. Vaillancourt, and M. K. Yau, 2007: Statistics and parameterizations of the effect of turbulence on the geometric collision kernel of cloud droplets. J. Atmos. Sci., 64, 938−954, https://doi.org/10.1175/JAS3872.1. |
Gao, Z., Y. G. Liu, X. L. Li, and C. S. Lu, 2018: Investigation of turbulent entrainment-mixing processes with a new particle-resolved direct numerical simulation model. J. Geophys. Res., 123, 2194−2214, https://doi.org/10.1002/2017JD027507. |
Gettelman, A., D. J. Gagne, C.-C. Chen, M. W. Christensen, Z. J. Lebo, H. Morrison, and G. Gantos, 2021: Machine learning the warm rain process. Journal of Advances in Modeling Earth Systems, 13, e2020MS002268, https://doi.org/10.1029/2020MS002268. |
Gettelman, A., and H. Morrison, 2015: Advanced two-moment bulk microphysics for global models. Part I: Off-line tests and comparison with other schemes. Journal of Climate, 28, 1268−1287, https://doi.org/10.1175/jcli-d-14-00102.1. |
Ghan, S. J., L. R. Leung, R. C. Easter, and H. Abdul-Razzak, 1997: Prediction of cloud droplet number in a general circulation model. J. Geophys. Res., 102, 21 777−21 794, https://doi.org/10.1029/97JD01810. |
Ghan, S. J., and Coauthors, 2011: Droplet nucleation: Physically-based parameterizations and comparative evaluation. Journal of Advances in Modeling Earth Systems, 3, M10001, https://doi.org/10.1029/2011MS000074. |
Gillespie, D. T., 1972: The stochastic coalescence model for cloud droplet growth. J. Atmos. Sci., 29, 1496−1510, https://doi.org/10.1175/1520-0469(1972)029<1496:TSCMFC>2.0.CO;2. |
Grabowski, W. W. and L.-P. Wang, 2013: Growth of cloud droplets in a turbulent environment. Annual Review of Fluid Mechanics, 45, 293−324, https://doi.org/10.1146/annurev-fluid-011212-140750. |
Grabowski, W. W., and G. C. Abade, 2017: Broadening of cloud droplet spectra through eddy hopping: Turbulent adiabatic parcel simulations. J. Atmos. Sci., 74, 1485−1493, https://doi.org/10.1175/JAS-D-17-0043.1. |
Grabowski, W. W., P. Dziekan, and H. Pawlowska, 2018: Lagrangian condensation microphysics with Twomey CCN activation. Geoscientific Model Development, 11, 103−120, https://doi.org/10.5194/gmd-11-103-2018. |
Grabowski, W. W., H. Morrison, S. I. Shima, G. C. Abade, P. Dziekan, and H. Pawlowska, 2019: Modeling of cloud microphysics: Can we do better. Bull. Amer. Meteor. Soc., 100, 655−672, https://doi.org/10.1175/BAMS-D-18-0005.1. |
Gu, Z. C., 1962: Recent investigations in the theory of the formation of the cloud-drop spectra. Acta Meteorologica Sinica, 32, 267−284, https://doi.org/10.11676/qxxb1962.027. (in Chinese with English abstract |
Guo, H., Y. G. Liu, and J. E. Penner, 2008: Does the threshold representation associated with the autoconversion process matter? Atmospheric Chemistry and Physics, 8, 1225−1230, https://doi.org/10.5194/acp-8-1225-2008. |
Hall, W. D., 1980: A detailed microphysical model within a two-dimensional dynamic framework: Model description and preliminary results. Journal of the Atmospheric Sciences, 37, 2486−2507, https://doi.org/10.1175/1520-0469(1980)037<2486:admmwa>2.0.co;2. |
Hansen, J. E., and L. D. Travis, 1974: Light scattering in planetary atmospheres. Space Science Reviews, 16, 527−610, https://doi.org/10.1007/BF00168069. |
Harrington, J. Y., G. Feingold, and W. R. Cotton, 2000: Radiative impacts on the growth of a population of drops within simulated summertime arctic stratus. J. Atmos. Sci., 57, 766−785, https://doi.org/10.1175/1520-0469(2000)057<0766:RIOTGO>2.0.CO;2. |
Harrington, J. Y., K. Sulia, and H. Morrison, 2013a: A method for adaptive habit prediction in bulk microphysical models. Part I: Theoretical development. J. Atmos. Sci., 70, 349−364, https://doi.org/10.1175/JAS-D-12-040.1. |
Harrington, J. Y., K. Sulia, and H. Morrison, 2013b: A method for adaptive habit prediction in bulk microphysical models. Part II: Parcel model corroboration. J. Atmos. Sci., 70, 365−376, https://doi.org/10.1175/JAS-D-12-0152.1. |
Hashino, T., and G. J. Tripoli, 2007: The Spectral Ice Habit Prediction System (SHIPS). Part I: Model description and simulation of the vapor deposition process. J. Atmos. Sci., 64, 2210−2237, https://doi.org/10.1175/JAS3963.1. |
Hoffmann, F., and G. Feingold, 2019: Entrainment and mixing in stratocumulus: Effects of a new explicit subgrid-scale scheme for large-eddy simulations with particle-based microphysics. J. Atmos. Sci., 76(7), 1955−1973, https://doi.org/10.1175/JAS-D-18-0318.1. |
Hoffmann, F., T. Yamaguchi, and G. Feingold, 2019: Inhomogeneous mixing in Lagrangian cloud models: Effects on the production of precipitation embryos. J. Atmos. Sci., 76, 113−133, https://doi.org/10.1175/JAS-D-18-0087.1. |
Howell, W. E., 1949: The growth of cloud drops in uniformly cooled air. J. Atmos. Sci., 6, 134−149, https://doi.org/10.1175/1520-0469(1949)006<0134:TGOCDI>2.0.CO;2. |
Hu, Z.-J., and G.-F. He, 1987: Numerical simulation of microprocesses in cumulonimbus clouds (I): Microphysical model. Acta Meteorologica Sinica, 45, 467−484. (in Chinese with English abstract) |
Hudson, J. G., S. Noble, and V. Jha, 2012: Cloud droplet spectral width relationship to CCN spectra and vertical velocity. J. Geophys. Res., 117, D11211, https://doi.org/10.1029/2012JD017546. |
Igel, A. L., and S. C. Van Den Heever, 2017: The importance of the shape of cloud droplet size distributions in shallow cumulus clouds. Part II: Bulk microphysics simulations. J. Atmos. Sci., 74(1), 259−273, https://doi.org/10.1175/JAS-D-15-0383.1. |
Ishimoto, H., K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, 2012: Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds. Journal of Quantitative Spectroscopy and Radiative Transfer, 113, 632−643, https://doi.org/10.1016/j.jqsrt.2012.01.017. |
Jarecka, D., W. W. Grabowski, and H. Pawlowska, 2009: Modeling of subgrid-scale mixing in large-eddy simulation of shallow convection. J. Atmos. Sci., 66(7), 2125−2133, https://doi.org/10.1175/2009JAS2929.1. |
Jarecka, D., W. W. Grabowski, H. Morrison, and H. Pawlowska, 2013: Homogeneity of the subgrid-scale turbulent mixing in large-eddy simulation of shallow convection. J. Atmos. Sci., 70, 2751−2767, https://doi.org/10.1175/JAS-D-13-042.1. |
Jaruga, A., and H. Pawlowska, 2018: Libcloudph++ 2.0: Aqueous-phase chemistry extension of the particle-based cloud microphysics scheme. Geoscientific Model Development, 11, 3623−3645, https://doi.org/10.5194/gmd-11-3623-2018. |
Jensen, E., and L. Pfister, 2004: Transport and freeze-drying in the tropical tropopause layer. J. Geophys. Res., 109, D02207, https://doi.org/10.1029/2003JD004022. |
Jiang, G.-S., and C.-W. Shu, 1996: Efficient implementation of weighted ENO schemes. J. Comput. Phys., 126(1), 202−228, https://doi.org/10.1006/jcph.1996.0130. |
Jimenez, P. A., and Coauthors, 2016: WRF-Solar: Description and clear-sky assessment of an augmented NWP model for solar power prediction. Bull. Amer. Meteor. Soc., 97, 1249−1264, https://doi.org/10.1175/BAMS-D-14-00279.1. |
Jiménez, P. A., S. Alessandrini, S. E. Haupt, A. J. Deng, B. Kosovic, J. A. Lee, and L. D. Monache, 2016: The role of unresolved clouds on short-range global horizontal irradiance predictability. Mon. Wea. Rev., 144, 3099−3107, https://doi.org/10.1175/MWR-D-16-0104.1. |
Johansen, A., A. N. Youdin, and Y. Lithwick, 2012: Adding particle collisions to the formation of asteroids and Kuiper belt objects via streaming instabilities. Astronomy & Astrophysics, 537, A125, https://doi.org/10.1051/0004-6361/201117701. |
Kabanov, A. S., I. P. Mazin, and V. I. Smirnov, 1971: Comment on “The theory of growth of cloud drops by condensation”. J. Atmos. Sci., 28(1), 129−130, https://doi.org/10.1175/1520-0469(1971)028<0129:COTOGO>2.0.CO;2. |
Kessler, E., 1969: On the distribution and continuity of water substance in atmospheric circulations. On the Distribution and Continuity of Water Substance in Atmosphere Circulations, E. Kessler, Ed., Springer, 1−84, https://doi.org/10.1007/978-1-935704-36-2_1. |
Khain, A., and M. Pinsky, 2018: Physical Processes in Clouds and Cloud Modeling. Cambridge University Press, https://doi.org/10.1017/9781139049481. |
Khain, A. P., L. R. Leung, B. Lynn, and S. Ghan, 2009: Effects of aerosols on the dynamics and microphysics of squall lines simulated by spectral bin and bulk parameterization schemes. J. Geophys. Res., 114, D22203, https://doi.org/10.1029/2009JD011902. |
Khain, A. P., and Coauthors, 2015: Representation of microphysical processes in cloud-resolving models: Spectral (bin) microphysics versus bulk parameterization. Rev. Geophys., 53, 247−322, https://doi.org/10.1002/2014rg000468. |
Khairoutdinov, M., and Y. Kogan, 2000: A new cloud physics parameterization in a large-eddy simulation model of marine stratocumulus. Mon. Wea. Rev., 128, 229−243, https://doi.org/10.1175/1520-0493(2000)128<0229:ANCPPI>2.0.CO;2. |
Khvorostyanov, V. I., and J. A. Curry, 1999a: Toward the theory of stochastic condensation in clouds. Part I: A general kinetic equation. J. Atmos. Sci., 56, 3985−3996, https://doi.org/10.1175/1520-0469(1999)056<3985:TTTOSC>2.0.CO;2. |
Khvorostyanov, V. I., and J. A. Curry, 1999b: Toward the theory of stochastic condensation in clouds. Part II: Analytical solutions of the gamma-distribution type. J. Atmos. Sci., 56, 3997−4013, https://doi.org/10.1175/1520-0469(1999)056<3997:TTTOSC>2.0.CO;2. |
Khvorostyanov, V. I., and J. A. Curry, 2008a: Kinetics of cloud drop formation and its parameterization for cloud and climate models. J. Atmos. Sci., 65, 2784−2802, https://doi.org/10.1175/2008JAS2606.1. |
Khvorostyanov, V. I., and J. A. Curry, 2008b: Analytical solutions to the stochastic kinetic equation for liquid and ice particle size spectra. Part I: Small-size fraction. J. Atmos. Sci., 65, 2025−2043, https://doi.org/10.1175/2007JAS2484.1. |
Khvorostyanov, V. I., and J. A. Curry, 2008c: Analytical solutions to the stochastic kinetic equation for liquid and ice particle size spectra. Part II: Large-size fraction in precipitating clouds. J. Atmos. Sci., 65, 2044−2063, https://doi.org/10.1175/2007JAS2485.1. |
Khvorostyanov, V. I., and J. A. Curry, 2014: Thermodynamics, Kinetics, and Microphysics of Clouds. Cambridge University Press, https://doi.org/10.1017/CBO9781139060004. |
Kogan, Y. L., and A. Belochitski, 2012: Parameterization of cloud microphysics based on full integral moments. J. Atmos. Sci., 69(7), 2229−2242, https://doi.org/10.1175/JAS-D-11-0268.1. |
Korolev, A., A. Khain, M. Pinsky, and J. French, 2016: Theoretical study of mixing in liquid clouds–Part 1: Classical concepts. Atmospheric Chemistry and Physics, 16, 9235−9254, https://doi.org/10.5194/acp-16-9235-2016. |
Kostinski, A. B., and R. A. Shaw, 2005: Fluctuations and luck in droplet growth by coalescence. Bull. Amer. Meteor. Soc., 86, 235−244, https://doi.org/10.1175/BAMS-86-2-235. |
Koziol, A. S., and H. G. Leighton, 1996: The effect of turbulence on the collision rates of small cloud drops. J. Atmos. Sci., 53, 1910−1920, https://doi.org/10.1175/1520-0469(1996)053<1910:TEOTOT>2.0.CO;2. |
Kumar, B., F. Janetzko, J. Schumacher, and R. A. Shaw, 2012: Extreme responses of a coupled scalar–particle system during turbulent mixing. New Journal of Physics, 14, 115020, https://doi.org/10.1088/1367-2630/14/11/115020. |
Kumar, B., J. Schumacher, and R. A. Shaw, 2014: Lagrangian mixing dynamics at the cloudy–clear air interface. J. Atmos. Sci., 71(7), 2564−2580, https://doi.org/10.1175/JAS-D-13-0294.1. |
Kumar, B., S. Bera, T. V. Prabha, and W. W. Grabowski, 2017: Cloud-edge mixing: Direct numerical simulation and observations in Indian monsoon cloud. Journal of Advances in Modeling Earth Systems, 9, 332−353, https://doi.org/10.1002/2016MS000731. |
Kumar, B., P. Götzfried, N. Suresh, J. Schumacher, and R. A. Shaw, 2018: Scale dependence of cloud microphysical response to turbulent entrainment and mixing. Journal of Advances in Modeling Earth Systems, 10, 2777−2785, https://doi.org/10.1029/2018MS001487. |
Lanotte, A. S., A. Seminara, and F. Toschi, 2009: Cloud Droplet Growth by Condensation in Homogeneous Isotropic Turbulence. J. Atmos. Sci., 66, 1685−1697, https://doi.org/10.1175/2008JAS2864.1. |
Latham, J., and R. L. Reed, 1977: Laboratory studies of the effects of mixing on the evolution of cloud droplet spectra. Quart. J. Roy. Meteor. Soc., 103(436), 297−306, https://doi.org/10.1002/qj.49710343607. |
Lawson, R. P., and Coauthors, 2019: A review of ice particle shapes in cirrus formed in situ and in anvils. J. Geophys. Res., 124, 10 049−10 090, https://doi.org/10.1029/2018JD030122. |
Lehmann, K., H. Siebert, and R. A. Shaw, 2009: Homogeneous and inhomogeneous mixing in cumulus clouds: Dependence on local turbulence structure. J. Atmos. Sci., 66, 3641−3659, https://doi.org/10.1175/2009JAS3012.1. |
Letu, H., H. Ishimoto, J. Riedi, T. Y. Nakajima, L. C. Labonnote, A. J. Baran, T. M. Nagao, and M. Sekiguchi, 2016: Investigation of ice particle habits to be used for ice cloud remote sensing for the GCOM-C satellite mission. Atmospheric Chemistry and Physics, 16, 12 28710.1029/2018JD03012212 303, |
Levin, L. M., and Y. S. Sedunov, 1966: J. Rech. Atmos., 2, 425−432. |
Li, M., and Coauthors, 2022: Investigation of ice cloud modeling capabilities for the irregularly shaped Voronoi ice scattering models in climate simulations. Atmospheric Chemistry and Physics, 22(7), 4809−4825, https://doi.org/10.5194/acp-22-4809-2022. |
Li, X.-Y., A. Brandenburg, N. E. L. Haugen, and G. Svensson, 2017: Eulerian and Lagrangian approaches to multidimensional condensation and collection. Journal of Advances in Modeling Earth Systems, 9, 1116−1137, https://doi.org/10.1002/2017MS000930. |
Li, X. W., W.-K. Tao, A. P. Khain, J. Simpson, and D. E. Johnson, 2009a: Sensitivity of a cloud-resolving model to bulk and explicit bin microphysical schemes. Part I: Validation with a PRE-STORM case. J. Atmos. Sci., 66, 3−21, https://doi.org/10.1175/2008JAS2646.1. |
Li, X. W., W.-K. Tao, A. P. Khain, J. Simpson, and D. E. Johnson, 2009b: Sensitivity of a cloud-resolving model to bulk and explicit bin microphysical schemes. Part II: Cloud microphysics and storm dynamics interactions. J. Atmos. Sci., 66, 22−40, https://doi.org/10.1175/2008JAS2647.1. |
Lim, K.‐S. S., and S. Y. Hong, 2010: Development of an effective double-moment cloud microphysics scheme with prognostic cloud condensation nuclei (CCN) for weather and climate models. Mon. Wea. Rev., 138(5), 1587−1612, https://doi.org/10.1175/2009mwr2968.1. |
Lin, Y. L., and B. A. Colle, 2011: A new bulk microphysical scheme that includes riming intensity and temperature-dependent ice characteristics. Mon. Wea. Rev., 139(3), 1013−1035, https://doi.org/10.1175/2010MWR3293.1. |
Lin, Y.-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Appl. Meteorol. Climatol., 22(6), 1065−1092, https://doi.org/10.1175/1520-0450(1983)022<1065:bpotsf>2.0.co;2. |
Lin, Y. L., L. J. Donner, and B. A. Colle, 2011: Parameterization of riming intensity and its impact on ice fall speed using ARM data. Mon. Wea. Rev., 139(3), 1036−1047, https://doi.org/10.1175/2010MWR3299.1. |
Liou, K. N., and S. C. Ou, 1989: The role of cloud microphysical processes in climate: An assessment from a one-dimensional perspective. J. Geophys. Res., 94D, 8599−8607. |
Liu, W. J., Y. G. Liu, X. Zhou, Y. Xie, Y. X. Han, S. Yoo, and M. Sengupta, 2021: Use of physics to improve solar forecast: Physics-informed persistence models for simultaneously forecasting GHI, DNI, and DHI. Solar Energy, 215, 252−265, https://doi.org/10.1016/j.solener.2020.12.045. |
Liu, W. J., Y. G. Liu, T. Zhang, Y. X. Han, X. Zhou, Y. Xie, and S. Yoo, 2022: Use of physics to improve solar forecast: Part II, machine learning and model interpretability. Solar Energy, 244, 362−378, https://doi.org/10.1016/j.solener.2022.08.040. |
Liu, Y. G., 1995: On the generalized theory of atmospheric particle systems. Adv. Atmos. Sci., 12, 419−438, https://doi.org/10.1007/BF02657003. |
Liu, Y. G., 1997: On the unified theory of atmospheric particle systems. Part II. Self-affine particles. Adv. Atmos. Sci., 14, 369−388, https://doi.org/10.1007/s00376-997-0057-2. |
Liu, Y. G., 2019: Introduction to the special section on fast physics in climate models: Parameterization, evaluation, and observation. J. Geophys. Res., 124, 8631−8644, https://doi.org/10.1029/2019JD030422. |
Liu, Y. G., J. Y. Chen, G. K. Lai, Y. M. Yang, and S. J. Yoo, 2018: Exploring machine learning models for cloud microphysics parameterizations. https://agu.confex.com/agu/fm18/meetingapp.cgi/Paper/392856. |
Liu, Y. G., and P. H. Daum, 2002: Anthropogenic aerosols – indirect warming effect from dispersion forcing. Nature, 419, 580−581, https://doi.org/10.1038/419580a. |
Liu, Y. G., and J. Hallett, 1997: The ‘1/3’ power law between effective radius and liquid-water content. Quart. J. Roy. Meteor. Soc., 123, 1789−1795, https://doi.org/10.1002/qj.49712354220. |
Liu, Y. G., and J. Hallett, 1998: On size distributions of cloud droplets growing by condensation: A new conceptual model. J. Atmos. Sci., 55, 527−536, https://doi.org/10.1175/1520-0469(1998)055<0527:OSDOCD>2.0.CO;2. |
Liu, Y. G. and P. H. Daum, 2000: Spectral dispersion of cloud droplet size distributions and the parameterization of cloud droplet effective radius. Geophy. Res. Lett., 27, 1903−1906, https://doi.org/10.1029/1999GL011011. |
Liu, Y. G., and P. H. Daum, 2004: Parameterization of the autoconversion process. Part I: Analytical formulation of the Kessler-type parameterizations. J. Atmos. Sci., 61, 1539−1548, https://doi.org/10.1175/1520-0469(2004)061<1539:POTAPI>2.0.CO;2. |
Liu, Y. G., L. G. You, W. N. Yang, and F. Liu, 1995: On the size distribution of cloud droplets. Atmospheric Research, 35, 201−216, https://doi.org/10.1016/0169-8095(94)00019-A. |
Liu, Y. G., P. H. Daum, and J. Hallett, 2002: A generalized systems theory for the effect of varying fluctuations on cloud droplet size distributions. J. Atmos. Sci., 59, 2279−2290, https://doi.org/10.1175/1520-0469(2002)059<2279:AGSTFT>2.0.CO;2. |
Liu, Y. G., P. H. Daum, and R. McGraw, 2004: An analytical expression for predicting the critical radius in the autoconversion parameterization. Geophys. Res. Lett., 31, L06121, https://doi.org/10.1029/2003GL019117. |
Liu, Y. G., P. H. Daum, and R. L. McGraw, 2005: Size truncation effect, threshold behavior, and a new type of autoconversion parameterization. Geophys. Res. Lett., 32, L11811, https://doi.org/10.1029/2005GL022636. |
Liu, Y. G., P. H. Daum, R. McGraw, and M. Miller, 2006a: Generalized threshold function accounting for effect of relative dispersion on threshold behavior of autoconversion process. Geophys. Res. Lett., 33, L11804, https://doi.org/10.1029/2005GL025500. |
Liu, Y. G., P. H. Daum, R. McGraw, and R. Wood, 2006b: Parameterization of the autoconversion process. Part II: Generalization of Sundqvist-type parameterizations. J. Atmos. Sci., 63, 1103−1109, https://doi.org/10.1175/JAS3675.1. |
Liu, Y. G., P. H. Daum, and S. S. Yum, 2006c: Analytical expression for the relative dispersion of the cloud droplet size distribution. Geophys. Res. Lett., 33, L02810, https://doi.org/10.1029/2005GL024052. |
Liu, Y. G., P. H. Daum, R. L. McGraw, M. A. Miller, and S. J. Niu, 2007: Theoretical expression for the autoconversion rate of the cloud droplet number concentration. Geophys. Res. Lett., 34, L16821, https://doi.org/10.1029/2007GL030389. |
Liu, Y. G., P. H. Daum, H. Guo, and Y. R. Peng, 2008a: Dispersion bias, dispersion effect, and the aerosol-cloud conundrum. Environmental Research Letters, 3, 045021, https://doi.org/10.1088/1748-9326/3/4/045021. |
Liu, Y. G., B. Geerts, M. Miller, P. H. Daum, and M. McGraw, 2008b: Threshold radar reflectivity for drizzling clouds. Geophys. Res. Lett, 35, L03807, https://doi.org/10.1029/2007GL031201. |
Liu, Y., and W. L. Li, 2015: A method for solving relative dispersion of the cloud droplet spectra. Science China Earth Sciences, 58(6), 929−938, https://doi.org/10.1007/s11430-015-5059-9. |
Loftus, A. M., W. R. Cotton, and G. G. Carrió, 2014: A triple-moment hail bulk microphysics scheme. Part I: Description and initial evaluation. Atmospheric Research, 149, 35−57, https://doi.org/10.1016/j.atmosres.2014.05.013. |
Lohmann, U., J. Feichter, C. C. Chuang, and J. E. Penner, 1999: Prediction of the number of cloud droplets in the ECHAM GCM. J. Geophys. Res., 104, 9169−9198, https://doi.org/10.1029/1999JD900046. |
Lou, X. F., Z. J. Hu, Y. Q. Shi, P. Y. Wang, and X. J. Zhou, 2003: Numerical simulations of a heavy rainfall case in South China. Adv. Atmos. Sci., 20, 128−138, https://doi.org/10.1007/BF03342057. |
Long, A. B., 1974: Solutions to the droplet collection equation for polynomial kernels. J. Atmos. Sci., 31, 1040−1052, https://doi.org/10.1175/1520-0469(1974)031<1040:STTDCE>2.0.CO;2. |
Lu, C. S., Y. G. Liu, and S. J. Niu, 2011: Examination of turbulent entrainment-mixing mechanisms using a combined approach. J. Geophys. Res., 116, D20207, https://doi.org/10.1029/2011JD015944. |
Lu, C. S., Y. G. Liu, and S. J. Niu, 2013a: A method for distinguishing and linking turbulent entrainment mixing and collision-coalescence in stratocumulus clouds. Chinese Science Bulletin, 58, 545−551, https://doi.org/10.1007/s11434-012-5556-6. |
Lu, C. S., Y. G. Liu, S. J. Niu, S. Krueger, and T. Wagner, 2013b: Exploring parameterization for turbulent entrainment-mixing processes in clouds. J. Geophys. Res., 118, 185−194, https://doi.org/10.1029/2012JD018464. |
Lu, C.-S., Y.-G. Liu, and S.-J. Niu, 2014a: Entrainment-mixing parameterization in shallow cumuli and effects of secondary mixing events. Chinese Science Bulletin, 59, 896−903, https://doi.org/10.1007/s11434-013-0097-1. |
Lu, C. S., Y. G. Liu, S. J. Niu, and S. Endo, 2014b: Scale dependence of entrainment-mixing mechanisms in cumulus clouds. J. Geophys. Res., 119(24), 13 877−13 890, https://doi.org/10.1002/2014JD022265. |
Lu, M.-L., W. C. Conant, H. H. Jonsson, V. Varutbangkul, R. C. Flagan, and J. H. Seinfeld, 2007: The Marine Stratus/Stratocumulus Experiment (MASE): Aerosol-cloud relationships in marine stratocumulus. J. Geophys. Res., 112, D10209, https://doi.org/10.1029/2006JD007985. |
Luo, S., and Coauthors, 2020: Parameterizations of entrainment-mixing mechanisms and their effects on cloud droplet spectral width based on numerical simulations. J. Geophys. Res., 125, e2020JD032972, https://doi.org/10.1029/2020JD032972. |
Luo, S., C. S. Lu, Y. G. Liu, W. H. Gao, L. Zhu, X. Q. Xu, J. J. Li, and X. H. Guo, 2021: Consideration of initial cloud droplet size distribution shapes in quantifying different entrainment-mixing mechanisms. J. Geophys. Res., 126, e2020JD034455, https://doi.org/10.1029/2020JD034455. |
Ma, J. Z., Y. Chen, W. Wang, P. Yan, H. J. Liu, S. Y. Yang, Z. J. Hu, and J. Lelieveld, 2010: Strong air pollution causes widespread haze-clouds over China. J. Geophys. Res., 115, D18204, https://doi.org/10.1029/2009JD013065. |
Mandelbrot, B. B., 1983: The Fractal Geometry of Nature,.W. H. Freeman and Company, New York. |
Mansell, E. R., C. L. Ziegler, and E. C. Bruning, 2010: Simulated electrification of a small thunderstorm with two-moment bulk microphysics. J. Atmos. Sci., 67, 171−194, https://doi.org/10.1175/2009JAS2965.1. |
Manton, M. J., 1979: On the broadening of a droplet distribution by turbulence near cloud base. Quart. J. Roy. Meteor. Soc., 105, 899−914, https://doi.org/10.1002/qj.49710544613. |
Manton, M. J., and W. R. Cotton, 1977: Formulation of approximate equations for modeling moist deep convection on the mesoscale. Atmospheric Science Paper No. 266, Colorado State University, 62 pp. |
Marquis, J., and J. Y. Harrington, 2005: Radiative influences on drop and cloud condensation nuclei equilibrium in stratocumulus. J. Geophys. Res., 110, D10205, https://doi.org/10.1029/2004JD005401. |
Marshak, A., and Coauthors, 2021: Aerosol properties in cloudy environments from remote sensing observations: A review of the current state of knowledge. Bull. Amer. Meteor. Soc., 102, E2177−E2197, https://doi.org/10.1175/BAMS-D-20-0225.1. |
Martin, G. M., D. W. Johnson, and A. Spice, 1994: The measurement and parameterization of effective radius of droplets in warm stratocumulus clouds. J. Atmos., Sci., 51, 1823−1842, https://doi.org/10.1175/1520-0469(1994)051<1823:TMAPOE>2.0.CO;2. |
Martins, J. A., and M. A. F. S. Dias, 2009: The impact of smoke from forest fires on the spectral dispersion of cloud droplet size distributions in the Amazonian region. Environmental Research Letters, 4(1), 015002, https://doi.org/10.1088/1748-9326/4/1/015002. |
Mason, B. J., and R. Ramanadham, 1954: Modification of the size distribution of falling raindrops by coalescence. Quart. J. Roy. Meteor. Soc., 80, 388−394, https://doi.org/10.1002/qj.49708034508. |
McGraw, R., and Y. G. Liu, 2003: Kinetic potential and barrier crossings: A model for warm cloud drizzle formation. Physical Review Letters, 90(1), 018501, https://doi.org/10.1103/PhysRevLett.90.018501. |
McGraw, R., and Y. G. Liu, 2004: Analytic formulation and parametrization of the kinetic potential theory for drizzle formation. Physical Review E, 70, 031606, https://doi.org/10.1103/PhysRevE.70.031606. |
McGraw, R. and Y. G. Liu, 2006: Brownian drift-diffusion model for evolution of droplet size distributions in turbulent clouds. Geophys. Res. Lett., 33, L03802, https://doi.org/10.1029/2005GL023545. |
McGraw, R., S. Nemesure, and S. E. Schwartz, 1998: Properties and evolution of aerosols with size distributions having identical moments. Journal of Aerosol Science, 29, 761−772, https://doi.org/10.1016/S0021-8502(97)10029-5. |
Meehl, G. A., C. A. Senior, V. Eyring, G. Flato, J.-F. Lamarque, R. J. Stouffer, K. E. Taylor, and M. Schlund, 2020: Context for interpreting equilibrium climate sensitivity and transient climate response from the CMIP6 Earth system models. Science Advance, 6, eaba1981, https://doi.org/10.1126/sciadv.aba1981. |
Mellado, J. P., C. S. Bretherton, B. Stevens, and M. C. Wyant, 2018: DNS and LES for simulating stratocumulus: Better together. Journal of Advances in Modeling Earth Systems, 10, 1421−1438, https://doi.org/10.1029/2018MS001312. |
Meyers, M. P., R. L.Walko, J. Y. Harrington, and W. R. & Cotton, 1997: New RAMS cloud microphysics parameterization. Part II: The two-moment scheme. Atmospheric Research, 45, 3−39, https://doi.org/10.1016/s0169-8095(97)00018-5. |
Milbrandt, J. A., and M. K. Yau, 2005a: A multimoment bulk microphysics parameterization. Part I: Analysis of the role of the spectral shape parameter. J. Atmos. Sci., 62(9), 3051−3064, https://doi.org/10.1175/jas3534.1. |
Milbrandt, J. A., and M. K. Yau, 2005b: A multimoment bulk microphysics parameterization. Part II: A proposed three-moment closure and scheme description. J. Atmos. Sci., 62(9), 3065−3081, https://doi.org/10.1175/jas3535.1. |
Milbrandt, J. A., and R. McTaggart-Cowan, 2010: Sedimentation-induced errors in bulk microphysics schemes. J. Atmos. Sci., 67(12), 3931−3948, https://doi.org/10.1175/2010jas3541.1. |
Milbrandt, J. A., and H. Morrison, 2016: Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part III: Introduction of multiple free categories. J. Atmos. Sci., 73(3), 975−995, https://doi.org/10.1175/jas-d-15-0204.1. |
Ming, Y., and Coauthors, 2007: Modeling the interactions between aerosols and liquid water clouds with a self-consistent cloud scheme in a general circulation model. Journal of the Atmospheric Sciences, 64, 1189−1209, https://doi.org/10.1175/jas3874.1. |
Mitchell, D. L., S. Mishra, and R. P. Lawson, 2011: Representing the ice fall speed in climate models: Results from Tropical Composition, Cloud and Climate Coupling (TC4) and the Indirect and Semi-Direct Aerosol Campaign (ISDAC). J. Geophys. Res., 116, D00T03, https://doi.org/10.1029/2010JD015433. |
Morrison, H., and A. Gettelman, 2008: A new two-moment bulk stratiform cloud microphysics scheme in the community atmosphere model, version 3 (CAM3). Part I: Description and Numerical Tests. J. Climate, 21(15), 3642−3659, https://doi.org/10.1175/2008JCLI2105.1. |
Morrison, H., and W. W. Grabowski, 2007: Comparison of bulk and bin warm rain microphysics models using a kinematic framework. Journal of the Atmospheric Sciences, 64, 2839−2861, https://doi.org/10.1175/jas3980. |
Morrison, H., and W. W. Grabowski, 2008: Modeling supersaturation and subgrid-scale mixing with two-moment bulk warm microphysics. J. Atmos. Sci., 65(3), 792−812, https://doi.org/10.1175/2007jas2374.1. |
Morrison, H., and J. A. Milbrandt, 2015: Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part I: Scheme description and idealized tests. J. Atmos. Sci., 72(1), 287−311, https://doi.org/10.1175/jas-d-14-0065.1. |
Morrison, H., J. A. Curry, and V. I. Khvorostyanov, 2005: A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description. J. Atmos. Sci., 62(6), 1665−1677, https://doi.org/10.1175/jas3446.1. |
Morrison, H., M. Witte, G. H. Bryan, J. Y. Harrington, and Z. J. Lebo, 2018: Broadening of modeled cloud droplet spectra using bin microphysics in an Eulerian spatial domain. J. Atmos. Sci., 75, 4005−4030, https://doi.org/10.1175/JAS-D-18-0055.1. |
Morrison, H., and Coauthors, 2020: Confronting the challenge of modeling cloud and precipitation microphysics. Journal of Advances in Modeling Earth Systems, 12, e2019MS001689, https://doi.org/10.1029/2019MS001689. |
Murakami, M., 1990: Numerical modeling of dynamical and microphysical evolution of an isolated convective cloud−The 19 July 1981 CCOPE Cloud. Journal of the Meteorological Society of Japan Ser. II, 68(2), 107−128, https://doi.org/10.2151/jmsj1965.68.2_107. |
Naumann, A. K., and A. Seifert, 2016: Evolution of the shape of the raindrop size distribution in simulated shallow cumulus. J. Atmos. Sci., 73(6), 2279−2297, https://doi.org/10.1175/jas-d-15-0263.1. |
Niederreiter, H., 1978: Quasi-Monte Carlo methods and pseudo-random numbers. Bulletin of the American Mathematical Society, 84(6), 957−1041, https://doi.org/10.1090/S0002-9904-1978-14532-7. |
Niu, S. J., C. S. Lu, Y. G. Liu, L. J. Zhao, J. J. Lv, and J. Yang, 2010: Analysis of the microphysical structure of heavy fog using a droplet spectrometer: A case study. Adv. Atmos. Sci., 27, 1259−1275, https://doi.org/10.1007/s00376-010-8192-6. |
Noh, Y., D. Oh, F. Hoffmann, and S. Raasch, 2018: A cloud microphysics parameterization for shallow cumulus clouds based on Lagrangian cloud model simulations. J. Atmos. Sci., 75, 4031−4047, https://doi.org/10.1175/JAS-D-18-0080.1. |
Onishi, R., and A. Seifert, 2016: Reynolds-number dependence of turbulence enhancement on collision growth. Atmospheric Chemistry and Physics, 16, 12 441−12 455, https://doi.org/10.5194/acp-16-12441-2016. |
Onishi, R., K. Takahashi, and J. C. Vassilicos, 2013: An efficient parallel simulation of interacting inertial particles in homogeneous isotropic turbulence. J. Comput. Phys., 242, 809−827, https://doi.org/10.1016/j.jcp.2013.02.027. |
Ormel, C. W., and M. Spaans, 2008: Monte Carlo simulation of particle interactions at high dynamic range: Advancing beyond the Googol. The Astrophysical Journal, 684, 1291−1309, https://doi.org/10.1086/590052. |
O’Rourke, P. J., 1981: Collective drop effects on vaporizing liquid sprays. PhD dissertation, Princeton University. |
Pandithurai, G., S. Dipu, T. V. Prabha, R. S. Maheskumar, J. R. Kulkarni, and B. N. Goswami, 2012: Aerosol effect on droplet spectral dispersion in warm continental cumuli. J. Geophys. Res., 117, D16202, https://doi.org/10.1029/2011JD016532. |
Paoli, R., J. Hélie, and T. Poinsot, 2004: Contrail formation in aircraft wakes. J. Fluid Mech., 502, 361−373, https://doi.org/10.1017/S0022112003007808. |
Paukert, M., J. Fan, P. J. Rasch, H. Morrison, J. A. Milbrandt, J. Shpund, and A. Khain, 2019: Three-moment representation of rain in a bulk microphysics model. Journal of Advances in Modeling Earth Systems, 11, 257−277, https://doi.org/10.1029/2018MS001512. |
Pawlowska, H., W. W. Grabowski, and J.-L. Brenguier, 2006: Observations of the width of cloud droplet spectra in stratocumulus. Geophys. Res. Lett., 33, L19810, https://doi.org/10.1029/2006GL026841. |
Peng, Y. R., and U. Lohmann, 2003: Sensitivity study of the spectral dispersion of the cloud droplet size distribution on the indirect aerosol effect. Geophys. Res. Lett., 30(10), 1507, https://doi.org/10.1029/2003GL017192. |
Peng, Y. R., U. Lohmann, R. Leaitch, and M. Kulmala, 2007: An investigation into the aerosol dispersion effect through the activation process in marine stratus clouds. J. Geophys. Res., 112, D11117, https://doi.org/10.1029/2006JD007401. |
Phillips, V. T. J., L. J. Donner, and S. T. Garner, 2007: Nucleation process in deep convection simulated by a cloud-system-resolving model with double-moment bulk microphysics. J. Atmos. Sci., 64, 738−761, https://doi.org/10.1175/JAS3869.1. |
Pinsky, M., A. Khain, and H. Krugliak, 2008: Collisions of cloud droplets in a turbulent flow. Part V: Application of detailed tables of turbulent collision rate enhancement to simulation of droplet spectra evolution. J. Atmos. Sci., 65, 357−374, https://doi.org/10.1175/2007JAS2358.1. |
Pinsky, M., A. Khain, and A. Korolev, 2016a: Theoretical analysis of mixing in liquid clouds–Part 3: Inhomogeneous mixing. Atmospheric Chemistry and Physics, 16, 9273−9297, https://doi.org/10.5194/acp-16-9273-2016. |
Pinsky, M., A. Khain, A. Korolev, and L. Magaritz-Ronen, 2016b: Theoretical investigation of mixing in warm clouds–Part 2: Homogeneous mixing. Atmospheric Chemistry and Physics, 16(14), 9255−9272, https://doi.org/10.5194/acp-16-9255-2016. |
Pinsky, M. B., A. P. Khain, and M. Shapiro, 2007: Collisions of cloud droplets in a turbulent flow. Part IV: Droplet hydrodynamic interaction. J. Atmos. Sci., 64, 2462−2482, https://doi.org/10.1175/JAS3952.1. |
Prabha, T. V., and Coauthors, 2012: Spectral width of premonsoon and monsoon clouds over Indo-Gangetic valley. J. Geophys. Res., 117, D20205, https://doi.org/10.1029/2011JD016837. |
Pruppacher, H. R., and J. D., Klett, 1997: Microphysics of clouds and precipitation. 2nd ed., Kluwer Academic Publishers, Dordrecht, The Netherlands, 954 pp. |
Przybylo, V. M., K. J. Sulia, C. G. Schmitt, Z. J. Lebo, and W. C. May, 2019: The Ice Particle and Aggregate Simulator (IPAS). Part I: Extracting dimensional properties of ice–ice aggregates for microphysical parameterization. J. Atmos. Sci., 76, 1661−1676, https://doi.org/10.1175/JAS-D-18-0187.1. |
Przybylo, V. M., K. J. Sulia, Z. J. Lebo, and C. G. Schmitt, 2022a: The Ice Particle and Aggregate Simulator (IPAS). Part II: Analysis of a database of theoretical aggregates for microphysical parameterization. J. Atmos. Sci., 79, 1633−1649, https://doi.org/10.1175/JAS-D-21-0179.1. |
Przybylo, V. M., K. J. Sulia, Z. J. Lebo, and C. G. Schmitt, 2022b: The Ice Particle and Aggregate Simulator (IPAS). Part III: Verification and analysis of ice–aggregate and aggregate–aggregate collection for microphysical parameterization. J. Atmos. Sci., 79, 1651−1667, https://doi.org/10.1175/JAS-D-21-0180.1. |
Raga, G. B., J. B. Jensen, and M. B. Baker, 1990: Characteristics of cumulus band clouds off the coast of Hawaii. J. Atmos. Sci., 47, 338−356, https://doi.org/10.1175/1520-0469(1990)047<0338:COCBCO>2.0.CO;2. |
Rasch, P. J., and J. E. Kristjánsson, 1998: A comparison of the CCM3 model climate using diagnosed and predicted condensate parameterizations. J. Climate, 11, 1587−1614, https://doi.org/10.1175/1520-0442(1998)011<1587:ACOTCM>2.0.CO;2. |
Reisner, J., R. M Rasmussen, and R. T. Bruintjes, 1998: Explicit forecasting of supercooled liquid water in winter storms using the MM mesoscale model. Quarterly Journal of the Royal Meteorological Society, 124, 1071−1107, https://doi.org/10.1002/qj.49712454804. |
Riechelmann, T., Y. Noh, and S. Raasch, 2012: A new method for large-eddy simulations of clouds with Lagrangian droplets including the effects of turbulent collision. New Journal of Physics, 14, 065008, https://doi.org/10.1088/1367-2630/14/6/065008. |
Rogers, R. R., and M. K. Yau, 1989: A Short Course in Cloud Physics. 3rd ed., Butterworth-Heinemann, 290 pp. |
Rosa, B., H. Parishani, O. Ayala, W. W. Grabowski, and L.-P. Wang, 2013: Kinematic and dynamic collision statistics of cloud droplets from high-resolution simulations. New Journal of Physics, 15, 045032, https://doi.org/10.1088/1367-2630/15/4/045032. |
Rothenberg, D., A. Avramov, and C. Wang, 2018: On the representation of aerosol activation and its influence on model-derived estimates of the aerosol indirect effect. Atmos. Chem. Phys., 18, 7961−7983, https://doi.org/10.5194/acp-18-7961-2018. |
Rotstayn, L. D., 1999: Indirect forcing by anthropogenic aerosols: A global climate model calculation of the effective-radius and cloud-lifetime effects. J. Geophys. Res., 104, 9369−9380, https://doi.org/10.1029/1998JD900009. |
Rotstayn, L. D., and Y. G. Liu, 2003: Sensitivity of the first indirect aerosol effect to an increase of cloud droplet spectral dispersion with droplet number concentration. J. Climate, 16, 3476−3481, https://doi.org/10.1175/1520-0442(2003)016<3476:SOTFIA>2.0.CO;2. |
Rotstayn, L. D., and Y. G. Liu, 2005: A smaller global estimate of the second indirect aerosol effect. Geophys. Res. Lett., 32, L05708−1-4. |
Rotstayn, L. D., and Y. G. Liu, 2009: Cloud droplet spectral dispersion and the indirect aerosol effect: Comparison of two treatments in a GCM. Geophys. Res. Lett., 36, L10801, https://doi.org/10.1029/2009GL038216. |
Rutledge, S. A., and P. V. Hobbs, 1984: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. XII: A diagnostic modeling study of precipitation development in narrow cold-frontal rainbands. Journal of the Atmospheri Sciences, 41, 2949−2972, https://doi.org/10.1175/1520-0469(1984)041<2949:TMAMSA>2.0.CO;2. |
Saffman, P. G., and J. S. Turner, 1956: On the collision of drops in turbulent clouds. J. Fluid Mech., 1, 16−30, https://doi.org/10.1017/S0022112056000020. |
Saleeby, S. M., S. R. Herbener, S. C. Van Den Heever, and T. L’Ecuyer, 2015: Impacts of cloud droplet–nucleating aerosols on shallow tropical convection. J. Atmos. Sci., 72(4), 1369−1385, https://doi.org/10.1175/jas-d-14-0153.1. |
Sardina, G., F. Picano, L. Brandt, and R. Caballero, 2015: Continuous growth of droplet size variance due to condensation in turbulent clouds. Physical Review Letters, 115, 184501, https://doi.org/10.1103/PhysRevLett.115.184501. |
Schmidt, D. P., and C. J. Rutland, 2000: A new droplet collision algorithm. J. Comput. Phys., 164, 62−80, https://doi.org/10.1006/jcph.2000.6568. |
Schmitt, C. G., and A. J. Heymsfield, 2010: The dimensional characteristics of ice crystal aggregates from fractal geometry. J. Atmos. Sci., 67, 1605−1616, https://doi.org/10.1175/2009JAS3187.1. |
Schmitt, C. G., K. Sulia, Z. J. Lebo, A. J. Heymsfield, and V. Przybyo, 2019: The fall speed variability of similarly sized ice particle aggregates. J. Appl. Meteorol. Climatol., 58, 1751−1761, https://doi.org/10.1175/JAMC-D-18-0291.1. |
Schneider, T., S. W. Lan, A. Stuart, and J. Teixeira, 2017: Earth system modeling 2.0: A blueprint for models that learn from observations and targeted high-resolution simulations. Geophys. Res. Lett., 44, 12 396−12 417, https://doi.org/10.1002/2017GL076101. |
Schwenkel, J., F. Hoffmann, and S. Raasch, 2018: Improving collisional growth in Lagrangian cloud models: Development and verification of a new splitting algorithm. Geoscientific Model Development, 11, 3929−3944, https://doi.org/10.5194/gmd-11-3929-2018. |
Sedunov, Y. S., 1974: Physics of Drop Formation in the Atmosphere. Wiley & Sons, 234 pp. |
Seifert, A., 2008: On the parameterization of evaporation of raindrops as simulated by a one-dimensional rainshaft model. J. Atmos. Sci., 65(11), 3608−3619, https://doi.org/10.1175/2008jas2586.1. |
Seifert, A., and K. D. Beheng, 2001: A double-moment parameterization for simulating autoconversion, accretion and selfcollection. Atmospheric Research, 59−60, 265−281, https://doi.org/10.1016/s0169-8095(01)00126-0. |
Seifert, A., and K. D. Beheng, 2006: A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description. Meteorol. Atmos. Phys., 92(1−2), 45−66, https://doi.org/10.1007/s00703-005-0112-4. |
Seifert, A., and S. Rasp, 2020: Potential and limitations of machine learning for modeling warm-rain cloud microphysical processes. Journal of Advances in Modeling Earth Systems, 12(12), e2020MS002301, https://doi.org/10.1029/2020MS002301. |
Seifert, A., J. Leinonen, C. Siewert, and S. Kneifel, 2019: The geometry of rimed aggregate snowflakes: A modeling study. Journal of Advances in Modeling Earth Systems, 11, 712−731, https://doi.org/10.1029/2018MS001519. |
Shan, Y. P., and Co-authors, 2020: Evaluating errors in gamma-function representations of the raindrop size distribution: A method for determining the optimal parameter set for use in bulk microphysics schemes. J. Atmos. Sci., 67, 513−529, https://doi.org/10.1175/JAS-D-18-0259.1. |
Shaw, R. A., 2003: Particle-turbulence interactions in atmospheric clouds. Annual Review of Fluid Mechanics, 35, 183−227, https://doi.org/10.1146/annurev.fluid.35.101101.161125. |
Shima, S., 2008: Estimation of the computational cost of super-droplet method. RIMS Kokyuroku, 1606, 110−118. |
Shima, S., K. Kusano, A. Kawano, T. Sugiyama, and S. Kawahara, 2009: The super-droplet method for the numerical simulation of clouds and precipitation: A particle-based and probabilistic microphysics model coupled with a non-hydrostatic model. Quart. J. Roy. Meteor. Soc., 135, 1307−1320, https://doi.org/10.1002/qj.441. |
Shima, S. I., Y. Sato, A. Hashimoto, and R. Misumi, 2020: Predicting the morphology of ice particles in deep convection using the super-droplet method: Development and evaluation of SCALE-SDM 0.2.5-2.2.0, -2.2.1, and -2.2.2. Geoscientific Model Development, 13, 4107−4157, https://doi.org/10.5194/gmd-13-4107-2020. |
Shipway, B. J., and A. A. Hill, 2012: Diagnosis of systematic differences between multiple parametrizations of warm rain microphysics using a kinematic framework. Quart. J. Roy. Meteor. Soc., 138(669), 2196−2211, https://doi.org/10.1002/qj.1913. |
Shirgaonkar, A., and S. Lele, 2006: Large eddy simulation of early stage contrails: Effect of atmospheric properties. Preprints, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, AIAA, 1−13, https://doi.org/10.2514/6.2006-1414. |
Slingo, A., 1989: A GCM parameterization for the shortwave radiative properties of water clouds. J. Atmos. Sci., 46, 1419−1427, https://doi.org/10.1175/1520-0469(1989)046<1419:AGPFTS>2.0.CO;2. |
Smoluchowski, M. V., 1916: Drei vorträge über diffusion, brownsche bewegung und koagulation von kolloidteilchen. Physik. Zeit., 17, 557−585. |
Sölch, I., and B. Kärcher, 2010: A large-eddy model for cirrus clouds with explicit aerosol and ice microphysics and Lagrangian ice particle tracking. Quart. J. Roy. Meteor. Soc., 136, 2074−2093, https://doi.org/10.1002/qj.689. |
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, https://doi.org/10.1175/1520-0469(1989)046<0869:GOCDBC>2.0.CO;2. |
Stensrud, D. J., 2007: Parameterization schemes: Keys to understanding numerical weather prediction models. Cambridge University Press. |
Stephens, G. L., 1978: Radiation profiles in extended water clouds, II, Parameterization schemes. J. Atmos. Sci .. 35. 2123−2132. |
Straka, J. M., 2009: Cloud and Precipitation Microphysics: Principles and Parameterizations. Cambridge University Press, https://doi.org/10.1017/CBO9780511581168. |
Straka, J. M., and E. M. Mansell, 2005: A bulk microphysics parameterization with multiple ice precipitation categories. J. Atmos. Sci., 44, 445−466. |
Su, C.-W., S. K. Krueger, P. A. McMurtry, and P. H. Austin, 1998: Linear eddy modeling of droplet spectral evolution during entrainment and mixing in cumulus clouds. Atmospheric research, 47, 41−58, https://doi.org/10.1016/S0169-8095(98)00039-8. |
Sulia, K. J., H. Morrison, and J. Y. Harrington, 2014: Dynamical and microphysical evolution during mixed-phase cloud glaciation simulated using the bulk adaptive habit prediction model. Journal of the Atmospheric Sciences, 71, 4158−4180, https://doi.org/10.1175/jas-d14-0070.1. |
Sundqvist, H., 1978: A parameterization scheme for nonconvective condensation including prediction of cloud water content. Quart. J. Roy. Meteor. Soc., 104, 677−690, https://doi.org/10.1002/qj.49710444110. |
Szyrmer, W., S. Laroche, and I. Zawadzki, 2005: A microphysical bulk formulation based on scaling normalization of the particle size distribution. Part I: Description. J. Atmos. Sci., 62(12), 4206−4221, https://doi.org/10.1175/jas3620.1. |
Telford, J. W., 1955: A new aspect of coalescence theory. J. Atmos. Sci., 12, 436−444, https://doi.org/10.1175/1520-0469(1955)012<0436:ANAOCT>2.0.CO;2. |
Telford, J. W., 1996: Clouds with turbulence; the role of entrainment. Atmospheric Research, 40, 261−282, https://doi.org/10.1016/0169-8095(95)00038-0. |
Thompson, G., and T. Eidhammer, 2014: A study of aerosol impacts on clouds and precipitation development in a large winter cyclone. J. Atmospheric Atmos. Sci., 71, 3636−3658, https://doi.org/10.1175/JAS-D-13-0305.1. |
Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 5095−5115, https://doi.org/10.1175/2008MWR2387.1. |
Twomey, S., 1977: The influence of pollution on the shortwave albedo of clouds. J. Atmos. Sci., 34, 1149−1152, https://doi.org/10.1175/1520-0469(1977)034<1149:TIOPOT>2.0.CO;2. |
Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distribution. J. Appl. Meteorol. Climatol., 22(10), 1764−1775, https://doi.org/10.1175/1520-0450(1983)022<1764:nvitaf>2.0.co;2. |
Unterstrasser, S., and I. Sölch, 2014: Optimisation of the simulation particle number in a Lagrangian ice microphysical model. Geoscientific Model Development, 7, 695−709, https://doi.org/10.5194/gmd-7-695-2014. |
Unterstrasser, S., F. Hoffmann, and M. Lerch, 2017: Collection/aggregation algorithms in Lagrangian cloud microphysical models: Rigorous evaluation in box model simulations. Geoscientific Model Development, 10, 1521−1548, https://doi.org/10.5194/gmd-10-1521-2017. |
Unterstrasser, S., F. Hoffmann, and M. Lerch, 2020: Collisional growth in a particle-based cloud microphysical model: Insights from column model simulations using LCM1D (v1.0). Geoscientific Model Development, 13, 5119−5145, https://doi.org/10.5194/gmd-13-5119-2020. |
Vaillancourt, P. A., and M. K. Yau, 2000: Review of particle-turbulence interactions and consequences for cloud physics. Bull. Amer. Meteor. Soc., 81, 285−298, https://doi.org/10.1175/1520-0477(2000)081<0285:ROPIAC>2.3.CO;2. |
Vaillancourt, P. A., M. K. Yau, and W. W. Grabowski, 2001: Microscopic approach to cloud droplet growth by condensation. Part I: Model description and results without turbulence. J. Atmos. Sci., 58, 1945−1964, https://doi.org/10.1175/1520-0469(2001)058<1945:MATCDG>2.0.CO;2. |
Vaillancourt, P. A., M. K. Yau, P. Bartello, and W. W. Grabowski, 2002: Microscopic approach to cloud droplet growth by condensation. Part II: Turbulence, clustering, and condensational growth. J. Atmos. Sci., 59, 3421−3435, https://doi.org/10.1175/1520-0469(2002)059<3421:MATCDG>2.0.CO;2. |
Verlinde, J., P. J. Flatau, and W. R. Cotton, 1990: Analytical solutions to the collection growth equation: Comparison with approximate methods and application to cloud micro-physics parameterization schemes. J. Atmos. Sci., 47, 2871−2880, https://doi.org/10.1175/1520-0469(1990)047<2871:ASTTCG>2.0.CO;2. |
Wacker, U., and C. Lupkes, 2009: On the selection of prognostic moments in parametrization schemes for drop sedimentation. Tellus, 61A, 498−511, https://doi.org/10.1111/j.1600-0870.2009.00405.x. |
Wacker, U., and A. Seifert, 2001: Evolution of rain water profiles resulting from pure sedimentation: Spectral vs. parameterized description. Atmospheric Research, 58(1), 19−39, https://doi.org/10.1016/s0169-8095(01)00081-3. |
Walko, R. L., W. R. Cotton, M. P. Meyers, and J. Y. Harrington, 1995: New RAMS cloud microphysics parameterization. Part I: The singlemoment scheme. Atmos. Res., 38, 29−62, https://doi.org/10.1016/0169-8095(94)00087-T. |
Wang, J., P. H. Daum, S. Yum, Y. Liu, G. Senum, M. Lu, J. Seinfeld, and H. Jonsson, 2009: Observations of marine stratocumulus microphysics and implications for processes controlling droplet spectra: results from the Marine Stratus/Stratocumulus Experiment (MASE). J. Geophys. Res. Atmos, 114, D18210, https://doi.org/10.1029/2008JD011035. |
Wang, L.-P., A. S. Wexler, and Y. Zhou, 1998: Statistical mechanical descriptions of turbulent coagulation. Physics of Fluids, 10, 2647−2651, https://doi.org/10.1063/1.869777. |
Wang, L.-P., O. Ayala, S. E. Kasprzak, and W. W. Grabowski, 2005: Theoretical formulation of collision rate and collision efficiency of hydrodynamically interacting cloud droplets in turbulent atmosphere. J. Atmos. Sci., 62, 2433−2450, https://doi.org/10.1175/JAS3492.1. |
Wang, L.-P., O. Ayala, B. Rosa, and W. W. Grabowski, 2008: Turbulent collision efficiency of heavy particles relevant to cloud droplets. New Journal of Physics, 10, 075013, https://doi.org/10.1088/1367-2630/10/7/075013. |
Wang, M. Q., Y. R. Peng, Y. G. Liu, Y. N. Liu, X. N. Xie, and Z. Y. Guo, 2020: Understanding cloud droplet spectral dispersion effect using empirical and semi-analytical parameterizations in NCAR CAM5.3. Earth and Space Science, 7, e2020EA001276, https://doi.org/10.1029/2020EA001276. |
Wang, Y., J. W. Fan, R. Y. Zhang, L. R. Leung, and C. Franklin, 2013: Improving bulk microphysics parameterizations in simulations of aerosol effects. J. Geophys. Res., 118, 5361−5379, https://doi.org/10.1002/jgrd.50432. |
Wang, Y., and Coauthors, 2018: Aerosol microphysical and radiative effects on continental cloud ensembles. Adv. Atmos. Sci., 35, 234−247, https://doi.org/10.1007/s00376-017-7091-5. |
Warner, J., 1969: The microstructure of cumulus cloud. Part I. General features of the droplet spectrum. J. Atmos. SCi., 26(5), 1049−1059, https://doi.org/10.1175/1520-0469(1969)026<1049:TMOCCP>2.0.CO;2. |
Warner, J., 1973: The microstructure of cumulus cloud: Part IV: The effect on the droplet spectrum of mixing between cloud and environment. J. Atmos. Sci., 30(2), 256−261, https://doi.org/10.1175/1520-0469(1973)030<0256:TMOCCP>2.0.CO;2. |
Weinstein, L. A., J. Loomis, B. Bhatia, D. M. Bierman, E. N. Wang, and G. Chen, 2015: Concentrating solar power. Chemical Reviews, 115, 12 797−12 838, https://doi.org/10.1021/acs.chemrev.5b00397. |
White, W. H., 1990: Particle size distributions that cannot be distinguished by their integral moments. Journal of Colloid and Interface Science, 135, 297−299, https://doi.org/10.1016/0021-9797(90)90312-C. |
Williams, M. M. R., 1986: Some topics in nuclear aerosol dynamics. Progress in Nuclear Energy, 17(1), 1−52, https://doi.org/10.1016/0149-1970(86)90041-7. |
Wisner, C., H. D. Orville, and C. Myers, 1972: A numerical model of a hail-bearing cloud. J. Atmos. Sci., 29(6), 1160−1181, https://doi.org/10.1175/1520-0469(1972)029<1160:ANMOAH>2.0.CO;2. |
Wood, R., S. Irons, and P. Jonas, 2002: How important is the spectral ripening effect in stratiform boundary layer clouds? Studies using simple trajectory analysis J. Atmos. Sci., 59, 2681−2693, https://doi.org/10.1175/1520-0469(2002)059<2681:HIITSR>2.0.CO;2. |
Wu, W., and G. M. McFarquhar, 2018: Statistical theory on the functional form of cloud particle size distributions. J. Atmos. Sci., 75(8), 2801−2814, https://doi.org/10.1175/JAS-D-17-0164.1. |
Xie, X. N., and X. D. Liu, 2011: Effects of spectral dispersion on clouds and precipitation in mesoscale convective systems. J. Geophys. Res., 116, D06202, https://doi.org/10.1029/2010JD014598. |
Xie, X.N., and X. D. Liu, 2015: Aerosol-cloud-precipitation interactions in WRF model: Sensitivity to autoconversion parameterization. J. Meteor. Res., 29(1), 72−81, https://doi.org/10.1007/s13351-014-4065-8. |
Xie, X. N., X. D. Liu, Y. R. Peng, Y. Wang, Z. G. Yue, and X. Z. Li, 2013: Numerical simulation of clouds and precipitation depending on different relationships between aerosol and cloud droplet spectral dispersion. Tellus B: Chemical and Physical Meteorology, 65, 19054, https://doi.org/10.3402/tellusb.v65i0.19054. |
Xie, X. N., H. Zhang, X. D. Liu, Y. R. Peng, and Y. G. Liu, 2017: Sensitivity study of cloud parameterizations with relative dispersion in CAM5.1: Impacts on aerosol indirect effects. Atmospheric Chemistry and Physics, 17, 5877−5892, https://doi.org/10.5194/acp-17-5877-2017. |
Xie, X. N., H. Zhang, X. D. Liu, Y. R. Peng, and Y. G. Liu, 2018: Role of microphysical parameterizations with droplet relative dispersion in IAP AGCM 4.1. Adv. Atmos. Sci., 35(2), 248−259, https://doi.org/10.1007/s00376-017-7083-5. |
Xie, Y., M. Sengupta, Y. G. Liu, H. Long, Q. Min, W. J. Liu, and A. Habte, 2020: A physics-based DNI model assessing all-sky circumsolar radiation. iScience, 23, 100893, https://doi.org/10.1016/j.isci.2020.100893. |
Xu, H. B., and Y. Duan, 2002: The accumulation of hydrometeor and depletion of cloud water in strongly convective cloud (hailstorm). Acta Meteorologica Sinica, 60(5), 575−584, https://doi.org/10.3321/j.issn:0577-6619.2002.05.008. (in Chinese with English abstract |
Xu, X. Q., C. S. Lu, Y. G. Liu, S. Luo, X. Zhou, S. Endo, L. Zhu, and Y. Wang, 2022: Influences of an entrainment-mixing parameterization on numerical simulations of cumulus and stratocumulus clouds. Atmospheric Chemistry and Physics, 22, 5459−5475, https://doi.org/10.5194/acp-22-5459-2022. |
Yano, J.-I., A. J. Heymsfield, and V. T. J. Phillips, 2016: Size distributions of hydrometeors: Analysis with the maximum entropy principle. J. Atmos. Sci., 73, 95−108, https://doi.org/10.1175/JAS-D-15-0097.1. |
Yeom, J. M., S. S. Yum, Y. G. Liu, and C. S. Lu, 2017: A study on the entrainment and mixing process in the continental stratocumulus clouds measured during the RACORO campaign. Atmospheric Research, 194, 89−99, https://doi.org/10.1016/j.atmosres.2017.04.028. |
Yu, R. C., Y. Zhang, J. J. Wang, J. Li, H. M. Chen, J. D. Gong, and J. Chen, 2019: Recent progress in numerical atmospheric modeling in China. Adv. Atmos. Sci., 36(9), 938−960, https://doi.org/10.1007/s00376-019-8203-1. |
Yum, S. S., and J. G. Hudson, 2005: Adiabatic predictions and observations of cloud droplet spectral broadness. Atmospheric Research, 73(3-4), 203−223, https://doi.org/10.1016/j.atmosres.2004.10.006. |
Yum, S., J. Wang, Y. Liu, G. Senum, and S. Sprinston., 2015: Cloud microphysical relationships and their implication on entrainment and mixing mechanism for the stratocumulus clouds measured during the VOCALS project. J. Geophys. Res. Atmos., 120, 5047−5069, https://doi.org/10.1002/2014JD022802. |
Zeng, X. P., A. J. Heymsfield, Z. Ulanowski, R. R. Neely III, X. W. Li, J. Gong, and D. L. Wu, 2022: The radiative effect on cloud microphysics from the arctic to the tropics. Bull. Amer. Meteor. Soc., 103, E2108−E2129, https://doi.org/10.1175/BAMS-D-21-0039.1. |
Zhang, G., J. Vivekanandan, and E. Brandes, 2001: A method for estimating rain rate and drop size distribution from polarimetric radar measurements. IEEE Trans. Geosci. Remote Sens., 39(4), 830−841, https://doi.org/10.1109/36.917906. |
Zhang, G. J., and X. L. Song, 2016: Parameterization of microphysical processes in convective clouds in global climate models. Meteor. Monogr., 56, 12.1−12.18, https://doi.org/10.1175/AMSMONOGRAPHS-D-15-0015.1. |
Zhang, K., X. Liu, M. Wang, J. M. Comstock, D. L. Mitchell, S. Mishra, and G. G. Mace, 2013: Evaluating and constraining ice cloud parameterizations in CAM5 using aircraft measurements from the SPARTICUS campaign. Atmos. Chem. Phys., 13, 4963−4982, https://doi.org/10.5194/acp-13-4963-2013. |
Zhang, X. W., and G. G. Zheng, 1994: A simple droplet spectrum derived from entropy theory. Atmospheric Research, 32, 189−193, https://doi.org/10.1016/0169-8095(94)90059-0. |
Zhao, X., Y. L. Lin, Y. R. Peng, B. Wang, H. Morrison, and A. Gettelman, 2017: A single ice approach using varying ice particle properties in global climate model microphysics. Journal of Advances in Modeling Earth Systems, 9, 2138−2157, https://doi.org/10.1002/2017MS000952. |
Zhao, X., Y. L. Lin, Y. L. Luo, Q. Qian, X. H. Liu, and B. A. Colle, 2021: A double-moment SBU-YLIN cloud microphysics scheme and its impact on a squall line simulation. Journal of Advances in Modeling Earth Systems, 13, e2021MS002545, https://doi.org/10.1029/2021MS002545. |
Zhou, X. J., 1963: Acta Meteorologica Sinica, 33, 97−107 (in Chinese). |
Zhou, Y., A. S. Wexler, and L.-P. Wang, 2001: Modelling turbulent collision of bidisperse inertial particles. J. Fluid Mech., 433, 77−104, https://doi.org/10.1017/S0022112000003372. |