Andsager, K., Beard, K. V., and Laird, N. F. (1999). Laboratory measurements of axis ratios for large raindrops. J. Atmos. Sci., 56, 2673–2683.
Asai, T. (1965). A numerical study of the air-mass transformation over the Japan sea in winter. J. Meteorol. Soc. Jpn., 43, 1–15.
Asai, T. and Kasahara, A. (1967). A theoretical study of the compensating downward motions associated with cumulus clouds. J. Atmos. Sci., 24, 487–496.
Auer, A. H. (1972). Inferences about ice nucleation from ice crystal observations. J. Atmos. Sci., 29, 311–317.
Aydin, K. and Seliga, T. (1984). Radar polarimetric backscattering properties of conical graupel. J. Atmos. Sci., 41, 1887–1892.
Bailey, M. and Hallett, J. (2004). Growth rates and habits of ice crystals between −20° and −70 °C. J. Atmos. Sci., 61, 514–544.
Bannon, P. R. (2002). Theoretical foundations for models of moist convection. J. Atmos. Sci., 59, 1967–1982.
Barge, B. L. and Isaac, G. A. (1973). The shape of Alberta hailstones. J. Rech. Atmos., 7, 11–20.
Bayewitz, M., Yerushalmi, H. J., Katz, S., and Shinnar, R. (1974). The extent of correlations in a stochastic coalescence process. J. Atmos. Sci., 31, 1604–1614.
Beard, K. (1976). Terminal velocity and shape of cloud and precipitation drops aloft. J. Atmos. Sci., 33, 851–864.
Beard, K. V. and Chuang, C. (1987). A new mode for the equilibrium shape of rain drops. J. Atmos. Sci., 44, 1509–1524.
Beard, K. V. and Ochs, H. T. (1984). Measured collection and coalescence efficiencies for accretion. J. Geophys. Res., 89, 7165–7169.
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, 698–710.
Beheng, K. D. (1981). Stochastic riming of plate like and columnar ice crystals. Pure Appl. Geophys., 119, 820–830.
Beheng, K. D. (1994). A parameterization of warm cloud microphysical conversion processes. Atmos. Res., 33, 193–206.
Beheng, K. D. and Doms, G. (1986). A general formulation of collection rates of cloud and raindrops using the kinetic equation and comparison with parameterizations. Contrib. Atmos. Phys., 59, 66–84.
Berry, E. X. (1967). Cloud droplet growth by collection. J. Atmos. Sci., 24, 688–701.
Berry, E. X. (1968a). Comments on “Cloud droplet coalescence: Statistical foundations and a one-dimensional sedimentation model.” J. Atmos. Sci., 25, 151–152.
Berry, E. X. (1968b). Modification of the warm rain process. Conference Proceedings, 1st National Conference on Weather Modification, Albany, NY, April 28–May 1, pp. 81–88.
Berry, E. X. and Reinhardt, R. L. (1974a). An analysis of cloud drop growth by collection: Part I. Double distributions. J. Atmos. Sci., 31, 1814–1824.
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.
Berry, E. X. and Reinhardt, R. L. (1974c). An analysis of cloud drop growth by collection: Part III. Accretion and self-collection. J. Atmos. Sci., 31, 2118–2126.
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.
Bigg, E. K. (1953). The supercooling of water. Proc. Phys. Soc. London, B66, 688–694.
Blanchard, D. C. (1950). The behavior of water drops at terminal velocity in air. Trans. Am. Geophys. Union, 31, 836–842.
Bleck, R. (1970). A fast approximative method for integrating the stochastic coalescence equation. J. Geophys. Res., 75, 5165–5171.
Boren, C. F. and Albrecht, B. A. (1998). Atmospheric Thermodynamics. Oxford: Oxford University Press.
Bott, A. (1998). A flux method for the numerical solution of the stochastic collection equation. J. Atmos. Sci., 55, 2284–2293.
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.
Braham, R. and Squires, P. (1974). Cloud physics 1974. Bull. Am. Meteor. Soc., 55, 543–586.
Bringi, V. N., Seliga, T. A., and Cooper, W. A. (1984). Analysis of aircraft hydrometeor spectra and differential reflectivity (ZDR) radar measurements during the Cooperative Convective Precipitation Experiment. Radio Sci., 19, 157–167.
Bringi, V. N., Chandrasekar, V., and Rongrui, X. (1998). Raindrop axis ratios and size distributions in Florida rainshafts: An assessment of multiparameter radar algorithms. IEEE Trans. Geosci. Remote Sens., 36, 703–715.
Brown, P. S. (1983). Some essential details for application of Bleck's method to the collision-break-up equation. J. Appl. Meteorol., 22, 693–697.
Brown, P. S. (1985). An implicit scheme for the efficient solution of the coalesence/collision-break-up equation. J. Comput. Phys., 58, 417–431.
Brown, P. S. (1986). Analysis of the Low and List drop-breakup formulation. J. Appl. Meteorol., 25, 313–321.
Brown, P. S. (1987). Parameterization of drop-spectrum evolution due to coalescence and breakup. J. Atmos. Sci., 44, 242–249.
Brown, P. S. (1988). The effects of filament, sheet, and disk breakup upon the drop spectrum. J. Atmos. Sci., 45, 712–718.
Brown, P. S. (1990). Reversals in evolving raindrop size distributions due to the effects of coalescence and breakup. J. Atmos. Sci., 47, 746–754.
Brown, P. S. (1991). Parameterization of the evolving drop-size distribution based on analytic solution of the linearized coalescence-breakup equation. J. Atmos. Sci., 48, 200–210.
Brown, P. S. (1993). Analysis and parameterization of the combined coalescence, breakup, and evaporation processes. J. Atmos. Sci., 50, 2940–2951.
Brown, P. S. (1997). Mass conservation considerations in analytic representation of raindrop fragment distributions. J. Atmos. Sci., 54, 1675–1687.
Brown, P. S. (1999). Analysis of model-produced raindrop size distributions in the small-drop range. J. Atmos. Sci., 56, 1382–1390.
Brown, P. S. and Whittlesey, S. N. (1992). Multiple equilibrium solutions in Bleck-type models of drop coalescence and breakup. J. Atmos. Sci., 49, 2319–2324.
Bryan, G. H. and Fritsch, J. M. (2002). A benchmark simulation for moist nonhydrostatic numerical models. Mon. Weather Rev., 130, 2917–2928.
Bryan, G. H. and Fritsch, J. M. (2004). A reevaluation of ice–liquid water potential temperature. Mon. Weather Rev., 132, 2421–2431.
Byers, H. R. (1965). Elements of Cloud Physics. Chicago, IL: The University of Chicago Press.
Carrió, G. G. and Nicolini, M. (1999). A double moment warm rain scheme: Description and test within a kinematic framework. Atmos. Res., 52, 1–16.
Chandrasekar, V., Cooper, W. A., and Bringi, V. N. (1988). Axis ratios and oscillations of raindrops. J. Atmos. Sci., 45, 1323–1333.
Chaumerliac, N., Richard, E., Rosset, R., and Nickerson, E. C. (1991). Impact of two microphysical schemes upon gas scavenging and deposition in a mesoscale meteorological model. J. Appl. Meteorol., 30, 88–97.
Chen, J. P. (1994). Predictions of saturation ratio for cloud microphysical models. J. Atmos. Sci., 51, 1332–1338.
Cheng, L. and English, M. (1983). A relationship between hailstone concentration and size. J. Atmos. Sci., 40, 204–213.
Cheng, L., English, M., and Wong, R. (1985). Hailstone size distributions and their relationship to storm thermodynamics. J. Appl. Meteorol., 24, 1059–1067.
Chong, S. L. and Chen, C. (1974). Water shells on ice pellets and hailstones. J. Atmos. Sci., 31, 1384–1391.
Clark, T. L. (1973). Numerical modeling of the dynamics and microphysics of warm cumulus convection. J. Atmos. Sci., 30, 857–878.
Clark, T. L. (1976). Use of log-normal distributions for numerical calculations of condensation and collection. J. Atmos. Sci., 33, 810–821.
Clark, T. L. (1977). A small-scale dynamical model using a terrain-following coordinate transformation. J. Comput. Phys., 24, 186–215.
Clark, T. L. (1979). Numerical simulations with a three-dimensional cloud model: Lateral boundary condition experiments and multicellular severe storm simulations. J. Atmos. Sci., 36, 2191–2215.
Clark, T. L. and Hall, W. (1979). A numerical experiment on stochastic condensation theory. J. Atmos. Sci., 36, 470–483.
Cober, S. G. and List, R. (1993). Measurements of the heat and mass transfer parameters characterizing conical graupel growth. J. Atmos. Sci., 50, 1591–1609.
Cohard, J.-M. and Pinty, J. P. (2000). A comprehensive two-moment warm microphysical bulk model scheme: I: Description and tests. Q. J. Roy. Meteor. Soc., 126, 1815–1842.
Cohard, J.-M., Pinty, J. P., and Suhre, K. (1998). On the parameterization of activation spectra from cloud condensation nuclei microphysical properties. J. Geophys. Res., 105, 11753–11766.
Cohard, J.-M., Pinty, J. P., and Bedos, C. (2000). Extending Twomey's analytical estimate of nucleated cloud droplet concentrations from CCN spectra. J. Atmos. Sci., 55, 3348–3357.
Cooper, W. A., Bruintjes, R. T., and Mather, G. K. (1997). Calculations pertaining to hygroscopic seeding with flares. J. Appl. Meteorol., 36, 1449–1469.
Cotton, W. R. (1972a). Numerical simulation of precipitation development in supercooled cumuli – Part I. Mon. Weather Rev., 100, 757–763.
Cotton, W. R. (1972b). Numerical simulation of precipitation development in supercooled cumuli – Part II. Mon. Weather Rev., 100, 764–784.
Cotton, W. R. and Anthes, R. A. (1989). Storm and Cloud Dynamics. San Diego, CA: Academic Press.
Cotton, W. R. and Tripoli, G. J. (1978). Cumulus convection in shear flow – three-dimensional numerical experiments. J. Atmos. Sci., 35, 1503–1521.
Cotton, W. R., Stephens, M. A., Nehrkorn, T., and Tripoli, G. J. (1982). The Colorado State University three-dimensional cloud model – 1982. Part II: An ice phase parameterization. J. Rech. Atmos., 16, 295–320.
Cotton, W. R., Tripoli, G. J., Rauber, R. M., and Mulvihill, E. A. (1986). Numerical simulation of the effects of varying ice crystal nucleation rates and aggregation processes on orographic snowfall. J. Climate Appl. Meteor., 25, 1658–1680.
Cotton, W. R. and coauthors (2003) RAMS (2001). Current status and future directions. Meteor. Atmos. Phys., 82, 5–29.
Curic, M. and Janc, D. (1997). On the sensitivity of hail accretion rates in numerical modeling. Tellus, 49A, 100–107.
Danielsen, E., Bleck, R., and Morris, D. (1972). Hail growth by stochastic collection in a cumulus model. J. Atmos. Sci., 29, 135–155.
Deardorff, J. W. (1980). Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound.-Layer Meteorol., 18, 495–527.
DeMott, P. J., Meyers, M. P., and Cotton, W. R. (1994). Parameterization and impact of ice initiation processes relevant to numerical model simulations of cirrus clouds. J. Atmos. Sci., 51, 77–90.
Dennis, A. and Musil, D. (1973). Calculations of hailstone growth and trajectories in a simple cloud model. J. Atmos. Sci., 30, 278–288.
Doms, G. and Beheng, K. D. (1986). Mathematical formulation of self collection, auto conversion, and accretion rates of cloud and raindrops. Meteorol. Rundsch., 39, 98–102.
Drake, J. C. and Mason, B. J. (1966). The melting of small ice spheres and cones. Q. J. Roy. Meteorol. Soc., 92, 500–509.
Dye, J. E., Knight, C. A., Toutenhootd, V., and Cannon, T. W. (1974). The Mechanism of precipitation formation in northeastern Colorado cumulus, III. Coordinated microphysical and radar observations and summary. J. Atmos. Sci., 29, 278–288.
English, M. (1973). Alberta hailstorms. Part II: Growth of large hail in the storm. Meteorol. Monogr., 36, 37–98.
Farley, R. D. (1987). Numerical modeling of hailstorms and hailstone growth. Part II: The role of low-density riming growth in hail production. J. Appl. Meteorol., 26, 234–254.
Farley, R. D. and Orville, H. (1986). Numerical modeling of hailstorms and hailstone growth. Part I: Preliminary model verification and sensitivity tests. J. Appl. Meteorol., 25, 2014–2035.
Farley, R. D., Price, P. E., Orville, H. D., and Hirsch, J. H. (1989). On the numerical simulation of graupel/hail initiation via the riming of snow in bulk water microphysical cloud models. J. Appl. Meteorol., 28, 1128–1131.
Feingold, G., Tzivion, (Tzitzvashvili), S., and Levin, Z. (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.
Feingold, G., Walko, R. L., Stevens, B., and Cotton, W. R. (1998). Simulations of marine stratocumulus using a new microphysics parameterization scheme. Atmos. Res., 47–48, 505–528.
Feng, J. Q. and Beard, K. V. (1991). A perturbation model of raindrop oscillation characteristics with aerodynamic effects. J. Atmos. Sci., 48, 1856–1868.
Flatau, P. J., Tripoli, G. J., Verlinde, J., and Cotton, W. R. (1989). The CSU-RAMS cloud microphysical module: General theory and documentation. Technical Report 451. (Available from the Department of Atmospheric Sciences, Colorado State University, Ft. Collins, CO 80523.)
Fletcher, N. H. (1962). The Physics of Rain Clouds. Cambridge: Cambridge University Press.
Foote, G. B. (1984). A study of hail growth utilizing observed storm conditions. J. Appl. Meteorol., 23, 84–101.
Gaudet, B. J. and Schmidt, J. M. (2005). Assessment of hydrometeor collection rates from exact and approximate equations. Part I: A new approximate scheme. J. Atmos. Sci., 62, 143–159.
Gaudet, B. J. and Schmidt, J. M. (2007). Assessment of hydrometeor collection rates from exact and approximate equations. Part II: Numerical bounding. J. Appl. Meteorol. Climatol., 46, 82–96.
Gillespie, D. T. (1972). The stochastic coalescence model for cloud droplet growth. J. Atmos. Sci., 29, 1496–1510.
Gillespie, D. T. (1975). Three models for the coalescence growth of cloud drops. J. Atmos. Sci., 32, 600–607.
Gilmore, M. S. and Straka, J. M. (2008). The Berry and Reinhardt autoconversion parameterization: A digest. J. Appl. Meteorol. Climatol., 47, 375–396.
Gilmore, M. S., Straka, J. M., and Rasmussen, E. N. (2004). Precipitation uncertainty due to variations in precipitation particle parameters within a simple microphysics scheme. Mon. Weather Rev., 132, 2610–2627.
Glickman, T. S. (2000). The Glossary of Meteorology, 2nd edn. Boston, MA: American Meteorological Society.
Goddard, J. W. F. and Cherry, S. M. (1984). The ability of dual-polarization radar measurements in rain (copolar linear) to predict rainfall and microwave attenuation. Radio Sci., 19, 201–208.
Goddard, J. W. F., Cherry, S. M., and Bringi, V. N. (1982). Comparison of dual-polarization radar measurements of rain with groundbased disdrometer measurements. J. Appl. Meteorol., 21, 252–256.
Golovin, A. M. (1963). The solution of the coagulation equation for cloud droplets in a rising air current. Isv. Ak. Nk. SSSR (Geophys. Ser.), 5, 783–791.
Greenan, B. J. and List, R. (1995). Experimental closure of the heat and mass transfer theory of spheroidal hailstones. J. Atmos. Sci., 52, 3797–3815.
Gunn, K. L. S. and Marshall, J. S. (1958). The distribution with size of aggregate snowflakes. J. Atmos. Sci., 15, 452–461.
Gunn, R. and Kinzer, G. D. (1949). The terminal velocity of fall for raindrops in stagnant air. J. Meteor., 6, 243–248.
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.
Hall, W. D. and Pruppacher, H. (1976). The survival of ice particles falling from cirrus clouds in subsaturated air. J. Atmos. Sci., 33, 1995–2006.
Hallet, J. and Mossop, S. C. (1974). Production of secondary ice particles during the riming process. Nature, 249, 26–28.
Hallgren, R. E. and Hosler, C. L. (1960). Preliminary results on the aggregation of ice crystals. Geophys. Monogr., Am. Geophys. Union, 5, 257–263.
Heymsfield, A. J. (1972). Ice crystal terminal velocities. J. Atmos. Sci., 29, 1348–1357.
Heymsfield, A. J. (1978). The characteristics of graupel particles in northeastern Colorado cumulus congestus clouds. J. Atmos. Sci., 35, 284–295.
Heymsfield, A. J. and Kajikawa, M. (1987). An improved approach to calculating terminal velocities of plate-like crystals and graupel. J. Atmos. Sci., 44, 1088–1099.
Heymsfield, A. J. and Pflaum, J. C. (1985). A quantitative assessment of the accuracy of techniques for calculating graupel growth. J. Atmos. Sci., 42, 2264–2274.
Heymsfield, A. J., Jameson, A. R., and Frank, H. W. (1980). Hail growth mechanisms in a Colorado storm: Part II: Hail formation processes. J. Atmos. Sci., 37, 1779–1807.
Hitchfield, W. and Stauder, M. (1967). The temperature of hailstones. J. Atmos. Sci., 24, 293–297.
Hobbs, P. V. (1974). Ice Physics. London: Oxford University Press.
Hosler, C. L. and Hallgren, R. E. (1961). Ice crystal aggregation. Nublia, 4, No. 1, 13–19.
Hu, Z. and Srivastava, R. (1995). Evolution of raindrop size distribution by coalescence, breakup, and evaporation: Theory and observations. J. Atmos. Sci., 52, 1761–1783.
Hubbert, J. V., Bringi, V. N., and Carey, L. D. (1998). CSU-CHILL polarimetric radar measurements from a severe hail storm in Eastern Colorado. J. Appl. Meteorol., 37, 749–775.
Huffman, P. J. and Vali, G. (1973). The effect of vapor depletion on ice nucleus measurements with membrane filters. J. Appl. Meteor., 12, 1018–1024.
Jameson, A. R. and Beard, K. V. (1982). Raindrop axial ratios. J. Appl. Meteorol., 21, 257–259.
Johnson, D. B. and Rasmussen, R. M. (1992). Hail growth hysteresis. J. Atmos. Sci., 49, 2525–2532.
Jones, D. M. (1959). The shape of raindrops. J. Atmos. Sci., 16, 504–510.
Joss, J. and Zawadzki, I. (1997). Raindrop distributions again? Preprints, 28th Conference On Radar Meteorology, Austin, TX, 7–12 September, pp. 326–327.
Kajikawa, M. and Heymsfield, A. J. (1989). Aggregation of ice crystals in cirrus. J. Atmos. Sci., 46, 3108–3121.
Kessler, E. (1969). On the distribution and continuity of water substance in atmospheric circulations. Meteorol. Monogr., No. 32.
Khain, A. P., Ovtchinnikov, M., Pinski, M., Pokrovsky, A., and Krugiliak, H. (2000). Notes on the state-of-the-art numerical modeling of cloud microphysics. Atmos. Res., 55, 159–224.
Khairoutdinov, M. F. and Kogan, Y. L. (1999). A large eddy simulation model with explicit microphysics: Validation against aircraft observations of a stratocumulus-topped boundary layer. J. Atmos. Sci., 56, 2115–2131.
Khairoutdinov, M. and Kogan, Y. (2000). A new cloud physics parameterization in a large-eddy simulation model of marine stratocumulus. Mon. Weather Rev., 128, 229–243.
Kinzer, G. D. and Gunn, R. (1951). The evaporation, temperature, and thermal relaxation-time of free falling waterdrops. J. Meteorol., 8, 71–83.
Klemp, J. B. and Wilhelmson, R. B. (1978). The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 1070–1096.
Knight, C. A. (1979). Observations of the morphology of melting snow. J. Atmos. Sci., 36, 1123–1130.
Knight, C. A. and Knight, N. C. (1970). Hailstone embryos. J. Atmos. Sci., 27, 659–666.
Knight, C. A. and Knight, N. C. (1973). Conical graupel. J. Atmos. Sci., 30, 118–124.
Knight, C. A. and Knight, N. C. (2001). Hailstorms. In Severe Convective Storms, ed. Doswell, C. A., AMS Monograph 50, ch. 6, pp. 223–254.
Knight, C. A. and Miller, L. (1993). First radar echoes from cumulus clouds. Bull. Am. Meteorol. Soc., 74, 179–188.
Knight, N. C. (1981). The climatology of hailstone embryos. J. Appl. Meteorol., 20, 750–755.
Knight, N. C. (1986). Hailstone shape factor and its relation to Radar interpretation of hail. J. Appl. Meteorol., 25, 1956–1958.
Koenig, R. and Murray, F. W. (1976). Ice-bearing cumulus evolution: Numerical simulations and general comparison against observations. J. Appl. Meteorol., 15, 742–762.
Kogan, Y. L. (1991). The simulation of a convective cloud in a 3-D model with explicit microphysics. Part I: Model description and sensitivity experiments. J. Atmos. Sci., 48, 1160–1189.
Kogan, Y. L. and Martin, W. J. (1994). Parameterization of bulk condensation in numerical cloud models. J. Atmos. Sci., 51, 1728–1739.
Komabayasi, M., Gonda, T., and Isono, K. (1964). Lifetime of water drops before breaking and size distribution of fragments. J. Meteorol. Soc. Jpn., 42, 330–340.
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.
Kry, P. R. and List, R. (1974). Angular motions of freely falling spheroidal hailstone models. Phys. Fluids, 17, 1093–1102.
Kubesh, R. J. and Beard, K. V. (1993). Laboratory measurements of spontaneous oscillations for moderate-sized raindrops. J. Atmos. Sci., 50, 1089–1098.
Kumjian, M. R. and Ryzhko, A. V. (2008). Polarimetric signatures in supercell thunderstorms. J. Appl. Meteorol. Climatol., 47, 1940–1961.
Langlois, W. E. (1973). A rapidly convergent procedure for computing large-scale condensation in a dynamical weather model. Tellus, 25, 86–87.
Laws, J. O. and Parsons, D. A. (1943). The relation of raindrop-size to intensity. Trans Am. Geophys. Union, 24, Part II, 452–460.
Lesins, G. and List, R. (1986). Sponginess and drop shedding of gyrating hailstones in a pressure-controlled icing wind tunnel. J. Atmos. Sci., 43, 2813–2825.
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.
List, R. (1986). Properties and growth of hailstones. Thunderstorm Dynamics and Morphology, ed. Kessler, E.. Norman, OK: University of Oklahoma Press, pp. 259–276.
List, R. and Gillespie, J. (1976). Evolution of raindrop spectra with collision-induced breakup. J. Atmos. Sci., 33, 2007–2013.
List, R. and Schemenauer, R. S. (1971). Free-fall behavior of planar snow crystals, conical graupel and small hail. J. Atmos. Sci., 28, 110–115.
List, R., Rentsch, U. W., Byram, A. C., and Lozowski, E. P. (1973). On the aerodynamics of spheroidal hailstone models. J. Atmos. Sci., 30, 653–661.
Liu, J. and Orville, H. (1969). Numerical modeling of precipitation and cloud shadow effects on mountain-induced cumuli. J. Atmos. Sci., 26, 1283–1298.
Liu, Y. and Daum, P. H. (2004). Parameterization of the autoconversion process. Part I: Analytical formulation of the Kessler-type parameterizations. J. Atmos. Sci., 61, 1539–1548.
Locatelli, J. D. and Hobbs, P. V. (1974). Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79, 2185–2197.
Loney, M. L., Zrnic, D. S., Straka, J. M., and Ryzhkov, A. V. (2002). Enhanced polarimetric radar signatures above the melting level in a supercell storm. J. Appl. Meteorol., 41, 1179–1194.
Long, A. B. (1974). Solutions to the droplet collection equation for polynomial kernels. J. Atmos. Sci., 31, 1040–1052.
Low, R. D. (1969). A generalized equation for the solution effect in droplet growth. J. Atmos. Sci., 26, 608–611.
Low, T. 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.
Low, T. and List, R. (1982b). Collision, coalescence and breakup of raindrops. Part II: Parameterization of fragment size distributions in breakup. J. Atmos. Sci., 39, 1607–1618.
Ludlam, F. H. (1958). The hail problem. Nubila, 1, 12–96.
Macklin, W. C. (1963). Heat transfer from hailstones. Quart. J. Roy. Meteorol. Soc., 89, 360–369.
Macklin, W. C. and Bailey, I. H. (1962). The density and structure of ice formed by accretion. Q. J. Roy. Meteorol. Soc., 88, 30–50.
Macklin, W. C. and Bailey, I. H. (1966). On the critical liquid water concentrations of large hailstones. Quart. J. Roy. Meteorol. Soc., 92, 297–300.
Magono, C. and Lee, C. W. (1966). Meteorological classification of natural snow crystals. J. Fac. Sci., Hokkaido Univ., Ser. VII, 2, 321–335.
Mansell, E. R., MacGorman, D. R., Ziegler, C. L., and Straka, J. M. (2002). Simulated three-dimensional branched lightning in a numerical thunderstorm model. J. Geophys. Res., 107 (9), doi: 10.1029/2000JD000244.
Mansell, E. R., MacGorman, D. R., Ziegler, C. L., and Straka, J. M. (2005). Charge structure and lightning sensitivity in a simulated multicell thunderstorm. J. Geophys. Res., 110, D12101, doi: 10.1029/2004JD005287.
Manton, M. J. and Cotton, W. R. (1977). Formulation of approximate equations for modeling moist convection on the mesoscale. Technical Report, Colorado State University, Fort Collins, CD.
Marshall, J. S. and Palmer, W. M. K. (1948). The distribution of raindrops with size. J. Meteorol., 5, 165–166.
Mason, B. J. (1957). The Physics of Clouds. Oxford: Clarendon Press.
Mason, B. J. (1971). The Physics of Clouds, 2nd edn. Oxford: Clarendon Press.
Matson, R. J. and Huggins, A. W. (1980). The direct measurement of the sizes, shapes, and kinematics of falling hailstones. J. Atmos. Sci., 37, 1107–1125.
McDonald, J. (1963). The saturation adjustment in numerical modelling of fog. J. Atmos. Sci., 20, 476–478.
McFarguhar, G. M. (2004). A new representation of breakup of raindrops and its implications for shapes of raindrop size distributions. J. Atmos. Sci., 61, 777–792.
McTaggart-Cowan, J. and List, R. (1975). Collision and breakup of water drops at terminal velocity. J. Atmos. Sci., 32, 1401–1411.
Meyers, M. P., DeMott, P. J., and Cotton, W. R. (1992). New primary ice-nucleation parameterizations in an explicit cloud model. J. Appl. Meteorol., 31, 708–721.
Meyers, M. P., Walko, R. L., Harrington, J. Y., and Cotton, W. R. (1997). New RAMS cloud microphysics parameterization. Part II. The two-moment scheme. Atmos. Res., 45, 3–39.
Milbrandt, J. A. and Yau, M. K. (2005a). A multimoment bulk microphysics parameterization. Part I: Analysis of the role of the spectral shape parameter. J. Atmos. Sci., 62, 3051–3064.
Milbrandt, J. A. and Yau, M. K. (2005b). A multimoment bulk microphysics parameterization. Part II: A proposed three-moment closure and scheme description. J. Atmos. Sci., 62, 3065–3081.
Mitra, S. K., Vohl, O., Ahr, M., and Pruppacher, H. R. (1990). A wind tunnel and theoretical study of the melting behavior of atmospheric ice particles. IV: Experiment and theory for snow flakes. J. Atmos. Sci., 47, 584–591.
Mizuno, H. (1990). Parameterization of the accretion process between different precipitation elements. J. Meteorol. Soc. Jpn., 68, 395–398.
Morrison, H. and Grabowski, W. W. (2007). Comparison of bulk and bin warm rain microphysical models using a kinematic framework. J. Atmos. Sci., 64, 2839–2861.
Morrison, H. and Grabowski, W. W. (2008). A novel approach for representing ice microphysics in models: Description and tests using a kinematic framework. J. Atmos. Sci., 65, 1528–1548.
Moss, M. S. and Rosenthal, S. L. (1975). On the estimation of planetary boundary layer variables in mature hurricanes. Mon. Weather Rev., 103, 980–988.
Mossop, S. C. (1976). Production of secondary ice particles during the growth of graupel riming. Q. J. Roy. Meteorol. Soc., 102, 25–44.
Mossop, S. C. and Kidder, R. E. (1962). Artificial hailstones. Bull. Obs. Puy. De Dom, 2, 65–79.
Murakami, M. (1990). Numerical modeling of dynamical and microphysical evolution of an isolated convective cloud – the 19 July 1981 CCOPE cloud. J. Meteorol. Soc. Jpn., 68, 107–128.
Nelson, S. P. (1980). A Study of Hail Production in a Supercell Storm using Doppler Derived Wind Field and a Numerical Hail Growth Model. NOAA Technical Memorandum ERL NSSL-89. National Severe Storm Laboratory. (NTIS PB81-17822Q.)
Nelson, S. P. (1983). The influence of storm flow structure on hail growth. J. Atmos. Sci., 40, 1965–1983.
Nelson, S. P. (1987). The hybrid multicellular–supercellular storm – an efficient hail producer. Part II. General characteristics and implications for hail growth. J. Atmos. Sci., 44, 2060–2073.
Nickerson, E. C., Richard, E., Rosset, R., and Smith, D. R. (1986). The numerical simulation of clouds, rains and airflow over the Vosges and Black Forest mountains: A meso-β model with parameterized microphysics. Mon. Weather Rev., 114, 398–414.
Ogura, Y. and Takahashi, T. (1973). The development of warm rain in a cumulus model. J. Atmos. Sci., 30, 262–277.
Ohtake, T. (1970). Factors affecting the size distribution of raindrops and snowflakes. J. Atmos. Sci., 27, 804–813.
Orlanski, I. (1976). A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys., 21, 251–269.
Orville, H. and Kopp, F. J. (1977). Numerical simulation of the history of a hailstorm. J. Atmos. Sci., 34, 1596–1618.
Passarelli, R. E. (1978). An approximate analytical model of the vapor deposition and aggregation growth of snowflakes. J. Atmos. Sci., 35, 118–124.
Passarelli, R. E. and Srivastava, R. C. (1979). A new aspect of snowflake aggregation theory. J. Atmos. Sci., 36, 484–493.
Pellett, J. L. and Dennis, A. S. (1974). Effects of heat storage in hailstones. Conference Proceedings, Conference on Cloud Physics, Tucson, AZ, October 21–24, pp. 63–66.
Pflaum, J. C. (1980). Hail formation via microphysical recycling. J. Atmos. Sci., 37, 160–173.
Pflaum, J. C., and Pruppacher, H. (1979). A wind tunnel investigation of the growth of graupel initiated from frozen drops. J. Atmos. Sci., 36, 680–689.
Proctor, F. H. (1987). The Terminal Area Simulation System. Vol. I: Theoretical Formulation. NASA Contractor Report 4046, NASA, Washington, DC. [Available from the National Technical Information Service, Springfield, VA, 22161.]
Pruppacher, H. R. and Beard, K. V. (1970). A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air. Q. J. Roy. Meteorol. Soc., 96, 247–256.
Pruppacher, H. R. and Klett, J. D. (1981). Microphysics of Clouds and Precipitation. Dordrecht: D. Reidel Publishing.
Pruppacher, H. R. and Klett, J. D. (1997). Microphysics of Clouds and Precipitation, 2nd edn. Dordrecht: Kluwer Academic Publishers.
Pruppacher, H. R. and Pitter, R. L. (1971). A semi-empirical determination of the shape of cloud and rain drops. J. Atmos. Sci., 28, 86–94.
Rasmussen, R. M. and Heymsfield, A. J. (1985). A generalized form for impact velocities used to determine graupel accretional densities. J. Atmos. Sci., 42, 2275–2279.
Rasmussen, R. M. and Heymsfield, A. J. (1987a). Melting and shedding of graupel and hail. Part I: Model physics. J. Atmos. Sci., 44, 2754–2763.
Rasmussen, R. M. and Heymsfield, A. J. (1987b). Melting and shedding of graupel and hail. Part II: Sensitivity study. J. Atmos. Sci., 44, 2764–2782.
Rasmussen, R. and Pruppacher, H. R. (1982). A wind tunnel and theoretical study of the melting behavior of atmospheric ice particles. I: A wind tunnel study of frozen drops of radius < 500 μm. J. Atmos. Sci., 39, 152–158.
Rasmussen, R. M., Levizzani, V., and Pruppacher, H. R. (1984). A wind tunnel and theoretical study on the melting behavior of atmospheric ice particles: III. Experiment and theory for spherical ice particles of radius > 500 μm. J. Atmos. Sci., 41, 381–388.
Rauber, R. M., Beard, K. V., and Andrews, B. M. (1991). A mechanism for giant raindrop formation in warm, shallow convective clouds. J. Atmos. Sci., 48, 1791–1797.
Reinhardt, R. L. (1972). An analysis of improved numerical solution to the stochastic collection equation for cloud drops. Ph.D. Dissertation, University of Nevada.
Reisner, J., Rasmussen, R. M., and Bruintjes, R. T. (1998). Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Q. J. Roy. Meteorol. Soc., 124, 1071–1107.
Rogers, D. C. (1973). The aggragation of natural ice crystals. M. S. Thesis, Department of Atmospheric Resources, University of Wyoming.
Rogers, R. R. and Yau, M. K. (1989). A Short Course in Cloud Physics. Pergamon Press.
Rotunno, R. and Emanuel, K. A. (1987). An air–sea interaction theory for tropical cyclones. Part II: Evolutionary study using a nonhydrostatic axisymmetric numerical model. J. Atmos. Sci., 44, 542–561.
Rutledge, S. A. and Hobbs, P. V. (1983). The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. VIII: A model for the “seeder-feeder” process in warm-frontal rainbands. J. Atmos. Sci., 40, 1185–1206.
Rutledge, S. A. and Hobbs, P. V. (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. J. Atmos. Sci., 41, 2949–2972.
Saleeby, S. M. and Cotton, W. R. (2004). A large-droplet mode and prognostic number concentration of cloud droplets in the Colorado State University Regional Atmospheric Modeling System (RAMS). Part I: Module descriptions and supercell test simulations. J. Appl. Meteorol., 43, 182–195.
Saleeby, S. M. and Cotton, W. R. (2005). A large-droplet mode and prognostic number concentration of cloud droplets in the Colorado State University Regional Atmospheric Modeling System (RAMS). Part II: Sensitivity to a Colorado winter snowfall event. J. Appl. Meteorol., 44, 1912–1929.
Saleeby, S. M. and Cotton, W. R. (2008). A binned approach to cloud-droplet riming implemented in a bulk microphysics model. J. Appl. Meteorol. Climatol., 47, 694–703.
Sauvageot, H. and Lacaux, J. P. (1995). The shape of averaged drop size distributions. J. Atmos. Sci., 52, 1070–1083.
Schlamp, R. J., Pruppacher, H. R., and Hamielec, H. R. (1975). A numerical investigation of the efficiency with which simple columnar ice crystals collide with supercooled water drops. J. Atmos. Sci., 32, 2330–2337.
Schoenberg-Ferrier, B. (1994). A double-moment multiple-phase four-class bulk ice scheme. Part I: Description. J. Atmos. Sci., 51, 249–280.
Schumann, T. E. W. (1938). The theory of hailstone formation. Q. J. Roy. Meteorol. Soc., 64, 3–21.
Scott, W. T. (1968). Analytical studies of cloud droplet coalescence. J. Atmos. Sci., 25, 54–65.
Scott, W. T. and Levin, Z. (1975). A comparison of formulations of stochastic collection. J. Atmos. Sci., 32, 843–847.
Seifert, A. (2008). On the parameterization of evaporation of raindrops as simulated by a one dimensional model. J. Atmos. Sci., 28, 741–751.
Seifert, A. and Beheng, K. D. (2001). A double-moment parameterization for simulating autoconversion, accretion and self-collection. Atmos. Res., 59–60, 265–281.
Seifert, A. and Beheng, K. D. (2005). A two-moment cloud microphysical parameterization for mixed phase clouds. Part 1: Model description. Meteorol. Atmos. Phys., doi: 10.1007/s00703-005-0112-4.
Shafrir, U. and Gal-Chen, T. (1971). A numerical study of collision efficiencies and coalescence parameters for droplet pairs with radii up to 300 microns. J. Atmos. Sci., 28, 741–751.
Simpson, J. and Wiggert, V. (1969). Models of precipitating cumulus towers. Mon. Weather Rev., 97, 471–489.
Smagorinski, J. (1963). General circulation experiments with the primitive equations. I: The basic experiments. Mon. Weather Rev., 91, 99–164.
Soong, S. T. (1974). Numerical simulation of warm rain development in an axisymmetric cloud model. J. Atmos. Sci., 31, 1262–1285.
Soong, S. T. and Ogura, Y. (1973). A comparison between axisymmetric and slab-symmetric cumulus cloud models. J. Atmos. Sci., 30, 879–893.
Srivastava, R. C. (1971). Size distribution of raindrops generated by their breakup and coalescence. J. Atmos. Sci., 28, 410–415.
Srivastava, R. (1989) Growth of cloud drops by condensation: A criticism of currently accepted theory and a new approach. J. Atmos. Sci., 46, 869–887.
Srivastava, R. C. and Coen, J. L. (1992). New explicit equations for the accurate calculation of the growth and evaporation of hydrometeors by the diffusion of water vapor. J. Atmos. Sci., 49, 1643–1651.
Stensrud, D. J. (2007). Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models. Cambridge: Cambridge University Press.
Stevens, B., Walko, R. L., Cotton, W. R., and Feingold, G. (1996). The spurious production of cloud-edge supersaturations by Eulerian models. Mon. Weather Rev., 124, 1034–1041.
Stewart, R. E., Marwitz, J. D., Pace, J. C., and Carbone, R. E. (1984). Characteristics through the melting layer of stratiform clouds. J. Atmos. Sci., 41, 3227–3237.
Straka, J. M. and Mansell, E. R. (2005). A bulk microphysics parameterization with multiple ice precipitation categories. J. Appl. Meteorol., 44, 445–466.
Straka, J. M. and Rasmussen, E. N. (1997). Toward improving microphysical parameterizations of conversion processes. J. Appl. Meteorol., 36, 896–902.
Straka, J. M., Zrnic, D. S., and Ryzhkov, A. V. (2000). Bulk hydrometeor classification and quantification using polarimetric radar data: Synthesis of relations. J. Appl. Meteorol., 39, 1341–1372.
Straka, J. M., Kanak, K. M., and Gilmore, M. S. (2007). The behavior of number concentration tendencies for the continuous collection growth equation using one- and two-moment bulk parameterization schemes. J. Appl. Meteorol. Climatol., 46, 1264–1274.
Stull, R. B. (1988). An Introduction to Boundary Layer Meteorology. Dordrecht: Kluwer Academic Publishers.
Takahashi, T. (1976). Hail in an axisymmetric cloud model. J. Atmos. Sci., 33, 1579–1601.
Tao, W. K., Simpson, J., and McCumber, M. (1989). An ice-water saturation adjustment. Mon. Weather Rev., 117, 231–235.
Telford, J. W. (1955). A new aspect of coalescence theory. J. Atmos. Sci., 12, 436–444.
Thompson, G., Rasmussen, R. M., and Manning, K. (2004). Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part I: Description and sensitivity analysis. Mon. Weather Rev., 132, 519–542.
Tokay, A. and Beard, K. V. (1996). A field study of raindrop oscillations. Part I: Observation of size spectra and evaluation of oscillation causes. J. Appl. Meteorol., 35, 1671–1687.
Tripoli, G. J. and Cotton, W. R. (1980). A numerical investigation of several factors contributing to the observed variable intensity of deep convection over south Florida. J. Appl. Meteorol., 19, 1037–1063.
Tripoli, G. J. and Cotton, W. R. (1981). The use of ice-liquid water potential temperature as a thermodynamic variable in deep atmospheric models. Mon. Weather Rev., 109, 1094–1102.
Twomey, S. (1959). The nuclei of natural cloud formation. Part II: The supersaturation in natural clouds and the variation of cloud droplet concentration. Geophys. Pure Appl., 43, 243–249.
Twomey, S. (1964). Statistical effects in the evolution of a distribution of cloud droplets by coalescence. J. Atmos. Sci., 21, 553–557.
Twomey, S. (1966). Computation of rain formation by coalescence. J. Atmos. Sci., 23, 405–411.
Tzivion (Tzitzvashvili), S., Feingold, G., and Levin, Z. (1987). An efficient numerical solution to the stochastic collection equation. J. Atmos. Sci., 44, 3139–3149.
Tzivion (Tzitzvashvili), S., Feingold, G., and Levin, Z. (1989). The evolution of raindrop spectra. Part II: Collisional collection/breakup and evaporation in a rainshaft. J. Atmos. Sci., 46, 3312–3328.
Ulbrich, C. W. (1983). Natural variations in the analytical form of the raindrop size distribution. J. Climate Appl. Meteorol., 22, 1764–1775.
Ulbrich, C. W. and Atlas, D. (1982). Hail parameter relations: A comprehensive digest. J. Appl. Meteor., 21, 22–43.
Vali, G. (1975). Remarks, on the mechanism of atmospheric ice nucleation. Proceedings of the 8th International Conference, on Nucleation, Leningrad, 23–29 September, ed. I. I. Gaivoronski, pp. 265–299.
Vali, G. (1994). Freezing rate due to heterogeneous nucleation. J. Atmos. Sci., 51, 1843–1856.
Broeke, M. S., Straka, J. M., and Rasmussen, E. N. (2008). Polarimetric radar observations at low levels during tornado life cycles in a small sample of classic Southern Plains supercells. J. Appl. Meteorol. Climatol., 47, 1232–1247.
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. Weather Rev., 121, 2776–2793.
Verlinde, J., Flatau, P. J., and Cotton, W. R. (1990). Analytical solutions to the collection growth equation: Comparison with approximate methods and application to cloud microphysics parameterization schemes. J. Atmos. Sci., 47, 2871–2880.
Walko, R. L., Cotton, W. R., Meyers, M. P., and Harrington, J. Y. (1995). New RAMS cloud microphysics parameterization: Part I. The single-moment scheme. Atmos. Res., 38, 29–62.
Walko, R. L., Cotton, W. R., Feingold, G., and Stevens, B. (2000). Efficient computation of vapor and heat diffusion between hydrometeors in a numerical model. Atmos. Res., 53, 171–183.
Wang, P. K. (1985). A convection diffusion model for the scavenging of submicron snow crystals of arbitrary shapes. J. Rech. Atmos., 19, 185–191.
Wang, P. K. (2002). Ice Microdynamics. San Diego, CA: Academic Press.
Wang, P. K. and Ji, W. (1992). A numerical study of the diffusional growth and riming rates of ice crystals in clouds. Preprints volume, 11th International Cloud Physics Conference, August 11–17, Montreal, Canada.
Warshaw, M. (1967). Cloud droplet coalescence: Statistical foundations and a one-dimensional sedimentation model. J. Atmos. Sci., 24, 278–286.
Wilhelmson, R. and Ogura, Y. (1972). The pressure perturbation and the numerical modeling of a cloud. J. Atmos. Sci., 29, 1295–1307.
Wisner, C. E., Orville, H. D., and Myers, C. G. (1972). A numerical model of a hail bearing cloud. J. Atmos. Sci., 29, 1160–1181.
Young, K. C. (1974a). A numerical simulation of wintertime, orographic precipitation: Part I. Description of model microphysics and numerical techniques. J. Atmos. Sci., 31, 1735–1748.
Young, K. C. (1974b). A numerical simulation of wintertime, orographic precipitation: Part II. Comparison of natural and AgI-seeded conditions. J. Atmos. Sci., 31, 1749–1767.
Young, K. C. (1975). The evolution of drop spectra due to condensation, coalescence and breakup. J. Atmos. Sci., 32, 965–973.
Young, K. C. (1993). Microphysical Processes in Clouds. London: Oxford University Press.
Ziegler, C. L. (1985). Retrieval of thermal and microphysical variables in observed convective storms. Part I: Model development and preliminary testing. J. Atmos. Sci., 42, 1487–1509.
Ziegler, C. L., Ray, P. S., and Knight, N. C. (1983). Hail growth in an Oklahoma multicell storm. J. Atmos. Sci., 40, 1768–1791.
