References

[1]
E. Kessler. On the continuity and distribution of water substance in atmospheric circulations. Atmospheric research 38, 109–145 (1995).
[2]
W. W. Grabowski. Toward cloud resolving modeling of large-scale tropical circulations: A simple cloud microphysics parameterization. Journal of the Atmospheric Sciences 55, 3283–3298 (1998).
[3]
C. M. Kaul, J. Teixeira and K. Suzuki. Sensitivities in large-eddy simulations of mixed-phase Arctic stratocumulus clouds using a simple microphysics approach. Monthly Weather Review 143, 4393–4421 (2015).
[4]
J.-P. Chen, T.-W. Hsieh, C.-Y. Lin and C.-K. Yu. Accurate parameterization of precipitation particles' fall speeds for bulk cloud microphysics schemes. Atmospheric Research 293 (2022).
[5]
V. I. Khvorostyanov and J. A. Curry. Terminal velocities of droplets and crystals: Power laws with continuous parameters over the size spectrum. Journal of the atmospheric sciences 59, 1872–1884 (2002).
[6]
M. Karrer, A. Seifert, C. Siewert, D. Ori, A. von Lerber and S. Kneifel. Ice Particle Properties Inferred from Aggregation Modelling. Journal of Advances in Modeling Earth Systems -1, e2020MS002066 (2020).
[7]
J. S. Marshall and W. M. Palmer. The distribution of raindrops with size. Journal of meteorology 5, 165–166 (1948).
[8]
W. W. Grabowski and P. K. Smolarkiewicz. Two-time-level semi-Lagrangian modeling of precipitating clouds. Monthly weather review 124, 487–497 (1996).
[9]
J. Y. Harrington, M. P. Meyers, R. L. Walko and W. R. Cotton. Parameterization of ice crystal conversion processes due to vapor deposition for mesoscale models using double-moment basis functions. Part I: Basic formulation and parcel model results. Journal of the atmospheric sciences 52, 4344–4366 (1995).
[10]
S. A. Rutledge and P. Hobbs. 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. Journal of the Atmospheric Sciences 40, 1185–1206 (1983).
[11]
S. A. Rutledge and P. V. Hobbs. 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 Atmospheric Sciences 41, 2949–2972 (1984).
[12]
H. Morrison and A. Gettelman. A new two-moment bulk stratiform cloud microphysics scheme in the Community Atmosphere Model, version 3 (CAM3). Part I: Description and numerical tests. Journal of Climate 21, 3642–3659 (2008).
[13]
A. Seifert and K. D. Beheng. A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description. Meteorology and atmospheric physics 92, 45–66 (2006).
[14]
Y. Ogura and T. Takahashi. Numerical simulation of the life cycle of a thunderstorm cell. Mon. Wea. Rev 99, 895–911 (1971).
[15]
R. Wood. Drizzle in stratiform boundary layer clouds. Part II: Microphysical aspects. Journal of the atmospheric sciences 62, 3034–3050 (2005).
[16]
B. J. Mason. Physics of clouds (Clarendon Press, 2010).
[17]
L.-P. Wang, C. N. Franklin, O. Ayala and W. W. Grabowski. Probability distributions of angle of approach and relative velocity for colliding droplets in a turbulent flow. Journal of the atmospheric sciences 63, 881–900 (2006).
[18]
M. Khairoutdinov and Y. Kogan. A New Cloud Physics Parameterization in a Large-Eddy Simulation Model of Marine Stratocumulus. Monthly Weather Review 128, 229–243 (2000).
[19]
K. Beheng. A parameterization of warm cloud microphysical conversion processes. Atmospheric Research 33, 193–206 (1994).
[20]
G. Tripoli and W. Cotton. A Numerical Investigation of Several Factors Contributing to the Observed Variable Intensity of Deep Convection over South Florida. Journal of Applied Meteorology and Climatology 19, 1037–1063 (1980).
[21]
Y. Liu and P. Daum. Parameterization of the Autoconversion Process.Part I: Analytical Formulation of the Kessler-Type Parameterizations. Journal of the Atmospheric Sciences 61, 1539–1548 (2004).
[22]
H. Morrison and J. A. Milbrandt. Parameterization of Cloud Microphysics Based on the Prediction of Bulk Ice Particle Properties. Part I: Scheme Description and Idealized Tests. Journal of the Atmospheric Sciences 72, 287–311 (2015).
[23]
P. R. Brown and P. N. Francis. Improved Measurements of the Ice Water Content in Cirrus Using a Total-Water Probe. Journal of Atmospheric and Oceanic Technology 12, 410–414 (1995).
[24]
D. L. Mitchell. Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities. Journal of the Atmospheric Sciences 53, 1710–1723 (1996).
[25]
A. J. Heymsfield. Properties of Tropical and Midlatitude Ice Cloud Particle Ensembles. Part II: Applications for Mesoscale and Climate Models. Journal of the Atmospheric Sciences 60, 2592–2611 (2003).
[26]
H. Morrison and W. W. Grabowski. A Novel Approach for Representing Ice Microphysics in Models: Description and Tests Using a Kinematic Framework. Journal of the Atmospheric Sciences 65, 1528–1548 (2008).
[27]
N. Desai, K. Chandrakar, G. Kinney, W. Cantrell and R. Shaw. Aerosol-Mediated Glaciation of Mixed-Phase Clouds: Steady-State Laboratory Measurements. Geophysical Research Letters 46, 9154–9162 (2019).
[28]
H. Abdul-Razzak, S. J. Ghan and C. Rivera-Carpio. A parameterization of aerosol activation: 1. Single aerosol type. Journal of Geophysical Research: Atmospheres 103, 6123–6131 (1998).
[29]
H. Abdul-Razzak and S. J. Ghan. A parameterization of aerosol activation: 2. Multiple aerosol types. Journal of Geophysical Research: Atmospheres 105, 6837–6844 (2000).
[30]
M. D. Petters and S. M. Kreidenweis. A single parameter representation of hygroscopic growth and cloud condensation nucleus activity. Atmospheric Chemistry and Physics 7, 1961–1971 (2007).
[31]
R. Rogers. An elementary parcel model with explicit condensation and supersaturation. Atmosphere 13, 192–204 (1975).
[32]
M. Baumgartner, C. Rolf, J.-U. Grooß, J. Schneider, T. Schorr, O. Möhler, P. Spichtinger and M. Krämer. New investigations on homogeneous ice nucleation: the effects of water activity and water saturation formulations. Atmospheric Chemistry and Physics 22, 65–91 (2022).
[33]
[34]
B. Luo, K. S. Carslaw, T. Peter and S. L. Clegg, vapour pressures of H2SO4/HNO3/HCl/HBr/H2O solutions to low stratospheric temperatures. Geophysical Research Letters 22, 247–250 (1995).
[35]
[36]
O. Möhler, P. R. Field, P. Connolly, S. Benz, H. Saathoff, M. Schnaiter, R. Wagner, R. Cotton, M. Krämer, A. Mangold and A. J. Heymsfield. Efficiency of the deposition mode ice nucleation on mineral dust particles. Atmospheric Chemistry and Physics 6, 3007–3021 (2006).
[37]
[38]
[39]
S. China, P. A. Alpert, B. Zhang, S. Schum, K. Dzepina, K. Wright, R. C. Owen, P. Fialho, L. R. Mazzoleni, C. Mazzoleni and D. A. Knopf. Ice cloud formation potential by free tropospheric particles from long-range transport over the Northern Atlantic Ocean. Journal of Geophysical Research: Atmospheres 122, 3065–3079 (2017).
[40]
P. A. Alpert, A. Boucly, S. Yang, H. Yang, K. Kilchhofer, Z. Luo, C. Padeste, S. Finizio, M. Ammann and B. Watts. Ice nucleation imaged with X-ray spectro-microscopy.  Environ. Sci.: Atmos. 2, 335–351 (2022).
[41]
G. Thompson, R. M. Rasmussen and K. Manning. Explicit Forecasts of Winter Precipitation Using an Improved Bulk Microphysics Scheme. Part I: Description and Sensitivity Analysis. Monthly Weather Review 132, 519–542 (2004).
[42]
S. Karthika, T. K. Radhakrishnan and P. Kalaichelvi. A Review of Classical and Nonclassical Nucleation Theories. Crystal Growth & Design 16, 6663–6681 (2016).
[43]
E. Bigg. The supercooling of water. Proc. Phys. Soc. 66B, 688–694 (1953).
[44]
R. H. Barklie and N. R. Gokhale. The freezing of supercooled wter drops. Alberta hal, 1958, and related studies. McGill University Stormy Weather Group Sci. Rep. MW-30, 43–64 (1959).
[45]
[46]
E. Dunne and e. al. Global atmospheric particle formation from CERN CLOUD measurements. Science 354, 1119–1124 (2016).
[47]
J. Kirkby and e. al. Ion-induced nucleation of pure biogenic particles. Nature 533, 521–526 (2016).
[48]
F. Riccobono and e. al. Oxidation Products of Biogenic Emissions Contribute to Nucleation of Atmospheric Particles. Science 344, 717–721 (2014).
[49]
H. Vehkamäki, M. Kulmala, I. Napari, K. E. Lehtinen, C. Timmreck, M. Noppel and A. Laaksonen. An improved parameterization for sulfuric acid–water nucleation rates for tropospheric and stratospheric conditions. Journal of Geophysical Research: Atmospheres 107 (2002).
[50]
K. E. Lehtinen, M. . Maso, M. Kulmala and V.-M. Kerminen. Estimating nucleation rates from apparent particle formation rates and vice versa: Revised formulation of the Kerminen–Kulmala equation. Journal of Aerosol Science 38, 988–994 (2007).
[51]
F. Glassmeier and U. Lohmann. Constraining Precipitation Susceptibility of Warm-, Ice-, and Mixed-Phase Clouds with Microphysical Equations. Journal of the Atmospheric Sciences 73, 5003–5023 (2016).
[52]
A. V. Korolev and I. P. Mazin. Supersaturation of Water Vapor in Clouds. Journal of the Atmospheric Sciences 60, 2957–2974 (2003).
[53]
B. Kärcher, J. Hendricks and U. Lohmann. Physically based parameterization of cirrus cloud formation for use in global atmospheric models. Journal of Geophysical Research: Atmospheres 111 (2006).
[54]
C. Tully, D. Neubauer and U. Lohmann. Assessing predicted cirrus ice properties between two deterministic ice formation parameterizations. Geoscientific Model Development 16, 2957–2973 (2023).
[55]
E. J. Jensen, G. S. Diskin, J. DiGangi, S. Woods, R. P. Lawson and T. V. Bui. Homogeneous Freezing Events Sampled in the Tropical Tropopause Layer. Journal of Geophysical Research: Atmospheres 127, e2022JD036535 (2022), e2022JD036535 2022JD036535.
[56]
P. A. Alpert and D. A. Knopf. Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model. Atmos. Chem. Phys. 16, 2083–2107 (2016).