Skip to main content
Have a personal or library account? Click to login
On the Geometry of Aggregate Snowflakes Cover

On the Geometry of Aggregate Snowflakes

Open Access
|Jun 2026

References

  1. Ball, P. (2011). In retrospect: On the six-cornered snowflake. Nature, 480, 455. 10.1038/480455a
  2. Basu, S., & Jones, C. E. (2004). A modified lognormal power-law distribution for the stellar initial mass function. Monthly Notices of the Royal Astronomical Society Letters, 347, L47L51. 10.1111/j.1365-2966.2004.07405.x
  3. Böhm, J. P. (1992a). A general hydrodynamic theory for mixed-phase microphysics. Part I: drag and fall speed of hydrometeors. Atmospheric Research, 27(4), 253274. 10.1016/0169-8095(92)90035-9
  4. Böhm, J. P. (1992b). A general hydrodynamic theory for mixed-phase microphysics. Part II: collision kernels for coalescence. Atmospheric Research, 27(4), 275290. 10.1016/0169-8095(92)90036-A
  5. Böhm, J. P. (1992c). A general hydrodynamic theory for mixed-phase microphysics. Part III: Riming and aggregation. Atmospheric Research, 28(2), 103123. 10.1016/0169-8095(92)90023-4
  6. Brath, M., Ekelund, R., Eriksson, P., Lemke, O., & Buehler, S. A. (2020). Microwave and submillimeter wave scattering of oriented ice particles. Atmospheric Measurement Techniques, 13(5), 23092333. 10.5194/amt-13-2309-2020
  7. Brdar, S., & Seifert, A. (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(1), 187206. 10.1002/2017MS001167
  8. Chabrier, G. (2003). Galactic stellar and substellar initial mass function. Publications of the Astronomical Society of the Pacific, 115, 763795. 10.1086/376392
  9. Chandrakar, K. K., Grabowski, W. W., Morrison, H., & Bryan, G. H. (2021). Impact of entrainment mixing and turbulent fluctuations on droplet size distributions in a cumulus cloud: An investigation using Lagrangian microphysics with a subgrid-scale model. Journal of the Atmospheric Sciences, 78(9), 29833005. 10.1175/JAS-D-20-0281.1
  10. Chellini, G., & Kneifel, S. (2024). Turbulence as a key driver of ice aggregation and riming in Arctic low-level mixed-phase clouds, revealed by long-term cloud radar observations. Geophysical Research Letters, 51(6), e2023GL106599. 10.1029/2023GL106599
  11. Connolly, P. J., Emersic, C., & Field, P. R. (2012). A laboratory investigation into the aggregation efficiency of small ice crystals. Atmospheric Chemistry and Physics, 12(4), 20552076. 10.5194/acp-12-2055-2012
  12. Draine, B. T., & Flatau, P. J. (1994). Discrete-dipole approximation for scattering calculations. Journal of the Optical Society of America A, 11(4), 14911499. 10.1364/JOSAA.11.001491
  13. Dunnavan, E. L. (2021). How snow aggregate ellipsoid shape and orientation variability affects fall speed and self-aggregation rates. Journal of the Atmospheric Sciences, 78(1), 5173. 10.1175/JAS-D-20-0128.1
  14. Dunnavan, E. L., Jiang, Z., Harrington, J. Y., Verlinde, J., Fitch, K., & Garrett, T. J. (2019). The shape and density evolution of snow aggregates. Journal of the Atmospheric Sciences, 76(12), 39193940. 10.1175/JAS-D-19-0066.1
  15. Gillespie, D. T. (1975). An exact method for numerically simulating the stochastic coalescence process in a cloud. Journal of the Atmospheric Sciences, 32(10), 19771989. 10.1175/1520-0469(1975)032<;1977:AEMFNS>2.0.CO;2
  16. Goldstein, H., Poole, C., & Safko, J. (2002). Classical mechanics by Herbert Goldstein, Charles Poole and John Safko. Addison Wesley.
  17. Grabowski, W. W., & Wang, L.-P. (2013). Growth of cloud droplets in a turbulent environment. Annual Review of Fluid Mechanics, 45(1), 293324. 10.1146/annurev-fluid-011212-140750
  18. Hales, T. (2024). The formal proof of the Kepler conjecture: A critical retrospective. arXiv. https://arxiv.org/abs/2402.08032.
  19. Karrer, M., Seifert, A., Siewert, C., Ori, D., von Lerber, A., & Kneifel, S. (2020). Ice particle properties inferred from aggregation modelling. Journal of Advances in Modeling Earth Systems, 12(8), e2020MS002066. 10.1029/2020MS002066
  20. Kneifel, S., von Lerber, A., Tiira, J., Moisseev, D., Kollias, P., & Leinonen, J. (2015). Observed relations between snowfall microphysics and triple-frequency radar measurements. Journal of Geophysical Research, 120(12), 60346055. 10.1002/2015JD023156
  21. Köbschall, K., Breitenbach, J., Roisman, I. V., Tropea, C., & Hussong, J. (2023). Geometric descriptors for the prediction of snowflake drag. Experiments in Fluids, 64(1), 4. 10.1007/s00348-022-03539-x
  22. Leinonen, J., Grazioli, J., & Berne, A. (2021). Reconstruction of the mass and geometry of snowfall particles from multi-angle snowflake camera (MASC) images. Atmospheric Measurement Techniques, 14(10), 68516866. https://amt.copernicus.org/articles/14/6851/2021/. 10.5194/amt-14-6851-2021
  23. Leinonen, J., & Moisseev, D. (2015). What do triple-frequency radar signatures reveal about aggregate snowflakes? Journal of Geophysical Research, 120(1), 229239. 10.1002/2014JD022072
  24. Leinonen, J., & Szyrmer, W. (2015). Radar signatures of snowflake riming: A modeling study. Earth and Space Science, 2(8), 346358. 10.1002/2015EA000102
  25. Libbrecht, K. G. (2019). Snow crystals. arXiv preprint arXiv:1910.06389.
  26. Locatelli, J. D., & Hobbs, P. V. (1974). Fall speeds and masses of solid precipitation particles. Journal of Geophysical Research, 79(15), 21852197. 10.1029/JC079i015p02185
  27. Lu, Y., Jiang, Z., Aydin, K., Verlinde, J., Clothiaux, E. E., & Botta, G. (2016). A polarimetric scattering database for non-spherical ice particles at microwave wavelengths. Atmospheric Measurement Techniques, 9(10), 51195134. https://amt.copernicus.org/articles/9/5119/2016/. 10.5194/amt-9-5119-2016
  28. Mason, S. L., Hogan, R. J., Westbrook, C. D., Kneifel, S., Moisseev, D., & von Terzi, L. (2019). The importance of particle size distribution and internal structure for triple-frequency radar retrievals of the morphology of snow. Atmospheric Measurement Techniques, 12(9), 49935018. 10.5194/amt-12-4993-2019
  29. Mitchell, D. L. (1996). Use of mass-and area-dimensional power laws for determining precipitation particle terminal velocities. Journal of the Atmospheric Sciences, 53(12), 17101723. 10.1175/1520-0469(1996)053<;1710:UOMAAD>2.0.CO;2
  30. Mitchell, D. L., Zhang, R., & Pitter, R. L. (1990). Mass-dimensional relationships for ice particles and the influence of riming on snowfall rates. Journal of Applied Meteorology and Climatology, 29(2), 153163. 10.1175/1520-0450(1990)029<;0153:MDRFIP>2.0.CO;2
  31. Moisseev, D. N., Lautaportti, S., Tyynela, J., & Lim, S. (2015). Dual-polarization radar signatures in snowstorms: Role of snowflake aggregation. Journal of Geophysical Research, 120(24), 12,64412,665. 10.1002/2015JD023884
  32. Morrison, H., Chandrakar, K. K., Shima, S.-I., Dziekan, P., & Grabowski, W. W. (2024). Impacts of stochastic coalescence variability on warm rain initiation using Lagrangian microphysics in box and large-eddy simulations. Journal of the Atmospheric Sciences, 81(6), 10671093. 10.1175/JAS-D-23-0132.1
  33. Morrison, H., van Lier-Walqui, M., Fridlind, A. M., Grabowski, W. W., Harrington, J. Y., Hoose, C., Korolev, A., Kumjian, M. R., Milbrandt, J. A., Pawlowska, H., et al. (2020). Confronting the challenge of modeling cloud and precipitation microphysics. Journal of Advances in Modeling Earth Systems, 12(8), e2019MS001689. 10.1029/2019MS001689
  34. Onishi, R., & Seifert, A. (2016). Reynolds-number dependence of turbulence enhancement on collision growth. Atmospheric Chemistry and Physics, 16(19), 1244112455. 10.5194/acp-16-12441-2016
  35. Ori, D., von Terzi, L., Karrer, M., & Kneifel, S. (2021). snowScatt 1.0: consistent model of microphysical and scattering properties of rimed and unrimed snowflakes based on the self-similar Rayleigh–Gans approximation. Geoscientific Model Development, 14(3), 15111531. 10.5194/gmd-14-1511-2021
  36. Przybylo, V. M., Sulia, K. J., Lebo, Z. J., & Schmitt, C. G. (2022). The ice particle and aggregate simulator (IPAS). Part II: Analysis of a database of theoretical aggregates for microphysical parameterization. Journal of the Atmospheric Sciences, 79(6), 16331649. 10.1175/JAS-D-21-0179.1
  37. Seifert, A., Leinonen, J., Siewert, C., & Kneifel, S. (2019). The geometry of rimed aggregate snowflakes: A modeling study. Journal of Advances in Modeling Earth Systems, 11(3), 712731. 10.1029/2018MS001519
  38. Shaw, R. A. (2003). Particle-turbulence interactions in atmospheric clouds. Annual Review of Fluid Mechanics, 35(1), 183227. 10.1146/annurev.fluid.35.101101.161125
  39. Shima, S.-i., Kusano, K., Kawano, A., Sugiyama, T., & Kawahara, S. (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. Quarterly Journal of the Royal Meteorological Society, 135(642), 13071320. 10.1002/qj.441
  40. Shima, S.-i., Sato, Y., Hashimoto, A., & Misumi, R. (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(9), 41074157. 10.5194/gmd-13-4107-2020
  41. Telford, J. W. (1955). A new aspect of coalescence theory. Journal of the Atmospheric Sciences, 12(5), 436444. 10.1175/1520-0469(1955)012<;0436:ANAOCT>2.0.CO;2
  42. von Terzi, L., Dias Neto, J., Ori, D., Myagkov, A., & Kneifel, S. (2022). Ice microphysical processes in the dendritic growth layer: A statistical analysis combining multi-frequency and polarimetric Doppler cloud radar observations. Atmospheric Chemistry and Physics, 22, 1179511821. 10.5194/acp-22-11795-2022
  43. von Terzi, L., Ori, D., & Kneifel, S. (2026). A microwave scattering database of oriented ice and snow particles: Supporting habit-dependent growth models and radar applications (McRadar 1.0.0). Geoscientific Model Development, 19(2), 887910. https://gmd.copernicus.org/articles/19/887/2026/. 10.5194/gmd-19-887-2026
  44. Welss, J.-N., Siewert, C., & Seifert, A. (2024). Explicit habit-prediction in the Lagrangian super-particle ice microphysics model McSnow. Journal of Advances in Modeling Earth Systems, 16(4), e2023MS003805. 10.1029/2023MS003805
  45. Westbrook, C., Ball, R., Field, P., & Heymsfield, A. J. (2004a). Theory of growth by differential sedimentation, with application to snowflake formation. Physical Review E, 70(2), 021403. 10.1103/PhysRevE.70.021403
  46. Westbrook, C. D., Ball, R. C., Field, P. R., & Heymsfield, A. J. (2004b). Universality in snowflake aggregation. Geophysical Research Letters, 31(15). 10.1029/2004GL020363
  47. Yurkin, M. A., & Hoekstra, A. G. (2007). The discrete dipole approximation: An overview and recent developments. Journal of Quantitative Spectroscopy and Radiative Transfer, 106(1–3), 558589. 10.1016/j.jqsrt.2007.01.034
  48. Yurkin, M. A., & Hoekstra, A. G. (2011). The discrete-dipole-approximation code ADDA: Capabilities and known limitations. Journal of Quantitative Spectroscopy and Radiative Transfer, 112(13), 22342247. 10.1016/j.jqsrt.2011.01.031
Language: English
Page range: 87 - 110
Submitted on: Oct 24, 2025
Accepted on: May 26, 2026
Published on: Jun 26, 2026
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services

© 2026 Axel Seifert, Fabian Jakub, Christoph Siewert, Leonie von Terzi, Stefan Kneifel, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.