Articles | Volume 26, issue 17
https://doi.org/10.5194/acp-26-12543-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/acp-26-12543-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A cellular automaton model of tropical oceanic rain clusters with criticality
Kevin K. W. Cheung
CORRESPONDING AUTHOR
School of Atmospheric Physics, Nanjing University of Information Science and Technology, Nanjing, 210044, China
Chee-Kiat Teo
Centre for Climate Research Singapore, 537054, Singapore
retired
Tieh-Yong Koh
Department of Physics, National University of Singapore, 119077, Singapore
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Hydrol. Earth Syst. Sci., 29, 3527–3543, https://doi.org/10.5194/hess-29-3527-2025, https://doi.org/10.5194/hess-29-3527-2025, 2025
Short summary
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This study evaluates two reanalysis datasets, which are critical in climate, weather research, and water resources analysis, for the Australian region in terms of simulating daily mean precipitation and six other selected precipitation extremes. While spatial patterns of mean precipitation are well reproduced, substantial biases exist in precipitation variability, trends, and extremes. Caution in applying these datasets is thus advised in terms of the latter aspects.
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Nat. Hazards Earth Syst. Sci. Discuss., https://doi.org/10.5194/nhess-2023-210, https://doi.org/10.5194/nhess-2023-210, 2024
Manuscript not accepted for further review
Short summary
Short summary
We have analyzed a severe wildfire event in Tasmania, Australia that also developed thunderstorm clouds. The drivers of this compound hazard were highly complex, which included climatic factors (above normal heavy rain seasons followed by heatwave), weather systems (fronts and high winds) to heighten fire severity and unstable atmosphere to develop thunderstorm clouds, all in coincidence. Such event has demonstrated the difficulty to assess wildfire risk in a warming climate.
Cited articles
Ahmed, F. and Neelin, J. D.: Explaining scales and statistics of tropical precipitation clusters with a stochastic model, J. Atmos. Sci., 76, 3063–3087, https://doi.org/10.1175/JAS-D-18-0368.1, 2019.
Bak, P., Tang, C., and Wiesenfeld, K.: Self-organized criticality: An explanation of the noise, Phys. Rev. Lett., 59, 381, https://doi.org/10.1103/PhysRevLett.59.381, 1987.
Bao, J., Sherwood, S., Colin, M., and Dixit, V.: The Robust Relationship Between Extreme Precipitation and Convective Organization in Idealized Numerical Modeling Simulations, J. Adv. Model. Earth Sy., 9, 2291–2303, https://doi.org/10.1002/2017MS001125, 2017.
Bengtsson, L. and Han, J.: Updates to NOAA's Unified Forecast System's cumulus convection parameterization scheme between GFSv16 and GFSv17, Weather Forecast., 39, https://doi.org/10.1175/WAF-D-23-0232.1, 2024.
Bengtsson, L., Körnich, H., Källén, E., and Svensson, G.: Large-scale dynamical response to subgrid-scale organization provided by cellular automata, J. Atmos. Sci., 68, 3132–3144, https://doi.org/10.1175/JAS-D-10-05028.1, 2011.
Bengtsson, L., Steinheimer, M., Bechtold, P., and Geleyn, J.-F.: A stochastic parametrization for deep convection using cellular automata, Q. J. Roy. Meteor. Soc., 139, 1533–1543, https://doi.org/10.1002/qj.2108, 2013.
Bengtsson, L., Bao, J., Pegion, P., Penland, C., Michelson, S., and Whitaker, J.: A model framework for stochastic representation of uncertainties associated with physical processes in NOAA's Next Generation Global Prediction System, Mon. Weather Rev., 147, 893–911, https://doi.org/10.1175/MWR-D-18-0238.1, 2019.
Bengtsson, L., Dias, J., Tulich, S., Gehne, M., and Bao, J.-W.: A stochastic parameterization of organized tropical convection using cellular automata for global forecasts in NOAA's Unified Forecast System, J. Adv. Model. Earth Syst., 13, e2020MS002260, https://doi.org/10.1029/2020MS002260, 2021.
Bengtsson, L., Gerard, L., Han, L., Gehne, M., Li, W., and Dias, J.: A prognostic-stochastic and scale-adaptive cumulus convection closure for improved tropical variability and convective gray-zone representation in NOAA's Unified Forecast System (UFS), Mon. Weather Rev., 150, 3211–3227, https://doi.org/10.1175/MWR-D-22-0114.1, 2022.
Biagioli, G. and Tompkins, A. M.: A dimensionless parameter for predicting convective self-aggregation onset in a stochastic reaction–diffusion model of tropical radiative–convective equilibrium, J. Adv. Model. Earth Syst., 15, e2022MS003231, https://doi.org/10.1029/2022MS003231, 2023.
Broadbent, S. and Hammersley, J.: Percolation processes: I. Crystals and mazes, Math. Proc. Cambridge, 53, 629–641, https://doi.org/10.1017/S0305004100032680, 1957.
Bröker, H. M. and Grassberger, P.: Random neighbor theory of the Olami-Feder-Christensen earthquake model, Phys. Rev. E, 56, 3944, https://doi.org/10.1103/PhysRevE.56.3944, 1997.
Cahalan, R. F. and Joseph, J. H.: Fractal statistics of cloud fields, Mon. Weather Rev., 117, 261–272, https://doi.org/10.1175/1520-0493(1989)117<0261:FSOCF>2.0.CO;2, 1989.
Cerlini, P., Saraceni, M., and Silvestri, L.: Competing Effect of Radiative and Moisture Feedback in Convective Aggregation States in Two CRMs, J. Adv. Model. Earth Sy., 13, https://doi.org/10.1029/2022MS003323, 2023.
Chabanol, M. L. and Hakim, V.: Analysis of a dissipative model of self-organized criticality with random neighbors, Phys. Rev. E, 56, R2343, https://doi.org/10.1103/PhysRevE.56.R2343, 1997.
Cheraghalizadeh, J., Luković, M., and Najafi, M. N.: Simulating cumulus clouds based on self-organized criticality, Physica A, 636, 129553, https://doi.org/10.1016/j.physa.2024.129553, 2024.
Christensen, K. and Moloney, N. R.: Complexity and Criticality, Imperial College Press, London, UK, ISBN 1-86094-504-X, ISBN 1-86094-517-1(pbk), 2005.
Craig, G. C. and Mack, J. M.: A coarsening model for self-organization of tropical convection, J. Geophys. Res.-Atmos., 118, 8761–8769, https://doi.org/10.1002/jgrd.50674, 2013.
De Carvalho, J. X. and Prado, C. P.: Self-organized criticality in the Olami-Feder-Christensen model, Phys. Rev. Letts., 84, 4006, https://doi.org/10.1103/PhysRevLett.84.4006, 2000.
Devineni, N., Lall, U., Xi, C., and Ward, P.: Scaling of extreme rainfall areas at a planetary scale, Chaos, 25, 075407, https://doi.org/10.1063/1.4921719, 2015.
Dickman, R., Vespignani, A., and Zapperi, S.: Self-organized criticality as an absorbing-state phase transition, Phys. Rev. E, 57, 5095, https://doi.org/10.1103/PhysRevE.57.5095, 1998.
Emanuel, K. A.: Atmospheric Convection, Oxford University Press, UK, ISBN 0-19-506630-8, 1994.
Graf, H.-F. and Yang, J.: Evaluation of a new convective cloud field model: precipitation over the maritime continent, Atmos. Chem. Phys., 7, 409–421, https://doi.org/10.5194/acp-7-409-2007, 2007.
Haerter, J. O.: Convective self-aggregation as a cold pool-driven critical phenomenon, Geophys. Res. Lett., 46, 4017–4028, https://doi.org/10.1029/2018GL081817, 2019.
Jakob, C. and Schumacher, C.: Precipitation and latent heating characteristics of the major tropical western Pacific cloud regimes, J. Climate, 21, 4348–4364, https://doi.org/10.1175/2008JCLI2122.1 2008.
kkwc26-cyber: kkwc26-cyber/Rain-CA: v1.0.0, Version v1.0.0, Zenodo [code], https://doi.org/10.5281/zenodo.22088024, 2026.
Li, Y., Yano, J., and Lin, Y.: Is atmospheric convection organized? Information entropy analysis, Geophys. Astro. Fluid, 113, 553–573, https://doi.org/10.1080/03091929.2018.1506449, 2019.
Li, Z., O'Gorman, P. A., and Rothman, D. H.: Tropical precipitation clusters, as islands on a rough water-vapor topography, Q. J. Roy. Meteor. Soc., 148, 403–417, 2022.
López, R. E.: The Lognormal Distribution and Cumulus Cloud Populations, Mon. Weather Rev., 105, 865–872, https://doi.org/10.1175/1520-0493(1977)105<0865:TLDACC>2.0.CO;2, 1977.
López, R. E.: Internal Structure and Development Processes of C-Scale Aggregates of Cumulus Clouds, Mon. Weather Rev., 106, 1488–1494, https://doi.org/10.1175/1520-0493(1978)106<1488:ISADPO>2.0.CO;2, 1978.
Lovejoy, S.: Area–perimeter relation for rain and cloud areas, Science, 216, 185–187, https://doi.org/10.1126/science.216.4542.185, 1982.
Malamud, B. D. and Turcotte, D. L.: Cellular-automata models applied to natural hazards, Comput. Sci. Eng., 2, 42–51, https://doi.org/10.1109/5992.841795, 2000.
Mapes, B. E.: Gregarious tropical convection, J. Atmos. Sci., 50, 2026–2037, https://doi.org/10.1175/1520-0469(1993)050<2026:GTC>2.0.CO;2, 1993.
Muller, C. J. and Romps, D.: Acceleration of tropical cyclogenesis by self-aggregation feedbacks, P. Natl. Acad. Sci. USA, 115, 2930–2935, https://doi.org/10.1073/pnas.1719967115, 2018.
Muller, C. J., Back, L. E., O'Gorman, P. A., and Emanuel, K. A.: A model for the relationship between tropical precipitation and column water vapor, Geophys. Res. Letts., 36, https://doi.org/10.1029/2009GL039667, 2009.
Nagel, K. and Raschke, E.: Self-organizing criticality in cloud formation?, Physica A, 182, 519–531, https://doi.org/10.1016/0378-4371(92)90018-L, 1992.
Najafi, M. N., Cheraghalizadeh, J., and Herrmann, H. J.: Self-organized criticality in cumulus clouds, Phys. Rev. E, 103, 052106, https://doi.org/10.1103/PhysRevE.103.052106, 2021.
Neggers, R. A. J. and Griewank, P. J.: A binomial stochastic framework for efficiently modeling discrete statistics of convective populations, J. Adv. Model. Earth Sy., 13, e2020MS002229, https://doi.org/10.1029/2020MS002229, 2021.
Neggers, R. A. J. and Griewank, P.: A decentralized approach for modeling organized convection based on thermal populations on microgrids, J. Adv. Model. Earth Sy., 14, e2022MS003042, https://doi.org/10.1029/2022MS003042, 2022.
Neggers, R. A. J., Groewank, P., and Heus, T.: Power-law scaling in the internal variability of cumulus cloud size distributions due to subsampling and spatial organization, J. Atmos. Sci., 76, 1489–1503, https://doi.org/10.1175/JAS-D-18-0194.1, 2019.
Nicholls, M. E., Pielke, R. A., and Cotton, W. R.: Thermally forced gravity waves in an atmosphere at rest, J. Atmos. Sci., 48, 1869–1884, https://doi.org/10.1175/1520-0469(1991)048<1869:TFGWIA>2.0.CO;2 1991.
Nober, F. J. and Graf, H. F.: A new convective cloud field model based on principles of self-organisation, Atmos. Chem. Phys., 5, 2749–2759, https://doi.org/10.5194/acp-5-2749-2005, 2005.
O'Brien, T. A., Li, F., Collins, W. D., Rauscher, S. A., Ringler, T. D., Taylor, M., Hagos, S. M., and Leung, L. R.: Observed scaling in clouds and precipitation and scale incognizance in regional to global atmospheric models, J. Climate, 26, 9313–9333, 2013.
Olami, Z., Feder, H. J. S., and Christensen, K.: Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes, Phys. Rev. Lett., 68, 1244, https://doi.org/10.1103/PhysRevLett.68.1244, 1992.
Otsuka, S., Trilaksono, N. J., and Yoden, S.: Comparing simulated size distributions of precipitation systems at different model resolution, SOLA, 13, 130–134, https://doi.org/10.2151/sola.2017-024, 2017.
Palmer, T. N.: On parametrizing scales that are only somewhat smaller than the smallest resolved scales, with application to convection and orography. Proceedings of the 1996 ECMWF workshop on convection, ECMWF, Shinfield Park, Reading, UK, 1997.
Palmer, T. N.: A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamic parametrization in weather and climate prediction models, Q. J. Roy. Meteor. Soc., 127, 279–304, https://doi.org/10.1002/QJ.49712757202, 2001.
Pendergrass, A.: Changing degree of convective organization as a mechanism for dynamic changes in extreme precipitation, Curr. Clim. Change Rep., 6, 47–54, https://doi.org/10.1007/s40641-020-00157-9, 2020.
Peters, O. and Neelin, J. D.: Critical phenomena in atmospheric precipitation, Nat. Phys., 2, 393–396, https://doi.org/10.1038/nphys314, 2006.
Peters, O., Neelin, J. D., and Nesbitt, S. W.: Mesoscale convective systems and critical clusters, J. Atmos. Sci., 66, 2913–2924, https://doi.org/10.1175/2008JAS2761.1, 2009.
Peters, O., Deluca, A., Corral, Á., Neelin, J. D., and Holloway, C. E.: Universality of rain event size distributions, J. Stat. Mech.-Theory E., 2010, P11030, https://doi.org/10.1088/1742-5468/2010/11/P11030, 2010.
Piegari, E., Cataudella, V., Di Maio, R., Milano, L., and Nicodemi, M.: Finite driving rate and anisotropy effects in landslide modeling, Phys. Rev. E, 73, 026123, https://doi.org/10.1103/PhysRevE.73.026123, 2006.
Pruessner, G.: Self-Organised Criticality: Theory, Models and Characterisation, Cambridge University Press, ISBN-10: 0521853354, ISBN-13: 978-0521853354, 2012.
Randall, D. and Huffman, G.: A stochastic model of cumulus clumping, J. Atmos. Sci., 37, 2068–2078, https://doi.org/10.1175/1520-0469(1980)037<2068:ASMOCC>2.0.CO;2, 1980.
Roca, R. and Fiolleau, T.: Extreme precipitation in the tropics is closely associated with long-lived convective systems, Communications Earth & Environment, 1, https://doi.org/10.1038/S43247-020-00015-4, 2020.
Savre, J. and Craig, G.: Fitting cumulus cloud size distributions from idealized cloud resolving model simulations, J. Adv. Model. Earth Sy., 15, https://doi.org/10.1029/2022MS003360, 2023.
Schubert, W.: A Retrospective View of Arakawa's Ideas on Cumulus Parameterisation, in: General Circulation Model Development: Past, Present and Future, edited by: Randall, D., Academic Press, 181–198, ISBN-10: 0125780109, ISBN-13: 978-0125780100, 2000.
Semie, A. and Bony, S.: Relationship between precipitation extremes and convective organization inferred from satellite observations, Geophys. Res. Lett., 47, https://doi.org/10.1029/2019GL086927, 2020.
Silva, A. R., Silva, A. R., and Gouvêa Jr., M. M.: A novel model to simulate cloud dynamics with cellular automaton, Environ. Modell. Softw., 122, 104537, https://doi.org/10.1016/j.envsoft.2019.104537, 2019.
Stauffer, D. and Aharony, A.: Introduction to Percolation Theory, 2nd revised edn., Taylor & Francis, 181 pp., ISBN-10: 0748402535 and ISBN-13: 978-0748402533, 1994.
Stechmann, S. N. and Neelin, J. D.: First-passage-time prototypes for precipitation statistics, J. Atmos. Sci., 71, 3269–3291, https://doi.org/10.1175/JAS-D-13-0268.1, 2014.
Stephan, C. C. and Stevens, B.: Dynamical imprints on precipitation cluster statistics across a hierarchy of high-resolution simulations, Atmos. Chem. Phys., 25, 1209–1226, https://doi.org/10.5194/acp-25-1209-2025, 2025.
Teo, C.-K., Huynh, H.-N., Koh, T.-Y., Cheung, K. K. W., Legras, B., Chew, L. Y., and Norford, L.: The universal scaling characteristics of tropical oceanic rain clusters, J. Geophys. Res.-Atmos., 122, 5582–5599, https://doi.org/10.1002/2016JD025921, 2017.
Teo, C.-K., Koh, T.-Y., Cheung, K. K. W., Legras, B., Huynh, H.-N., Chew, L.-Y., and Norford, L.: Scaling characteristics of modelled tropical oceanic rain clusters, Q. J. Roy. Meteor. Soc., 147, 1055–1069, https://doi.org/10.1002/qj.3959, 2021.
Traxl, D., Boers, N., Rheinwalt, A., Goswami, B., and Kurths, J.: The size distribution of spatiotemporal extreme rainfall clusters around the globe, Geophys. Res. Lett., 43, 9939–9947, 2016.
Vespignani, A. and Zapperi, S.: How self-organized criticality works: A unified mean-field picture, Phys. Rev. E, 57, 6345, https://doi.org/10.1103/PhysRevE.57.6345, 1998.
Wing, A. A. and Emanuel, K.: Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations, J. Adv. Model. Earth Sy., 6, 59–74, https://doi.org/10.1002/2013MS000269, 2014.
Wing, A. A., Emanuel, K., Holloway, C. E., and Muller, C.: Convective self-aggregation in numerical simulations: A review, in: Shallow Clouds, Water Vapor, Circulation, and Climate Sensitivity. Space Sciences Series of ISSI, Vol. 65, edited by: Pincus, R., Winker, D., Bony, S., and Stevens, B., Springer, Cham, https://doi.org/10.1007/978-3-319-77273-8_1, 2017.
Wood, R. and Field, P. R.: The distribution of cloud horizontal sizes, J. Climate, 24, 4800–4816, https://doi.org/10.1175/2011JCLI4056.1, 2011.
Yao, L., Yang, D., and Tan, Z.: A vertically resolved MSE framework highlights the role of the boundary layer in convective self-aggregation, J. Atmos. Sci., 79, 1615–1631, https://doi.org/10.1175/JAS-D-20-0254.1, 2022.
Zhang, Y. and Wang, K.: Global precipitation system size, Environ. Res. Lett., 16, 054005, https://doi.org/10.1088/1748-9326/abf394, 2021.
Short summary
This study presents a cellular automaton (CA) model of tropical oceanic rain clusters based on atmospheric stability and gravity-wave interactions. The model reproduces power-law distributions for cluster area and rain rate, exhibiting criticality similar to 2D percolation. The scaling exponent for cluster area is robust to model parameters and matches simulations over the Indian Ocean and Atlantic, although it differs from some observational estimates, suggesting further model tuning is needed.
This study presents a cellular automaton (CA) model of tropical oceanic rain clusters based on...
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