Articles | Volume 19, issue 6
https://doi.org/10.5194/gmd-19-2437-2026
© 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/gmd-19-2437-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Deep learning representation of the aerosol size distribution
Donifan Barahona
CORRESPONDING AUTHOR
NASA, Goddard Space Flight Center, Greenbelt, MD, USA
Katherine H. Breen
NASA, Goddard Space Flight Center, Greenbelt, MD, USA
Morgan State University, Baltimore, MD, USA
Karoline Block
Leipzig Institute for Meteorology, Faculty of Physics and Earth Sciences, University of Leipzig, Leipzig, Germany
Anton Darmenov
NASA, Goddard Space Flight Center, Greenbelt, MD, USA
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Increases in atmospheric aerosols affect the scattering and absorption of solar radiation by altering the macrophysical and microphysical processes of clouds. We analyzed aerosol–cloud interactions in response to degassing events from the Kilauea volcano in 2008 and 2018 by comparing satellite and simulated cloud properties. Results showed a threshold response to overcome meteorological effects that is largely controlled by aerosol concentration, composition, plume height, and ENSO state.
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Adriana Rocha-Lima, Peter R. Colarco, Anton S. Darmenov, Edward P. Nowottnick, Arlindo M. da Silva, and Luke D. Oman
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Observations show an increasing aerosol optical depth trend in the Middle East between 2003–2012. We evaluate the NASA Goddard Earth Observing System (GEOS) model's ability to capture these trends and examine the meteorological and surface parameters driving dust emissions. Our results highlight the importance of data assimilation for long-term trends of atmospheric aerosols and support the hypothesis that vegetation cover loss may have contributed to increasing dust emissions in the period.
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In June 2019, smoke particles from a Canadian wildfire event were transported to Europe. The long-range-transported smoke plumes were monitored with a spaceborne lidar and reanalysis models. Based on the aerosol mass concentrations estimated from the observations, the reanalysis models had difficulties in reproducing the amount and location of the smoke aerosols during the transport event. Consequently, more spaceborne lidar missions are needed for reliable monitoring of aerosol plumes.
Karoline Block, Mahnoosh Haghighatnasab, Daniel G. Partridge, Philip Stier, and Johannes Quaas
Earth Syst. Sci. Data, 16, 443–470, https://doi.org/10.5194/essd-16-443-2024, https://doi.org/10.5194/essd-16-443-2024, 2024
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Aerosols being able to act as condensation nuclei for cloud droplets (CCNs) are a key element in cloud formation but very difficult to determine. In this study we present a new global vertically resolved CCN dataset for various humidity conditions and aerosols. It is obtained using an atmospheric model (CAMS reanalysis) that is fed by satellite observations of light extinction (AOD). We investigate and evaluate the abundance of CCNs in the atmosphere and their temporal and spatial occurrence.
Mahnoosh Haghighatnasab, Jan Kretzschmar, Karoline Block, and Johannes Quaas
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The impact of aerosols emitted by the Holuhraun volcanic eruption on liquid clouds was assessed from a pair of cloud-system-resolving simulations along with satellite retrievals. Inside and outside the plume were compared in terms of their statistical distributions. Analyses indicated enhancement for cloud droplet number concentration inside the volcano plume in model simulations and satellite retrievals, while there was on average a small effect on both liquid water path and cloud fraction.
Ehud Strobach, Andrea Molod, Donifan Barahona, Atanas Trayanov, Dimitris Menemenlis, and Gael Forget
Geosci. Model Dev., 15, 2309–2324, https://doi.org/10.5194/gmd-15-2309-2022, https://doi.org/10.5194/gmd-15-2309-2022, 2022
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The Green's functions methodology offers a systematic, easy-to-implement, computationally cheap, scalable, and extendable method to tune uncertain parameters in models accounting for the dependent response of the model to a change in various parameters. Herein, we successfully show for the first time that long-term errors in earth system models can be considerably reduced using Green's functions methodology. The method can be easily applied to any model containing uncertain parameters.
Huisheng Bian, Eunjee Lee, Randal D. Koster, Donifan Barahona, Mian Chin, Peter R. Colarco, Anton Darmenov, Sarith Mahanama, Michael Manyin, Peter Norris, John Shilling, Hongbin Yu, and Fanwei Zeng
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The study using the NASA Earth system model shows ~2.6 % increase in burning season gross primary production and ~1.5 % increase in annual net primary production across the Amazon Basin during 2010–2016 due to the change in surface downward direct and diffuse photosynthetically active radiation by biomass burning aerosols. Such an aerosol effect is strongly dependent on the presence of clouds. The cloud fraction at which aerosols switch from stimulating to inhibiting plant growth occurs at ~0.8.
Xiaoxia Shang, Tero Mielonen, Antti Lipponen, Elina Giannakaki, Ari Leskinen, Virginie Buchard, Anton S. Darmenov, Antti Kukkurainen, Antti Arola, Ewan O'Connor, Anne Hirsikko, and Mika Komppula
Atmos. Meas. Tech., 14, 6159–6179, https://doi.org/10.5194/amt-14-6159-2021, https://doi.org/10.5194/amt-14-6159-2021, 2021
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The long-range-transported smoke particles from a Canadian wildfire event were observed with a multi-wavelength Raman polarization lidar and a ceilometer over Kuopio, Finland, in June 2019. The optical properties and the mass concentration estimations were reported for such aged smoke aerosols over northern Europe.
Katherine H. Breen, Donifan Barahona, Tianle Yuan, Huisheng Bian, and Scott C. James
Atmos. Chem. Phys., 21, 7749–7771, https://doi.org/10.5194/acp-21-7749-2021, https://doi.org/10.5194/acp-21-7749-2021, 2021
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Increases in atmospheric aerosols affect the scattering and absorption of solar radiation by altering the macrophysical and microphysical processes of clouds. We analyzed aerosol–cloud interactions in response to degassing events from the Kilauea volcano in 2008 and 2018 by comparing satellite and simulated cloud properties. Results showed a threshold response to overcome meteorological effects that is largely controlled by aerosol concentration, composition, plume height, and ENSO state.
Cited articles
Aas, K., Jullum, M., and Løland, A.: Explaining individual predictions when features are dependent: More accurate approximations to Shapley values, Artif. Intell., 298, 103502, https://doi.org/10.1016/j.artint.2021.103502, 2021. a
Adachi, K. and Buseck, P. R.: Internally mixed soot, sulfates, and organic matter in aerosol particles from Mexico City, Atmos. Chem. Phys., 8, 6469–6481, https://doi.org/10.5194/acp-8-6469-2008, 2008. a
Adams, P. J. and Seinfeld, J. H.: Predicting global aerosol size distributions in general circulation models, J. Geophys. Res.-Atmos., 107, https://doi.org/10.1029/2001JD001010, 2002. a
Amunsen, C., Hanssen, J., Semb, A., and Steinnes, E.: Long-range atmospheric transport of trace elements to southern Norway, Atmos. Environ. A Gen., 26, 1309–1324, https://doi.org/10.1016/0960-1686(92)90391-W, 1992. a
Aquila, V., Hendricks, J., Lauer, A., Riemer, N., Vogel, H., Baumgardner, D., Minikin, A., Petzold, A., Schwarz, J. P., Spackman, J. R., Weinzierl, B., Righi, M., and Dall'Amico, M.: MADE-in: a new aerosol microphysics submodel for global simulation of insoluble particles and their mixing state, Geosci. Model Dev., 4, 325–355, https://doi.org/10.5194/gmd-4-325-2011, 2011. a
Arfin, T., Pillai, A. M., Mathew, N., Tirpude, A., Bang, R., and Mondal, P.: An overview of atmospheric aerosol and their effects on human health, Environ. Sci. Pollut. R., 30, 125347–125369, https://doi.org/10.1007/s11356-023-29652-w, 2023. a
Asmi, A., Wiedensohler, A., Laj, P., Fjaeraa, A.-M., Sellegri, K., Birmili, W., Weingartner, E., Baltensperger, U., Zdimal, V., Zikova, N., Putaud, J.-P., Marinoni, A., Tunved, P., Hansson, H.-C., Fiebig, M., Kivekäs, N., Lihavainen, H., Asmi, E., Ulevicius, V., Aalto, P. P., Swietlicki, E., Kristensson, A., Mihalopoulos, N., Kalivitis, N., Kalapov, I., Kiss, G., de Leeuw, G., Henzing, B., Harrison, R. M., Beddows, D., O'Dowd, C., Jennings, S. G., Flentje, H., Weinhold, K., Meinhardt, F., Ries, L., and Kulmala, M.: Number size distributions and seasonality of submicron particles in Europe 2008–2009, Atmos. Chem. Phys., 11, 5505–5538, https://doi.org/10.5194/acp-11-5505-2011, 2011. a, b, c, d, e, f
Barahona, D. and Breen, K.: MAMnet, Zenodo [code], https://doi.org/10.5281/zenodo.15190121, 2025. a, b
Barahona, D., Molod, A., Bacmeister, J., Nenes, A., Gettelman, A., Morrison, H., Phillips, V., and Eichmann, A.: Development of two-moment cloud microphysics for liquid and ice within the NASA Goddard Earth Observing System Model (GEOS-5), Geosci. Model Dev., 7, 1733–1766, https://doi.org/10.5194/gmd-7-1733-2014, 2014. a, b, c
Barahona, D., Breen, K. H., Kalesse-Los, H., and Röttenbacher, J.: Deep Learning Parameterization of Vertical Wind Velocity Variability via Constrained Adversarial Training, Artificial Intelligence for the Earth Systems, 3, e230025, https://doi.org/10.1175/AIES-D-23-0025.1, 2024. a, b
Bender, F. A.-M.: Aerosol forcing: Still uncertain, still relevant, AGU Advances, 1, e2019AV000128, https://doi.org/10.1029/2019AV000128, 2020. a
Bender, F. A.-M., Frey, L., McCoy, D. T., Grosvenor, D. P., and Mohrmann, J. K.: Assessment of aerosol–cloud–radiation correlations in satellite observations, climate models and reanalysis, Cli. Dynam., 52, 4371–4392, https://doi.org/10.1007/s00382-018-4384-z, 2019. a
Bengio, Y., Goodfellow, I., and Courville, A.: Deep learning, vol. 1, MIT Press Cambridge, MA, USA, ISBN 978-0262035613, 2017. a
Birmili, W., Berresheim, H., Plass-Dülmer, C., Elste, T., Gilge, S., Wiedensohler, A., and Uhrner, U.: The Hohenpeissenberg aerosol formation experiment (HAFEX): a long-term study including size-resolved aerosol, H2SO4, OH, and monoterpenes measurements, Atmos. Chem. Phys., 3, 361–376, https://doi.org/10.5194/acp-3-361-2003, 2003. a
Block, K.: Cloud condensation nuclei (CCN) numbers derived from CAMS reanalysis EAC4 (Version 1), World Data Center for Climate (WDCC) at DKRZ [data set], https://doi.org/10.26050/WDCC/QUAERERE_CCNCAMS_v1, 2023. a, b
Brenowitz, N. D. and Bretherton, C. S.: Spatially extended tests of a neural network parametrization trained by coarse-graining, J. Adv. Model. Earth Sy., 11, 2728–2744, https://doi.org/10.1029/2019MS001711, 2019. a
Buchard, V., Randles, C., Da Silva, A., Darmenov, A., Colarco, P., Govindaraju, R., Ferrare, R., Hair, J., Beyersdorf, A., Ziemba, L., and Yu, H.: The MERRA-2 aerosol reanalysis, 1980 onward. Part II: Evaluation and case studies, J. Climate, 30, 6851–6872, https://doi.org/10.1175/JCLI-D-16-0613.1, 2017. a, b, c
Buda, M., Maki, A., and Mazurowski, M. A.: A systematic study of the class imbalance problem in convolutional neural networks, Neural Networks, 106, 249–259, https://doi.org/10.1016/j.neunet.2018.07.011, 2018. a
CALIPSO: Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observation Lidar Level 2 Aerosol Profile V4-20, NASA [data set], https://doi.org/10.5067/CALIOP/CALIPSO/LID_L2_05KMAPRO-STANDARD-V4-20, 2023. a
C̆ervenkova, J. and Vá n̆a, M.: Trend Assessment of deposition, throughfall and runoff water chemistry at the ICP-IM station Kosetice, Czech Republic, IAHS-AISH Publication, 336, 103–108, 2010. a
Charron, A., Birmili, W., and Harrison, R. M.: Factors influencing new particle formation at the rural site, Harwell, United Kingdom, J. Geophys. Res.-Atmos., 112, https://doi.org/10.1029/2007JD008425, 2007. a
Chin, M., Rood, R. B., Lin, S.-J., Müller, J.-F., and Thompson, A. M.: Atmospheric sulfur cycle simulated in the global model GOCART: Model description and global properties, J. Geophys. Res.-Atmos., 105, 24671–24687, https://doi.org/10.1029/2000JD900384, 2000. a, b
Chollet, F.: Keras, GitHub [code], https://github.com/fchollet/keras (last access: 23 March 2026), 2015. a
Choudhury, G. and Tesche, M.: Estimating cloud condensation nuclei concentrations from CALIPSO lidar measurements, Atmos. Meas. Tech., 15, 639–654, https://doi.org/10.5194/amt-15-639-2022, 2022. a, b, c, d
Christensen, M. W., Jones, W. K., and Stier, P.: Aerosols enhance cloud lifetime and brightness along the stratus-to-cumulus transition, P. Natl. Acad. Sci. USA, 117, 17591–17598, https://doi.org/10.1073/pnas.1921231117, 2020. a
Chu, D., Kaufman, Y., Ichoku, C., Remer, L., Tanré, D., and Holben, B.: Validation of MODIS aerosol optical depth retrieval over land, Geophys. Res. Lett., 29, https://doi.org/10.1029/2001GL013205, 2002. a
Colarco, P., da Silva, A., Chin, M., and Diehl, T.: Online simulations of global aerosol distributions in the NASA GEOS-4 model and comparisons to satellite and ground-based aerosol optical depth, J. Geophys. Res., 115, D14207, https://doi.org/10.1029/2009JD012820, 2010a. a, b
Colarco, P., da Silva, A., Chin, M., and Diehl, T.: Online simulations of global aerosol distributions in the NASA GEOS-4 model and comparisons to satellite and ground-based aerosol optical depth, J. Geophys. Res.-Atmos., 115, https://doi.org/10.1029/2009JD012820, 2010b. a
Engler, C., Rose, D., Wehner, B., Wiedensohler, A., Brüggemann, E., Gnauk, T., Spindler, G., Tuch, T., and Birmili, W.: Size distributions of non-volatile particle residuals (Dp<800 nm) at a rural site in Germany and relation to air mass origin, Atmos. Chem. Phys., 7, 5785–5802, https://doi.org/10.5194/acp-7-5785-2007, 2007. a
Forster, P., Ramaswamy, V., Artaxo, P., Berntsen, T., Betts, R., Fahey, D. W., Haywood, J., Lean, J., Lowe, D. C., Myhre, G., Nganga, J., Prinn, R., Raga, G., Schulz, M., and Van Dorland, R.: Changes in Atmospheric Constituents and in Radiative Forcing, in: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., and Miller, H. L., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, ISBN 9780521880091, 2007. a
Fountoukis, C. and Nenes, A.: Continued development of a cloud droplet formation parameterization for global climate models, J. Geophys. Res.-Atmos., 110, https://doi.org/10.1029/2004JD005591, 2005. a
Gelaro, R., McCarty, W., Suárez, M. J., Todling, R., Molod, A., Takacs, L., Randles, C. A., Darmenov, A., Bosilovich, M. G., Reichle, R., Wargan, K., Coy, L., Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A., da Silva, A. M., Gu, W., Kim, G.-K., Koster, R., Lucchesi, R., Merkova, D., Nielsen, J. E., Partyka, G., Pawson, S., Putman, W., Rienecker, M., Schubert, S. D., Sienkiewicz, M., and Zhao, B.: The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2), J. Climate, 30, 5419–5454, https://doi.org/10.1175/JCLI-D-16-0758.1, 2017. a, b, c
Ginoux, P., Chin, M., Tegen, I., Prospero, J. M., Holben, B., Dubovik, O., and Lin, S.-J.: Sources and distributions of dust aerosols simulated with the GOCART model, J. Geophys. Res.-Atmos., 106, 20255–20273, https://doi.org/10.1029/2000JD000053, 2001. a
GMAO: MERRA-2 inst3_3d_asm_Nv: 3d,3-Hourly,Instantaneous,Model-Level,Assimilation,Assimilated Meteorological Fields V5.12.4, Goddard Earth Sciences Data and Information Services Center (GES DISC) [data set], https://doi.org/10.5067/WWQSXQ8IVFW8, 2015. a
GMAO: GiOcean Coupled Reanalysis, GMAO [data set], https://portal.nccs.nasa.gov/datashare/gmao/GiOCEAN/ (last access: 23 March 2026), 2025. a
Gong, X., Wex, H., Müller, T., Henning, S., Voigtländer, J., Wiedensohler, A., and Stratmann, F.: Understanding aerosol microphysical properties from 10 years of data collected at Cabo Verde based on an unsupervised machine learning classification, Atmos. Chem. Phys., 22, 5175–5194, https://doi.org/10.5194/acp-22-5175-2022, 2022. a
Gruening, C., Adam, M., Cavalli, F., Cavalli, P., Dell’Acqua, A., Martins Dos Santos, S., Pagliari, V., Roux, D., and Putaud, J.: JRC Ispra EMEP–GAW Regional Station for Atmos. Res, Tech. Rep. JRC55382, European Commission, https://publications.jrc.ec.europa.eu/repository/handle/JRC55382 (last access: 23 March 2026), 2009. a
Gueymard, C. A. and Yang, D.: Worldwide validation of CAMS and MERRA-2 reanalysis aerosol optical depth products using 15 years of AERONET observations, Atmos. Environ., 225, 117216, https://doi.org/10.1016/j.atmosenv.2019.117216, 2020. a
Harder, P., Watson-Parris, D., Stier, P., Strassel, D., Gauger, N. R., and Keuper, J.: Physics-Informed Learning of Aerosol Microphysics, arXiv [preprint], https://doi.org/10.48550/arXiv.2207.11786, 24 July 2022. a, b
Hari, P., Nikinmaa, E., Pohja, T., Siivola, E., Bäck, J., Vesala, T., and Kulmala, M.: Station for measuring ecosystem-atmosphere relations: SMEAR, in: Physical and physiological forest ecology, Springer Nature, 471–487, https://doi.org/10.1007/978-94-007-5603-8_9, 2013. a
Inness, A., Ades, M., Agustí-Panareda, A., Barré, J., Benedictow, A., Blechschmidt, A.-M., Dominguez, J. J., Engelen, R., Eskes, H., Flemming, J., Huijnen, V., Jones, L., Kipling, Z., Massart, S., Parrington, M., Peuch, V.-H., Razinger, M., Remy, S., Schulz, M., and Suttie, M.: The CAMS reanalysis of atmospheric composition, Atmos. Chem. Phys., 19, 3515–3556, https://doi.org/10.5194/acp-19-3515-2019, 2019. a, b, c
Japkowicz, N. and Stephen, S.: The class imbalance problem: A systematic study, Intell. Data Anal., 6, 429–449, https://doi.org/10.3233/IDA-2002-6504, 2002. a
Jeggle, K., Neubauer, D., Camps-Valls, G., and Lohmann, U.: Understanding cirrus clouds using explainable machine learning, Environmental Data Science, 2, e19, https://doi.org/10.1017/eds.2023.14, 2023. a
Jennings, S., O'Dowd, C., O'Connor, T., and McGovern, F.: Physical characteristics of the ambient aerosol at Mace Head, Atmos. Environ. A Gen., 25, 557–562, https://doi.org/10.1016/0960-1686(91)90052-9, 1991. a
Jia, Y., Andersen, H., and Cermak, J.: Analysis of the cloud fraction adjustment to aerosols and its dependence on meteorological controls using explainable machine learning, Atmos. Chem. Phys., 24, 13025–13045, https://doi.org/10.5194/acp-24-13025-2024, 2024. a
Jones, A., Roberts, D., and Slingo, A.: A climate model study of indirect radiative forcing by anthropogenic sulphate aerosols, Nature, 370, 450–453, https://doi.org/10.1038/370450a0, 1994. a
Jurányi, Z., Gysel, M., Weingartner, E., Bukowiecki, N., Kammermann, L., and Baltensperger, U.: A 17 month climatology of the cloud condensation nuclei number concentration at the high alpine site Jungfraujoch, J. Geophys. Res.-Atmos., 116, https://doi.org/10.1029/2010JD015199, 2011. a
Kingma, D. P. and Ba, J.: Adam: A method for stochastic optimization, arXiv [preprint], https://doi.org/10.48550/arXiv.1412.6980, 22 December 2014. a
Kirpes, R. M., Bondy, A. L., Bonanno, D., Moffet, R. C., Wang, B., Laskin, A., Ault, A. P., and Pratt, K. A.: Secondary sulfate is internally mixed with sea spray aerosol and organic aerosol in the winter Arctic, Atmos. Chem. Phys., 18, 3937–3949, https://doi.org/10.5194/acp-18-3937-2018, 2018. a
Kiss, G., Varga, B., Galambos, I., and Ganszky, I.: Characterization of water-soluble organic matter isolated from atmospheric fine aerosol, J. Geophys. Res.-Atmos., 107, https://doi.org/10.1029/2001JD000603, 2002. a
Kreidenweis, S. M., Koehler, K., DeMott, P. J., Prenni, A. J., Carrico, C., and Ervens, B.: Water activity and activation diameters from hygroscopicity data - Part I: Theory and application to inorganic salts, Atmos. Chem. Phys., 5, 1357–1370, https://doi.org/10.5194/acp-5-1357-2005, 2005. a
Kristensson, A., Dal Maso, M., Swietlicki, E., Hussein, T., Zhou, J., Kerminen, V.-M., and Kulmala, M.: Characterization of new particle formation events at a background site in Southern Sweden: relation to air mass history, Tellus B, 60, 330–344, https://doi.org/10.1111/j.1600-0889.2008.00345.x, 2008. a
Kwon, Y., An, S. A., Song, H.-J., and Sung, K.: Particulate Matter Prediction and Shapley Value Interpretation in Korea through a Deep Learning Model, SOLA, 19, 225–231, https://doi.org/10.2151/sola.2023-029, 2023. a
Langner, J. and Rodhe, H.: A global three-dimensional model of the tropospheric sulfur cycle, J. Atmos. Chem., 13, 225–263, https://doi.org/10.1007/BF00058134, 1991. a
Lee, L. A., Pringle, K. J., Reddington, C. L., Mann, G. W., Stier, P., Spracklen, D. V., Pierce, J. R., and Carslaw, K. S.: The magnitude and causes of uncertainty in global model simulations of cloud condensation nuclei, Atmos. Chem. Phys., 13, 8879–8914, https://doi.org/10.5194/acp-13-8879-2013, 2013. a
Lihavainen, H., Kerminen, V.-M., Komppula, M., Hyvärinen, A.-P., Laakia, J., Saarikoski, S., Makkonen, U., Kivekäs, N., Hillamo, R., Kulmala, M., and Viisanen, Y.: Measurements of the relation between aerosol properties and microphysics and chemistry of low level liquid water clouds in Northern Finland, Atmos. Chem. Phys., 8, 6925–6938, https://doi.org/10.5194/acp-8-6925-2008, 2008. a
Liu, X., Easter, R. C., Ghan, S. J., Zaveri, R., Rasch, P., Shi, X., Lamarque, J.-F., Gettelman, A., Morrison, H., Vitt, F., Conley, A., Park, S., Neale, R., Hannay, C., Ekman, A. M. L., Hess, P., Mahowald, N., Collins, W., Iacono, M. J., Bretherton, C. S., Flanner, M. G., and Mitchell, D.: Toward a minimal representation of aerosols in climate models: description and evaluation in the Community Atmosphere Model CAM5, Geosci. Model Dev., 5, 709–739, https://doi.org/10.5194/gmd-5-709-2012, 2012. a, b, c, d
Lundberg, S. M. and Lee, S.-I.: A unified approach to interpreting model predictions, Advances in neural information processing systems, 30, https://doi.org/10.48550/arXiv.1705.07874, 22 May 2017. a
Lundberg, S. M., Erion, G., Chen, H., DeGrave, A., Prutkin, J. M., Nair, B., Katz, R., Himmelfarb, J., Bansal, N., and Lee, S.-I.: From local explanations to global understanding with explainable AI for trees, Nature Machine Intelligence, 2, 56–67, https://doi.org/10.1038/s42256-019-0138-9, 2020. a
Ma, P. L. and Stinis, P.: Developing a simulator-based satellite dataset for using machine learning techniques to derive aerosol-cloud-precipitation interactions in models and observations in a consistent framework, Tech. rep., Pacific Northwest National Laboratory (PNNL), Richland, WA (United States), https://doi.org/10.2172/1984697, 2020. a
Mann, G. W., Carslaw, K. S., Spracklen, D. V., Ridley, D. A., Manktelow, P. T., Chipperfield, M. P., Pickering, S. J., and Johnson, C. E.: Description and evaluation of GLOMAP-mode: a modal global aerosol microphysics model for the UKCA composition-climate model, Geosci. Model Dev., 3, 519–551, https://doi.org/10.5194/gmd-3-519-2010, 2010. a
Marinoni, A., Cristofanelli, P., Calzolari, F., Roccato, F., Bonafè, U., and Bonasoni, P.: Continuous measurements of aerosol physical parameters at the Mt. Cimone GAW Station (2165 m asl, Italy), Sci. Total Environ., 391, 241–251, https://doi.org/10.1016/j.scitotenv.2007.10.004, 2008. a
McCoy, D., Bender, F.-M., Mohrmann, J., Hartmann, D., Wood, R., and Grosvenor, D.: The global aerosol-cloud first indirect effect estimated using MODIS, MERRA, and AeroCom, J. Geophys. Res.-Atmos., 122, 1779–1796, https://doi.org/10.1002/2016JD026141, 2017. a
Mihalopoulos, N., Stephanou, E., Kanakidou, M., Pilitsidis, S., and Bousquet, P.: Tropospheric aerosol ionic composition in the Eastern Mediterranean region, Tellus B, 49, 314–326, https://doi.org/10.3402/tellusb.v49i3.15970, 1997. a
Molod, A., Takacs, L., Suarez, M., and Bacmeister, J.: Development of the GEOS-5 atmospheric general circulation model: evolution from MERRA to MERRA2, Geosci. Model Dev., 8, 1339–1356, https://doi.org/10.5194/gmd-8-1339-2015, 2015. a
Molod, A., Hackert, E., Vikhliaev, Y., Zhao, B., Barahona, D., Vernieres, G., Borovikov, A., Kovach, R. M., Marshak, J., Schubert, S., Li, Z., Lim, Y.-K., Andrews, L. C., Cullather, R., Koster, R., Achuthavarier, D., Carton, J., Coy, L., Friere, J. L. M., Longo, K. M., Nakada, K., and Pawson, S.: GEOS-S2S version 2: The GMAO high-resolution coupled model and assimilation system for seasonal prediction, J. Geophys. Res.-Atmos., 125, e2019JD031767, https://doi.org/10.1029/2019JD031767, 2020. a, b
Nair, A. A., Yu, F., Campuzano-Jost, P., DeMott, P. J., Levin, E. J. T., Jimenez, J. L., Peischl, J., Pollack, I. B., Fredrickson, C. D., Beyersdorf, A. J., Nault, B. A., Park, M., Yum, S. S., Palm, B. B., Xu, L., Bourgeois, I., Anderson, B. E., Nenes, A., Ziemba, L. D., Moore, R. H., Lee, T., Park, T., Thompson, C. R., Flocke, F., Huey, L. G., Kim, M. J., and Peng, Q.: Machine Learning Uncovers Aerosol Size Information From Chemistry and Meteorology to Quantify Potential Cloud-Forming Particles, Geophys. Res. Lett., 48, e2021GL094133, https://doi.org/10.1029/2021GL094133, 2021. a
NCAR: NCAR Command Language (Version 6.6.2), UCAR/NCAR/CISL/TDD [software], https://doi.org/10.5065/D6WD3XH5, 2019. a
Nojarov, P., Ivanov, P., Kalapov, I., Penev, I., and Drenska, M.: Connection between ozone concentration and atmosphere circulation at peak Moussala, Theor. Appl. Climatol., 98, 201–208, https://doi.org/10.1007/s00704-009-0173-2, 2009. a
O'Malley, T., Bursztein, E., Long, J., Chollet, F., Jin, H., and Invernizzi, L.: Keras Tuner, https://github.com/keras-team/keras-tuner (last access: 23 March 2026), 2019. a
Ott, J., Pritchard, M., Best, N., Linstead, E., Curcic, M., and Baldi, P.: A Fortran-Keras deep learning bridge for scientific computing, Scientific Programming, 2020, https://doi.org/10.1155/2020/8888811, 2020. a
Philippin, S., Laj, P., Putaud, J.-P., Wiedensohler, A., Leeuw, G. D., Fjaeraa, A. M., Platt, U., Baltensperger, U., and Fiebig, M.: EUSAAR-An unprecedented network of aerosol observation in Europe, Journal of Aerosol Research (Earozoru Kenkyu), 24, 78–83, https://doi.org/10.11203/jar.24.78, 2009. a
Pierce, J. R., Croft, B., Kodros, J. K., D'Andrea, S. D., and Martin, R. V.: The importance of interstitial particle scavenging by cloud droplets in shaping the remote aerosol size distribution and global aerosol-climate effects, Atmos. Chem. Phys., 15, 6147–6158, https://doi.org/10.5194/acp-15-6147-2015, 2015. a
Randles, C. A., da Silva, A. M., Buchard, V., Colarco, P. R., Darmenov, A., Govindaraju, R., Smirnov, A., Holben, B., Ferrare, R., Hair, J., Shinozuka, Y., and Flynn, C. J.: The MERRA-2 Aerosol Reanalysis, 1980 Onward. Part I: System Description and Data Assimilation Evaluation, J. Climate, 30, 6823–6850, https://doi.org/10.1175/JCLI-D-16-0609.1, 2017. a, b, c, d, e
Rasp, S., Pritchard, M. S., and Gentine, P.: Deep learning to represent subgrid processes in climate models, P. Natl. Acad. Sci. USA, 115, 9684–9689, https://doi.org/10.1073/pnas.1810286115, 2018. a, b
Reddington, C., Carslaw, K., Stier, P., Schutgens, N., Coe, H., Liu, D., Allan, J., Pringle, K., Lee, L., Yoshioka, M., Johnson, J. S., Regayre, L. A., Spracklen, D. V., Mann, G. W., Clarke, A., Hermann, M., Henning, S., Wex, H., Kristensen, T. B., Leaitch, W. R., Pöschl, U., Rose, D., Andreae, M. O., Schmale, J., Kondo, Y., Oshima, N., Schwarz, J. P., Nenes, A., Anderson, B., Roberts, G. C., Snider, J. R., Leck, C., Quinn, P. K., Chi, X., Ding, A., Jimenez, J. L., and Zhang, Q.: The Global Aerosol Synthesis and Science Project (GASSP): measurements and modeling to reduce uncertainty, B. Am. Meteorol. Soc., 98, 1857–1877, https://doi.org/10.1175/BAMS-D-15-00317.1, 2017. a
Remer, L. A., Kaufman, Y., Tanré, D., Mattoo, S., Chu, D., Martins, J. V., Li, R.-R., Ichoku, C., Levy, R., Kleidman, R., Eck, T. F., Vermote, E., and Holben, B. N.: The MODIS aerosol algorithm, products, and validation, J. Atmos. Sci., 62, 947–973, https://doi.org/10.1175/JAS3385.1, 2005. a, b
Reynolds, R. W., Rayner, N. A., Smith, T. M., Stokes, D. C., and Wang, W.: An improved in situ and satellite SST analysis for climate, J. Climate, 15, 1609–1625, https://doi.org/10.1175/1520-0442(2002)015<1609:AIISAS>2.0.CO;2, 2002. a
Riemer, N., Ault, A., West, M., Craig, R., and Curtis, J.: Aerosol mixing state: Measurements, modeling, and impacts, Rev. Geophys., 57, 187–249, https://doi.org/10.1029/2018RG000615, 2019. a, b, c, d
Rienecker, M., Suarez, M., Todling, R., Bacmeister, J., Takacs, L., Liu, H.-C., Gu, W., Sienkiewicz, M., Koster, R., Gelaro, R., Stajner, I., and Nielsen, J.: The GEOS-5 Data Assimilation System – Documentation of Versions 5.0.1, 5.1.0, and 5.2.0., vol. 27 of Technical Report Series on Global Modeling and Data Assimilation, NASA Goddard Space Flight Center, Greenbelt, MD, USA, https://ntrs.nasa.gov/citations/20120011955 (last access: 23 March 2026), 2008. a
Russchenberg, H., Bosveld, F., Swart, D., ten Brink, H., de Leeuw, G., Uijlenhoet, R., Arbesser-Rastburg, B., van der Marel, H., Ligthart, L., Boers, R., and Apituley, A.: Ground-based atmospheric remote sensing in the Netherlands: European outlook, IEICE T. Commun., 88, 2252–2258, https://doi.org/10.1093/ietcom/e88-b.6.2252, 2005. a
Seinfeld, J. H., Bretherton, C., Carslaw, K. S., Coe, H., DeMott, P. J., Dunlea, E. J., Feingold, G., Ghan, S., Guenther, A. B., Kahn, R., Kraucunas, I., Kreidenweis, S. M., Molina, M. J., Nenes, A., Penner, J. E., Prather, K. A., Ramanathan, V., Ramaswamy, V., Rasch, P. J., Ravishankara, A. R., Rosenfeld, D., Stephens, G., and Wood, R.: Improving our fundamental understanding of the role of aerosol- cloud interactions in the climate system, P. Natl. Acad. Sci. USA, 113, 5781–5790, https://doi.org/10.1073/pnas.1514043113, 2016. a, b
Silva, S. J., Ma, P.-L., Hardin, J. C., and Rothenberg, D.: Physically regularized machine learning emulators of aerosol activation , Geosci. Model Dev., 14, 3067–3077, https://doi.org/10.5194/gmd-14-3067-2021, 2021. a
Stier, P., Feichter, J., Kinne, S., Kloster, S., Vignati, E., Wilson, J., Ganzeveld, L., Tegen, I., Werner, M., Balkanski, Y., Schulz, M., Boucher, O., Minikin, A., and Petzold, A.: The aerosol-climate model ECHAM5-HAM, Atmos. Chem. Phys., 5, 1125–1156, https://doi.org/10.5194/acp-5-1125-2005, 2005. a
Stier, P., van den Heever, S. C., Christensen, M. W., Gryspeerdt, E., Dagan, G., Saleeby, S. M., Bollasina, M., Donner, L., Emanuel, K., Ekman, A. M., Feingold, G., Field, P., Forster, P., Haywood, J., Kahn, R., Koren, I., Kummerow, C., L’Ecuyer, T., Lohmann, U., Ming, Y., Myhre, G., Quaas, J., Rosenfeld, D., Samset, B., Seifert, A., Stephens, G., and Tao, W. K.: Multifaceted aerosol effects on precipitation, Nat. Geosci., 17, 719–732, https://doi.org/10.1038/s41561-024-01482-6, 2024. a
Ström, J., Umegård, J., Tørseth, K., Tunved, P., Hansson, H.-C., Holmén, K., Wismann, V., Herber, A., and König-Langlo, G.: One year of particle size distribution and aerosol chemical composition measurements at the Zeppelin Station, Svalbard, March 2000–March 2001, Phys. Chem. Earth Pt. A/B/C, 28, 1181–1190, https://doi.org/10.1016/j.pce.2003.08.058, 2003. a
Su, X., Huang, Y., Wang, L., Cao, M., and Feng, L.: Validation and diurnal variation evaluation of MERRA-2 multiple aerosol properties on a global scale, Atmos. Environ., 311, 120019, https://doi.org/10.1016/j.atmosenv.2023.120019, 2023. a
Sun, E., Che, H., Xu, X., Wang, Z., Lu, C., Gui, K., Zhao, H., Zheng, Y., Wang, Y., Wang, H., Sun, T., Liang, Y., Li, X., Sheng, Z., An, L., Zhang, X., and Shi, G.: Variation in MERRA-2 aerosol optical depth over the Yangtze River Delta from 1980 to 2016, Theor. Appl. Climatol., 136, 363–375, https://doi.org/10.1007/s00704-018-2490-9, 2019. a
Takacs, L. L., Suárez, M. J., and Todling, R.: The stability of incremental analysis update, Mon. Weather Rev., 146, 3259–3275, https://doi.org/10.1175/MWR-D-18-0117.1, 2018. a
Tunved, P., Ström, J., and Hansson, H.-C.: An investigation of processes controlling the evolution of the boundary layer aerosol size distribution properties at the Swedish background station Aspvreten, Atmos. Chem. Phys., 4, 2581–2592, https://doi.org/10.5194/acp-4-2581-2004, 2004. a
Ukhov, A., Mostamandi, S., da Silva, A., Flemming, J., Alshehri, Y., Shevchenko, I., and Stenchikov, G.: Assessment of natural and anthropogenic aerosol air pollution in the Middle East using MERRA-2, CAMS data assimilation products, and high-resolution WRF-Chem model simulations, Atmos. Chem. Phys., 20, 9281–9310, https://doi.org/10.5194/acp-20-9281-2020, 2020. a
Ulevicius, V., Byčenkienė, S., Remeikis, V., Garbaras, A., Kecorius, S., Andriejauskienė, J., Jasinevičienė, D., and Mocnik, G.: Characterization of pollution events in the East Baltic region affected by regional biomass fire emissions, Atmos. Res., 98, 190–200, https://doi.org/10.1016/j.atmosres.2010.03.021, 2010. a
Uno, I., Eguchi, K., Yumimoto, K., Takemura, T., Shimizu, A., Uematsu, M., Liu, Z., Wang, Z., Hara, Y., and Sugimoto, N.: Asian dust transported one full circuit around the globe, Nat. Geosci., 2, 557–560, https://doi.org/10.1038/ngeo583, 2009. a
Venzac, H., Sellegri, K., Villani, P., Picard, D., and Laj, P.: Seasonal variation of aerosol size distributions in the free troposphere and residual layer at the puy de Dôme station, France, Atmos. Chem. Phys., 9, 1465–1478, https://doi.org/10.5194/acp-9-1465-2009, 2009. a
Virtanen, A., Joutsensaari, J., Kokkola, H., Partridge, D. G., Blichner, S., Seland, Ø., Holopainen, E., Tovazzi, E., Lipponen, A., Mikkonen, S., Leskinen, A., Hyvärinen, A.-P., Zieger, P., Krejci, R., Ekman, A. M. L., Riipinen, I., Quaas, J., and Romakkaniemi, S.: High sensitivity of cloud formation to aerosol changes, Nat. Geosci., https://doi.org/10.1038/s41561-025-01662-y, 2025. a
Watson-Parris, D., Schutgens, N., Reddington, C., Pringle, K. J., Liu, D., Allan, J. D., Coe, H., Carslaw, K. S., and Stier, P.: In situ constraints on the vertical distribution of global aerosol, Atmos. Chem. Phys., 19, 11765–11790, https://doi.org/10.5194/acp-19-11765-2019, 2019. a, b, c
Whitby, E. R. and McMurry, P. H.: Modal aerosol dynamics modeling, Aerosol Sci. Tech., 27, 673–688, https://doi.org/10.1080/02786829708965504, 1997. a
Wilson, J., Cuvelier, C., and Raes, F.: A modeling study of global mixed aerosol fields, J. Geophys. Res.-Atmos., 106, 34081–34108, https://doi.org/10.1029/2000JD000198, 2001. a
Winter, E.: The shapley value, Handbook of Game Theory with Economic Applications, 3, 2025–2054, https://doi.org/10.1016/S1574-0005(02)03016-3, 2002. a
Yu, S., Ma, P.-L., Singh, B., Silva, S., and Pritchard, M.: Two-step hyperparameter optimization method: Accelerating hyperparameter search by using a fraction of a training dataset, Artificial Intelligence for the Earth Systems, 3, e230013, https://doi.org/10.1175/AIES-D-23-0013.1, 2024. a
Zhang, H., Sharma, G., Dhawan, S., Dhanraj, D., Li, Z., and Biswas, P.: Comparison of discrete, discrete-sectional, modal and moment models for aerosol dynamics simulations, Aerosol Sci. Tech., 54, 739–760, https://doi.org/10.1080/02786826.2020.1723787, 2020. a
Zhou, C., Shen, X., Liu, Z., Zhang, Y., and Xin, J.: Simulating aerosol size distribution and mass concentration with simultaneous nucleation, condensation/coagulation, and deposition with the GRAPES–CUACE, Journal of Meteorological Research, 32, 265–278, https://doi.org/10.1007/s13351-018-7116-8, 2018. a
Zhu, H., Martin, R. V., Croft, B., Zhai, S., Li, C., Bindle, L., Pierce, J. R., Chang, R. Y.-W., Anderson, B. E., Ziemba, L. D., Hair, J. W., Ferrare, R. A., Hostetler, C. A., Singh, I., Chatterjee, D., Jimenez, J. L., Campuzano-Jost, P., Nault, B. A., Dibb, J. E., Schwarz, J. S., and Weinheimer, A.: Parameterization of size of organic and secondary inorganic aerosol for efficient representation of global aerosol optical properties, Atmos. Chem. Phys., 23, 5023–5042, https://doi.org/10.5194/acp-23-5023-2023, 2023. a
Short summary
Particulate matter impacts Earth's radiation, clouds, and human health, but modeling their size is challenging due to computational and observational limits. We developed a machine learning model to predict aerosol size distributions, which accurately replicates advanced models and field measurements.
Particulate matter impacts Earth's radiation, clouds, and human health, but modeling their size...