Atmos. Meas. Tech., 9, 1113–1133, https://doi.org/10.5194/amt-9-1113-2016, 2016.

GRASP Open repository: https://access-request.grasp-cloud.com/service/gitlab, last access: 14 August 2022.

Guerrero-Rascado, J. L., Landulfo, E., Antuña, J. C., de Melo Jorge Barbosa, H., Barja, B., Bastidas, Á. E., Bedoya, A. E., da Costa, R. F., Estevan, R., Forno, R., Gouveia, D. A., Jiménez, C., Larroza, E. G., da Silva Lopes, F. J., Montilla-Rosero, E., de Aruda Moreira, G., Nakaema, W. M., Nisperuza, D., Alegria, D., Múnera, M., Otero, L., Papandrea, S., Pallota, J. V., Pawelko, E., Quel, E. J., Ristori, P., Rodrigues, P. F., Salvador, J., Sánchez, M. F., and Silva, A.: Latin American Lidar Network (LALINET) for aerosol research: Diagnosis on network instrumentation, J. Atmos. Sol.-Terr. Phys., 138, 112–120, 2016.

Herreras, M., Román, R., Cazorla, A., Toledano, C., Lyamani, H., Torres, B., Cachorro, V., Olmo, F., Alados-Arboledas, L., and de Frutos, A.: Evaluation of retrieved aerosol extinction profiles using as reference the aerosol optical depth differences between various heights, Atmos. Res., 230, 104625, https://doi.org/10.1016/j.atmosres.2019.104625, 2019.

Holben, B. N., Eck, T. F., Slutsker, I. A., Tanre, D., Buis, J., Setzer, A., Vermote, E., Reagan, J. A., Kaufman, Y., Nakajima, T., Lavenu, F., Jankowiak, I., and Smirnov, A.: AERONET – A federated instrument network and data archive for aerosol characterization, Remote Sens. Environ., 66, 1–16, https://doi.org/10.1016/s0034-4257(98)00031-5, 1998.

Holben, B. N., Eck, T., Slutsker, I., Smirnov, A., Sinyuk, A., Schafer, J., Giles, D., and Dubovik, O.: AERONET’s version 2.0 quality assurance criteria, in: Remote Sensing of the Atmosphere and Clouds, International Society for Optics and Photonics, Proc. SPIE 6408, 64080Q, https://doi.org/10.1117/12.706524, 2006.

Hu, Q., Goloub, P., Veselovskii, I., Bravo-Aranda, J.-A., Popovici, I. E., Podvin, T., Haeffelin, M., Lopatin, A., Dubovik, O., Pietras, C., Huang, X., Torres, B., and Chen, C.: Long-range-transported Canadian smoke plumes in the lower stratosphere over northern France, Atmos. Chem. Phys., 19, 1173–1193, https://doi.org/10.5194/acp-19-1173-2019, 2019.

IPCC: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Masson-Delmotte, V., Zhai, P., Pirani, A., Connors, S. L., Péan, C., Berger, S., Caud, N., Chen, Y., Goldfarb, L., Gomis, M. I., Huang, M., Leitzell, K., Lonnoy, E., Matthews, J. B. R., Maycock, T. K., Waterfield, T., Yelekçi, O., Yu, R., and Zhou, B., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, in press, 2021.

Kaufman, Y. J., Tanre, D., Holben, B., Mattoo, S., Remer, L., Eck, T., Vaughan, J., and Chatenet, B.: Aerosol radiative impact on spectral solar flux at the surface, derived from principal-plane sky measurements, J. Atmos. Sci., 59, 635–646, 2002.

Li, L., Dubovik, O., Derimian, Y., Schuster, G. L., Lapyonok, T., Litvinov, P., Ducos, F., Fuertes, D., Chen, C., Li, Z., Lopatin, A., Torres, B., and Che, H.: Retrieval of aerosol components directly from satellite and ground-based measurements, Atmos. Chem. Phys., 19, 13409–13443, https://doi.org/10.5194/acp-19-13409-2019, 2019.

Li, Z., Goloub, P., Dubovik, O., Blarel, L., Zhang, W., Podvin, T., Sinyuk, A., Sorokin, M., Chen, H., Holben, B., Tanré, D., Canini, M., and Buis, J.-P.: Improvements for ground-based re-

mote sensing of atmospheric aerosol properties by additional polarimetric measurements, J. Quant. Spectrosc. Ra., 110, 1954–1961, https://doi.org/10.1016/j.jqsrt.2009.04.009, 2009.

Lopatin, A., Dubovik, O., Chaikovsky, A., Goloub, P., Lapyonok, T., Tanré, D., and Litvinov, P.: Enhancement of aerosol characterization using synergy of lidar and sun-photometer coincident observations: the GARRLiC algorithm, Atmos. Meas. Tech., 6, 2065–2088, https://doi.org/10.5194/amt-6-2065-2013, 2013.

Lopatin, A., Dubovik, O., Fuertes, D., Stenchikov, G., Lapyonok, T., Veselovskii, I., Wienhold, F. G., Shevchenko, I., Hu, Q., and Parajuli, S.: Synergy processing of diverse ground-based remote sensing and in situ data using the GRASP algorithm: applications to radiometer, lidar and radiosonde observations, Atmos. Meas. Tech., 14, 2575–2614, https://doi.org/10.5194/amt-14-2575-2021, 2021.

Nakajima, T., Tonna, G., Rao, R., Boi, P., Kaufman, Y., and Holben, B.: Use of sky brightness measurements from ground for remote sensing of particulate polydispersions, Appl. Optics, 35, 2672–2686, https://doi.org/10.1364/AO.35.002672, 1996.

Nakajima, T., Campanelli, M., Che, H., Estellés, V., Irie, H., Kim, S.-W., Kim, J., Liu, D., Nishizawa, T., Pandithurai, G., Soni, V. K., Thana, B., Tugjsurn, N.-U., Aoki, K., Go, S., Hashimoto, M., Higurashi, A., Kazadzis, S., Khatri, P., Kouremeti, N., Kudo, R., Marengo, F., Momoi, M., Ningombam, S. S., Ryder, C. L., Uchiyama, A., and Yamazaki, A.: An overview of and issues with sky radiometer technology and SKYNET, Atmos. Meas. Tech., 13, 4195–4218, https://doi.org/10.5194/amt-13-4195-2020, 2020.

NASA: AERONET data access, https://aeronet.gsfc.nasa.gov/, last access: 14 August 2022.

Ortega, J. M. and Rheinboldt, W. C.: Iterative solution of nonlinear equations in several variables, SIAM, https://doi.org/10.1137/1.9780898719468, 1970.

Phillips, D. L.: A technique for the numerical solution of certain integral equations of the first kind, J. ACM, 9, 84–97, https://doi.org/10.1145/321105.321114, 1962.

Press, W. H., Teukolsky, S. A., Flannery, B. P., and Vetterling, W. T.: Numerical recipes in Fortran 77: The art of scientific computing, Cambridge university press, Fortran numerical recipes, Vol. 1, ISBN 052143064X, 1992.

Puthukkudy, A., Martins, J. V., Remer, L. A., Xu, X., Dubovik, O., Litvinov, P., McBride, B., Burton, S., and Barbosa, H. M. J.: Retrieval of aerosol properties from Airborne HyperAngular Rainbow Polarimeter (AirHARP) observations during ACEPOL 2017, Atmos. Meas. Tech., 13, 5207–5236, https://doi.org/10.5194/amt-13-5207-2020, 2020.

Rodgers, C. D.: Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation, Rev. Geophys., 14, 609–624, https://doi.org/10.1029/rg014i004p00609, 1976.

Rodgers, C. D.: Characterization and error analysis of profiles retrieved from remote sounding measurements, J. Geophys. Res.-Atmos., 95, 5587–5595, https://doi.org/10.1029/jd095id05p05587, 1990.

Rodgers, C. D.: Inverse methods for atmospheric sounding: theory and practice, Vol. 2, World Scientific, ISBN 981-02-2740-X, 2000.

Rolph, G., Stein, A., and Stunder, B.: Real-time environmental applications and display system: READY, Environ. Modell. Softw.,
95, 210–228, https://doi.org/10.1016/j.envsoft.2017.06.025, 2017.

Román, R., Cazorla, A., Toledano, C., Olmo, F., Cachorro, V., de Frutos, A., and Alados-Arboledas, L.: Cloud cover detection combining high dynamic range sky images and ceilometer measurements, Atmos. Res., 196, 224–236, https://doi.org/10.1016/j.rse.2017.05.013, 2017.

Román, R., Torres, B., Fuertes, D., Cachorro, V. E., Dubovik, O., Toledano, C., Cazorla, A., Barreto, A., Bosch, J. L., Lapyonok, T., González, R., Goloub, P., Perrone, M. R., Olmo, F. J., de Frutos, A., and Alados-Arboledas, L.: Retrieval of aerosol profiles combining sunphotometer and ceilometer measurements in GRASP code, Atmos. Res., 204, 161–177, https://doi.org/10.1016/j.atmosres.2018.01.021, 2018.

Sayer, A. M., Govaerts, Y., Kolmonen, P., Lipponen, A., Luf farelli, M., Mielonen, T., Patadia, F., Popp, T., Povey, A. C., Stebel, K., and Witek, M. L.: A review and framework for the evaluation of pixel-level uncertainty estimates in satellite aerosol remote sensing, Atmos. Meas. Tech., 13, 373–404, https://doi.org/10.5194/amt-13-373-2020, 2020.

Schuster, G. L., Espinosa, W. R., Ziemba, L. D., Beyersdorf, A. J., Rocha-Lima, A., Anderson, B. E., Martins, J. V., Dubovik, O., Ducos, F., Fuertes, D., Lapyonok, T., Shook, M., Derimian, Y., and Moore, R. H.: A laboratory experiment for the Statistical Evaluation of Aerosol Retrieval (STEAR) algorithms, Remote Sens., 11, 498, https://doi.org/10.3390/rs11050498, 2019.

Sinyuk, A., Holben, B. N., Eck, T. F., Giles, D. M., Slutsker, I., Korkin, S., Schafer, J. S., Smirnov, A., Sorokin, M., and Lyapustin, A.: The AERONET Version 3 aerosol retrieval algorithm, associated uncertainties and comparisons to Version 2, Atmos. Meas. Tech., 13, 3375–3411, https://doi.org/10.5194/amt-13-3375-2020, 2020.

Stein, A. F., Draxler, R. R., Rolph, G. D., Stunder, B. J., Cohen, M. D., and Ngan, F.: NOAA's HYSPLIT atmospheric transport and dispersion modeling system, B. Am. Meteorol. Soc., 96, 2059–2077, https://doi.org/10.1175/BAMS-D-14-00110.1, 2015.

Tikhonov, A. N.: On the solution of ill-posed problems and the method of regularization, Russian Academy of Sciences, Doklady Akademii Nauk, 151, 501–504, 1963.

Titos, G., Ealo, M., Román, R., Cazorla, A., Sola, Y., Dubovik, O., Alastuey, A., and Pandolfi, M.: Retrieval of aerosol properties from ceilometer and photometer measurements: long-term evaluation with in situ data and statistical analysis at Montsec (southern Pyrenees), Atmos. Meas. Tech., 12, 3255–3267, https://doi.org/10.5194/amt-12-3255-2019, 2019.

Torres, B. and Fuertes, D.: Characterization of aerosol size properties from measurements of spectral optical depth: a global validation of the GRASP-AOD code using long-term AERONET data, Atmos. Meas. Tech., 14, 4471–4506, https://doi.org/10.5194/amt-14-4471-2021, 2021.

Torres, B., Dubovik, O., Toledano, C., Berjon, A., Cachorro, V. E., Lapyonok, T., Litvinov, P., and Goloub, P.: Sensitivity of aerosol retrieval to geometrical configuration of ground-based sun/sky radiometer observations, Atmos. Chem. Phys., 14, 847–875, https://doi.org/10.5194/acp-14-847-2014, 2014.

Torres, B., Dubovik, O., Fuertes, D., Schuster, G., Cachorro, V. E., Lapyonok, T., Goloub, P., Blarel, L., Barreto, A., Mallet, M., Toledano, C., and Tanré, D.: Advanced characterisation of aerosol size properties from measurements of spectral optical depth using the GRASP algorithm, Atmos. Meas. Tech., 10, 3743–3781, https://doi.org/10.5194/amt-10-3743-2017, 2017.

Tsekeri, A., Lopatin, A., Amiridis, V., Marinou, E., Igloffstein, J., Siomos, N., Solomos, S., Kokkalis, P., Engelmann, R., Baars, H., Gratsea, M., Raptis, P. I., Binietoglou, I., Mihalopoulos, N., Kalivitis, N., Kouvarakis, G., Bartsotas, N., Kallos, G., Basart, S., Schuettemeyer, D., Wandinger, U., Ansmann, A., Chaikovsky, A. P., and Dubovik, O.: GARRLiC and LIRIC: strengths and limitations for the characterization of dust and marine particles along with their mixtures, Atmos. Meas. Tech., 10, 4995–5016, https://doi.org/10.5194/amt-10-4995-2017, 2017.

Twomey, S.: On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature, J. ACM, 10, 97–101, https://doi.org/10.1145/321150.321157, 1963.

Twomey, S.: Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions, J. Comput. Phys., 18, 188–200, https://doi.org/10.1016/0021-9991(75)90028-5, 1975.

Twomey, S. (Ed.): Introduction to the mathematics of inversion in remote sensing and indirect measurement, in: Developments in Geomathematics, Amsterdam, Elsevier Scientific Publishing Co., 253 pp., ISBN 0-444-41547-3, 1977.

Volten, H., Munoz, O., Rol, E., De Haan, J., Vassen, W., Hovenier, J., Muinonen, K., and Nousiainen, T.: Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm, J. Geophys. Res.-Atmos., 106, 17375–17401, https://doi.org/10.1029/2001JD900068, 2001.

Xu, X., Wang, J., Zeng, J., Spurr, R., Liu, X., Dubovik, O., Li, L., Li, Z., Mishchenko, M. I., Siniuk, A., et al.: Retrieval of aerosol microphysical properties from AERONET photopolarimetric measurements: 2. A new research algorithm and case demonstration, J. Geophys. Res.-Atmos., 120, 7079–7098, https://doi.org/10.1002/2015JD023113, 2015.