[1] Boucher O, Randall D, Artaxo P et al. Clouds and aerosols[M]. Climate change 2013‒the physical science basis, 571-658(2014).

[2] Haywood J, Boucher O. Estimates of the direct and indirect radiative forcing due to tropospheric aerosols: a review[J]. Reviews of Geophysics, 38, 513-543(2000).

[3] Lohmann U, Feichter J. Global indirect aerosol effects: a review[J]. Atmospheric Chemistry and Physics, 5, 715-737(2005).

[4] Forster P, Storelvmo T, Armour K et al. The earth’s energy budget, climate feedbacks and climate sensitivity[M]. Climate change 2021‒the physical science basis, 923-1054(2023).

[5] Ansmann A, Wandinger U, Riebesell M et al. Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar[J]. Applied Optics, 31, 7113-7131(1992).

[6] Winker D M, Vaughan M A, Omar A et al. Overview of the CALIPSO mission and CALIOP data processing algorithms[J]. Journal of Atmospheric and Oceanic Technology, 26, 2310-2323(2009).

[7] Pappalardo G, Amodeo A, Apituley A et al. EARLINET: towards an advanced sustainable European aerosol lidar network[J]. Atmospheric Measurement Techniques, 7, 2389-2409(2014).

[8] Welton E J, Campbell J R, Spinhirne J D et al. Global monitoring of clouds and aerosols using a network of micropulse lidar systems[J]. Proceedings of SPIE, 4153, 151-158(2001).

[9] Sugimoto N, Shimizu A, Matsui I et al. A method for estimating the fraction of mineral dust in particulate matter using PM2.5-to-PM10 ratios[J]. Particuology, 28, 114-120(2016).

[10] Hansen P C, O’Leary D P. The use of the L-curve in the regularization of discrete ill-posed problems[J]. SIAM Journal on Scientific Computing, 14, 1487-1503(1993).

[11] Engl H W, Hanke M, Neubauer A[M]. Regularization of inverse problems(1996).

[12] Twomey S[M]. Introduction to the mathematics of inversion in remote sensing and indirect measurements(1977).

[13] Doicu A, Trautmann T, Schreier F[M]. Numerical regularization for atmospheric inverse problems(2010).

[14] King M D, Byrne D M, Herman B M et al. Aerosol size distributions obtained by inversion of spectral optical depth measurements[J]. Journal of the Atmospheric Sciences, 35, 2153-2167(1978).

[15] Nakajima T, King M D, Spinhirne J D et al. Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. part II: marine stratocumulus observations[J]. Journal of the Atmospheric Sciences, 48, 728-751(1991).

[16] Tikhonov A N, Arsenin V Y[M]. Solutions of ill-posed problems(1977).

[17] Phillips D L. A technique for the numerical solution of certain integral equations of the first kind[J]. Journal of the ACM, 9, 84-97(1962).

[18] Müller D, Wandinger U, Ansmann A. Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: theory[J]. Applied Optics, 38, 2346-2357(1999).

[19] Müller D, Ansmann A, Wagner F et al. European pollution outbreaks during ACE 2: microphysical particle properties and single-scattering albedo inferred from multiwavelength lidar observations[J]. Journal of Geophysical Research: Atmospheres, 107, AAC3-1(2002).

[20] Müller D, Ansmann A, Mattis I et al. Aerosol-type-dependent lidar ratios observed with Raman lidar[J]. Journal of Geophysical Research: Atmospheres, 112, D16202(2007).

[21] Böckmann C. Hybrid regularization method for the ill-posed inversion of multiwavelength lidar data in the retrieval of aerosol size distributions[J]. Applied Optics, 40, 1329-1342(2001).

[22] Böckmann C, Mironova I, Müller D et al. Microphysical aerosol parameters from multiwavelength lidar[J]. Journal of the Optical Society of America A, 22, 518-528(2005).

[23] Veselovskii I, Kolgotin A, Griaznov V et al. Inversion with regularization for the retrieval of tropospheric aerosol parameters from multiwavelength lidar sounding[J]. Applied Optics, 41, 3685-3699(2002).

[24] Veselovskii I, Kolgotin A, Griaznov V et al. Inversion of multiwavelength Raman lidar data for retrieval of bimodal aerosol size distribution[J]. Applied Optics, 43, 1180-1195(2004).

[25] Veselovskii I, Dubovik O, Kolgotin A et al. Application of randomly oriented spheroids for retrieval of dust particle parameters from multiwavelength lidar measurements[J]. Journal of Geophysical Research: Atmospheres, 115, D21203(2010).

[26] Veselovskii I, Goloub P, Podvin T et al. Retrieval of optical and physical properties of African dust from multiwavelength Raman lidar measurements during the SHADOW campaign in Senegal[J]. Atmospheric Chemistry and Physics, 16, 7013-7028(2016).

[27] Qin R R, Yao W Y, Wang N et al. An algorithm of aerosol extinction coefficient retrieval from dual-wavelength Mie lidar observations[J]. Laser & Optoelectronics Progress, 61, 0501004(2024).

[28] Gao Y C, Li S C, Wei F L et al. New algorithm and analysis of exponential iterative inversion for aerosol lidar[J]. Laser & Optoelectronics Progress, 61, 2301005(2024).

[29] Di H G, Hou X L, Zhao H et al. Detections and analyses of aerosol optical properties under different weather conditions using multi-wavelength Mie lidar[J]. Acta Physica Sinica, 63, 244206(2014).

[30] Osterloh L, Pérez C, Böhme D et al. Parallel software for retrieval of aerosol distribution from LIDAR data in the framework of EARLINET-ASOS[J]. Computer Physics Communications, 180, 2095-2102(2009).

[31] Osterloh L, Böckmann C, Mamouri R E et al. An adaptive base point algorithm for the retrieval of aerosol microphysical properties[J]. The Open Atmospheric Science Journal, 5, 61-73(2011).

[32] Osterloh L, Böckmann C, Nicolae D et al. Regularized inversion of microphysical atmospheric particle parameters: theory and application[J]. Journal of Computational Physics, 237, 79-94(2013).

[33] Müller D, Chemyakin E, Kolgotin A et al. Automated, unsupervised inversion of multiwavelength lidar data with TiARA: assessment of retrieval performance of microphysical parameters using simulated data[J]. Applied Optics, 58, 4981-5008(2019).

[34] Golub G H, Heath M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter[J]. Technometrics, 21, 215-223(1979).

[35] Rodgers C D[M]. Inverse methods for atmospheric sounding: theory and practice(2000).

[36] Dubovik O, King M D. A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements[J]. Journal of Geophysical Research: Atmospheres, 105, 20673-20696(2000).

[37] Burton S P, Ferrare R A, Vaughan M A et al. Aerosol classification from airborne HSRL and comparisons with the CALIPSO vertical feature mask[J]. Atmospheric Measurement Techniques, 6, 1397-1412(2013).

[38] Xu X G, Wang J. Retrieval of aerosol microphysical properties from AERONET photopolarimetric measurements: 1. Information content analysis[J]. Journal of Geophysical Research: Atmospheres, 120, 7059-7078(2015).

[39] Nicolae D, Vasilescu J, Talianu C et al. A neural network aerosol-typing algorithm based on lidar data[J]. Atmospheric Chemistry and Physics, 18, 14511-14537(2018).

[40] Gelman A, Carlin J B, Stern H S et al[M]. Bayesian data analysis(2013).

[41] O’Hagan A, Forster J J[M]. Kendall’s advanced theory of statistics, volume 2B: Bayesian inference(2005).

[42] Bishop C M[M]. Pattern recognition and machine learning(2006).

[43] Evensen G[M]. Data assimilation: the ensemble Kalman filter(2009).

[44] Jackson C, Sen M K, Stoffa P L. An efficient stochastic Bayesian approach to optimal parameter and uncertainty estimation for climate model predictions[J]. Journal of Climate, 17, 2828-2841(2004).

[45] Loew A, Bell W, Brocca L et al. Validation practices for satellite-based Earth observation data across communities[J]. Reviews of Geophysics, 55, 779-817(2017).

[46] Tipping M E. Sparse Bayesian learning and the relevance vector machine[J]. Journal of Machine Learning Research, 1, 211-244(2001).

[47] Jordan M I, Ghahramani Z, Jaakkola T S et al. An introduction to variational methods for graphical models[M]. Learning in graphical models, 89, 105-161(1998).

[48] Robert C, Casella G[M]. Monte Carlo statistical methods(2010).

[49] Tipping M E. Sparse Bayesian learning and the relevance vector machine[J]. Journal of Machine Learning Research, 1, 211-244(2001).

[50] Seinfeld J H, Pandis S N[M]. Atmospheric chemistry and physics: from air pollution to climate change, 3rd edition(2016).

[51] Dubovik O, Holben B, Eck T F et al. Variability of absorption and optical properties of key aerosol types observed in worldwide locations[J]. Journal of the Atmospheric Sciences, 59, 590-608(2002).

[52] McComiskey A, Schwartz S E, Schmid B et al. Direct aerosol forcing: Calculation from observables and sensitivities to inputs[J]. Journal of Geophysical Research (Atmospheres), 113, D09202(2008).