TY - JOUR A1 - Samaras, Stefanos A1 - Nicolae, Doina A1 - Böckmann, Christine A1 - Vasilescu, Jeni A1 - Binietoglou, Ioannis A1 - Labzovskii, Lev A1 - Toanca, Florica A1 - Papayannis, Alexandros T1 - Using Raman-lidar-based regularized microphysical retrievals and Aerosol Mass Spectrometer measurements for the characterization of biomass burning aerosols JF - Journal of computational physics N2 - In this work we extract the microphysical properties of aerosols for a collection of measurement cases with low volume depolarization ratio originating from fire sources captured by the Raman lidar located at the National Institute of Optoelectronics (INOE) in Bucharest. Our algorithm was tested not only for pure smoke but also for mixed smoke and urban aerosols of variable age and growth. Applying a sensitivity analysis on initial parameter settings of our retrieval code was proved vital for producing semi-automatized retrievals with a hybrid regularization method developed at the Institute of Mathematics of Potsdam University. A direct quantitative comparison of the retrieved microphysical properties with measurements from a Compact Time of Flight Aerosol Mass Spectrometer (CToF-AMS) is used to validate our algorithm. Microphysical retrievals performed with sun photometer data are also used to explore our results. Focusing on the fine mode we observed remarkable similarities between the retrieved size distribution and the one measured by the AMS. More complicated atmospheric structures and the factor of absorption appear to depend more on particle radius being subject to variation. A good correlation was found between the aerosol effective radius and particle age, using the ratio of lidar ratios (LR: aerosol extinction to backscatter ratios) as an indicator for the latter. Finally, the dependence on relative humidity of aerosol effective radii measured on the ground and within the layers aloft show similar patterns. (C) 2015 Elsevier Inc. All rights reserved. KW - Aerosols KW - Microphysical properties KW - Lidar KW - AMS KW - AERONET Y1 - 2015 U6 - https://doi.org/10.1016/j.jcp.2015.06.045 SN - 0021-9991 SN - 1090-2716 VL - 299 SP - 156 EP - 174 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Böckmann, Christine A1 - Bernutat, Claudia A1 - Fischer, Silva T1 - The nonlinear LIDAR-equation : an inverse ill-posed problem Y1 - 1998 ER - TY - JOUR A1 - Pornsawad, Pornsarp A1 - Böckmann, Christine A1 - Panitsupakamon, Wannapa T1 - The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative JF - Electronic transactions on numerical analysis - ETNA N2 - The backward heat problem with time-fractional derivative in Caputo's sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg-Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a Hölder-type source condition. Numerical examples for one and two dimensions are provided. KW - ill-posed problems KW - time-fractional derivative KW - backward heat problem KW - Levenberg-Marquardt method KW - a posteriori stopping rule KW - optimal order Y1 - 2022 SN - 978-3-7001-8258-0 U6 - https://doi.org/10.1553/etna_vol57s67 SN - 1068-9613 VL - 57 SP - 67 EP - 79 PB - Kent State University CY - Kent ER - TY - JOUR A1 - Böckmann, Christine A1 - Sarközi, Janos T1 - The Ill-posed Problem of Multiwavelength Lidar Data by a Hybrid Method of Variable Projection Y1 - 1999 ER - TY - JOUR A1 - Perera, Upeksha A1 - Böckmann, Christine T1 - Solutions of Sturm-Liouville problems JF - Mathematics N2 - This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm-Liouville problems. Next, a concrete implementation to the inverse Sturm-Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm-Liouville problems of higher order (for n=2,4) are verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides a method that can be adapted successfully for solving a direct (regular/singular) or inverse Sturm-Liouville problem (SLP) of an arbitrary order with arbitrary boundary conditions. KW - Sturm-Liouville problems of higher order KW - singular Sturm-Liouville KW - problems KW - inverse Sturm-Liouville problems Y1 - 2020 U6 - https://doi.org/10.3390/math8112074 SN - 2227-7390 VL - 8 IS - 11 PB - MDPI CY - Basel ER - TY - JOUR A1 - Perera, Upeksha A1 - Böckmann, Christine T1 - Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion JF - Mathematics N2 - In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively. KW - higher-order Sturm–Liouville problems KW - inverse Sturm–Liouville problems KW - Magnus expansion Y1 - 2019 U6 - https://doi.org/10.3390/math7060544 SN - 2227-7390 VL - 7 IS - 6 PB - MDPI CY - Basel, Schweiz ER - TY - JOUR A1 - Böckmann, Christine A1 - Osterloh, Lukas T1 - Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data JF - Inverse problems in science and engineering N2 - The Runge-Kutta type regularization method was recently proposed as a potent tool for the iterative solution of nonlinear ill-posed problems. In this paper we analyze the applicability of this regularization method for solving inverse problems arising in atmospheric remote sensing, particularly for the retrieval of spheroidal particle distribution. Our numerical simulations reveal that the Runge-Kutta type regularization method is able to retrieve two-dimensional particle distributions using optical backscatter and extinction coefficient profiles, as well as depolarization information. KW - inverse ill-posed problem KW - iterative regularization KW - integral equation KW - laser remote sensing KW - inverse scattering KW - aerosol size distribution KW - 65R32 KW - 47A52 KW - 65R20 KW - 78A46 Y1 - 2014 U6 - https://doi.org/10.1080/17415977.2013.830615 SN - 1741-5977 SN - 1741-5985 VL - 22 IS - 1 SP - 150 EP - 165 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Soupiona, Ourania A1 - Samaras, Stefanos A1 - Ortiz-Amezcua, Pablo A1 - Böckmann, Christine A1 - Papayannis, Alexandros D. A1 - Moreira, Gregori De Arruda A1 - Benavent-Oltra, Jose Antonio A1 - Guerrero-Rascado, Juan Luis A1 - Bedoya-Velásquez, Andres Esteban A1 - Olmo-Reyes, Francisco José A1 - Román, Roberto A1 - Kokkalis, Panagiotis A1 - Mylonaki, Maria A1 - Alados-Arboledas, Lucas A1 - Papanikolaou, Christina Anna A1 - Foskinis, Romanos T1 - Retrieval of optical and microphysical properties of transported Saharan dust over Athens and Granada based on multi-wavelength Raman lidar measurements: Study of the mixing processes JF - Atmospheric environment : air pollution ; emissions, transport and dispersion, transformation, deposition effects, micrometeorology, urban atmosphere, global atmosphere N2 - In this paper we extract the aerosol microphysical properties for a collection of mineral dust cases measured by multi-wavelength depolarization Raman lidar systems located at the National Technical University of Athens (NTUA, Athens, Greece) and the Andalusian Institute for Earth System Research (IISTA-CEAMA, Granada, Spain). The lidar-based retrievals were carried out with the Spheroidal Inversion eXperiments software tool (SphInX) developed at the University of Potsdam (Germany). The software uses regularized inversion of a two-dimensional enhancement of the Mie model based on the spheroid-particle approximation with the aspect ratio determining the particle shape. The selection of the cases was based on the transport time from the source regions to the measuring sites. The aerosol optical depth as measured by AERONET ranged from 0.27 to 0.54 (at 500 nm) depending on the intensity of each event. Our analysis showed the hourly mean particle linear depolarization ratio and particle lidar ratio values at 532 nm ranging from 11 to 34% and from 42 to 79 sr respectively, depending on the mixing status, the corresponding air mass pathways and their transport time. Cases with shorter transport time showed good agreement in terms of the optical and SphInX-retrieved microphysical properties between Athens and Granada providing a complex refractive index value equal to 1.4 + 0.004i. On the other hand, the results for cases with higher transport time deviated from the aforementioned ones as well as from each other, providing, in particular, an imaginary part of the refractive index ranging from 0.002 to 0.005. Reconstructions of two-dimensional shape-size distributions for each selected layer showed that the dominant effective particle shape was prolate with diverse spherical contributions. The retrieved volume concentrations reflect overall the intensity of the episodes. Y1 - 2019 U6 - https://doi.org/10.1016/j.atmosenv.2019.116824 SN - 1352-2310 SN - 1873-2844 VL - 214 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Böckmann, Christine A1 - Biele, Jens A1 - Neuber, Roland A1 - Niebsch, Jenny T1 - Retrieval of Multimodal aerosol size distribution by Inversion of Multiwavelength data Y1 - 1997 SN - 0-8194-2525-7 ER - TY - JOUR A1 - Pornsawad, Pornsarp A1 - D'Amico, Giuseppe A1 - Böckmann, Christine A1 - Amodeo, Aldo A1 - Pappalardo, Gelsomina T1 - Retrieval of aerosol extinction coefficient profiles from Raman lidar data by inversion method JF - Applied optics N2 - We regard the problem of differentiation occurring in the retrieval of aerosol extinction coefficient profiles from inelastic Raman lidar signals by searching for a stable solution of the resulting Volterra integral equation. An algorithm based on a projection method and iterative regularization together with the L-curve method has been performed on synthetic and measured lidar signals. A strategy to choose a suitable range for the integration within the framework of the retrieval of optical properties is proposed here for the first time to our knowledge. The Monte Carlo procedure has been adapted to treat the uncertainty in the retrieval of extinction coefficients. Y1 - 2012 U6 - https://doi.org/10.1364/AO.51.002035 SN - 1559-128X SN - 2155-3165 VL - 51 IS - 12 SP - 2035 EP - 2044 PB - Optical Society of America CY - Washington ER - TY - JOUR A1 - Hoffmann, Anne A1 - Osterloh, Lukas A1 - Stone, Robert A1 - Lampert, Astrid A1 - Ritter, Christoph A1 - Stock, Maria A1 - Tunved, Peter A1 - Hennig, Tabea A1 - Böckmann, Christine A1 - Li, Shao-Meng A1 - Eleftheriadis, Kostas A1 - Maturilli, Marion A1 - Orgis, Thomas A1 - Herber, Andreas A1 - Neuber, Roland A1 - Dethloff, Klaus T1 - Remote sensing and in-situ measurements of tropospheric aerosol, a PAMARCMiP case study JF - Atmospheric environment : air pollution ; emissions, transport and dispersion, transformation, deposition effects, micrometeorology, urban atmosphere, global atmosphere N2 - In this work, a closure experiment for tropospheric aerosol is presented. Aerosol size distributions and single scattering albedo from remote sensing data are compared to those measured in-situ. An aerosol pollution event on 4 April 2009 was observed by ground based and airborne lidar and photometer in and around Ny-Alesund, Spitsbergen, as well as by DMPS, nephelometer and particle soot absorption photometer at the nearby Zeppelin Mountain Research Station. The presented measurements were conducted in an area of 40 x 20 km around Ny-Alesund as part of the 2009 Polar Airborne Measurements and Arctic Regional Climate Model Simulation Project (PAMARCMiP). Aerosol mainly in the accumulation mode was found in the lower troposphere, however, enhanced backscattering was observed up to the tropopause altitude. A comparison of meteorological data available at different locations reveals a stable multi-layer-structure of the lower troposphere. It is followed by the retrieval of optical and microphysical aerosol parameters. Extinction values have been derived using two different methods, and it was found that extinction (especially in the UV) derived from Raman lidar data significantly surpasses the extinction derived from photometer AOD profiles. Airborne lidar data shows volume depolarization values to be less than 2.5% between 500 m and 2.5 km altitude, hence, particles in this range can be assumed to be of spherical shape. In-situ particle number concentrations measured at the Zeppelin Mountain Research Station at 474 m altitude peak at about 0.18 mu m diameter, which was also found for the microphysical inversion calculations performed at 850 m and 1500 m altitude. Number concentrations depend on the assumed extinction values, and slightly decrease with altitude as well as the effective particle diameter. A low imaginary part in the derived refractive index suggests weakly absorbing aerosols, which is confirmed by low black carbon concentrations, measured at the Zeppelin Mountain as well as on board the Polar 5 aircraft. KW - Arctic KW - Aerosols KW - Lidar KW - Arctic haze Y1 - 2012 U6 - https://doi.org/10.1016/j.atmosenv.2011.11.027 SN - 1352-2310 VL - 52 IS - 3 SP - 56 EP - 66 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Osterloh, Lukas A1 - Böckmann, Christine A1 - Nicolae, Doina A1 - Nemuc, Anca T1 - Regularized inversion of microphysical atmospheric particle parameters - theory and application JF - Journal of computational physics N2 - Retrieving the distribution of aerosols in the atmosphere via remote sensing techniques is a highly complex task that requires dealing with a wide range of different problems stemming both from Physics and Mathematics. We focus on retrieving this distribution from multi-wavelength lidar data for aerosol ensembles consisting of spherical particles via an iterative regularization technique. The optical efficiencies for spherical scatterers are examined to account for the behavior of the underlying integral equation. The ill-posedness of the problem and the conditioning of the discretized problem are analyzed. Some critical points in the model, like the assumed wavelength-independence of the refractive index and the fixed grid of investigated refractive indices, are studied with regard to their expected impact on the regularized solution. A new Monte-Carlo type method is proposed for retrieval of the refractive index. To validate the results, the developed algorithm is applied to two measurement cases of burning biomass gained from multi-wavelength Raman lidar. KW - Inverse ill-posed problem KW - Regularization KW - Lidar remote sensing KW - Microphysical particle properties Y1 - 2013 U6 - https://doi.org/10.1016/j.jcp.2012.11.040 SN - 0021-9991 VL - 237 IS - 11 SP - 79 EP - 94 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Kirsche, Andreas A1 - Böckmann, Christine T1 - Rational approximations for ill-conditioned equation systems N2 - In this study we present iterative methods using rational approximations, e.g... Pade approximants, which work very well for strongly ill-conditioned systems. In principle all methods of the family are convergent. One type of those methods has the advantage that their convergence behavior is very fast without additional a-priori information on the optimal relaxation parameter. (c) 2005 Elsevier Inc. All rights reserved Y1 - 2005 ER - TY - JOUR A1 - Böckmann, Christine T1 - Projection method for lidar measurements Y1 - 1997 SN - 981-02-2918-6 ER - TY - JOUR A1 - Kirsche, Andreas A1 - Böckmann, Christine T1 - Pade iteration method for regularization JF - Applied mathematics and computation N2 - In this study we present iterative regularization methods using rational approximations, in particular, Pade approximants, which work well for ill-posed problems. We prove that the (k,j)-Pade method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Pade method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Bockmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385-397] where this method was treated to solve ill-conditioned equation systems. (c) 2006 Elsevier Inc. All rights reserved. KW - Pade approximants KW - iterative regularization KW - ill-posed problem Y1 - 2006 U6 - https://doi.org/10.1016/j.amc.2006.01.011 SN - 0096-3003 VL - 180 IS - 2 SP - 648 EP - 663 PB - Elsevier CY - New York ER - TY - JOUR A1 - Böckmann, Christine A1 - Niebsch, Jenny T1 - Mollifier Methods for Aerosol Size Distribution Y1 - 1997 ER - TY - JOUR A1 - Pornsawad, Pornsarp A1 - Böckmann, Christine T1 - Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems JF - Numerical functional analysis and optimization : an international journal of rapid publication N2 - This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under a Holder-type sourcewise condition if the Frechet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt, Lobatto, and Radau methods. KW - Nonlinear ill-posed problems KW - Runge-Kutta methods KW - regularization methods KW - Holder-type source condition KW - stopping rules Y1 - 2016 U6 - https://doi.org/10.1080/01630563.2016.1219744 SN - 0163-0563 SN - 1532-2467 VL - 37 SP - 1562 EP - 1589 PB - Wiley-VCH CY - Philadelphia ER - TY - JOUR A1 - Ritter, Christoph A1 - Ángeles Burgos, María A1 - Böckmann, Christine A1 - Mateos, David A1 - Lisok, Justyna A1 - Markowicz, Krzysztof M. A1 - Moroni, Beatrice A1 - Cappelletti, David A1 - Udisti, Roberto A1 - Maturilli, Marion A1 - Neuber, Roland T1 - Microphysical properties and radiative impact of an intense biomass burning aerosol event measured over Ny-angstrom lesund, Spitsbergen in July 2015 JF - Tellus - Series B, Chemical and Physical Meteorology N2 - In this work, an evaluation of an intense biomass burning event observed over Ny-angstrom lesund (Spitsbergen, European Arctic) in July 2015 is presented. Data from the multi-wavelengths Raman-lidar KARL, a sun photometer and radiosonde measurements are used to derive some microphysical properties of the biomass burning aerosol as size distribution, refractive index and single scattering albedo at different relative humidities. Predominantly particles in the accumulation mode have been found with a bi-modal distribution and dominance of the smaller mode. Above 80% relative humidity, hygroscopic growth in terms of an increase of particle diameter and a slight decrease of the index of refraction (real and imaginary part) has been found. Values of the single scattering albedo around 0.9 both at 355nm and 532nm indicate some absorption by the aerosol. Values of the lidar ratio are around 26sr for 355nm and around 50sr for 532nm, almost independent of the relative humidity. Further, data from the photometer and surface radiation values from the local baseline surface radiation network (BSRN) have been applied to derive the radiative impact of the biomass burning event purely from observational data by comparison with a clear background day. We found a strong cooling for the visible radiation and a slight warming in the infra-red. The net aerosol forcing, derived by comparison with a clear background day purely from observational data, obtained a value of -95 W/m(2) per unit AOD500. KW - aerosol KW - lidar KW - retrieval of aerosol properties KW - radiative forcing KW - Arctic aerosol Y1 - 2018 U6 - https://doi.org/10.1080/16000889.2018.1539618 SN - 1600-0889 VL - 70 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Müller, Detlef A1 - Böckmann, Christine A1 - Kolgotin, Alexei A1 - Schneidenbach, Lars A1 - Chemyakin, Eduard A1 - Rosemann, Julia A1 - Znak, Pavel A1 - Romanov, Anton T1 - Microphysical particle properties derived from inversion algorithms developed in the framework of EARLINET JF - Atmospheric measurement techniques : an interactive open access journal of the European Geosciences Union N2 - We present a summary on the current status of two inversion algorithms that are used in EARLINET (European Aerosol Research Lidar Network) for the inversion of data collected with EARLINET multiwavelength Raman lidars. These instruments measure backscatter coefficients at 355, 532, and 1064 nm, and extinction coefficients at 355 and 532 nm. Development of these two algorithms started in 2000 when EARLINET was founded. The algorithms are based on a manually controlled inversion of optical data which allows for detailed sensitivity studies. The algorithms allow us to derive particle effective radius as well as volume and surface area concentration with comparably high confidence. The retrieval of the real and imaginary parts of the complex refractive index still is a challenge in view of the accuracy required for these parameters in climate change studies in which light absorption needs to be known with high accuracy. It is an extreme challenge to retrieve the real part with an accuracy better than 0.05 and the imaginary part with accuracy better than 0.005-0.1 or +/- 50 %. Single-scattering albedo can be computed from the retrieved microphysical parameters and allows us to categorize aerosols into high-and low-absorbing aerosols. On the basis of a few exemplary simulations with synthetic optical data we discuss the current status of these manually operated algorithms, the potentially achievable accuracy of data products, and the goals for future work. One algorithm was used with the purpose of testing how well microphysical parameters can be derived if the real part of the complex refractive index is known to at least 0.05 or 0.1. The other algorithm was used to find out how well microphysical parameters can be derived if this constraint for the real part is not applied. The optical data used in our study cover a range of Angstrom exponents and extinction-to-backscatter (lidar) ratios that are found from lidar measurements of various aerosol types. We also tested aerosol scenarios that are considered highly unlikely, e.g. the lidar ratios fall outside the commonly accepted range of values measured with Raman lidar, even though the underlying microphysical particle properties are not uncommon. The goal of this part of the study is to test the robustness of the algorithms towards their ability to identify aerosol types that have not been measured so far, but cannot be ruled out based on our current knowledge of aerosol physics. We computed the optical data from monomodal logarithmic particle size distributions, i.e. we explicitly excluded the more complicated case of bimodal particle size distributions which is a topic of ongoing research work. Another constraint is that we only considered particles of spherical shape in our simulations. We considered particle radii as large as 7-10 mu m in our simulations where the Potsdam algorithm is limited to the lower value. We considered optical-data errors of 15% in the simulation studies. We target 50% uncertainty as a reasonable threshold for our data products, though we attempt to obtain data products with less uncertainty in future work. Y1 - 2016 U6 - https://doi.org/10.5194/amt-9-5007-2016 SN - 1867-1381 SN - 1867-8548 VL - 9 SP - 5007 EP - 5035 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Ortiz-Amezcua, Pablo A1 - Guerrero-Rascado, Juan Luis A1 - Jose Granados-Munoz, Maria A1 - Benavent-Oltra, Jose Antonio A1 - Böckmann, Christine A1 - Samaras, Stefanos A1 - Stachlewska, Iwona Sylwia A1 - Janicka, Lucja A1 - Baars, Holger A1 - Bohlmann, Stephanie A1 - Alados-Arboledas, Lucas T1 - Microphysical characterization of long-range transported biomass burning particles from North America at three EARLINET stations JF - Atmospheric Chemistry and Physics N2 - Strong events of long-range transported biomass burning aerosol were detected during July 2013 at three EARLINET (European Aerosol Research Lidar Network) stations, namely Granada (Spain), Leipzig (Germany) and Warsaw (Poland). Satellite observations from MODIS (Moderate Resolution Imaging Spectroradiometer) and CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) instruments, as well as modeling tools such as HYSPLIT (Hybrid Single-Particle Lagrangian Integrated Trajectory) and NAAPS (Navy Aerosol Analysis and Prediction System), have been used to estimate the sources and transport paths of those North American forest fire smoke particles. A multiwavelength Raman lidar technique was applied to obtain vertically resolved particle optical properties, and further inversion of those properties with a regularization algorithm allowed for retrieving microphysical information on the studied particles. The results highlight the presence of smoke layers of 1-2 km thickness, located at about 5 km a.s.l. altitude over Granada and Leipzig and around 2.5 km a.s.l. at Warsaw. These layers were intense, as they accounted for more than 30% of the total AOD (aerosol optical depth) in all cases, and presented optical and microphysical features typical for different aging degrees: color ratio of lidar ratios (LR532/LR355) around 2, alpha-related angstrom exponents of less than 1, effective radii of 0.3 mu m and large values of single scattering albedos (SSA), nearly spectrally independent. The intensive microphysical properties were compared with columnar retrievals form co-located AERONET (Aerosol Robotic Network) stations. The intensity of the layers was also characterized in terms of particle volume concentration, and then an experimental relationship between this magnitude and the particle extinction coefficient was established. Y1 - 2017 U6 - https://doi.org/10.5194/acp-17-5931-2017 SN - 1680-7316 SN - 1680-7324 VL - 17 SP - 5931 EP - 5946 PB - Copernicus CY - Göttingen ER -