@article{SoupionaSamarasOrtizAmezcuaetal.2019,
  author    = {Soupiona, Ourania and Samaras, Stefanos and Ortiz-Amezcua, Pablo and B{\"o}ckmann, Christine and Papayannis, Alexandros D. and Moreira, Gregori De Arruda and Benavent-Oltra, Jose Antonio and Guerrero-Rascado, Juan Luis and Bedoya-Vel{\´a}squez, Andres Esteban and Olmo-Reyes, Francisco Jos{\´e} and Rom{\´a}n, Roberto and Kokkalis, Panagiotis and Mylonaki, Maria and Alados-Arboledas, Lucas and Papanikolaou, Christina Anna and Foskinis, Romanos},
  title     = {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},
  series = {Atmospheric environment : air pollution ; emissions, transport and dispersion, transformation, deposition effects, micrometeorology, urban atmosphere, global atmosphere},
  volume    = {214},
  journal   = {Atmospheric environment : air pollution ; emissions, transport and dispersion, transformation, deposition effects, micrometeorology, urban atmosphere, global atmosphere},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {1352-2310},
  doi       = {10.1016/j.atmosenv.2019.116824},
  pages     = {15},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{KirscheBoeckmann2006,
  author    = {Kirsche, Andreas and B{\"o}ckmann, Christine},
  title     = {Pade iteration method for regularization},
  series = {Applied mathematics and computation},
  volume    = {180},
  journal   = {Applied mathematics and computation},
  number    = {2},
  publisher = {Elsevier},
  address   = {New York},
  issn      = {0096-3003},
  doi       = {10.1016/j.amc.2006.01.011},
  pages     = {648 -- 663},
  year      = {2006},
  abstract  = {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.},
  language  = {en}
}
@article{BoeckmannKirsche2006,
  author    = {B{\"o}ckmann, Christine and Kirsche, Andreas},
  title     = {Iterative regularization method for lidar remote sensing},
  issn      = {0010-4655},
  doi       = {10.1016/j.cpc.2005.12.019},
  year      = {2006},
  abstract  = {In this paper we present an inversion algorithm for ill-posed problems arising in atmospheric remote sensing. The proposed method is an iterative Runge-Kutta type regularization method. Those methods are better well known for solving differential equations. We adapted them for solving inverse ill-posed problems. The numerical performances of the algorithm are studied by means of simulations concerning the retrieval of aerosol particle size distributions from lidar observations.},
  language  = {en}
}
@article{BoeckmannMironovaMuller2005,
  author    = {B{\"o}ckmann, Christine and Mironova, I. and Muller, D.},
  title     = {Microphysical aerosol parameters from multiwavelength lidar},
  issn      = {1084-7529},
  year      = {2005},
  abstract  = {The hybrid regularization technique developed at the Institute of Mathematics of Potsdam University (IMP) is used to derive microphysical properties such as effective radius, surface-area concentration, and volume concentration, as well as the single-scattering albedo and a mean complex refractive index, from multiwavelength lidar measurements. We present the continuation of investigations of the IMP method. Theoretical studies of the degree of ill-posedness of the underlying model, simulation results with respect to the analysis of the retrieval error of microphysical particle properties from multiwavelength lidar data, and a comparison of results for different numbers of backscatter and extinction coefficients are presented. Our analysis shows that the backscatter operator has a smaller degree of ill- posedness than the operator for extinction. This fact underlines the importance of backscatter data. Moreover, the degree of ill-posedness increases with increasing particle absorption, i.e., depends on the imaginary part of the refractive index and does not depend significantly on the real part. Furthermore, an extensive simulation study was carried out for logarithmic-normal size distributions with different median radii, mode widths, and real and imaginary parts of refractive indices. The errors of the retrieved particle properties obtained from the inversion of three backscatter (355, 532, and 1064 nm) and two extinction (355 and 532 nm) coefficients were compared with the uncertainties for the case of six backscatter (400. 710, 800 nm. additionally) and the same two extinction coefficients. For known complex refractive index and up to 20\% normally distributed noise, we found that the retrieval errors for effective radius, surface-area concentration, and volume concentration stay below approximately 15\% in both cases. Simulations were also made with unknown complex refractive index. In that case the integrated parameters stay below approximately 30\%, and the imaginary part of the refractive index stays below 35\% for input noise up to 10\% in both cases. In general, the quality of the retrieved aerosol parameters depends strongly on the imaginary part owing to the degree of ill-posedness. It is shown that under certain constraints a minimum data set of three backscatter coefficients and two extinction coefficients is sufficient for a successful inversion. The IMP algorithm was finally tested for a measurement case. (C) 2005 Optical Society of America},
  language  = {en}
}
@article{KirscheBoeckmann2005,
  author    = {Kirsche, Andreas and B{\"o}ckmann, Christine},
  title     = {Rational approximations for ill-conditioned equation systems},
  year      = {2005},
  abstract  = {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},
  language  = {en}
}
@article{BoeckmannWandingerAnsmannetal.2004,
  author    = {B{\"o}ckmann, Christine and Wandinger, Ulla and Ansmann, Albert and B{\"o}senberg, Jens and Amiridis, Vassilis and Boselli, Antonella and Delaval, Arnaud and De Tomasi, Ferdinando de and Frioud, Max and Grigorov, Ivan Videnov and Hagard, Arne and Horvat, Matej and Iarlori, Marco and Komguem, Leonce and Kreipl, Stephan and Larchevque, Gilles and Matthias, Volker and Papayannis, Alexandros and Pappalardo, GGelsomina and Rocadenbosch, Francesc and Rodrigues, Jose Ant{\´o}nio and Schneider, Johannes and Shcherbakov, Valery and Wiegner, Matthias},
  title     = {Aerosol lidar intercomparison in the framework of the EARLINET project : 2. Aerosol backscatter algorithms},
  issn      = {0003-6935},
  year      = {2004},
  abstract  = {An intercomparison of aerosol backscatter lidar algorithms was performed in 2001 within the framework of the European Aerosol Research Lidar Network to Establish an Aerosol Climatology (EARLINET). The objective of this research was to test the correctness of the algorithms and the influence of the lidar ratio used by the various lidar teams involved in the EARLINET for calculation of backscatter-coefficient profiles from the lidar signals. The exercise consisted of processing synthetic lidar signals of various degrees of difficulty. One of these profiles contained height- dependent lidar ratios to test the vertical influence of those profiles on the various retrieval algorithms. Furthermore, a realistic incomplete overlap of laser beam and receiver field of view was introduced to remind the teams to take great care in the nearest range to the lidar. The intercomparison was performed in three stages with increasing knowledge on the input parameters. First, only the lidar signals were distributed; this is the most realistic stage. Afterward the lidar ratio profiles and the reference values at calibration height were provided. The unknown height- dependent lidar ratio had the largest influence on the retrieval, whereas the unknown reference value was of minor importance. These results show the necessity of making additional independent measurements, which can provide us with a suitable approximation of the lidar ratio. The final stage proves in general, that the data evaluation schemes of the different groups of lidar systems work well. (C) 2004 Optical Society of America},
  language  = {en}
}
@phdthesis{Boeckmann2002,
  author    = {B{\"o}ckmann, Christine},
  title     = {Bestimmung atmosph{\"a}rischer Aerosolparameter mit Hilfe von regularisierenden Inversionsverfahren},
  pages     = {167 S. : Anh.},
  year      = {2002},
  language  = {de}
}
@unpublished{MeklerBoeckmannSokolovskaia2000,
  author    = {Mekler, A. A. and B{\"o}ckmann, Christine and Sokolovskaia, N.},
  title     = {Particle distribution from spectral Mie-scattering: kernel representation and singular-value spectrum},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14948},
  year      = {2000},
  abstract  = {This paper deals with the Mie scattering kernels for multi-spectral data. The kernels may be represented in form of power series. Furthermore, the singular-value spectrum and the degree of ill-posedness in dependence on the refractive index of the particles are numerically approximated. A special hybrid regularization technique allows us to determine via inversion the particle distributions of different types.},
  language  = {en}
}
@unpublished{BoeckmannSarkoezi1999,
  author    = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos},
  title     = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14847},
  year      = {1999},
  abstract  = {The ill-posed problem of aerosol distribution determination from a small number of backscatter and extinction lidar measurements was solved successfully via a hybrid method by a variable dimension of projection with B-Splines. Numerical simulation results with noisy data at different measurement situations show that it is possible to derive a reconstruction of the aerosol distribution only with 4 measurements.},
  language  = {en}
}
@unpublished{BoeckmannNiebsch1998,
  author    = {B{\"o}ckmann, Christine and Niebsch, Jenny},
  title     = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14725},
  year      = {1998},
  abstract  = {The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.},
  language  = {en}
}
@unpublished{BoeckmannBieleNeuberetal.1997,
  author    = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny},
  title     = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14360},
  year      = {1997},
  abstract  = {The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.},
  language  = {en}
}
@article{AckermannFiermentBroddeetal.1998,
  author    = {Ackermann, Peter and Fierment, Gerold and Brodde, Peter and Zierke, Irene and Balderjahn, Ingo and Kamm, Birgit and Wallschl{\"a}ger, Hans-Dieter and B{\"o}ckmann, Christine and Soyez, Konrad and Schmeer, Ernst and Blumenstein, Oswald and Berndt, Peter},
  title     = {Umweltforschung f{\"u}r das Land Brandenburg},
  series = {Brandenburgische Umwelt-Berichte : BUB ; Schriftenreihe der Mathematisch-Naturwissenschaftlichen Fakult{\"a}t der Universit{\"a}t Potsdam},
  volume    = {2},
  journal   = {Brandenburgische Umwelt-Berichte : BUB ; Schriftenreihe der Mathematisch-Naturwissenschaftlichen Fakult{\"a}t der Universit{\"a}t Potsdam},
  issn      = {1434-2375},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-3645},
  pages     = {120 -- 135},
  year      = {1998},
  abstract  = {Brandenburgisches Umweltforschungszentrum e.V.: Arbeitsgruppe: Nachhaltigkeit ; Arbeitsgruppe: Umwelt- und Biotechnologie ; Arbeitsgruppe: Umweltmanagement ; Arbeitsgruppe: Umweltsoziologie ; Zentrum f{\"u}r Umweltwissenschaften: Arbeitsgruppe: Betriebliches Umweltmanagement/Umweltbewußtes Konsumentenverhalten ; Arbeitsgruppe: Gr{\"u}ne Bioraffinerie ; Arbeitsgruppe: Integrierter Arten- und Biotopschutz ; Arbeitsgruppe: LIDAR-Inversionen ; Arbeitsgruppe: FG {\"O}kotechnologie ; Arbeitsgruppe: Regenerative Energien ; Arbeitsgruppe: Stoffdynamik in Geosystemen ; Arbeitsgruppe: Umweltbildung},
  language  = {de}
}
@article{Boeckmann1998,
  author    = {B{\"o}ckmann, Christine},
  title     = {Umweltforschung f{\"u}r das Land Brandenburg},
  series = {Brandenburgische Umwelt-Berichte : BUB ; Schriftenreihe der Mathematisch-Naturwissenschaftlichen Fakult{\"a}t der Universit{\"a}t Potsdam},
  volume    = {2},
  journal   = {Brandenburgische Umwelt-Berichte : BUB ; Schriftenreihe der Mathematisch-Naturwissenschaftlichen Fakult{\"a}t der Universit{\"a}t Potsdam},
  issn      = {1434-2375},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-3678},
  pages     = {60 -- 63},
  year      = {1998},
  language  = {de}
}
@misc{PornsawadSungcharoenBoeckmann2020,
  author    = {Pornsawad, Pornsarp and Sungcharoen, Parada and B{\"o}ckmann, Christine},
  title     = {Convergence rate of the modified Landweber method for solving inverse potential problems},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1034},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47194},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471942},
  pages     = {24},
  year      = {2020},
  abstract  = {In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.},
  language  = {en}
}
@incollection{AscheBoeckmannLaueetal.2000,
  author    = {Asche, Hartmut and B{\"o}ckmann, Christine and Laue, Steffen and L{\"o}hmannsr{\"o}ben, Hans-Gerd and Lemke, Matthias and Schober, Lars and Reich, Oliver and L{\"u}ck, Erika and Sch{\"u}tte, Marc and Domsch, Horst and Makower, Alexander and Scheller, Frieder W. and St{\"o}cklein, Wolfgang and Wollenberger, Ursula and Schultze, Rainer and Hengstermann, Theo and Schael, Frank},
  title     = {Umweltforschung f{\"u}r das Land Brandenburg : Projekt Umweltanalytik / Umweltmeßtechnik / Informationssysteme},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-3862},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {176 -- 227},
  year      = {2000},
  language  = {de}
}
@article{PereraBoeckmann2020,
  author    = {Perera, Upeksha and B{\"o}ckmann, Christine},
  title     = {Solutions of Sturm-Liouville problems},
  series = {Mathematics},
  volume    = {8},
  journal   = {Mathematics},
  number    = {11},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2227-7390},
  doi       = {10.3390/math8112074},
  pages     = {14},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@article{BoeckmannBernutatFischer1998,
  author    = {B{\"o}ckmann, Christine and Bernutat, Claudia and Fischer, Silva},
  title     = {The nonlinear LIDAR-equation : an inverse ill-posed problem},
  year      = {1998},
  language  = {en}
}
@article{BernutatBoeckmannRamlau1998,
  author    = {Bernutat, Claudia and B{\"o}ckmann, Christine and Ramlau, Ronny},
  title     = {Examination of the Nonlinear LIDAR-Operator : an Inverse Ill-posed Problem},
  year      = {1998},
  language  = {en}
}
@article{BoesenbergAlpersBoeckmannetal.1998,
  author    = {B{\"o}senberg, Jens and Alpers, Matthias and B{\"o}ckmann, Christine and J{\"a}ger, Horst and Matthias, Volker and Trickl, Thomas and Wandinger, Ulla and Wiegner, Matthias},
  title     = {A Lidar Network for the Establishment of an Aerosol Climatology},
  year      = {1998},
  language  = {en}
}
@article{BoeckmannBieleNeuber1998,
  author    = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland},
  title     = {Analysis of multi-wavelength lidar data by inversion with mollifier method},
  year      = {1998},
  language  = {en}
}
@article{Boeckmann1998,
  author    = {B{\"o}ckmann, Christine},
  title     = {Auswertung von multispektralen Lidarmeßdaten},
  year      = {1998},
  language  = {de}
}
@article{BoeckmannNiebsch1998,
  author    = {B{\"o}ckmann, Christine and Niebsch, Jenny},
  title     = {Inverse Scattering Problems of the Nonlinear LIDAR-Equation},
  year      = {1998},
  language  = {en}
}
@article{OsterlohBoeckmannNicolaeetal.2013,
  author    = {Osterloh, Lukas and B{\"o}ckmann, Christine and Nicolae, Doina and Nemuc, Anca},
  title     = {Regularized inversion of microphysical atmospheric particle parameters - theory and application},
  series = {Journal of computational physics},
  volume    = {237},
  journal   = {Journal of computational physics},
  number    = {11},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2012.11.040},
  pages     = {79 -- 94},
  year      = {2013},
  abstract  = {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.},
  language  = {en}
}
@article{Boeckmann1996,
  author    = {B{\"o}ckmann, Christine},
  title     = {Curve fitting and identification of physical spectra},
  year      = {1996},
  language  = {en}
}
@book{Boeckmann1997,
  author    = {B{\"o}ckmann, Christine},
  title     = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data},
  series = {Preprint NLD},
  volume    = {38},
  journal   = {Preprint NLD},
  publisher = {Univ. Potsdam},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {[12] S. : graph. Darst.},
  year      = {1997},
  language  = {en}
}
@article{Boeckmann1996,
  author    = {B{\"o}ckmann, Christine},
  title     = {Curve fitting and identification of physical spectra},
  year      = {1996},
  language  = {en}
}
@article{Boeckmann1995,
  author    = {B{\"o}ckmann, Christine},
  title     = {A modification of the trust-region Gauss-Newton method to solve separable nonlinear least squares problems},
  year      = {1995},
  language  = {en}
}
@article{RattanaBoeckmann2013,
  author    = {Rattana, Amornrat and B{\"o}ckmann, Christine},
  title     = {Matrix methods for computing eigenvalues of Sturm-Liouville problems of order four},
  series = {Journal of computational and applied mathematics},
  volume    = {249},
  journal   = {Journal of computational and applied mathematics},
  number    = {8},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0377-0427},
  doi       = {10.1016/j.cam.2013.02.024},
  pages     = {144 -- 156},
  year      = {2013},
  abstract  = {This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions. Furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's methods as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods is investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.},
  language  = {en}
}
@article{BoeckmannBieleNeuberetal.1997,
  author    = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny},
  title     = {Retrieval of Multimodal aerosol size distribution by Inversion of Multiwavelength data},
  isbn      = {0-8194-2525-7},
  year      = {1997},
  language  = {en}
}
@article{Boeckmann1997,
  author    = {B{\"o}ckmann, Christine},
  title     = {Projection method for lidar measurements},
  isbn      = {981-02-2918-6},
  year      = {1997},
  language  = {en}
}
@article{BoeckmannNiebsch1997,
  author    = {B{\"o}ckmann, Christine and Niebsch, Jenny},
  title     = {Mollifier Methods for Aerosol Size Distribution},
  year      = {1997},
  language  = {en}
}
@article{KammaneeBoeckmann2009,
  author    = {Kammanee, Athassawat and B{\"o}ckmann, Christine},
  title     = {Boundary value method for inverse Sturm-Liouville problems},
  issn      = {0096-3003},
  doi       = {10.1016/j.amc.2009.04.002},
  year      = {2009},
  abstract  = {In this paper we present a method to recover symmetric and non-symmetric potential functions of inverse Sturm- Liouville problems from the knowledge of eigenvalues. The linear multistep method coupled with suitable boundary conditions known as boundary value method (BVM) is the main tool to approximate the eigenvalues in each iteration step of the used Newton method. The BVM was extended to work for Neumann-Neumann boundary conditions. Moreover, a suitable approximation for the asymptotic correction of the eigenvalues is given. Numerical results demonstrate that the method is able to give good results for both symmetric and non-symmetric potentials.},
  language  = {en}
}
@book{BoeckmannNiebsch1998,
  author    = {B{\"o}ckmann, Christine and Niebsch, Jenny},
  title     = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on operator},
  series = {Preprint NLD},
  volume    = {47},
  journal   = {Preprint NLD},
  publisher = {Univ. Potsdam},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {16 S. : Abb.},
  year      = {1998},
  language  = {en}
}
@book{Boeckmann1992,
  author    = {B{\"o}ckmann, Christine},
  title     = {A modification of the Trust-Region Gauss-Newton method to solve separable nonlinear least squares problems},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 17},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {14 Bl.},
  year      = {1992},
  language  = {en}
}
@book{Boeckmann1992,
  author    = {B{\"o}ckmann, Christine},
  title     = {Curve fitting and identification of physical spectra},
  series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  volume    = {1992, 18},
  journal   = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {17 Bl.},
  year      = {1992},
  language  = {en}
}
@book{BoeckmannNiebsch1996,
  author    = {B{\"o}ckmann, Christine and Niebsch, Jenny},
  title     = {A mollifier method for aerosol size},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1996, 07},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {[5] Bl.},
  year      = {1996},
  language  = {en}
}
@article{BoeckmannKammaneeBraunss2011,
  author    = {B{\"o}ckmann, Christine and Kammanee, Athassawat and Braunss, Andreas},
  title     = {Logarithmic convergence rate of Levenberg-Marquardt method with application to an inverse potential problem},
  series = {Journal of inverse and ill-posed problems},
  volume    = {19},
  journal   = {Journal of inverse and ill-posed problems},
  number    = {3},
  publisher = {De Gruyter},
  address   = {Berlin},
  issn      = {0928-0219},
  doi       = {10.1515/JIIP.2011.034},
  pages     = {345 -- 367},
  year      = {2011},
  abstract  = {We prove logarithmic convergence rate of the Levenberg-Marquardt method in a Hilbert space if a logarithmic source condition is satisfied. This method is applied to an inverse potential problem. Numerical implementations demonstrate the convergence rate.},
  language  = {en}
}
@misc{OsterlohaBoeckmannNicolaeetal.2014,
  author    = {Osterloha, Lukas and B{\"o}ckmann, Christine and Nicolae, Doina and Nemuc, Anca},
  title     = {Regularized inversion of microphysical atmospheric particle parameters: Theory and application (vol 237, pg 79, 2013)},
  series = {Journal of computational physics},
  volume    = {275},
  journal   = {Journal of computational physics},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2014.07.041},
  pages     = {696 -- 696},
  year      = {2014},
  language  = {en}
}
@article{BoeckmannOsterloh2014,
  author    = {B{\"o}ckmann, Christine and Osterloh, Lukas},
  title     = {Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data},
  series = {Inverse problems in science and engineering},
  volume    = {22},
  journal   = {Inverse problems in science and engineering},
  number    = {1},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1741-5977},
  doi       = {10.1080/17415977.2013.830615},
  pages     = {150 -- 165},
  year      = {2014},
  abstract  = {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.},
  language  = {en}
}
@article{AltundagBoeckmannTaseli2015,
  author    = {Altundag, H{\"u}seyin and B{\"o}ckmann, Christine and Taseli, Hasan},
  title     = {Inverse Sturm-Liouville problems with pseudospectral methods},
  series = {International journal of computer mathematics},
  volume    = {92},
  journal   = {International journal of computer mathematics},
  number    = {7},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {0020-7160},
  doi       = {10.1080/00207160.2014.939646},
  pages     = {1373 -- 1384},
  year      = {2015},
  abstract  = {In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is treated by considering numerically the asymptotic limit of the associated problem on a finite interval (-L, L). In spite of this treatment, the problem has still an ill-conditioned structure unlike the classical regular ones and needs regularization techniques. Direct computation of eigenvalues in iterative solution procedure is made by means of pseudospectral methods. A fairly detailed description of the numerical algorithm and its applications to specific examples are presented to illustrate the accuracy and convergence behaviour of the proposed approach.},
  language  = {en}
}
@article{PornsawadD'AmicoBoeckmannetal.2012,
  author    = {Pornsawad, Pornsarp and D'Amico, Giuseppe and B{\"o}ckmann, Christine and Amodeo, Aldo and Pappalardo, Gelsomina},
  title     = {Retrieval of aerosol extinction coefficient profiles from Raman lidar data by inversion method},
  series = {Applied optics},
  volume    = {51},
  journal   = {Applied optics},
  number    = {12},
  publisher = {Optical Society of America},
  address   = {Washington},
  issn      = {1559-128X},
  doi       = {10.1364/AO.51.002035},
  pages     = {2035 -- 2044},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@article{BoeckmannKammanee2011,
  author    = {B{\"o}ckmann, Christine and Kammanee, Athassawat},
  title     = {Broyden method for inverse non-symmetric Sturm-Liouville problems},
  series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians},
  volume    = {51},
  journal   = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians},
  number    = {3},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0006-3835},
  doi       = {10.1007/s10543-011-0317-5},
  pages     = {513 -- 528},
  year      = {2011},
  abstract  = {In this paper, we propose a derivative-free method for recovering symmetric and non-symmetric potential functions of inverse Sturm-Liouville problems from the knowledge of eigenvalues. A class of boundary value methods obtained as an extension of Numerov's method is the major tool for approximating the eigenvalues in each Broyden iteration step. Numerical examples demonstrate that the method is able to reduce the number of iteration steps, in particular for non-symmetric potentials, without accuracy loss.},
  language  = {en}
}
@article{SamarasNicolaeBoeckmannetal.2015,
  author    = {Samaras, Stefanos and Nicolae, Doina and B{\"o}ckmann, Christine and Vasilescu, Jeni and Binietoglou, Ioannis and Labzovskii, Lev and Toanca, Florica and Papayannis, Alexandros},
  title     = {Using Raman-lidar-based regularized microphysical retrievals and Aerosol Mass Spectrometer measurements for the characterization of biomass burning aerosols},
  series = {Journal of computational physics},
  volume    = {299},
  journal   = {Journal of computational physics},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2015.06.045},
  pages     = {156 -- 174},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@misc{MuellerBoeckmannKolgotinetal.2016,
  author    = {M{\"u}ller, Detlef and B{\"o}ckmann, Christine and Kolgotin, Alexei and Schneidenbach, Lars and Chemyakin, Eduard and Rosemann, Julia and Znak, Pavel and Romanov, Anton},
  title     = {Microphysical particle properties derived from inversion algorithms developed in the framework of EARLINET},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {565},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41193},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-411934},
  pages     = {29},
  year      = {2016},
  abstract  = {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.},
  language  = {en}
}
@unpublished{RattanaBoeckmann2012,
  author    = {Rattana, Amornrat and B{\"o}ckmann, Christine},
  title     = {Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order four},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59279},
  year      = {2012},
  abstract  = {This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.},
  language  = {en}
}
@article{MuellerBoeckmannKolgotinetal.2016,
  author    = {M{\"u}ller, Detlef and B{\"o}ckmann, Christine and Kolgotin, Alexei and Schneidenbach, Lars and Chemyakin, Eduard and Rosemann, Julia and Znak, Pavel and Romanov, Anton},
  title     = {Microphysical particle properties derived from inversion algorithms developed in the framework of EARLINET},
  series = {Atmospheric measurement techniques : an interactive open access journal of the European Geosciences Union},
  volume    = {9},
  journal   = {Atmospheric measurement techniques : an interactive open access journal of the European Geosciences Union},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {1867-1381},
  doi       = {10.5194/amt-9-5007-2016},
  pages     = {5007 -- 5035},
  year      = {2016},
  abstract  = {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.},
  language  = {en}
}
@article{PornsawadBoeckmann2016,
  author    = {Pornsawad, Pornsarp and B{\"o}ckmann, Christine},
  title     = {Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems},
  series = {Numerical functional analysis and optimization : an international journal of rapid publication},
  volume    = {37},
  journal   = {Numerical functional analysis and optimization : an international journal of rapid publication},
  publisher = {Wiley-VCH},
  address   = {Philadelphia},
  issn      = {0163-0563},
  doi       = {10.1080/01630563.2016.1219744},
  pages     = {1562 -- 1589},
  year      = {2016},
  abstract  = {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.},
  language  = {en}
}
@article{BoeckmannBrueckner2001,
  author    = {B{\"o}ckmann, Christine and Br{\"u}ckner, Axel},
  title     = {100 years of the Runge-Kutta method : a brief editing for schools},
  issn      = {0268-3679},
  year      = {2001},
  abstract  = {This paper reports on the historical development of the Runge-Kutta methods beginning with the simple Euler method up to an embedded 13-stage method. Moreover, the design and the use of those methods under error order, stability and computation time conditions is edited for students of numerical analysis at undergraduate level. The second part presents applications in natural sciences, compares different methods and illustrates some of the difficulties of numerical solutions.},
  language  = {en}
}
@article{Boeckmann2000,
  author    = {B{\"o}ckmann, Christine},
  title     = {Evaluation of Multi-spectral Lidar Measurements of the Tropo- and Stratosphere via Modern Mathematical Methods for Inverse III- posed Problems to Determine the Aerosol Size Distribution},
  year      = {2000},
  language  = {en}
}
@article{WiegnerBoesenbergBoeckmannetal.1999,
  author    = {Wiegner, Matthias and B{\"o}senberg, Jens and B{\"o}ckmann, Christine and Eixmann, Ronald and Freudenthaler, Volker and Mattis, Ina and Trickl, Thomas},
  title     = {Lidar Network to Establish an Aerosol Climatology},
  year      = {1999},
  language  = {en}
}
@article{BoeckmannSarkoeziAlthausen1999,
  author    = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos and Althausen, Dietrich},
  title     = {Collocation Methods for Ill-posed Inverse Problems of Multiwavelength Lidar Measurements and Applications on LACE 98-Data},
  year      = {1999},
  language  = {en}
}
@article{BoeckmannSarkoezi1999,
  author    = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos},
  title     = {The Ill-posed Problem of Multiwavelength Lidar Data by a Hybrid Method of Variable Projection},
  year      = {1999},
  language  = {en}
}
@book{BoeckmannSarkoezi1999,
  author    = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos},
  title     = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection},
  series = {Preprint NLD},
  volume    = {53},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {[7] S. : graph. Darst.},
  year      = {1999},
  language  = {en}
}
@misc{KellermannMichalowskyGerschetal.2004,
  author    = {Kellermann, Rudolf and Michalowsky, Ulrike and Gersch, Jana and B{\"o}ckmann, Christine and Dethloff, Klaus and Gerhard-Multhaupt, Reimund and Klein, Armin and Resch-Esser, Ursula},
  title     = {Portal = Ideeller Lohn: Ehrenamtliches Engagement an der Uni},
  number    = {09-10/2004},
  organization    = {Universit{\"a}t Potsdam, Referat f{\"u}r Presse- und {\"O}ffentlichkeitsarbeit},
  issn      = {1618-6893},
  doi       = {10.25932/publishup-43981},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-439810},
  pages     = {47},
  year      = {2004},
  abstract  = {Aus dem Inhalt: - Ideeller Lohn: Ehrenamtliches Engagement an der Uni - Millionenpreis f{\"u}r Quantenphysiker - Erfolgreiche erste Kinderuni - Virtuelles Institut f{\"u}r Klimaforschung},
  language  = {de}
}
@unpublished{PornsawadBoeckmann2014,
  author    = {Pornsawad, Pornsarp and B{\"o}ckmann, Christine},
  title     = {Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems},
  volume    = {3},
  number    = {7},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70834},
  pages     = {30},
  year      = {2014},
  abstract  = {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 H{\"o}lder-type source-wise condition if the Fr{\´e}chet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.},
  language  = {en}
}
@misc{BoeckmannOsterloh2014,
  author    = {B{\"o}ckmann, Christine and Osterloh, Lukas},
  title     = {Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {907},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-44120},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-441200},
  pages     = {150 -- 165},
  year      = {2014},
  abstract  = {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.},
  language  = {en}
}
@misc{PornsawadSapsakulBoeckmann2019,
  author    = {Pornsawad, Pornsarp and Sapsakul, Nantawan and B{\"o}ckmann, Christine},
  title     = {A modified asymptotical regularization of nonlinear ill-posed problems},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1335},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47343},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-473433},
  pages     = {19},
  year      = {2019},
  abstract  = {In this paper, we investigate the continuous version of modified iterative Runge-Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))-𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.},
  language  = {en}
}
@misc{PereraBoeckmann2019,
  author    = {Perera, Upeksha and B{\"o}ckmann, Christine},
  title     = {Solutions of direct and inverse even-order Sturm-Liouville problems using Magnus expansion},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1336},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47341},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-473414},
  pages     = {24},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{PereraBoeckmann2019,
  author    = {Perera, Upeksha and B{\"o}ckmann, Christine},
  title     = {Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion},
  series = {Mathematics},
  volume    = {7},
  journal   = {Mathematics},
  number    = {6},
  publisher = {MDPI},
  address   = {Basel, Schweiz},
  issn      = {2227-7390},
  doi       = {10.3390/math7060544},
  pages     = {24},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{PornsawadSapsakulBoeckmann2019,
  author    = {Pornsawad, Pornsarp and Sapsakul, Nantawan and B{\"o}ckmann, Christine},
  title     = {A modified asymptotical regularization of nonlinear ill-posed problems},
  series = {Mathematics},
  volume    = {7},
  journal   = {Mathematics},
  edition   = {5},
  publisher = {MDPI},
  address   = {Basel, Schweiz},
  issn      = {2227-7390},
  doi       = {10.3390/math7050419},
  pages     = {19},
  year      = {2019},
  abstract  = {In this paper, we investigate the continuous version of modified iterative Runge-Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))-𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.},
  language  = {en}
}
@article{PornsawadSungcharoenBoeckmann2020,
  author    = {Pornsawad, Pornsarp and Sungcharoen, Parada and B{\"o}ckmann, Christine},
  title     = {Convergence rate of the modified Landweber method for solving inverse potential problems},
  series = {Mathematics : open access journal},
  volume    = {8},
  journal   = {Mathematics : open access journal},
  number    = {4},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2227-7390},
  doi       = {10.3390/math8040608},
  pages     = {22},
  year      = {2020},
  abstract  = {In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.},
  language  = {en}
}
@incollection{LueckBalderjahnKammetal.2000,
  author    = {L{\"u}ck, Erika and Balderjahn, Ingo and Kamm, Birgit and Greil, Holle and Wallschl{\"a}ger, Hans-Dieter and Jessel, Beate and B{\"o}ckmann, Christine and Oberh{\"a}nsli, Roland and Soyez, Konrad and Schmeer, Ernst and Blumenstein, Oswald and Berndt, Klaus-Peter and Edeling, Thomas and Friedrich, Sabine and Kaden, Klaus and Scheller, Frieder W. and Petersen, Hans-Georg and Asche, Hartmut and Bronstert, Axel and Giest, Hartmut and Gaedke, Ursula and L{\"o}hmannsr{\"o}ben, Hans-Gerd and Jeltsch, Florian and J{\"a}nkel, Ralph and Gzik, Axel and Bork, Hans-Rudolf and Bork, Hans-Rudolf},
  title     = {Umweltforschung f{\"u}r das Land Brandenburg : Arbeitsgruppen und Professuren},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-3797},
  publisher      = {Universit{\"a}t Potsdam},
  year      = {2000},
  language  = {de}
}
@misc{OrtizAmezcuaGuerreroRascadoGranadosMunozetal.2017,
  author    = {Ortiz-Amezcua, Pablo and Guerrero-Rascado, Juan Luis and Granados-Mu{\~n}oz, Mar{\´i}a Jos{\´e} and Benavent-Oltra, Jos{\´e} Antonio and B{\"o}ckmann, Christine and Samaras, Stefanos and Stachlewska, Iwona Sylwia and Janicka, Łucja and Baars, Holger and Bohlmann, Stephanie and Alados-Arboledas, Lucas},
  title     = {Microphysical characterization of long-range transported biomass burning particles from North America at three EARLINET stations},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {614},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41660},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416603},
  pages     = {5931 -- 5946},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{HoffmannOsterlohStoneetal.2012,
  author    = {Hoffmann, Anne and Osterloh, Lukas and Stone, Robert and Lampert, Astrid and Ritter, Christoph and Stock, Maria and Tunved, Peter and Hennig, Tabea and B{\"o}ckmann, Christine and Li, Shao-Meng and Eleftheriadis, Kostas and Maturilli, Marion and Orgis, Thomas and Herber, Andreas and Neuber, Roland and Dethloff, Klaus},
  title     = {Remote sensing and in-situ measurements of tropospheric aerosol, a PAMARCMiP case study},
  series = {Atmospheric environment : air pollution ; emissions, transport and dispersion, transformation, deposition effects, micrometeorology, urban atmosphere, global atmosphere},
  volume    = {52},
  journal   = {Atmospheric environment : air pollution ; emissions, transport and dispersion, transformation, deposition effects, micrometeorology, urban atmosphere, global atmosphere},
  number    = {3},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {1352-2310},
  doi       = {10.1016/j.atmosenv.2011.11.027},
  pages     = {56 -- 66},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@article{RitterAngelesBurgosBoeckmannetal.2018,
  author    = {Ritter, Christoph and {\´A}ngeles Burgos, Mar{\´i}a and B{\"o}ckmann, Christine and Mateos, David and Lisok, Justyna and Markowicz, Krzysztof M. and Moroni, Beatrice and Cappelletti, David and Udisti, Roberto and Maturilli, Marion and Neuber, Roland},
  title     = {Microphysical properties and radiative impact of an intense biomass burning aerosol event measured over Ny-angstrom lesund, Spitsbergen in July 2015},
  series = {Tellus - Series B, Chemical and Physical Meteorology},
  volume    = {70},
  journal   = {Tellus - Series B, Chemical and Physical Meteorology},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1600-0889},
  doi       = {10.1080/16000889.2018.1539618},
  pages     = {23},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{OrtizAmezcuaGuerreroRascadoJoseGranadosMunozetal.2017,
  author    = {Ortiz-Amezcua, Pablo and Guerrero-Rascado, Juan Luis and Jose Granados-Munoz, Maria and Benavent-Oltra, Jose Antonio and B{\"o}ckmann, Christine and Samaras, Stefanos and Stachlewska, Iwona Sylwia and Janicka, Lucja and Baars, Holger and Bohlmann, Stephanie and Alados-Arboledas, Lucas},
  title     = {Microphysical characterization of long-range transported biomass burning particles from North America at three EARLINET stations},
  series = {Atmospheric Chemistry and Physics},
  volume    = {17},
  journal   = {Atmospheric Chemistry and Physics},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {1680-7316},
  doi       = {10.5194/acp-17-5931-2017},
  pages     = {5931 -- 5946},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@misc{BoeckmannRitterCappelletti2018,
  author    = {B{\"o}ckmann, Christine and Ritter, Christoph and Cappelletti, David},
  title     = {Mathematical tool for a closure study of aerosol microphysical property retrieval using lidar and photometer data},
  series = {IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium},
  journal   = {IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium},
  publisher = {IEEE},
  address   = {New York},
  isbn      = {978-1-5386-7150-4},
  issn      = {2153-6996},
  doi       = {10.1109/IGARSS.2018.8518674},
  pages     = {5575 -- 5578},
  year      = {2018},
  abstract  = {We present a project combining lidar, photometer and particle counter data with a regularization software tool for a closure study of aerosol microphysical property retrieval. In a first step only lidar data are used to retrieve the particle size distribution (PSD). Secondly, photometer data are added, which results in a good consistency of the retrieved PSDs. Finally, those retrieved PSDs may be compared with the measured PSD from a particle counter. The data here were taken in Ny Alesund, Svalbard, as an example.},
  language  = {en}
}
@article{DubeBoeckmannRitter2022,
  author    = {Dube, Jonas and B{\"o}ckmann, Christine and Ritter, Christoph},
  title     = {Lidar-Derived Aerosol Properties from Ny-{\AA}lesund, Svalbard during the MOSAiC Spring 2020},
  series = {Remote sensing / Molecular Diversity Preservation International (MDPI)},
  volume    = {14},
  journal   = {Remote sensing / Molecular Diversity Preservation International (MDPI)},
  number    = {11},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2072-4292},
  doi       = {10.3390/rs14112578},
  pages     = {17},
  year      = {2022},
  abstract  = {In this work, we present Raman lidar data (from a Nd:YAG operating at 355 nm, 532 nm and 1064 nm) from the international research village Ny-Alesund for the time period of January to April 2020 during the Arctic haze season of the MOSAiC winter. We present values of the aerosol backscatter, the lidar ratio and the backscatter Angstrom exponent, though the latter depends on wavelength. The aerosol polarization was generally below 2\%, indicating mostly spherical particles. We observed that events with high backscatter and high lidar ratio did not coincide. In fact, the highest lidar ratios (LR > 75 sr at 532 nm) were already found by January and may have been caused by hygroscopic growth, rather than by advection of more continental aerosol. Further, we performed an inversion of the lidar data to retrieve a refractive index and a size distribution of the aerosol. Our results suggest that in the free troposphere (above approximate to 2500 m) the aerosol size distribution is quite constant in time, with dominance of small particles with a modal radius well below 100 nm. On the contrary, below approximate to 2000 m in altitude, we frequently found gradients in aerosol backscatter and even size distribution, sometimes in accordance with gradients of wind speed, humidity or elevated temperature inversions, as if the aerosol was strongly modified by vertical displacement in what we call the "mechanical boundary layer". Finally, we present an indication that additional meteorological soundings during MOSAiC campaign did not necessarily improve the fidelity of air backtrajectories.},
  language  = {en}
}