TY  - INPR
A1  - Rattana, Amornrat
A1  - Böckmann, Christine
T1  - Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order four
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)13 
KW  - Finite difference method
KW  - Numerov's method
KW  - Boundary value methods
KW  - Fourth order Sturm-Liouville problem
KW  - Eigenvalues
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59279
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  - 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  -