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The Ill-posed Problem of Multiwavelength Lidar Data by a Hybrid Method of Variable Projection
(1999)
The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection
(1999)
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.
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.
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.
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.
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.
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.
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.
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.