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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.
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.
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.
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.
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.
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, 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, 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.
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.