Majorization, 4G Theorem and Schr\"odinger perturbations

Schr\"odinger perturbations of transition densities by singular potentials may fail to be comparable with the original transition density. For instance this is so for the transition density of a subordinator perturbed by any time-independent unbounded potential. In order to estimate such perturbations it is convenient to use an auxilary transition density as a majorant and the 4G inequality for the original transition density and the majorant. We prove the 4G inequality for the $1/2$-stable and inverse Gaussian subordinators, discuss the corresponding class of admissible potentials and indicate estimates for the resulting transition densities of Schr\"odinger operators. The connection of the transition densities to their generators is made via the weak-type notion of fundamental solution.Comment: 17 pages, editorial changes and some details added in proofs, to appear in Journal of Evolution Equation

Properties of aerosol and surface derived from OLCI/Sentinel-3A using GRASP approach: Retrieval development and preliminary validation

The Ocean and Land Color Instrument (OLCI) onboard the Copernicus Sentinel-3A satellite is a medium-resolution and multi-spectral push-broom imager acquiring radiance in 21 spectral bands covering from the visible to the far near-infrared. These measurements are primary dedicated to land & ocean color applications, but actually include also reliable information for atmospheric aerosol and surface brightness characterization. In the framework of the EUMETSAT funded study to support the Copernicus Program, we describe the retrieval of aerosol and surface properties from OLCI single-viewing multi-spectral Top-Of-Atmosphere (TOA) radiances based on the Generalized Retrieval of Atmosphere and Surface Properties (GRASP) algorithm. The high potential of the OLCI/GRASP configuration stems from the attempt to retrieve both aerosol load and surface reflectance simultaneously using a globally consistent high-level approach. For example, both over land and ocean surfaces OLCI/GRASP uses 9 spectral channels (albeit with different weights), strictly the same prescribed aerosol models and globally the same a priori constraints (though with some differences for observations over land and ocean). Due to the lack of angular multi-viewing information, the directional properties of underlying surface are strongly constrained in the retrieval: over ocean the Fresnel reflection together with foam/whitecap albedo are exclusively computed using a priori wind speed; over land, the Bidirectional Reflectance Distribution Function (BRDF) is slightly adjusted from a priori values of climatological Ross-Li volumetric and geometric terms. Meanwhile, the isotropic reflectance is retrieved globally under mild spectral smoothness constraints. It should be noticed that OLCI/GRASP configuration employs innovative multi-pixel concept (Dubovik et al., 2011) that enhance retrieval by simultaneously inverting large group of pixels. The concept allows for benefiting from knowledge about natural variability of the retrieved parameters. The obtained OLCI/GRASP products were validated with the Aerosol Robotic Network (AERONET) and Maritime Aerosol Network (MAN) and intercompared with the Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol and surface products. The overall performance is quite comparable to the community-referenced MODIS. Over ocean the OLCI/GRASP results are encouraging with 67% of the AOD (550 nm) satisfying the Global Climate Observing System (GCOS) requirement using AERONET coastal sites and 74% using MAN deep ocean measurements, and an AOD (550 nm) bias 0.01 with AERONET and nearly zero bias with MAN. Over land, 48% of OLCI/GRASP AOD (550 nm) satisfy the GCOS requirement and a bias within ±0.01 for total and AOD < 0.2. Key challenges are identified and discussed: adequate screening of cloud contaminations, retrieval of aerosol over bright surfaces and in the regions containing complex mixtures of aerosol

Ultra-Stable Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research (5STAR)

The Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research (4STAR) combines airborne sun tracking and sky scanning with diffraction spectroscopy to improve knowledge of atmospheric constituents and their links to airpollution and climate. Direct beam hyperspectral measurement of optical depth improves retrievals of gas constituentsand determination of aerosol properties. Sky scanning enhances retrievals of aerosol type and size distribution.Hyperspectral cloud-transmitted radiance measurements enable the retrieval of cloud properties from below clouds.These measurements tighten the closure between satellite and ground-based measurements. 4STAR incorporates amodular sun-tracking sky-scanning optical head with optical fiber signal transmission to rack mounted spectrometers,permitting miniaturization of the external optical tracking head, and future detector evolution.4STAR has supported a broad range of flight experiments since it was first flown in 2010. This experience provides thebasis for a series of improvements directed toward reducing measurement uncertainty and calibration complexity, andexpanding future measurement capabilities, to be incorporated into a new 5STAR instrument. A 9-channel photodioderadiometer with AERONET-matched bandpass filters will be incorporated to improve calibration stability. A wide dynamic range tracking camera will provide a high precision solar position tracking signal as well as an image of sky conditions around the solar axis. An ultrasonic window cleaning system design will be tested. A UV spectrometer tailored for formaldehyde and SO2 gas retrievals will be added to the spectrometer enclosure. Finally, expansion capability for a 4 channel polarized radiometer to measure the Stokes polarization vector of sky light will be incorporated. This paper presents initial progress on this next-generation 5STAR instrument

Lidar-Radiometer Inversion Code (LIRIC) for the retrieval of vertical aerosol properties from combined lidar/radiometer data: development and distribution in EARLINET

The financial support by the European Union's Horizon 2020 research and innovation programme (ACTRIS-2, grant agreement no. 654109) is gratefully acknowledged. The background of LIRIC algorithm and software was developed under the ACTRIS Research Infrastructure project, grant agreement no. 262254, within the European Union Seventh Framework Programme, which financial support is gratefully acknowledged.r I. Binietoglou received funding from the European Union's Seventh Framework Programme for research, technological development and demonstration under the grant agreement no. 289923 - ITARS.This paper presents a detailed description of LIRIC (LIdar-Radiometer Inversion Code) algorithm for simultaneous processing of coincident lidar and radiometric (sun photometric) observations for the retrieval of the aerosol concentration vertical profiles. As the lidar/radiometric input data we use measurements from European Aerosol Research Lidar Network (EARLINET) lidars and collocated sun-photometers of Aerosol Robotic Network (AERONET). The LIRIC data processing provides sequential inversion of the combined lidar and radiometric data. The algorithm starts with the estimations of column-integrated aerosol parameters from radiometric measurements followed by the retrieval of height dependent concentrations of fine and coarse aerosols from lidar signals using integrated column characteristics of aerosol layer as a priori constraints. The use of polarized lidar observations allows us to discriminate between spherical and non-spherical particles of the coarse aerosol mode. The LIRIC software package was implemented and tested at a number of EARLINET stations. Intercomparison of the LIRIC-based aerosol retrievals was performed for the observations by seven EARLINET lidars in Leipzig, Germany on 25 May 2009. We found close agreement between the aerosol parameters derived from different lidars that supports high robustness of the LIRIC algorithm. The sensitivity of the retrieval results to the possible reduction of the available observation data is also discussed.European Union (EU) 654109ACTRIS Research Infrastructure project within the European Union 262254European Union (EU) 289923 - ITAR

Lidar-Radiometer Inversion Code (LIRIC) for the retrieval of vertical aerosol properties from combined lidar/radiometer data: Development and distribution in EARLINET

This paper presents a detailed description of LIRIC (LIdar-Radiometer Inversion Code) algorithm for simultaneous processing of coincident lidar and radiometric (sun photometric) observations for the retrieval of the aerosol concentration vertical profiles. As the lidar/radiometric input data we use measurements from European Aerosol Research Lidar Network (EARLINET) lidars and collocated sun-photometers of Aerosol Robotic Network (AERONET). The LIRIC data processing provides sequential inversion of the combined lidar and radiometric data. The algorithm starts with the estimations of column-integrated aerosol parameters from radiometric measurements followed by the retrieval of height dependent concentrations of fine and coarse aerosols from lidar signals using integrated column characteristics of aerosol layer as a priori constraints. The use of polarized lidar observations allows us to discriminate between spherical and non-spherical particles of the coarse aerosol mode. The LIRIC software package was implemented and tested at a number of EARLINET stations. Intercomparison of the LIRIC-based aerosol retrievals was performed for the observations by seven EARLINET lidars in Leipzig, Germany on 25 May 2009. We found close agreement between the aerosol parameters derived from different lidars that supports high robustness of the LIRIC algorithm. The sensitivity of the retrieval results to the possible reduction of the available observation data is also discussed

Détermination des propriétés optiques et microphysiques des aérosols atmosphériques à partir des mesures de photomètre solaire aéroporté

Les aérosols atmosphériques constituent l’une des plus grandes incertitudes dans l’étude des processus de changement climatique. La diversité des leurs sources et mécanismes de formation rendent la distribution spatiale des aérosols très inhomogène ce qui nécessite la mise en place d’une instrumentation et de méthodes d’observation sophistiquées. Un nouveau photomètre solaire aéroporté PLASMA permet d’effectuer des mesures d’épaisseur optique des aérosols sur une large gamme spectrale (0.34−2.25 μm) et à différentes altitudes. La détermination de la distribution verticale des propriétés optiques des aérosols peut ainsi être utilisée pour valider les algorithmes d’inversion des mesures lidar. Il est possible de remonter à la distribution de taille des particules d’aérosol à différents niveaux. En outre, l’instrument peut être installé sur un véhicule afin de mesurer les profils horizontaux du contenu des aérosols. Cette étude est consacrée à la caractérisation et à l’étalonnage de l’instrument et à l’analyse de plusieurs jeux de données. De nombreuses mesures au sol, aéroportées et depuis un véhicule ont réalisées et sont comparées aux mesures d’autres instruments. L’étude de la sensibilité de l’algorithme d’inversion de Oleg Dubovik a montré qu’il est possible d’obtenir la distribution en tailles des particules à partir de mesures d’épaisseur optique quand l’indice de réfraction est connu avec une certaine précision. Les mesures aéroportées ont ainsi été inversées et les distributions de tailles obtenues pour différentes altitudes. Cette information permettra de mieux comprendre les processus de formation et la répartition spatiale des aérosols dans l’atmosphère.Atmospheric aerosols still represents one of the greatest uncertainty in the study of the processes of climate change. The diversity of aerosol sources and their formation mechanisms make the spatial distribution of aerosols very inhomogenous and requires numerous instruments and different approaches for their analysis. A new multi-wavelength airborne sun photometer PLASMA (Photomètre Léger Aéroporté pour la Surveillance des Masses d’Air) developed in the Laboratory of Atmospheric Optics allows providing on-board measurements of aerosol optical depth over a wide (0.34 − 2.25 μm) spectral range and at different altitudes. The information of vertical distribution of aerosol optical properties can be then used to validate the lidar processing algorithms. It is possible to retrieve from PLASMA measurements the size distribution of the aerosol particles at different levels. Also, the instrument can be installed on an automobile in order to measure the horizontal profiles of AOT. This study is dedicated to characterization and calibration of PLASMA and to the analysis of several data sets. Numerous ground-based, airborne and automobile measurements were held and compared with other instruments. Sensitivity study of the Dubovik’s inversion algorithm showed that it is possible to get the particle’s size distribution from only AOD measurements assuming a value of the refractive index within a limited domain. Airborne PLASMA measurements were inverted and size distributions of the aerosol particles were obtained at different altitudes. This new information is helpful to better understand the formation and spatial distribution of aerosols in the atmosphere

Characterization of temporal and spatial variability of aerosols from ground-based climatology: towards evaluation of satellite mission requirements

International audienc

Algorithm and software for the retrieval of vertical aerosol properties using combined lidar/radiometer data: dissemination in EARLINET

Ten combined lidar and sun-radiometer stations in theEuropean Aerosol Research Lidar Network(EARLINET) have been testing technique and software for retrieving aerosol microstructure parameters from coordinated lidar and sun-radiometer data with the aim of creating new type of routing cooperative observations. The paper presents description of a program package and preliminary results of testing measurements at some stations.Peer Reviewe

Algorithm and software for the retrieval of vertical aerosol properties using combined lidar/radiometer data: dissemination in EARLINET

Ten combined lidar and sun-radiometer stations in theEuropean Aerosol Research Lidar Network(EARLINET) have been testing technique and software for retrieving aerosol microstructure parameters from coordinated lidar and sun-radiometer data with the aim of creating new type of routing cooperative observations. The paper presents description of a program package and preliminary results of testing measurements at some stations.Peer ReviewedPostprint (published version