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In this paper, we investigate the combination of multigrid methods and neural networks, starting from a Finite Element discretization of an elliptic PDE. Multigrid methods use interpolation operators to transfer information between different levels of approximation. These operators are crucial for fast convergence of multigrid, but they are generally unknown. We propose Deep Neural Network models for learning interpolation operators and we build a multilevel hierarchy based on the output of the network. We investigate the accuracy of the interpolation operator predicted by the Neural Network, testing it with different network architectures. This Neural Network approach for the construction of grid operators can then be extended for an automatic definition of multilevel solvers, allowing a portable solution in scientific computing, Comment: To appear in Springer Journal: "The 26th International Domain Decomposition Conference (DD26)"

Model simulations of solar irradiance reaching the Earth's surface during a solar eclipse constitute a useful tool for studying the impact of this phenomenon on the radiance propagation through the atmosphere. A simple approach to extend the use of an algorithm already adopted for evaluating the variations in the extraterrestrial solar radiation during a total eclipse is proposed for a partial eclipse case. The application is based on the assessment of the distance between the apparent solar and lunar disk centers on the celestial hemisphere, using the local circumstances and the ratio between the Sun and Moon radii as input parameters. It was found that during the eclipse of March 29, 2006, the present approach led to an estimate of the surface UV solar irradiance trend differing by no more than \pm5% from the corresponding trend observed at Bologna (Italy)., Comment: 5 pages, 3 figures and 1 table

Multi-year sets of ground-based sun-photometer measurements conducted at 12 Arctic sites and 9 Antarctic sites were examined to determine daily mean values of aerosol optical thickness tau(lambda) at visible and near-infrared wavelengths, from which best-fit values of Ångström's exponent alpha were calculated. Analyzing these data, the monthly mean values of tau(0.50 micrometers) and alpha and the relative frequency histograms of the daily mean values of both parameters were determined for winter-spring and summer-autumn in the Arctic and for austral summer in Antarctica. The Arctic and Antarctic covariance plots of the seasonal median values of alpha versus tau(0.50 micrometers) showed: (i) a considerable increase in tau(0.50 micrometers) for the Arctic aerosol from summer to winter-spring, without marked changes in alpha; and (ii) a marked increase in tau(0.50 micrometer) passing from the Antarctic Plateau to coastal sites, whereas alpha decreased considerably due to the larger fraction of sea-salt aerosol. Good agreement was found when comparing ground-based sun-photometer measurements of tau(lambda) and alpha at Arctic and Antarctic coastal sites with Microtops measurements conducted during numerous AERONET/MAN cruises from 2006 to 2013 in three Arctic Ocean sectors and in coastal and off-shore regions of the Southern Atlantic, Pacific, and Indian Oceans, and the Antarctic Peninsula. Lidar measurements were also examined to characterize vertical profiles of the aerosol backscattering coefficient measured throughout the year at Ny-Ålesund. Satellite-based MODIS, MISR, and AATSR retrievals of tau(lambda) over large parts of the oceanic polar regions during spring and summer were in close agreement with ship-borne and coastal ground-based sun-photometer measurements. An overview of the chemical composition of mode particles is also presented, based on in-situ measurements at Arctic and Antarctic sites. Fourteen log-normal aerosol number size-distributions were defined to represent the average features of nuclei, accumulation and coarse mode particles for Arctic haze, summer background aerosol, Asian dust and boreal forest fire smoke, and for various background austral summer aerosol types at coastal and high-altitude Antarctic sites. The main columnar aerosol optical characteristics were determined for all 14 particle modes, based on in-situ measurements of the scattering and absorption coefficients. Diurnally averaged direct aerosol-induced radiative forcing and efficiency were calculated for a set of multimodal aerosol extinction models, using various Bidirectional Reflectance Distribution Function models over vegetation-covered, oceanic and snow-covered surfaces. These gave a reliable measure of the pronounced effects of aerosols on the radiation balance of the surface-atmosphere system over polar regions.

Analyses of aerosol optical depth (AOD) and colurnmn water vapor (CWV) measurements acquired with NASA Ames Research Center's 6-channel Airborne Tracking Sunphotometer (AATS-6) operated aboard the R/V Professor Vodyanitskiy during the 2nd Aerosol Characterization Experiment (ACE-2) are discussed. Data are compared with various in situ and remote measurements for selected cases. The focus is on 10 July, when the Pelican airplane flew within 70 km of the ship near the time of a NOAA-14/AVHRR satellite overpass and AOD measurements with the 14-channel Ames Airborne Tracking Sunphotometer (AATS-14) above the marine boundary layer (MBL) permitted calculation of AOD within the MBL from the AATS-6 measurements. A detailed column closure test is performed for MBL AOD on 10 July by comparing the AATS-6 MBL AODs with corresponding values calculated by combining shipboard particle size distribution measurements with models of hygroscopic growth and radiosonde humidity profiles (plus assumptions on the vertical profile of the dry particle size distribution and composition). Large differences (30-80% in the mid-visible) between measured and reconstructed AODs are obtained, in large part because of the high sensitivity of the closure methodology to hygroscopic growth models, which vary considerably and have not been validated over the necessary range of particle size/composition distributions. The wavelength dependence of AATS-6 AODs is compared with the corresponding dependence of aerosol extinction calculated from shipboard measurements of aerosol size distribution and of total scattering mearured by a shipboard integrating nephelometer for several days. Results are highly variable, illustrating further the great difficulty of deriving column values from point measurements. AATS-6 CWV values are shown to agree well with corresponding values derived from radiosonde measurements during 8 soundings on 7 days and also with values calculated from measurements taken on 10 July with the AATS-14 and the University of Washington Passive Humidigraph aboard the Pelican.