Atmospheric Lidar
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Atmospheric Lidar
Atmospheric lidar is a class of instruments that uses laser light to study atmospheric properties from the ground up to the top of the atmosphere. Such instruments have been used to study, among other, atmospheric gases, aerosols, clouds, and temperature. History The basic concepts to study the atmosphere using light were developed before World War II. In 1930, E.H. Synge proposed to study the density of the upper atmosphere using a searchlight beam . In the following years, searchlight beams were used to study cloud altitude using both scanning and pulsed light. Advanced techniques to study cloud properties using scattered light with different wavelengths were also proposed. With the first experiments, light scattering patterns were observed in the troposphere that were not compatible with a pure molecular atmosphere. This incompatibility was attributed to suspended haze particles. Similar techniques were also developed in the U.S.S.R. The searchlight beam technique continued ...
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Atmosphere Of Earth
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for liquid water to exist on the Earth's surface, absorbing ultraviolet solar radiation, warming the surface through heat retention (greenhouse effect), and reducing temperature extremes between day and night (the diurnal temperature variation). By mole fraction (i.e., by number of molecules), dry air contains 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide, and small amounts of other gases. Air also contains a variable amount of water vapor, on average around 1% at sea level, and 0.4% over the entire atmosphere. Air composition, temperature, and atmospheric pressure vary with altitude. Within the atmosphere, air suitable for use in photosynthesis by terrestrial plants and breathing of terrestrial animals is found only in ...
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Lidar Sketch
Lidar (, also LIDAR, or LiDAR; sometimes LADAR) is a method for determining ranges (variable distance) by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver. It can also be used to make digital 3-D representations of areas on the Earth's surface and ocean bottom of the intertidal and near coastal zone by varying the wavelength of light. It has terrestrial, airborne, and mobile applications. ''Lidar'' is an acronym of "light detection and ranging" or "laser imaging, detection, and ranging". It is sometimes called 3-D laser scanning, a special combination of 3-D scanning and laser scanning. Lidar is commonly used to make high-resolution maps, with applications in surveying, geodesy, geomatics, archaeology, geography, geology, geomorphology, seismology, forestry, atmospheric physics, laser guidance, airborne laser swath mapping (ALSM), and laser altimetry. It is also used in control and navigation for some aut ...
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Ozone
Ozone (), or trioxygen, is an inorganic molecule with the chemical formula . It is a pale blue gas with a distinctively pungent smell. It is an allotrope of oxygen that is much less stable than the diatomic allotrope , breaking down in the lower atmosphere to (dioxygen). Ozone is formed from dioxygen by the action of ultraviolet (UV) light and electrical discharges within the Earth's atmosphere. It is present in very low concentrations throughout the latter, with its highest concentration high in the ozone layer of the stratosphere, which absorbs most of the Sun's ultraviolet (UV) radiation. Ozone's odour is reminiscent of chlorine, and detectable by many people at concentrations of as little as in air. Ozone's O3 structure was determined in 1865. The molecule was later proven to have a bent structure and to be weakly diamagnetic. In standard conditions, ozone is a pale blue gas that condenses at cryogenic temperatures to a dark blue liquid and finally a violet-black soli ...
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Water Vapor
(99.9839 °C) , - , Boiling point , , - , specific gas constant , 461.5 J/( kg·K) , - , Heat of vaporization , 2.27 MJ/kg , - , Heat capacity , 1.864 kJ/(kg·K) Water vapor, water vapour or aqueous vapor is the gaseous phase of water. It is one state of water within the hydrosphere. Water vapor can be produced from the evaporation or boiling of liquid water or from the sublimation of ice. Water vapor is transparent, like most constituents of the atmosphere. Under typical atmospheric conditions, water vapor is continuously generated by evaporation and removed by condensation. It is less dense than most of the other constituents of air and triggers convection currents that can lead to clouds. Being a component of Earth's hydrosphere and hydrologic cycle, it is particularly abundant in Earth's atmosphere, where it acts as a greenhouse gas and warming feedback, contributing more to total greenhouse effect than non-condensable gases such as carbon dioxide an ...
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Christine Böckmann
Christine Böckmann (née Hense, born 1955) is a German applied mathematician, numerical analyst Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ..., and expert on atmospheric lidar. She is an ''Academic ranks in Germany, außerplanmäßiger Professor'' of mathematics at the University of Potsdam, and one of the Principal Investigators of EARLINET, the European Aerosol Research Lidar Network. Böckmann studied mathematics at the Dresden University of Technology, earning a diploma in 1980 and completing her doctorate (Dr. rer. nat.) in 1984. Her dissertation, ''Ein ableitungsfreies Verfahren vom Gauß-Newton-Typ zur Lösung von nichtlinearen Quadratmittelproblemen mit separierten Variablen'', was supervised by Hubert Schwetlick. She subsequently completed a habilitation at the Uni ...
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Cross-validation (statistics)
Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set. Cross-validation is a resampling method that uses different portions of the data to test and train a model on different iterations. It is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. In a prediction problem, a model is usually given a dataset of ''known data'' on which training is run (''training dataset''), and a dataset of ''unknown data'' (or ''first seen'' data) against which the model is tested (called the validation dataset or ''testing set''). The goal of cross-validation is to test the model's ability to predict new data that was not used in estimating it, in order to flag problems like overfitting or selection bias and to give an insight o ...
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Tikhonov Regularization
Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems. It is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters. In general, the method provides improved efficiency in parameter estimation problems in exchange for a tolerable amount of bias (see bias–variance tradeoff). The theory was first introduced by Hoerl and Kennard in 1970 in their ''Technometrics'' papers “RIDGE regressions: biased estimation of nonorthogonal problems” and “RIDGE regressions: applications in nonorthogonal problems”. This was the result of ten years of research into the field of ridge analysis. ...
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Singular Value Decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an \ m \times n\ complex matrix is a factorization of the form \ \mathbf = \mathbf\ , where is an \ m \times m\ complex unitary matrix, \ \mathbf\ is an \ m \times n\ rectangular diagonal matrix with non-negative real numbers on the diagonal, is an n \times n complex unitary matrix, and \ \mathbf\ is the conjugate transpose of . Such decomposition always exists for any complex matrix. If is real, then and can be guaranteed to be real orthogonal matrices; in such contexts, the SVD is often denoted \ \mathbf^\mathsf\ . The diagonal entries \ \sigma_i = \Sigma_\ of \ \mathbf\ are uniquely determined by and are known as the singular values of . The n ...
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Regularization (mathematics)
In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, following delineation is particularly helpful: * Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem. These terms could be priors, penalties, or constraints. Explicit regularization is commonly employed with ill-posed optimization problems. The regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique. * Implicit regularization is all other forms of regularization. This includes, for example, early stopping, using a robust loss function, and discarding outliers. Implicit regularization is essentially ubiquitous in modern machine learning appr ...
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Single-scattering Albedo
Single-scattering albedo is the ratio of scattering efficiency to total extinction efficiency (which is also termed "attenuance", a sum of scattering and absorption). Most often it is defined for small-particle scattering of electromagnetic waves. Single-scattering albedo is unitless, and a value of unity implies that all particle extinction is due to scattering; conversely, a single-scattering albedo of zero implies that all extinction is due to absorption. For spherical particles one can calculate single-scattering albedo from Mie theory and knowledge of bulk properties of material such as refractive index. For non-spherical particles one could use discrete dipole approximation or other methods of computational electromagnetics. The albedo of particles of shapes which are easily parameterized in non-standard co-ordinate systems may be determined through solutions of Maxwell's equation analogues in such coordinate systems. Scattering albedo equations have yet to be determined in ...
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Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, , where ''θ''1 and ''θ''2 are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices ''n''1 and ''n''2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity ( Fresnel's equations) and Brewster's angle. The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that medium is , where '' ...
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Angstrom Exponent
The Angstrom exponentGregory L. Schuster, Oleg Dubovik and Brent N. Holben (2006): "Angstrom exponent and bimodal aerosol size distributions". ''Journal of Geophysical Research: Atmospheres'', volume 111, issue D7, article D07207, pages 1-14. Itaru Sano (2004): "Optical thickness and Angstrom exponent of aerosols over the land and ocean from space-borne polarimetric data". ''Advances in Space Research'', volume 34, issue 4, pages 833-837. or Ångström exponentD. A. Lack1 and J. M. Langridge (2013): "On the attribution of black and brown carbon light absorption using the Ångström exponent". ''Atmospheric Chemistry and Physics'', volume 13, issue 20, pages 10535-10543. Ji Li, Chao Liu, Yan Yin, and K. Raghavendra Kumar (2016): "Numerical investigation on the Ångström exponent of black carbon aerosol". ''Journal of Geophysical Research: Atmospheres'', volume 121, issue 7, pages 3506-3518. is a parameter that describes how the optical thickness of an aerosol typically depends on th ...
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