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Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements
01 Jan 1977-
About: The article was published on 1977-01-01 and is currently open access. It has received 797 citations till now. The article focuses on the topics: Inversion (meteorology).
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TL;DR: The developed algorithm is adapted for the retrieval of aerosol properties from measurements made by ground-based Sun-sky scanning radiometers used in the Aerosol Robotic Network (AERONET) and allows a choice of normal or lognormal noise assumptions.
Abstract: The problem of deriving a complete set of aerosol optical properties from Sun and sky radiance measurements is discussed. Algorithm development is focused on improving aerosol retrievals by means of including a detailed statistical optimization of the influence of noise in the inversion procedure. The methodological aspects of such an optimization are discussed in detail and revised according to both modern findings in inversion theory and practical experience in remote sensing. Accordingly, the proposed inversion algorithm is built on the principles of statistical estimation: the spectral radiances and various a priori constraints on aerosol characteristics are considered as multisource data that are known with predetermined accuracy. The inversion is designed as a search for the best fit of all input data by a theoretical model that takes into account the different levels of accuracy of the fitted data. The algorithm allows a choice of normal or lognormal noise assumptions. The multivariable fitting is implemented by a stable numerical procedure combining matrix inversion and univariant relaxation. The theoretical inversion scheme has been realized in the advanced algorithm retrieving aerosol size distribution together with complex refractive index from the spectral measurements of direct and diffuse radiation. The aerosol particles are modeled as homogeneous spheres. The atmospheric radiative transfer modeling is implemented with well-established publicly available radiative transfer codes. The retrieved refractive indices can be wavelength dependent; however, the extended smoothness constraints are applied to its spectral dependence (and indirectly through smoothness constraints on retrieved size distributions). The positive effects of statistical optimization on the retrieval results as well as the importance of applying a priori constraints are discussed in detail for the retrieval of both aerosol size distribution and complex refractive index. The developed algorithm is adapted for the retrieval of aerosol properties from measurements made by ground-based Sun-sky scanning radiometers used in the Aerosol Robotic Network (AERONET). The results of numerical tests together with examples of experimental data inversions are presented.
2,122 citations
Cites background or methods from "Introduction to the Mathematics of ..."
...Choosing the strength of a priori constraints is, however, an especially challenging problem [e.g., Rodgers, 1976; Twomey, 1977; King, 19821, which becomes even more challenging when such different parameters as particle size distribution and complex refractive index are retrieved simultaneously....
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...Values of the Lagrange multiplier: In the literature devoted to inversion techniques [e.g., Twomey, 1977; Tikhonov and Arsenin, 1977; Tarantola, 19871 the Lagrange multiplier is defined as a nonnegative multiplier that serves to weight the contribution of a priori (smoothness) constraints, relative…...
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...0 1 -2 1 1 This matrix is most commonly used for aerosol size distribution retrieval [cf. Twomey, 1977; King et al., 1978; King, 1982; Nakajima et al., 19961....
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TL;DR: In this article, a new inversion concept for simultaneously retrieving aerosol size distribution, complex refractive index, and single scattering albedo from spectral measurements of direct and diffuse radiation was proposed.
Abstract: Sensitivity studies are conducted regarding aerosol optical property retrieval from radiances measured by ground-based Sun-sky scanning radiometers of the Aerosol Robotic Network (AERONET). These studies focus on testing a new inversion concept for simultaneously retrieving aerosol size distribution, complex refractive index, and single- scattering albedo from spectral measurements of direct and diffuse radiation. The perturbations of the inversion resulting from random errors, instrumental offsets, and known uncertainties in the atmospheric radiation model are analyzed. Sun or sky channel miscalibration, inaccurate azimuth angle pointing during sky radiance measurements, and inaccuracy in accounting for surface reflectance are considered as error sources. The effects of these errors on the characterization of three typical and optically distinct aerosols with bimodal size distributions (weakly absorbing water-soluble aerosol, absorbing biomass-burning aerosol, and desert dust) are considered. The aerosol particles are assumed in the retrieval to be polydispersed homogeneous spheres with the same complex refractive index. Therefore we also examined how inversions with such an assumption bias the retrievals in the case of nonspherical dust aerosols and in the case of externally or internally mixed spherical particles with different refractive indices. The analysis shows successful retrieval of all aerosol characteristics (size distribution, complex refractive index, and single-scattering albedo), provided the inversion includes the data combination of spectral optical depth together with sky radiances in the full solar almucantar (with angular coverage of scattering angles up to 100" or more). The retrieval accuracy is acceptable for most remote sensing applications even in the presence of rather strong systematic or random uncertainties in the measurements. The major limitations relate to the characterization of low optical depth situations for all aerosol types, where high relative errors may occur in the direct radiation measurements of aerosol optical depth. Also, the results of tests indicate that a decrease of angular coverage of scattering (scattering angles of 75" or less) in the sky radiance results in the loss of practical information about refractive index. Accurate azimuth angle pointing is critical for the characterization of dust. Scattering by nonspherical dust particles requires special analysis, whereby approximation of the aerosol by spheres allows us to derive single-scattering albedo by inverting spectral optical depth together with sky radiances in the full solar almucantar. Inverting sky radiances measured in the first 40" scattering angle only, where nonspherical effects are minor, results in accurate retrievals of aerosol size distributions of nonspherical particles.
1,562 citations
TL;DR: In this paper, the authors present a cloud-screening algorithm for ground-based sun-photometer measurements of aerosol optical depth in the Aerosol Robotic Network (AERONET).
1,311 citations
Goddard Space Flight Center1, Lille University of Science and Technology2, Goddard Institute for Space Studies3, Texas A&M University4, University of Maryland, Baltimore County5, University of Amsterdam6, Spanish National Research Council7, Royal Netherlands Meteorological Institute8, Radboud University Nijmegen9
TL;DR: In this article, the authors used shape mixtures of randomly oriented spheroids for modeling desert dust aerosol light scattering, and the results indicated that nonspherical particles with aspect ratios similar to 1.5 dominate in desert dust plumes, while in the case of background maritime aerosol spherical particles are dominant.
Abstract: [ 1] The possibility of using shape mixtures of randomly oriented spheroids for modeling desert dust aerosol light scattering is discussed. For reducing calculation time, look-up tables were simulated for quadrature coefficients employed in the numerical integration of spheroid optical properties over size and shape. The calculations were done for 25 bins of the spheroid axis ratio ranging from similar to 0.3 ( flattened spheroids) to similar to 3.0 ( elongated spheroids) and for 41 narrow size bins covering the size parameter range from similar to 0.012 to similar to 625. The look-up tables were arranged into a software package, which allows fast, accurate, and flexible modeling of scattering by randomly oriented spheroids with different size and shape distributions. In order to evaluate spheroid model and explore the possibility of aerosol shape identification, the software tool has been integrated into inversion algorithms for retrieving detailed aerosol properties from laboratory or remote sensing polarimetric measurements of light scattering. The application of this retrieval technique to laboratory measurements by Volten et al. ( 2001) has shown that spheroids can closely reproduce mineral dust light scattering matrices. The spheroid model was utilized for retrievals of aerosol properties from atmospheric radiation measured by AERONET ground-based Sun/sky-radiometers. It is shown that mixtures of spheroids allow rather accurate fitting of measured spectral and angular dependencies of observed intensity and polarization. Moreover, it is shown that for aerosol mixtures with a significant fraction of coarse-mode particles ( radii >= similar to 1 mu m), the nonsphericity of aerosol particles can be detected as part of AERONET retrievals. The retrieval results indicate that nonspherical particles with aspect ratios similar to 1.5 and higher dominate in desert dust plumes, while in the case of background maritime aerosol spherical particles are dominant. Finally, the potential of using AERONET derived spheroid mixtures for modeling the effects of aerosol particle nonsphericity in other remote sensing techniques is discussed. For example, the variability of lidar measurements ( extinction to backscattering ratio and signal depolarization ratio) is illustrated and analyzed. Also, some potentially important differences in the sensitivity of angular light scattering to parameters of nonspherical versus spherical aerosols are revealed and discussed.
1,260 citations
TL;DR: A survey of kernel-based regularization and its connections with reproducing kernel Hilbert spaces and Bayesian estimation of Gaussian processes to demonstrate that learning techniques tailored to the specific features of dynamic systems may outperform conventional parametric approaches for identification of stable linear systems.
683 citations