Retrieval of the optical properties of aerosols from aureole and extinction data.
TL;DR: Solution of the small-angle approximation of Weinman et al.1 is piled on the solution of the truncation approximation to synthesize the intensity field in the solar aureole to estimate the forward parts of the aerosol phase functions and retrieval of aerosol volume spectra.
Abstract: Solution of the small-angle approximation of Weinman et al.1 is piled on the solution of the truncation approximation to synthesize the intensity field in the solar aureole. Accuracy within ±3% is attained for almost all parts of the sky and for air masses less than ∼5. An iterative algorithm utilizing this calculation scheme is applied to the spectral aureole and extinction measurements to estimate the forward parts of the aerosol phase functions and to retrieve the aerosol volume spectra from them.
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TL;DR: The operation and philosophy of the monitoring system, the precision and accuracy of the measuring radiometers, a brief description of the processing system, and access to the database are discussed.
6,535 citations
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 methods from "Retrieval of the optical properties..."
...This type of smoothing is commonly used in aerosol optical properties retrievals [e.g., King et al., 1978; Shaw, 1979; King, 1982; Nakajima et al., 1983, 1996; Spinhirne and King, 1995; Dubovik et al., 19951....
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TL;DR: In this paper, the authors used the EOS moderate resolution imaging spectroradiometer (MODIS) using dark land targets to estimate the optical thickness and columnar mass concentration of the accumulation mode.
Abstract: Daily distribution of the aerosol optical thickness and columnar mass concentration will be derived over the continents, from the EOS moderate resolution imaging spectroradiometer (MODIS) using dark land targets. Dark land covers are mainly vegetated areas and dark soils observed in the red and blue channels; therefore the method will be limited to the moist parts of the continents (excluding water and ice cover). After the launch of MODIS the distribution of elevated aerosol concentrations, for example, biomass burning in the tropics or urban industrial aerosol in the midlatitudes, will be continuously monitored. The algorithm takes advantage of the MODIS wide spectral range and high spatial resolution and the strong spectral dependence of the aerosol opacity for most aerosol types that result in low optical thickness in the mid-IR (2.1 and 3.8 pm). The main steps of the algorithm are (1) identification of dark pixels in the mid-IR; (2) estimation of their reflectance at 0.47 and 0.66 pm; and (3) derivation of the optical thickness and mass concentration of the accumulation mode from the detected radiance. To differentiate between dust and aerosol dominated by accumulation mode particles, for example, smoke or sulfates, ratios of the aerosol path radiance at 0.47 and 0.66 pm are used. New dynamic aerosol models for biomass burning aerosol, dust and aerosol from industrial/urban origin, are used to determine the aerosol optical properties used in the algorithm. The error in the retrieved aerosol optical thicknesses, r,, is expected to be AT, = 0.05 5 0.27,. Daily values are stored on a resolution of 10 X 10 pixels (1 km nadir resolution). Weighted and gridded 8-day and monthly composites of the optical thickness, the aerosol mass concentration and spectral radiative forcing are generated for selected scattering angles to increase the accuracy. The daily aerosol information over land and oceans (Tunr& et al., this issue), combined with continuous aerosol remote sensing from the ground, will be used to study aerosol climatology, to monitor the sources and sinks of specific aerosol types, and to study the interaction of aerosol with water vapor and clouds and their radiative forcing of climate. The aerosol information will also be used for atmospheric corrections of remotely sensed surface reflectance. In this paper, examples of applications and validations are provided.
1,608 citations
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 spectral radiance of an aerosol with a bilognormal size distribution is simulated with a single lognormal aerosol, with an appropriate mean radius and width of distribution.
Abstract: Spectral radiances measured at the top of the atmosphere in a wide spectral range (0.55–2.13 μm) are used to monitor the aerosol optical thickness and the aerosol size distribution (integrated on the vertical column) of the ambient (undisturbed) aerosol over the oceans. Even for the moderate resolution imaging spectrometer (MODIS) wide spectral range, only three parameters that describe the aerosol loading and size distribution can be retrieved. These three parameters are not always unique. For instance, the spectral radiance of an aerosol with a bilognormal size distribution can be simulated very well with a single lognormal aerosol with an appropriate mean radius and width of distribution. Preassumptions on the general structure of the size distribution are therefore required in the inversion of MODIS data. The retrieval of the aerosol properties is performed using lookup table computations. The volume size distribution in the lookup table is described with two lognormal modes: a single mode to describe the accumulation mode particles (radius 1.0 μm). Note that two accumulation modes may be present, one dominated by gas phase processes and a second dominated by cloud phase processes. The coarse mode can also be split into several partially overlapping modes describing maritime salt particles and dust. The aerosol parameters we expect to retrieve are η, the fractional contribution of the accumulation mode to scattering; τ, the spectral optical thickness; and rm, the mean particle size of the dominant mode. Additional radiative quantities such as asymmetry parameter and effective radius are derived subsequently. The impact of the surface conditions, wind speed and chlorophyll content on the retrieval is estimated, the impact of potential sources of error like the calibration of the instrument is also tested. The algorithm has been applied successfully to actual data sets provided by the Thematic Mapper on Landsat 5 and by the MODIS airborne simulator on the ER-2 and tested against ground and airborne measurements. A first estimate of the general accuracy is Δτ = ±0.05±0.05τ (at 550 nm), Δrm = 0.3rm, Δη = ±0.25.
944 citations
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TL;DR: In this paper, the delta-Eddington approximation was used to calculate monochromatic radiative fluxes in an absorbing-scattering atmosphere, by combining a Dirac delta function and a two-term approximation, which overcomes the poor accuracy of the Eddington approximation for highly asymmetric phase functions.
Abstract: This paper presents a rapid yet accurate method, the “delta-Eddington” approximation, for calculating monochromatic radiative fluxes in an absorbing-scattering atmosphere. By combining a Dirac delta function and a two-term approximation, it overcomes the poor accuracy of the Eddington approximation for highly asymmetric phase functions. The fraction of scattering into the truncated forward peak is taken proportional to the square of the phase function asymmetry factor, which distinguishes the delta-Eddington approximation from others of similar nature. Comparisons of delta-Eddington albedos, transnmissivities and absorptivities with more exact calculations reveal typical differences of 0–0.022 and maximum differences of 0.15 over wide ranges of optical depth, sun angle, surface albedo, single-scattering albedo and phase function asymmetry. Delta-Eddington fluxes are in error, on the average, by no more than 0.5%0, and at the maximum by no more than 2% of the incident flux. This computationally fa...
1,075 citations
TL;DR: The purpose of the present note is to show how the same result can be obtained in a way which requires the inversion of only one matrix, whereas the method described by Phillips involves the inversions of two matrices.
Abstract: In a recent paper Phillips [1] discussed the problem of the unwanted oscillations often found in numerical solutions to integral equations of the first kind and described a method whereby a controlled smoothing could be induced in the solution obtained by the inversion of the quadrature approximation to the integral equation. The purpose of the present note is to show how the same result can be obtained in a way which requires the inversion of only one matrix, whereas the method described by Phillips involves the inversion of two matrices. The method to be described also possesses the advantage that it allows solutions in cases where the matrix of quadrature coefficients is not square (i.e. the number of observations exceeds the number of unknowns).
881 citations
TL;DR: The delta-M method as discussed by the authors is a natural extension of the delta-Eddington approximation to all orders M of angular approximation, which relies essentially on matching the first 2M phase function moments and using a Dirac delta-function representation of forward scattering.
Abstract: The delta–M method represents a natural extension of the recently proposed delta–Eddington approximation to all orders M of angular approximation. It relies essentially on matching the first 2M phase function moments and using a Dirac delta–function representation of forward scattering. Computed fluxes are remarkably accurate at very low orders M of approximation, even when the phase function is strongly asymmetric; thus the associated M × M matrix computations remain small and manageable. Flux is automatically conserved, making phase function “renormalization” unnecessary. Phase function truncation is effected in a much more attractive manner than in the past; furthermore, truncation tends to zero as M → ∞. Errors are shown to oscillate with (roughly) exponentially decreasing amplitude as M increases; which has the curious consequence that increasing M by small amounts does not necessarily reduce error. Mie computations associated with the δ–M method can be considerably reduced, based on a simpl...
506 citations
TL;DR: In this paper, a semi-empirical theory is developed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation, which is used when the particle size parameter x (ratio of particle circumference to wavelength) is less than some upper bound x sub zero (about 5).
Abstract: A semiempirical theory is developed which is based on simple physical principles and comparisons with laboratory measurements. The ultimate utility of this approach rests on its ability to successfully reproduce the observed single-scattering phase function for a wide variety of particle shapes, sizes and refractive indices. This approximate theory is developed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation. Mie theory is used when the particle size parameter x (ratio of particle circumference to wavelength) is less than some upper bound x sub zero (about 5). For x greater than x sub zero, the interaction is divided into three components: diffraction, external reflection and transmission. The application of the theory is illustrated by considering the influence of the shape of tropospheric aerosols on their contribution to the earth's global albedo.
312 citations
TL;DR: In this paper, the authors presented a new method which sidesteps the ill conditioning, guarantees convergence to the unique best least-squares fit, gives positive coefficients, and produces fits orders of magnitude more accurate than any which have so far been published.
275 citations