Retrieval Of Aerosol Size Distribution Research Articles

Retrieval of Aerosol Size Distributions From In Situ Particle Counter Measurements: Instrument Counting Efficiency and Comparisons With Satellite Measurements.

The method to derive aerosol size distributions from in situ stratospheric measurements from the University of Wyoming is modified to include an explicit counting efficiency function (CEF) to describe the channel‐dependent instrument counting efficiency. This is motivated by Kovilakam and Deshler's (2015, https://doi.org/10.1002/2015JD023303) discovery of an error in the calibration method applied to the optical particle counter (OPC40) developed in the late 1980s and used from 1991 to 2012. The method can be applied to other optical aerosol instruments for which counting efficiencies have been measured. The CEF employed is the integral of the Gaussian distribution representing the instrument response at any one aerosol channel, the aerosol counting efficiency. Results using the CEF are compared to previous derivations of aerosol size distributions (Deshler et al., 2003, https://doi.org/10.1029/2002JD002514) applied to the measurements before and after Kovilakam and Deshler's correction of number concentration for the OPC40 calibration error. The CEF method is found, without any tuning parameter, to reproduce or improve upon the Kovilakam and Deshler's results, thus accounting for the calibration error without any external comparisons other than the laboratory determined counting efficiency at each aerosol channel. Moments of the new aerosol size distributions compare well with aerosol extinctions measured by Stratospheric Aerosol and Gas Experiment II and Halogen Occultation Experiment in the volcanic period 1991–1996, generally within ±40%, the precision of OPC40 moments, and in the nonvolcanic period after 1996, generally within ±20%. Stratospheric Aerosol and Gas Experiment II and Halogen Occultation Experiment estimates of aerosol surface area are generally in agreement with those derived using the new CEF method.

Retrieval of aerosol size distribution using improved quantum-behaved particle swarm optimization on spectral extinction measurements

An improved quantum-behaved particle swarm optimization (IQPSO) algorithm is employed to determine aerosol size distribution (ASD). The direct problem is solved using the anomalous diffraction approximation and Lambert–Beer's Law. Compared with the standard particle swarm optimization algorithm, the stochastic particle size optimization algorithm and the original QPSO, our IQPSO has faster convergence speed and higher accuracy within a smaller number of generations. Optimization parameters for the IQPSO were also evaluated; we recommend using four measurement wavelengths and 50 particles. Size distributions of various aerosol types were estimated using the IQPSO under dependent and independent models. Finally, experimental ASDs at different locations in Harbin were recovered using the IQPSO. All our results confirm that the IQPSO algorithm is an effective and reliable technique for estimating ASD.

Observations of rapid aerosol optical depth enhancements in the vicinity of polluted cumulus clouds

Abstract. During the July 2011 Deriving Information on Surface conditions from Column and Vertically Resolved Observations Relevant to Air Quality (DISCOVER-AQ) field experiment in Maryland, significant enhancements in Aerosol Robotic Network (AERONET) sun–sky radiometer measured aerosol optical depth (AOD) were observed in the immediate vicinity of non-precipitating cumulus clouds on some days. Both measured Ångström exponents and aerosol size distribution retrievals made before, during and after cumulus development often suggest little change in fine mode particle size; therefore, implying possible new particle formation in addition to cloud processing and humidification of existing particles. In addition to sun–sky radiometer measurements of large enhancements of fine mode AOD, lidar measurements made from both ground-based and aircraft-based instruments during the experiment also measured large increases in aerosol signal at altitudes associated with the presence of fair weather cumulus clouds. These data show modifications of the aerosol vertical profile as a result of the aerosol enhancements at and below cloud altitudes. The airborne lidar data were utilized to estimate the spatial extent of these aerosol enhancements, finding increased AOD, backscatter and extinction out to 2.5 km distance from the cloud edge. Furthermore, in situ measurements made from aircraft vertical profiles over an AERONET site during the experiment also showed large increases in aerosol scattering and aerosol volume after cloud formation as compared to before. The 15-year AERONET database of AOD measurements at the Goddard Space Flight Center (GSFC), Maryland site, was investigated in order to obtain a climatological perspective of this phenomenon of AOD enhancement. Analysis of the diurnal cycle of AOD in summer showed significant increases in AOD from morning to late afternoon, corresponding to the diurnal cycle of cumulus development.

Retrieval of aerosol size distribution from multi-angle polarized measurements assisted by intensity measurements over East China

Integrating multi-angle, multi-spectral, and polarized measurements can improve the accuracy of retrieved aerosol microphysical properties, such as aerosol size distribution and complex refractive index. Using polarized measurements assisted by intensity measurements, a new algorithm to retrieve aerosol size distribution is developed. Constrained by fine-mode aerosol optical depth (AOD) extracted from polarization and anisotropy of reflectances for atmospheric science coupled with observations from a LIDAR (PARASOL) intensity measurements, aerosol size distribution is retrieved from multi-angle polarized measurements of PARASOL. The retrieved results of our algorithm are compared with ground-based measurements from Beijing, Xianghe, and Hong Kong Polytechnic University (PolyU) sites in the PHOtométrie pour le Traitement Opérational de Normalisation Satellitaire (PHOTONS) network included in the worldwide Aerosol Robotic Network (AERONET), and the correlation coefficient of AOD is greater than 0.7, whereas the modal radii is greater than AERONET/PHOTONS. The discussions of complex refractive index, fixed surface reflectance in the blue, fixed parameters for the coarse‐mode size distribution, and restricted range for fine/coarse fraction show the potential for algorithm improvement in the future.

Aerosol size distribution retrievals from sunphotometer measurements: Theoretical evaluation of errors due to circumsolar and related effects

Abstract The uncertainty in particle size distribution retrievals is analyzed theoretically and numerically when using aerosol optical depth (AOD) data affected by three distinct error-inducing effects. Specifically, circumsolar radiation (CS), optical mass (OM), and solar disk’s brightness distribution (BD) effects are taken into consideration here. Because of these effects, the theoretical AOD is affected by an error, ∂AOD, that consequently translates into errors in the determined (apparent) particle size distribution (PSD). Through comparison of the apparent and the true size distributions, the relative error, ∂PSD, is calculated here as a function of particle radius for various instrument’s fields of view (aperture) and solar zenith angles. It is shown that, in general, the CS effect overestimates the number of submicron-sized particles, and that the significance of this effect increases with the aperture. In case of maritime aerosols, the CS effect may also lead to an underestimation of the number concentration of large micron-sized particles. The BD and OM effects become important, and possibly predominant, when AOD is low. Assuming large particles dominate in the atmosphere, the BD effect tends to underestimate the concentration of the smallest aerosol particles. In general, the PSD(apparent)/PSD(true) ratio is affected by the CS effect equally over all particle sizes. The relative errors in PSD are typically smaller than 40–60%, but can exceptionally exceed 100%, which means that the apparent PSD may then be twice as large as the true PSD. This extreme situation typically occurs with maritime aerosols under elevated humidity conditions. Recent instruments tend to be designed with smaller apertures than ever before, which lower the CS-induced errors to an acceptable level in most cases.

Approximate method for fast retrieval of particle size distribution in spectral extinction technique

Generalized eikonal approximation (GEA) method, used as an alternative to the rigorous Mie theory in this paper, is introduced for retrieval of the particle size distribution (PSD) in the independent model. To compute the extinction efficiency accurately, the combination of GEA method and Mie theory is adopted, which can not only extend the applicable range of the approximation method but also improve the speed of the whole retrieval. Both simulations and experimental results show the method can be successfully applied to retrieval of PSD when the refractive index is within the validity range. By using this method, we find the complexity and computation time of the retrieval are significantly reduced, and the memory resources can also be saved effectively. Thus all of these factors make the method more suitable for realization of on-line particle sizing. Full Text: PDF References C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998) [CrossRef] H.Y. Zuo et al., "Technique to improve the accuracy of the retrieval of aerosol size-distribution", Opt. Lett. 35, 1380 (2010) [CrossRef] M.Z. Li, D. Wilkinson, "Particle size distribution determination from spectral extinction using evolutionary programming", Chem. Eng. Sci. 56, 3045 (2001) [CrossRef] X.Z. Li et al., "Geometrical-optics approximation of forward scattering by gradient-index spheres", Appl. Opt. 46, 5241 (2007) [CrossRef] X.G. Sun, H. Tang, J.M. Dai, "Retrieval of particle size distribution in the dependent model using the moment method", Opt. Exp. 15, 11507 (2007) [CrossRef] S.K. Sharma, D.J. Somerford, Light Scattering by Optically Soft Particles: Theory and Applications (Springer-Praxis, 2006) T.W. Chen, "High energy light scattering in the generalized eikonal approximation", Appl. Opt. 28, 4096 (1989) [CrossRef] M. Kandlikar, G. Ramachandran, "Inverse methods for analysing aerosol spectrometer measurements: a critical review", J. Aerosol Sci. 30, 413 (1999) [CrossRef]

Technique to improve the accuracy of the retrieval of aerosol size-distribution

A technique to improve the accuracy of the retrieval of aerosol size-distribution is introduced. This technique includes a wavelength-selecting method and a "function model." The wavelength-selecting method is used to select the suitable wavelengths for the retrieval of aerosol size-distribution, and the function model is used to express the aerosol size-distributions with a fewer parameters. By using this technique, the accuracy of the retrieval of aerosol size-distribution can be improved.

Characterization of atmospheric aerosols using MFRSR measurements

Measurements by multifilter rotating shadowband radiometers (MFRSRs) constitute a valuable global data set with contributions from hundreds of instruments deployed worldwide. The geographical coverage of MFRSR networks is complementary to that of AERONET and often provides better spatial density of measurement sites, especially in the United States. We describe our recently updated analysis algorithm for MFRSR data that allows partitioning of the spectral aerosol optical depth (AOD) into fine and coarse mode AOD and retrieval of the fine mode effective radius. Our recent sensitivity study demonstrated that for a typical measurement accuracy 0.01 of AOD, the trade‐offs between the spectral aerosol extinction and NO2 absorption in the visible range effectively prevent unambiguous retrieval of NO2 column from MFRSR data and may also bias aerosol size distribution retrievals. This has prompted us to adopt a new retrieval approach, which utilizes climatological NO2 (based on SCIAMACHY satellite retrievals) and uses column ozone from TOMS measurements. The performance of this new approach was evaluated using the long‐term data set from the Southern Great Plains (SGP) site operated by the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) Program. We present a detailed intercomparison of total, fine, and coarse mode AOD and fine mode effective radius between two MFRSRs located at the SGP's Central Facility and with the correlative AERONET Sun‐sky inversion results (Version 2) derived from a collocated CIMEL Sun photometer. The comparison between two MFRSRs demonstrated good consistency of both the measurements and the analysis. Agreement with AERONET inversions is remarkably good, in that differences in AOD components do not exceed the expected measurement accuracy of 0.01, while the retrieved values of fine mode effective radius show no relative bias and only 0.03 μm random error (standard deviation of the differences). We show that if only data with large enough AOD (more than 0.06 at 870 nm) are selected, this error is reduced by a factor of two, becoming about 10% of a typical fine mode effective radius value.

Retrieval of size distribution for urban aerosols using multispectral optical data

We are dealing with retrieval of aerosol size distribution using multispectral extinction data collected in highly industrialized urban region. Especially, a role of the particle morphology is in the focus of this work. As well known, at present, still many retrieval algorithms are based on simple Lorenz-Mie's theory applicable for perfectly spherical and homogeneous particles, because that approach is fast and can handle the whole size distribution of particles. However, the solid-phase aerosols never render simple geometries, and rather than being spherical or spheroidal they are quite irregular. It is shown, that identification of the modal radius aM of both, the size distribution f(a) and the distribution of geometrical cross section s(a) of aerosol particles is not significantly influenced by the particle's morphology in case the aspect ratio is smaller than 2 and the particles are randomly oriented in the atmospheric environment. On the other hand, the amount of medium-sized particles (radius of which is larger than the modal radius) can be underestimated if distribution of non-spherical grains is substituted by system of volume equivalent spheres. Retrieved volume content of fine aerosols (as characterized by PM2.5 and PM1.0) can be potentially affected by inappropriate assumption on the particle shape.

Aerosol properties in a Chinese semiarid region

Abstract Aerosol optical properties and atmospheric water vapor content for 1999–2000 were obtained from ground-based solar radiometer measurements in Dunhuang, China. Seasonal changes of aerosol optical depth (AOD) and Angstrom wavelength parameter (ALPHA) were observed. Large values of AOD (at 500 nm) greater than 1.0 combined with low values of ALPHA less than 0.2 were mainly observed in spring and summer, which is consistent with the seasonal dust production from Gobi and Taklamaken deserts. The maximum monthly average of AOD was around 0.37 and occurred in the April of 1999, which was more than three times larger than the minimum monthly average in the November of 2000 (around 0.115). Thirty-three percent and 49% of observations of AOD in autumn and winter was larger than 0.2, respectively, whereas in spring, the percentage was approximately 63%. There was a large spread in ALPHAs in all seasons when AODs were less than 0.2. With the increase of AOD, ALPHAs decreased rapidly and were around zero finally. The large spread of ALPHA for low AODs and the domination of low turbidity in Dunhuang (nearly half of AODs less than 0.2) resulted in the negligible seasonal change of ALPHA. The domination of coarse particles over fine particles was also shown in aerosol size distribution retrievals, with the volume concentration ratio of coarse to fine particles being nearly 30. The volume mean radii and standard deviation of size distribution showed an insignificant correlation with AOD based on the analysis of all available retrievals, illustrating that it is suitable to use a fixed size model in the analysis of the dust climate forcing. During the dust outbreak episode, a rapid increase of AOD and a decrease of ALPHA were observed, ALPHA being usually less than 0.2 and even negative occasionally. The interesting result was that the volume mean radii of size distribution during the dust outbreak episode increased remarkably with the dust loading, which indicated that a dynamic size model should be used in the simulation of dust effects on meso-scale weather system in the semiarid region. The distinct seasonal change of water vapor content was observed, with high water vapor contents occurred in summer. The influence of water vapor on aerosol properties was absent due to the low humidification capability of dust aerosols and the different seasonal variation of aerosol properties and water vapor content.

Synthesis inverse mapping method applied to the retrieval of aerosol size distributions from extinction measurements

The problem of inverting aerosol extinction data in the near‐UV to near‐IR range to retrieve aerosol size distributions is addressed by means of a recently developed method called “synthesis inverse mapping.” The rationale and the algebra of the method are developed, and the full error budget is discussed. The performance of the algorithm is evaluated with respect to standard monomodal and bimodal distributions published in the literature. The new method allows error amplification control and estimation of the smoothing error, and it is well suited for operational fast retrieval.

Runge-Kutta Type Methods for Ill-Posed Problems and the Retrieval of Aerosol Size Distributions

The present paper deals with new explicit and implicit Runge-Kutta type iteration methods as a regularization tool for ill-posed problems. These methods are a generalization of the well-known Landweber method. An application to Atmospheric Physics in determining the aerosol size distribution is given.

Hybrid regularization method for the ill-posed inversion of multiwavelength lidar data in the retrieval of aerosol size distributions

A specially developed method is proposed to retrieve the particle volume distribution, the mean refractive index, and other important physical parameters, e.g., the effective radius, volume, surface area, and number concentrations of tropospheric and stratospheric aerosols, from optical data by use of multiple wavelengths. This algorithm requires neither a priori knowledge of the analytical shape of the distribution nor an initial guess of the distribution. As a result, even bimodal and multimodal distributions can be retrieved without any advance knowledge of the number of modes. The nonlinear ill-posed inversion is achieved by means of a hybrid method combining regularization by discretization, variable higher-order B-spline functions and a truncated singular-value decomposition. The method can be used to handle different lidar devices that work with various values and numbers of wavelengths. It is shown, to my knowledge for the first time, that only one extinction and three backscatter coefficients are sufficient for the solution. Moreover, measurement errors up to 20% are allowed. This result could be achieved by a judicious fusion of different properties of three suitable regularization parameters. Finally, numerical results with an additional unknown refractive index show the possibility of successfully recovering both unknowns simultaneously from the lidar data: the aerosol volume distribution and the refractive index.

Retrieval of aerosol size distributions and integral properties from simulated extinction measurements at SAGE III wavelengths by the linear minimizing error method

The retrieval of aerosol size distribution and integral properties from simulated aerosol extinction measurements of the new satellite instrument, the Stratospheric Aerosol and Gas Experiment (SAGE) III, is investigated. The retrieval method used in this study is the newly proposed linear minimizing error (LME) method. This approach assumes that the aerosol size distribution can be approximated by a histogram of number density as a function of particle size. The retrieved number density in each bin and the integral properties, including surface area and volume densities, are expressed as a linear combination of the SAGE III aerosol extinction coefficients at eight or fewer wavelengths. The coefficients in the weighted linear combination are obtained by minimizing the average of retrieval errors over a set of testing size distributions. The choice of aerosol channels for retrieval was first determined by comparing the average composite errors of the integral properties retrieved from different combinations of aerosol extinctions. The accuracy of the proposed method was studied by comparing the actual and retrieved properties for six aerosol size distributions. Results of this investigation indicate that unimodal, as well as bimodal, lognormal size distributions can be retrieved with reasonable accuracy. When all eight aerosol extinctions are available for retrieval, the average composite errors, which include systematic errors and errors due to measurement uncertainties for the retrieval of surface area and volume densities, are 9.4±4.3 and 4.7±2.0%, respectively. The retrieved aerosol integral properties are more accurate than those retrieved from SAGE II. However, it is not advantageous to use all eight SAGE III wavelengths for retrieval. The proper choice of aerosol extinctions for retrieval is elucidated. The derived formulas listed in this paper can be easily used by investigators to retrieve aerosol integral properties and estimate the retrieval errors from SAGE III aerosol extinctions at different altitudes for a variety of purposes. The application of the LME method to instrumental design is discussed.

Wavelength dependence of the optical depth of biomass burning, urban, and desert dust aerosols

The Angstrom wavelength exponent α, which is the slope of the logarithm of aerosol optical depth (τa) versus the logarithm of wavelength (λ), is commonly used to characterize the wavelength dependence of τa and to provide some basic information on the aerosol size distribution. This parameter is frequently computed from the spectral measurements of both ground‐based sunphotometers and from satellite and aircraft remote sensing retrievals. However, spectral variation of α is typically not considered in the analysis and comparison of values from different techniques. We analyze the spectral measurements of τa from 340 to 1020 nm obtained from ground‐based Aerosol Robotic Network radiometers located in various locations where either biomass burning, urban, or desert dust aerosols are prevalent. Aerosol size distribution retrievals obtained from combined solar extinction and sky radiance measurements are also utilized in the analysis. These data show that there is significant curvature in the ln τa versus ln λ relationship for aerosol size distributions dominated by accumulation mode aerosols (biomass burning and urban). Mie theory calculations of α for biomass burning smoke (for a case of aged smoke at high optical depth) agree well with observations, confirming that large spectral variations in α are due to the dominance of accumulation mode aerosols. A second order polynomial fit to the ln τa versus ln λ data provides excellent agreement with differences in τa of the order of the uncertainty in the measurements (∼0.01‐0.02). The significant curvature in ln τa versus ln λ for high optical depth accumulation mode dominated aerosols results in α values differing by a factor of 3–5 from 340 to 870 nm. We characterize the curvature in ln τa versus ln λ by the second derivative α′ and suggest that this parameter be utilized in conjunction with α to characterize the spectral dependence of τa. The second derivative of ln τa versus ln λ gives an indication of the relative influence of accumulation mode versus coarse mode particles on optical properties.

A new approach to retrieval of aerosol size distributions and integral properties from SAGE II aerosol extinction spectra

A new approach to the retrieval of aerosol size distributions and integral properties from Stratospheric Aerosol and Gas Experiment (SAGE) II aerosol extinction spectra is proposed. This method assumes that the aerosol size distribution can be approximated by a histogram of number density as a function of particle size. The retrieved number density in each bin is expressed as a linear combination of the SAGE II aerosol extinctions at four or fewer wavelengths. The coefficients in the weighted linear combination are obtained by minimizing the retrieval error averaged for a set of testing size distributions. The same method has been applied to retrieve aerosol surface area and volume densities from SAGE II aerosol extinctions. The retrieval accuracy was studied by calculating the aerosol surface area and volume densities for six aerosol size distributions retrieved by using the proposed linear minimizing error method. In general, the retrieval error increases with the decreasing number of wavelength‐dependent extinction measurements available for retrieval. Besides accuracy, the proposed method has the advantage of not requiring an initial guess or a weighting function. Furthermore, it is very simple and fast. Another advantage is that the proposed method can still be applied to the case when the number of reliable aerosol extinction is less than four. The formulas presented in this paper can be used easily by investigators to retrieve surface area and volume densities from SAGE II aerosol extinction spectra at different altitudes for a variety of purposes. The proposed new method can also be extended to retrieve properties from other remote sensing systems. The application of the proposed method for instrument design is discussed.

Use of sky brightness measurements from ground for remote sensing of particulate polydispersions

The software code SKYEAD.pack for retrieval of aerosol size distribution and optical thickness from data of direct and diffuse solar radiation is described; measurements are carried out with sky radiometers in the wavelength range 0.369-1.048 µm. The treatment of the radiative transfer problem concerning the optical quantities is mainly based on the IMS (improved multiple and single scattering) method, which uses the delta-M approximation for the truncation of the aerosol phase function and corrects the solution for the first- and second-order scattering. Both linear and nonlinear inversion methods can be used for retrieving the size distribution. Improved calibration methods for both direct and diffuse radiation, the data-analysis procedure, the results from the proposed code, and several connected problems are discussed. The results can be summarized as follows: (a) the SKYRAD.pack code can retrieve the columnar aerosol features with accuracy and efficiency in several environmental situations, provided the input parameters are correctly given; (b) when data of both direct and diffuse solar radiation are used, the detectable radius interval for aerosol particles is approximately from 0.03 to 10 µm; (c) besides the retrieval of the aerosol features, the data-analysis procedure also permits the determination of average values for three input parameters (real and imaginary aerosol refractive index, ground albedo) from the optical data; (d) absolute calibrations for the sky radiometer are not needed, and calibrations for direct and diffuse radiation can be carried out with field data; (e) the nonlinear inversion gives satisfactory results in a larger radius interval, without the unrealistic humps that occur with the linear inversion, but the results strongly depend on the first-guess spectrum; (f) aerosol features retrieved from simulated data showed a better agreement with the given data for the linear inversion than for the nonlinear inversion.

Retrieval analysis of aerosol-size distribution with simulated extinction measurements at SAGE III wavelengths

The retrieval of aerosol-size distribution from simulated aerosol-extinction-coefficient measurements of the new satellite instrument, the Stratospheric Aerosol and Gas Experiment (SAGE) III, is investigated. A detailed discussion on the aerosol-size-distribution information content of the SAGE III aerosol-extinction-coefficient measurement is provided. Results of the investigation indicate that unimodal as well as bimodal log-normal size distributions can be inferred. In addition, it is shown that a shape-constraint-free size distribution can be derived from SAGE III aerosol measurements by use of the randomized minimization search technique and the optimal estimation theory.

Numerical simulation of the retrieval of aerosol size distribution from multiwavelength laser radar measurements

A numerical investigation was carried out into the feasibility of deriving the aerosol size distribution from aerosol volume extinction and backscattering coefficient measurements by a multiwavelength laser radar. This study employs the regularization method for matrix inversion with the first-order B-spline function as basis functions to approximate the aerosol size distribution. The results of numerical simulations show that (1) the effects of roundoff errors in the numerical calculation are negligible and the approximation errors in the size distribution by the B-spline function are small, (2) the reconstruction errors in the size distribution at its peak are about twice as large as the relative measurement errors when the Lagrange multiplier, which determines the degree of smoothness in the reconstruction, is suitably chosen, and (3) the variation in the complex refractive index due to the humidity change does not produce large errors in the size distribution.

Improved inversion procedure for the retrieval of aerosol size distributions using aureole measurements

An improved inversion procedure for the retrieval of aerosol size distributions using aureole data is presented. The inversion procedure involved a modified Twomey–Chahine algorithm using differential kernels with subsequent averaging and smoothing of the inverted size distributions. The numerical simulations were performed by calculating the angular scattering coefficients between 1.08° and 10° for the wavelength of 0.2537 μm using four different aerosol models, including a realistic noise estimate of 4%. It is demonstrated that the differential kernel method is superior to the conventional direct kernel approach.