Retrieval Of Particle Size Distribution Research Articles

Ocean color algorithm for the retrieval of the particle size distribution and carbon-based phytoplankton size classes using a two-component coated-sphere backscattering model

Abstract. The particle size distribution (PSD) of suspended particles in near-surface seawater is a key property linking biogeochemical and ecosystem characteristics with optical properties that affect ocean color remote sensing. Phytoplankton size affects their physiological characteristics and ecosystem and biogeochemical roles, e.g., in the biological carbon pump, which has an important role in the global carbon cycle and thus climate. It is thus important to develop capabilities for measurement and predictive understanding of the structure and function of oceanic ecosystems, including the PSD, phytoplankton size classes (PSCs), and phytoplankton functional types (PFTs). Here, we present an ocean color satellite algorithm for the retrieval of the parameters of an assumed power-law PSD. The forward optical model considers two distinct particle populations: phytoplankton and non-algal particles (NAPs). Phytoplankton are modeled as coated spheres following the Equivalent Algal Populations (EAP) framework, and NAPs are modeled as homogeneous spheres. The forward model uses Mie and Aden–Kerker scattering computations, for homogeneous and coated spheres, respectively, to model the total particulate spectral backscattering coefficient as the sum of phytoplankton and NAP backscattering. The PSD retrieval is achieved via spectral angle mapping (SAM), which uses backscattering end-members created by the forward model. The PSD is used to retrieve size-partitioned absolute and fractional phytoplankton carbon concentrations (i.e., carbon-based PSCs), as well as particulate organic carbon (POC), using allometric coefficients. This model formulation also allows the estimation of chlorophyll a concentration via the retrieved PSD, as well as percent of backscattering due to NAPs vs. phytoplankton. The PSD algorithm is operationally applied to the merged Ocean Colour Climate Change Initiative (OC-CCI) v5.0 ocean color data set. Results of an initial validation effort are also presented using PSD, POC, and picophytoplankton carbon in situ measurements. Validation results indicate the need for an empirical tuning for the absolute phytoplankton carbon concentrations; however these results and comparison with other phytoplankton carbon algorithms are ambiguous as to the need for the tuning. The latter finding illustrates the continued need for high-quality, consistent, large global data sets of PSD, phytoplankton carbon, and related variables to facilitate future algorithm improvements.

Retrieval of particle size distribution based on a multi-objective genetic algorithm for multi-wavelength lidar

Introduction: Aerosols affect the radiation budget of the Earth’s atmospheric system. The aerosol particle size distribution (PSD) is one of the main parameters for characterizing the effect of aerosol on radiative forcing.Methods: The extinction coefficient and backscattering coefficient at 355 and 532 nm and backscattering coefficient at 1064 nm of aerosol particles over Yinchuan area, China, which measured by a multi-wavelength lidar developed by North Minzu University, were used to retrieve the aerosol PSD. In view of the disadvantages of traditional regularization methods, the elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) is selected to retrieve PSD.Results and Discussion: To verify the feasibility for retrieval of aerosol PSD, the NSGA-II with different errors in the input optical signal was simulated, in which the errors of the inverted PSD are still in the acceptable range when 35% error added into the optical parameters. Moreover, some experiments were carried out under different atmospheric conditions, including background sunny, cloudy and dusty days, and comparisons were performed with Multiple Population Genetic Algorithm (MPGA) and Simple Genetic Alogrithm (SGA) method. The results show that the retrieval effect of NSGA-II was better than that of MPGA and SGA, and the NSGA-II is very suitable for retrieve PSD by using the multi-wavelength lidar data.

A Novel In Silico Monte Carlo Approach to Optimize a PSD Estimation Problem. Generation of Data Fusion Experiment Rules

This article analyzes the performance of combining information from Scanning Electron Microscopy (SEM) micrographs with Static Light Scattering (SLS) measurements for retrieving the so-called Particle Size Distribution (PSD) in terms of experimental features. The corresponding data fusion is implemented using a novel Monte Carlo-based method consisting in a SMF (Sampling-Mapping-Filtering) approach. This approach provides an important reference to assess the strategy of the experiment for this specific problem by means of solving an inverse problem. Furthermore, low levels of volume fraction and a PSD represented by log-normal distributions are considered in order to reduce processing and model errors due to ill-posedness. The prior statistics corresponding to the SEM micrographs have been achieved by means of the Jackknife procedure used as a resampling technique. The likelihood term considers iid normal measurements generated from the Local Monodisperse Approximation (LMA) and also makes use of the same model as forward linear model, in an inversion case known as inverse crime. However, it has been proved that the LMA performs well in practice for low fraction volume systems as considered here. The PSD retrieval is measured in terms of improvement in precision with respect to one of the log-normal parameters in SEM micrographs, i.e., the desirability. Estimates are expressed as a function of a typical system parameter such as polydispersity, as well as experimental variables, i.e., number of particles per micrograph (PPM) and noise level $\varepsilon$ in the SLS measurements. These estimations are then analyzed by means of the Box-Behnken (BB) design and the response surface methodology (RSM) in order to generate a surrogate model from which rules for the optimization of the experiment are made when desirability is maximized. Finally, a Rule-Based System (RBS) is proposed for future use.

Influence of dispersion on particle size-distribution based on multi-wavelength scattering measurement

We demonstrate that the dispersion of the refractive index (RI) influences the retrieval accuracy of the particle size distribution (PSD) in the multi-wavelength angular scattering measurement. A numeric simulation was performed, which indicated that the dispersion results in a 10% to 50% error on scattering intensity measurement at certain scattering angles. In addition, although the dispersion showed little effect on the ill-posedness of the scattering kernel, the difference between the dispersion and no dispersion in the scattering kernel is so amplified in PSD inversion that accuracy decreases to such an extent that it becomes unacceptable. The accuracy of PSD retrieval, considering dispersion, was higher than that without dispersion. Finally, it was also proposed that variation of RI with incident wavelength must be considered in designing the scattering kernel to improve the retrieval accuracy in the multi-wavelength angular scattering measurement.

Retrieval of particle size distribution of polar stratospheric clouds based on Wide-Angle Color and Polarization Analysis

The intensive polar stratospheric vortex in the Arctic that shifted to northern Europe in the winter of 2019–2020 caused low temperatures and the frequent occurrence of polar stratospheric clouds followed by a significant decrease in the total ozone content. Polarimetry and multi-color photometry using all-sky cameras in Lovozero (Murmansk Region, Russia, 68.0°N, 35.1°E) together with a new method of cloud field separation against the twilight background allowed for finding the light scattering characteristics related to the particle size distribution of polar stratospheric clouds. The results are compared with lidar and balloon experiments. The conditions of the appearance of visually bright polar stratospheric clouds of type I are discussed.

Linking rain into ice microphysics across the melting layer in stratiform rain: a closure study

Abstract. This study investigates the link between rain and ice microphysics across the melting layer in stratiform rain systems using measurements from vertically pointing multi-frequency Doppler radars. A novel methodology to examine the variability of the precipitation rate and the mass-weighted melted diameter (Dm) across the melting region is proposed and applied to a 6 h long case study, observed during the TRIPEx-pol field campaign at the Jülich Observatory for Cloud Evolution Core Facility and covering a gamut of ice microphysical processes. The methodology is based on an optimal estimation (OE) retrieval of particle size distributions (PSDs) and dynamics (turbulence and vertical motions) from observed multi-frequency radar Doppler spectra applied both above and below the melting layer. First, the retrieval is applied in the rain region; based on a one-to-one conversion of raindrops into snowflakes, the retrieved drop size distributions (DSDs) are propagated upward to provide the mass-flux-preserving PSDs of snow. These ice PSDs are used to simulate radar reflectivities above the melting layer for different snow models and they are evaluated for a consistency with the actual radar measurements. Second, the OE snow retrieval where Doppler spectra are simulated based on different snow models, which consistently compute fall speeds and electromagnetic properties, is performed. The results corresponding to the best-matching models are then used to estimate snow fluxes and Dm, which are directly compared to the corresponding rain quantities. For the case study, the total accumulation of rain (2.30 mm) and the melted equivalent accumulation of snow (1.93 mm) show a 19 % difference. The analysis suggests that the mass flux through the melting zone is well preserved except the periods of intense riming where the precipitation rates were higher in rain than in the ice above. This is potentially due to additional condensation within the melting zone in correspondence to high relative humidity and collision and coalescence with the cloud droplets whose occurrence is ubiquitous with riming. It is shown that the mean mass-weighted diameter of ice is strongly related to the characteristic size of the underlying rain except the period of extreme aggregation where breakup of melting snowflakes significantly reduces Dm. The proposed methodology can be applied to long-term observations to advance our knowledge of the processes occurring across the melting region; this can then be used to improve assumptions underpinning spaceborne radar precipitation retrievals.

Establishment and Preliminary Application of the Forward Modeling Method for Doppler Spectral Density of Ice Particles

Owing to the various shapes of ice particles, the relationships between fall velocity, backscattering cross-section, mass, and particle size are complicated. This affects the application of cloud radar Doppler spectral density data in the retrieval of the microphysical properties of ice crystals. In this study, under the assumption of six particle shape types, the relationships between particle mass, fall velocity, backscattering cross-section, and particle size were established based on existing research. Variations of Doppler spectral density with the same particle size distribution (PSD) of different ice particle types are discussed. The radar-retrieved liquid and ice PSDs, water content, and mean volume-weighted particle diameter were compared with airborne in situ observations in the Xingtai, Hebei Province, China, in 2018. The results showed the following. (1) For the particles with the same equivalent diameter (De), the fall velocity of the aggregates was the largest, followed by hexagonal columns, hexagonal plates, sector plates, and stellar crystals, with the ice spheres falling two to three times faster than ice crystals with the same De. Hexagonal columns had the largest backscattering cross-section, followed by stellar crystals and sector plates, and the backscattering cross-sections of hexagonal plates and the two types of aggregates were very close to those of ice spheres. (2) The width of the simulated radar Doppler spectral density generated by various ice crystal types with the same PSD was mainly affected by the particle’s falling velocity, which increased with the particle size. Turbulence had different degrees of influence on the Doppler spectrum of different ice crystals, and it also brought large errors to the PSD retrieval. (3) PSD comparisons showed that each ice crystal type retrieved from the cloud radar corresponded well to aircraft observations within a certain scale range, when assuming that only a certain type of ice crystals existed in the cloud, which could fully prove the feasibility of retrieving ice PSDs from the reflectivity spectral density.

Machine-learning-based computationally efficient particle size distribution retrieval from bulk optical properties.

Retrieval of particle size distribution from bulk optical properties based on evolutionary algorithms is usually computationally expensive. In this paper, we report an efficient numerical approach to solving the inverse scattering problem by accelerating the calculation of bulk optical properties based on machine learning. With the assumption of spherical particles, the forward scattering by particles is first solved by Mie scattering theory and then approximated by machine learning. The particle swarm optimization algorithm is finally employed to optimize the particle size distribution parameters by minimizing the deviation between the target and simulated bulk optical properties. The accuracies of machine learning and particle swarm optimization are separately investigated. Meanwhile, both monomodal and bimodal size distributions are tested, considering the influences of random noise. Results show that machine learning is capable of accurately predicting the scattering efficiency for a specific size distribution in approximately 0.5 µs on a standalone computer. Therefore, the proposed method has the potential to serve as a powerful tool in real-time particle size measurement due to its advantages of simplicity and high efficiency.

An Inverse Numerical Simulation for Simultaneous Measurement of Non Spherical Particle Size and Optical Constant by Forward Elastic Light Scattering and Transmittance

This numerical study investigates the feasibility of simultaneous retrieval of particle size distribution (PSD) and optical constants of spheroids by optical spectroscopy. In this simulation the particles are considered as spheroid. The aspect ratio of an oblate and prolate spheroid is set as 0.8 and 1.2, respectively. At this constant aspect ratio, the particle’s orientation has been changed by altering its major semi-axis. Two continuous wavelength lasers are employed to irradiate the particle samples. Multi-angle and multi-wavelengths elastic forward scattering intensity and the spectral collimated transmittance are employed to measure signals. For forward scattering, the spheroid is effectively replaced by a sphere of an approximated radius and the modified Mie theory is employed to calculate the scattering intensity. For the collimated transmittance, the extinction efficiency of non-spherical particle is measured based on the extended anomalous diffraction approximation. The Log-Normal distribution is used to get the volume frequency distribution of the particles and the inverse process is done by using the improved quantum particle swarm optimization. Two different sets of optical constant (e.g., complex refractive index), semi-major axis of non-spherical particle and discrete rate are retrieved by the inverse simulation. The results show that, the proposed spectroscopic technique can retrieve PSD and optical constants of non-spherical particles simultaneously within the tolerable error limit less than 10%.

Precise size distribution measurement of aerosol particles and fog droplets in the open atmosphere.

A precise measurement for the aerosol particle size distribution and fog droplet size distribution simultaneously in the open atmosphere is proposed. The extinction coefficient and small-angle forward scattering measurement are integrated into the detection for particle size distribution in the open atmosphere, and can achieve the fine detection of the particles in the atmosphere with radius between 0.1 to 30 μm. The key technology including optimal scattering angle in small-angle forward scattering measurement and optimal wavelengths selection are discussed and solved in detail. The fourteen different particle size distributions including aerosol size distributions and fog droplet size distributions are used for the determination of optimal forward scattering angle and wavelengths. The optimal forward scattering angle is calculated to be 1.1°. Seven wavelengths for extinction coefficients and five wavelengths for forward scattering coefficients are chosen for the retrieval of particle size distribution in the measurement. The regularization inversion of optical parameters for the retrieval of particle size distribution is described. The aerosol particle size distributions measured by particle spectrometer and actual fog particle size distributions are used for the method test and the reconstructions of particle size distributions. The inversion results show that the method can achieve the precise measurements of aerosol particle size distribution and fog droplet size distribution. The error influence on the inversion results of distributions is discussed. Based on the sensitivity analysis of inversion results, the feasibility of measurement in the real atmosphere is analyzed and discussed, and the scheme of detection system is provided.

Rapid ice aggregation process revealed through triple-wavelength Doppler spectrum radar analysis

Abstract. We have identified a region of an ice cloud where a sharp transition of dual-wavelength ratio occurs at a fixed height for longer than 20 min. In this paper we provide evidence that rapid aggregation of ice particles occurred in this region, creating large particles. This evidence comes from triple-wavelength Doppler spectrum radar data that were fortuitously being collected. Through quantitative comparison of the Doppler spectra from the three radars we are able to estimate the ice particle size distribution (of particles larger than 0.75 mm) at different heights in the cloud. This allows us to investigate the evolution of the ice particle size distribution and determine whether the evolution is consistent with aggregation, riming or vapour deposition. The newly developed method allows us to isolate the signal from the larger (non-Rayleigh scattering) particles in the distribution. Therefore, a particle size distribution retrieval is possible in areas of the cloud where the dual-wavelength ratio method would fail because the bulk dual-wavelength ratio value is too close to zero. The ice particles grow rapidly from a maximum size of 0.75 to 5 mm while falling less than 500 m in under 10 min. This rapid growth is shown to agree well with theoretical estimates of aggregation, with aggregation efficiency being approximately 0.7, and is inconsistent with other growth processes, e.g. growth by vapour deposition or riming. The aggregation occurs in the middle of the cloud and is not present throughout the entire lifetime of the cloud. However, the layer of rapid aggregation is very well defined at a constant height, where the temperature is −15 ∘C and lasts for at least 20 min (approximate horizontal distance: 24 km). Immediately above this layer, the radar Doppler spectrum is bi-modal, which signals the formation of new small ice particles at that height. We suggest that these newly formed particles, at approximately −15 ∘C, grow dendritic arms, enabling them to easily interlock and accelerate the aggregation process. The large estimated aggregation efficiency in this cloud is consistent with recent laboratory studies for dendrites at this temperature.

Improve the precision and accuracy of retrieval of particle size-distribution based the unconstrained linear regression

In this paper, we try to find a way to take into account both of the precision and accuracy of particle sizing that based on Mie scattering. It is known that in the retrieval of particle size distribution one of the most important issues is to solve the ill-conditioned problem. Due to the ill-conditioned problem, the retrieval is very imprecision usually. The biased estimation methods can improve the precision effectively, which, therefore, is widely used. But the price is the decrease of the retrieval accuracy, because such method, after all, is of bias. It is known that the unconstrained linear regression (ULR) is unbiased, therefore, based on this ULR, both of the retrieval precision and accuracy can be taken into account.

Combining kernel matrix optimization and regularization to improve particle size distribution retrieval

A new method combining Tikhonov regularization and kernel matrix optimization by multi-wavelength incidence is proposed for retrieving particle size distribution (PSD) in an independent model with improved accuracy and stability. In comparison to individual regularization or multi-wavelength least squares, the proposed method exhibited better anti-noise capability, higher accuracy and stability. While standard regularization typically makes use of the unit matrix, it is not universal for different PSDs, particularly for Junge distributions. Thus, a suitable regularization matrix was chosen by numerical simulation, with the second-order differential matrix found to be appropriate for most PSD types.

Aerosol diffusion battery: The retrieval of particle size distribution with the help of analytical formulas

A new algorithm is proposed for the determination of aerosol particle size distribution from a set of screen diffusion battery penetrations. The idea is to determine the size spectra of the fractio...

A rapid approximate inversion of extinction data for partially absorbing particles

Retrieval of particle size distribution from extinction data is solved analytically using a product kernel concept and its extension to partially absorbing materials. While a conventional analytical method overestimates the portion of large particles, the correction to the integral formula makes the solution acceptable also for larger absorbing particles. A set of numerical experiments on synthetically generated aerosol optical depths has proven improved accuracy of new formula that is simple and keeps requirements on computational time or memory consumption low enough. The numerical tests shown that original and reproduced size distributions are quite consistent, including the peak position and full width at half maximum. The main advantage of the analytical approach presented here is its easy applicability in fast sampling of rapidly evolving particulate systems, where quick estimation of modal radius or PM1.0, PM2.5 and other fractions of the aerosol population is required.

Retrieval of particle size distribution from aerosol optical thickness using an improved particle swarm optimization algorithm

Particle size distribution is essential for describing direct and indirect radiation of aerosols. Because the relationship between the aerosol size distribution and optical thickness (AOT) is an ill-posed Fredholm integral equation of the first type, the traditional techniques for determining such size distributions, such as the Phillips–Twomey regularization method, are often ambiguous. Here, we use an approach based on an improved particle swarm optimization algorithm (IPSO) to retrieve aerosol size distribution. Using AOT data measured by a CE318 sun photometer in Yinchuan, we compared the aerosol size distributions retrieved using a simple genetic algorithm, a basic particle swarm optimization algorithm and the IPSO. Aerosol size distributions for different weather conditions were analyzed, including sunny, dusty and hazy conditions. Our results show that the IPSO-based inversion method retrieved aerosol size distributions under all weather conditions, showing great potential for similar size distribution inversions.

Analytical algorithm to determine the spherical particle size distribution from spectral absorption measurements

A modified anomalous diffraction theory (MADT) by including the effects of reflection and refraction is proposed. With respect to MADT, an analytical technique for retrieval of spherical particle size distribution (PSD), based on absorption was developed. Also, an MADT transform pair between the size distribution and the absorption spectrum was constructed. This provides a new tool to study the related particle optical properties. By Gaver–Stehfest inversion method, the derived complex-inversion formula is finally converted into the new real-inversion formula so that the measured absorption data can be applied directly. The inversion experiments show that the use of extended precision instead of double precision arithmetic can produce more reliable results at the expense of CPU time. The effects of complex refractive index on retrieval of PSD were examined. Also it was found that an appropriate reduction of the truncation number with the smoothing technique improved the anti-noise ability for the algorithm.

Influence of cell length on retrieval of particle size-distribution based on light scattering

In this paper, a study about the retrieval accuracy of particle size-distribution based on scattered light distribution is reported. A view is proposed that the ratio (L/R) of the sample cell length (L) to the cell—detectors distance (R) affects the retrieval accuracy. The numeric simulation indicates that the larger the L/R, the larger the retrieval error. Therefore, in future related measurement and studies, the ratio of L/R must be taken into account.

Determination of particle size distribution by light extinction method using improved pattern search algorithm with Tikhonov smoothing functional

An inversion technique which combines the pattern search algorithm with the Tikhonov smoothing functional for retrieval of particle size distribution (PSD) by light extinction method is proposed. In the unparameterized shape-independent model, we first transform the PSD inversion problem into an optimization problem, with the Tikhonov smoothing functional employed to model the objective function. The optimization problem is then solved by the pattern search algorithm. To ensure good convergence rate and accuracy of the whole retrieval, a competitive strategy for determining the initial point of the pattern search algorithm is also designed. The accuracy and limitations of the proposed technique are tested by the inversion results of synthetic and real standard polystyrene particles immersed in water. In addition, the issues about the objective function and computation time are further discussed. Both simulation and experimental results show that the technique can be successfully applied to retrieve the PSD with high reliability and stability in the presence of random noise. Compared with the Phillips–Twomey method and genetic algorithm, the proposed technique has certain advantages in terms of reaching a more accurate and steady optimal solution with less computational effort, thus making this technique more suitable for quick and accurate measurement of PSD.

Generalized eikonal approximation for fast retrieval of particle size distribution in spectral extinction technique

In retrieving particle size distribution from spectral extinction data, a critical issue is the calculation of extinction efficiency, which affects the accuracy and rapidity of the whole retrieval. The generalized eikonal approximation (GEA) method, used as an alternative to the rigorous Mie theory, is introduced for retrieval of the unparameterized shape-independent particle size distribution (PSD). To compute the extinction efficiency more efficiently, the combination of GEA method and Mie theory is adopted in this paper, which not only extends the applicable range of the approximation method but also improves the speed of the whole retrieval. Within the framework of the combined approximation method, the accuracy and limitations of the retrieval are investigated. Moreover, the retrieval time and memory requirement are also discussed. Both simulations and experimental results show that the combined approximation method can be successfully applied to retrieval of PSD when the refractive index is within the validity range. The retrieval results we present demonstrate the high reliability and stability of the method. 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 making this method more suitable for online particle sizing.