Shape Of Distribution Function Research Articles

Retrieval of hourly aerosol single scattering albedo over land using geostationary satellite data

The single scattering albedo (SSA) of aerosol particles is one of the key variables that determine aerosol radiative forcing. Herein, an Algorithm for the retrieval of Single scattering albedo over Land (ASL) is proposed for application to full-disk data from the advanced Himawari imager (AHI) sensor flying on board the Himawari-8 satellite. In this algorithm, an atmospheric radiative transfer model known as the USM (the top of the atmosphere reflectance as the sum of Un-scattered, Single-scattered, and Multiple-scattered components) is used to calculate the SSA instead of predetermining the aerosol model; the USM is constrained by the surface bidirectional reflectance distribution function shape and aerosol optical depth (AOD) in the retrieval process. Combining two consecutive observations and a 2 * 2 pixel window, the optimal estimation algorithm is adopted to obtain the optimal solution for the aerosol SSA. These SSA results are evaluated by comparing with aerosol robotic network (AERONET) data. Linear regression shows that SSAASL = 0.60*SSSAERONET + 0.38, with a correlation coefficient (0.7284), mean absolute error (0.0319), mean bias error (0.00324), root mean square error (0.0427), and ~80.11% of the ASL SSA data within an uncertainty of ±0.05 of the AERONET data. A comparison of the ASL SSA products with collocated Himawari-8 SSA products (Version 03, officially released by the Japan Meteorological Agency (JMA), referred to herein as JMA SSA) shows that the accuracy of the ASL SSA is better than that of the JMA SSA products. For the SSA retrieval in large AODs (>0.4), the validation metrics vs. AERONET data are better.

THEMIS Observations of Magnetosheath‐Origin Foreshock Ions

AbstractThe ion foreshock, filled with backstreaming foreshock ions, is very dynamic with many transient structures that disturb the bow shock and the magnetosphere‐ionosphere system. It has been shown that foreshock ions can be generated through either solar wind reflection at the bow shock or leakage from the magnetosheath. While solar wind reflection is widely believed to be the dominant generation process, our investigation using Time History of Events and Macroscale Interactions during Substorms mission observations reveals that the relative importance of magnetosheath leakage has been underestimated. We show from case studies that when the magnetosheath ions exhibit field‐aligned anisotropy, a large fraction of them attains sufficient field‐aligned speed to escape upstream, resulting in very high foreshock ion density. The observed foreshock ion density, velocity, phase space density, and distribution function shape are consistent with such an escape or leakage process. Our results suggest that magnetosheath leakage could be a significant contributor to the formation of the ion foreshock. Further characterization of the magnetosheath leakage process is a critical step toward building predictive models of the ion foreshock, a necessary step to better forecast foreshock‐driven space weather effects.

Estimating photometric redshift from mock flux for CSST survey by using weighted Random Forest

ABSTRACT Accurate estimation of photometric redshifts (photo-z) is crucial in studies of both galaxy evolution and cosmology using current and future large sky surveys. In this study, we employ Random Forest (RF), a machine learning algorithm, to estimate photo-z and investigate the systematic uncertainties affecting the results. Using galaxy flux and colour as input features, we construct a mapping between input features and redshift by using a training set of simulated data, generated from the Hubble Space Telescope Advanced Camera for Surveys (HST-ACS) and COSMOS catalogue, with the expected instrumental effects of the planned China Space Station Telescope (CSST). To improve the accuracy and confidence of predictions, we incorporate inverse variance weighting and perturb the catalogue using input feature errors. Our results show that weighted RF can achieve a photo-z accuracy of $\rm \sigma _{NMAD}=0.025$ and an outlier fraction of $\rm \eta =2.045\ \hbox{per cent}$, significantly better than the values of $\rm \sigma _{NMAD}=0.043$ and $\rm \eta =6.45\ \hbox{per cent}$ obtained by the widely used Easy and Accurate Zphot from Yale (EAZY) software, which uses template-fitting method. Furthermore, we have calculated the importance of each input feature for different redshift ranges and found that the most important input features reflect the approximate position of the break features in galaxy spectra, demonstrating the algorithm’s ability to extract physical information from data. Additionally, we have established confidence indices and error bars for each prediction value based on the shape of the redshift probability distribution function, suggesting that screening sources with high confidence can further reduce the outlier fraction.

Effect of stereo-chemistry and hydrophilic nature of synthetic carboxylic acid polymers on conformation, intermolecular structure and hydration at air-water interface

Conformation, intermolecular structure and hydration of different stereo-isomers of poly(methacrylic acid) and poly(acrylic acid), specifically isotactic-poly(methacrylic acid) (i-PMA), syndiotactic-poly(methacrylic acid) (s-PMA) and syndiotactic-poly(acrylic acid) (s-PAA) at vacuum-water interface were studied using molecular dynamics simulations. The adsorbed chain conformation was analyzed by radius-of-gyration components parallel and perpendicular to the interface, relative shape anisotropy parameter, distribution and autocorrelation function of dihedral angles, and orientation distribution of different groups relative to interface plane. i-PMA and s-PAA adsorb in planar conformation (i-PMA is curved compared to s-PAA) whereas s-PMA adsorbs in random coil conformation. Different chemical groups of s-PAA and i-PMA show preferential orientation whereas it is absent in the case of s-PMA. The random coil conformation of s-PMA exhibits greater intra-chain hydrogen bonding whereas extended chain of s-PAA exhibits greater polymer-water hydrogen bonding. The overall contribution to polymer-water hydrogen bonds by carbonyl oxygen atoms is greater than that by hydroxyl hydrogen atom. Water molecules hydrogen bonded to s-PAA show faster dynamics compared to those bonded to i-PMA and s-PMA. The slower dynamics of polymer-water hydrogen bonds is correlated to the slower dynamics of polymer conformations. Knowledge of orientation of chemical groups is useful for understanding binding of adsorbed polymer with other polymers and ligands.

Diffusion and incidence of helium on tungsten surface

In this study, we investigated the diffusion and incidence of helium on tungsten surfaces using first principles and molecular dynamics methods. For three common tungsten surfaces (100, 111, 110), we found that the diffusion barrier of helium is positively/negatively correlated with the interatomic spacing/surface atomic density. The diffusion barriers of helium are relatively similar on the three surfaces, ranging from 5.82 to 6.50 eV. The diffusion barrier of helium on the tungsten surface represents the lower limit of the incidence barrier for helium implantation into tungsten. In our simulation, only helium with an incidence energy greater than 7 eV has the potential to be implanted into tungsten. Generally speaking, the implantation ratio of helium increases with increasing incidence energy and decreases with increasing substrate temperature (although the effect is minor). At a constant temperature, the implantation ratio of helium exhibits an exponential relationship with the incidence energy. The depth distribution of helium can be well described by Gamma distribution function, and the shape and scale parameters of the gamma distribution function can be determined based on the mean and variance of the helium depth distribution. The proposed fitting function allows for the quantitative description of the mean and variance of the helium depth distribution based on the incidence conditions (incident energy E and substrate temperature T), thereby determining the helium depth distribution. This has important implications for the in-depth study of helium-induced tungsten surface fuzz formation.

Extreme value statistical analysis of meteorological parameters observed at Rawatbhata Rajasthan site

Abstract Knowledge of extreme meteorological parameters plays an important role, for the selection of any civil structure at nuclear site or to design important nuclear structures to withstand design basis values of meteorological extremes that are likely to occur during the lifetime of these structures. The method used for the evaluation of extreme parameters is least square fit method. In this study, statistical analyses of extreme values of meteorological parameters at Rawatbhata Rajasthan site (RR site) are presented for the period 1980 to 2022 and for rainfall, it is for the period 1964 to 2022. Meteorological parameters such as extreme wind speed and wind gust (5 min) at 10 m and 30 m heights, extreme surface air temperature, extreme atmospheric pressure and extreme rainfall (yearly, monthly, and daily) are evaluated and discussed. From the extreme value analysis, it is observed that the variables for monthly maximum rainfall, annual maximum rainfall, maximum air temperature, maximum atmospheric pressure, maximum hourly wind speed at 10 m and 30 m heights and wind gust (5 min.) at 10 m height obey Fisher-Tippette Type I distribution, whereas daily maximum rainfall, annual minimum rainfall, minimum air temperature, minimum relative humidity, minimum atmospheric pressure and wind gust (5 min.) at 30 m height obey Fisher-Tippette Type II distribution. Distribution function parameters, i.e., location, scale, and shape parameter for each variable, have been determined and design basis values corresponding to return periods of 50 years and 100 years are derived and presented. The derived extreme values are particularly useful for arriving at suitable design values to ensure the safety of civil structures at RR site area with respect to stresses due to weather conditions. The values are also compared with corresponding values at other nuclear reactor sites of Tarapur, Narora, and Kalpakkam.

Reliability analysis of angle ply woven GFRP composite under in-plane loading condition using two parameter Weibull distribution

This study presents an analysis of the reliability of woven angle ply GFRP under both static and dynamic loading conditions. Hand lay-up technique was used to fabricate 8-ply laminates with four different fibre orientations (0°/90°, ±15°, ±30°, and ± 45°). The laminates were then tested for their tensile properties and fatigue behavior. When compared to specimens reinforced with different fibre orientations, specimens with (0°/90°) fibre orientation showed the highest failure stress and lowest failure strain. Theoretical model based on the Weibull distribution has been employed to determine theoretical tensile strength and mean fatigue life values for prepared laminates. Weibull parameters were used to generate S-N curves for various reliability levels (R = 0.10, 0.368, 0.50, and 0.99). The variation in the experimental results was investigated using the Weibull distribution function's shape factor (α) and coefficient of variance. These S-N curves were developed to assist designers in determining the first failure time as well as reliability and safety constraints. Finally, the study showed that the scatter value in all sample groups decreased to a failure criterion of approximately 106 cycles, and the scatter values were closer to each other.

Retrieval and validation of long-term aerosol optical depth from AVHRR data over China

ABSTRACT Advanced Very High Resolution Radiometer (AVHRR) onboard National Oceanic and Atmospheric Administration (NOAA) satellites can provide over 40 years of global remote sensing observations, which can be used to retrieve long-term aerosol optical depth (AOD). This is of great significance to the study of global climate change. In this paper, we proposed an algorithm to jointly calculate AOD and land surface properties from AVHRR observations. With assumptions that AOD doesn’t vary in adjacent space and earth surface property doesn’t vary in two days, the algorithm considered non-Lambertian surface reflection based on the shape of bidirectional reflectance distribution function (BRDF shape) and obtained AOD and surface property by optimal estimation (OE) method. The algorithm has been applied to NOAA-7, 9, 11, 14, 16, 18, and 19 satellites and AVHRR-retrieved AOD with 5 × 10 km over China (15°–60° N, 70°–140°E) has been obtained from 1982 to 2016. Comparisons of AVHRR-retrieved AOD against AErosol RObotic NETwork (AERONET) (in and around China) and China Aerosol Remote Sensing Network (CARSNET) AOD show good consistency with 62.62% points within the uncertainty of Δτ = ± (0.05 + 0.25τ) and root-mean-square error (RMSE) of 0.26. Further comparison of the monthly mean AOD of multiple AOD datasets in the ‘Beijing’, ‘Dalanzadgad’, ‘NCU_Taiwan’ and ‘Kanpur’ stations shows that the results of the algorithm are stable. The yearly averaged AOD data also has similar agreements with MERRA-2 (The Modern-Era Retrospective analysis for Research and Applications, Version 2) and AVHRRDB data (AVHRR ‘Deep Blue’ aerosol data set). The multi-year mean correlation coefficient is 0.70 and 0.61 and the percentages within the uncertainty are 80.01% and 67.29% compared with MERRA-2 AOD and AVHRRDB AOD respectively.

Soot nanoparticle sizing in counterflow flames using in-situ particle sampling and differential mobility analysis verified with two-colour time-resolved laser-induced incandescence

The emphasis of this work is on the development of an intrusive particle sampling system to track the evolution of soot nanoparticles in ethylene counterflow diffusion flames. The overarching objective is to determine the mobility size distributions in a spatially resolved manner using the developed probe system coupled with differential mobility analysis, i.e., a scanning mobility particle sizer (SMPS). The probe system involves a tailor-made quartz probe, gas supply, pressure control periphery, and a traverse system enabling a precise positioning along the flame axis. In preliminary experiments, the dilution ratio of the quartz probe as function of boundary conditions as well as particle losses during intrusive particle sampling are studied. To demonstrate the capability of the developed particle sampling system, results from ethylene counterflow diffusion flames with different fuel mass fractions and strain rates are presented and compared with results derived by non-intrusive laser-based diagnostics, i.e., two-colour time-resolved laser induced incandescence (2C-TiRe-LII). Results of these experiments indicate that the particle sampling system is capable of tracking the development of particle size distributions – independent of the distribution function, i.e., mono-, bi- or multimodal shape – in counterflow flames. Likewise, the agreement between soot volume fractions and particle size distributions measured via intrusive particle sampling coupled with differential mobility analysis and non-intrusive laser-based 2C-TiRe-LII is excellent at varying the fuel mass fractions and strain rates of the ethylene counterflow flames.

Turbulent droplet breakage in a von Kármán flow cell

Droplet dispersion in liquid–liquid systems is a crucial step in many unit operations throughout the chemical, food, and pharmaceutic industries, where improper operation causes billions of dollars of loss annually. A theoretical background for the description of droplet breakup has been established, but many assumptions are still unconfirmed by experimental observations. In this investigation, a von Kármán swirling flow device was used to produce homogeneous, low-intensity turbulence suitable for carrying out droplet breakage experiments using optical image analysis. Individual droplets of known, adjustable, and repeatable sizes were introduced into an isotropic turbulent flow field providing novel control over two of the most important factors impacting droplet breakage: turbulence dissipation rate and parent droplet size. Introducing droplets one at a time, large data sets were gathered using canola, safflower, and sesame oils for the droplet phase and water as the continuous phase. Automated image analysis was used to determine breakage time, breakage probability, and child droplet size distribution for various turbulence intensities. Breakage time and breakage probability were observed to increase with increasing parent droplet size, consistent with the classic and widely used Coulaloglou–Tavlarides breakage model (C–T model). The shape of the child drop size distribution function was found to depend upon the size of the parent droplet.

Метод расчета надежности шарнирно- стержневых систем при интервальной оценке случайных величин

The article describes a method for the reliability analysis of hinge-rod systems (trusses) with an interval estimation of the variability limits of random variables. In practical tasks of structural reliability analysis, it is often not possible to obtain complete statistical data that is necessary for a probabilistic and statistical approach in accordance with GOST 27751-2014. The use of alternative theories of data analysis makes it possible to obtain a define assessment of reliability with incomplete statistical data without introducing unconfirmed hypotheses about the form and shape of probability distribution functions of random variables. In this paper, it is proposed to use data on the limits of variability of random variables (an interval analysis) to assess the reliability of hinge-rod systems on the truss example. A comparative analysis of the truss reliability is given by two approaches (the classical probabilistic-statistical and the proposed interval approach). By the interval approach, the reliability of the truss is lower due to the fact that the interval estimation takes into account other possible distributions within a given interval that differ from the normal probability distribution. In the case when it is impossible to determine the type of probability distribution, but the limits of variability for random variables are known, the use of the presented method is a more cautious for the safety of truss operation.

The effect of anode axial position on the performance of a miniaturized cylindrical Hall thruster with a cusp-type magnetic field

A 200 W cylindrical Hall thruster with a cusp-type magnetic field was proposed, manifesting convergent plume and high specific impulse. In this paper, a series of ring-shaped anodes are designed and the influence of anode axial position on the performance of CHT with a cusp-type magnetic field is studied. The experimental results indicate that the thruster keeps stable operation at the condition of 140–270 W discharge power. When the anode moves axially towards the upstream cusp field, the thrust enhances from 6.5 mN to 7.6 mN and specific impulse enhances from 1658 s to 1939 s significantly. These improvements of thruster performance should be attributed to the enhancement of current utilization, propellant utilization and acceleration efficiency. According to the analyses on the discharge characteristics, it is revealed that as the anode moves upstream, the electron transport path could be extended, the magnetic field in this extended path could impede electron cross-field transport and facilitate the ionization intensity, yielding to the enhancement of current utilization and propellant utilization efficiency. Moreover, along with this enhancement of upstream ionization at the given anode flow rate, the main ionization region is thought to move upstream and then separate more apparently from the acceleration region, which has been demonstrated by the narrowing of ion energy distribution function shape. This change in acceleration region could decrease the ion energy loss and enhance acceleration efficiency. This work is beneficial for optimizing the electrode structure of thruster and recognize the ionization and acceleration process under the cusp magnetic field.

Rüzgar enerji uygulamaları için Weibull dağılım parametrelerinin tahmini: Türkiye’nin Dinar bölgesi için bir çalışma

In this study, the wind energy characteristics of Dinar region were researched. Required wind data was provided by the Dinar Meteorology Station of the Turkish State Meteorology Service. Wind data was recorded hourly between June 2015 and May 2020. The two variable Weibull probability distribution function was used to research wind characteristics of the region. Six different methods were used to calculate shape (k) and scale (c) variables of the probability distribution function. These are moment, graph, Justus empirical, energy trend, energy pattern and maximum likehood estimation methods. The performance of these methods were compared with four different statistical error analysis methods. These are root mean square error (RMSE), coefficient of determination (R2), chi-square error (X2) and mean absolute error (MAE). According to the results, maximum likehood estimation and energy trend methods have been the most successful methods in the calculation of Weibull parameters. In addition, this study is an important preliminary study in determining the wind energy characteristic of the region.

Structure of the ion acceleration region in cylindrical Hall thruster plasmas

We investigated the structure of the ion acceleration region and the shape of the ion velocity distribution function (IVDF) in cylindrical Hall thruster plasmas, using laser-induced fluorescence spectroscopy on Xe II metastable ions. On the thruster axis, the acceleration front is located deeper than a half-length of the discharge channel length, and the acceleration region reaches up to 3 times the discharge channel length (several centimeters) away from the channel exit, regardless of the discharge condition. It is noteworthy that ion acceleration mostly (more than 70%) takes place outside the discharge channel. The IVDF is close to a single Gaussian inside the discharge channel. It however becomes substantially asymmetric when moving downstream. Double Gaussian distributions including cold and hot ion groups was in good agreement with the measured ion velocity distributions downstream with an R-squared greater than 0.995.

The Effects of Magnetic Fields and Outflow Feedback on the Shape and Evolution of the Density Probability Distribution Function in Turbulent Star-forming Clouds

Abstract Using a suite of 3D hydrodynamical simulations of star-forming molecular clouds, we investigate how the density probability distribution function (PDF) changes when including gravity, turbulence, magnetic fields, and protostellar outflows and heating. We find that the density PDF is not lognormal when outflows and self-gravity are considered. Self-gravity produces a power-law tail at high densities, and the inclusion of stellar feedback from protostellar outflows and heating produces significant time-varying deviations from a lognormal distribution at low densities. The simulation with outflows has an excess of diffuse gas compared to the simulations without outflows, exhibits an increased average sonic Mach number, and maintains a slower star formation rate (SFR) over the entire duration of the run. We study the mass transfer between the diffuse gas in the lognormal peak of the PDF, the collapsing gas in the power-law tail, and the stars. We find that the mass fraction in the power-law tail is constant, such that the stars form out of the power-law gas at the same rate at which the gas from the lognormal part replenishes the power law. We find that turbulence does not provide significant support in the dense gas associated with the power-law tail. When including outflows and magnetic fields in addition to driven turbulence, the rate of mass transfer from the lognormal to the power law, and then to the stars, becomes significantly slower, resulting in slower SFRs and longer depletion times.

Determining hyporheic removal rates of trace organic compounds using non-parametric conservative transport with multiple sorption models

Assessing the transport and reactive processes of contaminants in freshwater streams is crucial in managing water resources sustainably. Particularly the hyporheic zone, the sediment-water interface where surface water and groundwater mix, may possess significant contaminant removal capacities due to its myriad physical, chemical, and microbiological processes. However, modelling approaches aiming at assessing the hyporheic zone’s reactivity are either based on simple assumptions, such as, predefining the shape of the residence times distribution (RTD) function, or are computationally not feasible due to a too detailed system characterisation. In addition, parent-daughter reactions of contaminants are barely investigated. The present study introduces a numerical modelling framework for assessing hyporheic reactions of contaminant transformation reactions based on a non-parametric residence time approach combined with multiple sorption models and first-order removal reactions. The proposed framework uses natural electrical conductivity fluctuations to determine conservative transport properties and is demonstrated by interpreting time series of hyporheic point measurements of trace organic compounds, such as pharmaceuticals, and their transformation products using two commonly-used sorption models, namely the simple retardation and the first-order kinetic sorption model. The developed approach gives similar reaction rate coefficient estimates for all contaminants considered for both sorption models tested. The findings highlight that (i) the accurate shape of the RTD is most certainly important for reactive parameter determination and (ii) the daughter reaction rate coefficient may be underestimated if its parent transformation is ignored. The model provides reactive parameter estimates of contaminant transformation reactions with high parameter identifiability and informs which specific parent-daughter-pathway has occurred.

Reinterpretation of proton strangeness between ATLAS and CMS measurements

We reexamine the shapes of the strange quark parton distribution functions (PDFs) of the proton by means of quantum chromodynamics (QCD) analysis of {\hera} deep inelastic scattering cross section measurement at DESY, and inclusive gauge boson production and $W$ boson production associated with a charm quark from LHC at CERN. We find that there is an overall agreement on the strange quark distributions obtained from CMS $W$ + charm and ATLAS $W/Z$ data at the parton momentum fraction range $x \lesssim 10^{-2}$. Meanwhile, there is also a strong tension between these data towards large $x$. We find that this tension fades away if the ATLAS measurement of $W/Z$ production is analyzed together with the ATLAS $W$ + charm data. The $W/Z$ and $W$ + charm data both from ATLAS and CMS experiments agree that the proton strangeness is enhanced towards small momentum fraction $x$ and is smoothly suppressed at large $x$. Furthermore, a strong $x$ dependence of the strange-to-non-strange parton ratio $R_s(x,Q^2)$ is observed.

Statistical analysis of extreme value of meteorological elements observed for the last 31 years (1989–2019) at Narora site

Understanding of extreme weather conditions at the site of interest is essentially required in the design of engineering structures so that the structures can withstand weather stresses. This paper presents an analysis of extreme values of meteorological elements observed at Narora site for the last three decades (1989–2019). The elements considered are extreme air temperature (°C), minimum relative humidity (%), extreme wind gust (km/h), maximum rainfall (mm) in a day and a month, and annual rainfall. The extreme value analysis reveals that the maximum air temperature, maximum wind gust at 30 m, maximum monthly rainfall, and maximum annual rainfall obey Fisher-Tippett Type-1/Gumbel extreme value distribution, whereas minimum air temperature, minimum relative humidity (%), annual daily maximum rainfall (mm), and annual minimum rainfall (mm) obey Fisher-Tippett Type-2/Frechet extreme value distribution function. Distribution function parameters, i.e., location, scale, and shape parameter for each variable, have been determined. Extreme values corresponding to return periods of 50, 100, and 1000 years are worked out using best fit linear regression curve as a compliance of the Atomic Energy Regulatory Board Safety Guide Recommendations. The derived extreme values are particularly useful to designer for arriving at suitable design basis values of different elements to ensure the safety of the reactors and other civil structures in Narora region, with respect to stresses due to weather conditions. Extreme values corresponding to return periods of 50 and 100 years at Narora are compared with corresponding values at other three nuclear reactor sites in India, namely, Tarapur, Kalpakkam, and Trombay. In addition, the time series pattern analysis of rainfall for 31 years at the Narora site closely following the 2-year moving average rainfall data pattern. These results can be used for water harvesting, irrigation, and floods management plans in the future.

Noise and delay can shape distribution functions in stochastic reaction dynamics

Noise and delay can shape distribution functions in stochastic reaction dynamics

Improving MODIS Aerosol Estimates Over Land With the Surface BRDF Reflectances Using the 3-D Discrete Cosine Transform and RossThick-LiSparse Models

The retrieval of aerosol properties over land from satellite sensors has always been a challenge. At present, several different algorithms for retrieving aerosol optical depth (AOD) have been developed from different satellite sensors. While each algorithm has its own advantages, the accuracy of AOD retrieval still needs to be further improved. To improve the retrieval accuracy of aerosol algorithms, it is necessary to provide a better method to describe the surface properties. In the current study, a new aerosol retrieval algorithm for Moderate Resolution Imaging Spectroradiometer (MODIS) images at a high spatial resolution of 500 m is proposed based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> bidirectional reflectance distribution function (BRDF) shape parameters database, which is reconstructed via the 3-D discrete cosine transform (DCT-PLS) method. Then, the surface reflectances are calculated from BRDF model (i.e., RossThick-LiSparse), and a non-Lambertian forward model used to describe the surface anisotropy. The new algorithm is used for processing the MODIS over the Beijing–Tianjin–Hebei of China, and Southeastern United States of America regions, and results are validated against AERONET AOD measurements as well as compared with the MODIS AOD products. The comparison showed that the estimation scheme of surface reflectance in this new algorithm significantly improved the AOD retrievals accuracy, with average correlation coefficient ~0.965 and root-mean-square error ~0.125; the number of AOD retrievals falling within expected error has increased to ~80.1%, and the overestimation uncertainty has been reduced compared with MODIS products. Due to the high spatial resolution and continuous spatial distributions of the AOD retrievals by the new algorithm, therefore, it can well-captured aerosol details over mixed surfaces and better useful for air pollution studies than the MODIS products at local and urban scales.