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Yongxiang Hu

Publications and source records attributed to Yongxiang Hu.

At least 19 records

Machine Learning Based Aerosol and Ocean Color Joint Retrieval Algorithm for Multiangle Polarimeters over Coastal Waters

NASA’s Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, recently launched in February 2024, carries two multiangle polarimeters (MAPs): the UMBC Hyper-Angular Rainbow Polarimeter (HARP2) and SRON Spectropolarimeter for Planetary Exploration One (SPEXone). Measurements from these MAPs will greatly advance ocean ecosystem and aerosol studies as their measurements contain rich information on microphysical properties of aerosols and hydrosols. The Multi-Angular Polarimetric Ocean coLor (MAPOL) joint retrieval algorithm has been developed to retrieve aerosol and ocean color information, which uses a vector radiative transfer (RT) model as the forward model. The RT model is computationally expensive, which makes processing a large amount of data challenging. FastMAPOL was developed to expedite retrieval using neural networks to replace the RT forward models. As a prototype study, FastMAPOL was initially limited to open ocean applications where the ocean Inherent Optical Properties (IOPs) were parameterized in terms of one parameter: chlorophyll-a concentration (Chla). In this study we further expand the FastMAPOL joint retrieval algorithm to incorporate NN based forward models for coastal waters, which use multi-parameter bio-optical models. In addition, aerosols are represented by six components, i.e., fine mode non absorbing insoluble (FNAI), brown carbon (BrC), black carbon (BC), fine mode non absorbing soluble (FNAS), sea salt (SS) and non-spherical dust (Dust). Sea salt and dust are coarse mode aerosols, while the other components are in the fine mode. The sizes and spectral refractive indices are fixed for each aerosol component, while their abundances are retrievable. The multi-parameter bio-optical model and aerosol components are chosen to represent the coastal marine environment. The retrieval algorithm is applied to synthetic measurements in three different configurations ofMAPs in the PACE mission: HARP2 observations only, SPEXone observations only and combined HARP2 and SPEXone observations. The retrieval results from synthetic measurements show that for aerosol retrieval the SPEXone-only configuration works equally well with the HAPR2-only configuration. On the other hand, for ocean color retrieval the SPEXone instrument provides better information due to its larger spectral coverage. For the surface parameters (wind speed), HARP2 measurements provide better information due to its wide field of view. Combined measurement configuration HARP2+SPEXone performed the best to retrieve all aerosol, ocean color and surface parameters. We also studied the impact of sun glint to aerosol and ocean color retrievals. The retrieval test revealed that wind speed and absorbing aerosol retrieval improves significantly when including measurements at glint geometries. Furthermore, the retrieval algorithm is equipped with modules for atmospheric correction and bidirectional reflectance distribution (BRDF) correction to obtain the remote sensing reflectance, which enables ocean biogeochemistry studies using the PACE polarimeter data.

PACE

High Spectral Resolution Lidar – Generation 2 (HSRL-2) Retrievals of Ocean Surface Wind Speed: Methodology and Evaluation

Ocean surface wind speed (i.e., wind speed 10 m above sea level) is a critical parameter used by atmospheric models to estimate the state of the marine atmospheric boundary layer (MABL). Accurate surface wind speed measurements in diverse locations are required to improve characterization of MABL dynamics and assess how models simulate large-scale phenomena related to climate change and global weather patterns. To provide these measurements, this study introduces and evaluates a new surface wind speed data product from the NASA Langley Research Center nadir-viewing High Spectral Resolution Lidar – generation 2 (HSRL-2) using data collected as part of the NASA Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE) mission. The HSRL-2 can directly measure vertically resolved aerosol backscatter and extinction profiles without additional constraints or assumptions, enabling the instrument to accurately derive atmospheric attenuation and directly determine surface reflectance (i.e., surface backscatter). Also, the high horizontal spatial resolution of the HSRL-2 retrievals (0.5 s or ∼ 75 m along track) allows the instrument to probe the fine-scale spatial variability in surface wind speeds over time along the flight track and over breaks in broken cloud fields. A rigorous evaluation of these retrievals is performed by comparing coincident HSRL-2 and National Center for Atmospheric Research (NCAR) Airborne Vertical Atmosphere Profiling System (AVAPS) dropsonde data, owing to the joint deployment of these two instruments on the ACTIVATE King Air aircraft. These comparisons show correlations of 0.89, slopes of 1.04 and 1.17, and y intercepts of −0.13 and −1.05 m s−1 for linear and bisector regressions, respectively, and the overall accuracy is calculated to be 0.15 ± 1.80 m s−1. It is also shown that the dropsonde surface wind speed data most closely follow the HSRL-2 distribution of wave slope variance using the distribution proposed by Hu et al. (2008) rather than the ones proposed by Cox and Munk (1954) and Wu (1990) for surface wind speeds below 7 m s−1, with this category comprising most of the ACTIVATE data set. The retrievals are then evaluated separately for surface wind speeds below 7 m s−1 and between 7 and 13.3 m s−1 and show that the HSRL-2 retrieves surface wind speeds with a bias of ∼ 0.5 m s−1 and an error of ∼ 1.5 m s−1, a finding not apparent in the cumulative comparisons. Also, it is shown that the HSRL-2 retrievals are more accurate in the summer (−0.18 ± 1.52 m s−1) than in the winter (0.63 ± 2.07 m s−1), but the HSRL-2 is still able to make numerous (N=236) accurate retrievals in the winter. Overall, this study highlights the abilities and assesses the performance of the HSRL-2 surface wind speed retrievals, and it is hoped that further evaluation of these retrievals will be performed using other airborne and satellite data sets.

Sanja Dmitrovic

Polarization Calibration Using Solar Radiation Background Signal Scattered from Dense Cirrus Clouds in the Visible and Ultraviolet Wavelength Regimes

In this presentation we describe the application of a previously developed technique that is now being used to correct the daytime polarization calibration of the CALIPSO lidar. The technique leverages the fact that the solar radiation background signals from dense cirrus clouds are largely unpolarized due to the internal multiple reflections within the non-spherical ice particles and the multiple scattering that occurs among these particles. Therefore, the ratio of polarization components of the cirrus background signals provides a good estimate for the polarization gain ratio (PGR) of the lidar. Using airborne backscatter lidar measurements, this technique was demonstrated to work well in the infrared regime. However, in the visible and ultraviolet regime, the molecular contribution is too large to be ignored, and thus corrections must be applied to account for the highly polarizing characteristics of the molecular scattering. Ignoring molecular scattering contributions can cause PGR errors of 2-3% at 532 nm, where the CALIPSO lidar makes its depolarization measurement. Because of the wavelength dependence of -4 of the molecular scattering, the PGR error can be even larger at the 355 nm wavelength that will be used by ESA’s EarthCARE lidar. To correct the molecular scattering contributions to the lidar received solar background signal, a look-up table has been created using a polarization-sensitive radiative transfer model. This presentation describes the theory and implementation of the molecular scattering correction.

Zhaoyan Liu

Reports From EXPORTS Modeling and Data-Mining Activities

EXPORTS -EXport Processes in the Ocean from RemoTe Sensing is NASA’s large field campaign focusing on development of a predictive understanding of the export, fate and carbon cycle impacts of the global net primary production. This co-funded program (NSF, private funding1, and international participation) was conceived in 2013, with EXPORTS Science plan published in 2016 (Siegel et al 2016, EXPORTS Writing Team 2015) and its implementation plan finalized in 2016 (EXPORTS Science Definition Team 2016). More details are presented in Siegel et al (2021). EXPORTS campaign is structured as a multiyear effort (Figure 1). It started with “Pre-EXPORTS” modeling and data-mining activity followed by a first phase with two major field programs and a second synthesis and modeling phase. The “Pre-EXPORTS” projects, total of 6 of them (Table 1), funded under A.3 Ocean Biology and Biogeochemistry 2015 call, helped to plan the field campaign (Resplandy et al 2019, Rousseaux & Gregg 2017), and supporting further global synthesis with datasets mined from the literature (e.g. Bisson et al (2020), Bisson et al (2018), Kramer and Siegel (2019)), directly responding to objectives outlined in Science Plan (see section 6 in Team (2015)) and Implementation team (see Figure 1 in Team (2016)). This document presents a compilation of the final reports of the Pre-EXPORTS funded projects, in hope of synthesizing the outcomes, and insuring the legacy of this program. Each of these reports contains a list of published papers, and reader should refer to them to see results in details.

Brandi J. McCarty

A Novel Approach to Solve Forward/Inverse Problems in Remote Sensing Applications

Inversion of electromagnetic (EM) signals reflected from or transmitted through a medium, or emitted by it due to internal sources can be used to investigate the optical and physical properties of a variety of scattering/absorbing/emitting materials. Such media encompass planetary atmospheres and surfaces (including water/snow/ice), and plant canopies. In many situations the signals emerging from such media can be described by a linear transport equation which in the case of EM radiation is the radiative transfer equation (RTE). Solutions of the RTE can be used as a forward model to solve the inverse problem to determine the medium state parameters giving rise to the emergent (reflected/transmitted/emitted) EM signals. A novel method is developed to determine layer-by-layer contributions to the emergent signals from such stratified, multilayered media based on the solution of the pertinent RTE. As a specific example of how this approach may be applied, the radiation reflected from a multilayered atmosphere is used to solve the problem relevant for EM probing by a space-based lidar system. The solutions agree with those obtained using the standard lidar approach for situations in which single scattering prevails, but this novel approach also yields reliable results for optically thick, multiple scattering aerosol and cloud layers that cannot be provided by the traditional lidar approach.

forward modeling

Effective Uncertainty Quantification for Multi-Angle Polarimetric Aerosol Remote Sensing Over Ocean

Multi-angle polarimetric (MAP) measurements can enable detailed characterization of aerosol microphysical and optical properties and improve atmospheric correction in ocean color remote sensing. Advanced retrieval algorithms have been developed to obtain multiple geophysical parameters in the atmosphere–ocean system. Theoretical pixel-wise retrieval uncertainties based on error propagation have been used to quantify retrieval performance and determine the quality of data products. However, standard error propagation techniques in high-dimensional retrievals may not always represent true retrieval errors well due to issues such as local minima and the nonlinear dependence of the forward model on the retrieved parameters near the solution. In this work, we analyze these theoretical uncertainty estimates and validate them using a flexible Monte Carlo approach. The Fast Multi-Angular Polarimetric Ocean coLor (FastMAPOL) retrieval algorithm, based on efficient neural network forward models, is used to conduct the retrievals and uncertainty quantification on both synthetic HARP2 (Hyper-Angular Rainbow Polarimeter 2) and AirHARP (airborne version of HARP2) datasets. In addition, for practical application of the uncertainty evaluation technique in operational data processing, we use the automatic differentiation method to calculate derivatives analytically based on the neural network models. Both the speed and accuracy associated with uncertainty quantification for MAP retrievals are addressed in this study. Pixel-wise retrieval uncertainties are further evaluated for the real AirHARP field campaign data. The uncertainty quantification methods and results can be used to evaluate the quality of data products, as well as guide MAP algorithm development for current and future satellite systems such as NASA’s Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission.

PACE

Polarimeter + Lidar–Derived Aerosol Particle Number Concentration

In this study, we propose a simple method to derive vertically resolved aerosol particle number concentration (Na) using combined polarimetric and lidar remote sensing observations. This method relies on accurate polarimeter retrievals of the fine-mode column-averaged aerosol particle extinction cross section and accurate lidar measurements of vertically resolved aerosol particle extinction coefficient such as those provided by multiwavelength high spectral resolution lidar. We compare the resulting lidar + polarimeter vertically resolved N(a) product to in situ N(a) data collected by airborne instruments during the NASA aerosol cloud meteorology interactions over the western Atlantic experiment (ACTIVATE). Based on all 35 joint ACTIVATE flights in 2020, we find a total of 32 collocated in situ and remote sensing profiles that occur on 11separate days, which contain a total of 322 cloud-free vertically resolved altitude bins of 150 m resolution. We demonstrate that the lidar + polarimeter N(a) agrees to within 106% for 90% of the 322 vertically resolved points. We also demonstrate similar agreement to within 121% for the polarimeter-derived column-averaged N(a). We find that the range-normalized mean absolute deviation (NMAD) for the polarimeter-derived column-averaged Na is 21%, and the NMAD for the lidar + polarimeter-derived vertically resolved Na is 16%. Taken together, these findings suggest that the error in the polarimeter-only column-averaged N(a) and the lidar + polarimeter vertically resolved N(a) are of similar magnitude and represent a significant improvement upon current remote sensing estimates of N(a).

RSP

A Radiative Transfer Simulator for PACE: Theory and Applications

A radiative transfer simulator was developed to compute the synthetic data of all three instruments onboard NASA’s Plankton Aerosol, Cloud, ocean Ecosystem (PACE) observatory, at the top of the atmosphere (TOA). The instrument suite includes the ocean color instrument (OCI), the HyperAngular Rainbow Polarimeter 2 (HARP2), and the Spectro-Polarimeter for Planetary Exploration 1 (SPEXone). The PACE simulator is wrapped around a monochromatic radiative transfer model based on the successive order of scattering (RTSOS), which accounts for atmosphere and ocean coupling, polarization, and gas absorption. Inelastic scattering, including Raman scattering from pure ocean water, fluorescence due to chlorophyll, and colored dissolved organic matter (CDOM), is also simulated. This PACE simulator can be used to explore the sensitivity of the hyperspectral and polarized reflectance of the Earth system with tunable atmosphere and ocean parameters, which include aerosol and cloud number concentration, refractive indices, and size distribution, ocean particle microphysical parameters, and solar and sensor-viewing geometry. The PACE simulator is used to study two important case studies. One is the impact of the significant uncertainty in pure ocean water absorption coefficient to the radiance field in the ultraviolet (UV) spectral region, which can be as much as 6%. The other is the influence of different amounts of brown carbon aerosols and CDOM on the polarized radiance field at TOA. The percentage variation of the radiance field due to CDOM is mostly for wavelengths smaller than 600 nm, while brown aerosols affect the whole spectrum from 350 to 890 nm, primarily due to covaried soot aerosols. Both case studies are important for aerosol and ocean color remote sensing and have not been previously reported in the literature.

PACE

Retrieving Aerosol Optical Depth and High Spatial Resolution Ocean Surface Wind Speed from CALIPSO: A Neural Network Approach

An innovative neural network retrieval algorithm is developed for retrieving ocean surface wind speed from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) lidar measurements. The neural network is trained with CALIPSO ocean surface and atmospheric backscatter measurements together with collocated Advanced Microwave Scanning Radiometer for EOS(AMSR-E) ocean surface wind speed. Ocean surface wind speeds are derived by applying the neural network algorithm to CALIPSO measurements between 2008 and 2020. CALIPSO wind speed measurement of 2015 also compare with Advanced Microwave Scanning Radiometer 2 (AMSR-2) measurements on the Global Change Observation Mission –Water "Shizuku"(GCOM-W) satellite. Aerosol optical depths are then derived from CALIPSO’s ocean surface backscatter signal and theoretical ocean surface reflectance calculated from CALIPSO wind speed and Cox-Munk wind –surface slope variance relation. This CALIPSO wind speed retrieval technique is an improvement from Hu et al. (2008), as it can be applied to most clear skies with optical depths up to 1.5 without making assumptions about aerosol lidar ratio.

wind aerosols CALIPSO

Atmospheric Correction Over Ocean for Hyperspectral Radiometers Using Multi-Angle Polarimetric Retrievals

We developed a fast and accurate POLYnomial based Atmospheric Correction (POLYAC) algorithm for hyperspectral radiometric measurements, which parameterizes the atmospheric path radiances using aerosol properties retrieved from co-located multi-wavelength Multi-Angle Polarimeter (MAP) measurements. This algorithm has been applied to co-located Spectrometer for Planetary Exploration (SPEX) airborne and Research Scanning Polarimeter (RSP) measurements, where SPEX airborne was used as a proxy of hyperspectral radiometers, and RSP as the MAP. The hyperspectral remote sensing reflectance obtained from POLYAC is accurate when compared to Aerosol Robotic Network (AERONET), and Visible Infrared Imaging Radiometer Suite (VIIRS) ocean color products. POLYAC provides a robust alternative atmospheric correction algorithm for hyperspectral or multi-spectral radiometric measurements for scenes involving coastal oceans and/or absorbing aerosols, where traditional atmospheric correction algorithms are less reliable.

ocean color

The case for a multi-channel polarization sensitive LIDAR for investigation of insolation-driven ices and atmospheres

All LIDAR instruments are not the same, and advancement of LIDAR technology requires an ongoing interest and demand from the community to foster further development of the required components. The purpose of this white paper is to make the decadal survey panel aware of the need for further technical development, and the potential payoff of investing experimental time, money and thought into the next generation of LIDARs. Technologies for development:​ We advocate for future development of LIDAR technologies to measure the ​polarization​ state of the reflected light at ​selected multiple wavelengths,​ chosen according to the species of interest (e.g., H​2​O and CO​2​ in the Martian setting).Key scientific questions: ​In the coming decade, dollars spent on these LIDAR technologies will go towards addressing key climate questions on Mars and other rocky bodies, particularly those with seasonally changing (i.e. insolation driven) plumes of multiple icy volatiles such as Mars, Enceladus, Triton, or Pluto, and insolation-driven dust lifting, such as cometary bodies and the Moon. We will show from examining past Martian and terrestrial lidars that orbital and landed LIDARs can be effective for producing new insights into insolation-driven processes in current planetary climate on several bodies, beyond that available to our current fleet of largely passive instruments on planetary missions

Adrian Jon Brown

Inversion of multiangular polarimetric measurements from the ACEPOL campaign: an application of improving aerosol property and hyperspectral ocean color retrievals

NASA's Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, scheduled for launch in the time frame of late 2022 to early 2023, will carry the Ocean Color Instrument (OCI), a hyperspectral scanning radiometer, and two multiangle polarimeters (MAPs), the UMBC Hyper-Angular Rainbow Polarimeter 2 (HARP2) and the SRON Spectro-Polarimeter for Planetary EXploration one (SPEXone). One purpose of the PACE MAPs is to better characterize aerosol properties, which can then be used to improve atmospheric correction for the retrieval of ocean color in coastal waters. Though this is theoretically promising, the use of MAP data in the atmospheric correction of colocated hyperspectral ocean color measurements have not yet been well demonstrated. In this work, we performed aerosol retrievals using the MAP measurements from the Research Scanning Polarimeter (RSP) and demonstrate its application to the atmospheric correction of hyperspectral radiometric measurements from SPEX airborne. Both measurements were collected on the same aircraft from the Aerosol Characterization from Polarimeter and Lidar (ACEPOL) field campaign in 2017. Two cases over ocean with small aerosol loading (aerosol optical depth ∼0.04) are identified including colocated RSP and SPEX airborne measurements and Aerosol Robotic Network (AERONET) ground-based observations. The aerosol retrievals are performed and compared with two options: one uses reflectance measurement only and the other uses both reflectance and polarization. It is demonstrated that polarization information helps reduce the uncertainties of aerosol microphysical and optical properties. The retrieved aerosol properties are then used to compute the contribution of atmosphere and ocean surface for atmospheric correction over the discrete bands from RSP measurements and the hyperspectral SPEX airborne measurements. The water-leaving signals determined this way are compared with both AERONET and Moderate Resolution Imaging Spectroradiometer (MODIS) ocean color products for performance analysis. The results and lessons learned from this work will provide a basis to fully exploit the information from the unique combination of sensors on PACE for aerosol characterization and ocean ecosystem research.

Meng Gao

Neural Network Reflectance Prediction Model for Both Open Ocean and Coastal Waters

Remote sensing of global ocean color is a valuable tool for understanding the ecology and biogeochemistry of the worlds oceans, and provides critical input to our knowledge of the global carbon cycle and the impacts of climate change. Ocean polarized reflectance contains information about the constituents of the upper ocean euphotic zone, such as colored dissolved organic matter (CDOM), sediments, phytoplankton, and pollutants. In order to retrieve the information on these constituents, remote sensing algorithms typically rely on radiative transfer models to interpret water color or remote-sensing reflectance; however, this can be resource-prohibitive for operational use due to the extensive CPU time involved in radiative transfer solutions. In this work, we report a fast model based on machine learning techniques, called Neural Network Reflectance Prediction Model (NNRPM), which can be used to predict ocean bidirectional polarized reflectance given inherent optical properties of ocean waters. This supervised model is trained using a large volume of data derived from radiative transfer simulations for coupled atmosphere and ocean systems using the successive order of scattering technique (SOS-CAOS). The performance of the model is validated against another large independent test dataset generated from SOS-CAOS. The model is able to predict both polarized and unpolarized reflectances with an absolute error (AE) less than 0.004 for 99% of test cases. We have also shown that the degree of linear polarization (DoLP) for unpolarized incident light can be predicted with an AE less than 0.002 for 99% of test cases. In general, the simulation time of SOS-CAOS depends on optical depth, and required accuracy. When comparing the average speeds of the NNRPM against the SOS-CAOS model for the same parameters, we see that the NNRPM is able to predict the Ocean BRDF 6000 times faster than SOS-CAOS. Both ultraviolet and visible wavelengths are included in the model to help differentiate between dissolved organic material and chlorophyll in the study of the open ocean and the coastal zone. The incorporation of this model into the retrieval algorithm will make the retrieval process more efficient, and thus applicable for operational use with global satellite observations.

radiative transfer

Ocean Subsurface Study from ICESat-2 Mission

NASA has launched the ICESat-2 mission in September 2018 with the primary purpose of monitoring changes in the cryosphere. Fortunately, the measured photons over ocean region provide great opportunity for the ocean subsurface study. We have proposed a novel algorithm to determine ocean subsurface optical properties, such as, diffuse attenuated coefficient, kd (/m), total backscattering coefficients bb (/m), attenuated backscatter coefficient and particulate backscattering coefficients b(sub bp) (/m) from ICESat-2/ATLAS lidar measurements. Our ICESat-2 ocean subsurface results reveal high vertical resolution of these optical properties through the water column that are hidden from the passive ocean color record. Moreover, we can estimate the particulate organic carbon (POC) and phytoplankton carbon biomass based on the ICESat-2 retrieved particulate backscattering coefficients b( sub bp) results. We will present and discuss the first ICESat-2 ocean subsurface profile results, especially in polar region where passive ocean color measurements are difficult to make. We will also present the multiple scattering effects on the ocean subsurface optical properties retrieval.

Xiaomei Lu

Cloud Remote Sensing with EPIC/DSCOVR Observations: A Sensitivity Study with Radiative Transfer Simulations

The Earth Polychromatic Imaging Camera (EPIC) onboard the Deep Space Climate Observatory (DSCOVR) views nearly the whole sunlit face of the Earth with 10 spectral bands ranging from the UV to the near-infrared, including two oxygen absorbing bands centered at 764 nm (A-band) and 687.75 nm (B-band). Clouds are among the primary remote sensing targets using EPIC images because of their important impacts on the Earth’s radiation budget. In order to facilitate the EPIC cloud data product development, we have built a radiative transfer simulator featuring flexible cloud microphysical parameters, gas absorptions, and the instrument line shape functions for each EPIC band. The radiative transfer simulator is used to explore the sensitivity of EPIC observations on liquid-phase cloud microphysical parameters, including optical depth, geometric thickness, and cloud top height. We found that the ratios of the reflectances in the oxygen A and B bands to their respective continuum measurements can be used to increase the confidence level of cloud masking over scenes with sun-glint. In addition, the 388 nm band can be used to differentiate low and high clouds with the uncertainty of roughly 2–3 km. Combining this information with the oxygen absorption bands, the cloud geometric thickness can be obtained with the rough uncertainty of 3–4 km.

atmospheric and ocean optics

Does Orbital Angular Momentum Have Effect on Laser’s Scattering by Molecular Atmosphere?

Lasers with orbital angular momentum (OAM) have potential applications in communication technology, manipulation of particles, and remote sensing. Because of its unusual light-scattering properties, the OAM laser’s interaction with a molecular atmosphere must be studied to ensure that it is not lossy for communication or remote-sensing applications that involve its transmission through an atmospheric environment. In this study, the finite-difference time-domain (FDTD) method [21] is applied to calculate the light scattering of the purely azimuthal (the radial mode number is assumed to be zero) Laguerre-Gaussian (LG) beams with OAM by very small dielectric particles. Not like Lorentz-Mie solutions, the FDTD method can calculate for particles off the central axis of the LG beam. It is found that when the particles are very small, and the topological charge number of the OAM of a laser is not extremely large, the laser’s OAM has little effect on the scattering phase function. This suggests that Rayleigh theory can be applied directly to calculate the light scattering by atmospheric molecules. The transmission of a laser beam with OAM in a molecular atmosphere is not different from that of a regular Gaussian beam.

Molecular atmosphere