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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

CFD Analysis of Spray Combustion and Radiation in OMV Thrust Chamber

The Variable Thrust Engine (VTE), developed by TRW, for the Orbit Maneuvering Vehicle (OMV) uses a hypergolic propellant combination of Monomethyl Hydrazine (MMH) and Nitrogen Tetroxide (NTO) as fuel and oxidizer, respectively. The propellants are pressure fed into the combustion chamber through a single pintle injection element. The performance of this engine is dependent on the pintle geometry and a number of complex physical phenomena and their mutual interactions. The most important among these are (1) atomization of the liquid jets into fine droplets; (2) the motion of these droplets in the gas field; (3) vaporization of the droplets (4) turbulent mixing of the fuel and oxidizer; and (5) hypergolic reaction between MMH and NTO. Each of the above phenomena by itself poses a considerable challenge to the technical community. In a reactive flow field of the kind occurring inside the VTE, the mutual interactions between these physical processes tend to further complicate the analysis. The objective of this work is to develop a comprehensive mathematical modeling methodology to analyze the flow field within the VTE. Using this model, the effect of flow parameters on various physical processes such as atomization, spray dynamics, combustion, and radiation is studied. This information can then be used to optimize design parameters and thus improve the performance of the engine. The REFLEQS CFD Code is used for solving the fluid dynamic equations. The spray dynamics is modeled using the Eulerian-Lagrangian approach. The discrete ordinate method with 12 ordinate directions is used to predict the radiative heat transfer in the OMV combustion chamber, nozzle, and the heat shield. The hypergolic reaction between MMH and NTO is predicted using an equilibrium chemistry model with 13 species. The results indicate that mixing and combustion is very sensitive to the droplet size. Smaller droplets evaporate faster than bigger droplets, leading to a well mixed zone in the combustion chamber. The radiative heat flux at combustion chamber and nozzle walls are an order of negligible less than the conductive heat flux. Simulations performed with the heat shield show that a negligible amount of fluid is entrained into the heat shield region. However, the heat shield is shown to be effective in protecting the OMV structure surrounding the engine from the radiated heat.

Giridharan, M. G.↗
NASA NTRS1999

A Simple Derivation of the Acoustic Boundary Condition in the Presence of Flow

In modelling the noise propagation in a duct of a ducted fan engine, the authors needed the boundary condition satisfied by the acoustic pressure on a lined duct wall in the presence of flow. The result in the form used by the authors was derived by M. K. Myers who presented a formal derivation of a related result by K. Taylor. A good review of the subject can be found in reference. Here, a brief and simple derivation of the acoustic boundary condition of Myers is given. The main difference in the derivation from that in reference is that the Gaussian co-ordinate system (q(sup 1), q(sup 2), q(sup 3)(q(sup 1), q(sup 2), t)) is used to specify the instantaneous position, i.e., Lagrangian variable, of the point on the mean position of the wall with curvilinear (Gaussian) co-ordinates (q(sup 1), q(sup 2)). Myers uses a locally orthogonal coordinate system which is somewhat less specific than what is used here.

Farassat, F.↗
NASA NTRS2001

Satellite Remote Sensing of Tropical Precipitation and Ice Clouds for GCM Verification

This project, supported by the NASA New Investigator Program, has primarily been funding a graduate student, Darren McKague. Since August 1999 Darren has been working part time at Raytheon, while continuing his PhD research. Darren is planning to finish his thesis work in May 2001, thus some of the work described here is ongoing. The proposed research was to use GOES visible and infrared imager data and SSM/I microwave data to obtain joint distributions of cirrus cloud ice mass and precipitation for a study region in the Eastern Tropical Pacific. These joint distributions of cirrus cloud and rainfall were to be compared to those from the CSU general circulation model to evaluate the cloud microphysical amd cumulus parameterizations in the GCM. Existing algorithms were to be used for the retrieval of cloud ice water path from GOES (Minnis) and rainfall from SSM/I (Wilheit). A theoretical study using radiative transfer models and realistic variations in cloud and precipitation profiles was to be used to estimate the retrieval errors. Due to the unavailability of the GOES satellite cloud retrieval algorithm from Dr. Minnis (a co-PI), there was a change in the approach and emphasis of the project. The new approach was to develop a completely new type of remote sensing algorithm - one to directly retrieve joint probability density functions (pdf's) of cloud properties from multi-dimensional histograms of satellite radiances. The usual approach is to retrieve individual pixels of variables (i.e. cloud optical depth), and then aggregate the information. Only statistical information is actually needed, however, and so a more direct method is desirable. We developed forward radiative transfer models for the SSM/I and GOES channels, originally for testing the retrieval algorithms. The visible and near infrared ice scattering information is obtained from geometric ray tracing of fractal ice crystals (Andreas Macke), while the mid-infrared and microwave scattering is computed with Mie scattering. The radiative transfer is performed with the Spherical Harmonic Discrete Ordinate Method (developed by the PI), and infrared molecular absorption is included with the correlated k-distribution method. The SHDOM radiances have been validated by comparison to version 2 of DISORT (the community "standard" discrete-ordinates radiative transfer model), however we use SHDOM since it is computationally more efficient.

Evans, K. Franklin↗
NASA NTRS2005

Co-Investigator for the Planet B NMS

This is the final report. The effort under this contract consisted mainly with meetings and discussions with our NASA/GSFC and ISAS partners of the neutral mass spectrometer team of the Nozomi mission. The activities were to serve the purpose to prepare and co-ordinate our activities in preparation for the anticipated data analysis and science interpretation of the data after Mars orbit insertion. Given the unfortunate initial delays this effort included a number of visits to ISAS in Tokyo and participation in co-ordination and science workshops. We participated in a paper describing the instrument, which was published. We also worked on certain theoretical calculations in order to evaluate measurement opportunities for the mass spectrometer at Mars. The major aspect of this effort was a series of calculations on the feasibility of measuring hot atoms in the upper atmosphere. We calculated the densities of hot oxygen and carbon. Although this work established that their abundance is probably below the sensitivity of the mass spectrometer, it was of scientific importance and the results were presented at scientific meetings and published in the open literature.

Nagy, Andrew↗
NASA NTRS2011

Analysis of the Radiative Transfer Equation with Highly Asymmetric Phase Function

This paper considers a scalar radiative transfer problem with high scattering anisotropy, Two computational methods are presented based on decomposition of the diffuse light field into a regular and anisotropic part. The first algorithm (DOMAS) singles out the anisotropic radiance in the forward scattering peak using the Small-Angle Modification of RTE. The second algorithm (DOM2+) separates the single scattering radiance as an anisotropic part, which largely defines the fine detail of the total radiance in the backscattering directions. In both cases, the anisotropic part is represented analytically. With anisotropy subtraction, the regular part of the signal. which requires a numerical solution, is essentially smoothed as a function of angles. Further, the transport equation is obtained for the regular part that contains an additional source function from the anisotropic part of the signal. This equation is solved with the discrete ordinates method. A conducted numerical analysis of this work showed that algorithm DOMAS has a strong advantage as compared to the standard discrete ordinates method for simulation of the radiance transmission, and DOM2 + is the best of the three for the reflection computations. Both algorithms offer at least a factor of three acceleration of convergence of the azimuthal series for highly anisotropic phase functions.

Korkin, Sergey V.↗
NASA NTRS2012

Computing Radiative Transfer in a 3D Medium

A package of software computes the time-dependent propagation of a narrow laser beam in an arbitrary three- dimensional (3D) medium with absorption and scattering, using the transient-discrete-ordinates method and a direct integration method. Unlike prior software that utilizes a Monte Carlo method, this software enables simulation at very small signal-to-noise ratios. The ability to simulate propagation of a narrow laser beam in a 3D medium is an improvement over other discrete-ordinate software. Unlike other direct-integration software, this software is not limited to simulation of propagation of thermal radiation with broad angular spread in three dimensions or of a laser pulse with narrow angular spread in two dimensions. Uses for this software include (1) computing scattering of a pulsed laser beam on a material having given elastic scattering and absorption profiles, and (2) evaluating concepts for laser-based instruments for sensing oceanic turbulence and related measurements of oceanic mixed-layer depths. With suitable augmentation, this software could be used to compute radiative transfer in ultrasound imaging in biological tissues, radiative transfer in the upper Earth crust for oil exploration, and propagation of laser pulses in telecommunication applications.

Von Allmen, Paul↗
NASA NTRS2014

Pre-Flight Advanced Clothing Study

All human space missions require significant logistical mass and volume that will become an excessive burden for long duration missions beyond low Earth orbit. The current International Space Station (ISS) crew wardrobe has already evolved not only to reduce some of the logistical burden but also to address crew preference. The present study was undertaken to find ways further to reduce this logistical burden while examining human response to different types of clothes. The primary objective of the study is to measure how long people can wear the same exercise garment, depending on the type of fabric and the presence of antimicrobial treatment. The secondary objective is to assess the reasons for length of wear from perceptions of clothing characteristics, including nine ordinal scales. Cardiovascular exercise was chosen as the activity in this experiment for its profuse sweating effect and because it is considered a more severe treatment applied to the clothes than every-day usage. Study garments were exercise T-shirts and shorts purchased from various vendors. Fabric construction, fabric composition, and finishing treatment were defined as the key variables. A web-based questionnaire was used for self-reported data collection. The study was divided in three balanced experiments: a cotton-polyester-wool (CPW) T-shirts study with 61 participants, a polyester-modacrylic-polyester/cocona (PMC) T-shirts study with 40 participants, and a shorts study with 70 participants. In the CPW study, the T-shirts were made of 100% cotton, or of 100% polyester or of 100% wool, and categorized into open and tight knit constructions. In the PMC study, the T-shirts were made of 100% polyester, or of 82% modacrylic, or of 95% polyester with 5% cocona fiber, without construction distinction. The shorts were made either of 100% cotton or of 100% polyester, and were knitted or woven. Some garments were treated with Bio-Protect 500 antimicrobial finish according the experimental design. The data collected from the questionnaire included garment identification, level of exertion, duration of exercise session, number of exercise sessions, an ordinal preference scale for nine sensory elements, and reason for retiring a used garment. From the analysis of the combined CPW and PMC shirt studies, there are statistically significant differences among the mean lifetimes of various types of shirts. The exercise shirts with the longest mean lifetimes are untreated wool (600 minutes), treated cotton (526 minutes), and untreated modacrylic (515 minutes). From the combined CPW and PMC shirt studies, the most preferred material was untreated open-knit wool, which is one of the two materials that jointly were worn the longest, untreated wool, both open-knit and tight-knit. For the CP shorts study, there were no statistically significant differences in mean lifetimes of the exercise shorts at the 5% significance level due to the treatment combinations. There was therefore no justification to examine differences among levels of main effects or interactions. The preference for shorts was in this order: untreated woven polyester, untreated knitted polyester, untreated woven cotton, and treated knitted cotton.The nine preference scales were tabulated to determine the preference responses at the end of those exercise periods which were prior to the period when a garment was retired and a new garment was started. The assumption is that an unfavorable assessment of a garment leads to its retirement. The scent scale response was predominantly unfavorable at the end of the exercise period immediately prior to the exercise period when a new garment was started. Additional work on wool clothing is needed to assess if this material can be part of a crew wardrobe for long duration missions. The results of this study informed the choice of fabrics for an upcoming ISS intra-vehicular clothing study.

Orndoff, Evelyne↗
NASA NTRS2018

Modified Geometric Truncation of the Scattering Phase Function

Phase function of light scattering on large atmospheric particles has very strong peak in forward direction constituting a challenge for accurate numerical calculations of radiance required in remote sensing problems. Scaling transformation replaces original phase function with a sum of the delta function and a new regular smooth phase function. Geometric truncation is one of the ways to construct such a smooth function. The replacement phase function coincides with the original one outside the forward cone and preserves the asymmetry parameter. It has discontinuity at the cone. Another simple functional form of the replacement phase function within the cone is suggested. It enables continuity and allows for a number of modifications. Three of them are considered in this study: preserving asymmetry parameter, providing continuity of the 1st derivative of the phase function, and preserving mean scattering angle. Yet another problem addressed in this study is objective selection of the width of the forward cone. That angle affects truncation fraction and values of the phase function within the cone. A heuristic approach providing unambiguous criterion of selection of the truncation angle is proposed. The approach has easy numerical implementation. Suggested modifications were tested on cloud phase function using discrete ordinates and Monte Carlo methods. It was shown that the modifications provide better accuracy of the radiance computation compare to the original geometric truncation with discrete ordinates while continuous derivative approach provides significant gain in computer time with Monte Carlo simulations.

Alexander Radkevich↗
NASA NTRS2020

Variation of Florida scrub vegetation along gradients of soil pH and landscape age on a barrier island complex

Florida scrub is a fire-maintained shrub vegetation of well-drained, sandy soils associated with ridge systems that originated as coastal dunes. It is unique to Florida and supports many rare plants and animals. Between 1992 and 2005, we sampled 30 stands of long-unburned scrub with 196 line-intercept transects (15 m length) across the Merritt Island-Cape Canaveral barrier island complex where dune ridges range from relatively recent to > 30,000 years old with a range of soil leaching and reaction. These data allow us to determine the relationships of landscape age and soil reaction on community composition. We recorded community composition in < 0.5 m and > 0.5 m height strata. We determined mapped soil type for all transects; for 151 transects we determined soil pH of the 0–15 cm and 15–30 cm layers. Hierarchical cluster analysis of stands (N=30) and transects (N=196) using 41 species (of 53) present in > 2 transects gave two groups: coastal scrub with Quercus virginiana (shrub form) and Serenoa repens as dominant species on the most alkaline soils, and oak-saw palmetto scrub with Quercus chapmanii, Quercus geminata, Quercus myrtifolia, and S. repens on the strongly to somewhat acidic soils. Direct gradient analysis indicated that dominant species except S. repens varied from acidic to alkaline soils. Indicator species analysis identified seven species that indicated acidic soils and five that indicated alkaline soils (P < 0.01). Nonmetric multidimensional scaling (NMS) ordination at the stand level separated the two groups along the first axis, and NMS ordination of the transect data showed the gradient of coastal to oak-saw palmetto scrub. Position of transects on the first axis was related to soil pH class, and to measured pH of the 0–15 cm and 15–30 cm layers. Soils show a progressive leaching of shell material from the surface horizons followed by podsolization; this process takes > 4,000 years. Our results indicate substantial differences between the community composition of scrub vegetation on recent alkaline soils compared to leached acidic soils.

Barrier island↗
NASA NTRS2022

Effects of Repeated Fire on Florida Oak-Saw Palmetto Scrub

Background: The dominant species of Florida oak-saw palmetto scrub sprout after burning from belowground rhizomes or fire-resistant aboveground buds with rapid reestablishment of cover. Responses to single fires are well documented; however, responses to repeated fires may differ. Fire return intervals, differences among sites, and species may influence responses. We used transect data from four sites on Kennedy Space Center/Merritt Island National Wildlife Refuge to test whether growth differed through repeated fires. Two sites burned five times in 36 years, one site burned five times in 25 years, and one burned four times in 18 years. We used linear mixed models that account for repeated measures to determine if the number of fires affected height, total cover ≥ 0.5 m and < 0.5 m, bare ground, and cover of the dominant oak (Quercus) ≥ 0.5 m and of saw palmetto (Serenoa repens) ≥ 0.5 m. We compared community composition through repeated fires using nonmetric multidimensional scaling ordination. Results: Height, total cover ≥ 0.5 m, and cover of the dominant oak ≥ 0.5 m and of saw palmetto ≥ 0.5 m increased with time since burn; total cover < 0.5 m and bare ground decreased. A quadratic term in the growth model was significant except for total cover < 0.5 m. There were site differences for all variables except bare ground. The number of fires decreased height, total cover ≥ 0.5 m, and cover of the dominant oak ≥ 0.5 and increased total cover < 0.5 m and bare ground but had no effect on cover of Serenoa repens ≥ 0.5 m. Community changes after repeated fires were similar in nonmetric multidimensional ordinations with time since burn correlated to the first or second axis. Conclusions: Scrub recovered from repeated fires at a range of intervals and seasons, but short return intervals reduced growth with responses differing among species.

Florida↗
NASA NTRSDate not supplied

Multiclass Flight Anomaly Detection Using Sensor Fusion Based on Dempster-Shafer Theory

As aviation systems in commercial operations continue to grow in complexity, the anomalies exhibited by these systems become more elaborate and difficult to detect. To address the challenge of detecting these complex anomalies, deep learning models have been used extensively in aviation anomaly detection studies, at the expense of end-user interpretability. Aiming to maintain the same level of interpretability as traditional threshold-exceedance methods, we continue our development of prediction models using ordinal patterns and their distributions throughout the flight. Specifically, this study extends our work into multiclass anomaly detection using sensor fusion based on Dempster-Shafer theory (DST), a second-order probability theory used to combine information from different sources of evidence. Our approach uses DST to reduce the uncertainty in the class predictions of an ensemble of classifiers. These classifiers rely on the similarity between flight data and class templates to make a prediction of the state of the aircraft. Our approach aims to take advantage of simple models trained on interpretable features (ordinal patterns) to correctly predict an anomaly and identify the flight dynamics linked to the anomaly. Our results show an improvement when using DST-based sensor fusion over simple majority voting. Additionally, our results provide insight into aircraft states linked to rare high-risk anomalies.

Risk detection↗
NASA NTRSDate not supplied

Multiclass Flight Anomaly Detection Using Sensor Fusion Based on Dempster-Shafer Theory

As aviation systems in commercial operations continue to grow in complexity, the anomalies exhibited by these systems become more elaborate and difficult to detect. To address the challenge of detecting these complex anomalies, deep learning models have been used extensively in aviation anomaly detection studies, at the expense of end-user interpretability. Aiming to maintain the same level of interpretability as traditional threshold-exceedance methods, we continue our development of prediction models using ordinal patterns and their distributions throughout the flight. Specifically, this study extends our work into multiclass anomaly detection using sensor fusion based on Dempster-Shafer theory (DST), a second-order probability theory used to combine information from different sources of evidence. Our approach uses DST toreduce the uncertainty in the class predictions of an ensemble of classifiers. These classifiers rely on the similarity between flight data and class templates to make a prediction of the state of the aircraft. Our approach aims to take advantage of simple models trained on interpretable features (ordinal patterns) to correctly predict an anomaly and identify the flight dynamics linked to the anomaly. Our results show an improvement when using DST-based sensor fusion over simple majority voting. Additionally, our results provide insight into aircraft states linked to rare high-risk anomalies.

Risk detection↗
NASA NTRSDate not supplied

Data Simulation Using VLIDORT and PCRTM and its Use for Radiometric Calibration of Hyperspectral UV-NIR-SWIR Sensors

Using the vector linearized discrete ordinate radiative transfer model (VLIDORT), a multiple-scattering multi-layer discrete ordinate scattering codes, coupled with a fast principal component (PC) radiative transfer model (PCRTM), we can simulate the radiation fields for hyperspectral UV-NIR-SWIR sensors from 250nm to 2500nm with a very high speed. Since the accurate gas absorptions, molecules and aerosol/cloud particle scatterings, and the surface reflectance have been considered in these simulations, these model data can be used for satellite or airborne sensor design, characterization, or end-to-end system level uncertainty assessment. Comparison of the modelled data with measured results has been a general practice for operational satellite sensor calibrations, such as the Ozone Mapping and Profiler Suite (OMPS) onboard on SNPP and NOAA-20. This presentation will give more details of this simulation system and models. Some examples of the generation of simulations data for CLARREO PathFinder (CPF) and the Surface Biology and Geology (SBG), as well as some examples to use these data for CPF and OMPS radiometric calibration will be presented.

Xiaozhen Xiong↗
DOE OSTI2020

Massively parallel transport sweeps on meshes with cyclic dependencies

When solving the first-order form of the linear Boltzmann equation, a common misconception is that the matrix-free computational method of “sweeping the mesh”, used in conjunction with the Discrete Ordinates method, is too complex or does not scale well enough to be implemented in modern high performance computing codes. This has led to considerable efforts in the development of matrix-based methods that are computationally expensive and is partly driven by the requirements placed on modern spatial discretizations. In particular, modern transport codes are required to support higher order elements, a concept that invariably adds a lot of complexity to sweeps because of the introduction of cyclic dependencies with curved mesh cells. In this article we will present a comprehensive implementation of sweeping, to a piecewise-linear DFEM spatial discretization with particular focus on handling cyclic dependencies and possible extensions to higher order spatial discretizations. We find that these methods are implemented in a new C++ simulation framework called Chi-Tech (). We present some typical simulation results with some performance aspects that one can expect during real world simulations, we also present a scaling study to >100k processes where Chi-Tech maintains greater than 80% efficiency solving a total of 87.7 trillion angular flux unknowns for a 116 group simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Predicting large-scale pool fire dynamics using an unsteady flamelet- and large-eddy simulation-based model suite

A low-Mach, unstructured, large-eddy-simulation-based, unsteady flamelet approach with a generalized heat loss combustion methodology (including soot generation and consumption mechanisms) is deployed to support a large-scale, quiescent, 5-m JP-8 pool fire validation study. The quiescent pool fire validation study deploys solution sensitivity procedures, i.e., the effect of mesh and time step refinement on capturing key fire dynamics such as fingering and puffing, as mesh resolutions approach O(1) cm. A novel design-order, discrete-ordinate-method discretization methodology is established by use of an analytical thermal/participating media radiation solution on both low-order hexahedral and tetrahedral mesh topologies in addition to quadratic hexahedral elements. Here, the coupling between heat losses and the flamelet thermochemical state is achieved by augmenting the unsteady flamelet equation set with a heat loss source term. Soot and radiation source terms are determined using flamelet approaches for the full range of heat losses experienced in fire applications including radiative extinction. The proposed modeling and simulation paradigm are validated using pool surface radiative heat flux, maximum centerline temperature location, and puffing frequency data, all of which are predicted within 10% accuracy. Simulations demonstrate that under-resolved meshes predict an overly conservative radiative heat flux magnitude with improved comparisons as compared to a previously deployed hybrid Reynolds-averaged Navier–Stokes/eddy dissipation concept-based methodology.

42 ENGINEERING↗
DOE OSTI2021

Solution Irregularity Remediation for Spatial Discretization Error Estimation for S N Transport Solutions

The discrete ordinates linear Boltzmann transport equation is typically solved in its spatially discretized form, incurring spatial discretization error. Quantification of this error for purposes such as adaptive mesh refinement or error analysis requires an a posteriori estimator, which utilizes the numerical solution to the spatially discretized equation to compute an estimate. Because the quality of the numerical solution informs the error estimate, irregularities, present in the true solution for any realistic problem configuration, tend to cause the largest deviation in the error estimate vis-a-vis the true error. In this paper, an analytical partial singular characteristic tracking (pSCT) procedure for reducing the estimator’s error is implemented within our novel residual source estimator for a zeroth-order discontinuous Galerkin scheme, at the additional cost of a single inner iteration. Here, a metric-based evaluation of the pSCT scheme versus the standard residual source estimator is performed over the parameter range of a Method of Manufactured Solutions test suite. The pSCT scheme generates near-ideal accuracy in the estimate in problems where the dominant source of the estimator’s error is the solution irregularity, namely, problems where the true solution is discontinuous and problems where the true solution’s first derivative is discontinuous and the scattering ratio is low. In problems where the scattering ratio is high and the true solution is discontinuous in the first derivative, the error in the scattering source, which is not converged by the pSCT scheme, is greater than the error incurred due to the irregularity. Ultimately, a pSCT scheme is judged to be useful for error estimation in problems where the computational cost of the scheme is justified. In the presence of many irregularities, such a scheme may be intractable for general use, but in benchmarks, as an analytical tool, or in problems that have nondissipative discontinuities, the scheme may prove invaluable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Solar and Battery Storage Permitting and Siting Requirements - Solar Prize Round 7 (CRADA Final Report)

The purpose of this project is to identify local zoning ordinances, state permitting requirements, federal regulatory bottlenecks throughout the development process, and the potential to use Large Language Models (LLM) and aggregate permitting and interconnection data for commercial and industrial (C&I), community, and utility-scale solar photovoltaic (PV) and battery storage projects.

14 SOLAR ENERGY↗
NASA NTRS2014

APC: A New Code for Atmospheric Polarization Computations

A new polarized radiative transfer code Atmospheric Polarization Computations (APC) is described. The code is based on separation of the diffuse light field into anisotropic and smooth (regular) parts. The anisotropic part is computed analytically. The smooth regular part is computed numerically using the discrete ordinates method. Vertical stratification of the atmosphere, common types of bidirectional surface reflection and scattering by spherical particles or spheroids are included. A particular consideration is given to computation of the bidirectional polarization distribution function (BPDF) of the waved ocean surface.

surface reflection↗