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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 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A simple bidirectional-reflectance model applied to a tallgrass canopy

The present bidirectional reflectance model is used to simulate spectral reflectance direction-changes in a tallgrass canopy; comparisons with field measurements show generally good agreement. An examination of the effects of 'hot spot' and soil-reflection inhomogeneous canopy characteristics indicates that both modeled and observed reflectances are strongly backscattered in the red band, but there is a more symmetric back/forward-scattering distribution in the near-IR. Modeled simulations for three leaf-angle distributions show that hemispherical reflectance errors could be reduced at an optimal solar zenith angle having the same magnitude for the three leaf-angle distributions, but decreasing with increasing canopy leaf-area index.

Gao, W.↗
NASA NTRS1997

Radiometric Calibration of the Earth Observing System's Imaging Sensors

The work on the grant was mainly directed towards developing new, accurate, redundant methods for the in-flight, absolute radiometric calibration of satellite multispectral imaging systems and refining the accuracy of methods already in use. Initially the work was in preparation for the calibration of MODIS and HIRIS (before the development of that sensor was canceled), with the realization it would be applicable to most imaging multi- or hyper-spectral sensors provided their spatial or spectral resolutions were not too coarse. The work on the grant involved three different ground-based, in-flight calibration methods reflectance-based radiance-based and diffuse-to-global irradiance ratio used with the reflectance-based method. This continuing research had the dual advantage of: (1) developing several independent methods to create the redundancy that is essential for the identification and hopefully the elimination of systematic errors; and (2) refining the measurement techniques and algorithms that can be used not only for improving calibration accuracy but also for the reverse process of retrieving ground reflectances from calibrated remote-sensing data. The grant also provided the support necessary for us to embark on other projects such as the ratioing radiometer approach to on-board calibration (this has been further developed by SBRS as the 'solar diffuser stability monitor' and is incorporated into the most important on-board calibration system for MODIS)- another example of the work, which was a spin-off from the grant funding, was a study of solar diffuser materials. Journal citations, titles and abstracts of publications authored by faculty, staff, and students are also attached.

Slater, Philip N.↗
NASA NTRS2001

Columnar Aerosol Single-Scattering Albedo and Phase Function Retrieved from Sky Radiance Over the Ocean: Measurements of African Dust

The single-scattering albedo and phase function of African mineral dust are retrieved from ground-based measurements of sky radiance collected in the Florida Keys. The retrieval algorithm employs the radiative transfer equation to solve by iteration for these two properties which best reproduce the observed sky radiance using an assumed aerosol vertical structure and measured aerosol optical depth. Thus, no assumptions regarding particle size, shape, or composition are required. The single-scattering albedo, presented at fourteen wavelengths between 380 and 870 nm, displays a spectral shape expected of iron-bearing minerals but is much higher than current dust models allow. This indicates the absorption of light by mineral dust is significantly overestimated in climate studies. Uncertainty in the retrieved albedo is less than 0.02 due to the small uncertainty in the solar-reflectance-based calibration (12.2%) method employed. The phase function retrieved at 860 nm is very robust under simulations of expected experimental errors, indicating retrieved phase functions at this wavelength may be confidently used to describe aerosol scattering characteristics. The phase function retrieved at 443 nm is very sensitive to expected experimental errors and should not be used to describe aerosol scattering. Radiative forcing by aerosol is the greatest source of uncertainty in current climate models. These results will help reduce uncertainty in the absorption of light by mineral dust. Assessment of the radiative impact of aerosol species is a key component to NASA's Earth System Enterprise.

Cattrall, Christopher↗
NASA NTRS1992

The onset of galactic winds in early-type galaxies

We completed the spectral analysis of 31 early-type galaxies to investigate whether their x-ray emission was predominantly due to thermal bremsstrahlung from a hot gaseous corona or emission from discrete, galactic sources such as x-ray binaries. If a corona dominates the x-ray emission, its spectra is expected to be relatively cool (0.5 - 1 keV) compared to the harder emission associated with x-ray binaries in our galaxy, the Magellanic Clouds and M31. While it is generally accepted that the x-ray emission in luminous E and S0 galaxies arises from hot coronae, the status of hot gas in lower luminosity (and hence lower mass) galaxies is less clear. Calculations show that, for a given supernova rate, a critical galaxy luminosity (mass) exists below which the gas cannot be gravitationally confined and a galactic wind is predicted to be effective in expelling gas from the galaxy. Since significant mass (a dark halo) is required to hold a hot, gaseous corona around a galaxy, we expect that the faintest, smallest galaxies will not have a hot corona, but their x-ray emission will be dominated by galactic sources or by an active galactic nuclei. In the sample we tested which spanned the absolute magnitude range from -21.5 to -19.5, we found that except for two galaxies whose x-ray emission was dominated by an active nucleus, that the others were consistent with emission from hot gas. We also found that there is a correlation between gas temperature and galaxy magnitude (mass), such that the brighter, more luminous galaxies have hotter gas temperatures. Thus even at relatively faint magnitudes, the dominant emission from early-type galaxies appears to be hot gas. We also carried out an investigation of the x-ray surface brightness distribution of the x-ray emission for about 100 early type galaxies to determine whether the x-ray emission from galaxies are extended. Extended x-ray emission is expected if the emission is due to a hot gaseous corona. We determined the ratio of the source counts in two annuli (0-80 arc seconds and 80-160 arc seconds) for each galaxy and analyzed these ratios using a maximum likelihood estimator to determine the errors on the ratios. Even for weak sources, this ratio provides a sensitive test for source extent. We then compared these ratios to a sample of quasars (all unresolved sources) and have determined which galaxies are extended and which are consistent with point sources. A first paper including the Einstein x-ray fluxes for 147 early-type galaxies has been published in the Astrophysical Journal Supplement Series (with Roberts, Hogg, Bregman, Forman entitled 'Interstellar Matter in Early-Type Galaxies'). A second paper will describe the spectral and extent analysis carried out for this galaxy sample. These results also have been presented at scientific conferences and in colloquia.

Jones, Christine↗
NASA NTRS1986

Thermal infrared opacity of the Mars atmosphere

An analytical technique is presented for the deriving Mars atmosphere opacity from data furnished by the IR Thermal Mapper (IRTM) instruments on the Viking landers. Each IRTM features four telescopes for viewing Mars in six spectral bands and seven spatial fields of view. The present study focuses on 20 microns measurements of the thermal inertia, 0.3-3.0 microns data for the surface albedo, and, finally, the 7, 9, and 15 microns data for the actual opacity derivations. The model takes into account the atmospheric temperature profile, scattering by dust, the surface emissivity and the variation of the surface/atmosphere temperature discontinuity. Analyses are carried out of the possible error factors and the model is used to generate opacity histories for the two Viking Lander sites. The results, when compared with other astronomical data, indicate that the method is sufficiently accurate to use opacity data to analyze the processes of storm genesis and to study local storms.

Martin, T. Z.↗
NASA NTRS1986

Statistical characterization of sea surface geometry for a wave slope field discontinuous in the mean square

Statistics of two-dimensional wave groups, of steep wave events, and of a cascade pattern manifested in the surface geometry in a developed sea state are derived. A systematic view is presented of the spectral moment problem, highlighting its physical meaning and showing its relationship with the theory of random fields. A solution of this problem is suggested that is appropriate to the case of wind-generated surface waves. The solution method treats the surface elevation field as specified on a spatial (temporal) running grid, developing an averaging procedure which employs the Taylor microscale as the mesh size. The technique is illustrated by first exposing errors in direct calculations of the effective surface impedance for a coherently reflected L-band radio wave. The technique is then used to study wave groups and steep waves for a Gaussian, two-dimensional, time-varying surface. Finally, the theory is applied to estimate breaking wave statistics,

Glazman, R. E.↗
NASA NTRS2014

Deciphering the Precision of Stereo IKONOS Canopy Height Models for U.S. Forests with G-LiHT Airborne LiDAR

Few studies have evaluated the precision of IKONOS stereo data for measuring forest canopy height. The high cost of airborne light detection and ranging (LiDAR) data collection for large area studies and the present lack of a spaceborne instrument lead to the need to explore other low cost options. The US Government currently has access to a large archive of commercial high-resolution imagery, which could be quite valuable to forest structure studies. At 1 m resolution, we here compared canopy height models (CHMs) and height data derived from Goddard's airborne LiDAR Hyper-spectral and Thermal Imager (G-LiHT) with three types of IKONOS stereo derived digital surface models (DSMs) that estimate CHMs by subtracting National Elevation Data (NED) digital terrain models (DTMs). We found the following in three different forested regions of the US after excluding heterogeneous and disturbed forest samples: (1) G-LiHT DTMs were highly correlated with NED DTMs with R (sup 2) greater than 0.98 and root mean square errors (RMSEs) less than 2.96 m; (2) when using one visually identifiable ground control point (GCP) from NED, G-LiHT DSMs and IKONOS DSMs had R (sup 2) greater than 0.84 and RMSEs of 2.7 to 4.1 m; and (3) one GCP CHMs for two study sites had R (sup 2) greater than 0.7 and RMSEs of 2.6 to 3 m where data were collected less than four years apart. Our results suggest that IKONOS stereo data are a useful LiDAR alternative where high-quality DTMs are available.

IKONOS↗
NASA NTRS2015

Intensity Conserving Spectral Fitting

The detailed shapes of spectral line profiles provide valuable information about the emitting plasma, especially when the plasma contains an unresolved mixture of velocities, temperatures, and densities. As a result of finite spectral resolution, the intensity measured by a spectrometer is the average intensity across a wavelength bin of non-zero size. It is assigned to the wavelength position at the center of the bin. However, the actual intensity at that discrete position will be different if the profile is curved, as it invariably is. Standard fitting routines (spline, Gaussian, etc.) do not account for this difference, and this can result in significant errors when making sensitive measurements. Detection of asymmetries in solar coronal emission lines is one example. Removal of line blends is another. We have developed an iterative procedure that corrects for this effect. It can be used with any fitting function, but we employ a cubic spline in a new analysis routine called Intensity Conserving Spline Interpolation (ICSI). As the name implies, it conserves the observed intensity within each wavelength bin, which ordinary fits do not. Given the rapid convergence, speed of computation, and ease of use, we suggest that ICSI be made a standard component of the processing pipeline for spectroscopic data.

Klimchuk, J. A.↗
NASA NTRS2019

Exploring the Utility of Machine Learning-Based Passive Microwave Brightness Temperature Data Assimilation over Terrestrial Snow in High Mountain Asia

This study explores the use of a support vector machine (SVM) as the observation operator within a passive microwave brightness temperature data assimilation framework (herein SVM-DA) to enhance the characterization of snow water equivalent (SWE) over High Mountain Asia (HMA). A series of synthetic twin experiments were conducted with the NASA Land Information System (LIS) at a number of locations across HMA. Overall, the SVM-DA framework is effective at improving SWE estimates (~70% reduction in RMSE relative to the Open Loop) for SWE depths less than 200 mm during dry snowpack conditions. The SVM-DA framework also improves SWE estimates in deep, wet snow (~45% reduction in RMSE) when snow liquid water is well estimated by the land surface model, but can lead to model degradation when snow liquid water estimates diverge from values used during SVM training. In particular, two key challenges of using the SVM-DA framework were observed over deep, wet snowpacks. First, variations in snow liquid water content dominate the brightness temperature spectral difference (TB) signal associated with emission from a wet snowpack, which can lead to abrupt changes in SWE during the analysis update. Second, the ensemble of SVM-based predictions can collapse (i.e., yield a near-zero standard deviation across the ensemble) when prior estimates of snow are outside the range of snow inputs used during the SVM training procedure. Such a scenario can lead to the presence of spurious error correlations between SWE and TB, and as a consequence, can result in degraded SWE estimates from the analysis update. These degraded analysis updates can be largely mitigated by applying rule-based approaches. For example, restricting the SWE update when the standard deviation of the predicted TB is greater than 0.05 K helps prevent the occurrence of filter divergence. Similarly, adding a thin layer (i.e., 5 mm) of SWE when the synthetic TB is larger than 5 K can improve SVM-DA performance in the presence of a precipitation dry bias. The study demonstrates that a carefully constructed SVM-DA framework cognizant of the inherent limitations of passive microwave-based SWE estimation holds promise for snow mass data assimilation.

Kwon, Yonghwan↗
NASA NTRSDate not supplied

MISR Level 1B1 Local Mode Radiance Data (MIB1LM_V1)

The results of two types of processing are included in this product. First, the Radiance Scaling operation converts the camera's digital number output to a measure of energy incident on the front optical surface. The measurement is expressed in units called radiance (energy per unit area, wavelength, and solid angle) as defined by the International Standard (SI). Second, Radiance Conditioning modifies the radiances to remove instrument-dependent effects. Specifically, image sharpening is applied, and focal-plane scattering is removed. Additionally, all radiances are adjusted to remove slight spectral sensitivity differences among the 1504 detector elements of each spectral band and each camera. In addition to the Level 1B1 radiometric product for MISR's Global Mode imagery, there is a separate Level 1B1 product for each high-resolution Local Mode scene. The Radiometric Product contains spectral radiances for all MISR channels (four spectral bands and nine cameras). Each radiance value represents the incident radiance averaged over the sensor's total band response. Processing includes both radiance scaling and conditioning steps. Radiance scaling converts the Level 1A data from digital counts to radiances using coefficients derived in combination with the On-Board Calibrator (OBC) and vicarious calibrations. The OBC contains Spectralon calibration panels which are deployed monthly and reflect sunlight into the cameras. The OBC detector standards then measure this reflected light to provide the calibration. Vicarious field campaigns are conducted less frequently but provide an independent methodology useful for reducing systematic errors. Radiance conditioning removes undesirable instrument effects. Image enhancement is provided by deconvolving the scene with the sensor's point-spread-function. Additionally, in-band scaling adjusts the reported radiances to correspond to a nominal band response profile. This frees the Level 2 software from the need to correct for detector element non-uniformities. No out-of-band correction is done for this product, nor are the data geometrically corrected or resampled at this point. In summary, the Level 1B1 Product contains the Data Numbers (DNs) radiometrically-scaled to radiances with no geometric resampling. [Location=GLOBAL] [Temporal_Coverage: Start_Date=2000-02-24; Stop_Date=] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=275 m for red band only; Longitude_Resolution=275 m for red band only; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=about 15 orbits/day].

NEAR IR IMAGERY↗
DOE OSTI2019

Multi-channel low-cost light spectrum measurement using a multilayer perceptron

Light is one of the most important elements for residential and work spaces, which affects visual performance, comfort, productivity and well-being. The measures that quantify the characteristics of a light source are derived directly from the spectral power distribution (SPD). In addition the SPD is an important factor influencing the quality of a light source. However, measuring light source spectrum with traditional spectrometers is expensive, difficult to adapt to normal spaces, and hard to integrate with other systems. To address these challenges, a low-cost spectrometer was developed using an artificial neural network, with a resolution of 5 nm in the visible spectrum. The reconstructed SPD has an error lower than 2% and allows the derivation of measurements to characterize the colour quality of light sources. Additionally, the device has wireless communication (Bluetooth and Wi-Fi) in real-time, which allows integration into lighting control applications and other Internet of things (IoT) applications.

Botero-Valencia, Juan Sebastián↗
DOE OSTI2022

A framework for feasibility-level validation of high-resolution wave hindcast models

The value of long-term wave hindcasts for investigating wave climates, wave energy resources, and extreme wave conditions has motivated research developing, calibrating and validating wave hindcast models. Past hindcast model validation studies examined the accuracy in modeling bulk wave parameters of overall sea states without considering the dependency of the model's skill within different sea states. In the present study, a framework for wave hindcast model validation is developed by examining the model accuracy for the most frequently occurring sea states, sea states contributing the most energy to total wave power, sea states associated with hurricane events, and those with the largest model error. Here, validations using bulk wave parameters and frequency-directional spectra at these key sea states and extreme wave conditions based on univariate and bivariate-contour methods provide insights to improve model accuracy, identifying the model's strong and weak points, and pathways for improvement, e.g., modeling wave-current interactions and adjusting wind data. This study adds to a growing body of research demonstrating that a carefully calibrated and verified spectral wave hindcast model can be used to estimate key wave energy parameters over a wide range of wave energy climates, as well as their spatial, temporal, frequency, directional, and probabilistic distributions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

X-ray continuum spectroscopy of inertial confinement fusion implosions at the National Ignition Facility

A methodology for measuring x-ray continuum spectra of inertial confinement fusion (ICF) implosions is described. The method relies on the use of ConSpec, a high-throughput spectrometer using a highly annealed pyrolytic graphite crystal , which measures the spectra in the ≃20–30 keV range. Due to its conical shape, the crystal is sagittally focusing a Bragg-reflected x-ray spectrum into a line, which enhances the recorded x-ray emission signal above the high neutron-induced background accompanying ICF implosions at the National Ignition Facility. To improve the overall measurement accuracy, the sensitivity of the spectrometer measured in an off-line x-ray laboratory setting was revised. The error analysis was expanded to include the accuracy of the off-line measurements, the effect of the neutron-induced background, as well as the influence of possible errors in alignment of the instrument to the ICF target. Here we demonstrate how the improved methodology is applied in the analysis of ConSpec data with examples of a relatively low-neutron-yield implosion using a tritium–hydrogen–deuterium mix as a fuel and a high-yield deuterium–tritium (DT) implosion producing high level of the background. In both cases, the shape of the measured spectrum agrees with the exponentially decaying spectral shape of bremsstrahlung emission to within ±10%. In the case of the high-yield DT experiment, non-monotonic deviations slightly exceeding the measurement uncertainties are observed and discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Classical and quantum computing of shear viscosity for ( 2 + 1 ) D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for ( 2 + 1 )-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density η s is consistent with a well-known holographic result 1 4 π at several temperatures on a 4 × 4 honeycomb lattice with the local electric representation truncated at j max = 1 2 . We also find the ratio of the spectral function and frequency ρ x y ( ω ) ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond j max = 1 2 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including j max truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Challenge Problem 1: Preliminary Model Development and Assessment of Flexible Heat Transfer Modeling Approaches

This report presents the modeling progress of a university consortium studying flexible modeling for turbulent heat transfer. In the context of advanced nuclear reactor design, where challenges include non-unity Prandtl fluids, free and mixed convection, and transitional flow, computational fluid dynamics methods are underutilized due to low confidence in modeling approaches and high computational cost. This report evaluates the performance of engineering CFD models in diabatic, buoyant turbulent flow. It finds that all turbulence models including several variants of the k-ε and k-ω models struggle to predict accurate turbulent momentum and heat transfer in such flows. The Nusselt numbers have been compared between the models and the DNS data, where calculations have been performed for each case and trends have shown a good agreement between DNS estimated Nusselt numbers and available correlations as well as experimental data. A novel DNS correlation for high Pr cases as they are transitioning from mixed convection to natural convection has been proposed. While Nusselt number errors relative to DNS range from 20% to 50%, the models capture similar trends to DNS with respect to Nusselt suppression and amplification under varying levels of buoyancy effect. This report also highlights model form error as a significant contributor to CFD predictions and proposes a framework for quantifying model error and improving confidence in CFD calculations. To improve the predictive capability of engineering CFD models, data-driven approaches for turbulence models are investigated. Theoretical frameworks based on the invariant tensor / vector basis neural networks for prediction of Reynolds stresses and turbulent heat fluxes are employed. The models are developed using direct numerical simulations data for forced convection flows of different fluids in vertical planar channel domain. The framework is implemented in spectral element solvers Nek5000 / nekRS and has shown a potential for future development and consideration of mixed convection flows.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Understanding Growth Dynamics and Yield Prediction of Sorghum Using High Temporal Resolution UAV Imagery Time Series and Machine Learning

Unmanned aerial vehicles (UAV) carrying multispectral cameras are increasingly being used for high-throughput phenotyping (HTP) of above-ground traits of crops to study genetic diversity, resource use efficiency and responses to abiotic or biotic stresses. There is significant unexplored potential for repeated data collection through a field season to reveal information on the rates of growth and provide predictions of the final yield. Generating such information early in the season would create opportunities for more efficient in-depth phenotyping and germplasm selection. This study tested the use of high-resolution time-series imagery (5 or 10 sampling dates) to understand the relationships between growth dynamics, temporal resolution and end-of-season above-ground biomass (AGB) in 869 diverse accessions of highly productive (mean AGB = 23.4 Mg/Ha), photoperiod sensitive sorghum. Canopy surface height (CSM), ground cover (GC), and five common spectral indices were considered as features of the crop phenotype. Spline curve fitting was used to integrate data from single flights into continuous time courses. Random Forest was used to predict end-of-season AGB from aerial imagery, and to identify the most informative variables driving predictions. Improved prediction of end-of-season AGB (RMSE reduction of 0.24 Mg/Ha) was achieved earlier in the growing season (10 to 20 days) by leveraging early- and mid-season measurement of the rate of change of geometric and spectral features. Early in the season, dynamic traits describing the rates of change of CSM and GC predicted end-of-season AGB best. Late in the season, CSM on a given date was the most influential predictor of end-of-season AGB. The power to predict end-of-season AGB was greatest at 50 days after planting, accounting for 63% of variance across this very diverse germplasm collection with modest error (RMSE 1.8 Mg/ha). End-of-season AGB could be predicted equally well when spline fitting was performed on data collected from five flights versus 10 flights over the growing season. This demonstrates a more valuable and efficient approach to using UAVs for HTP, while also proposing strategies to add further value.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1973

Emission and reflection from healthy and stressed natural targets with computer analysis of spectroradiometric and multispectral scanner data

Special emphasis was on corn plants, and the healthy targets were differentiated from stressed ones by remote sensing. Infrared radiometry of plants is reviewed thoroughly with emphasis on agricultural crops. Theory and error analysis of the determination of emittance of a natural target by radiometer is discussed. Experiments were conducted on corn (Zea mays L.) plants with long wavelength spectroradiometer under field conditions. Analysis of multispectral scanner data of ten selected flightlines of Corn Blight Watch Experiment of 1972 indicated: (1) There was no regular pattern of the mean response of the higher level/levels blighted corn vs. lower level/levels blighted corn in any of the spectral channels. (2) The greater the difference between the blight levels, the more statistically separable they usually were in subsets of one, two, three and four spectral channels.

Kumar, R.↗
NASA NTRS1980

Accuracies of three computationally efficient algorithms for computing atmospheric transmittances

Three algorithms for calculating polychromatic atmospheric transmittance functions have been tested using a set of eleven distinct temperature profiles in order to compare transmittance accuracies achievable by the three methods. The comparison of rms errors demonstrates that the iterative method of McMillin and Fleming (1976) is the most accurate of the efficient algorithms currently available for gases with constant mixing ratios; its accuracy approaches that of the spectroscopic parameters and the computational approximations used in the ground-truth line-by-line calculations. The method of Arking et al. (1974), while less accurate, has the advantage of being perfectly general and easily adapted to cases where spectral bandwidths are varied

Mcmillin, L. M.↗