Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Relative accuracy”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Comments on the Leimanis solution of self-excited rigid body

An attempt is made to apply the solutions contained in a book by Leimanis (1965), which includes the Bodewadt solution, to the performance assessment of the Galileo spacecraft during spin up and spin down maneuvers. Because the Galileo is not precisely symmetric, however, the Bodewadt solution fails to achieve the desired accuracy for useful analysis. It is noted that in the case of the Leimanis solution, the analytic results are incorrect for theoretical reasons. In order to remedy this situation, analytic solutions are developed which satisfy the criterion of high accuracy and provide a useful analytic tool for the performance assessment and maneuver analysis of the Galileo spacecraft and many similar near symmetric spinning spacecraft. Simulation results suggest the relative accuracies of the Bodewadt solution and the author's solution, while the restricted regions of validity of the Leimanis solution are clearly indicated.

Longuski, J. M.↗
NASA NTRS1981

Quantitative interpretation of cloud radiances observed with a 94 GHz scanning radiometer

A description is presented of the results of a theoretical study to evaluate the remote sensing technique to determine integrated liquid water content. The considered technique uses 94 GHz passive microwave observations as applied to nonprecipitation clouds over the ocean. The study indicates that it is possible to infer the precipitable water of the atmosphere with a useful accuracy from a single 94 GHz nadir measurement and an estimated sea surface temperature. It is demonstrated that the integrated liquid water content of nonprecipitable clouds can be estimated with a relative accuracy of 20% to 30% depending on the atmospheric water vapor content from a microwave passive measurement at 94 GHz in the presence of clouds and in cloud free areas in the vicinity of the cloud in conjunction with information on the sea surface and cloud top temperatures.

Szejwach, G.↗
NASA NTRS2002

Evaluation of Small Mass Spectrometer Systems

This work is aimed at understanding the aspects of designing a miniature mass spectrometer (MS) system. A multitude of commercial and government sectors, such as the military, environmental agencies and industrial manufacturers of semiconductors, refrigerants, and petroleum products, would find a small, portable, rugged and reliable MS system beneficial. Several types of small MS systems are evaluated and discussed, including linear quadrupole, quadrupole ion trap, time of flight and sector. The performance of each system in terms of accuracy, precision, limits of detection, response time, recovery time, scan rate, volume and weight is assessed. A performance scale is setup to rank each systems and an overall performance score is given to each system. All experiments involved the analysis of hydrogen, helium, oxygen and argon in a nitrogen background with the concentrations of the components of interest ranging from 0-5000 part-per-million (ppm). The relative accuracies of the systems vary from < 1% to approx. 40% with an average below 10%. Relative precisions varied from 1% to 20%, with an average below 5%. The detection limits had a large distribution, ranging from 0.2 to 170 ppm. The systems had a diverse response time ranging from 4 s to 210 s as did the recovery time with a 6 s to 210 s distribution. Most instruments had scan times near, 1 s, however one instrument exceeded 13 s. System weights varied from 9 to 52 kg and sizes from 15 x 10(exp 3)cu cm to 110 x 10(exp 3) cu cm.

Arkin, C. Richard↗
DOE OSTI2022

Towards Elucidating Structure–Spectra Relationships in Rhamnogalacturonan II: Computational Protocols for Accurate 13C and 1H Shifts for Apiose and Its Borate Esters

Apiose is a naturally occurring, uncommon branched-chain pentose found in plant cell walls as part of the complex polysaccharide Rhamnogalacturonan II (RG-II). The structural elucidation of the three-dimensional structure of RG-II by nuclear magnetic resonance (NMR) spectroscopy is significantly complicated by the ability of apiose to cross-link via borate ester linkages to form RG-II dimers. Here, we developed a computational approach to gain insight into the structure–spectra relationships of apio–borate complexes in an effort to complement experimental assignments of NMR signals in RG-II. Our protocol involved structure optimizations using density functional theory (DFT) followed by isotropic magnetic shielding constant calculations using the gauge-invariant atomic orbital (GIAO) approach to predict chemical shifts. We evaluated the accuracy of 23 different functional–basis set (FBS) combinations with and without implicit solvation for predicting the experimental 1 H and 13 C shifts of a methyl apioside and its three borate derivatives. The computed NMR predictions were evaluated on the basis of the overall shift accuracy, relative shift ordering, and the ability to distinguish between dimers and monomers. We demonstrate that the consideration of implicit solvation during geometry optimizations in addition to the magnetic shielding constant calculations greatly increases the accuracy of NMR chemical shift predictions and can correctly reproduce the ordering of the 13 C shifts and yield predictions that are, on average, within 1.50 ppm for 13 C and 0.12 ppm for 1 H shifts for apio–borate compounds.

BASIC BIOLOGICAL SCIENCES,BIOMASS FUELS↗
NASA NTRS1992

A three-parameter approximation for radiative transfer in nonhomogeneous atmospheres - Application to the O3 9.6-micron band

A three-parameter scaling approximation is developed in conjunction with random models for the computation of transmittance along nonhomogeneous atmospheres. In addition to the scaled path length and pressure, a third parameter is introduced to account for intermediate absorption. With reference to the results derived from line-by-line calculations, the accuracy of this scaling approximation is assessed in different atmospheric conditions. For the O3 9.6-micron band where the Curtis-Godson and other conventional scaling methods usually produce large errors, the present model can achieve relative accuracies within about 1 percent in transmittance and the downward surface flux. Accuracy of about 0.15 K/d can be obtained in cooling rate calculations. The present three-parameter approximation is well suited for radiative transfer parameterizations in which the demand for high accuracy is required in the transmittance and flux calculations.

Fu, Qiang↗
DOE OSTI2023

Accuracy of ghost rotationally invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size

Here, we compare the accuracy of the ghost rotationally invariant slave-boson (g-RISB) theory and dynamical mean field theory (DMFT) on the single-band Hubbard model, as a function of the number of bath sites in the embedding impurity Hamiltonian. Our benchmark calculations confirm that the accuracy of g-RISB can be systematically improved by increasing the number of bath sites, similar to DMFT. With a few bath sites, we observe that g-RISB is systematically more accurate than DMFT for the ground-state observables. On the other hand, the relative accuracy of these methods is generally comparable for the quasiparticle weight and the spectral function. As expected, we observe that g-RISB satisfies the variational principle in infinite dimensions, as the total energy decreases monotonically towards the exact value as a function of the number of bath sites, suggesting that the g-RISB wave function may approach the exact ground state in infinite dimensions. Our results suggest that the g-RISB is a promising method for first-principles simulations of strongly correlated matter, which can capture the behavior of both static and dynamical observables, at a relatively low computational cost.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2006

Proceedings of the 2004 High Spatial Resolution Commercial Imagery Workshop

Topics covered include: NASA Applied Sciences Program; USGS Land Remote Sensing: Overview; QuickBird System Status and Product Overview; ORBIMAGE Overview; IKONOS 2004 Calibration and Validation Status; OrbView-3 Spatial Characterization; On-Orbit Modulation Transfer Function (MTF) Measurement of QuickBird; Spatial Resolution Characterization for QuickBird Image Products 2003-2004 Season; Image Quality Evaluation of QuickBird Super Resolution and Revisit of IKONOS: Civil and Commercial Application Project (CCAP); On-Orbit System MTF Measurement; QuickBird Post Launch Geopositional Characterization Update; OrbView-3 Geometric Calibration and Geopositional Accuracy; Geopositional Statistical Methods; QuickBird and OrbView-3 Geopositional Accuracy Assessment; Initial On-Orbit Spatial Resolution Characterization of OrbView-3 Panchromatic Images; Laboratory Measurement of Bidirectional Reflectance of Radiometric Tarps; Stennis Space Center Verification and Validation Capabilities; Joint Agency Commercial Imagery Evaluation (JACIE) Team; Adjacency Effects in High Resolution Imagery; Effect of Pulse Width vs. GSD on MTF Estimation; Camera and Sensor Calibration at the USGS; QuickBird Geometric Verification; Comparison of MODTRAN to Heritage-based Results in Vicarious Calibration at University of Arizona; Using Remotely Sensed Imagery to Determine Impervious Surface in Sioux Falls, South Dakota; Estimating Sub-Pixel Proportions of Sagebrush with a Regression Tree; How Do YOU Use the National Land Cover Dataset?; The National Map Hazards Data Distribution System; Recording a Troubled World; What Does This-Have to Do with This?; When Can a Picture Save a Thousand Homes?; InSAR Studies of Alaska Volcanoes; Earth Observing-1 (EO-1) Data Products; Improving Access to the USGS Aerial Film Collections: High Resolution Scanners; Improving Access to the USGS Aerial Film Collections: Phoenix Digitizing System Product Distribution; System and Product Characterization: Issues Approach; Innovative Approaches to Analysis of Lidar Data for the National Map; Changes in Imperviousness near Military Installations; Geopositional Accuracy Evaluations of QuickBird and OrbView-3: Civil and Commercial Applications Project (CCAP); Geometric Accuracy Assessment: OrbView ORTHO Products; QuickBird Radiometric Calibration Update; OrbView-3 Radiometric Calibration; QuickBird Radiometric Characterization; NASA Radiometric Characterization; Establishing and Verifying the Traceability of Remote-Sensing Measurements to International Standards; QuickBird Applications; Airport Mapping and Perpetual Monitoring Using IKONOS; OrbView-3 Relative Accuracy Results and Impacts on Exploitation and Accuracy Improvement; Using Remotely Sensed Imagery to Determine Impervious Surface in Sioux Falls, South Dakota; Applying High-Resolution Satellite Imagery and Remotely Sensed Data to Local Government Applications: Sioux Falls, South Dakota; Automatic Co-Registration of QuickBird Data for Change Detection Applications; Developing Coastal Surface Roughness Maps Using ASTER and QuickBird Data Sources; Automated, Near-Real Time Cloud and Cloud Shadow Detection in High Resolution VNIR Imagery; Science Applications of High Resolution Imagery at the USGS EROS Data Center; Draft Plan for Characterizing Commercial Data Products in Support of Earth Science Research; Atmospheric Correction Prototype Algorithm for High Spatial Resolution Multispectral Earth Observing Imaging Systems; Determining Regional Arctic Tundra Carbon Exchange: A Bottom-Up Approach; Using IKONOS Imagery to Assess Impervious Surface Area, Riparian Buffers and Stream Health in the Mid-Atlantic Region; Commercial Remote Sensing Space Policy Civil Implementation Update; USGS Commercial Remote Sensing Data Contracts (CRSDC); and Commercial Remote Sensing Space Policy (CRSSP): Civil Near-Term Requirements Collection Update.

Source record↗
NASA NTRS1984

Intercomparison of planetary-scale diagnostics derived from separate satellite and radiosonde time-mean temperature fields

The planetary-scale components of the extratropical Northern Hemisphere troposphere-stratosphere 1973-74 winter circulation are diagnosed using separate time-mean temperature fields based on radiosonde and satellite observations. Meridional cross-sections of zonal wind together with, for zonal wavenumbers 1, 2 and 3, the streamfunction amplitude, phase and Eliassen-Palm flux are displayed, with the relative accuracy of the satellite-derived diagnostics assessed through comparison with the 'ground-truth' radiosonde information. The satellite and radiosonde diagnostics compare most favourably in terms of zonal wind speed and shear, direction of wave propagation and meridional wave structure - all of which are closely related to the differential properties of the atmospheric temperature field. The intensity of the satellite-derived patterns of tropospheric wave propagation is underestimated due to the effects of spatial smoothing and residual cloud contamination present in the satellite radiance measurements.

Miles, T.↗
DOE OSTI2026

Machine learning for seismic low-frequency extrapolation

The cycle-skipping problem that plagues full waveform inversion (FWI) can be at least partially mitigated if low frequencies (which encode the kinematics of wave propagation in seismic data) are recorded. However, seismic sources and receivers are band-limited, so seismic data does not generally include signals down to 0 Hz. To improve our ability to solve the seismic inverse problem, one can synthesize this missing low-frequency (LF) content from the recorded high-frequency (HF) data using machine learning (ML) models. Deep learning models such as convolutional neural networks (CNNs) demonstrate impressive ability to perform low frequency extrapolation. However, such models require powerful hardware (GPU machines) and careful training. We assess the extrapolation capabilities of three different ML models that do not require GPU machines, namely, random forest, Gaussian process regression and gradient boosting, on both synthetic and real data. Experimental results on two synthetic data sets (generated from a low velocity lens embedded in a homogeneous medium, and the Marmousi model) demonstrate that FWI applied to the extrapolated data consistently improves inversion accuracy relative to FWI applied to the original data sets that do not contain low frequencies. Application of low-frequency extrapolation to real data from the Northwest Shelf of Australia demonstrates that tree-based ML models such as gradient boosting can outperform CNNs in terms of both accuracy and computational cost on non-GPU architectures.

58 GEOSCIENCES↗
NASA NTRSDate not supplied

Developing Fast and Accurate Radiative Transfer Models to Meet the Needs of Modern Satellite Remote Sensing Applications

Modern hyperspectral satellite remote sensors provide highly accurate measurements the Earth’s Top-of-Atmosphere (TOA) radiance, reflectance, or polarized spectra with hundreds to thousands of spectral channels and with millions of observations per day. The large data volume and high spectral dimensionality of the data pose challenges for retrieval algorithms. To process the satellite Level-1 data (e.g. calibrated TOA spectra) into Level-2 products (e.g. atmospheric and surface properties) using physical-based retrieval algorithms, accurate and fast Radiative Transfer Models (RTMs) are needed. RTMs are usually the limiting factor in determining the speed of a level-2 algorithm. For example, more than one million Line-by-Line (LBL) radiative transfer (RT) calculations are needed in order to properly capture the spectral contributions of important atmospheric molecules for an IR hyperspectral sensor with a spectral coverage from 3.5 m to 15 m or a solar hyperspectral sensor with spectral coverage from 0.25 m to 2.5 m. In this presentation, we will discuss advantages and disadvantages of different ways (e.g. correlated k and effective transmittance) to accelerate the speed of a fast RTM. We finally describe a Principal Component-based Radiative Transfer Model (PCRTM), which can calculate TOA radiance or reflectance spectra from 50 cm-1 to 40,000 cm-1 (200 m to 0.25 m). It has demonstrated very good accuracy relative to reference LBL RTMs and saves orders of magnitude in computational time. The PCRTM has been used in many satellite remote sensing applications. Examples include forward modeling in Level-2 and Level-3 retrieval algorithms, high fidelity satellite instrument simulators and instrument performance trade studies, spectral and radiometric accuracy characterizations of satellite Level-1 data, tools for inter-satellite calibrations, tools for satellite RTM lookup table generations, and tools for generating physically based training datasets for Artificial Intelligence (AI) algorithms.

climate data record↗
DOE OSTI2020

Computationally Predicted High-Throughput Free-Energy Phase Diagrams for the Discovery of Solid-State Hydrogen Storage Reactions

The design of multinary solid-state material systems that undergo reversible phase changes via changes in temperature and pressure provides a potential means of safely storing hydrogen. However, fully mapping the stabilities of known or newly targeted compounds relative to competing phases at reaction conditions has previously required many stringent experiments or computationally demanding calculations of each compound’s change in Gibbs energy with respect to temperature, G(T). Here, we have extended the approach of constructing chemical potential phase diagrams based on ΔG f (T) to enable the analysis of phase stability at non-zero temperatures. We first performed density functional theory calculations to compute the formation enthalpies of binary, ternary, and quaternary compounds within several compositional spaces of current interest for solid-state hydrogen storage. Temperature effects on solid compound stability were then accounted for using our recently introduced machine learned descriptor for the temperature-dependent contribution G δ (T) to the Gibbs energy G(T). From these Gibbs energies, we evaluated each compound’s stability relative to competing compounds over a wide range of conditions and show using chemical potential and composition phase diagrams that the predicted stable phases and H2 release reactions are consistent with experimental observations. This demonstrates that our approach rapidly computes the thermochemistry of hydrogen release reactions for compounds at sufficiently high accuracy relative to experiment to provide a powerful framework for analyzing hydrogen storage materials. This framework based on G(T) enables the accelerated discovery of active materials for a variety of technologies that rely on solid-state reactions involving these materials.

08 HYDROGEN↗
NASA NTRS1993

The effect of sub-surface volume scattering on the accuracy of ice-sheet altimeter retracking algorithms

The NASA and ESA retracking algorithms are compared with an algorithm based upon a combined surface and volume (S/V) scattering model. First, the S/V, NASA, and ESA algorithms were used to retrack over 400,000 altimeter return waveforms from the Greenland and Antarctic ice sheets. The surface elevations from the S/V algorithm were compared with the elevations produced by the NASA and ESA algorithms to determine the relative accuracy of these algorithms when subsurface volume-scattering occurs. The results show that the NASA algorithm produced surface elevations within 35 to 50 cm of the S/V algorithm, while the performance of the ESA algorithm was slightly worse. Next, by analyzing several thousand satellite crossover points from the Antarctic data set, we determined the retracking algorithm that produced the most repeatable surface elevations. The elevations derived from the S/V algorithm had the smallest RMS error for the region of the East Antarctic plateau examined here. The ESA algorithm produced erroneous estimates of elevation change when seasonal variations were present; it measured 0.7 to 1.6-m change in elevation over a 6-month period on the East Antarctic plateau where accumulation rates are only 10 cm/year.

Davis, Curt H.↗
DOE OSTI2023

Optimizing the regularization in size-consistent second-order Brillouin-Wigner perturbation theory

Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter ($α$) was set to recover the exact dissociation limit of H 2 in a minimal basis set. Alternatively $α$ can be viewed as a regularization parameter, where each value of $α$ represents a valid variant of BW-s2, which we denote as BW-s2($α$). In this work, we semi-empirically optimize $α$ for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the ab initio parameterization of BW-s2 and MP2. We demonstrate that the optimal $α$ parameter ($α$ = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2($α$) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2($α$) is iterative $\mathcal{O}$($N^5$), this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Multitask graph neural networks for elastoplastic response prediction in dual-phase polycrystals

Microstructure-sensitive prediction of elastoplastic response remains a recurring bottleneck in multiscale damage and fatigue modeling, where large ensembles of statistically distinct polycrystals are required to quantify variability and extreme-value behavior. In this work, we develop a multitask graph neural network (GNN) surrogate that maps dual-phase ferrite–martensite polycrystal microstructures to Statistical Volume Element (SVE)-level elastoplastic Quantities of Interest (QoIs). Each SVE is represented as a grain-adjacency graph, with node features encoding phase, geometry, and crystallographic orientation, and edge features encoding relative misorientation. A message-passing graph convolution generates node embeddings, which are pooled into a graph representation and passed to a multitask regression head that jointly predicts 10 scalar QoIs and vector-valued stress–strain responses in orthogonal loading directions across multiple martensite volume fractions and SVE sizes. Results show high accuracy for scalar QoIs and strong agreement for full stress–strain trajectories, with population envelopes reproducing both median behavior and finite-SVE variability across compositions and partition scales. A unified model trained on pooled volume-fraction data preserves most within-regime accuracy relative to regime-specific models while also capturing the broader cross-regime variation reflected in the pooled test set. Distributional comparisons further demonstrate that the surrogate preserves heterogeneity under SVE partitioning, enabling statistically consistent block-wise random-field construction for mesoscale analyses. Overall, the proposed grain-graph surrogate provides a practical pathway to accelerate ensemble-based studies of SVE-level constitutive variability in dual-phase polycrystals.

Crystal plasticity↗
NASA NTRS2012

Observing System Simulations for the NASA ASCENDS Lidar CO2 Mission Concept: Substantiating Science Measurement Requirements

The NASA ASCENDS mission (Active Sensing of Carbon Emissions, Nights, Days, and Seasons) is envisioned as the next generation of dedicated, space-based CO2 observing systems, currently planned for launch in about the year 2022. Recommended by the US National Academy of Sciences Decadal Survey, active (lidar) sensing of CO2 from space has several potentially significant advantages, in comparison to current and planned passive CO2 instruments, that promise to advance CO2 measurement capability and carbon cycle understanding into the next decade. Assessment and testing of possible lidar instrument technologies indicates that such sensors are more than feasible, however, the measurement precision and accuracy requirements remain at unprecedented levels of stringency. It is, therefore, important to quantitatively and consistently evaluate the measurement capabilities and requirements for the prospective active system in the context of advancing our knowledge of carbon flux distributions and their dependence on underlying physical processes. This amounts to establishing minimum requirements for precision, relative accuracy, spatial/temporal coverage and resolution, vertical information content, interferences, and possibly the tradeoffs among these parameters, while at the same time framing a mission that can be implemented within a constrained budget. Here, we present results of observing system simulation studies, commissioned by the ASCENDS Science Requirements Definition Team, for a range of possible mission implementation options that are intended to substantiate science measurement requirements for a laser-based CO2 space instrument.

Kawa, Stephan R.↗
NASA NTRS1984

The accuracy of mesoscale temperature and dewpoint fields retrieved from VAS satellite and conventional surface data

The Visible Infrared Spin-Scan Radiometer (VISSR) Atmospheric Sounder (VAS) is a twelve channel imaging radiometer on the Geostationary Operational Environmental Satellites (GOES). It is pointed out that the instrument is designed to monitor the evolution of tropospheric temperature and moisture fields at mesoscale resolution. Since the numerical qualities of VAS soundings affect their usefulness, a quantitative verification of the absolute and relative accuracy of VAS soundings appears highly desirable. The present investigation is concerned with an objective verification for two VAS case studies. Absolute accuray is measured by comparing the VAS retrievals to the radiosonde values at the network sites. Absolute temperature accuracy is found to be + or - 2 C below 500 mb, while absolute dewpoint accuracy is + or - 2 to + or - 3 C below 850 mb.

Chesters, D.↗
NASA NTRS1983

An analytical and experimental study of zoning in plagioclase

A detailed electron microprobe study has been conducted on natural and experimentally grown zoned plagioclase feldspars. Discontinuous, sector, and oscillatory chemical zoning are observed superimposed on continuous normal or reverse zoning trends. The relative accuracy of 3 element (Na, Ca, K) microprobe traverses was found statistically to be 2 mole percent. Comparison of microprobe data on natural zoned plagioclase with zoned plagioclase grown in controlled experiments has shown that it may be possible to distinguish zonal development resulting from physio-chemical changes to the bulk magma from zoning related to local kinetic control on the growth of individual crystals.

Smith, R. K.↗
NASA NTRS1993

Comparative accuracy of diffuse radiative properties computed using selected multiple scattering approximations

Computational results have been obtained for the spherical albedo, global transmission, and global absorption of plane-parallel layers composed of cloud droplets. These computations, obtained using the doubling method for the entire range of single scattering albedos and for optical depths between 0.1 and 100, are compared with corresponding results obtained using selected multiple scattering approximations. The spherical albedo and global absorption computed using asymptotic theory are found to be accurate to better than 5 percent for all values of the single scattering albedo, provided the optical thickness exceeds about 2. The diffuse two-stream approximations have relative accuracies that are much worse than 5 percent for the spherical albedo over most of the parameter space, yet are accurate to within 5 percent in the global absorption when the absorption is significant. The integrated delta-Eddington scheme appears to be the most suitable model over the entire range of variables, generally producing relative errors of less than 5 percent in both the spherical albedo and global absorption.

HARSHVARDHAN↗