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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 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Modelling and Experimental Validation of Improved Performance of Lithium-Ion Batteries Having Thick Electrodes with Laser-Ablated Micro-Structures

For widespread adoption of electric vehicles, lithium-ion batteries (LiBs) need to achieve energy densities of >275 Wh/kg, cost less than $100/Wh, and charge to more than 80% capacity within 15 minutes. Increasing the battery electrode thicknesses is one way to increase cell energy densities while also saving on cell manufacturing cost by increasing the ratio of electrode active material to inactive material within each cell. However, increased electrode loading is often accompanied by decreased Li+-ion diffusion across the full thick electrodes. This leads to significant cell polarization that prevents full capacity utilization and accelerates cell degradation, especially at fast charging/discharging rates. The introduction of secondary pore networks in thick battery electrodes alleviates some of the trade-offs between energy and power performance. These microstructures provide low tortuosity pathways for facile Li+-ion diffusion deep into the thick electrodes, diminishing detrimental concentration gradients within the cell. Ultrafast-pulsed laser ablation is a promising method to introduce micro pores or channels in thick battery electrodes as it allows for precise control of pattern geometries, results in minimal damage to the electrode and can be introduced into existing roll-to-roll electrode manufacturing lines. Herein, the limitations of thick planer electrodes and the advanced predictive models to identify optimal electrode patterns for improved cycling performance will be presented. The impact of electrode laser patterning to create secondary pore networks also will be discussed. Materials characterization techniques (SEM-EDS, XRD) were used to explore the affect ultrafast laser ablation had on the electrode materials’ morphology and structure. The improvements in the patterned electrodes’ electrochemical cycling performances and degrees of wetting will be compared to a pristine baseline case. Finally, the discrepancies between experimentally obtained data and model predictions will be explained.

DIRECT ENERGY CONVERSION,ENERGY STORAGE↗
NASA NTRS1996

The Lyman-Continuum Fluxes and Stellar Parameters of O and Early B-Type Stars

Using the results of the most recent stellar atmosphere models applied to a sample of hot stars, we construct calibrations of effective temperature (T(sub eff)), and gravity (log(sub g)) with a spectral type and luminosity class for Galactic 0-type and early B-type stars. From the model results we also derive an empirical relation between the bolometric correction and T(sub eff) and log g. Using a sample of stars with known distances located in OB associations in the Galaxy and the Large Magellanic Cloud, we derive a new calibration of M(sub v) with spectral class. With these new calibrations and the stellar atmosphere models of Kurucz, we calculate the physical parameters and ionizing photon luminosities in the H(0) and He(0) continua for O and early B-type stars. We find substantial differences between our values of the Lyman- continuum luminosity and those reported in the literature. We also discuss the systematic discrepancy between O-type stellar masses derived from spectroscopic models and those derived from evolutionary tracks. Most likely, the cause of this 'mass discrepancy' lies primarily in the atmospheric models, which are plane parallel and hydrostatic and therefore do not account for an extended atmosphere and the velocity fields in a stellar wind. Finally, we present a new computation of the Lyman-continuum luminosity from 429 known O stars located within 2.5 kpc of the Sun. We find the total ionizing luminosity from this population ((Q(sub 0)(sup T(sub ot))) = 7.0 x 10(exp 51) photons/s) to be 47% larger than that determined using the Lyman continuum values tabulated by Panagia.

Vacca, William D.↗
NASA NTRSDate not supplied

State-Specific Kinetic Modeling for Predictions of Radiative Heating in H 2 /He Entry Flows

A 23-species State-to-State (StS) thermochemical model for H 2 /He mixtures is developed and used to simulate 1-D shocks at conditions relevant for ice and gas giant entry flows. To implement this StS model, a literature review of the state-specific excitation and ionization rates of atomic H is first performed. While electron impact rates from various sources are found to be in relatively good agreement, large discrepancies are found in the limited data available on heavy particle impact rates. To investigate the impact of these discrepancies on the predicted shock and radiance profiles, simulations are performed for three different versions of the kinetic model, each with a different set of heavy particle impact rates from the literature. Of these three models, two are found to over-predict and one is found to under-predict the radiance values seen in corresponding experimental data from the NASA Ames Electric Arc Shock Tube (EAST) facility. A sensitivity analysis to the electron and heavy particle impact rates is then performed, from which an improved kinetic model with modified rates is proposed. This modified kinetic model is found to reproduce the total integrated radiance seen in the EAST experiments accurately. This suggests that the associated radiative heating that would be encountered by an entry probe in these environments would be well predicted by this kinetic model. However, some discrepancies are still found i the relative contributions to the total radiance from different spectral features, suggesting that additional improvements to the kinetic model still need to be made.

Outer Planet↗
NASA NTRS1976

Pulsar average wave forms and hollow-cone beam models

Pulsar wave forms have been analyzed from observations conducted over a wide radio-frequency range to assess the wave-form morphologies and to measure wave-form widths. The results of the analysis compare favorably with the predictions of a model with a hollow-cone beam of fixed dimensions and with random orientation of both the observer and the cone axis with respect to the pulsar spin axis. A class of three-component wave forms is included in the model by adding a central pencil beam to the hollow-cone hypothesis. The consequences of a number of discrepancies between observations and quantitative predictions of the model are discussed.

Backer, D. C.↗
DOE OSTI2023

First Direct Measurement Constraining the Ar 34 ( α , p ) K 37 Reaction Cross Section for Mixed Hydrogen and Helium Burning in Accreting Neutron Stars

The rate of the final step in the astrophysical αp process, the 34 Ar(α,p) 37 K reaction, suffers from large uncertainties due to a lack of experimental data, despite having a considerable impact on the observable light curves of x-ray bursts and the composition of the ashes of hydrogen and helium burning on accreting neutron stars. Here, we present the first direct measurement constraining the 34Ar(α,p)37K reaction cross section, using the Jet Experiments in Nuclear Structure and Astrophysics gas jet target. The combined cross section for the 34 Ar,Cl(α,p) 37 K,Ar reaction is found to agree well with Hauser-Feshbach predictions. The 34 Ar(α,2p) 36 Ar cross section, which can be exclusively attributed to the 34 Ar beam component, also agrees to within the typical uncertainties quoted for statistical models. This indicates the applicability of the statistical model for predicting astrophysical (α,p) reaction rates in this part of the αp process, in contrast to earlier findings from indirect reaction studies indicating orders-of-magnitude discrepancies. This removes a significant uncertainty in models of hydrogen and helium burning on accreting neutron stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Using Machine Learning to Generate a GISS ModelE Calibrated Physics Ensemble (CPE)

A neural network (NN) surrogate of the NASA GISS ModelE atmosphere (version E3) is trained on a perturbed parameter ensemble (PPE) spanning 45 physics parameters and 36 outputs. The NN is leveraged in a Markov Chain Monte Carlo (MCMC) Bayesian parameter inference framework to generate a second posterior constrained ensemble coined a “calibrated physics ensemble,” or CPE. The CPE members are characterized by diverse parameter combinations and are, by definition, close to top-of-atmosphere radiative balance, and must broadly agree with numerous hydrologic, energy cycle and radiative forcing metrics simultaneously. Global observations of numerous cloud, environment, and radiation properties (provided by global satellite products) are crucial for CPE generation. The inference framework explicitly accounts for discrepancies (or biases) in satellite products during CPE generation. We demonstrate that product discrepancies strongly impact calibration of important model parameter settings (e.g., convective plume entrainment rates; fall speed for cloud ice). Structural improvements new to E3 are retained across CPE members (e.g., stratocumulus simulation). Notably, the framework improved the simulation of shallow cumulus and Amazon rainfall while not degrading radiation fields, an upgrade that neither default parameters nor Latin Hypercube parameter searching achieved. Analyses of the initial PPE suggested several parameters were unimportant for output variation. However, many “unimportant” parameters were needed for CPE generation, a result that brings to the forefront how parameter importance should be determined in PPEs. From the CPE, two diverse 45-dimensional parameter configurations are retained to generate radiatively-balanced, auto-tuned atmospheres that were used in two E3 submissions to CMIP6.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1988

Observations and wind-forced model simulations of the mean seasonal cycle in tropical Pacific sea surface topography

This paper quantitatively evaluates simulations of the mean seasonal cycle in the tropical Pacific Ocean, using a multiple vertical-mode version of the Busalacchi and O'Brien (1980) linear model. The period studied (1979-1981) includes several coincident oceanic and surface wind data sets, as well as a fairly regular seasonal cycle leading into the 1982-1983 El Nino. Simulated mean seasonal cycles in dynamic height and sea level are compared with observed variations in expendable bathythermograph and island tide gauge data averaged over the same period. It was found that, although all simulations show characteristic features of the mean meridional ridge-trough structure in surface topography, simulated north and south equatorial ridges at 20 deg N and 20 deg S are much higher than those observed. Only weak equatorial ridges were generated near 4 N, and none of the simulations exhibited a significant equatorial trough. These discrepancies are attributed to limitations in model physics and to the wind forcing.

Mcphaden, Michael J.↗
NASA NTRS1998

An Improved Magnetic Field Model for Jupiter's Inner Magnetosphere Using a Microsignature of Amalthea

Observation of a particle absorption microsignature of the Jovian satellite Amalthea during the Pioneer II close flyby of Jupiter on December 3, 1974, has been described by McKibben et al. The microsignature was also observed by the University of Iowa/Pioneer II instrument in the distribution of protons in the kinetic energy range 0.61 less than T(sub p) less than 3.41 MeV but has not been previously reported. The finer time resolution and superior data quality of the latter observations provide a fresh basis for assessing the accuracy with which various published magnetic field models of Jupiter's magnetic field models describe Jupiter's magnetic field for radial distances of the order of or less than several planetary radii. The expected time of occurrence of the minimum of Amalthea's microsignature was calculated for each model and compared to the time of the observed minimum. The discrepancy between these two times was significant for each of the published models, but it could be reduced to zero by interpolating between two of the closely related models. The spherical harmonic coefficients of this combination model are tabulated. Also included is a novel method for calculating the intensity-time profile of the microsignature. In a later paper, the improved model is utilized to analyze the energetic particle measurements in Jupiter's innermost magnetosphere by the Galileo entry probe in December 1995.

Randall, Bruce A.↗
NASA NTRS1974

Analytical and experimental investigation of a 1/8-scale dynamic model of the shuttle orbiter. Volume 1: Summary report

A 1/8-scale structural dynamics model of the space shuttle orbiter was analyzed using the NASA Structural Analysis System (NASTRAN). Comparison of the calculated eigenvalues with preliminary test data for the unrestrained condition indicate that the analytical model was consistently stiffer, being about 20% higher in the first mode. The eigenvectors show reasonably good agreement with test data. A series of analytical and experimental investigations undertaken to resolve the discrepancy are described. Modifications in the NASTRAN model based upon these investigations resulted in close agreement for both eigenvalues and eigenvectors.

Mason, P. W.↗
NASA NTRS2004

The Magnetic Field in the Outer Heliosphere

One of the great achievements of Parker was the prediction that the solar magnetic field would be drawn into Archimedian spirals as it is carried away from the Sun by the solar wind. This prediction has been amply confirmed by many in situ measurements in the intervening four decades. But, Parker made his prediction for a solar wind that expands into infinite space while we now know that the local interstellar medium (LISM) is far from empty and, in fact, confines the solar wind to a finite volume, known as the heliosphere, that extends to approximately 100 AU in the upstream direction (the solar system is moving through the LISM). Voyagers 1/2, presently at -80 AU, are approaching the upstream boundaries of the heliosphere and returning data on the properties of the magnetic field. This is important for understanding how galactic cosmic rays (GCRs) reach the Earth. Voyagers show that the IMF at 10-80 AU behaves much as Parker predicted - with two important exceptions. This is not surprising since the field is essentially passively advected by the solar wind out to 80 AU. But, new models say that nearer the heliosphere boundaries the field plays a major role in the solar wind-LISM interaction. However, of the many physical ingredients that constitute the outer heliosphere, the magnetic field poses some of the most interesting and difficult numerical modeling problems. Presently, only a few results have been published and much remains to be done. Here I will summarize the expected and measured behavior of the magnetic field at 80 AU. Then I will describe modeling predictions beyond 80 AU: magnetic "tornadoes", polarity envelopes, the Axford-Cranfill effect, inner and outer magnetic walls and more. I will also list what I believe to be important new modeling objectives. Finally, I will speculate on what is happening with the magnetic field near the nose of the heliosphere. My conclusion is that models of GCR modulation rarely incorporate even crudely realistic magnetic fields so it is a wonder that they are as successful as they are and no surprise that there are still important discrepancies between GCR modulation observations and the models.

Suess, S. T.↗
NASA NTRS1981

Studies of the role of metastables and doubly ionized species in the chemical and thermal structure of the Venusian and Martian ionospheres

Models of the upper atmospheres of Mars and Venus were constructed using Viking and Pioneer Venus data. The neutral densities, with the exception of NO, N(4S), N(2D) and N(2P) were taken from the measured values, along with the neutral, ion, and electron temperatures. Using solar fluxes and relevant cross sections, the production rates of ions and neutral fragments by photo and electron impact processes were computed. These production rates were combined with chemical production rates and loss along with one dimensional transport eddy diffusion, molecular and ambi polar diffusion, and thermal diffusion, to determine the densities of ions and odd nitrogen species. Preliminary calculations show that the chemistry of metastables and doubly ionized species is important in the ionospheres of Mars and Venus. Production of N(+) in metastable reactions is particularly important, and it explains the discrepancy between the measurements of earlier models. Production of CO(+) is also affected. Reactions of O(++) and O(+)(2D) with N2 have important consequences for the escape rate of atomic nitrogen from the Martian atmosphere.

Fox, J. L.↗
DOE OSTI2022

Modeling the distribution of the endangered Jemez Mountains salamander (Plethodon neomexicanus) in relation to geology, topography, and climate

The Jemez Mountains salamander (Plethodon neomexicanus; hereafter JMS) is an endangered salamander restricted to the Jemez Mountains in north-central New Mexico, United States. This strictly terrestrial and lungless species requires moist surface conditions for activities such as mating and foraging. Threats to its current habitat include fire suppression and ensuing severe fires, changes in forest composition, habitat fragmentation, and climate change. Forest composition changes resulting from reduced fire frequency and increased tree density suggest that its current aboveground habitat does not mirror its historically successful habitat regime. However, because of its limited habitat area and underground behavior, we hypothesized that geology and topography might play a significant role in the current distribution of the salamander. We modeled the distribution of the JMS using a machine learning algorithm to assess how geology, topography, and climate variables influence its distribution. The best habitat suitability model indicates that geology type and maximum winter temperature (November to March) were most important in predicting the distribution of the salamander (23.5% and 50.3% permutation importance, respectively). Minimum winter temperature was also an important variable (21.4%), suggesting this also plays a role in salamander habitat. Our habitat suitability map reveals low uncertainty in model predictions, and we found slight discrepancies between the designated critical habitat and the most suitable areas for the JMS. Because geological features are important to its distribution, we recommend that geological and topographical data are considered, both during survey design and in the description of localities of JMS records once detected.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Measurements of ϒ states production in 𝑝 + 𝑝 collisions at $\sqrt{s}$ = 500 GeV with STAR: Cross sections, ratios, and multiplicity dependence

We report measurements of ϒ⁡(1⁢𝑆), ϒ⁡(2⁢𝑆) and ϒ⁡(3⁢𝑆) production in 𝑝 + 𝑝 collisions at $\sqrt{s}$ =500 GeV by the STAR experiment in year 2011, corresponding to an integrated luminosity ℒ int = 13 pb −1 . The results provide precise cross sections, transverse momentum (𝑝 T ) and rapidity (𝑦) spectra, as well as cross section ratios for 𝑝 T < 10 GeV/c and |𝑦| < 1. The dependence of the ϒ yield on charged particle multiplicity has also been measured, offering new insights into the mechanisms of quarkonium production. The data are compared to various theoretical models: the color evaporation model (CEM) accurately describes the ϒ⁡(1⁢𝑆) production, while the color glass condensate+nonrelativistic quantum chromodynamics (CGC+NRQCD) model overestimates the data, particularly at low 𝑝 T . Conversely, the color singlet model (CSM) underestimates the rapidity dependence. These discrepancies highlight the need for further development in understanding the production dynamics of heavy quarkonia in high-energy hadronic collisions. The trend in the multiplicity dependence is consistent with CGC/saturation and string percolation models or ϒ production happening in multiple parton interactions modeled by PYTHIA 8.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1995

Heliomagnetic latitude dependence of the heliospheric magnetic field

Previous studies have revealed systematic variations of the interplanetary magnetic field with heliographic latitude. Luhmann et al. (1987) modeled Pioneer Venus (PVO) and ISEE-3 observations by assuming an asymmetric dependence on heliolatitude with stronger fields in the northern hemisphere. In a subsequent study, using data from ISEE-3/ICE and IMP-8, Burton et al. (1990) found evidence for a similar asymmetry. However, neither model has been completely successful. The model derived from PVO/ICE observations agrees quite well near solar maximum but shows significant discrepancies during the descending phase of the solar cycle. The model derived from the ICE/IMP-8 comparison suffers from significant phase delays between the difference in field magnitude at the two spacecraft and their latitude difference. In an attempt to account for these phase shifts, the IMP-8 and ICE data have been reexamined in heliomagnetic coordinates which are defined by the orientation of the solar magnetic dipole. The latitude and longitude of the dipole inferred from the data have then been compared with those implicit in source surface calculations. The IMP/ICE correlations have been extended into the recent solar maximum and descending phase. Comparisons have also been carried out between IMP-8 and Ulysses as it traveled to -30 deg south heliographic latitude.

Burton, M. E.↗
NASA NTRS2003

Cloud Modeling Using Field Project Data for the Study of Precipitation Processes

The use of cloud-resolving models (CRMs) in the study of precipitation process and their relation to the large-scale environment can be generally categorized into two approaches. The first approach is so called "cloud ensemble modeling". In this approach, many clouds of different size in various stages of their lifecycles can be present at any model simulation time. Large-scale effects are derived from observations and imposed into the model as the main forcing. The advantage of this approach is that the modeled convection will be forced to have the same intensity, thermodynamic budget and organization as the obserations.This approach will also allow CRMs to perform multi-day or multi-week time integrations. The second approach usually requires initial temperature and water vapor profiles that have a medium to large CAPE, and open lateral boundary conditions are used. The modeled clouds could be termed "self-forced convection". Model improvements, such as in the microphysics, are achieved using the second approach. In cloud ensemble modeling, accurate large-scale advective tendencies for temperature and water vapor are the main forcing for the CRMs. We found that the large-scale advective terms for temperature and water vapor are not always consistent, For example, large-scale forcing could indicate strong drying which would produce cooling in the model through evaporation but not contain large-scale advective heating to compensate. This discrepancy in forcing would cause differences between the observed and modeled latent heating profiles. Good measurements of other quantities (i.e., surface fluxes and radiation) are also required to perform variational objective analysis that computes and minimizes a "cost function" that constrains the difference between the large-scale advective forcing in temperature and water vapor. With self-forced convection, accurate vertical distributions of temperature, moisture (water vapor), and horizontal winds are required. The timing of the measurements relative to cloud development is crucial (i.e., prior to cloud triggering). Microphysical measurements (i.e., the cloud number concentration and size distribution) can also be used in this second approach but are of secondary importance with cloud ensemble modeling. In this paper, data collected during TRMM field campaigns (FCs; i.e., SCSMEX, LBA and KWAJEX) which were aimed at validating TRMM products (i.e., rainfall and the vertical distribution of latent heating) will be used to examine the impact of errors in the initial conditions (e.g.., soundings an large-scale forcing) on simulated rainfall distributions and brightness. Rainfall and precipitations simulated from a CRM will also be compared with those estimated by a schocastic model.

Tao, W.-K.↗
NASA NTRS2016

Regime-Based Evaluation of Cloudiness in CMIP5 Models

The concept of Cloud Regimes (CRs) is used to develop a framework for evaluating the cloudiness of 12 fifth Coupled Model Intercomparison Project (CMIP5) models. Reference CRs come from existing global International Satellite Cloud Climatology Project (ISCCP) weather states. The evaluation is made possible by the implementation in several CMIP5 models of the ISCCP simulator generating for each gridcell daily joint histograms of cloud optical thickness and cloud top pressure. Model performance is assessed with several metrics such as CR global cloud fraction (CF), CR relative frequency of occurrence (RFO), their product (long-term average total cloud amount [TCA]), cross-correlations of CR RFO maps, and a metric of resemblance between model and ISCCP CRs. In terms of CR global RFO, arguably the most fundamental metric, the models perform unsatisfactorily overall, except for CRs representing thick storm clouds. Because model CR CF is internally constrained by our method, RFO discrepancies yield also substantial TCA errors. Our findings support previous studies showing that CMIP5 models underestimate cloudiness. The multi-model mean performs well in matching observed RFO maps for many CRs, but is not the best for this or other metrics. When overall performance across all CRs is assessed, some models, despite their shortcomings, apparently outperform Moderate Resolution Imaging Spectroradiometer (MODIS) cloud observations evaluated against ISCCP as if they were another model output. Lastly, cloud simulation performance is contrasted with each model's equilibrium climate sensitivity (ECS) in order to gain insight on whether good cloud simulation pairs with particular values of this parameter.

cloud climatology↗
NASA NTRS2003

On the Computation of Space-Time Correlations by Large-Eddy Simulation

Numerical comparisons in decaying isotropic turbulence suggest that there exist discrepancies in time correlations evaluated by DNS and LES using eddy-viscosity-type SGS models. This is consistent with the previous observations in forced isotropic turbulence. Therefore, forcing is not the main cause of the discrepancies. Comparisons among different SGS models in the LES also indicate that the model choice affects the time correlations in the LES. The multi-scale LES method using the dynamic Smagorinsky model on the small scale equation is the most accurate of the all models, the classic Smagorinsky model is the least accurate and the dynamic Smagorinsky model and spectral eddy viscosity model give intermediate results with small differences. The generalized sweeping hypothesis implies that time correlations in decaying isotropic turbulence are mainly determined by the instantaneous energy spectra and sweeping velocities. The analysis based on the sweeping hypothesis explains the discrepancies in our numerical simulations: the LES overpredicts the decorrelation time scales because the sweeping velocities are smaller than the DNS values, and underpredicts the magnitudes of time correlations because the energy spectrum levels are lower than the DNS ones. Since the sweeping velocity is determined by the energy spectra, one concludes that an accurate prediction of the instantaneous energy spectra guarantees the accuracy of time correlations. An analytical expression of sound power spectra based on Lighthill's theory and the quasi-normal closure assumption suggests that the sound power spectra are sensitive to errors in time correlations. Small errors in time correlations can cause significant errors in the sound power spectra, which exhibit a sizable drop at moderate to high frequencies accompanied by a shift of the peaks to lower frequencies. Based on the above analysis, two possible ways to improve the acoustic power spectrum predictions can be considered. The first is to construct better SGS models to improve the LES accuracy for time correlations. The second is to remedy the temporal statistics of the Lighthill stress tensor in order to "recover" the contribution from the unresolved scales in LES to time correlations.

He, Guo-Wei↗
NASA NTRS1998

Influence of Subpixel Scale Cloud Top Structure on Reflectances from Overcast Stratiform Cloud Layers

Recent observational studies have shown that satellite retrievals of cloud optical depth based on plane-parallel model theory suffer from systematic biases that depend on viewing geometry, even when observations are restricted to overcast marine stratus layers, arguably the closest to plane parallel in nature. At moderate to low sun elevations, the plane-parallel model significantly overestimates the reflectance dependence on view angle in the forward-scattering direction but shows a similar dependence in the backscattering direction. Theoretical simulations are performed that show that the likely cause for this discrepancy is because the plane-parallel model assumption does not account for subpixel, scale variations in cloud-top height (i.e., "cloud bumps"). Monte Carlo simulation, comparing ID model radiances to radiances from overcast cloud field with 1) cloud-top height variation, but constant cloud volume extinction; 2) flat tops but horizontal variations in cloud volume extinction; and 3) variations in both cloud top height and cloud extinction are performed over a approximately equal to 4 km x 4 km domain (roughly the size of an individual GAC AVHRR pixel). The comparisons show that when cloud-top height variations are included, departures from 1D theory are remarkably similar (qualitatively) to those obtained observationally. In contrast, when clouds are assumed flat and only cloud extinction is variable, reflectance differences are much smaller and do not show any view-angle dependence. When both cloud-top height and cloud extinction variations are included, however, large increases in cloud extinction variability can enhance reflectance difference. The reason 3D-1D reflectance differences are more sensitive to cloud-top height variations in the forward-scattering direction (at moderate to low, sun elevations) is because photons leaving the cloud field in that direction experience fewer scattering events (low-order scattering) and are restricted to the topmost portions of the cloud. While reflectance deviations from 1D theory are much larger for bumpy clouds than for flat clouds with variable cloud extinction, differences in cloud albedo are comparable for these two cases.

Loeb, N. G.↗