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DOE OSTI2023

Solid and gas thermal conductivity models improvement and validation in various porous insulation materials

In the past few decades, significant efforts have been made to improve the theoretical understanding of thermal transport mechanisms in thermal insulation materials and push the thermal conductivity's lower limits. However, most works focused singularly on specific types of materials, and the models used for thermal conductivity predictions are diverse - a model that fits one material might not fit others. Here, we improve and unify the gas and solid thermal conductivity models for porous materials. Through experimental characterization of several different materials as well as literature data for other materials, these models are validated. Further, we have also found that the pressure-dependent gas thermal conductivity of most materials can be well fitted by using one or two pore sizes without using a complex pore size distribution. With the refined models, we decompose the effective thermal conductivity of several thermal insulation materials into gas, solid, and radiation contributions. For cellular (polystyrene and polyurethane) foams, the relative contributions from air, solid, and radiation are 58–75%, 3–11%, 16–38%, respectively. For granular porous materials (polyurethane and silica in this work), the contributions from air, solid, and radiation are 45–66%, 34–46%, and 0–8%, respectively. This work is expected to provide guidance on the design and optimization of the next generation of thermal insulation materials, for example, through the effort of reducing gas conduction and radiation in foams and suppressing gas and solid conduction in aerogels.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Overcoming significant challenges in extracting off-stoichiometric thermodynamics using the compound energy formalism through complementary use of experimental and first principles data: A case study of Ba 1-x Sr x FeO 3-δ

The compound energy formalism (CEF) is a powerful framework to describe the thermodynamics of metal oxides as a function of off-stoichiometry, temperature, and composition. The thermodynamic properties are crucial materials design attributes in metal oxide-based oxygen-exchange chemical processes. Despite the richness of information an accurate CEF model provides, a method to determine a unique and accurate fit for oxygen exchange materials remains elusive. This contribution details a method for fitting the CEF model that overcomes the current fitting challenges through three innovations: 1) the combination of density functional theory calculations with experimental data decorrelates excess terms and delineates the enthalpic/entropic contributions to the Gibbs free energy; 2) a systematic determination of the important CEF model terms, removing thermodynamic predetermining human intervention; 3) a self-consistent solution of the starting oxygen offstoichiometry (δ 0 ) of thermogravimetric measurements. Thus, our method enables the reliable extraction of off-stoichiometric metal oxide thermodynamic properties and facilitates rapid materials compositional screening, and reliable process design of systems dependent on off-stoichiometric redox-active metal oxides. We apply this method to a Ba x Sr 1-x FeO 3-δ test case. We find by systematically examining the performance of the CEF model fit with and without each innovation that all three innovations are necessary for an accurate fit. We determined that reduction enthalpy is higher and more sensitive to off-stoichiometry when the Sr fraction is large (139.5 and 185.3 kJ/mol O 2 for SrFeO 3 at δ = 0 and δ = 0.5, respectively vs. nearly constant 83 kJ/mol O 2 for BaFeO 3 ). However, the reduction entropy is mostly insensitive to Sr fraction, but highly dependent on δ suggesting larger contributions in the non-configurational entropy parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Timing the r -process Enrichment of the Ultra-faint Dwarf Galaxy Reticulum II

The ultra-faint dwarf galaxy Reticulum II (Ret II) exhibits a unique chemical evolution history, with ${72}_{-12}^{+10}$% of its stars strongly enhanced in r-process elements. We present deep Hubble Space Telescope photometry of Ret II and analyze its star formation history. As in other ultra-faint dwarfs, the color–magnitude diagram is best fit by a model consisting of two bursts of star formation. If we assume that the bursts were instantaneous, then the older burst occurred around the epoch of reionization, forming ~80% of the stars in the galaxy, while the remainder of the stars formed ~3 Gyr later. When the bursts are allowed to have nonzero durations, we obtain slightly better fits. The best-fitting model in this case consists of two bursts beginning before reionization, with approximately half the stars formed in a short (100 Myr) burst and the other half in a more extended period lasting 2.6 Gyr. Considering the full set of viable star formation history models, we find that 28% of the stars formed within 500 ± 200 Myr of the onset of star formation. The combination of the star formation history and the prevalence of r-process-enhanced stars demonstrates that the r-process elements in Ret II must have been synthesized early in its initial star-forming phase. We therefore constrain the delay time between the formation of the first stars in Ret II and the r-process nucleosynthesis to be less than 500 Myr. This measurement rules out an r-process source with a delay time of several Gyr or more, such as GW170817.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Time-integrated activity coefficient estimation for radionuclide therapy using PET and a pharmacokinetic model: A simulation study on the effect of sampling schedule and noise

Purpose: The aim of this study was to investigate the accuracy of PET-based treatment planning for predicting the time-integrated activity coefficients (TIACs). Methods: The parameters of a physiologically based pharmacokinetic (PBPK) model were fitted to the biokinetic data of 15 patients to derive assumed true parameters and were used to construct true mathematical patient phantoms (MPPs). Biokinetics of 150 MBq {sup 68}Ga-DOTATATE-PET was simulated with different noise levels [fractional standard deviation (FSD) 10%, 1%, 0.1%, and 0.01%], and seven combinations of measurements at 30 min, 1 h, and 4 h p.i. PBPK model parameters were fitted to the simulated noisy PET data using population-based Bayesian parameters to construct predicted MPPs. Therapy simulations were performed as 30 min infusion of {sup 90}Y-DOTATATE of 3.3 GBq in both true and predicted MPPs. Prediction accuracy was then calculated as relative variability v{sub organ} between TIACs from both MPPs. Results: Large variability values of one time-point protocols [e.g., FSD = 1%, 240 min p.i., v{sub kidneys} = (9 ± 6)%, and v{sub tumor} = (27 ± 26)%] show inaccurate prediction. Accurate TIAC prediction of the kidneys was obtained for the case of two measurements (1 and 4 h p.i.), e.g., FSD = 1%, v{sub kidneys} = (7 ± 3)%, and v{sub tumor} = (22 ± 10)%, or three measurements, e.g., FSD = 1%, v{sub kidneys} = (7 ± 3)%, and v{sub tumor} = (22 ± 9)%. Conclusions: {sup 68}Ga-DOTATATE-PET measurements could possibly be used to predict the TIACs of {sup 90}Y-DOTATATE when using a PBPK model and population-based Bayesian parameters. The two time-point measurement at 1 and 4 h p.i. with a noise up to FSD = 1% allows an accurate prediction of the TIACs in kidneys.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2010

Galactic Black Holes in the Hard State: A Multi-Wavelength View of Accretion and Ejection

The canonical hard state is associated with emission from all three fundamental accretion components: the accretion disk, the hot accretion disk corona and the jet. On top of these, the hard state also hosts very rich temporal variability properties (low frequency QPOs in the PDS, time lags, long time scale evolution). Our group has been working on the major questions of the hard state both observationally (with mult i-wavelength campaigns using RXTE, Swift, Suzaku, Spitzer, VLA, ATCA, SMARTS) and theoretically (through jet models that can fit entire SEDs). Through spectral and temporal analysis we seek to determine the geometry of accretion components, and relate the geometry to the formation and emission from a jet. In this presentation I will review the recent contributions of our group to the field, including the Swift results on the disk geometry at low accretion rates, the jet model fits to the hard state SEDs (including Spitzer data) of GRO J1655-40, and the final results on the evolution of spectral (including X-ray, radio and infrared) and temporal properties of elected black holes in the hard states. I will also talk about impact of ASTROSAT to the science objective of our group.

Kalemci↗

DOE OSTI2023

Uncertain characterization of reservoir fluids due to brittleness of equation of state regression

Equations of state (EoS) play a central role in modeling the phase equilibrium of fluid mixtures. Their parameterization involves fitting a model to experimental data, i.e., solving a nonlinear, non-convex, multivariate optimization problem. The latter requires one to select design variables, domains of definition for each variable, and weights assigned to individual measurements. We demonstrate that subjective choices of an optimization algorithm and an initial guess also impact the regression process. Consequently, EoS predictions are fundamentally uncertain even after the EoS tuning to a limited set of experimental data points. We demonstrate this observation for two hydrocarbon reservoir fluids, in which five properties of the heaviest carbon fraction are treated as design variables. While all the optimization algorithms and initial guesses match experimental data for the gas and liquid properties, the resulting EoS parameterizations lead to dramatically different predictions of the fluid’s thermophysical behavior in the unsampled pressure and temperature regions. In conclusion, we propose the probabilistic treatment of design variables to quantify the predictive uncertainty of the resulting fluid models.

15 GEOTHERMAL ENERGY↗

DOE OSTI2021

Surrogate modelling the Baryonic Universe II: On forward modelling the colours of individual and populations of galaxies

ABSTRACT Among the properties shaping the light of a galaxy, the star formation history (SFH) is one of the most challenging to model due to the variety of correlated physical processes regulating star formation. In this work, we leverage the stellar population synthesis model fsps, together with SFHs predicted by the hydrodynamical simulation IllustrisTNG and the empirical model universemachine, to study the impact of star formation variability on galaxy colours. We start by introducing a model-independent metric to quantify the burstiness of a galaxy formation model, and we use this metric to demonstrate that universemachine predicts SFHs with more burstiness relative to IllustrisTNG. Using this metric and principal component analysis, we construct families of SFH models with adjustable variability, and we show that the precision of broad-band optical and near-infrared colours degrades as the level of unresolved short-term variability increases. We use the same technique to demonstrate that variability in metallicity and dust attenuation presents a practically negligible impact on colours relative to star formation variability. We additionally provide a model-independent fitting function capturing how the level of unresolved star formation variability translates into imprecision in predictions for galaxy colours; our fitting function can be used to determine the minimal SFH model that reproduces colours with some target precision. Finally, we show that modelling the colours of individual galaxies with per cent-level precision demands resorting to complex SFH models, while producing precise colours for galaxy populations can be achieved using models with just a few degrees of freedom.

Chaves-Montero, Jonás (ORCID:0000000295534261)↗

DOE OSTI2017

A nondestructive method to estimate the chlorophyll content of Arabidopsis seedlings

Chlorophyll content decreases in plants under stress conditions, therefore it is used commonly as an indicator of plant health. Arabidopsis thaliana offers a convenient and fast way to test physiological phenotypes of mutations and treatments. But, chlorophyll measurements with conventional solvent extraction are not applicable to Arabidopsis leaves due to their small size, especially when grown on culture dishes. We provide a nondestructive method for chlorophyll measurement whereby the red, green and blue (RGB) values of a color leaf image is used to estimate the chlorophyll content from Arabidopsis leaves. The method accommodates different profiles of digital cameras by incorporating the ColorChecker chart to make the digital negative profiles, to adjust the white balance, and to calibrate the exposure rate differences caused by the environment so that this method is applicable in any environment. We chose an exponential function model to estimate chlorophyll content from the RGB values, and fitted the model parameters with physical measurements of chlorophyll contents. As further proof of utility, this method was used to estimate chlorophyll content of G protein mutants grown on different sugar to nitrogen ratios. Our method is a simple, fast, inexpensive, and nondestructive estimation of chlorophyll content of Arabidopsis seedlings. This method lead to the discovery that G proteins are important in sensing the C/N balance to control chlorophyll content in Arabidopsis.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

West Flank Coso FORGE: Magnetotelluric Inversion

The Coso Magnetotelluric (MT) dataset of which the West Flank FORGE MT data is a subset, was collected by Schlumberger / WesternGeco and initially processed by the WesternGeco GeoSolutions Integrated EM Center of Excellence in Milan, Italy. The 2011 data was based on 99 soundings that were centered on the West Flank geothermal prospect. The new soundings along with previous data from 2003 and 2006 were incorporated into a 3D inversion. Full impedance tensor data were inverted in the 1-3000 Hz range. The modelling report notes several noise sources, specifically the DC powerline that is 20,000 feet west of the survey area, and may have affected data in the 0.02 to 10 Hz range. Model cell dimensions of 450 x 450 x 65 feet were used to avoid computational instability in the 3D model. The fit between calculated and observed MT values for the final model run had an RMS value of 1.807. The included figure from the WesternGeco report shows the sounding locations from the 2011, 2006 and 2003 surveys.

15 GEOTHERMAL ENERGY↗

NASA NTRS1972

Automation of reliability evaluation procedures through CARE - The computer-aided reliability estimation program.

Description of an on-line interactive computer program called CARE (Computer-Aided Reliability Estimation) which can model self-repair and fault-tolerant organizations and perform certain other functions. Essentially CARE consists of a repository of mathematical equations defining the various basic redundancy schemes. These equations, under program control, are then interrelated to generate the desired mathematical model to fit the architecture of the system under evaluation. The mathematical model is then supplied with ground instances of its variables and is then evaluated to generate values for the reliability-theoretic functions applied to the model.

Mathur, F. P.↗

NASA NTRS2011

Thermal Properties and Evolution of a Coronal Cavity as Observed by the X-Ray Telescope on Hinode

Coronal cavities are voids in coronal emission often observed above high latitude filament channels. sometimes, these cavities have areas of bright x-ray emission in their centers (i.e. Hudson et al 1999). In this study, we use data from the x-ray Telescope (XRT) on Hinode to examine the thermal emission properties of a cavity observed during July 2008 that contains bright x-ray emission in its center. using ratios of XRT filters, we find evidence for elevated temperatures in the cavity center. The area of elevated temperature evolves from a ring-shaped structure at the be~inning of the observation, to an elongated structure two days later, finally appearing as a compact round source four days after the initial observation. We use a morphological model to fit the cavity emission, and find that a uniform structure running through the cavity does not fit the observations well. Instead, the observations are reproduced by modeling several short cavity "cores" with different parameters on different days. These changing core parameters may be due to some observed activity heating different parts of the cavity core at different times. We also find that core temperatures of 1.75 MK, 1.7 MK and 2.25 MK (for 19 July, 21 July and 23 July, respectively) in the model lead to structures that are consistent with the data, and that line-of-sight effects serve to lower the effective temperature derived from the filter ratio. page

Reeves, K. K.↗

NASA NTRS2011

Thermal Properties of A Solar Coronal Cavity Observed with the X-Ray Telescope on Hinode

Coronal cavities are voids in coronal emission often observed above high latitude filament channels. Sometimes, these cavities have areas of bright X-ray emission in their centers. In this study, we use data from the X-ray Telescope (XRT) on the Hinode satellite to examine the thermal emission properties of a cavity observed during July 2008 that contains bright X-ray emission in its center. Using ratios of XRT filters, we find evidence for elevated temperatures in the cavity center. The area of elevated temperature evolves from a ring-shaped structure at the beginning of the observation, to an elongated structure two days later, finally appearing as a compact round source four days after the initial observation. We use a morphological model to fit the cavity emission, and find that a uniform structure running through the cavity does not fit the observations well. Instead, the observations are reproduced by modeling several short cylindrical cavity "cores" with different parameters on different days. These changing core parameters may be due to some observed activity heating different parts of the cavity core at different times. We find that core temperatures of 1.75 MK, 1.7 MK and 2.0 MK (for July 19, July 21 and July 23, respectively) in the model lead to structures that are consistent with the data, and that line-of-sight effects serve to lower the effective temperature derived from the filter ratio.

Reeves, Katherine K.↗

NASA NTRS2022

Comparison of Likelihood Methods for Generalized Linear Mixed Models with Application to Quiet Supersonic Flights 2018 Data

Repeated measurement will be a feature of the survey data collected during the Quesst missionX-59 community response tests (CRT). Since each participant will report his or her categorical level of annoyance in response to multiple events, the responses from any single individual may be correlated with one another. Several models within the class of generalized linear mixed models (GLMM) are pertinent to the analysis of correlated categorical outcomes; the random intercept logistic regression model is one example. Both Bayesian and frequentist methods for fitting these models are available, with frequentist methods relying on some form of approximation (of either an integral or the integrand) that appears in the marginal likelihood function. Given several anticipated similarities of the X-59 CRT data to data collected during a past risk reduction, Quiet Supersonic Flights 2018 (QSF18), this short note is intended to create awareness. It documents an instance in which a reported population average dose-response relationship derived from QSF18 single event data was distorted by the integral approximation applied in likelihood-based methods. We review some of the available literature on the topic, compare the outputs of several different computational approaches implemented in available statistical software, and present simple corrective actions that may be useful during the Quesst mission.

dose-response model↗

DOE OSTI2019

Probing Galaxy assembly bias in BOSS galaxies using void probabilities

ABSTRACT We measure the void probability function (VPF) of galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS). The VPF provides complementary information to standard two-point statistics in that it is sensitive to galaxy bias in the most extreme underdensities in the cosmic web. Thus, the VPF is ideal for testing whether halo occupation of galaxies depends on large-scale density, an effect known as galaxy assembly bias. We find that standard HOD model – one parameterized by halo mass only – fit only to the two-point function, accurately predicts the VPF. Additionally, for HOD models where density dependence is explicitly incorporated, the best-fitting models fit to the combination of the correlation function and the VPF have zero density dependence. Thus, galaxy assembly bias is not a strong source of systematic uncertainty when modelling the clustering of massive galaxies.

Walsh, Kilian↗

NASA NTRS1992

Derivation of surface properties from Magellan altimetry data

The fit of the Hagfors model to the Magellan altimetry data provides a means to characterize the surface properties of Venus. However, the derived surface properties are only meaningful if the model provides a good representation of the data. The Hagfors model provides a good representation of the data. The Hagfors model is generally a realistic fit to surface scattering properties of a nadir-directed antenna such as the Magellan altimeter; however, some regions of the surface of Venus are poorly described by the existing model, according to the goodness of fit parameter provided on the ARCDR CD-ROMs. Poorly characterized regions need to be identified and fit to new models in order to derive more accurate surface properties for use in inferring the geological processes that affect the surface in those regions. We have compared the goodness of fit of the Hagfors model to the distribution of features across the planet, and preliminary results show a correlation between steep topographic slopes and poor fits to the standard model, as has been noticed by others. In this paper, we investigate possible relations between many classes of features and the ability of the Hagfors model to fit the observed echo profiles. In the regions that are not well characterized by existing models, we calculate new models that compensate for topographic relief in order to derive improved estimates of surface properties. Areas investigated to date span from longitude 315 through 45, at all latitudes covered by Magellan. A survey of those areas yields preliminary results that suggest that topographically high regions are well suited to the current implementation of the Hagfors model. Striking examples of such large-scale good fits are Alpha Regio, the northern edges of Lada Terra, and the southern edge of Ishtar Terra. Other features that are typically well fit are the rims of coronae such as Heng-O and the peaks of volcanos such as Gula Mons. Surprisingly, topographically low regions, such as the ubiquitous plains areas, are modeled poorly in comparison. However, this generalization has has exceptions: Lakshmi Planum is an elevated region that is not well fit compared to the rest of neighboring Ishtar, while the southern parts of topographically low Guinevere Planitia are characterized quite well by the Hagfors model. Features that are candidates for improved models are impact craters, coronae, ridges of significant scale, complex ridged terrains, moderate-sized mountains, and sharp terrain boundaries. These features are chosen because the goodness of fit is likely to be most affected either by departures from normal incidence angles or by sharp changes in terrain type within a single footprint. Most large features that are elevated with respect to their surroundings will suffer from steep slope effects, and smaller coronae and impact craters will probably suffer due to rapid changes in their appearance within a single footprint (10-20 km).

Lovell, Amy J.↗

NASA NTRS2012

A Peculiar Class of Debris Disks from Herschel/DUNES: A Steep Fall Off in the Far Infrared

Context. The existence of debris disks around old main sequence stars is usually explained by continuous replenishment of small dust grains through collisions from a reservoir of larger objects. Aims. We present photometric data of debris disks around HIP 103389 (HD199260), HIP 100350 (HN Peg, HD206860), and HIP 114948 (HD 219482), obtained in the context of our Herschel Open TIme Key Program DUNES (DUst around NEarby Stars). Methods. We used Herschel/PACS to detect the thermal emission of the three debris disks with a 30 sigma sensitivity of a few mJy at l00 micron and 160 micron. In addition, we obtained Herschel/PACS photometric data at 70 micron for HIP 103389. These observations are complemented by a large variety of optical to far-infrared photometric data. Two different approaches are applied to reduce the Herschel data to investigate the impact of data reduction on the photometry. We fit analytical models to the available spectral energy distribution (SED) data using the fitting method of simulated therma1 annealing as well as a classical grid search method. Results. The SEDs of the three disks potentially exhibit an unusually steep decrease at wavelengths >= 70 micron. We investigate the significance of the peculiar shape of these SEDs and the impact on models of the disks provided it is real. Using grain compositions that have been applied successfully for modeling of many other debris disks, our modeling reveals that such a steep decrease of the SEDs in the long wavelength regime is inconsistent with a power-law exponent of the grain size distribution -3.5 expected from a standard equilibrium collisional cascade. In contrast, a steep grain size distribution or, alternatively an upper grain size in the range of few tens of micrometers are implied. This suggests that a very distinct range of grain sizes would dominate the thermal. emission of such disks. However, we demonstrate that the understanding of the data of faint sources obtained with Herschel is still incomplete and that the significance of our results depends on the version of the data reduction pipeline used. Conclusions. A new mechanism to produce the dust in the presented debris disks, deviations from the conditions required for a standard equilibrium collisional cascade (grain size exponent of -3.5), and/or significantly different dust properties would be necessary to explain the potentially steep SED shape of the three debris disks presented.

Ertel, S.↗

DOE OSTI2018

Ion mass dependence of irradiation-induced damage accumulation in KTaO 3

Damage production and amorphization resulting from the interaction of medium-energy (from 40 to 480 keV) noble-gas ions (from He to Kr) with potassium tantalate (KTaO 3 ) are determined using ion channeling measurements. A disorder accumulation model has been fit to the maximum damage concentration versus ion fluence to extract the cross sections for direct-impact and defect-stimulated amorphization, and the results indicate that defect-stimulated amorphization is the dominant mechanism. These cross sections exhibit a strong dependence on the calculated cross sections for displacing lattice atoms, indicating a dominant contribution of nuclear interactions to the defect production and amorphization processes under the irradiation conditions used in this study. Furthermore, these experimental findings, along with the model fits, suggest that the difference in recoil spectra between He and the other heavier ions may be the main driving force for the decreased damage efficiency observed for He ions, which results in a reduced rate of damage accumulation.

36 MATERIALS SCIENCE↗

NASA NTRS2010

Analysis of Snow Bidirectional Reflectance from ARCTAS Spring-2008 Campaign

The spring 2008 Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) experiment was one of major intensive field campaigns of the International Polar Year aimed at detailed characterization of atmospheric physical and chemical processes in the Arctic region. A part of this campaign was a unique snow bidirectional reflectance experiment on the NASA P-3B aircraft conducted on 7 and 15 April by the Cloud Absorption Radiometer (CAR) jointly with airborne Ames Airborne Tracking Sunphotometer (AATS) and ground-based Aerosol Robotic Network (AERONET) sunphotometers. The CAR data were atmospherically corrected to derive snow bidirectional reflectance at high 1 degree angular resolution in view zenith and azimuthal angles along with surface albedo. The derived albedo was generally in good agreement with ground albedo measurements collected on 15 April. The CAR snow bidirectional reflectance factor (BRF) was used to study the accuracy of analytical Ross-Thick Li-Sparse (RTLS), Modified Rahman-Pinty-Verstraete (MRPV) and Asymptotic Analytical Radiative Transfer (AART) BRF models. Except for the glint region (azimuthal angles phi less than 40 degrees), the best fit MRPV and RTLS models fit snow BRF to within 0.05. The plane-parallel radiative transfer (PPRT) solution was also analyzed with the models of spheres, spheroids, randomly oriented fractal crystals, and with a synthetic phase function. The latter merged the model of spheroids for the forward scattering angles with the fractal model in the backscattering direction. The PPRT solution with synthetic phase function provided the best fit to measured BRF in the full range of angles. Regardless of the snow grain shape, the PPRT model significantly over-/underestimated snow BRF in the glint/backscattering regions, respectively, which agrees with other studies. To improve agreement with experiment, we introduced a model of macroscopic snow surface roughness by averaging the PPRT solution over the slope distribution function and by adding a simple model of shadows. With macroscopic roughness described by two parameters, the AART model achieved an accuracy of about plus or minus 0.05 with a possible bias of plus or minus 0.03 in the spectral range 0.4-2.2 micrometers. This high accuracy holds at view zenith angles below 55-60 degrees covering the practically important range for remote sensing applications, and includes both glint and backscattering directions.

Lyapustin, A.↗