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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Deep Learning Estimation of Daily Ground–Level NO 2 Concentrations from Remote Sensing Data

The limited number of nitrogen dioxide (NO 2 ) surface measurements calls for the development of highly accurate approaches to estimating surface NO 2 concentrations. In this study, we leverage a new satellite instrument, the TROPOspheric Monitoring Instrument (TROPOMI), along with other predictor variables, to estimate daily surface NO 2 concentrations over Texas in 2019. We use the deep convolutional neural network (Deep-CNN), an advanced deep learning algorithm, to obtain estimates and achieve a correlation coefficient (R) of 0.91, an index of agreement (IOA) of 0.95, and a mean absolute bias (MAB) of 1.75 ppb in surface NO 2 estimation. Additionally, we leverage a novel approach, SHapley Additive exPlanations (SHAP), to describe how Deep-CNN understands each predictor variable. The SHAP results show that the Deep-CNN model has an advanced understanding of the dataset, revealing that TROPOMI closely captures levels of NO 2 . In addition, we show the superiority of our Deep-CNN model at estimating surface NO 2 over other well-known machine learning and regression models in the field, including the support vector machines (SVM), random forest (RF), and multiple linear regression (MLR). Although SVM and RF show strong capabilities at estimating surface NO 2 concentrations, their accuracy is inferior to that of the Deep-CNN model, ranking second and third in model accuracy in this study. The MLR, however, shows a poor ability at NO 2 estimation and ranks last among all models. Furthermore, testing the impact of sample size on model performance, we also show that, compared to other models, Deep-CNN needs more samples to trigger its strength at surface NO 2 estimation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A best-practice guide to predicting plant traits from leaf-level hyperspectral data using partial least squares regression

Partial least squares regression (PLSR) modelling is a statistical technique for correlating datasets, and involves the fitting of a linear regression between two matrices. One application of PLSR enables leaf traits to be estimated from hyperspectral optical reflectance data, facilitating rapid, high-throughput, non-destructive plant phenotyping. This technique is of interest and importance in a wide range of contexts including crop breeding and ecosystem monitoring. The lack of a consensus in the literature on how to perform PLSR means that interpreting model results can be challenging, applying existing models to novel datasets can be impossible, and unknown or undisclosed assumptions can lead to incorrect or spurious predictions. We address this lack of consensus by proposing best practices for using PLSR to predict plant traits from leaf-level hyperspectral data, including a discussion of when PLSR is applicable, and recommendations for data collection. Further, we provide a tutorial to demonstrate how to develop a PLSR model, in the form of an R script accompanying this manuscript. This practical guide will assist all those interpreting and using PLSR models to predict leaf traits from spectral data, and advocates for a unified approach to using PLSR for predicting traits from spectra in the plant sciences.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1976

Ocean color spectra measured off the Oregon coast - Characteristic vectors

The ocean color spectrum is defined as the ratio of the spectrum of light upwelled from the sea to the spectrum of light incident on the sea surface. Ocean color spectra, observed from an airplane flown over waters off Oregon, are analyzed. The original spectra are resolved into fifty-five wavelength bands, each 5 nm wide. The shapes of these spectra are parameterized by, and shown to be accurately recoverable from, their first four principal components. These components are the scalar projections of each spectrum on the first four characteristic vectors of the sample covariance matrix. Regression equations are found with which phytoplankton pigment concentration and water transparency may be estimated as linear functions of the principal components. Pigment concentration estimates thus obtained are imprecise. The poor fit is at least partly due to the inappropriateness of the linear regression model and the neglect of other optically important substances typically present in sea water.

Mueller, J. L.↗
NASA NTRS1996

Intramuscular Pressure Measurement During Locomotion in Humans

To assess the usefulness of intramuscular pressure (IMP) measurement for studying muscle function during gait, IMP was recorded in the soleus and tibialis anterior muscles of ten volunteers during, treadmill walking, and running using transducer-tipped catheters. Soleus IMP exhibited single peaks during late-stance phase of walking (181 +/- 69 mmHg, mean +/- S.E.) and running (269 +/- 95 mmHg). Tibialis anterior IMP showed a biphasic response, with the largest peak (90 +/- 15 mmHg during walking and 151 +/- 25 mmHg during running) occurring shortly after heel strike. IMP magnitude increased with gait speed in both muscles. Linear regression of soleus IMP against ankle joint torque obtained by a dynamometer in two subjects produced linear relationships (r = 0.97). Application of these relationships to IMP data yielded estimated peak soleus moment contributions of 0.95-165 Nm/Kg during walking, and 1.43-2.70 Nm/Kg during running. IMP results from local muscle tissue deformations caused by muscle force development and thus, provides a direct, practical index of muscle function during locomotion in humans.

Ballard, Ricard E.↗
NASA NTRS2021

Expanding the application of soil moisture monitoring systems through regression-based transformation

Relative to other geophysical variables, soil moisture (SM) estimates derived from land surface models (LSMs) and land data assimilation systems (LDAS) are difficult to transfer between platforms and applications. This difficulty stems from the highly model-dependent nature of LSM SM estimates and differences in the vertical support of discretized SM values. As a result, operational SM estimates generated by one LSM (or LDAS) cannot generally be directly applied to a hydrologic monitoring or forecast system designed around a second LSM. This lack of transferability is particularly problematic for LDAS applications, where the time, expertise, and computational resources required to generate an operational LDAS analysis cannot be practically duplicated for every LSM-specific application. Here, we develop a set of simple regression tools for translating SM estimates between LSMs and multiple LDAS analyses. Results demonstrate that simple multivariate linear regression - utilizing independent variables based on multi-layer and temporally lagged SM estimates - can significantly improve upon baseline transformation approaches using direct percentile matching. The proposed regression approaches are effective for both the LSM-to-LSM and LDAS-to-LDAS transformation of multi-layer SM percentiles. Application of this approach will expand the utility of existing, high-quality (but LSM-specific) operational sources of SM information like the NASA Soil Moisture Active Passive Level-4 Soil Moisture product.

Soil Moisture↗
DOE OSTI2022

An ℓ 0 ℓ 2 -norm regularized regression model for construction of robust cluster expansions in multicomponent systems

In this work we introduce ℓ 0 ℓ 2 -norm regularization and hierarchy constraints into linear regression for the construction of cluster expansions to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The ℓ 2 -norm regularization is used to suppress intrinsic data noise, while the ℓ 0 -norm is used to penalize the number of nonzero elements in the solution. The hierarchy relation between clusters imposes relevant physics and is naturally included by the MIQP paradigm. As such, sparseness and cluster hierarchy can be well optimized to obtain a robust, converged set of effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of ℓ 0 ℓ 2 -norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation, convergence speed, and the reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional ℓ 1 -norm regularized cluster expansion models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Constraining primordial non-Gaussianity from DESI quasar targets and Planck CMB lensing

We detect the cross-correlation between 2.7 million DESI quasar targets across 14,700 deg 2 (180 quasars deg -2 ) and Planck 2018 CMB lensing at ~30σ. We use the cross-correlation on very large scales to constrain local primordial non-Gaussianity via the scale dependence of quasar bias. The DESI quasar targets lie at an effective redshift of 1.51 and are separated into four imaging regions of varying depth and image quality. We select quasar targets from Legacy Survey DR9 imaging, apply additional flux and photometric redshift cuts to improve the purity and reduce the fraction of unclassified redshifts, and use early DESI spectroscopy of 194,000 quasar targets to determine their redshift distribution and stellar contamination fraction (2.6%). Due to significant excess large-scale power in the quasar autocorrelation, we apply weights to mitigate contamination from imaging systematics such as depth, extinction, and stellar density. We use realistic contaminated mocks to determine the greatest number of systematic modes that we can fit, before we are biased by overfitting and spuriously remove real power. We find that linear regression with one to seven imaging templates removed per region accurately recovers the input cross-power, f NL and linear bias. As in previous analyses, our fNL constraint depends on the linear primordial non-Gaussianity bias parameter, b Φ = 2(b - p)δ c assuming universality of the halo mass function. We measure f NL = -26 +45 -40 with p = 1.6 (f NL = -18 +29 -27 with p = 1.0), and find that this result is robust under several systematics tests. Future spectroscopic quasar cross-correlations with Planck lensing can tighten the f NL constraints by a factor of 2 if they can remove the excess power on large scales in the quasar auto power spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The relationship between urinary selenium levels and risk of gestational diabetes mellitus: A nested case–control study

Background Selenium (Se) is an essential trace element for the human body. Serum Se and urinary Se are also biomarkers to assess Se exposure status. However, studies focusing on the association between urinary Se and the risk of gestational diabetes mellitus (GDM) are rare. Objective To investigate the association between urinary Se and the risk of GDM. Methods A nested case–control study based on a prospective birth cohort in Wuhan, China, which focuses on the effects of prenatal environmental factors exposure on pregnant women and children’s health was conducted. Two hundred and twenty-six cases and 452 controls were included. Maternal urine samples were collected before GDM diagnosis, and the urinary Se levels were determined. We assessed the association of urinary Se with GDM by conditional logistic regression with maternal urinary Se level as a categorical variable, and estimated the association between Se and glucose levels by multiple linear regression. The potential modifier roles of maternal age and fetal sex have also been assessed. Results Lower urinary level of Se was significantly associated with a higher risk of GDM (OR = 2.35 for the tertile 1, 95% CI:1.36-4.06; adjusted OR = 1.79 for the tertile 2, 95%CI:1.09-2.95; p for trend = 0.01). Fetal sex had an interaction with Se in the association with GDM. The association was more pronounced among pregnant women with female fetuses than with male fetuses. Discussion Our study suggested a significant negative association between urinary Se and the risk of GDM, and this association may vary depending on the fetal sex.

Liu, Yuanxia↗
NASA NTRS1987

Relationship of Thematic Mapper simulator data to leaf area index of temperate coniferous forests

Regional relationships between remote sensing data and the leaf area index (LAI) of coniferous forests were analyzed using data acquired by an Airborne Thematic Mapper. Eighteen coniferous forest stands with a range of projected leaf area index of 0.6-16.1 were sampled from an environmental gradient in moisture and temperature across west-central Oregon. Spectral radiance measurements to account for atmospheric effects were acquired above the canopies from a radiometer mounted on a helicopter. A strong positive relationship was observed between LAI of closed canopy forest stands and the ratio of near-infrared and red spectral bands. A linear regression based on LAI explained 83 percent of the variation in the ratio of the atmospherically corrected bands. A log-linear equation fit the asymptotic characteristic of the relationship better, explaining 91 percent of the variance. The positive relationship is explained by a strong asymptotic inverse relationship between LAI and red radiation and a relatively flat response between LAI and near-infrared radiation.

Peterson, David L.↗
DOE OSTI2024

Performance Comparison of Machine Learning Models for Ultrasonic Nondestructive Evaluation of Alkali-Silica Reaction in Concrete

Alkali-silica reaction (ASR) causes concrete degradation, leading to cracking, rebar corrosion, and reduced structural integrity, which raises safety concerns. Ultrasonic nondestructive evaluation (NDE) effectively assesses concrete properties and monitors ASR progression. However, its deployment and analysis require specialized expertise and subjective interpretation. As computational power increases, artificial intelligence (AI) and machine learning (ML) algorithms are increasingly being used to automate NDE data analysis across various industries for AI-assisted automation. Regulatory agencies are adapting to this technological shift, prompting a need to evaluate current ML technologies’ capabilities and limitations in assessing concrete material properties and damage. This report presents a comparative analysis of four ML regression models for predicting concrete material damage induced by ASR expansion using long-term ultrasonic data monitoring. The models investigated include linear regression (LR), support vector regression (SVR), shallow neural networks (NN), and deep neural networks (DNN). LR, SVR, and shallow NN models use features extracted from ultrasonic signals, whereas the DNN model processes time-domain ultrasonic signals and frequency spectra directly. The study systematically compared the models’ performance from various perspectives, including model input, prediction performance, and generalization ability. The findings indicate significant variability in model performance, with some ML algorithms achieving very high or very low prediction accuracy depending on the preprocessing and feature engineering (extraction and selection) applied. Key insights include the observation that shallow ML models (LR, SVR, and shallow NNs) require meticulous preprocessing and feature extraction to achieve high accuracy. In contrast, the DNN model, although it bypasses the need for feature engineering, necessitates extensive preprocessing to mitigate noise and computational demands. The SVR model emerged as the top performer among the shallow models, and the DNN model exhibited superior performance on specific datasets but struggled with generalization across specimens from different batches. Additionally, the SVR model is sensitive to temperature variations, whereas the DNN model is robust in this regard. Using recurrent neural networks is recommended for future ASR expansion prediction studies. Recurrent neural networks’ inherent ability to capture temporal dependencies and long-term patterns makes them well suited for analyzing sequential ultrasonic monitoring data. Overall, the results and conclusions of this study could provide insights into the capabilities and effectiveness of ML when applied to ultrasonic NDE data and help identify best practices for using ML for ultrasonic NDE of concrete material properties.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Error quantification of the Arrhenius blending rule for viscosity of hydrocarbon mixtures

Six hundred and seventy-five measurements of dynamic viscosity and density have been used to assess the prediction error of the Arrhenius blending rule for kinematic viscosity of hydrocarbon mixtures. Major trends within the data show that mixture complexity–binary to hundreds of components—and temperature are more important determinants of prediction error than differences in molecular size or hydrogen saturation between the components of the mixtures. Over the range evaluated, no correlation between prediction error and mole fractions was observed, suggesting the log of viscosity truly is linear in mole fraction, as indicated by the Arrhenius blending rule. Mixture complexity and temperature also impact molar volume and its prediction. However, a linear regression between the two model errors explains less than 20% of the observed variation, indicating that mixture viscosity and/or molar volume are not linear with respect to temperature and/or mixture complexity. Extensive discussion of the intermolecular forces and the geometric arrangement of molecules and vacancies in liquids, which ultimately determines its viscosity, is brought into context with the implicit approximations behind the Arrhenius blending rule. The complexity of this physics is not compatible with a simple algebraic correction to the model. However, sufficient data is now available to determine confidence intervals around the prediction of fuel viscosity based on its component mole fractions and viscosities. At -40°C, when all identified components are pure molecules the modeling error is 13.2% of the predicted (nominal) viscosity times the root mean square of the component mole fractions.

10 SYNTHETIC FUELS↗
DOE OSTI2022

In Silico Prediction of the Toxicity of Nitroaromatic Compounds: Application of Ensemble Learning QSAR Approach

In this work, a dataset of more than 200 nitroaromatic compounds is used to develop Quantitative Structure–Activity Relationship (QSAR) models for the estimation of in vivo toxicity based on 50% lethal dose to rats (LD 50 ). An initial set of 4885 molecular descriptors was generated and applied to build Support Vector Regression (SVR) models. The best two SVR models, SVR_A and SVR_B, were selected to build an Ensemble Model by means of Multiple Linear Regression (MLR). The obtained Ensemble Model showed improved performance over the base SVR models in the training set (R 2 = 0.88), validation set (R 2 = 0.95), and true external test set (R 2 = 0.92). The models were also internally validated by 5-fold cross-validation and Y-scrambling experiments, showing that the models have high levels of goodness-of-fit, robustness and predictivity. The contribution of descriptors to the toxicity in the models was assessed using the Accumulated Local Effect (ALE) technique. The proposed approach provides an important tool to assess toxicity of nitroaromatic compounds, based on the ensemble QSAR model and the structural relationship to toxicity by analyzed contribution of the involved descriptors.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1983

Fitting of satellite and in-situ ocean surface temperatures Results for polymode during the winter of 1977-1978

For the period considered, December 1977 through February 1978, bivariate Gaussian discriminant function cloud identification revealed that more than 93 percent of the 8-km resolution GOES infrared pixels were cloud contaminated. Cloud-free in-situ calibration points were distributed in nonrandom groups; this resulted in systematic errors when using least squares techniques. Surfaces and regression lines were least squares fitted between satellite and in-situ data; use was also made of differences and ratios. The best results were achieved with a regression in the form of the infrared radiative transfer equation; but this was no better than + or - 0.9 K. Because of extensive cloudiness, the linear regressions were seldom useful, and temperature ratios with + or - 1.3 K experimental errors best represent the applicability of GEOS data to sea surface temperatures.

Maul, G. A.↗
NASA NTRS1972

Application of stepwise multiple regression techniques to inversion of Nimbus 'IRIS' observations.

Exploratory studies with Nimbus-3 infrared interferometer-spectrometer (IRIS) data indicate that, in addition to temperature, such meteorological parameters as geopotential heights of pressure surfaces, tropopause pressure, and tropopause temperature can be inferred from the observed spectra with the use of simple regression equations. The technique of screening the IRIS spectral data by means of stepwise regression to obtain the best radiation predictors of meteorological parameters is validated. The simplicity of application of the technique and the simplicity of the derived linear regression equations - which contain only a few terms - suggest usefulness for this approach. Based upon the results obtained, suggestions are made for further development and exploitation of the stepwise regression analysis technique.

Ohring, G.↗
NASA NTRS2021

Dealing with Ion LET Uncertainties: An Application of Generalized Linear Models

Although most SEE rate estimation methods presume a fit to SEE cross section vs. LET, fitting SEE data is challenging because the data are not compatible with the assumptions of many common fitting techniques (e.g. linear regression. The difficulty of fitting such data is compounded when the LET of the ion responsible for an SEE is uncertain. We modify a Generalized Linear Model SEE data fitting methodology to accommodate uncertain LET and apply the method to the problem of backside heavy-ion SEE testing to demonstrate the utility of the method, explore the dependence of systematic errors that arise from improper treatment of LET uncertainty and develop guidelines for minimizing such systematic errors when proper treatment is not possible. Additional applications are suggested and assessed for suitability of treatment by the model.

Single-event effects↗
DOE OSTI2021

Development of a Filtered CFD-DEM Drag Model with Multiscale Markers Using an Artificial Neural Network and Nonlinear Regression

Here, the accuracy of coarse-grained Euler-Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved sub-grid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macro-scale markers using fine grid Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) simulations. The traditional non-linear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen-Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R 2 values. The utilization of the gas inlet velocity as an additional macro-scale marker reduced the errors by up to 55.3% in the tested cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2006

On the Observed Changes in Upper Stratospheric and Mesospheric Temperatures from UARS HALOE

Temperature versus pressure or T(p) time series from the Halogen Occultation Experiment (HALOE) on the Upper Atmosphere Research Satellite (UARS) have been extended and re-analyzed for the period of 1991-2005 and for the upper stratosphere and mesosphere in 10-degree wide latitude zones from 60S to 60N. Even though sampling from a solar occultation experiment is somewhat limited, it is shown to be quite adequate for developing both the seasonal and longer-term variations in T(p). Multiple linear regression (MLR) techniques were used in the re-analyses for the seasonal and the significant interannual, solar cycle (SC-like or decadal-scale), and linear trend terms. A simple SC-like term of 11-yr period was fitted to the time series residuals after accounting for the seasonal and interannual terms. Highly significant SC-like responses were found for both the upper mesosphere and the upper stratosphere. The phases of these SC-like terms were checked for their continuity with latitude and pressure-altitude, and in almost all cases they are directly in-phase with that of standard proxies for the solar flux variations. The analyzed, max minus min, responses at low latitudes are of order 1 K, while at middle latitudes they are as large as 3 K in the upper mesosphere. Highly significant, linear cooling trends were found at middle latitudes of the middle to upper mesosphere (about -2 K/decade), at tropical latitudes of the middle mesosphere (about -1 K/decade), and at 2 hPa (or order -1 K/decade).

Remsberg, Ellis E.↗
NASA NTRSDate not supplied

A Combined Al-Mg/Pb-Pb Age of the Solar System

Astrophysical models of planet formation and protoplanetary disk evolution demand precise and accurate timing of the sequence of events in the solar nebula, relative to a time t=0, usually taken to be during the short epoch of CAI (Ca-rich, Al-rich inclusion) formation. Most CAIs formed withlive26Al (mean-life τ26= 1.034 Myr [1]), with an abundance 26Al/27Al ≈ (26Al/27Al)SS= 5.23 × 10-5[2]. We adopt this as the widespread level of 26Al in the solar nebula at t=0. Assuming spatial homogeneity of 26Al, an inclusion that had less 26Al, (26Al/27Al)0, formed a time Δt26= τ26ln[(26Al/27Al)SS/ (26Al/27Al)0] after t=0.These ages are typical precise to within ±0.1 Myr. Igneous bulk meteorites and inclusions can be relatively dated by the Al-Mg chronometer, but only ifΔt26<6 Myr. The Pb-Pb system is useful as a longer relative chronometer. It yields absolute ages tPb using 207Pb/206Pb, 206Pb/204Pb, and 238U/235U ratios measured indifferent portions of a sample, assuming certain half-lives [4]. These absolute ages are uncertain to within ±9 Myr due to uncertainties in the 235U half-life[3], but times of formation ΔtPb= tCAI–tPb relative to t=0, are more precise(±0.5Myr),iftCAI can be found. Here, tCAI means the Pb-Pb age that would be measured in CAIs using the half-lives the community typically uses, if they achieved isotopic closure at t=0. Unfortunately, direct Pb-Pb dating of CAIs has not definitively determined tCAI. Based on four CAIs with canonical (26Al/27Al)0,[5,6] found tPb= 4567.30 ± 0.16 Myr. No other CAI ages with measured 238U/235U have been reported in the refereed literature, but there are hints of other CAIs with ages tPb= 4568.0 ± 0.2 Myr [7] and tPb= 4568.3 ± 0.2 Myr [8].It is unclear whether anyof these igneous type B CAIs isotopically closed at t=0 or represents tCAI. Instead of measurements, we advocate finding tCAI by minimizing the discrepancies between the Al-Mg and Pb-Pb chronometers. Assuming Δt26=ΔtPb, we find the implied t’CAI= tPb+Δt26, then define t*CAIas the weighted mean of the t’CAI. t*CAIis the best guess for the Pb-Pb age of t=0; the assumption of homogeneity is justified if the t’CAI cluster within errors around t*CAI. This statistical approach is similar to, but improves on, that of[9]. We find t*CAI= 4568.73 ± 0.16 Myr. Below we discuss our methodology and the implications of this age for CAIs, 1.4 Myr older than the reported and typically used age 4567.30±0.16 Myr. Methods: We base our estimate of t*CAIon five achondrites for which published (26Al/27Al)0and Pb-Pb ages exist: the quenched angrites D’Orbigny, Sahara 99555 (SAH 99555), and Northwest Africa (NWA) 1670; the pseudo-eucrite Asuka 881394; and the inner disk achondrite. All are “NC” (non-carbonaceous) achondrites that likely cooled quickly enough that the Al-Mg and Pb-Pb systems achieved isotopic closure simultaneously. We also considered the “CC” (carbonaceous chondrite-like) achondrites NWA 2796 and NWA 6704, butdo not include them in our fit. Al-Mg and Pb-Pb seem not to have closed simultaneously, possibly because formation in the outer disk from volatile-rich composition led to slower cooling. Of the 8 chondrules from NWA 5697 measured by [20,21], we also consider the 4 for which 238U/235U was measured: 2-C1, 5-C2, 3-C5, 11-C1.Depending on their post-formation thermal histories, the Al-Mg and Pb-Pb systems in chondrules may or may not have closed simultaneously. Table 1: (26Al/27Al)0, Pb-Pb ages of selected samplesSample(26Al/27Al)0/ 10-6RefPb-PbRefD’Orbigny3.98±0.15104563.43±0.19♮10-12SAH 995553.64±0.18104563.88±0.2712NWA16705.92±0.59104564.39±0.24*10Asuka 88139413.1±0.5613-154564.98±0.1715NWA 73253.03±0.14164563.4±2.616NWA 27963.94±0.16174562.89±0.5917NWA 67043.03±0.14184562.76±0.26192-C17.56±1.53204567.57±0.56*215-C27.04±1.51204567.54±0.52*213-C58.85±1.83204566.20±0.63*2111-C15.55±1.84204565.84±0.72*21*regression based on one subset of data points ♮weighted mean of two datasets Pb-Pb ages are proportional to the intercept of the line formed by linear regression of 207Pb/206Pb vs. 206Pb/204Pb data from various washes, leachates and residues of acid dissolution of a sample. Because contamination by terrestrial or primordial Pb is pervasive, some fractions must be excluded from regressions to ensure a fit with acceptable mean squares weighted deviation (MSWD). Usually points are excluded based on low [Pb], or low 206Pb/204Pb ratio(low radiogenic component), with single outliers identified [11,12,15,16,17]. In the starred examples (Table 1)and the case of 3 CAI Pb-Pb ages [5], up to half the points were excluded solely because did not fit a pre-determined line. This approach is vulnerable to confirmation bias and produces fits with low MSWD and too-low Pb-Pb age uncertainty. Regressing the same data points as [10], were produce the Pb-Pb age of NWA 1670 of 4564.39±0.24 Myr. But selecting other combinations of data points, other, equally valid, isochrons yield ages from 4563.77±0.21 Myr to 4564.64±0.23 Myr. Similar arguments apply to the Pb-Pb isochrons built by [21] for chondrules 2-C1 (we find 4567.33±0.44 to 4567.85±0.46 Myr), 5-C2 (4566.84±0.53 to 4567.70±0.44 Myr), 3-C5 (4565.84±0.54to 4567.04±0.54)and 11-C1 (4565.36±0.51 to 4565.74±0.45 Myr). Our adopted ages for these and NWA 1670 are listed in Table 2.Table 2. tCAI estimated from various components, using our regressions for the chondrules & NWA 1670.SampleΔt26(Myr)tPb(Myr)t’CAI(Myr)D’Orbigny5.05±0.044563.43±0.194568.48±0.19SAH 995555.14±0.054563.88±0.274569.02±0.27NWA16704.64±0.104564.21±0.634568.85±0.67Asuka 8813943.81±0.044564.98±0.174568.79±0.17NWA 73255.33±0.054563.4±2.64568.7±2.6NWA 27965.06±0.044562.89±0.594567.95±0.59NWA 67045.29±0.134562.76±0.264568.05±0.292-C12.00±0.214567.59±0.704569.59±0.725-C22.07±0.224567.23±0.914569.30±0.933-C51.84±0.214566.44±1.124568.28±1.1411-C12.32±0.344565.52±0.664567.84±0.73achondrite4568.72±0.16chondrules4568.76±0.58combined4568.73±0.16A weighted average of the five NC achondrites(or just D’Orbigny, SAH 99555 and Asuka 881394)yields t*CAI= 4568.72 ± 0.16Myr. All are consistent with this value to within 1.8σ, and MSWD=1.5. Including the 4 U-corrected chondrules, t*CAI= 4568.73± 0.16Myrwith MSWD=1.66, which is statistically significant. All chondrules and NC achondrites are consistent with this to within 1.8σ, (Figure 1).Figure 1. Al-Mg formation times after t=0 vs. Pb-Pb ages. The five NC achondrites and four chondrules are consistent with a Pb-Pb age of t=0 of 4568.7 Myr. Discussion: The data from achondrites and chondrules are consistent with a single Pb-Pb age at t=0, justifying the assumption of 26Al homogeneity. The age, 4568.7 Myr, is ≈1.4 Myr older than the commonly accepted Pb-Pb age of CAIs that formed with canonical 26Al/27Al at t=0 [3]. Others have interpreted the discrepancy to signify 26Al heterogeneity in the CAI-forming region[5,21]. We suggest instead that CAIs were exposed to transient heating events that reset the Pb-Pb system without disturbing the Al-Mg system. Notably, chondrules typically experienced transient heating at these times in the nebula [22]. If so, direct measurements of CAIs will not yield as reliable a Pb-Pb age of t=0 as statistical approaches like this and that of [9].References:[1] Auer et al. 2009. [2] Jacobsen, B et al. 2008, EPSL 272, 353-364. [3] Tissot, Fet al. 2017, GCA 213, 593-617.[4] Villa, I et al. 2016, GCA 172, 387-392.[5] Amelin, Y et al. 2010, EPSL 300, 343-350.[6] Connelly, Jet al. 2012, Science 338, 651.[7] Bouvier, Aet al. 2011, LPICo 1639, 9054. [8] Bouvier, Aand Wadhwa, M2010, Nat Geosci 3, 637-641.[9] Nyquist, Let al. 2009, GCA 73, 5115-5136.[10] Schiller et al. 2015. [11] Wadhwa & Brennecka 2012. [12] Tissot et al. 2017. [13] Nyquist et al. 2003. [14] Wadhwa et al. 2009. [15] Wimpenny et al. 2019, GCA 244, 478-501.[16] Koefoed et al. 2016, GCA 183, 31-45. [17] Bouvier, A et al. 2011, GCA 75, 5310-5323. [18] Sanborn, Met al. 2019, GCA 245, 577-596. [19] Amelin, Yet al. 2019, GCA 245, 628-642.[20] Bollard, Jet al. 2017, Sci Adv 3 ,e1700407. [21] Bollard, Jet al. 2019, GCA 260, 62-83.[22] Villeneuve, J et al. 2009, Science 325, 985

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