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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 721 records · Page 40

Automated Probabilistic Finite Element Model Calibration Tool Based on Uncertainty Quantification and Machine Learning

Qualification and certification of safety critical parts is a hurdle to the adoption of metallic additively manufactured components for aerospace vehicle applications. Challenges include variability in part properties due to inconsistent defect distribution and microstructure. Understanding of the process through finite element modeling (FEM), and process control through in-situ monitoring, may result in significant improvements; however, solutions useful to manufacturers will require large volumes of data and automated data utilization. Toward this end, a generalizable automated FEM calibration paradigm is developed. This paradigm leverages existing and novel tools from machine learning and uncertainty quantification to enable the automatic calibration of FEMs without requiring prior knowledge of the model performance across input parameter space, including meshing and solver settings, which can require time consuming manual model probing or cause noisy and inconsistent predictions. The result is a probabilistic distribution of calibrated and validated FEM input parameters targeting measured data.

Additive manufacturing model calibration finite el↗

Uncertainty Quantification Enabled by Automatic Differentiation for Hydrodynamic Simulation of Shock‐to‐Detonation Transition in High Explosives

Quantifying the effects of uncertainty in a reactive burn model on the run-to-detonation time in high explosives (HEs) provides a robust methodology for assessing the probability of an HE failing the IHE qualification standard. Moreover, uncertainty quantification helps evaluate whether the model calibration accurately represents data outside the calibration set. This study uses a specialized hydrodynamic simulation code for modeling detonation to determine the run-to-detonation time of the HE PBX 9502 for various impact velocities. To quickly approximate uncertainties in the model, a surrogate was constructed using a Taylor series expansion centered at the mean of the input parameters. To obtain the sensitivities required for constructing the Taylor series, HYP-percomplex Automatic Differentiation (HYPAD) was implemented. HYPAD is a methodology for infusing existing codes with automatic differentiation capabilities by augmenting variables with one or more imaginary units to compute step-size independent partial derivatives. These derivatives are accurate to machine precision with respect to the implemented numerical algorithm, meaning their accuracy reflects that of the underlying method (e.g., integration or discretization schemes). Using reduced order modeling techniques, the mean and standard deviation of the run-to-detonation time of a shock within PBX 9502 were computed for a number of initial impact velocities. A weighted least squares regression was then performed to obtain a best fit curve and prediction interval for the computed statistics. Historical data points from explosively driven wedge tests were utilized to validate the prediction interval, ensuring its reliability in predicting future outcomes. With this prediction interval and a known safety constraint curve, the most probable point of failure and the probability of failure for the HE PBX 9502 were determined.

97 MATHEMATICS AND COMPUTING↗

Data-Driven Modeling and Correction of Vehicle Dynamics

We develop a data-driven framework for learning and correcting nonautonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need for data-driven correction. Moreover, nonautonomous dynamics are governed by time-dependent control inputs, which pose challenges in learning predictive models directly from temporal snapshot data. To address these, we reformulate the vehicle dynamics via a local parameterization of the time-dependent inputs, yielding a modified system composed ofa sequence of local parametric dynamical systems. Here, we approximate these parametric systems using two complementary approaches. First, we employ the dimension reduction and interpolation in parameter space (DRIPS) methodology to construct efficient linear surrogate models, equipped with lifted observable spaces and manifold-based operator interpolation. This enables data-efficient learning of vehicle models whose dynamics admit accurate linear representations in the lifted spaces. Second, for more strongly nonlinear systems, we employ flow map learning (FML), a deep neural network (DNN) approach that approximates the parametric evolution map without requiring special treatment of nonlinearities. We further extend FML with a transfer-learning-based model correction procedure, enabling the correction of misspecified prior models using only a sparse set of high-fidelity or experimental measurements, without assuming a prescribed form for the correction term. Through a suite of numerical experiments on unicycle, simplified bicycle, and slip-based bicycle models, we demonstrate that DRIPS offers robust and highly data-efficient learning of nonautonomous vehicle dynamics, while FML provides expressive nonlinear modeling and effective correction of model-form errors under severe data scarcity.

data-driven modeling↗

Uncertainty in Simulating Wheat Yields Under Climate Change

Projections of climate change impacts on crop yields are inherently uncertain1. Uncertainty is often quantified when projecting future greenhouse gas emissions and their influence on climate2. However, multi-model uncertainty analysis of crop responses to climate change is rare because systematic and objective comparisons among process-based crop simulation models1,3 are difficult4. Here we present the largest standardized model intercomparison for climate change impacts so far. We found that individual crop models are able to simulate measured wheat grain yields accurately under a range of environments, particularly if the input information is sufficient. However, simulated climate change impacts vary across models owing to differences in model structures and parameter values. A greater proportion of the uncertainty in climate change impact projections was due to variations among crop models than to variations among downscaled general circulation models. Uncertainties in simulated impacts increased with CO2 concentrations and associated warming. These impact uncertainties can be reduced by improving temperature and CO2 relationships in models and better quantified through use of multi-model ensembles. Less uncertainty in describing how climate change may affect agricultural productivity will aid adaptation strategy development and policymaking.

exhaust gases↗

Critical Infrastructure Decision-Making under Long-Term Climate Hazard Uncertainty: The Need for an Integrated, Multidisciplinary Approach

U.S. critical infrastructure assets are often designed to operate for decades, and yet long-term planning practices have historically ignored climate change. With the current pace of changing operational conditions and severe weather hazards, research is needed to improve our ability to translate complex, uncertain risk assessment data into actionable inputs to improve decision-making for infrastructure planning. Decisions made today need to explicitly account for climate change – the chronic stressors, the evolution of severe weather events, and the wide-ranging uncertainties. If done well, decision making with climate in mind will result in increased resilience and decreased impacts to our lives, economies, and national security. We present a three-tier approach to create the research products needed in this space: bringing together climate projection data, severe weather event modeling, asset-level impacts, and contextspecific decision constraints and requirements. At each step, it is crucial to capture uncertainties and to communicate those uncertainties to decision-makers. While many components of the necessary research are mature (i.e., climate projection data), there has been little effort to develop proven tools for long-term planning in this space. The combination of chronic and acute stressors, spatial and temporal uncertainties, and interdependencies among infrastructure sectors coalesce into a complex decision space. By applying known methods from decision science and data analysis, we can work to demonstrate the value of an interdisciplinary approach to climate-hazard decision making for longterm infrastructure planning.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Design and execution of a verification, validation, and uncertainty quantification plan for a numerical model of left ventricular flow after LVAD implantation

Left ventricular assist devices (LVADs) are implantable pumps that act as a life support therapy for patients with severe heart failure. Despite improving the survival rate, LVAD therapy can carry major complications. Particularly, the flow distortion introduced by the LVAD in the left ventricle (LV) may induce thrombus formation. While previous works have used numerical models to study the impact of multiple variables in the intra-LV stagnation regions, a comprehensive validation analysis has never been executed. The main goal of this work is to present a model of the LV-LVAD system and to design and follow a verification, validation and uncertainty quantification (VVUQ) plan based on the ASME V&V40 and V&V20 standards to ensure credible predictions. The experiment used to validate the simulation is the SDSU cardiac simulator, a bench mock-up of the cardiovascular system that allows mimicking multiple operation conditions for the heart-LVAD system. The numerical model is based on Alya, the BSC’s in-house platform for numerical modelling. Alya solves the Navier-Stokes equation with an Arbitrary Lagrangian-Eulerian (ALE) formulation in a deformable ventricle and includes pressure-driven valves, a 0D Windkessel model for the arterial output and a LVAD boundary condition modeled through a dynamic pressure-flow performance curve. The designed VVUQ plan involves: (a) a risk analysis and the associated credibility goals; (b) a verification stage to ensure correctness in the numerical solution procedure; (c) a sensitivity analysis to quantify the impact of the inputs on the four quantities of interest (QoIs) (average aortic root flow $Q^{avg}_{Ao}$, maximum aortic root flow $Q^{max}_{Ao}$, average LVAD flow $Q^{avg}_{VAD}$, and maximum LVAD flow $Q^{max}_{VAD}$; (d) an uncertainty quantification using six validation experiments that include extreme operating conditions. Numerical code verification tests ensured correctness of the solution procedure and numerical calculation verification showed a grid convergence index (GCI)95% <3.3%. The total Sobol indices obtained during the sensitivity analysis demonstrated that the ejection fraction, the heart rate, and the pump performance curve coefficients are the most impactful inputs for the analysed QoIs. The Minkowski norm is used as validation metric for the uncertainty quantification. It shows that the midpoint cases have more accurate results when compared to the extreme cases. The total computational cost of the simulations was above 100 [core-years] executed in around three weeks time span in Marenostrum IV supercomputer. This work details a novel numerical model for the LV-LVAD system, that is supported by the design and execution of a VVUQ plan created following recognised international standards. We present a methodology demonstrating that stringent VVUQ according to ASME standards is feasible but computationally expensive.

59 BASIC BIOLOGICAL SCIENCES↗

Evaluating Coastal Landscape Response to Sea-Level Rise in the Northeastern United States - Approach and Methods

The U.S. Geological Survey is examining effects of future sea-level rise on the coastal landscape from Maine to Virginia by producing spatially explicit, probabilistic predictions using sea-level projections, vertical land movement rates (due to isostacy), elevation data, and land-cover data. Sea-level-rise scenarios used as model inputs are generated by using multiple sources of information, including Coupled Model Intercomparison Project Phase 5 models following representative concentration pathways 4.5 and 8.5 in the Intergovernmental Panel on Climate Change Fifth Assessment Report. A Bayesian network is used to develop a predictive coastal response model that integrates the sea-level, elevation, and land-cover data with assigned probabilities that account for interactions with coastal geomorphology as well as the corresponding ecological and societal systems it supports. The effects of sea-level rise are presented as (1) level of landscape submergence and (2) coastal response type characterized as either static (that is, inundation) or dynamic (that is, landform or landscape change). Results are produced at a spatial scale of 30 meters for four decades (the 2020s, 2030s, 2050s, and 2080s). The probabilistic predictions can be applied to landscape management decisions based on sea-level-rise effects as well as on assessments of the prediction uncertainty and need for improved data or fundamental understanding. This report describes the methods used to produce predictions, including information on input datasets; the modeling approach; model outputs; data-quality-control procedures; and information on how to access the data and metadata online.

terrain↗

Comparison of Entry Descent and Landing Aerodynamic Databases with Uncertainty Quantification Developed Using Machine Learning Techniques

When developing the aerodynamic databases for use in trajectory simulations, it is important to develop a system of metrics to qualify which aerodynamic models are best to use. Since aerodynamics are just one input into trajectory simulations, the results of these simulations do not reflect on the quality of the aerodynamic database used. This means that aerodynamic database comparisons must be done offline. While traditional metrics that focus on mean/nominal predictions are a good first step, more robust estimates of the prediction interval become important as more focused uncertainty models are developed. We explore the limitations of evaluating aerodynamic models based purely on nominal-centered response surfaces. Before elaborating and evaluating metrics based on distributed models, the value of evaluating prediction interval and confidence interval are discussed to conclude that prediction intervals are more relevant to the use of trajectory analysis. Several metrics to evaluate the prediction interval are introduced with a focus on the standard calibration metric. Finally, we compare candidate models using both mean and distributed metrics. A finalized candidate model developed using state of the art machine learning methods is compared to a baseline model developed using traditional aerodynamic database modeling techniques.

Aerodynamic Database↗

Toward a more realistic representation of surface albedo in NASA CERES-derived surface radiative fluxes

Accurate multidecadal radiative flux records are vital to understand Arctic amplification and constrain climate model uncertainties. Uncertainty in the NASA Clouds and the Earth’s Radiant Energy System (CERES)-derived irradiances is larger over sea ice than any other surface type and comes from several sources. The year-long Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition in the central Arctic provides a rare opportunity to explore uncertainty in CERES-derived radiative fluxes. First, a systematic and statistically robust assessment of surface shortwave and longwave fluxes was conducted using in situ measurements from MOSAiC flux stations. The CERES Synoptic 1degree (SYN1deg) product overestimates the downwelling shortwave flux by +11.40 Wm –2 and underestimates the upwelling shortwave flux by –15.70 Wm –2 and downwelling longwave fluxes by –12.58 Wm –2 at the surface during summer. In addition, large differences are found in the upwelling longwave flux when the surface approaches the melting point (approximately 0°C). The biases in downwelling shortwave and longwave fluxes suggest that the atmosphere represented in CERES is too optically thin. The large negative bias in upwelling shortwave flux can be attributed in large part to lower surface albedo (–0.15) in satellite footprint relative to surface sensors. Additionally, the results show that the spectral surface albedo used in SYN1deg overestimates albedo in visible and mid-infrared bands. A series of radiative transfer model perturbation experiments are performed to quantify the factors contributing to the differences. The CERES-MOSAiC broadband albedo differences (approximately 20 Wm –2 ) explain a larger portion of the upwelling shortwave flux difference than the spectral albedo shape differences (approximately 3 Wm –2 ). In addition, the differences between perturbation experiments using hourly and monthly MOSAiC surface albedo suggest that approximately 25% of the sea ice surface albedo variability is explained by factors not correlated with daily sea ice concentration variability. Biases in net shortwave and longwave flux can be reduced to less than half by adjusting both albedo and cloud inputs toward observed values. The results indicate that improvements in the surface albedo and cloud data would substantially reduce the uncertainty in the Arctic surface radiation budget derived from CERES data products.

54 ENVIRONMENTAL SCIENCES↗

Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.

Autoencoders↗

Probabilistic Structural Evaluation of Uncertainties in Radiator Sandwich Panel Design

The Jupiter Icy Moons Orbiter (JIMO) Space System is part of the NASA's Prometheus Program. As part of the JIMO engineering team at NASA Glenn Research Center, the structural design of the JIMO Heat Rejection Subsystem (HRS) is evaluated. An initial goal of this study was to perform sensitivity analyses to determine the relative importance of the input variables on the structural responses of the radiator panel. The desire was to let the sensitivity analysis information identify the important parameters. The probabilistic analysis methods illustrated here support this objective. The probabilistic structural performance evaluation of a HRS radiator sandwich panel was performed. The radiator panel structural performance was assessed in the presence of uncertainties in the loading, fabrication process variables, and material properties. The stress and displacement contours of the deterministic structural analysis at mean probability was performed and results presented. It is followed by a probabilistic evaluation to determine the effect of the primitive variables on the radiator panel structural performance. Based on uncertainties in material properties, structural geometry and loading, the results of the displacement and stress analysis are used as an input file for the probabilistic analysis of the panel. The sensitivity of the structural responses, such as maximum displacement and maximum tensile and compressive stresses of the facesheet in x and y directions and maximum VonMises stresses of the tube, to the loading and design variables is determined under the boundary condition where all edges of the radiator panel are pinned. Based on this study, design critical material and geometric parameters of the considered sandwich panel are identified.

Kuguoglu, Latife↗

Explainable discrepancy checker and diagnosis for digital Twin-based supervisory control system

By virtually representing a physical object and process, a digital twin (DT) enables optimal autonomous operations by combining classical and novel frameworks in sensors, state predictions, and multi-input/multi-output systems. A DT’s values depend on how well models estimate quantities of interest and on how uncertainty is handled. Moreover, DTs often combine physics-based and data-driven models with mixed fidelities, where classical uncertainty quantification (UQ) struggles with many sources of uncertainty and real-time constraints. Here, this work presents a UQ-based discrepancy checking and diagnosis tool for a DT-based supervisory control system. The tool is developed using metadata from an automated DT development process to learn correlations between sources of uncertainties and outcomes. During operation, it compares predictions with measurements, attributes discrepancies to dominant sources, and recommends parameter and configuration updates. We verify the workflow on a synthetic temperature-control problem and deploy it on a virtual Thermal Energy Delivery System, reducing mismatch and improving control robustness.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

"Hidden" hydrothermal technical potential & technoeconomics: Revealing permeability & fluids with more data

Historical hydrothermal estimates have largely relied on temperature or heat flow estimates ignoring the need for natural flowing fluids. More accurate hydrothermal estimates require some indication of permeability and fluids that naturally exist in the subsurface. This paper describes a novel approach that includes proxies of permeability and fluids in hydrothermal estimates by leveraging the relatively data-rich Great Basin. Specifically, nameplate capacities (megawatts) of operating geothermal plants, negative (0 megawatt) locations and 48 geophysical and geologic features are used to used in eXtreme Gradient Boosting (XGBoost) regression to make hydrothermal capacity predictions. Additionally, this work inputs the XGBoost-based hydrothermal predictions into the Renewable Energy Potential (reV) model to quantify technical capacity, its uncertainty and techno-economics. Compared to historical hydrothermal estimates, these predictions adhere to the 37 operating geothermal plants and negative locations. We present a method for subsampling the negative sites to bring the labels into balance that uses the geologic domain knowledge to proportionally represent negatives. Overall, the distributions of the hydrothermal technical capacity and the site levelized cost of energy are respectively much tighter, lower and more accurate than the previous estimates for the Great Basin, as they include geological and geophysical surrogates for permeability and fluids. Percentile (50th and 90th, median and high estimate, respectively) models provide bookends for these metrics.

13 HYDRO ENERGY↗

Boron Coordination in Multicomponent Glasses: Analytical Models and Machine Learning With Uncertainty

Borosilicate glasses are extensively used in a variety of applications from kitchenware to nuclear waste immobilization due to the strong network formed by the Si-O-B bond that makes it resistant to chemical corrosion and gives it a low thermal expansion. Boron, however, exists in both trigonal BO3 and tetrahedral BO4 bonds in glass systems, which impacts the chemical durability and thermal resistance of the glass, amongst other properties. Boron coordination (N4), or the ratio of the amount of BO4 to BO3 within a glass, may aid in predicting these properties but is difficult to derive without experimental data due to the complexity of impacts from varied glass compositions and processing factors. For this reason, compositional models have been developed to predict boron coordination, but the models typically include a limited number of glass components. To help fill this gap in the models, in this work, a diverse multicomponent glass dataset of 809 glasses is compiled from a literature search, and then a number of analytical and machine learning (ML) models are trained on the dataset. Previously developed modified Bernstein and modified Du Stebbins analytical models were fitted to update parameters with the new dataset. Then, partially Bayesian neural networks, Gaussian process regressor, and heteroskedastic deterministic neural networks were evaluated. The ML models examined all have different strategies to overcome the potential for overfitting as a result of a limited training dataset, and return results that account for model uncertainty, which can be valuable for understanding model reliability. For the first time, cooling rate is introduced as an input parameter for ML models, showing consistent improvements in performance and solidifying the importance of including parameters outside of composition alone for N4 prediction. The machine learning models examined here show promise in accurate predictions of boron coordination in borosilicate glasses, all achieving R2 values of 0.91.

boron coordination↗

Tapsolver: A Python Package For The Simulation And Analysis Of Tap Reactor Experiments

TAPsolver is a python package, which automates TAP simulation and analysis routines. TAPsolver is built around the python packages FEniCS and Dolfin-Adjoint, which help take advantage of model adjoints to provide automatic derivatives. TAPsolver is flexible, with reaction mechanisms and rate constants that can be set through input files that allow users to take advantage of the different functionalities, which include sensitivity analyses, parameter optimization and uncertainty quantification.

Yonge, Adam↗

NUCLEI (SciDAC-4) effort at The University of Tennessee, Knoxville

This Report summarizes the accomplishments of NUCLEI researchers at The University of Tennessee, Knoxville (UTK) and those supported via subcontracts at the University of North Carolina at Chapel Hill (UNC) and Iowa State University (ISU). The SciDAC-4 NUCLEI collaboration had the goal to advance the computation of atomic nuclei and to make reliable predictions including uncertainty estimates for observables of interest. These goals were achieved by developing improved nuclear interactions and currents that are input to the computations, and by advancing the algorithms and techniques used for computing nuclear observables of interest. The computed results advanced our understanding of how nuclei work; they helped to guide and interpret experiments at existing low-energy nuclear physics facilities, the Facility for Rare Isotope Beams, Jefferson Laboratory, and neutrino experiments. In addition, predictions were made that await confrontation with experimental results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

LOCOMOTIVES - Comprehensive Impact and Cost Assessment Framework of Carbon Lowering Approaches for the US Rail Freight System

The goal of this project is to develop a tool to aid railroads and other stakeholders assess and approach the decarbonization of freight rail operations by identifying new, viable low-carbon energy storage and conversion systems for future locomotive systems and how they should be deployed on the existing US freight rail network. In the first quarter, the project focused on collecting data, establishing a simulation workflow, and engaging industry through the creation of the Industry Advisory Board (IAB). In the second quarter, the project focused on selecting fuel pathways and powertrain technologies, setting performance targets, conducting a techno-economic analyses, and developing the simulation framework that would serve as the backbone of the future toolhead. The third quarter involved developing an industry-oriented interactive dashboard powered by a five-step sequential framework, as well as holding industry advisory board meetings as per the initial technology-to-market plan. In the remaining project quarters, the NUFRIEND dashboard were fine-tuned with the help of IAB member feedback and in-depth scenario analyses were conducted to support the techno-economic analysis of energy sources. Additionally, dashboard documentation, project insights, and open-source code on GitHub were prepared and released. Throughout the project, the team completed testing and analysis of all model components, integrated all initial test scenarios, and conducted stakeholder engagement. Lower-carbon drop-in fuels can be deployed as admixtures and are considered uniform across the network at a desired penetration rate, while hydrogen and battery-electric technology deployment poses a more complex problem as they require significant investments to be made in the siting of refueling/charging facilities and the replacement of locomotive fleets. Thus, strategies for locating and sizing refueling/charging facilities on a railroad’s network to meet their energy demands were developed to inform deployment decisions. To address this challenge, the Northwestern University Freight Rail Infrastructure & Energy Network Decarbonization (NUFRIEND) framework presents a five-step sequential framework to select O-D paths, locate facilities, reroute flows, size facilities, and evaluate the deployment for alternative energy sources that require locomotive powertrains to be converted and new refueling infrastructure to be deployed. The NUFRIEND Framework is an industry-oriented tool for simulating the deployment of new energy technologies across the US freight rail network. The framework provides a comprehensive network-level optimization and scenario simulation tool for decarbonizing the freight rail sector, addressing the uncertainties surrounding technological developments by supporting sensitivity analyses for different operational and technological parameters through a transparent and flexible input module. It offers practical alternatives to diesel locomotives and can be applied for any railroad considering the specific network structure and freight demand, outputting evaluation metrics for the associated emissions and costs relative to diesel operations. A number of relevant simulation scenarios were run and analyzed for key insights on the value of different alternative technologies for freight rail decarbonization. The project developments and findings have been presented at numerous conferences and events.

08 HYDROGEN↗

Results of thermal environment measurements on the thermal cannister experiment and get away special enclosure

Because the OSS-1 pallet contained a variety of instruments with irregular surface geometry and properties which limited predictability, the total absorbed flux on thermal canister radiators was measured to determine heat rejection capability. The instrumentation and sensor cup design and locations for the thermal canister experiment are illustrated. Graphs show flux sensor history in hot and coal orbits. Kapton erosion is also considered. Results show that the flux levels measured in all STS attitudes are higher than predictions. In cold and moderate attitudes, flight results are a factor of two to three higher than predicts. In hot attitude, much better agreement occurred. It is concluded that in cold or moderate attitudes other sources may be contributing to added inputs (albedo, Earth shine, shuttle background). In hot attitude, smaller differences could be attributed to coatings assumptions or calculation uncertainty.

Ollendorf, S.↗