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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 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Online Parameter Estimation Methods for Adaptive Cruise Control Systems

Modeling Adaptive Cruise Control (ACC) vehicles enables the understanding of the impact of these vehicles on traffic flow. In this work, two online methods are used to provide real time system identification of ACC enabled vehicles. The first technique is a recursive least squares (RLS) approach, while the second method solves a nonlinear joint state and parameter estimation problem via particle filtering (PF). We provide a parameter identifiability analysis for both methods to analytically show that the model parameters are not identifiable using equilibrium driving. The accuracy and computational runtime of the online methods are compared to a commonly used offline simulation-based optimization (i.e., batch optimization) approach. The methods are tested on synthetic data as well as on empirical data collected directly from a 2019 model year ACC vehicle using data from sensors that are part of the stock ACC system. The online methods are scalable and provide comparable accuracy to the batch method. RLS runs in real time and is two orders of magnitude faster than the batch method for modest sized (e.g., 15 min) datasets. The particle filter also runs in real- time, and is also suitable in streaming applications in which the datasets can grow arbitrarily large.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2018

A Comparison of Different Methods of Separation of Continuous Overlapping Spectral Lines

Several methods of separation of continuous overlapping spectral lines are compared. In the majority of methods, the profile of each line is modeled by a Gaussian or Lorentzian, and total measured spectrum z is processed. Number of lines N and their parameters are usually estimated by the method of derivatives; however, the differentiation of noisy spectrum z causes large errors. To improve the differentiation accuracy, it is proposed to use smoothing splines. In the Fourier-self-deconvolution method, apodization (artificial truncation of the interferogram) is used to resolve overlapping lines, which makes it possible to resolve lines, but at the expense of a significant decrease in their widths. In this work, reducing the widths of lines is not used for their resolution, but rather, true line profiles are reconstructed by minimizing the residual functional with the modified coordinate-descent method using the decremental-constraint technique, and also, for comparison, with the Nelder–Mead simplex method. In the Manoilov method, the parameters of lines (peaks) are determined from convolutions of spectrum derivatives with individual peaks. In that method, the notion of the degree of overlap has been also introduced. In this work, we introduce a generalized degree of overlap for the case in which the amplitudes, widths, and spacings between neighboring lines are different. Numerical illustrations are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Unified Geometric Multigrid Algorithm for Hybridized High-Order Finite Element Methods

In this paper, we consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable to any locally conservative hybridized finite element method including multinumerics with different hybridized methods in different parts of the domain. For these methods, the linear system involves only the unknowns residing on the mesh skeleton, and constructing intergrid transfer operators is therefore not trivial. The key to our geometric multigrid algorithm is the physics-based energy-preserving intergrid transfer operators which depend only on the fine scale DtN maps. Thanks to these operators, we completely avoid upscaling of parameters and no information regarding subgrid physics is explicitly required on coarse meshes. Moreover, our algorithm is agglomeration-based and can straightforwardly handle unstructured meshes. We perform extensive numerical studies with hybridized mixed methods, hybridized discontinuous Galerkin methods, weak Galerkin methods, and hybridized versions of interior penalty discontinuous Galerkin methods on a range of elliptic problems including subsurface flow through highly heterogeneous porous media. We compare the performance of different smoothers and analyze the effect of stabilization parameters on the scalability of the multigrid algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The interplay of machine learning-based resonant anomaly detection methods

Abstract Machine learning-based anomaly detection (AD) methods are promising tools for extending the coverage of searches for physics beyond the Standard Model (BSM). One class of AD methods that has received significant attention is resonant anomaly detection, where the BSM physics is assumed to be localized in at least one known variable. While there have been many methods proposed to identify such a BSM signal that make use of simulated or detected data in different ways, there has not yet been a study of the methods’ complementarity. To this end, we address two questions. First, in the absence of any signal, do different methods pick the same events as signal-like? If not, then we can significantly reduce the false-positive rate by comparing different methods on the same dataset. Second, if there is a signal, are different methods fully correlated? Even if their maximum performance is the same, since we do not know how much signal is present, it may be beneficial to combine approaches. Using the Large Hadron Collider (LHC) Olympics dataset, we provide quantitative answers to these questions. We find that there are significant gains possible by combining multiple methods, which will strengthen the search program at the LHC and beyond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗
DOE OSTI2025

A Comparison of Machine Learning Methods of Association Tested on Dense Nodal Arrays

The association of phase picks to form events is one of the fundamental components of seismology. Large and dense sensor networks, such as >1000 geophone arrays (and distributed acoustic sensing), offer unique challenges in association due to the vast numbers of observations and high likelihood of errant picks. In addition, the large number of stations can greatly increase the time it takes to perform the association. For this reason, machine learning (ML) methods might provide a more optimal method of association for such networks. In this work, we examine how well ML methods (e.g., Gaussian mixture model association, PhaseLink, and Graph Earthquake Neural Interpretation Engine) can incorporate dense seismic arrays into regional networks and how well they handle the increasing numbers of stations. Here, we test their capabilities on two dense seismic deployments, one within Rock Valley Nevada (52 nodes and a 9-station sparse local network), and the LArge-n Seismic Survey in Oklahoma dense nodal array (>1800 vertical-component geophones). Processing data from these two different styles of dense seismic deployments allows testing of how the ML algorithms can merge array data with a broader regional network, how they deal with poorly picked phases, and how they handle anthropogenic noise. We compare the ML-associated bulletins to those obtained using the Rapid Earthquake Association and Location algorithm, a more traditional method of association. We find that there are very small differences in results between the methods for small networks (<100 stations) with low pick rates. For large networks (>1000), there are enough errant picks that some of the ML methods start to create false events out of noise. We also find that the ML methods vary in computation time significantly but are all faster than the traditional method tested here.

58 GEOSCIENCES↗
DOE OSTI2017

Optical-based spectroscopic methods for measuring chemical, optical, and physical properties of thin polymer waveguide films

Non-destructive optical-based spectroscopic methods are needed for analyzing “real world” devices that consist of thin polymer waveguide films. Many applications (e.g., sensors, microelectronics, optics, and biomedical applications, etc.) utilize thin polymer waveguide films, and non-destructive characterization methods based on Fourier transform (FT)-plasmon waveguide spectroscopy (PWR) and scanning angle (SA) Raman spectroscopy are used to extract optical, physical, and chemical properties simultaneously. The FT-PWR method measures reflected light at polymer waveguide interface as both the incident frequency (wavelength) and incident angle are scanned. This method uses p- and s-polarized light to simultaneously extract the polymer waveguide thickness and apparent anisotropic indices of refraction. Polystyrene waveguide films ranging from 360 to 800 nm are used to demonstrate the method and it has an average 0.4% relative error when compared to profilometry and atomic force microscopy measurements. SA Raman spectroscopy is used to measure mixed waveguide polymer films consisting of polystyrene-block-poly(methyl methacrylate) and homopolymer poly(methyl methacrylate) (PS-b-PMMA:PMMA), and poly(2-vinylnapthalene)-block-poly(methyl methacrylate) (P2VN-b-PMMA). PMMA homopolymer is added to the PS-b-PMMA solutions to vary the chemical composition. The chemical composition of each mixed film is quantified (SA Raman peak amplitude ratios) and averaged over all incident angles and is termed the Raman amplitude ratio (rps). This parameter is used to calculate the refractive index of each mixed waveguide polymer film. The refractive index is an input parameter for sum square electric field (SSEF) calculations, which are used to model SA Raman spectra as a function of incident angle to extract the film thickness. The mixed polymer waveguide film thicknesses ranged from 495 to 971 nm, and the SA Raman spectroscopy method has an average 5% difference between the values determined by profilometry. The SA Raman spectroscopy method developed for mixed polymer waveguide films is used to measure the chemical composition and extract interface locations in bilayer and trilayer films consisting of PMMA/PS or PMMA/PS/PMMA, respectively. The rps value is averaged over angle ranges corresponding to waveguide mode 0 and waveguide mode 1 for the bilayer and trilayer films, respectively. Six multilayer films are analyzed and their total thicknesses range from 330 to 1260 nm. Iterative SSEF calculations are used to model the SA Raman spectra as a function of incident angle, and the best fit to the experimental data is used to extract the total thickness and interface location(s). The method has an axial spatial resolution of 7 to 80 nm and provides comparable values to films measured by profilometry with an average 8% and 7% difference for the bilayer and trilayer films, respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Evaluation of methods to determine strain ranges for use in SMT design curves

This report describes progress on developing a new method for creep-fatigue design that reduces over conservatism, improves the treatment of elastic follow up effects, and simplifies the design procedure, when compared to the existing ASME Boiler and Pressure Vessels Code, Section III, Division 5 method for creep-fatigue design. Specifically, this report describes the development of one of the three components of the new creep-fatigue design method: a design analysis method to represent the steady cyclic strain range in a component in elevated temperature service. The method developed here uses an elastic perfectly plastic (EPP) analysis with a pseudoyield stress selected to bound the width of the steady state stress-strain hysteresis loop. The report also provides a description of the in-development creep-fatigue design method, including a plan to complete the method by developing design curves and a method to account for stress multiaxiality.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2019

A Test of ASTM Methods E1245-03 and E562-11 in Calculating the Volume Fraction of Carbides in a U-10Mo Foil

Volume fraction measurements of carbides in DU-10Mo castings and foils were performed as part of a round robin study aimed at ensuring characterization efforts by multiple laboratories were yielding consistent results. Three of the four labs employed an automatic image analysis method to determine volume fraction of carbides in the metal and reported results around 2%. The other laboratory used a grid intercept count method and reported a fraction percentage of above 5%, about 3% higher than the other labs. At LANL, the method ASTM E1245-03, Determining the Inclusion or Second-Phase Constituent Content of Metals by Automatic Image Analysis was employed with a result of 2.02 ± .26%. There was a need to resolve the large discrepancy in volume fraction measurements reported from the round robin participant that used the grid intercept method. To do this, the grid intercept method outlined in ASTM E562-11, Determining Volume Fraction by Systematic Manual Point Count was also performed on the exact set of micrographs already analyzed by image analysis software at LANL. Calculations carried out following the manual point count method reported a percentage of 2.2 ± .6% similar to the result yielded by the automated image analysis method. Explanations for discrepancies in the results of the two methods are proposed.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Initial Development of an Improved Creep-Fatigue Design Method that Avoids the Separate Evaluation of Creep and Fatigue Damage and Eliminates the Requirement for Stress Classification

This report describes a method for capturing the effect of strain range, temperature, hold time, and elastic follow up on the cyclic life of a material undergoing uniaxial load. Developing design correlations of this type requires methods for extrapolating experimental data as a function of hold time and follow up factor. Various extrapolation methods are developed and discussed here and recommendations are developed for the final approaches to be adopted for design use. The report also describes comparisons between the new creep-fatigue design method, described here, and current creep-fatigue design methods in the ASME Boiler and Pressure Vessel Code and associated nuclear Code Cases. These comparisons demonstrate several advantages of the new method: it is easier to execute and is less over conservative than many current approaches. This report, along with a companion on extending these results to multiaxial load and on combining load cycles, represents the accumulation of several years of work on the development of this new approach to creep-fatigue design, combining an elastic perfectly plastic analysis method with simplified model tests measuring the effect of elastic follow up on creep-fatigue cyclic life. The conclusions to this report describe a path forward to developing the required design data for high temperature advanced reactor structural materials and guiding the adoption of the new method in the ASME Boiler and Pressure Vessel Code and related standards.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Glycolate Analysis in Tank 22: Developing and Testing Analytical Methods for the Savannah River Site Liquid Waste System

Researchers developed and tested a range of techniques to support a low mg/L Limit of Quantitation (LOQ) of glycolate in radioactive Tank 22 waste solution by Ion Chromatography (IC) and by proton NMR. For the IC method, Dionex OnGuard II cartridges were tested as a means of removing alkali earth and transition metals that can interfere during ion chromatography applications especially when analyzing for low-concentration, chelating analytes. Additionally, concentrations of nitrate in the raw Tank 22 sample (5,000 to 10,000 mg/L) were managed by using reasonable levels of sample dilution. The resulting IC performance quality was enhanced by improving the baseline, increasing sensitivity [Limit of Quantitation (LOQ) of 12 mg/L and Limit of Detection (LOD) of 4.0 mg/L], and resolving analytes into well-defined Gaussian peaks when using the Dionex OnGuard II H⁺ cartridges to remove matrix interferences. High concentrations of nitrate limited the performance of the IC method. To achieve an acceptable baseline, samples with high nitrate content require more dilution, resulting in higher detection limits. Tests on samples with higher concentrations of nitrate (Tank 30 and 32 supernate with approximately 150000 mg/L nitrate) suggested that IC detection limits for glycolate in these samples would be > 500 mg/L. Thus, an LOQ of 12 mg/L is not feasible by this IC method on evaporator feed samples. An alternative method of glycolate analysis, using proton nuclear magnetic resonance (H NMR), was developed by the research team. In initial tests, the H NMR technique provided reasonable quantitation of glycolate in Tank 22 conditions by direct observation of the liquid. The H NMR method may provide improved detection limits for solutions with higher nitrate concentrations. We recommend further development of this analysis for high nitrate LWS samples such as evaporator feed and evaporator drop tank content. A method for pretreatment of samples using crystalline silicotitanate (CST) was developed and tested. The objective of the pretreatment was to facilitate analysis of samples with higher levels of radioactivity. The pretreatment did not influence the glycolate concentration in solution, and the pretreatment is projected to reduce Cs 137 activity in a sample by a factor of 16,200. The double strike CST pretreatment was demonstrated and would allow milliliters of higher activity samples to be transferred from the Shielded Cells and handled in a containment unit for glycolate analysis. The various studies validated IC and H NMR methods for glycolate analysis, defined the range of applicability, and demonstrated key supporting analytical protocols. Based on the results, high quality glycolate analysis of Tank 22 is feasible down to approximately 12 mg/L, with the potential for broader applicability of the methods to other conditions in the Savannah River Site Liquid Waste System (LWS).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

An efficient method to estimate the probability density of seismic Green's functions

We present a computationally efficient method to approximate the probability distribution of seismic Green's functions given the uncertainty of an Earth model. The method is based on the Karhunen-Loève (KL) theorem and an approximation of the Green's function (or seismogram) covariance. Using Monte Carlo (MC) simulations as a control case, we demonstrate that our KL-based method can accurately reproduce a probability distribution of seismograms that results from an uncertain Earth model for a MC-derived seismogram covariance. We then describe a method to estimate the covariance of the seismograms resulting from those Earth models that is not based on MC simulations. We use the estimated Green's function covariance in conjunction with our KL-based method to produce a Green's function probability distribution, and compare that distribution to a Green's function probability distribution produced using a MC finite difference method. We find that the Green's function probability distribution approximated using our KL-based method generally mimics that produced using the MC simulations, especially for direct-arriving body waves. However the accuracy of the KL-based method generally decreases for later times in the simulated Green's function distribution.

58 GEOSCIENCES↗
DOE OSTI2021

Harnessing Condorcet Methods to Improve Decision-making Based on Ranked Data

Decision-makers must often choose between multiple alternatives based on their relative merits across a variety of criteria. These multiple-criteria decision-making (MCDM) problems must be approached in an objective, measurable, and transparent fashion to obtain well-supported outcomes. The challenge of using sets of ranked data to identify the optimal choice is not unlike the challenge of using ranked ballots to identify the winner of an election in a preference voting system. As such, the methods of rank aggregation used in elections can be applied to help resolve MCDM problems. Previous research into the design of elections and ballots has yielded many algorithms with well-understood properties. A subset of these, called Condorcet methods, reliably identify the “Condorcet winner,” if it exists, giving the result that would defeat any other in a pairwise comparison. That, in addition to several other desirable qualities, makes Condorcet methods like the Schulze method, Ranked Pairs, and Copeland’s method, effective and scalable means for tackling MCDM problems. These rank aggregation methods have been implemented in JavaScript functions for incorporation into a web-based MCDM decision tool. These algorithms can be applied in a wide variety of contexts (for example, determining the “best” environmental remediation method or selecting a subcontractor) to facilitate effective decision-making. The performance of the JavaScript Condorcet prototype tool was compared across the implemented algorithms and with both a non-Condorcet rank aggregation method as well as an implementation of the Simple Multi-Attribute Rating Technique (SMART) algorithm.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Benchmark Analysis for the Optical Dilatometry Method Using Silicon Carbide Temperature Monitors

The main objective of this project was to conduct a benchmark analysis for the optical dilatometry method by using NSUF’s SiC temperature monitors: two (2) SiC temperature monitors provided by NSUF’s BSU-8242 experiment and two (2) SiC temperature monitors provided by NSUF’s GE-Hitachi experiment. Per the BSU-8242 experiment, KGT-3597 and KGT-3591 had a design temperature of 400°C and an exposure of 3 dpa. Per the GE-Hitachi experiment, KGT-3341 and KGT-3336 had a design temperature of 290°C +/- 50°C and an exposure of 0.5–1 dpa. The KGT-3336 SiC monitor was split into two pieces during the decontamination process, making the dilatometry method the only way to analyze both those pieces. The BSU-8242 monitors revealed peak irradiation temperatures under the design temperature, and the GE-Hitachi monitors revealed peak irradiation temperatures within the design temperature range. The optical dilatometry method measured the peak irradiation temperature of BSU-8242 KGT-3597 to be 330°C, while the resistivity method measured the peak irradiation temperature of BSU-8242 KGT-3591 to be 320°C +/- 20°C. The optical dilatometry method measured the peak irradiation temperatures of the pieces of GE-Hitachi KGT-3336 to be 260°C (for the larger piece) and 220°C (for the smaller piece), while the resistivity method measured the peak irradiation temperature of GE-Hitachi KGT-3341 to be 300°C, with an accuracy range of -50°C to +20°C. Both methods of SiC temperature monitor analysis produced very similar peak irradiation temperatures for each pair of SiC passive monitors from the two experiments, BSU-8242 and GE-Hitachi. The results show dilatometry method to be a reliable and less time-intensive process for determining irradiation temperatures from passive SiC thermometry.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Chelation ion chromatography as an automated, and cost-effective analytical technique for REE determination: method development and applications

Rare earth elements (REEs), as critical minerals, have important uses in modern energy and technologies, yet are vulnerable to potential supply chain disruptions. To establish domestic REE supply chain, efficient REE detection methods for resource characterization and mineral processing will be needed to accelerate innovations for domestic REE recovery. This study developed a rapid, novel, and cost-effective for REE detection method using ion chromatography (IC) for aqueous samples. Various REE-targeted eluent gradients and post-column agent compositions were tested on the chelation ion chromatography (CIC) with UV-vis detector for optimal separation and quantification of REEs within approximately 20 min. The single-channel pump to deliver the post-column solution to UV-vis detector was replaced with a 4-channel gradient pump, to increase operation and maintenance efficiencies. After method optimization, resulting calibration curves for more than ten REEs achieved high coefficients of determination (R2>0.999) and low relatively standard deviations (below 3.24%), demonstrating sub-ppm level detection limits (0.0897 to 0.1149 mg/L). The reliability of the CIC method was validated through comparison with inductively coupled plasma mass spectrometry (ICP-MS), showing strong agreement in REE recovery from certified standards. The impact of metal ions and salts on REE recovery using CIC was also systematically investigated. CIC consistently exhibited reliable performance in the presence of salt solutions such as NaCl and Na₂SO₄ (up to 10,000 mg/L). Our study also found the presence of high concentrations of Al ions (at 10,000 mg/L) significantly influenced REE determination, and elevated concentrations of Ca ions affected the recovery of specific REEs, including La, Ce, and Pr. The CIC method was further tested on REE-containing eluents from solvent extraction tests out of fly ash leachates. REE detection from these real processing fluids were reported to achieve 90% to 100% recovery rate from our IC method, compared to ICP-MS results. This study underscores the potential of CIC as a reliable and efficient alternative for REE determination in complex matrices. It also highlights the importance of minimizing select interfering metal ions in solutions to ensure accurate results. The REE CIC method presents a promising, low-maintenance, salt-tolerant, and cost-effective alternative to traditional analytical methods for REE analysis.

detection of rare earth elements (REE)↗
DOE OSTI2022

Assessment of Bacterial Inoculant Delivery Methods for Cereal Crops

Despite growing evidence that plant growth-promoting bacteria can be used to improve crop vigor, a comparison of the different methods of delivery to determine which is optimal has not been published. An optimal inoculation method ensures that the inoculant colonizes the host plant so that its potential for plant growth-promotion is fully evaluated. The objective of this study was to compare the efficacy of three seed coating methods, seedling priming, and soil drench for delivering three bacterial inoculants to the sorghum rhizosphere and root endosphere. The methods were compared across multiple time points under axenic conditions and colonization efficiency was determined by quantitative polymerase chain reaction (qPCR). Two seed coating methods were also assessed in the field to test the reproducibility of the greenhouse results under non-sterile conditions. In the greenhouse seed coating methods were more successful in delivering the Gram-positive inoculant (Terrabacter sp.) while better colonization from the Gram-negative bacteria (Chitinophaga pinensis and Caulobacter rhizosphaerae) was observed with seedling priming and soil drench. This suggested that Gram-positive bacteria may be more suitable for the seed coating methods possibly because of their thick peptidoglycan cell wall. We also demonstrated that prolonged seed coating for 12 h could effectively enhance the colonization of C. pinensis, an endophytic bacterium, but not the rhizosphere colonizing C. rhizosphaerae. In the field only a small amount of inoculant was detected in the rhizosphere. This comparison demonstrates the importance of using the appropriate inoculation method for testing different types of bacteria for their plant growth-promotion potential.

Terrabacter↗
DOE OSTI2022

A new method for inferring city emissions and lifetimes of nitrogen oxides from high-resolution nitrogen dioxide observations: a model study

We present a new method to infer emissions and lifetimes of nitrogen oxides (NO x ) based on tropospheric nitrogen dioxide (NO 2 ) observations together with reanalysis wind fields for cities located in polluted backgrounds. Since the accuracy of the method is difficult to assess due to lack of “true values” that can be used as a benchmark, we apply the method to synthetic NO 2 observations derived from the NASA-Unified Weather Research and Forecasting (NU-WRF) model at a high horizontal spatial resolution of 4 km × 4 km for cities over the continental United States. We compare the inferred emissions and lifetimes with the values given by the NU-WRF model to evaluate the method. The method is applicable to 26 US cities. The derived results are generally in good agreement with the values given by the model, with the relative differences of 2 % ± 17 % (mean ± standard deviation) and 15 % ± 25 % for lifetimes and emissions, respectively. Our investigation suggests that the use of wind data prior to the satellite overpass time improves the performance of the method. The correlation coefficients between inferred and NU-WRF lifetimes increase from 0.56 to 0.79 and for emissions increase from 0.88 to 0.96 when comparing results based on wind fields sampled simultaneously with satellite observations and averaged over 9 h data prior to satellite observations, respectively. We estimate that uncertainties in NO x lifetime and emissions arising from the method are approximately 15 % and 20 %, respectively, for typical (US) cities. The total uncertainties reach up to 43% (lifetimes) and 45% (emissions) by considering the additional uncertainties associated with satellite NO 2 observations and wind data. We expect this new method to be applicable to NO 2 observations from the TROPOspheric Monitoring Instrument (TROPOMI) and geostationary satellites, such as Geostationary Environment Monitoring Spectrometer (GEMS) or the Tropospheric Emissions: Monitoring Pollution (TEMPO) instrument, to estimate urban NO x emissions and lifetimes globally.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1972

Numerical method for the solution of large systems of differential equations of the boundary layer type

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

Green, M. J.↗