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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 541 records · Page 30

The entropy of galaxy spectra: how much information is encoded?

Abstract The inverse problem of extracting the stellar population content of galaxy spectra is analysed here from a basic standpoint based on information theory. By interpreting spectra as probability distribution functions, we find that galaxy spectra have high entropy, thus leading to a rather low effective information content. The highest variation in entropy is unsurprisingly found in regions that have been well studied for decades with the conventional approach. We target a set of six spectral regions that show the highest variation in entropy – the 4000 Å break being the most informative one. As a test case with real data, we measure the entropy of a set of high-quality spectra from the Sloan Digital Sky Survey, and contrast entropy-based results with the traditional method based on line strengths. The data are classified into star-forming (SF), quiescent (Q), and active galactic nucleus (AGN) galaxies, and show – independently of any physical model – that AGN spectra can be interpreted as a transition between SF and Q galaxies, with SF galaxies featuring a more diverse variation in entropy. The high level of entanglement complicates the determination of population parameters in a robust, unbiased way, and affects traditional methods that compare models with observations, as well as machine learning (especially deep learning) algorithms that rely on the statistical properties of the data to assess the variations among spectra. Entropy provides a new avenue to improve population synthesis models so that they give a more faithful representation of real galaxy spectra.

Ferreras, Ignacio (ORCID:0000000345843127)↗

Advancing spatiotemporal forecasts of CO 2 plume migration using deep learning networks with transfer learning and interpretation analysis

Accurate and timely forecasts of CO 2 plume distribution throughout the injection and post-injection phases are crucial for detecting plume migration, assessing leakage risks, and supporting operational decisions in geologic carbon storage (GCS). Current convolutional neural network-based approaches primarily focus on spatial information and overlook temporal dependencies in plume distributions, thus limiting their ability to capture dynamic movement effects and provide accurate predictions of plume migration. In this work, we propose two deep learning models, Auto-Encoder (AE)-LSTM and Encoder-Decoder (ED)-ConvLSTM, each uniquely designed to capture both spatial and temporal features. We apply the proposed methods to forecast the dynamic distribution of CO 2 plumes based on 108 reservoir simulations over a 30-year injection and a 30-year post-injection period. The results indicate that the ED-ConvLSTM model outperforms the AE-LSTM model in accurately predicting the spatiotemporal dynamics of CO 2 plume migration, achieving R 2 values above 0.99. To provide a deeper understanding of these model predictions, we employ a gradient-based explanation method on the trained models. This approach provides insights into the influence of input variables on plume migration forecasts and uncovers the underlying prediction mechanisms of the proposed models. Furthermore, we introduce a transfer learning technique, enabling fast and accurate plume migration forecasting in the post-injection phase by leveraging the trained model during the injection phase. This reduces the necessity for extensive data collection or re-training. In conclusion, the methods proposed in our work enhances the performance and interpretability of CO 2 plume migration forecasts, thereby facilitating informed decision-making throughout the entire lifecycle of GCS applications.

58 GEOSCIENCES↗

Machine Learning Emulation of Spatial Deposition from a Multi-Physics Ensemble of Weather and Atmospheric Transport Models

In the event of an accidental or intentional hazardous material release in the atmosphere, researchers often run physics-based atmospheric transport and dispersion models to predict the extent and variation of the contaminant spread. These predictions are imperfect due to propagated uncertainty from atmospheric model physics (or parameterizations) and weather data initial conditions. Ensembles of simulations can be used to estimate uncertainty, but running large ensembles is often very time consuming and resource intensive, even using large supercomputers. In this paper, we present a machine-learning-based method which can be used to quickly emulate spatial deposition patterns from a multi-physics ensemble of dispersion simulations. We use a hybrid linear and logistic regression method that can predict deposition in more than 100,000 grid cells with as few as fifty training examples. Logistic regression provides probabilistic predictions of the presence or absence of hazardous materials, while linear regression predicts the quantity of hazardous materials. The coefficients of the linear regressions also open avenues of exploration regarding interpretability—the presented model can be used to find which physics schemes are most important over different spatial areas. A single regression prediction is on the order of 10,000 times faster than running a weather and dispersion simulation. However, considering the number of weather and dispersion simulations needed to train the regressions, the speed-up achieved when considering the whole ensemble is about 24 times. Ultimately, this work will allow atmospheric researchers to produce potential contamination scenarios with uncertainty estimates faster than previously possible, aiding public servants and first responders.

97 MATHEMATICS AND COMPUTING↗

The Andromeda gamma-ray excess: background systematics of the millisecond pulsars and dark matter interpretations

ABSTRACT Since the discovery of an excess in gamma rays in the direction of M31, its cause has been unclear. Published interpretations focus on dark matter or stellar related origins. Studies of a similar excess in the Milky Way centre motivate a correlation of the spatial morphology of the signal with the distribution of stellar mass in M31. However, a robust determination of the best theory for the observed excess emission is challenging due to uncertainties in the astrophysical gamma-ray foreground model. We perform a spectro-morphological analysis of the M31 gamma-ray excess using state-of-the-art templates for the distribution of stellar mass in M31 and novel astrophysical foreground models for its sky region. We construct maps for the old stellar populations of M31 based on data from the PAndAS survey and carefully remove the foreground stars. We also produce improved astrophysical foreground models via novel image inpainting techniques based on machine learning methods. Our stellar maps, mimicking the location of a population of millisecond pulsars in the bulge of M31, reach a 5.4σ significance, making them as strongly favoured as the simple phenomenological models usually considered in the literature, e.g. disc-like templates. This detection is robust to generous variations of the astrophysical foreground model. Once the stellar templates are included in the astrophysical model, we show that the dark matter annihilation interpretation of the signal is unwarranted. We demonstrate that about one million unresolved millisecond pulsars naturally explain the observed gamma-ray luminosity per stellar mass, energy spectrum, and stellar bulge-to-disc flux ratio.

79 ASTRONOMY AND ASTROPHYSICS↗

Towards physics-informed explainable machine learning and causal models for materials research

From emergent material descriptions to estimation of properties stemming from structures to optimization of process parameters for achieving best performance – all key facets of materials science and related fields have experienced tremendous growth with the introduction of data-driven models. This gradual progression goes at par with developments of machine learning workflows, from purely data-driven shallow models to those that are well-capable in encoding more complex graphs, symbolic representations, invariances, and positional embeddings. Furthermore, this perspective aims at summarizing strategic aspects of such transitions while providing insights into the requirements of bringing in explainable, interpretable predictive models, and causal learning to aid in materials design and discovery. Although the focus remains on a variety of functional materials by providing a handful of case studies, the applications of such integrated methodologies are universal to facilitate fundamental understandings of materials physics while enabling autonomous experiments.

36 MATERIALS SCIENCE↗

A Mass‐Conserving‐Perceptron for Machine‐Learning‐Based Modeling of Geoscientific Systems

Although decades of effort have been devoted to building Physical-Conceptual (PC) models for predicting the time-series evolution of geoscientific systems, recent work shows that Machine Learning (ML) based Gated Recurrent Neural Network technology can be used to develop models that are much more accurate. However, the difficulty of extracting physical understanding from ML-based models complicates their utility for enhancing scientific knowledge regarding system structure and function. Here, we propose a physically interpretable Mass-Conserving-Perceptron (MCP) as a way to bridge the gap between PC-based and ML-based modeling approaches. The MCP exploits the inherent isomorphism between the directed graph structures underlying both PC models and GRNNs to explicitly represent the mass-conserving nature of physical processes while enabling the functional nature of such processes to be directly learned (in an interpretable manner) from available data using off-the-shelf ML technology. As a proof of concept, we investigate the functional expressivity (capacity) of the MCP, explore its ability to parsimoniously represent the rainfall-runoff (RR) dynamics of the Leaf River Basin, and demonstrate its utility for scientific hypothesis testing. To conclude, we discuss extensions of the concept to enable ML-based physical-conceptual representation of the coupled nature of mass-energy-information flows through geoscientific systems.

58 GEOSCIENCES↗

A multifidelity deep operator network approach to closure for multiscale systems

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set of generalized (or latent) variables. Despite their success, PROMs can be susceptible to inaccuracies, even instabilities, due to the improper accounting of the interaction between the resolved and unresolved scales of the multiscale system (known as the closure problem). In the current work, we interpret closure as a multifidelity problem and use a multifidelity deep operator network (DeepONet) framework to address it. In addition, to enhance the stability and/or accuracy of the multifidelity-based closure, we employ the recently developed ``in-the-loop" training approach from the literature on coupling physics and machine learning models. The resulting approach is tested on shock advection for the one-dimensional viscous Burgers equation and vortex merging for the two-dimensional Navier-Stokes equations. Furthermore, the numerical experiments show significant improvement of the predictive ability of the closure-corrected PROM over the un-corrected one both in the interpolative and the extrapolative regimes.

42 ENGINEERING↗

Learning-based approach to plasticity in athermal sheared amorphous packings: Improving softness

The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between the plastic dynamics and the structure of a particle’s local environment remains an open question. Previously, machine learning was used to identify a structural predictor of rearrangements called “softness.” Although softness has been shown to predict which particles will rearrange with high accuracy, the method can be difficult to implement in experiments where data are limited and the combinations of descriptors it identifies are often difficult to interpret physically. Here, we address both of these weaknesses, presenting two major improvements to the standard softness method. First, we present a natural representation of each particle’s observed mobility, allowing for the use of statistical models that are both simpler and provide greater accuracy in limited datasets. Second, we employ persistent homology as a systematic means of identifying simple, topologically informed, structural quantities that are easy to interpret and measure experimentally. We test our methods on two-dimensional athermal packings of soft spheres under quasi-static shear. We find that the same structural information that predicts small variations in the response is also predictive of where plastic events will localize. We also find that an excellent accuracy is achieved in athermal sheared packings using simply a particle’s species and the number of nearest neighbor contacts.

36 MATERIALS SCIENCE↗

Neural simulation-based inference of the neutron star equation of state directly from telescope spectra

Neutron stars provide a unique opportunity to study strongly interacting matter under extreme density conditions. The intricacies of matter inside neutron stars and their equation of state are not directly visible, but determine bulk properties, such as mass and radius, which affect the star's thermal X-ray emissions. However, the telescope spectra of these emissions are also affected by the stellar distance, hydrogen column, and effective surface temperature, which are not always well-constrained. Uncertainties on these nuisance parameters must be accounted for when making a robust estimation of the equation of state. In this study, we develop a novel methodology that, for the first time, can infer the full posterior distribution of both the equation of state and nuisance parameters directly from telescope observations. This method relies on the use of neural likelihood estimation, in which normalizing flows use samples of simulated telescope data to learn the likelihood of the neutron star spectra as a function of these parameters, coupled with Hamiltonian Monte Carlo methods to efficiently sample from the corresponding posterior distribution. Our approach surpasses the accuracy of previous methods, improves the interpretability of the results by providing access to the full posterior distribution, and naturally scales to a growing number of neutron star observations expected in the coming years.

79 ASTRONOMY AND ASTROPHYSICS↗

The data-driven future of high-energy-density physics

High-energy-density physics is the field of physics concerned with studying matter at extremely high temperatures and densities. Such conditions produce highly nonlinear plasmas, in which several phenomena that can normally be treated independently of one another become strongly coupled. The study of these plasmas is important for our understanding of astrophysics, nuclear fusion and fundamental physics—however, the nonlinearities and strong couplings present in these extreme physical systems makes them very difficult to understand theoretically or to optimize experimentally. Here we argue that machine learning models and data-driven methods are in the process of reshaping our exploration of these extreme systems that have hitherto proved far too nonlinear for human researchers. Furthermore, from a fundamental perspective, our understanding can be improved by the way in which machine learning models can rapidly discover complex interactions in large datasets. From a practical point of view, the newest generation of extreme physics facilities can perform experiments multiple times a second (as opposed to approximately daily), thus moving away from human-based control towards automatic control based on real-time interpretation of diagnostic data and updates of the physics model. To make the most of these emerging opportunities, we suggest proposals for the community in terms of research design, training, best practice and support for synthetic diagnostics and data analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Systematic characterization of unknown compounds via dimensionality reduction of time series

Analysis of ambient aerosols provides valuable insight into particle sources and formation chemistry. However, due to the complexity of atmospheric data and the dynamic nature of aerosol composition, a substantial fraction of data often become discarded by conventional analysis methods. Furthermore, a large fraction of chemical species within those data are unidentifiable due to a lack of matching spectral information, resulting in suboptimal characterization of chemical composition. Previous work has demonstrated techniques for cataloging analytes in a chromatographic dataset by deconvolution of mass spectra, but integration of these analytes throughout a large dataset remains time consuming. Here, we present a method to automatically identify an ion for quantitation for single-ion chromatogram based peak fitting and integration, enabling comprehensive integration of analytes with minimal user interaction. The resulting time series are clustered with a machine-learning based dimensionality reduction technique to systematically investigate the underlying characteristics of the categorized analytes and gain new insights into the chemical composition and physicochemical properties of the unidentifiable analytes. We apply these methods to existing atmospheric datasets collected in Manacapuru, Brazil during the GoAmazon2014/5 campaign to identify new analytes and interpret their variability and transformations in the atmosphere. The analysis results generate 408 time series from cataloged analytes of interest, and the clustering of those time series with spherical k-means results in 8 distinct clusters. We find the analytes form clusters based on their distinct physicochemical properties, demonstrating the method’s ability to systematically identify and selectively filter contaminants and instrumental analytes and characterize the unidentifiable analytes.

54 ENVIRONMENTAL SCIENCES↗

Observational process data analytics using causal inference

Voluminous process data are available with the paradigm shift toward smart manufacturing. However, most historical data are observational, containing noncausal correlations due to confounders and mediators. Estimating causal effects from observational data remains a bottleneck in leveraging them for active applications such as optimization and control. Further, this work aims to introduce a causal modeling framework for analyzing observational process data and extracting quantitative causal information. We demonstrate a real-world application in steel manufacturing where causal inference is used to analyze observational production data and improve the steelmaking process. Additionally, we propose a novel formulation for identifying critical process parameters from observational data, where causal inference is combined with variance-based methods to estimate corresponding risks of interventions to the manufacturing system. The proposed methods are compared with statistical ones to illustrate that causally interpreting statistical correlation leads to problematic results, while the provided workflow generates satisfactory strategies for process improvement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SSTDR and FDR Detection of Un-Energized and Energized Cable Anomalies Including Thermal Degradation Using Machine Learning

Historically, cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages. A related technology that has found some acceptance in the aircraft and rail industry is spread spectrum time domain reflectometry (SSTDR). This technology has been implemented with a custom commercial instrument by LiveWire Innovation that is designed to operate on live cables up to 1000 volts and with a bandwidth of 48 MHz. Initial evaluation by the Pacific Northwest National Laboratory (PNNL) of the Live Wire system indicated that a broader bandwidth (BW) SSTDR may be better for many kinds of flaws. This led PNNL to develop an SSTDR laboratory instrument suitable for tests up to 500 MHz bandwidth. Testing on energized cables is also desirable for online monitoring systems so an inductive clamshell coupler was developed that allows energized cables to be tested up to at least 5 kV and likely higher voltage levels. Dielectric spectroscopy and tan delta testing plus various laboratory destructive tests were included in this data acquisition campaign directed to feed a machine learning (ML) study. With these kinds of developments, online energized cable tests may be possible with industrial adoption of such hardware advances but it will be completely impractical to have highly skilled data analysts continually examine these complex signals for indications of damage or compromised conditions. If online testing is to be implemented in new test hardware, it must be accompanied by software that can interpret the signals and alert plant operators of changing or degraded conditions. The thermally aged, shielded cable investigated here was separately treated for ML analysis. Visual analysis of electrical data showed generally increasing peaks where the cable entered and exited the oven. These peaks were not exactly aligned with expected locations, but these differences were attributed to velocity of propagation calibration errors. Only supervised ML was applied to the thermally aged data as this data was only available shortly before the committed publication date of this report. The supervised ML was structured to divide the 0 to 70-day responses as ‘normal’ from 0 to 35 days or ‘anomalous’ from 36 to 70 days, based on cable tensile elongation at break (EAB) insulation characterization. Using 80% of the data for training and 20% for testing, the supervised ML predicted normal versus anomalous was 70% accurate. Important conclusions include: • Accuracy to predict the presence of cable damage is improved from the 2023 effort by more training data. Weighted accuracies for comparisons among the instruments ranged from 67 to 89 % for unsupervised ML and 71 to 99% for supervised ML. • Based on the synthetic data tests, the unsupervised models are more generalizable to unseen anomalies. The Multi-Layer Perceptron classifier (MLP) model reported as high as 99.7% accuracy on the test data, but this dropped to 58.3% when tested on the synthetic data. In contrast, the unsupervised Pointwise model only achieved 89.7% accuracy on the experimental data but reported 78.3% accuracy on the synthetic data. • The best anomaly indicators are higher frequency (400 MHz BW) FDR data. Other tests may be interesting but for this study, this was the best predicter.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Feature selection with distance correlation

Choosing which properties of the data to use as input to multivariate decision algorithms—also known as feature selection—is an important step in solving any problem with machine learning. While there is a clear trend towards training sophisticated deep networks on large numbers of relatively unprocessed inputs (so-called automated feature engineering), for many tasks in physics, sets of theoretically well-motivated and well-understood features already exist. Working with such features can bring many benefits, including greater interpretability, reduced training and run time, and enhanced stability and robustness. We develop a new feature selection method based on distance correlation, and demonstrate its effectiveness on the tasks of boosted top- and W -tagging. Using our method to select features from a set of over 7,000 energy flow polynomials, we show that we can match the performance of much deeper architectures, by using only ten features and two orders-of-magnitude fewer model parameters. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Data-Enabled Fusion Technology (Final Scientific/Technical Report)

Advancing Scientific Understanding in Fusion Energy and Machine Learning This research represented a significant step forward in machine learning (ML) applications for fusion energy experiments. The project integrated advanced data-driven modeling, optimization techniques, and artificial intelligence to enhance the predictive capabilities and operational efficiency of plasma-based fusion systems. Specifically, tasks focused on ML-enhanced diagnostics, operator guidance tools, and predictive modeling helped improve the ability to interpret complex fusion experiments. Key areas of advancement included: 1) data-driven plasma control, i.e., using ML algorithms to optimize experimental conditions and classify plasma behaviors based on historical data; 2) spectroscopy and diagnostics, i.e., applying AI models to extract previously inaccessible insights from experimental spectroscopy data; and 3) configuration mapping and operator guidance, i.e., developing a predictive framework to assist scientists in identifying the most effective experimental parameters, reducing reliance on manual adjustments. By refining these ML-driven techniques, the project contributed to the broader scientific community’s understanding of plasma dynamics and fusion energy viability. Technical Effectiveness and Economic Feasibility The methods investigated demonstrated high technical effectiveness, as reflected in milestones assessing the predictive accuracy, performance, and optimization of fusion configurations. The development of an Operator Guidance Tool (OGT), for example, led to more precise control of plasma conditions by learning from experimental data and offering real-time adjustments. From an economic standpoint, DeFT provided: 1) the ability to reduce trial-and-error experimentation, which lowered operational costs; 2) improved data interpretation methods, which enabled more efficient resource allocation in large-scale fusion research projects; and 3) the automation of key diagnostic tasks, which reduced manual labor and human error, increasing overall efficiency. 13 The final assessments of predictive models and optimization strategies demonstrated that these approaches were scalable and could be implemented across multiple fusion energy research programs. Public Benefit and Societal Impact This project contributed directly to the broader goal of achieving sustainable and commercially viable fusion energy, which had profound implications for clean energy production and climate change mitigation. The integration of AI-driven solutions into fusion research: 1) sped up scientific discovery, accelerating progress towards achieving energy breakthroughs; 2) reduced the cost of experimentation, making fusion research more accessible; and 3) provided a framework for future AI applications in high-energy physics, benefiting adjacent fields like space exploration, material science, and renewable energy. Additionally, by fostering collaborations between AI researchers and plasma physicists, this project promoted interdisciplinary innovation that could lead to broader applications beyond fusion research.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Neutrino interaction vertex reconstruction in DUNE with Pandora deep learning

The Pandora Software Development Kit and algorithm libraries perform reconstruction of neutrino interactions in liquid argon time projection chamber detectors. Pandora is the primary event reconstruction software used at the Deep Underground Neutrino Experiment, which will operate four large-scale liquid argon time projection chambers at the far detector site in South Dakota, producing high-resolution images of charged particles emerging from neutrino interactions. While these high-resolution images provide excellent opportunities for physics, the complex topologies require sophisticated pattern recognition capabilities to interpret signals from the detectors as physically meaningful objects that form the inputs to physics analyses. A critical component is the identification of the neutrino interaction vertex. Subsequent reconstruction algorithms use this location to identify the individual primary particles and ensure they each result in a separate reconstructed particle. A new vertex-finding procedure described in this article integrates a U-ResNet neural network performing hit-level classification into the multi-algorithm approach used by Pandora to identify the neutrino interaction vertex. The machine learning solution is seamlessly integrated into a chain of pattern-recognition algorithms. The technique substantially outperforms the previous BDT-based solution, with a more than 20% increase in the efficiency of sub-1 cm vertex reconstruction across all neutrino flavours.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Accounting for Training Data Error in Machine Learning Applied to Earth Observations

Remote sensing, or Earth Observation (EO), is increasingly used to understand Earth system dynamics and create continuous and categorical maps of biophysical properties and land cover, especially based on recent advances in machine learning (ML). ML models typically require large, spatially explicit training datasets to make accurate predictions. Training data (TD) are typically generated by digitizing polygons on high spatial-resolution imagery, by collecting in situ data, or by using pre-existing datasets. TD are often assumed to accurately represent the truth, but in practice almost always have error, stemming from (1) sample design, and (2) sample collection errors. The latter is particularly relevant for image-interpreted TD, an increasingly commonly used method due to its practicality and the increasing training sample size requirements of modern ML algorithms. TD errors can cause substantial errors in the maps created using ML algorithms, which may impact map use and interpretation. Despite these potential errors and their real-world consequences for map-based decisions, TD error is often not accounted for or reported in EO research. Here we review the current practices for collecting and handling TD. We identify the sources of TD error, and illustrate their impacts using several case studies representing different EO applications (infrastructure mapping, global surface flux estimates, and agricultural monitoring), and provide guidelines for minimizing and accounting for TD errors. To harmonize terminology, we distinguish TD from three other classes of data that should be used to create and assess ML models: training reference data, used to assess the quality of TD during data generation; validation data, used to iteratively improve models; and map reference data, used only for final accuracy assessment. We focus primarily on TD, but our advice is generally applicable to all four classes, and we ground our review in established best practices for map accuracy assessment literature. EO researchers should start by determining the tolerable levels of map error and appropriate error metrics. Next, TD error should be minimized during sample design by choosing a representative spatio-temporal collection strategy, by using spatially and temporally relevant imagery and ancillary data sources during TD creation, and by selecting a set of legend definitions supported by the data. Furthermore, TD error can be minimized during the collection of individual samples by using consensus-based collection strategies, by directly comparing interpreted training observations against expert-generated training reference data to derive TD error metrics, and by providing image interpreters with thorough application-specific training. We strongly advise that TD error is incorporated in model outputs, either directly in bias and variance estimates or, at a minimum, by documenting the sources and implications of error. TD should be fully documented and made available via an open TD repository, allowing others to replicate and assess its use. To guide researchers in this process, we propose three tiers of TD error accounting standards. Finally, we advise researchers to clearly communicate the magnitude and impacts of TD error on map outputs, with specific consideration given to the likely map audience.

58 GEOSCIENCES↗