Search NASA⌕ Search

SEARCH · Search NASA

Results for “singularities in general relativity”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

72 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Regularization prescription for the mixing between nonlocal gluon and quark operators

It is well known that in the study of mixing between nonlocal gluon and quark bilinear operators there exists an ambiguity when relating coordinate space and momentum space results. In this work, we show that this ambiguity is due to the lack of a proper regularization prescription of the singularity that arises when the separation between the gluon/quark fields approaches zero. We then demonstrate that dimensional regularization resolves this issue and yields consistent results in both coordinate and momentum space. This prescription is also compatible with lattice extractions of parton distributions from nonlocal operators.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Accurate numerical, integral methods for computing drift-kinetic Trubnikov-Rosenbluth potentials

A novel numerical method is employed to compute the integral form of the axi-symmetric Trubnikov-Rosenbluth potentials. Two methods for quadrature in pitch-angle are described and their convergence properties are studied. Careful attention is given to quadrature over a singular Green's function. Here it is shown that an infinite series representation of the Green's function can be used more efficiently than its closed form involving complete elliptic integrals. Then a collocation method in speed, with its associated quadrature scheme, is laid out and its convergence properties are studied. Using the proposed scheme, accurate low-order moments of the field collision operator are obtained using relatively few velocity space degrees of freedom. The scheme is showcased by solving for the equilibrium, axi-symmetric bootstrap current in tokamaks. A C 0 Gauss-Lobatto-Legendre finite element pitch-angle basis with vertex nodes at the trapped/passing boundary is shown, in the context of the integral methods used, to be much more efficient than the more common Legendre polynomial expansion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Celestial operator product expansions and w 1+∞ symmetry for all spins

The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of w 1+∞ . In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of w 1+∞ on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

The Cosmological Bootstrap: Spinning correlators from symmetries and factorization

We extend the cosmological bootstrap to correlators involving massless spinning particles, focusing on spin-1 and spin-2. In de Sitter space, these correlators are constrained both by symmetries and by locality. In particular, the de Sitter isometries become conformal symmetries on the future boundary of the spacetime, which are reflected in a set of Ward identities that the boundary correlators must satisfy. We solve these Ward identities by acting with weight-shifting operators on scalar seed solutions. Using this weight-shifting approach, we derive three- and four-point correlators of massless spin-1 and spin-2 fields with conformally coupled scalars. Four-point functions arising from tree-level exchange are singular in particular kinematic configurations, and the coefficients of these singularities satisfy certain factorization properties. We show that in many cases these factorization limits fix the structure of the correlators uniquely, without having to solve the conformal Ward identities. The additional constraint of locality for massless spinning particles manifests itself as current conservation on the boundary. We find that the four-point functions only satisfy current conservation if the s, t, and u-channels are related to each other, leading to nontrivial constraints on the couplings between the conserved currents and other operators in the theory. For spin-1 currents this implies charge conservation, while for spin-2 currents we recover the equivalence principle from a purely boundary perspective. For multiple spin-1 fields, we recover the structure of Yang--Mills theory. Finally, we apply our methods to slow-roll inflation and derive a few phenomenologically relevant scalar-tensor three-point functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Adaptive Space-Time Methods for Large Scale Optimal Design

When modeling complex physical systems with advanced dynamics, such as shocks and singularities, many classic methods for solving partial differential equations can return inaccurate or unusable results. One way to resolve these complex dynamics is through r-adaptive refinement methods, in which a fixed number of mesh points are shifted to areas of high interest. The mesh refinement map can be found through the solution of the Monge-Ampére equation, a highly nonlinear partial differential equation. Due to its nonlinearity, the numerical solution of the Monge-Ampére equation is nontrivial and has previously required computationally expensive methods. In this report, we detail our novel optimization-based, multigrid-enabled solver for a low-order finite element approximation of the Monge-Ampére equation. This fast and scalable solver makes r-adaptive meshing more readily available for problems related to large-scale optimal design. Beyond mesh adaptivity, our report discusses additional applications where our fast solver for the Monge-Ampére equation could be easily applied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Time evolution of ML-MCTDH wavefunctions. II. Application of the projector splitting integrator

The multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach can suffer from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of regularization of the EOMs. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here, we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to 106 bath modes and find that for these problems, the PSI requires roughly 3–4 orders of magnitude fewer Hamiltonian evaluations and 2–3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH and 2–3/1–2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to ~1.3×10 9 parameters to obtain accurate dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Unidirectional amplification in the frozen mode regime enabled by a nonlinear defect

A stationary inflection point (SIP) is a spectral singularity of the Bloch dispersion relation ω(k) of a periodic structure where the first and the second derivatives of ω with respect to k vanish. An SIP is associated with a third-order exceptional point degeneracy in the spectrum of the unit-cell transfer matrix, where there is a collapse of one propagating and two evanescent Bloch modes. At the SIP frequency, the incident wave can be efficiently converted into the frozen mode with greatly enhanced amplitude and vanishing group velocity. This can be very attractive for applications, including light amplification. Due to its non-resonant nature, the frozen mode regime (FMR) has fundamental advantages over common cavity resonances. Furthermore, we propose, a novel, to the best of our knowledge, scheme for FMR-based unidirectional amplifiers by leveraging a tailored amplification/attenuation mechanism and a single nonlinear defect. The defect breaks the directional symmetry of the periodic structure and enables nonlinearity-related unidirectional amplification/attenuation in the vicinity of the SIP frequency. We demonstrate the robustness of the amplification mechanism to local impurities and parasitic nonlinearity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Equation-of-Motion Coupled-Cluster Cumulant Green’s Function for Excited States and X-ray Spectra

Green’s function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states and spectra. Conventional methods using the Dyson equation or the cumulant expansion are typically based on the GW self-energy approximation. In order to extend this approximation in molecular systems, a non-perturbative real-time coupled-cluster cumulant Green’s function approach has been introduced, where the cumulant is obtained as the solution to a set of coupled first order, non-linear differential equations. This approach naturally includes non-linear corrections to conventional cumulant Green’s function techniques where the cumulant is linear in the GW self-energy. The method yields the spectral function associated with the core Green’s function, which is directly related to the x-ray photoemission spectra (XPS) of molecular systems. The approach also yields very good results for binding energies and satellite excitations. The x-ray absorption spectrum (XAS) is then obtained as a convolution of the core spectral function and an effective one-body absorption spectrum. Here this approach is extended to include the full coupled-cluster-singles (CCS) core Green’s function by including the complete form of the non-linear contributions to the cumulant as well as all single, double, and triple cluster excitations in the CC amplitude equations. This approach naturally builds in orthogonality and shake-up effects analogous to those in the Mahan-Noizeres-de Dominicis edge singularity corrections that enhance the XAS near the edge. Themethod is illustrated for the XPS and XAS of NH 3 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Past-completeness of inflationary spacetimes

Here, we discuss the question of whether or not inflationary spacetimes can be geodesically complete in the infinite past. Geodesic completeness is a necessary condition for averting an initial singularity during eternal inflation. It is frequently argued that cosmological models which are expanding sufficiently fast (having average Hubble expansion rate H avg > 0) must be incomplete in null and timelike past directions. This well-known conjecture relies on specific bounds on the integral of the Hubble parameter over a past- directed timelike or null geodesic. As stated, we show this claim is an open issue. We show that the calculation of H avg yields a continuum of results for a given spacetime predicated upon the underlying topological assumptions. We present an improved definition for H avg and introduce an uncountably infinite cohort of cosmological solutions which are geodesically complete despite having H avg > 0. We discuss a standardized definition for inflationary spacetimes as well as quantum (semiclassical) cosmological concerns over physically reasonable scale factors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Elastocaloric signatures of symmetric and antisymmetric strain-tuning of quadrupolar and magnetic phases in DyB 2 C 2

The adiabatic elastocaloric effect measures the temperature change of a given system with strain and provides a thermodynamic probe of the entropic landscape in the temperature-strain space. Here, we demonstrate that the DC bias strain-dependence of AC elastocaloric effect allows decomposition of the latter into symmetric (rotation-symmetry-preserving) and antisymmetric (rotation-symmetry-breaking) strain channels, using a tetragonal f -electron intermetallic DyB 2 C 2 —whose antiferroquadrupolar order breaks local fourfold rotational symmetries while globally remaining tetragonal—as a showcase example. We capture the strain evolution of its quadrupolar and magnetic phase transitions using both singularities in the elastocaloric coefficient and its jumps at the transitions, and the latter we show follows a modified Ehrenfest relation. We find that antisymmetric strain couples to the underlying order parameter in a biquadratic (linear-quadratic) manner in the antiferroquadrupolar (canted antiferromagnetic) phase, which are attributed to a preserved (broken) global tetragonal symmetry, respectively. The broken tetragonal symmetry in the magnetic phase is further evidenced by elastocaloric strain-hysteresis and optical birefringence. Additionally, within the staggered quadrupolar order, the observed elastocaloric response reflects a quadratic increase of entropy with antisymmetric strain, analogous to the role magnetic field plays for Ising antiferromagnetic orders by promoting pseudospin flips. Our results demonstrate AC elastocaloric effect as a compact and incisive thermodynamic probe into the coupling between electronic degrees of freedom and strain in free energy, which holds the potential for investigating and understanding the symmetry of a wide variety of ordered phases in broader classes of quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Generalized symmetry in dynamical gravity

We explore generalized symmetry in the context of nonlinear dynamical gravity. Our basic strategy is to transcribe known results from Yang-Mills theory directly to gravity via the tetrad formalism, which recasts general relativity as a gauge theory of the local Lorentz group. By analogy, we deduce that gravity exhibits a one-form symmetry implemented by an operator U α labeled by a center element α of the Lorentz group and associated with a certain area measured in Planck units. The corresponding charged line operator W ρ is the holonomy in a spin representation ρ, which is the gravitational analog of a Wilson loop. The topological linking of U α and W ρ has an elegant physical interpretation from classical gravitation: the former materializes an exotic chiral cosmic string defect whose quantized conical deficit angle is measured by the latter. We verify this claim explicitly in an AdS-Schwarzschild black hole background. Notably, our conclusions imply that the standard model exhibits a new symmetry of nature at scales below the lightest neutrino mass. More generally, the absence of global symmetries in quantum gravity suggests that the gravitational one-form symmetry is either gauged or explicitly broken. The latter mandates the existence of fermions. Finally, we comment on generalizations to magnetic higher-form or higher-group gravitational symmetries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Retrieval of energy spectra for all flavours of neutrinos from core-collapse supernova with multiple detectors

ABSTRACT We present a new method by which to retrieve energy spectrum for all falvours of neutrinos from core-collapse supernova (CCSN). In the retrieval process, we do not assume any analytic formulas to express the energy spectrum of neutrinos but rather take a direct way of spectrum reconstruction from the observed data; the singular value decomposition algorithm with a newly developed adaptive energy-gridding technique is adopted. We employ three independent reaction channels having different flavour sensitivity to neutrinos. Two reaction channels, inverse beta decay on proton and elastic scattering on electrons, from a water Cherenkov detector such as Super-Kamiokande (SK) and Hyper-Kamiokande (HK), and a charged current reaction channel with Argon from the Deep Underground Neutrino Experiment (DUNE) are adopted. Given neutrino oscillation models, we iteratively search the neutrino energy spectra at the CCSN source until they provide the consistent event counts in the three reaction channels. We test the capability of our method by demonstrating the spectrum retrieval to a theoretical neutrino data computed by our recent three-dimensional CCSN simulation. Although the energy spectrum with either electron-type or electron-type antineutrinos at the CCSN source has relatively large error compared to that of other species, the joint analysis with HK + DUNE or SK + DUNE will provide precise energy spectrum of all flavours of neutrinos at the source. Finally, we discuss perspectives for improvements of our method by using neutrino data of other detectors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The cosmological bootstrap: inflationary correlators from symmetries and singularities

Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and the particle content of the theory. For example, four-particle amplitudes are analytic for contact interactions and have simple poles with appropriately positive residues for tree-level exchange. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlation functions are controlled by an approximate conformal symmetry on the boundary of the spacetime. After systematically classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities (and the correct normalization of physical ones) completely fixes this correlator. Moreover, a “spin-raising” operator relates it to the correlators associated with the exchange of particles with spin, while “weight-shifting” operators map it to the four-point function of massless scalars. We explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. Using our formalism, we reproduce many classic results in the literature, such as the three-point function of slow-roll inflation, and provide a complete classification of all inflationary three- and four-point functions arising from weakly broken conformal symmetry. Remarkably, the inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta, which can also be directly connected with the signals for particle production seen in the squeezed limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Constellation's best estimate alternate source term methodology overview

Safety analyses for a nuclear power plants need to consider postulated accidents that results in at risk of accidental release of radiation. The regulations require plant specific safety analysis reports to include an evaluation of the requirements of 10CFR50.67. Such a safety analysis report mandates limits such that calculated radiological consequences relative to certain dose locations do not exceed a total effective dose equivalent (TEDE) limits following a postulated release of radioactivity. Calculations are performed to estimate the radiological consequences, in terms of dose, to people and equipment to ensure the estimated doses are within the prescribed limits. Analysis should demonstrate, with reasonable assurance, that these prescribed limits are complied with. Conventional methodologies utilize conservative approaches to address lack of uncertainty quantification in the utilized approaches, methods, and/or inputs. These built-in excess conservatisms often result in compounding effects and hence overly conservative results in the estimated radiological consequences, which leads to inaccurate margin evaluation for operation and accident mitigation. Therefore, evaluating accurate dose consequences is needed for both operational and safety reasons. The research documented in this paper provides an overview of Constellation's Best Estimate Alternate Source Term (BEAST) Methodology. BEAST methodology relies upon the use of realistic yet bounding input distributions for key analysis parameters, which replaces use of conservative deterministic singular inputs that bound overall analysis domain. This approach enables evaluating a more accurate accident analysis response, while enabling a bounding licensing basis envelope via more accurate quantification of uncertainty in the application. Therefore, built-in margin for a given scenario is more accurately evaluated.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Explainable Artificial Intelligence Technology for Predictive Maintenance

The domestic nuclear power plant fleet has relied on labor-intensive and time-consuming preventive maintenance programs, thus driving up operation and maintenance costs to achieve high-capacity factors. Artificial intelligence and machine learning can help simplify complex problems, such as diagnosing equipment degradation, to enable more effective decision-making. Benefits will be felt not only within existing analog and digital instrumentation and control, but also work processes, the integration of people with technology, and most importantly, the business case. Together, these hold promise to make nuclear power more efficient and reduce costs associated with operation and maintenance. While the artificial intelligence and machine learning technologies hold significant promise in the nuclear industry, there are challenges or barriers to their adoption. This report outlines the those different machine learning adoption barriers (categorized as historical, technical, economic, regulatory, and user) that the industry must overcome to realize the full benefits of artificial intelligence and machine learning capabilities for long-term economic sustainability. This report also provides solutions for some of these barriers by focusing on improving the explainability of machine learning to encourage trust from the end-user. Trust and explainability are essential to machine learning adoption. This report focuses on research-developed solutions to some of these barriers while analyzing a non-safety-related system, namely the circulating water system. This system frequently experiences waterbox fouling which our models preemptively diagnoses then explains to the operator how those conclusions were reached. This report presents and discusses the inherent trade-off between machine learning performance (in terms of accuracy) and explainability, where highly accurate machine learning methods (such as deep-learning) are the least explainable, and the most explainable methods (such as decision trees) are the least accurate. In addition, explainability of artificial intelligence techniques in terms of transparency and post-hoc metrics are discussed. This report outlines the importance of data novelty and value of new information in evaluating both the explainability and trustworthiness. Novelty detection helps to establish consistency or inconsistency of the new data with respect to the training data. On the other hand, value of information could be a part of the user-centric visualization recommendation system that request additional information to be collected, thereby strengthening the machine learning outcomes. During this project, a copyrighted user-centric visualization that aligns with a human-in-the-loop approach was developed. The user-centric visualization presents different levels of information and can be tailored as per user credentials to gain user confidence. One of the salient features of the user-centric visualization is it presents machine learning methods with explainability metrics. A simplified version of the user-centric visualization was presented to 32 users with varying levels of machine learning expertise. Feedback was solicited to test the hypothesis that the app contained sufficient explainability and that the users would trust the algorithm. Overall, the app was positively received, and the hypothesis was supported. This report discusses the trust-but-verify framework – a potential approach to build user trust artificial intelligence. The framework discusses trust from the human level to artificial intelligence level. The fundamental premise of the trust but verify framework is derived from an observation of nuclear safety culture (i.e., nuclear power plant personnel do not rely on a singular source of data to make a decision). This also ties back to the user-centric visualization that presents different levels of information to achieve both explainability and trustworthiness of artificial intelligence. Even so, the adoption of artificial intelligence and machine learning in the nuclear industry faces additional barriers, namely regulatory and stakeholder readiness. To overcome these challenges, new solutions must gain regulatory approval and cater to stakeholder needs. The Nuclear Regulatory Committee has a 5-year strategic plan which prepares them for reviewing artificial intelligence technologies in licensee submissions. Early and frequent engagement with the regulator is encouraged. Additionally, artificial intelligence solutions should incorporate human-in-the-loop considerations and offer explainability. Stakeholders must prepare by hiring or training staff to adapt to advancing technology in everyday plant tasks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Chirality in the Kagome Metal CsV 3 ⁢Sb 5

Using x-ray photoelectron diffraction (XPD) and angle-resolved photoemission spectroscopy, we study photoemission intensity changes related to changes in the geometric and electronic structure in the kagome metal CsV 3 ⁢Sb 5 upon transition to an unconventional charge density wave (CDW) state. The XPD patterns reveal the presence of a chiral atomic structure in the CDW phase. Furthermore, using circularly polarized x-rays, we have found a pronounced nontrivial circular dichroism in the angular distribution of the valence band photoemission in the CDW phase, indicating a chirality of the electronic structure. This observation is consistent with the proposed orbital loop current order. In view of a negligible spontaneous Kerr signal in recent magneto-optical studies, the results suggest an antiferromagnetic coupling of the orbital magnetic moments along the 𝑐 axis. Here, while the inherent structural chirality may also induce circular dichroism, the observed asymmetry values seem to be too large in the case of the weak structural distortions caused by the CDW.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

HarDWR - Raw Water Rights Records

A dataset within the Harmonized Database of Western U.S. Water Rights (HarDWR). For a detailed description of the database, please see the meta-record v2.0. Changelog v2.0 - Switched source data from collecting records from each state independently to using the WestDAAT dataset v1.0 - Initial public release Description In order to hold a water right in the western United States, an entity, (e.g., an individual, corporation, municipality, sovereign government, or non-profit) must register a physical document with the state's water regulatory agency. State water agencies each maintain their own database containing all registered water right documents within the state, along with relevant metadata such as the point of diversion and place of use of the water. All western U.S. states have digitized their individual water rights databases, as well as geospatial data defining the areas in which water rights are managed. Each state maintains and provides their own water rights data in accordance with individual state regulations and standards. In addition, while all states make their water rights publicly available, each provides their records in unique formats, meaning that file types, field availability, and terms vary from state to state. This leads to additional challenges to managing resources which cross state lines, or conducting consistent multi-state water analyses. For the first version of HarDWR, we collected the water rights databases from 11 Western States of the United States. In order to preform regional analyses with the collected data, the raw records had to be harmonized into one single format. The Water Data Exchange (WaDE) is a program dedicated to the sharing of water-related data for the Western U.S. in a singular consistent format. Created by the Western States Water Council (WSWC) to facilitate the collection and dissemination of water data among WSWC's member states and the public, WaDE provides an important service for those interested in water resource planning and management in their focus region. Of the services which WaDE provides, the one of the most interesting is the WestDAAT dataset, which is a collection of water rights data provided by the 18 WSWC member states that have been standardized into a single format, much like we had done on a more limited scale with HarDWR v1. For this version of HarDWR we decided to use WestDAAT, specifically a snapshot created in Feburary 2024, as our water rights source data. A full explanation of the benefits gained from this switch can be found in the description of the updated Harmonized Water Rights Records v2.0, but in short it has allowed us to focus more of our efforts on answering research questions and gaining a more realistic understanding of how water rights are allocated. For more information on how the data for WestDAAT was collected, please see the WaDE data summary. Terms of Use While WaDE works directly with the state agencies to collect and standardize the water rights records, the ultimate authority for the water rights data remains the individual states. Each state, and their respective water right authorities, have made their water right records available for non-commercial reference uses. In addition, the states make no guarantees as to the completeness, accuracy, or timeliness of their respective databases, let alone the modifications which we, the authors of this paper, have made to the collected records. None of the states should be held liable for using this data outside of its intended use. As several of the states update their water rights databases daily, the information provided here is not the latest possible, and should not be used for legal purposes. WestDAAT itself has irregular updates. Additional questions about the data the source states provided should be directed to the respective state agencies (see methods.csv and organization.csv files described below). In addition, although data was presented here was not collected directly from the states, several states requested specifically worked disclaimers when sharing their data. These disclaimers are included here as an acknowledgement from where the water rights data is primarily sourced. Colorado: "The data made available here has been modified for use from its original source, which is the State of Colorado. THE STATE OF COLORADO MAKES NO REPRESENTATIONS OR WARRANTY AS TO THE COMPLETENESS, ACCURACY, TIMELINESS, OR CONTENT OF ANY DATA MADE AVAILABLE THROUGH THIS SITE. THE STATE OF COLORADO EXPRESSLY DISCLAIMS ALL WARRANTIES, WHETHER EXPRESS OR IMPLIED, INCLUDING ANY IMPLIED WARRANTIES OF MERCHANTABILITY, OR FITNESS FOR A PARTICULAR PURPOSE. The data is subject to change as modifications and updates are complete. It is understood that the information contained in the Web feed is being used at one's own risk." Montana: "The Montana State Library provides this product/service for informational purposes only. The Library did not produce it for, nor is it suitable for legal, engineering, or surveying purposes. Consumers of this information should review or consult the primary data and information sources to ascertain the viability of the information for their purposes. The Library provides these data in good faith but does not represent or warrant its accuracy, adequacy, or completeness. In no event shall the Library be liable for any incorrect results or analysis; any direct, indirect, special, or consequential damages to any party; or any lost profits arising out of or in connection with the use or the inability to use the data or the services provided. The Library makes these data and services available as a convenience to the public, and for no other purpose. The Library reserves the right to change or revise published data and/or services at any time." Oregon: "This product is for informational purposes and may not have been prepared for, or be suitable for legal, engineering, or surveying purposes. Users of this information should review or consult the primary data and information sources to ascertain the usability of the information." File Descriptions The unmodified February, 2024 WestDAAT snapshot is composed of nine files. Below is a brief description of each file, as well as how they were utilized for HarDWR. WaDEDataDictionaryTerms.xlsx: As the file's name implies, this is a data dictionary for all of the below named files. This file describes the column names for each of the following files, with the exception of citation.txt which does not have any columns. The descriptions for each file are divided by tab,with the same name as their associated file, within this document. allocationamount.csv: The "main" file of the group, it contains the water right records for each state. Of particular note, each water right is broken down into one or more water allocations. Allocations may be withdrawn from one or more locations, or even multiple allocations associated with a particular location. This is a more subtle and realistic representation of how water is used than what was available in the first version of HarDWR. For the records from some states, this can mean that multiple allocations listed under a single right will appear as rows within this file. citation.txt: A combination of contact information for WaDE personnel, disclaimer about how the data should be used, and guidelines for citing WestDAAT. methods.csv: A file describing the source and method by which WaDE collected water rights data from each state. organization.csv: A file listing the water rights authoritative agencies for each state. sites.csv: This file provides the geographic, and other descriptors, of the physical location of allocations, called 'sites'. To reiterate, it is possible for one allocation to be associated with multiple sites, as well as one site to be associated with multiple allocations. The two descriptors which we were most interested in where the site's coordinates, as well as whether the site was classified as a Point of Diversion (POD) or a Place of Use (POU). As a general rule, PODs are geographic points, while POUs are areas typically represented as property boundaries or irregularly shaped polygons. sites_pouGeometry.csv: For those allocations with a POU site, this file contains the defining points for the associated polygons. variables.csv: A file describing the units in which an allocation's water amount is reported within WestDAAT. This information is essentially a repeat of the 'AllocationFlow_CFS' and 'AllocationVolume_AF' columns within allocationamount.csv, at least for our purposes. watersources: This file describes the source of water from which each site extracts from. For our purposes, this table was used to determine whether the water came from Surface Water, Groundwater, or Unspecified Water.

Lisk, Matthew↗