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DOE OSTI2022

A review of water valuation metrics: Supporting sustainable water use in manufacturing

In the manufacturing sector, water has been often considered too cheap to conserve. Such thinking relies on water valuations that limit the value of water to the price paid. Using such simple methods, the share of water cost to total manufacturing cost is significantly small, <3%. As a result, conserving water and enabling technology uptake is difficult to justify economically and slow to advance, hindering progress toward sustainable water use. However, the value of water to a manufacturer is far greater than the price paid. Valuations such as the true cost of water consider the additional in-plant treatment and energy costs and have been gaining greater traction in the manufacturing sector. However, true cost alone still undervalues water by not accounting for economic and social costs related to scarcity and environmental externalities. This paper makes the case and presents a framework for valuing manufacturing water beyond the price paid and the true cost. The proposed fuller valuation of manufacturing water takes into account the internal and opportunity costs associated with the realization of water risks. The paper follows with a review of a wide range of water valuation metrics, both at the specific industry level and regional/economy-wide level. The use of various valuation metrics incorporating the relationship between the change in value with change in water use, such as marginal value of water, shadow price, and elasticity at the specific industry level, has been limited in the U.S. manufacturing sector. Further, a limited number of studies exist on data-intensive subjective evaluation techniques such as computable general equilibrium modeling and input-output modeling for regional water valuation. After reviewing water value metrics, several recent case studies from manufacturers from the literature are presented to illustrate both the promise and challenges of a fuller valuation of water as proposed here. Some large multinational corporations have moved toward assessing the value of water via supply chain sustainability initiatives, environmental profit and loss accounting, estimating risk-adjusted values of water, hydro-economic modeling, natural capital asset valuation, and developing value chain indices. This paper provides policymakers and technology developers a framework for monetizing water value beyond its true cost and current metrics. If adopted, such fuller water valuations can help make the business case for the development and deployment of cost-effective water-conserving technologies, thereby improving the sustainability of the manufacturing sector with respect to water.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A Unified Metric for Fast Frequency Response in Low-Inertia Power Systems

Future power systems with more inverter-based resources (IBRs), will be vulnerable to frequency decline contingencies. Fast frequency response (FFR) provided by IBRs is a good candidate to arrest frequency excursions. Diverse types of FFR have been proposed, and some have been deployed in our power systems. Without a unified quantification of FFR, it is hard for the grid operators to compare and fully leverage the FFR capabilities of IBRs. This work introduces a potential unified metric that quantifies two key characteristics of FFR and describes its application to three prevailing FFR types. We then use metric-to-frequency mapping to validate the accuracy of the metric in predicting the impact of a given FFR on the trajectory of a frequency event. The results show that the proposed metric is simple yet accurately captures the ability of diverse forms of FFR to improve system frequency dynamics.

effective inertia↗
DOE OSTI2022

Resilience Metrics for Building-Level Electrical Distribution Systems with Energy Storage

The energy system infrastructure that delivers power to a building's loads needs to be resilient to withstand and recover from extreme outages (e.g., grid faults that leave millions of people without power during severe weather events). Building-level electrical distribution systems (BEDSs) distribute power from a building's energy sources - including the grid, solar photovoltaic (PV) panels, and batteries - to its loads, including lighting, HVAC, and plug loads. BEDS with storage can provide resilience by distributing local electricity supply to critical loads during an outage. Quantitative metrics are needed to assess the resilience improvements associated with new BEDS and storage system technologies. In this paper, we apply an existing metric, the probability of outage survival curve (POSC), to BEDS with storage and propose novel metrics that improve upon POSC. Through a simulation-based case study, we demonstrate how these metrics are impacted by the BEDS design and how they can be used to design a resilient system.

buildings↗
DOE OSTI2021

Extreme metrics from large ensembles: investigating the effects of ensemble size on their estimates

Abstract. We consider the problem of estimating the ensemble sizes required to characterize the forced component and the internal variability of a number of extreme metrics. While we exploit existing large ensembles, our perspective is that of a modeling center wanting to estimate a priori such sizes on the basis of an existing small ensemble (we assume the availability of only five members here). We therefore ask if such a small-size ensemble is sufficient to estimate accurately the population variance (i.e., the ensemble internal variability) and then apply a well-established formula that quantifies the expected error in the estimation of the population mean (i.e., the forced component) as a function of the sample size n, here taken to mean the ensemble size. We find that indeed we can anticipate errors in the estimation of the forced component for temperature and precipitation extremes as a function of n by plugging into the formula an estimate of the population variance derived on the basis of five members. For a range of spatial and temporal scales, forcing levels (we use simulations under Representative Concentration Pathway 8.5) and two models considered here as our proof of concept, it appears that an ensemble size of 20 or 25 members can provide estimates of the forced component for the extreme metrics considered that remain within small absolute and percentage errors. Additional members beyond 20 or 25 add only marginal precision to the estimate, and this remains true when statistical inference through extreme value analysis is used. We then ask about the ensemble size required to estimate the ensemble variance (a measure of internal variability) along the length of the simulation and – importantly – about the ensemble size required to detect significant changes in such variance along the simulation with increased external forcings. Using the F test, we find that estimates on the basis of only 5 or 10 ensemble members accurately represent the full ensemble variance even when the analysis is conducted at the grid-point scale. The detection of changes in the variance when comparing different times along the simulation, especially for the precipitation-based metrics, requires larger sizes but not larger than 15 or 20 members. While we recognize that there will always exist applications and metric definitions requiring larger statistical power and therefore ensemble sizes, our results suggest that for a wide range of analysis targets and scales an effective estimate of both forced component and internal variability can be achieved with sizes below 30 members. This invites consideration of the possibility of exploring additional sources of uncertainty, such as physics parameter settings, when designing ensemble simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Resilience Metrics for Building-Level Electrical Distribution Systems with Energy Storage: Preprint

The energy system infrastructure that delivers power to a building's loads needs to be resilient, such that it can withstand and recover from extreme outages (e.g., grid faults that leave millions of people without power during severe weather events). Building-level electrical distribution systems (BEDSs) distribute power from a building's energy sources - including the grid, solar photovoltaic (PV) panels, and batteries - to its loads, including lighting, HVAC, and plug loads. BEDS with storage can provide resilience by distributing local electricity supply to critical loads during an outage. Quantitative metrics are needed to assess the resilience improvements associated with new BEDS and storage system technologies. In this paper, we apply an existing metric, the probability of outage survival curve (POSC), to BEDS with storage and propose a set of novel metrics that improve upon POSC. Through a simulation-based case study, we demonstrate how these metrics are impacted by the BEDS design and how they can be used to design a resilient system.

buildings↗
DOE OSTI2022

A Unified Metric for Fast Frequency Response in Low-Inertia Power Systems: Preprint

Future power system with more inverter-based resources (IBRs) is vulnerable to the frequency-decline contingency. Fast frequency response (FFR) provided by IBRs is a good candidate to arrest the frequency excursion. Diverse types of FFRs have been integrated into the power system. Without a unified quantification of FFRs, it is hard for the grid operators to fully leverage the FFR capabilities of IBRs. This work introduces potential unified metrics of prevailing FFRs. We utilized the metric-to-frequency (M2F) mapping to validate the accuracy of the metrics. The results show the proposed metric to be simple yet accurate.

effective inertia↗
DOE OSTI2025

Understanding ERE and iVOC Metrics for Graded CdSeTe Absorbers

PL-based external radiative efficiency (ERE) and implied open-circuit voltage (iVOC) metrics were introduced for thin-film solar absorbers to better understand the voltage deficit and diagnose losses in solar cells. Traditionally, elevated ERE and iVOC measurements are associated with diminished recombination within the solar device, a rationale heavily reliant on the assumption of a uniform bandgap and high carrier mobilities in the absorber. Recently, very low mobilities in CdSeTe absorbers (< 1 cm2/(V.s)) were measured using the light-induced transient grading technique. In this study, we use a detailed numerical model of iVOC to investigate the possible reasons of elevated iVOC in realistic CdSeTe absorbers with a graded Se profile. In particular, we examine how the bandgap nonuniformity and the reduced hole mobility in graded CdSeTe absorbers affect iVOC measurements. We show that high iVOC may result from inflated quasi-Fermi level splitting in the high-Se region in the front part of a CdSeTe absorber with slow hole transport. We reproduce the experimentally reported 360 mV increase in iVOC-VOC gap with reduced doping using a model with sub-1 cm2/(V.s) hole mobility in the high-Se region. Based on our results, we conclude that the iVOC metric (or ERE metric) should not be used as a sole metric of CdSeTe absorber quality. We discuss possible ways to extract useful information from the iVOC-VOC gap by supplementing the front-side illumination measurements with back-side illumination measurements.

14 SOLAR ENERGY↗
DOE OSTI2025

Explainable artificial intelligence relates perovskite luminescence images to current-voltage metrics

As the demand for low-cost, high-efficiency solar energy technologies grows, metal halide perovskite (MHP) solar cells have emerged as a promising candidate for next-generation photovoltaics due to their high power conversion efficiencies. However, their poor durability and issues with manufacturing consistency remain significant barriers to commercialization. In this work, we develop deep learning models to support materials characterization and provide insight into features and processes influencing performance. The models are trained using transfer learning of a pretrained model to predict relevant current-voltage (IV) metrics based on different combinations of input electroluminescence (EL) and photoluminescence (PL) images of MHP devices. We examine which image types are most informative in accurately predicting different IV metrics. Additionally, we use explainable artificial intelligence (XAI) techniques to provide insights into specific spatial features in the devices that drive differences in performance. We find that stabilized luminescence images (e.g. those collected after biasing the devices for at least 1 min) are better for predicting metrics of open-circuit voltage (by PL) and short-circuit current (by PL with EL), but that predicting fill factor and overall power output may use the time-evolution of EL images. Based on attribution masks generated by integrated gradients for each device performance metric, we further suggest different loss mechanisms associated with categories of large and small spatial defects. Overall, this case study highlights the potential applicability of XAI methodology for streamlining MHP device analysis and accelerating detailed understanding of the relationships between spatial defects and impacts on performance.

14 SOLAR ENERGY↗
DOE OSTI2021

Deep-Learning-Derived Evaluation Metrics Enable Effective Benchmarking of Computational Tools for Phosphopeptide Identification

Tandem mass spectrometry (MS/MS)-based phosphoproteomics is a powerful technology for global phosphorylation analysis. However, applying four computational pipelines to a typical mass spectrometry (MS)-based phosphoproteomic dataset from a human cancer study, we observed a large discrepancy among the reported phosphopeptide identification and phosphosite localization results, underscoring a critical need for benchmarking. While efforts have been made to compare performance of computational pipelines using data from synthetic phosphopeptides, evaluations involving real application data have been largely limited to comparing the numbers of phosphopeptide identifications due to the lack of appropriate evaluation metrics. We investigated three deep learning-derived features as potential evaluation metrics: phosphosite probability, Delta RT and spectral similarity. Predicted phosphosite probability is computed by MusiteDeep, which provides high accuracy as previously reported; Delta RT is defined as the absolute retention time (RT) difference between RTs observed and predicted by AutoRT; and spectral similarity is defined as the Pearson’s correlation coefficient between spectra observed and predicted by pDeep2. Using a synthetic peptide dataset, we found that both Delta RT and spectral similarity provided excellent discrimination between correct and incorrect peptide-spectrum matches (PSMs) both when incorrect PSMs involved wrong peptide sequences and even when incorrect PSMs were caused by only incorrect phosphosite localization. Based on these results, we used all the three deep learning-derived features as evaluation metrics to compare different computational pipelines on diverse set of phosphoproteomic datasets and showed their utility in benchmarking performance of the pipelines. The benchmark metrics demonstrated in this study will enable users to select computational pipelines and parameters for routine analysis of phosphoproteomics data and will offer guidance for developers to improve computational methods.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Earth Mover’s Distance as a Metric to Evaluate the Extent of Charge Transfer in Excitations Using Discretized Real-Space Densities

This paper presents a novel theoretical measure, μ EMD , based on the earth mover's distance (EMD), for quantifying the density shift caused by electronic excitations in molecules. As input, the EMD metric uses only the discretized ground- and excited-state electron densities in real space, rendering it compatible with almost all electronic structure methods used to calculate excited states. The EMD metric is compared against other popular theoretical metrics for describing the extent of electron-hole separation in a wide range of excited states (valence, Rydberg, charge transfer, etc.). Further, the results showcase the EMD metric's effectiveness across all excitation types and suggest that it is useful as an additional tool to characterize electronic excitations. The study also reveals that μ EMD can function as a promising diagnostic tool for predicting the failure of pure exchange-correlation functionals. Specifically, we show statistical relationships among the functional-driven errors, the exact exchange content within the functional, and the magnitude of μ EMD values.

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

Assessing Radiative Feedbacks and Their Contribution to the Arctic Amplification Measured by Various Metrics

Arctic amplification (AA), characterized by a more rapid surface air temperature (SAT) warming in the Arctic than the global average, is a major feature of global climate warming. Various metrics have been used to quantify AA based on SAT anomalies, trends, or variability, and they can yield quite different conclusions regarding the magnitude and temporal patterns of AA. This study examines and compares various AA metrics for their temporal consistency in the region north of 70°N from the early twentieth to the early 21st century using observational data and reanalysis products. We also quantify contributions of different radiative feedback mechanisms to AA based on short-term climate variability in reanalysis and model data using the Kernel-Gregory approach. Albedo and lapse rate feedbacks are positive and comparable, with albedo feedback being the leading contributor for all AA metrics. The net cloud feedback, which has large uncertainties, depends strongly on the data sets and AA metrics used. By quantifying the influence of internal variability on AA and related feedbacks based on global climate model ensemble simulations, we find that water vapor and cloud feedbacks are most heavily affected by internal variability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

The efficacy of Lewis affinity scale metrics to represent solvent interactions with reagent salts in all-inorganic metal halide perovskite solutions

Solvents employed in the solution processing of metal halide perovskites are known to play a key role in defining the morphology and properties of the resulting thin film, and thus the performance of perovskite solar cell devices. Accurate metrics are needed that are capable of differentiating among candidates, finding solvents that adequately solubilize the various precursor species in solution and facilitate the nucleation and growth of these materials. Existing metrics such as the unsaturated Mayer bond order (UMBO) and the Gutmann donor number (DN) have been tested for lead iodide perovskite systems; but there has yet to be a comprehensive study on their transferability to lead-free perovskite solutions. Here, we use ab initio methods (density functional theory) and regression analysis tools to study the usefulness of DN and BF 3 affinity scales in this regard. We compared the relative effectiveness of these scales to describe interactions between solvents and BXn perovskite salts of lead (Pb 2+ ), tin (Sn 2+ and Sn 4+ ), germanium (Ge 2+ ), bismuth (Bi 3+ ), and antimony (Sb 3+ and Sb 5+ ). The DN proved to be a better representation than the BF 3 of such interactions, reflecting the closer similarity of these species to the “parent” SbCl 5 Lewis acid than to BF 3 . In addition, we have uncovered the usefulness of the lithium cation affinity metric (LCA) to describe the strength of interactions between solvents and A-site cations (e.g. Na + , K + , Rb + and Cs + ) in all-inorganic metal halide perovskite solutions. We find that the coordination strengths of solvents towards species in all-inorganic metal halide perovskite solutions are best described by two different metrics with distinct modes of action: DN differentiates among BX n salt complexes, and LCA among A-site cation species. This revelation can help guide the choice of solvent to optimize processing conditions. It also emphasizes the importance of selecting solvents whose DN and LCA optimize coordination to key Lewis acid species in all-inorganic perovskite solutions.

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

Operational resilience metrics for power systems with penetration of renewable resources

Abstract Modern power grid is evolving towards carbon neutrality by deploying increasing amount of renewable energy resources. However, the impact of renewable generation on power system planning and operation is not sufficiently investigated, especially the capability of renewable penetrated power systems to resist and recover from major disturbances, which is a critical concern for system operators. Novel metrics and evaluation methodologies are needed to depict systems’ ability in response to events caused by natural disasters, and quantitatively evaluate system performance in various time scales. In this paper, operational resilience metrics are proposed for power systems with penetration of renewable energy resources based on transient stability principles. A systematic methodology is proposed to quantitatively assess the evolution of system performance during various stages of the disaster process. Based on the proposed metrics, a resilience‐oriented disaster management strategy is designed and validated using the modified IEEE 39‐bus test system. The simulation results demonstrate the validity of the proposed metrics and strategy, and show that the system resilience is enhanced during the mitigation of fault conditions.

Gui, Jianzhong↗
DOE OSTI2025

Metrics and extrapolation of resonant magnetic perturbation thresholds for ELM suppression

This large database study of resonant magnetic perturbation (RMP) edge localized mode (ELM) suppression thresholds in the AUG, DIII-D, EAST, and KSTAR tokamaks details the key strengths and weaknesses of RMP metrics. The RMP ELM suppression database used for this work contains plasma information at the time of transition from ELMing to ELM suppressed states where a clear experimental threshold is identified. The experimental threshold distributions are compared for five metrics: (1) the island overlap width, (2) pedestal top Chirikov overlap, (3) peeling edge displacement, (4) pedestal top resonant drive, and (5) edge dominant mode overlap. The distributions, the regularity of the dependence on RMP coil currents, and the sensitivities of a given metric to equilibrium reconstruction details are compared. The overlap metric proves to be a good compromise between including the appropriate plasma response physics and maintaining a numerical robustness. This quantity does not exhibit clear power-law scalings for projection, but machine learning can assist in predicting thresholds within the existing parameter ranges and providing uncertainty quantification of those predictions. Two new first-principles models, one utilizing a threshold from the non-linear Modified Rutherford equation evaluated at the pedestal top and one utilizing the SLAYER code to calculate the linear tearing threshold from torque balance, offer possible paths to extrapolation beyond the existing database parameter space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Heat metrics and thresholds reshape population exposure and inequality signals

Extreme heat is intensifying worldwide, yet estimates of heat hazard and exposure inequality depend on both the heat metric and how extreme days are defined. Using summer 2022 across the Mediterranean, we quantify population heat exposure with four metrics—land surface temperature (LST), air temperature (Ta), heat index (HI), and wet-bulb globe temperature (WBGT)—under absolute (fixed-value) and relative (anomaly-based) thresholds. Under absolute thresholds, total heat exposure differs by more than two orders of magnitude across metrics (31.3 billion person-days for Ta vs 0.3 billion for HI). Geographic hotspots also diverge: WBGT concentrates in humid coastal North Africa (e.g. the Nile Delta), whereas Ta and LST are more widespread. Under relative thresholds, exposure totals converge and cross-metric hotspot agreement increases (e.g. Ta–WBGT top-tercile overlap increases from 10.7% to 29.0%), shifting hotspots toward densely populated southern Europe. Crucially, the exposure–deprivation relationship also reverses across threshold frameworks: absolute thresholds concentrate exposure in more deprived North Africa and the Middle East, whereas relative thresholds shift the burden toward less-deprived European cities. This sensitivity is decision-relevant: city rankings based on WBGT exposure duration are almost completely reordered when switching threshold frameworks. Threshold choice therefore systematically reshapes hotspot patterns and inequality signals. Reporting both absolute and relative exposures can reveal hidden hotspots and support more targeted heat-risk monitoring and intervention planning.

Mediterranean↗
DOE OSTI2025

Single Kerr-Schild metric for Taub-NUT instanton

It is shown that a complex coordinate transformation maps the Taub-Newman-Unti-Tamburino instanton metric to a Kerr-Schild metric. This metric involves a semi-infinite line defect as the gravitational analog of the Dirac string, much like the original metric. Moreover, it facilitates three versions of classical double copy correspondence with the self-dual dyon in electromagnetism, one of which involves a nonlocal operator. The relevance to the Newman-Janis algorithm is briefly noted. Published by the American Physical Society 2025

Kim, Joon-Hwi (ORCID:000000025474123X)↗
DOE OSTI2025

Integrated Metrics for County-Level Resilience Ranking Using Entropy and TOPSIS

In the face of atypical weather events, power infrastructure failures, and limited resources for resilience investment, energy decision-makers need data-driven metrics to allocate resilience investments and maximize the reduction of power outage impacts. For state-level planning, for instance, ranking the resilience of each county is key to ensuring effective distribution of resources. In such cases, resilience for each spatial unit is multifaceted and is captured by a set of indicators (i.e., metrics) that can be combined into an overall score that reduces the complexity of power outage dynamics to a single decision metric. However, weighting of these indicators is often addressed by simplifying assumptions (i.e., equal weights) or semi-subjective methods that rely on user-defined weights that can introduce biases (e.g., weighted average score). Within the disaster risk reduction and resilience engineering community, a recurring challenge in multicriteria decision-making is the objective weighting of indicators for composite indices. To address this issue, we have leveraged a Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) combined with an entropy-based weighting approach to calculated the integrated scores. This method objectively determines the importance of each metric, better discerns between spatial units (i.e., counties), and offers a more reliable ranking of counties according to their relative resilience attributes. By improving methods for integrating resilience indicators, our approach helps planners and decision-makers prioritize resources more effectively for more efficient resilience investments.

Bhusal, Narayan [Oak Ridge National Laboratory (OR↗
DOE OSTI2023

Metrics for Evaluating Grid Service Provision from Communities of Grid-interactive and Efficient Buildings and other DER

Tapping into the flexibility of aggregations of Grid-interactive and Efficiency Buildings (GEBs) represent a large opportunity to cost-effectively improve operations in future low-carbon power grids. The US Department of Energy's Connected Communities program seeks to demonstrate collections of these GEBs at 10 different sites across the country. However, consistent metrics for evaluation across all projects are needed to build confidence in the approach. This paper presents the metrics relating to Grid Service Provision that will be computed at the 10 demonstrations. The metrics proposed quantity the magnitude of service offers, the consistency and quality of services provided by the community, and the individual DER contributions to the community-level service. The goal of this work is to present these metrics and describe some of their intended insights. The hope is that these insights will be useful and build confidence for grid operators, regulators, and aggregators and practitioners as they look to deploy these resources in grids of the future.

MacDonald, Jason S↗