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DOE OSTI2021

Material Interactions in Severe Accidents – Benchmarking the MELCOR V2.2 Eutectics Model for a BWR-3 Mark-I Station Blackout: Part II – Uncertainty Analysis

Single case comparisons between severe accident simulations can provide detailed insights into severe accident model behavior, however, they cannot offer insights into model uncertainty, sensitivity to uncertain parameters, or underlying model biases.Here in this analysis, the single case benchmark comparison of the MELCOR material interaction models for a station blackout (SBO) scenario of a boiling water reactor (BWR) using representative Fukushima Daiichi Unit 1 boundary conditions is expanded to include an uncertainty analysis. As part of this uncertainty analysis, 1200 simulations are performed for each material interaction model (2400 total), with random sampling of 14 uncertain MELCOR input parameters. Input parameters are selected for their impact on models representing core degradation processes. These include candling, fuel rod failure, debris quenching and dryout. The analysis performed here is not a traditional “best-estimate” uncertainty analysis that uses best-estimate parameters or identifies best-estimate figure of merit distributions. Instead, it is an exploratory uncertainty analysis that identifies and interrogates underlying model form biases of the two material interaction models (eutectics and interactive materials models). Uniform distributions are applied to all uncertain parameters to ensure coverage of the model parameter uncertainty space. Key findings from this study include underlying model form biases exhibited by material interaction models, and notable differences in accident progression outcomes between the material interaction models. This uncertainty study extends and confirms the conclusions from the first part of this study, which compared the impact of material interaction modeling on simulation of a short-term station blackout scenario with representative Fukushima Daiichi Unit I boundary conditions. In particular, this study confirms that the eutectics model generally exhibits accelerated degradation and failure of fuel components, the core plate, and the lower head. The eutectics model also has a tendency to exhibit a greater degree of core degradation, greater debris mass formation, and larger debris mass ejection. Finally, the eutectics model exhibits higher maximum temperatures for fuel, cladding, particulate debris, oxidic molten pool, and metallic molten pool components than the interactive materials model; interactive materials model simulations exhibit a soft “limitation” on maximum temperatures that is related to the temperature at which material relocation occurs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Online distributed price-based control of DR resources with competitive guarantees

Demand response (DR) of building HVAC load can provide crucial demand-side flexibility for the future smart grid. Compared to direct load control, price-based control can respect the customers’ autonomy and privacy. However, it is challenging for price-based control to attain provable performance guarantees under future uncertainty. In this paper, we propose a framework for a utility to perform price-based control of flexible building load within the utility’s service area, in order to attain competitive performance guarantees in terms of controlling the system peak demand under future uncertainty. By adopting a two-step approach, our online price-based control solution can attain a provable competitive ratio for all possible realizations within a given uncertainty set. Simulation experiments demonstrate that, with a robustification procedure, our solution can perform well not only for worst-case inputs, but also for average-case inputs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

On the quantification and efficient propagation of imprecise probabilities with copula dependence

This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be mutually independent or correlated by a multivariate Gaussian distribution. However, this subjective assumption may introduce bias in the response estimate if the real dependence structure deviates from this assumption. In this work, we overcome this limitation by introducing a flexible copula dependence model to capture complex dependencies. Here, a hierarchical Bayesian multimodel approach is proposed to quantify uncertainty in dependence model-form and model parameters that result from small data sets. This approach begins by identifying, through Bayesian multimodel inference, a set of candidate marginal models and their corresponding model probabilities, and then estimating the uncertainty in the copula-based dependence structure, which is conditional on the marginals and their parameters. The overall uncertainties integrating marginals and copulas are probabilistically represented by an ensemble of multivariate candidate densities. A novel importance sampling reweighting approach is proposed to efficiently propagate the overall uncertainties through a computational model. Through an example studying the influence of constituent properties on the out-of-plane properties of transversely isotropic E-glass fiber composites, we show that the composite property with copula-based dependence model converges to the true estimate as data set size increases, while an independence or arbitrary Gaussian correlation assumption leads to a biased estimate.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

GenAI4UQ: A software for forward and inverse uncertainty quantification using conditional generative AI

We introduce GenAI4UQ, a software package for forward and inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting. GenAI4UQ leverages a generative AI-based conditional modeling framework to address limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo (MCMC) methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of input parameters and generation of predictions directly from observations. The software supports rapid ensemble forecasting with robust uncertainty quantification while maintaining computational and storage efficiency. Built-in auto-tuning of hyperparameters simplifies model training, ensuring accessibility for users with varying expertise. Its versatile conditional generative framework is applicable across diverse scientific domains. While GenAI4UQ offers significant advantages in flexibility and efficiency, users should interpret its uncertainty estimates with caution in data-sparse scenarios, as the model may overestimate uncertainty—an effect common to all surrogate-based approaches including MCMC with surrogate models. Despite this, GenAI4UQ transforms inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Sensitivity analysis of numerical modeling input parameters on floating offshore wind turbine loads

Abstract. Floating wind turbines must withstand a unique and challenging set of loads from the wind and ocean environment. To de-risk development, accurate predictions of these loads are necessary. Uncertainty in modeling predictions leads to larger required safety factors, increasing project costs and the levelized cost of energy. Complex aero-hydro-elastic modeling tools use many input parameters to represent the wind, waves, current, aerodynamic loads, hydrodynamic loads, and structural properties. It is helpful to understand which of these parameters ultimately drives a design. In this work, an ultimate and fatigue-proxy load sensitivity analysis was performed with 35 different input parameters, using an elementary effects approach to identify the most influential parameters for a case study involving the National Renewable Energy Laboratory (NREL) 5 MW baseline wind turbine atop the OC4-DeepCwind semisubmersible during normal operation. The importance of each parameter was evaluated using 14 response quantities of interest across three operational wind speed conditions. The study concludes that turbulent wind velocity standard deviation is the parameter with the strongest sensitivity; this value is important not just for turbine loads, but also for the global system response. The system center of mass in the wind direction is found to have the highest impact on the system rotation and tower loads. The current velocity is found to be the most dominating parameter for the system global motion and consequently the mooring loads. All tested wind turbulence parameters in addition to the standard deviation are also found to be influential. Wave characteristics are influential for some fatigue-proxy loading but do not significantly impact the extreme ultimate loads in these operational load cases. The required number of random seeds for stochastic environmental conditions is considered to ensure that the sensitivities are due to the input parameters and not due to the seed. The required number of analysis points in the parameter space is identified so that the conclusions represent a global sensitivity. The results are specific to the platform, turbine, and choice of parameter ranges, but the demonstrated approach can be applied widely to guide focus in parameter uncertainty.

17 WIND ENERGY↗

DOE OSTI2020

Precise measurements of branching fractions for $ {\mathrm{D}}_{\mathrm{s}}^{+} $ meson decays to two pseudoscalar mesons

We measure the branching fractions for seven $D$$^{+}_{s}$ two-body decays to pseudo-scalar mesons, by analyzing data collected at √s = 4.178 ~ 4.226 GeV with the BESIII detector at the BEPCII collider. The branching fractions are determined to be $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({D}_s^{+}\to {K}^{+}\eta \hbox{'}\right)=\left(2.68\pm 0.17\pm 0.17\pm 0.08\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to \eta \hbox{'}{\pi}^{+}\right)=\left(37.8\pm 0.4\pm 2.1\pm 1.2\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}\eta \right)=\left(1.62\pm 0.10\pm 0.03\pm 0.05\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to \eta {\pi}^{+}\right)=\left(17.41\pm 0.18\pm 0.27\pm 0.54\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}{K}_S^0\right)=\left(15.02\pm 0.10\pm 0.27\pm 0.47\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}_S^0{\pi}^{+}\right)=\left(1.109\pm 0.034\pm 0.023\pm 0.035\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}{\pi}^0\right)=\left(0.748\pm 0.049\pm 0.018\pm 0.035\right)\times {10}^{-3},\end{array}} $$ B D s + → K + η ' = 2.68 ± 0.17 ± 0.17 ± 0.08 × 10 - 3 , B D s + → η ' π + = 37.8 ± 0.4 ± 2.1 ± 1.2 × 10 - 3 , B D s + → K + η = 1.62 ± 0.10 ± 0.03 ± 0.05 × 10 - 3 , B D s + → η π + = 17.41 ± 0.18 ± 0.27 ± 0.54 × 10 - 3 , B D s + → K + K S 0 = 15.02 ± 0.10 ± 0.27 ± 0.47 × 10 - 3 , B D s + → K S 0 π + = 1.109 ± 0.034 ± 0.023 ± 0.035 × 10 - 3 , B D s + → K + π 0 = 0.748 ± 0.049 ± 0.018 ± 0.035 × 10 - 3 , where the first uncertainties are statistical, the second are systematic, and the third are from external input branching fraction of the normalization mode $ {D}_s^{+} $ D s + → K + K - π + . Precision of our measurements is significantly improved compared with that of the current world average values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Measurement of branching fractions of ${\Lambda}_{\textrm{c}}^{+}$ decays to Σ⁺K⁺K⁻, Σ⁺Φ and Σ⁺K⁺π⁻(π 0 )

Based on 4.5 fb - 1 data taken at seven center-of-mass energies ranging from 4.600 to 4.699 GeV with the BESIII detector at the BEPCII collider, we measure the branching fractions of $ {\Lambda}_c^{+} $ → Σ + + hadrons relative to $ {\Lambda}_c^{+} $ → Σ + π + π - . Combining with the world average branching fraction of $ {\Lambda}_c^{+} $ → Σ + π + π - , their branching fractions are measured to be (0 . 377 ± 0 . 042 ± 0 . 020 ± 0 . 021)% for $ {\Lambda}_c^{+} $ → Σ + K + K - , (0 . 200 ± 0 . 023 ± 0 . 011 ± 0 . 011)% for $ {\Lambda}_c^{+} $ → Σ + K + π - , (0 . 414 ± 0 . 080 ± 0 . 030 ± 0 . 023)% for $ {\Lambda}_c^{+} $ → Σ + Φ and (0 . 197 ± 0 . 036 ± 0 . 009 ± 0 . 011)% for $ {\Lambda}_c^{+} $ → Σ + K + K - (non- Φ ). In all the above results, the first uncertainties are statistical, the second are systematic and the third are from external input of the branching fraction of $ {\Lambda}_c^{+} $ → Σ + π + π - . Since no signal for $ {\Lambda}_c^{+} $ → Σ + K + π - π 0 is observed, the upper limit of its branching fraction is determined to be 0.13% at the 90% confidence level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Probabilistic inversion of circular phase spectra: application to two-station phase-velocity dispersion estimation in western Canada

SUMMARY Periodic directional and temporal measurements are common in seismology, and necessitate specific statistical analyses that are appropriate for circular quantities. In this work, we explore the use of a von Mises distribution as a representation of errors on circular seismological observations. Specifically, we automate the estimation of surface-wave phase-velocity dispersion for the teleseismic two-station method, which generally suffers from a 2π phase ambiguity. The use of Bayesian inverse techniques, which aim to rigorously quantify model parameter uncertainty, have become widespread throughout seismology over the last decade. Here, we apply Bayesian inversion to measurements of surface-wave phase spectra in order to estimate 1-D, path-averaged Earth structure between station pairs. The dispersion curve and associated uncertainties are additional results of the inversion, which can then be used as input for subsequent analyses (e.g. tomography). We demonstrate this technique through application to surface-wave recordings from long-running seismic stations throughout western Canada. Our results for over 10 000 station pairs reveal first-order tectonic features consistent with previous studies, which provides confidence in our approach as well as an initial step towards resolving a full 3-D seismic velocity model for the region. This work also presents a foundation for the inversion of surface-wave phase spectra to estimate 3-D Earth structure directly. Finally, the ideas presented in this work are not limited to the inversion of surface-wave phase spectra, but can also be considered for Bayesian geophysical inversion of any circular quantities.

Gosselin, Jeremy M. (ORCID:0000000203754102)↗

DOE OSTI2025

Bayesian analysis of the 86 Sr ⁢(𝛼,𝛼) reaction to constrain the 86 Sr ⁢(𝛼,𝑛) cross section at astrophysical energies

The alpha optical model potential (𝛼-OMP ) is a phenomenological approach used to describe elastic scattering where multiple reaction channels are open. It is one of the most critical inputs for the calculation of thermonuclear reaction rates in explosive stellar environments, but uncertainties within the 𝛼-OMP lead to imprecise predictions hindering comparisons between calculations and observations. In order to improve the precision of the 𝛼-OMP, additional nuclear physics data are required. In this paper, a measurement of the 86 Sr (𝛼, 𝛼) elastic scattering cross section at multiple energies is reported. Here, a local optical potential is constructed via a fully Bayesian analysis of the elastic scattering data. The resulting uncertainties on the low-energy cross sections relevant to nuclear astrophysics are then calculated and shown to be on the order of 50%.

59 ≤ A ≤ 89↗

DOE OSTI2022

Origin of Plutonium-244 in the Early Solar System

We investigate the origin in the early Solar System of the short-lived radionuclide 244 Pu (with a half life of 80 Myr) produced by the rapid (r) neutron-capture process. We consider two large sets of r-process nucleosynthesis models and analyse if the origin of 244 Pu in the ESS is consistent with that of the other r and slow (s) neutron-capture process radioactive nuclei. Uncertainties on the r-process models come from both the nuclear physics input and the astrophysical site. The former strongly affects the ratios of isotopes of close mass ( 129 I/ 127 I, 244 Pu/ 238 U, and 247 Pu/ 235 U). The 129 I/ 247 Cm ratio, instead, which involves isotopes of a very different mass, is much more variable than those listed above and is more affected by the physics of the astrophysical site. We consider possible scenarios for the evolution of the abundances of these radioactive nuclei in the galactic interstellar medium and verify under which scenarios and conditions solutions can be found for the origin of 244 Pu that are consistent with the origin of the other isotopes. Solutions are generally found for all the possible different regimes controlled by the interval (δ) between additions from the source to the parcel of interstellar medium gas that ended up in the Solar System, relative to decay timescales. If r-process ejecta in interstellar medium are mixed within a relatively small area (leading to a long δ), we derive that the last event that explains the 129 I and 247 Cm abundances in the early Solar System can also account for the abundance of 244 Pu. Due to its longer half life, however, 244 Pu may have originated from a few events instead of one only. If r-process ejecta in interstellar medium are mixed within a relatively large area (leading to a short δ), we derive that the time elapsed from the formation of the molecular cloud to the formation of the Sun was 9-16 Myr.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Presentation: Scenario Timeline Exploration

Slides to discuss a current project with DOE. Topic focus is on: - Advanced reactors will be able to use risk insights for many design aspects - We need bounding scenarios for screening and scoping purposes - We need realistic scenarios for input into the licensing basis safety-case - We need to manage inherent uncertainty - We need to automate the safety-case creation as much as possible

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2020

A spatial emergent constraint on the sensitivity of soil carbon turnover to global warming

Carbon cycle feedbacks represent large uncertainties in climate change projections, and the response of soil carbon to climate change contributes the greatest uncertainty to this. Future changes in soil carbon depend on changes in litter and root inputs from plants and especially on reductions in the turnover time of soil carbon (τ s ) with warming. An approximation to the latter term for the top one metre of soil (ΔC s,τ ) can be diagnosed from projections made with the CMIP6 and CMIP5 Earth System Models (ESMs), and is found to span a large range even at 2 °C of global warming (-196 ± 117 PgC). Here, we present a constraint on ΔC s,τ , which makes use of current heterotrophic respiration and the spatial variability of τs inferred from observations. This spatial emergent constraint allows us to halve the uncertainty in ΔC s,τ at 2 °C to -232 ± 52 PgC.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Benchmark Calculation for the Peach Bottom Unit 2 Cycles 1-3 Using the SCALE 6.3/Polaris–PARCS v3.4.2 Code Package

In this study, benchmark calculations were performed for Peach Bottom Unit 2 cycles 1–3 to validate the SCALE 6.3/Polaris–PARCS v3.4.2 with the ENDF/B-VII.1 AMPX 56-group library by comparing the simulated results with the measured data. The benchmark results will be used to evaluate uncertainties of the SCALE/Polaris–PARCS code package for boiling water reactor physics analysis for key nuclear parameters such as reactivity and assembly power peaking factors. This report details plant and fuel design specifications and input data for SCALE/Polaris, GenPMAXS and PARCS. Additionally, detailed information is provided for all the input and output files produced for the benchmark calculations. The benchmark results were summarized such that they can be used to evaluate uncertainties with other benchmark results for key nuclear parameters.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Fantômas unconfined: global QCD fits with Bézier parameterizations

Fantômas is a C++ toolkit for exploring the parametrization dependence of parton distribution functions (PDFs) and other correlator functions in quantum chromodynamics (QCD). Fantômas facilitates the generation of adaptable polynomial parametrizations for PDFs, called metamorphs, to find best-fit PDF solutions and quantify the epistemic uncertainty associated with the parametrizations during their fitting. The method employs Bézier curves as universal approximators for a variety of PDF shapes. Integrated into the xFitter framework for the global QCD analysis, Fantômas provides a foundation for general models of PDFs, while reducing the computational time compared to the approaches utilizing traditional polynomial parametrizations as well as providing an interpretable alternative to neural-network-based models. This paper outlines the structure and practical usage of the Fantômas toolkit, including its inputs, outputs, and implementation within xFitter. It also provides a practical example of using Fantômas for uncertainty quantification as well as the combination of PDF fits into a single ensemble.

Bézier curves↗

DOE OSTI2024

Benchmark Calculation for the Hatch Unit 1 Cycles 1-3 Using the SCALE 6.3/Polaris–PARCS v3.4.2 Code Package

This study was the performance of the benchmark calculation for the Hatch Unit 1 cycles 1–3, to validate the SCALE 6.3/Polaris–PARCS v3.4.2 with the ENDF/B-VII.1 AMPX 56-group library by comparing the simulated results with the measured data. The benchmark results will be used in evaluating uncertainties of the SCALE/Polaris–PARCS code package for boiling water reactor (BWR) physics analysis for key nuclear parameters such as reactivity and assembly power peaking factors. This report details plant and fuel design specifications and input data for SCALE/Polaris, GenPMAXS and PARCS, and additionally, detailed information is provided for all the input and output files produced for the benchmark calculations. The benchmark results were summarized such that they can be used in evaluating uncertainties for key nuclear parameters with other BWR benchmark results.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Significant impact of forcing uncertainty in a large ensemble of climate model simulations

Forcing due to solar and volcanic variability, on the natural side, and greenhouse gas and aerosol emissions, on the anthropogenic side, are the main inputs to climate models. Reliable climate model simulations of past and future climate change depend crucially upon them. Here we analyze large ensembles of simulations using a comprehensive Earth System Model to quantify uncertainties in global climate change attributable to differences in prescribed forcings. The different forcings considered here are those used in the two most recent phases of the Coupled Model Intercomparison Project (CMIP), namely CMIP5 and CMIP6. We show significant differences in simulated global surface air temperature due to volcanic aerosol forcing in the second half of the 19th century and in the early 21st century. The latter arise from small-to-moderate eruptions incorporated in CMIP6 simulations but not in CMIP5 simulations. We also find significant differences in global surface air temperature and Arctic sea ice area due to anthropogenic aerosol forcing in the second half of the 20th century and early 21st century. These differences are as large as those obtained in different versions of an Earth System Model employing identical forcings. In simulations from 2015 to 2100, we find significant differences in the rates of projected global warming arising from CMIP5 and CMIP6 concentration pathways that differ slightly but are equivalent in terms of their nominal radiative forcing levels in 2100. Our results highlight the influence of assumptions about natural and anthropogenic aerosol loadings on carbon budgets, the likelihood of meeting Paris targets, and the equivalence of future forcing scenarios.

54 ENVIRONMENTAL SCIENCES↗