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DOE OSTI2022

Computational Response Theory for Dynamics

Quantifying the sensitivity - how a quantity of interest (QoI) varies with respect to a parameter – and response – the representation of a QoI as a function of a parameter - of a computer model of a parametric dynamical system is an important and challenging problem. Traditional methods fail in this context since sensitive dependence on initial conditions implies that the sensitivity and response of a QoI may be ill-conditioned or not well-defined. If a chaotic model has an ergodic attractor, then ergodic averages of QoIs are well-defined quantities and their sensitivity can be used to characterize model sensitivity. The response theorem gives sufficient conditions such that the local forward sensitivity – the derivative with respect to a given parameter - of an ergodic average of a QoI is well-defined. We describe a method based on ergodic and response theory for computing the sensitivity and response of a given QoI with respect to a given parameter in a chaotic model with an ergodic and hyperbolic attractor. This method does not require computation of ensembles of the model with perturbed parameter values. The method is demonstrated and some of the computations are validated on the Lorenz 63 and Lorenz 96 models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Probabilistic projections of the Amery Ice Shelf catchment, Antarctica, under conditions of high ice-shelf basal melt

Abstract. Antarctica's Lambert Glacier drains about one-sixth of the ice from the East Antarctic Ice Sheet and is considered stable due to the strong buttressing provided by the Amery Ice Shelf. While previous projections of the sea-level contribution from this sector of the ice sheet have predicted significant mass loss only with near-complete removal of the ice shelf, the ocean warming necessary for this was deemed unlikely. Recent climate projections through 2300 indicate that sufficient ocean warming is a distinct possibility after 2100. This work explores the impact of parametric uncertainty on projections of the response of the Lambert–Amery system (hereafter “the Amery sector”) to abrupt ocean warming through Bayesian calibration of a perturbed-parameter ice-sheet model ensemble. We address the computational cost of uncertainty quantification for ice-sheet model projections via statistical emulation, which employs surrogate models for fast and inexpensive parameter space exploration while retaining critical features of the high-fidelity simulations. To this end, we build Gaussian process (GP) emulators from simulations of the Amery sector at a medium resolution (4–20 km mesh) using the Model for Prediction Across Scales (MPAS)-Albany Land Ice (MALI) model. We consider six input parameters that control basal friction, ice stiffness, calving, and ice-shelf basal melting. From these, we generate 200 perturbed input parameter initializations using space filling Sobol sampling. For our end-to-end probabilistic modeling workflow, we first train emulators on the simulation ensemble and then calibrate the input parameters using observations of the mass balance, grounding line movement, and calving front movement with priors assigned via expert knowledge. Next, we use MALI to project a subset of simulations to 2300 using ocean and atmosphere forcings from a climate model for both low- and high-greenhouse-gas-emission scenarios. From these simulation outputs, we build multivariate emulators by combining GP regression with principal component dimension reduction to emulate multivariate sea-level contribution time series data from the MALI simulations. We then use these emulators to propagate uncertainty from model input parameters to predictions of glacier mass loss through 2300, demonstrating that the calibrated posterior distributions have both greater mass loss and reduced variance compared to the uncalibrated prior distributions. Parametric uncertainty is large enough through about 2130 that the two projections under different emission scenarios are indistinguishable from one another. However, after rapid ocean warming in the first half of the 22nd century, the projections become statistically distinct within decades. Overall, this study demonstrates an efficient Bayesian calibration and uncertainty propagation workflow for ice-sheet model projections and identifies the potential for large sea-level rise contributions from the Amery sector of the Antarctic Ice Sheet after 2100 under high-greenhouse-gas-emission scenarios.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Huge ensembles – Part 1: Design of ensemble weather forecasts using spherical Fourier neural operators

Abstract. Simulating low-likelihood high-impact extreme weather events in a warming world is a significant and challenging task for current ensemble forecasting systems. While these systems presently use up to 100 members, larger ensembles could enrich the sampling of internal variability. They may capture the long tails associated with climate hazards better than traditional ensemble sizes. Due to computational constraints, it is infeasible to generate huge ensembles (comprised of 1000–10 000 members) with traditional, physics-based numerical models. In this two-part paper, we replace traditional numerical simulations with machine learning (ML) to generate hindcasts of huge ensembles. In Part 1, we construct an ensemble weather forecasting system based on spherical Fourier neural operators (SFNOs), and we discuss important design decisions for constructing such an ensemble. The ensemble represents model uncertainty through perturbed-parameter techniques, and it represents initial condition uncertainty through bred vectors, which sample the fastest-growing modes of the forecast. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (IFS) as a baseline, we develop an evaluation pipeline composed of mean, spectral, and extreme diagnostics. With large-scale, distributed SFNOs with 1.1 billion learned parameters, we achieve calibrated probabilistic forecasts. As the trajectories of the individual members diverge, the ML ensemble mean spectra degrade with lead time, consistent with physical expectations. However, the individual ensemble members' spectra stay constant with lead time. Therefore, these members simulate realistic weather states during the rollout, and the ML ensemble passes a crucial spectral test in the literature. The IFS and ML ensembles have similar extreme forecast indices, and we show that the ML extreme weather forecasts are reliable and discriminating. These diagnostics ensure that the ensemble can reliably simulate the time evolution of the atmosphere, including low-likelihood high-impact extremes. In Part 2, we generate a huge ensemble initialized each day in summer 2023, and we characterize the simulations of extremes.

Mahesh, Ankur↗

DOE OSTI2023

Assessing the nexus between groundwater and solar energy plants in a desert basin with a dual-model approach under uncertainty

Globally, many solar power plants and other types of renewable energy are being located in water-scarce regions. Many projects rely on groundwater resources whose sustainability is uncertain. In the Chuckwalla Basin in California, quantification of recharge and trans-valley underflow is needed to estimate the impacts of solar project withdrawals on the water table. However, such estimates are highly challenging due to data scarcity, heterogeneous soils and long residence times. Conventional assessment employs isolated groundwater models configured with crude and uniform estimates of recharge. Here, we employ a data-constrained surface subsurface processes model, PAWS+CLM, to provide an ensemble of recharges and underflows with perturbed parameters. Then, the Parameter Estimation (PEST) package is used to calibrate MODFLOW aquifer conductivity and filter out implausible recharges. The novel dual-model approach, potentially applicable in other arid regions, can effectively assimilate groundwater head observations, reject unrealistic parameters, and narrow the range of estimated drawdowns. Simulated recharge concentrates along alluvial fans at the mountain fronts and ephemeral washes where run-off water infiltrates. If an evenly distributed recharge was assumed, it resulted in under-estimated drawdown and larger uncertainty bounds. The withdrawals are approaching total inflow, suggesting the system will be nearing, if not exceeding, its sustainable groundwater production capacity, and a boom of such projects will not be sustainable. Especially, the cost/benefit of pumped-storage projects is called into question as the initial-fill phase depletes entire area’s recharge. Our study highlights the stress on groundwater resources of solar development, and that the speed of groundwater recovery does not indicate sustainability. Main point 1: A novel dual model approach, involving an integrated surface/subsurface model and a groundwater parameter-estimation model, was able to better constrain the model. Main point 2: The groundwater system may be nearing, if not exceeding, its sustainable groundwater production capacity and the speed of recovery is not indicative of sustainability. Main point 3: Results from using conventionally-assumed uniform recharge distort calibrated K fields and impacts assessment

14 SOLAR ENERGY↗

DOE OSTI2021

Ensuring statistical reproducibility of ocean model simulations in the age of hybrid computing

Novel high performance computing systems that feature hybrid architectures require large scale code refactoring to unravel underlying exploitable parallelism. Such redesign can often be accompanied with machine-precision changes as the order of computation cannot always be maintained. For chaotic systems like climate models, these round-off level differences can grow rapidly. Systematic errors may also manifest initially as machine-precision differences. Isolating genuine round off level differences from such errors remains a challenge. Here, we apply two-sample equality of distribution tests to evaluate statistical reproducibility of the ocean model component of US Department of Energy's Energy Exascale Earth System Model (E3SM). A 2-year control simulation ensemble is compared to a modified ensemble as a test case - after a known non-bit-for-bit change in a model component is introduced - to evaluate the null hypothesis that the two ensembles are statistically indistinguishable. To quantify the false negative rates of these tests, we conduct a formal power analysis using a targeted suite of short simulation ensembles. The ensemble suite contains several perturbed ensembles, each with a progressively different climate than the baseline ensemble - obtained by perturbing the magnitude of a single model tuning parameter, the Gent and McWilliams κ, in a controlled manner. The null hypothesis is evaluated for each of perturbed ensembles using these tests. The power analysis informs on the detection limits of the tests for given ensemble size allowing model developers to evaluate the impact of an introduced non-bit-for-bit change to the model.

Mahajan, Salil↗

DOE OSTI2022

Modeling the Joint Effects of Vegetation Characteristics and Soil Properties on Ecosystem Dynamics in a Panama Tropical Forest

Abstract In tropical forests, both vegetation characteristics and soil properties are important not only for controlling energy, water, and gas exchanges directly but also determining the competition among species, successional dynamics, forest structure and composition. However, the joint effects of the two factors have received limited attention in Earth system model development. Here we use a vegetation demographic model, the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) implemented in the Energy Exascale Earth System Model (E3SM) Land Model (ELM), ELM‐FATES, to explore how plant traits and soil properties affect tropical forest growth and composition concurrently. A large ensemble of simulations with perturbed vegetation and soil hydrological parameters is conducted at the Barro Colorado Island, Panama. The simulations are compared against observed carbon, energy, and water fluxes. We find that soil hydrological parameters, particularly the scaling exponent of the soil retention curve ( B sw ), play crucial roles in controlling forest diversity, with higher B sw values (>7) favoring late successional species in competition, and lower B sw values (1 ∼ 7) promoting the coexistence of early and late successional plants. Considering the additional impact of soil properties resolves a systematic bias of FATES in simulating sensible/latent heat partitioning with repercussion on water budget and plant coexistence. A greater fraction of deeper tree roots can help maintain the dry‐season soil moisture and plant gas exchange. As soil properties are as important as vegetation parameters in predicting tropical forest dynamics, more efforts are needed to improve parameterizations of soil functions and belowground processes and their interactions with aboveground vegetation dynamics.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Assessing the Sensitivity of the Tropical Cyclone Boundary Layer to the Parameterization of Momentum Flux in the Community Earth System Model

Recent studies have demonstrated that high-resolution (~25 km) Earth System Models (ESMs) have the potential to skillfully predict tropical cyclone (TC) occurrence and intensity. However, biases in ESM TCs still exist, largely due to the need to parameterize processes such as boundary layer (PBL) turbulence. Building on past studies, we hypothesize that the depiction of the TC PBL in ESMs is sensitive to the configuration of the PBL parameterization scheme, and that the targeted perturbation of tunable parameters can reduce biases. The Morris one-at-a-time (MOAT) method is implemented to assess the sensitivity of the TC PBL to tunable parameters in the PBL scheme in an idealized configuration of the Community Atmosphere Model, version 6 (CAM6). The MOAT method objectively identifies several parameters in an experimental version of the Cloud Layers Unified by Binormals (CLUBB) scheme that appreciably influence the structure of the TC PBL. We then perturb the parameters identified by the MOAT method within a suite of CAM6 ensemble simulations and find a reduction in model biases compared to observations and a high-resolution, cloud-resolving model. Importantly, we demonstrate that the high-sensitivity parameters are tied to PBL processes that reduce turbulent mixing and effective eddy diffusivity, and that in CAM6 these parameters alter the TC PBL in a manner consistent with past modeling studies. In this way, we provide an initial identification of process-based input parameters that, when altered, have the potential to improve TC predictions by ESMs.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Enhanced climate reproducibility testing with false discovery rate correction

Simulating the Earth's climate is an important and complex problem, thus climate models are similarly complex, comprised of millions of lines of code. In order to appropriately utilize the latest computational and software infrastructure advancements in Earth system models running on modern hybrid computing architectures to improve their performance, precision, accuracy, or all three; it is important to ensure that model simulations are repeatable and robust. This introduces the need for establishing statistical or non-bit-for-bit reproducibility, since bit-for-bit reproducibility may not always be achievable. Here, we propose a short-simulation ensemble-based test for an atmosphere model to evaluate the null hypothesis that modified model results are statistically equivalent to that of the original model. We implement this test in version 2 of the US Department of Energy's Energy Exascale Earth System Model (E3SM). The test evaluates a standard set of output variables across the two simulation ensembles and uses a false discovery rate correction to account for multiple testing. The false positive rates of the test are examined using re-sampling techniques on large simulation ensembles and are found to be lower than the currently implemented bootstrapping-based testing approach in E3SM. We also evaluate the statistical power of the test using perturbed simulation ensemble suites, each with a progressively larger magnitude of change to a tuning parameter. The new test is generally found to exhibit more statistical power than the current approach, being able to detect smaller changes in parameter values with higher confidence.

Kelleher, Michael E. [Oak Ridge National Laborator↗

DOE OSTI2020

Sensitivity Study for Forecasting Variables of WRF-Solar Using a Tangent Linear Approach

Integrating solar generation in recent years has highlighted the need for improved accuracy in predicting solar power. Confidence in solar power forecasting can be achieved by designing an ensemble that provides reliable probabilistic information for solar radiation with reduced uncertainty and error. Ideally, ensemble members are created through the optimized perturbation of the initial conditions in numerical weather prediction (NWP) models. Tangent linear models are capable of efficiently investigating the sensitivity of solar radiation to model input parameters because they do not require individual perturbation of each variable. This sensitivity study using tangent linear models provide us the capability to identify the right variables to perturb in an ensemble prediction system. In this study, we developed tangent linear models for WRF-Solar modules that directly impact the computation of solar radiation and the simulation of cloud formation and dissipation including the Fast All-sky Model for Solar Applications (FARMS), the Noah land surface model (LSM), the Thompson microphysics, the Mello-Yamada-Nakanishi-Niino (MYNN) boundary layer parameterization, and the Deng scheme for a shallow-convection parameterization. A sensitivity analysis was conducted under various scenarios based on satellite observations and model simulations from the National Solar Radiation Data Base (NSRDB) and WRF-Solar, respectively. Critical forecasting variables that are highly sensitive to the forecasting of global horizontal irradiance (GHI), direct normal irradiance (DNI), cloud mixing ratio, cloud tendency, cloud fraction, and sensible and latent heat fluxes were determined using the relevant WRF-Solar module. This study will be used as a guidance on future research leading to high-quality probabilistic solar forecasting. In this presentation, we discuss the validation of tangent linear approach for WRF-Solar modules and illustrate how the sensitivity results are valuable in the improvement of probabilistic solar prediction.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

The WRF-Solar Ensemble Prediction System: Development, Test, and Validation

Providing reliable probabilistic solar radiation information is needed to improve management of the uncertainty and variability of solar generation. Thus, guidance on how to develop skillful and accurate ensemble forecasts is essential and it will ultimately contribute to integration of high amounts of solar energy on the grid. A team from the National Renewable Energy Laboratory and the National Center for Atmospheric Research had been collaborating to develop the WRF-Solar ensemble prediction system (WRF-Solar EPS) in the past three years to produce probabilistic solar irradiance forecasts and better predict solar energy by quantifying forecast uncertainty. The WRF-Solar EPS basically generates ensemble members for solar irradiance based on stochastic perturbations to provide intraday and day-ahead probabilistic forecasts. This study will present main research steps in developing the WRF-Solar EPS including: (a) tangent linear analysis for identifying key input variables of six WRF-Solar modules significantly related to predicting of cloud and solar irradiance, (b) combining stochastic perturbation technique with the WRF-Solar model, and (c) ensemble calibration method to decrease error and uncertainty of ensemble-based solar forecasts. The capability of WRF-Solar EPS is now updated to the most recent version of standard WRF model. This presentation will summarize comprehensive results from the evaluation of forecasts against the National Solar Radiation Data Base as well as ground-measured observations. Moreover, we will introduce the user's guide for WRF-Solar EPS (e.g., parameters to configure stochastic perturbations) and future extension of this research.

day-ahead forecast↗

DOE OSTI2023

Probing supersymmetric black holes with surface defects

It has long been conjectured that the large N deconfinement phase transition of $\mathcal{N}$ = 4 SU(N) super-Yang-Mills corresponds via AdS/CFT to the Hawking-Page transition in which black holes dominate the thermal ensemble, and quantitative evidence of this has come through the recent matching of the superconformal index of $\frac{1}{16}$-BPS states to the supersymmetric black hole entropy. Here we introduce the half-BPS Gukov-Witten surface defect as a probe of the superconformal index, which also serves as an order parameter for the deconfinement transition. This can be studied directly in field theory as a modification of the usual unitary matrix model or in the dual description as a D3-brane probe in the background of a (complex) supersymmetric black hole. Using a saddle point approximation, we determine our defect index in the large N limit as a simple function of the chemical potentials and show independently that it is reproduced by the renormalized action of the brane in the black hole background. Along the way, we also comment on the Cardy limit and the thermodynamics of the D3-brane in the generalized ensemble. The defect index sharply distinguishes between the confining and the deconfining phases of the gauge theory and thus is a supersymmetric non-perturbative order parameter for these large N phase transitions which deserves further investigation. Finally, our work provides an example where the properties of a black hole coupled to an external system can be analyzed precisely.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning

This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.

17 WIND ENERGY↗

DOE OSTI2026

Data and scripts associated with a manuscript analyzing ELM-FATES parameter sensitivity under pre-fire and postfire scenarios using machine learning

NOTE: The manuscript associated with this data package is currently in review. The data may be revised based on reviewer feedback. Upon manuscript acceptance, this data package will be updated with the final dataset and additional metadata. This data package is associated with the manuscript “Fire Severity-Dependent Shifts in Vegetation Parameter Sensitivity: A Pre- and Post-Fire Analysis Using ELM-FATES and Explainable AI” submitted to Journal of Advances in Modeling Earth Systems (Zahura et al. 2026). The study examines vegetation physiological parameters controlling pre-fire and post-fire vegetation dynamics. To support this analysis, 73 vegetation parameters in Functionally Assembled Terrestrial Ecosystem Simulator (FATES) (Fisher et al., 2018) , which is coupled with E3SM (Energy Exascale Earth System Model) land model (ELM, ELM-FATES), were perturbed using a Sobol sequence to generate 1,024 ensemble members for two plant functional types: needleleaf evergreen extratropical trees (NEET) and C3 grass. Simulations were conducted for the pre-fire period (2016) and post-fire period (2018–2023). Burn severity was represented by modifying the Nesterov index in FATES to 75,000, 150,000, and 300,000 for low, moderate, and high severity, respectively. A no-fire scenario was also included. Simulations were performed for 16 grid cells in the American River Watershed across different burn severities and plant functional types. XGBoost (eXtreme Gradient Boosting) models were trained using the parameter ensembles and ELM-FATES-simulated outputs, including leaf area index (LAI), gross primary productivity (GPP), aboveground biomass, vegetation evaporation, transpiration, and soil evaporation. Models were trained separately for each year and burn severity, followed by SHAP (SHapley Additive exPlanations) analysis to identify changes in dominant parameters after fire disturbance. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. The data package contains the ELM-FATES simulation data. The scripts and data related to the analysis will be added later. The inputs and outputs from ELM-FATES are inside the “FATES” folder. “FATES_domain_surface” contains the domain and surface netcdfs that were used to run ELM-FATES in the study area. “FATES_parameters” contains the 1024 ensembles that were generated using Sobol sequence. “FATES_outputs” folder contains ELM-FATES simulated variables. All files are .csv and .nc (NetCDF).

Aboveground biomass↗

DOE OSTI2022

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

fluctuations correlations↗

DOE OSTI2024

A method for examining ensemble averaging forms during the transition to turbulence in HED systems for application to RANS models

This paper discusses a strategy to initialize a two-dimensional (2D) Reynolds-averaged Navier–Stokes model [LANL's Besnard–Harlow–Rauenzahn (BHR) model] in order to describe an unsteady transitional Richtmyer–Meshkov (RM)-induced flow observed in on-going high-energy-density ensemble experiments performed on the OMEGA-EP facility. The experiments consist of a nominal single-mode perturbation (initial amplitude a 0 ≈ 10 and wavelength $λ$ = 100μm) with target-to-target variations in the surface roughness subjected to the RM instability with delayed Rayleigh–Taylor in a heavy-to-light configuration. Our strategy leverages high-resolution three-dimensional (3D) implicit large eddy simulations (ILES) simulations to initialize BHR-relevant parameters and subsequently validate the 2D BHR results against the 3D ILES simulations. A suite of five 3D ILES simulations corresponding to five experimental target profiles is undertaken to generate an ensemble dataset. Using ensemble averages from the 3D simulations to initialize the turbulent kinetic energy in the BHR model ( K 0 ) demonstrates the ability of the model to predict the time evolution of the interface as well as the density-specific-volume covariance, b . To quantify the sensitivity of the BHR results to the choice of K 0 and the initial turbulent length scale, S 0 , we execute a parameter sweep spanning four orders of magnitude for both S 0 and K 0 , generating a parameter space consisting of 26 simulations. The Pearson's correlation coefficient is used as a measure of discrepancy between the 2D BHR and 3D ILES simulations and reveals that the ranges 8≲S 0 ≲20 μm and 10 9 ≲K 0 ≲10 10 cm 2 /s 2 produce predictions that agree best with the 3D ILES results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Studying Rate of Fire Spread Using Landscape Statistics and FIRETEC

Wildfires are multi-system and multi-scale processes that are influenced by the land and atmosphere. Here, we study the influence of land, in terms of topography and vegetation, on uphill and downhill fire spread using data of the state of California as a testbed. The California landscape is first quantified by reclassifying its dominant vegetation types into grass, trees, and shrubs. Next, statistics of slope, vegetation height, and live fuel moisture percentage for each dominant vegetation type are gathered to create ensembles of idealized computational fluid dynamics (CFD) model simulations representative of the landscape. Rate of spread values for each CFD simulation are recorded to observe the differences in perturbing slope and fuel moisture for each vegetation type. We have found that all vegetation types prefer slopes of less than 30 degrees. Trees in the California data are 10 to 40 meters high, whereas shrub heights are less than 3 meters and grass heights are less than 1 meter. The live fuel moisture percentage of both trees and shrubs fluctuates around approximately 100% over one year (2019-2020). Using these parameters as inputs into the CFD model, fire spread rate is found to be fastest in the grass ensemble (maximum 12 m s -1 ), followed by shrubs (maximum 10 m s -1 ) and lastly by trees (maximum 7 m s -1 ). Increasing slope increases the spread rate of the uphill fire but the downhill spread decreases for slopes greater than 15 degrees. Increasing fuel moisture decreases the spread rate both up and down the hill. This study highlights the impacts that topography and vegetation have on fire spread.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Renormalized quark masses using gradient flow

We propose a new and simple method for determining the renormalized quark masses from lattice simulations. Renormalized quark masses are an important input to many phenomenological applications, including searching and modeling physics beyond the Standard Model. The nonperturbative renormalization is performed using gradient flow combined with the short-flow-time expansion that is improved by renormalization group (RG) running to match to the $\overline{MS}$ scheme. Implementing the RG running perturbatively, we demonstrate this method works reliably at least up to the charm-quark mass and exhibits an easily attainable “windowing condition.” Using RBC/UKQCD’s (2+1)-flavor Shamir domain-wall fermion ensembles with Iwasaki gauge action, we find 𝑚 $\overline{MS}$ 𝑠⁡ (𝜇 = 2 GeV) = 89⁢(3) MeV and 𝑚 $\overline{MS}$ 𝑐 ⁡(𝜇 = 3 GeV) = 972⁢(16) MeV. These results predict the scale-independent ratio 𝑚 𝑐 /𝑚 𝑠 = 12.1⁢(4). Generalization to other observables is possible, providing an efficient approach to determine nonperturbatively renormalized fermionic observables like form factors or bag parameters from lattice simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗