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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 OSTI2020

On the Correspondence between Seasonal Forecast Biases and Long-Term Climate Biases in Sea Surface Temperature

In this paper, the correspondence between mean sea surface temperature (SST) biases in retrospective seasonal forecasts (hindcasts) and long-term climate simulations from five global climate models is examined to diagnose the degree to which systematic SST biases develop on seasonal time scales. The hindcasts are from the North American Multi-Model Ensemble and the climate simulations are from the Coupled Model Intercomparison Project. The analysis suggests that most robust climatological SST biases begin to form within 6 months of a realistically initialized integration, although the growth rate varies with location, time, and model. In regions with large biases, interannual variability and ensemble spread is much smaller than the climatological bias. Additional ensemble hindcasts of the Community Earth System Model with a different initialization method suggest that initial conditions do matter for the initial bias growth, but the overall global bias patterns are similar after 6 months. A hindcast approach is more suitable to study biases over the tropics and sub-tropics than over the extra-tropics because of smaller initial biases and faster bias growth. The rapid emergence of SST biases makes it likely that fast processes with times scales shorter than the seasonal time scales in the atmosphere and upper ocean are responsible for a substantial part of the climatological SST biases. Studying the growth of biases may provide important clues to the causes and ultimately the amelioration of these biases. Further, initialized seasonal hindcasts can profitably be used in the development of high-resolution coupled ocean-atmosphere models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi–Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.

Shen, Tong (ORCID:0000000206292468)↗

DOE OSTI2016

An overview of uncertainty quantification techniques with application to oceanic and oil‐spill simulations

Abstract We give an overview of four different ensemble‐based techniques for uncertainty quantification and illustrate their application in the context of oil plume simulations. These techniques share the common paradigm of constructing a model proxy that efficiently captures the functional dependence of the model output on uncertain model inputs. This proxy is then used to explore the space of uncertain inputs using a large number of samples, so that reliable estimates of the model's output statistics can be calculated. Three of these techniques use polynomial chaos (PC) expansions to construct the model proxy, but they differ in their approach to determining the expansions' coefficients; the fourth technique uses Gaussian Process Regression (GPR). An integral plume model for simulating the Deepwater Horizon oil‐gas blowout provides examples for illustrating the different techniques. A Monte Carlo ensemble of 50,000 model simulations is used for gauging the performance of the different proxies. The examples illustrate how regression‐based techniques can outperform projection‐based techniques when the model output is noisy. They also demonstrate that robust uncertainty analysis can be performed at a fraction of the cost of the Monte Carlo calculation.

Iskandarani, Mohamed↗

NASA NTRS2018

The Influence of Prescribed Boundary Conditions on Near-Surface Temperature over the Arctic in the MERRA-2 Atmospheric Model

An accurate historical record of evolving Arctic conditions is integral to furthering our understanding of climate processes and to providing a foundation for predicting future climate scenarios in northern high latitudes. Atmospheric reanalyses are seen as an important source of information on the recent past for the data-sparse Arctic region. An assessment of near-surface Arctic air temperatures finds significant discrepancies among the various modern reanalyses. An important point is the treatment of surface boundary conditions: specifically, the sea ice cover and sea surface temperatures (SSTs) over the Arctic Ocean. Reanalyses use different methodologies and data sources for SSTs and sea ice concentration boundary forcing. Notably, the Modern Era Retrospective analysis for Research and Applications, version 2 (MERRA-2) and the European Centre for Medium-Range Weather Forecasts Interim Re-Analysis (ERA-Interim) both use boundary forcing derived from the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) over an extended, overlapping period of time. This allows for an examination of differences between the two systems while both concurrently employ the same fractional sea ice coverage. To further understand these differences, an ensemble of AMIP-style simulations using the MERRA-2 atmospheric model - but without data assimilation - shows considerable differences in Arctic temperatures as compared to reanalyses, particularly in autumn and winter months. Results from the AMIP simulations suggest that the surface representation over sea ice used in the MERRA-2 model provides an intrinsic warm bias and obfuscates Arctic Amplification, an established feature present in observations and reanalyses. An additional ensemble of AMIP-style simulations using the MERRA-2 atmospheric model was performed using boundary conditions derived from the ERA-Interim reanalysis. An in-depth comparison of surface temperatures over the Arctic from the two reanalyses and two AMIP-style ensembles will be presented, along with an assessment of the effects of the varying Arctic temperature time series on the atmospheric general circulation and energy budget.

Collow, Allison B. Marquardt↗

DOE OSTI2022

Enabling machine learning-ready HPC ensembles with Merlin

With the growing complexity of computational and experimental facilities, many scientific researchers are turning to machine learning (ML) techniques to analyze large scale ensemble data. With complexities such as multi-component workflows, heterogeneous machine architectures, parallel file systems, and batch scheduling, care must be taken to facilitate this analysis in a high performance computing (HPC) environment. Here, we present Merlin, a workflow framework to enable large ML-friendly ensembles of scientific HPC simulations. By augmenting traditional HPC with distributed compute technologies, Merlin aims to lower the barrier for scientific subject matter experts to incorporate ML into their analysis. As a producer–consumer workflow model, Merlin enables multi-machine, cross-batch job, dynamically allocated yet persistent workflows capable of utilizing surge-compute resources. Key features of Merlin are a flexible HPC-centric interface, low per-task overhead, multi-tiered fault recovery, and a hierarchical sampling algorithm that allows for $\mathscr{O}$(N) task execution and $\mathscr{O}$(N ln N) task queuing to ensembles of millions of tasks. In addition to Merlin’s design, we test the algorithm’s performance in an HPC center and demonstrate the ability to enqueue 40 million simulations in 100 s, with a 30 millisecond per-task overhead that is independent of ensemble size. Finally, we describe some example applications that Merlin has enabled on leadership-class HPC resources, such as the ML-augmented optimization of nuclear fusion experiments and the calibration of infectious disease models to study the progression of and possible mitigation strategies for COVID-19.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Protein folding from heterogeneous unfolded state revealed by time-resolved X-ray solution scattering

One of the most challenging tasks in biological science is to understand how a protein folds. In theoretical studies, the hypothesis adopting a funnel-like free-energy landscape has been recognized as a prominent scheme for explaining protein folding in views of both internal energy and conformational heterogeneity of a protein. Despite numerous experimental efforts, however, comprehensively studying protein folding with respect to its global conformational changes in conjunction with the heterogeneity has been elusive. Here we investigate the redox-coupled folding dynamics of equine heart cytochrome c (cyt-c) induced by external electron injection by using time-resolved X-ray solution scattering. A systematic kinetic analysis unveils a kinetic model for its folding with a stretched exponential behavior during the transition toward the folded state. With the aid of the ensemble optimization method combined with molecular dynamics simulations, we found that during the folding the heterogeneously populated ensemble of the unfolded state is converted to a narrowly populated ensemble of folded conformations. These observations obtained from the kinetic and the structural analyses of X-ray scattering data reveal that the folding dynamics of cyt-c accompanies many parallel pathways associated with the heterogeneously populated ensemble of unfolded conformations, resulting in the stretched exponential kinetics at room temperature. This finding provides direct evidence with a view to microscopic protein conformations that the cyt-c folding initiates from a highly heterogeneous unfolded state, passes through still diverse intermediate structures, and reaches structural homogeneity by arriving at the folded state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2014

How Do Various Maize Crop Models Vary in Their Responses to Climate Change Factors?

Potential consequences of climate change on crop production can be studied using mechanistic crop simulation models. While a broad variety of maize simulation models exist, it is not known whether different models diverge on grain yield responses to changes in climatic factors, or whether they agree in their general trends related to phenology, growth, and yield. With the goal of analyzing the sensitivity of simulated yields to changes in temperature and atmospheric carbon dioxide concentrations [CO2], we present the largest maize crop model intercomparison to date, including 23 different models. These models were evaluated for four locations representing a wide range of maize production conditions in the world: Lusignan (France), Ames (USA), Rio Verde (Brazil) and Morogoro (Tanzania). While individual models differed considerably in absolute yield simulation at the four sites, an ensemble of a minimum number of models was able to simulate absolute yields accurately at the four sites even with low data for calibration, thus suggesting that using an ensemble of models has merit. Temperature increase had strong negative influence on modeled yield response of roughly -0.5 Mg ha(sup 1) per degC. Doubling [CO2] from 360 to 720 lmol mol 1 increased grain yield by 7.5% on average across models and the sites. That would therefore make temperature the main factor altering maize yields at the end of this century. Furthermore, there was a large uncertainty in the yield response to [CO2] among models. Model responses to temperature and [CO2] did not differ whether models were simulated with low calibration information or, simulated with high level of calibration information.

carbon dioxide↗

DOE OSTI2020

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMD is a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

high-performance computing↗

DOE OSTI2023

Fluctuating hydrodynamics and the Rayleigh–Plateau instability

The Rayleigh–Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to interfacial energy densities. Consequently, at these scales, thermal fluctuations play a significant role in the dynamics of the instability. These microscopic effects have previously been investigated numerically using particle-based simulations, such as molecular dynamics (MD), and stochastic partial differential equation–based hydrodynamic models, such as stochastic lubrication theory. In this paper, we present an incompressible fluctuating hydrodynamics model with a diffuse-interface formulation for binary fluid mixtures designed for the study of stochastic interfacial phenomena. An efficient numerical algorithm is outlined and validated in numerical simulations of stable equilibrium interfaces. We present results from simulations of the Rayleigh–Plateau instability for long cylinders pinching into droplets for Ohnesorge numbers of Oh = 0.5 and 5.0. Both stochastic and perturbed deterministic simulations are analyzed and ensemble results show significant differences in the temporal evolution of the minimum radius near pinching. Short cylinders, with lengths less than their circumference, were also investigated. As previously observed in MD simulations, we find that thermal fluctuations cause these to pinch in cases where a perturbed cylinder would be stable deterministically. Finally, we show that the fluctuating hydrodynamics model can be applied to study a broader range of surface tension–driven phenomena.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Reconstruction of the 1997/1998 El Nino from TOPEX/POSEIDON and TOGA/TAO Data Using a Massively Parallel Pacific-Ocean Model and Ensemble Kalman Filter

Two massively parallel data assimilation systems in which the model forecast-error covariances are estimated from the distribution of an ensemble of model integrations are applied to the assimilation of 97-98 TOPEX/POSEIDON altimetry and TOGA/TAO temperature data into a Pacific basin version the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. in the first system, ensemble of model runs forced by an ensemble of atmospheric model simulations is used to calculate asymptotic error statistics. The data assimilation then occurs in the reduced phase space spanned by the corresponding leading empirical orthogonal functions. The second system is an ensemble Kalman filter in which new error statistics are computed during each assimilation cycle from the time-dependent ensemble distribution. The data assimilation experiments are conducted on NSIPP's 512-processor CRAY T3E. The two data assimilation systems are validated by withholding part of the data and quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The pros and cons of each system are discussed.

Keppenne, C. L.↗

DOE OSTI2011

The Community Climate System Model Version 4

The fourth version of the Community Climate System Model (CCSM4) was recently completed and released to the climate community. This paper describes developments to all the CCSM components, and documents fully coupled pre-industrial control runs compared to the previous version, CCSM3. Using the standard atmosphere and land resolution of 1{sup o} results in the sea surface temperature biases in the major upwelling regions being comparable to the 1.4{sup o} resolution CCSM3. Two changes to the deep convection scheme in the atmosphere component result in the CCSM4 producing El Nino/Southern Oscillation variability with a much more realistic frequency distribution than the CCSM3, although the amplitude is too large compared to observations. They also improve the representation of the Madden-Julian Oscillation, and the frequency distribution of tropical precipitation. A new overflow parameterization in the ocean component leads to an improved simulation of the deep ocean density structure, especially in the North Atlantic. Changes to the CCSM4 land component lead to a much improved annual cycle of water storage, especially in the tropics. The CCSM4 sea ice component uses much more realistic albedos than the CCSM3, and the Arctic sea ice concentration is improved in the CCSM4. An ensemble of 20th century simulations runs produce an excellent match to the observed September Arctic sea ice extent from 1979 to 2005. The CCSM4 ensemble mean increase in globally-averaged surface temperature between 1850 and 2005 is larger than the observed increase by about 0.4 C. This is consistent with the fact that the CCSM4 does not include a representation of the indirect effects of aerosols, although other factors may come into play. The CCSM4 still has significant biases, such as the mean precipitation distribution in the tropical Pacific Ocean, too much low cloud in the Arctic, and the latitudinal distributions of short-wave and long-wave cloud forcings.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Large-scale molecular dynamics simulations of bubble collapse in water: Effects of system size, water model, and nitrogen

Molecular dynamics simulations in the microcanonical ensemble are performed to study the collapse of a bubble in liquid water using the single-site mW and the four-site TIP4P/2005 water models. To study system size effects, simulations for pure water systems are performed using periodically replicated simulation boxes with linear dimensions, L, ranging from 32 to 512 nm with the largest systems containing 8.7 × 10 6 and 4.5 × 10 9 molecules for the TIP4P/2005 and mW water models, respectively. The computationally more efficient mW water model allows us to reach converging behavior when the bubble dynamics results are plotted in reduced units, and the limiting behavior can be obtained through linear extrapolation in L –1 . Qualitative differences are observed between simulations with the mW and TIP4P/2005 water models, but they can be explained by the models’ differences in predicted viscosity and surface tension. Although bubble collapse occurs on time scales of only hundreds of picoseconds, the system sizes used here are sufficiently large to obtain bubble dynamics consistent with the Rayleigh–Plesset equation when using the models’ thermophysical properties as input. For the conditions explored here, extreme heating of the interfacial water molecules near the time of collapse is observed for the larger mW water systems (but the model underpredicts the viscosity), whereas heating is less pronounced for the TIP4P/2005 water systems because its larger viscosity contribution slows the collapse dynamics. The presence of nitrogen within the bubble only starts to affect bubble dynamics near the very end of the initial collapse, leading to an incomplete collapse and strong rebound for the mW water model. Although nitrogen is non-condensable at 300 K, it becomes highly compressed and reaches a liquid-like density near the collapse point. We find that the dissolution of nitrogen is much slower than the movement of the collapsing water front, and the re-expansion of the dense nitrogen droplet gives rise to bubble rebound. The incompatibility of the collapse and dissolution time scales should be considered for continuum-scale modeling of bubble dynamics. Finally, we also confirm that the diffusion coefficient for dissolved nitrogen is insensitive to pressure as the liquid transitions from a compressed to a stretched state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Surface roughness scattering of electrons in bulk mosfets

Surface-roughness scattering of electrons at the Si-SiO 2 interface is a very important consideration when analyzing Si metal-oxide-semiconductor field-effect transistors (MOSFETs). Scattering reduces the mobility of the electrons and degrades the device performance. 250-nm and 50-nm bulk MOSFETs were simulated with varying device parameters and mesh sizes in order to compare the effects of surface-roughness scattering in multiple devices. The simulation framework includes the ensemble Monte Carlo method used to solve the Boltzmann transport equation coupled with a successive over-relaxation method used to solve the two-dimensional Poisson's equation. Four methods for simulating the surface-roughness scattering of electrons were implemented on both devices and compared: the constant specularity parameter, the momentum-dependent specularity parameter, and the real-space-roughness method with both uniform and varying electric fields. The specularity parameter is the probability of an electron scattering speculariy from a rough surface. It can be chosen as a constant, characterizing partially diffuse scattering of all electrons from the surface the same way, or it can be momentum dependent, where the size of rms roughness and the normal component of the electron wave number determine the probability of electron-momentum randomization. The real-space rough surface method uses the rms roughness height and correlation length of an actual MOSFET to simulate a rough interface. Due to their charge, electrons scatter from the electric field and not directly from the surface. If the electric field is kept uniform, the electrons do not perceive the roughness and scatter as if from a at surface. However, if the field is allowed to vary, the electrons scatter from the varying electric field as they would in a MOSFET. These methods were implemented for both the 50-nm and 250-nm MOSFETs, and using the rms roughness heights and correlation lengths for real devices. The current-voltage and mobility-electric field curves were plotted for each method on the two devices and compared. The conclusion is that the specularity-parameter methods are valuable as simple models for relatively smooth interfaces. However, they have limitations, as they cannot accurately describe the drastic reduction in the current and the electron mobility that occur in MOSFETs with very rough Si-SiO 2 interfaces.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Uncertainty quantification and optimization of precipitating hydrometeor parameters for winter precipitation in a cloud microphysics scheme

The precipitating hydrometeor parameters used in cloud microphysics schemes carry inherent uncertainties. The quantification of these uncertainties, together with parameter optimization, can significantly improve precipitation forecasts. This study investigates the effects of 13 parameters in the Weather Research and Forecasting (WRF) Double-Moment 6-class (WDM6) microphysics scheme, which define the hydrometeor characteristics such as fall velocity–diameter and mass–diameter relationships, as well as the shape parameter of the drop size distribution for precipitating particles such as rain, snow, and graupel on simulated winter precipitation. A comparison between the model's pre-defined parameters and observations from the International Collaborative Experiments for the PyeongChang 2018 Olympic and Paralympic winter games (ICE-POP 2018) field campaign reveals that the fall velocity–diameter relationship for rain, the mass–diameter relationships for snow and graupel, and the shape parameters for all precipitating particles in the WDM6 scheme deviate from the median values observed by the two-dimensional video disdrometer (2DVD). To quantify parameter sensitivities, a perturbed parameter ensemble (PPE) of 256 simulations was conducted within parameter ranges constrained by 2DVD observations for three winter precipitation cases. Bayesian optimization was then applied to identify parameter sets that minimized the root mean square error (RMSE) for each case, achieving reductions of up to 30.2 %. These results demonstrate that ensemble-based uncertainty quantification and parameter optimization can help identify key parameters and provide a pathway to improving precipitation simulation performance. In addition, measurement sites can be strategically selected based on regions that show high sensitivity to variations in hydrometeor characteristic parameters.

Bayesian optimization↗

DOE OSTI2012

Isotropic–nematic phase transition in the Lebwohl–Lasher model from density of states simulations

Density of states Monte Carlo simulations have been performed to study the isotropic–nematic (IN) transition of the Lebwohl–Lasher model for liquid crystals. The IN transition temperature was calculated as a function of system size using expanded ensemble density of states simulations with histogram reweighting. The IN temperature for infinite system size was obtained by extrapolation of three independent measures. Finally, a subsequent analysis of the kinetics in the model showed that the transition occurs via spinodal decomposition through aggregation of clusters of liquid crystal molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Assessing climate-change-induced flood risk in the Conasauga River watershed: an application of ensemble hydrodynamic inundation modeling

Abstract. This study evaluates the impact of potential future climate change on flood regimes, floodplain protection, and electricity infrastructures across the Conasauga River watershed in the southeastern United States through ensemble hydrodynamic inundation modeling. The ensemble streamflow scenarios were simulated by the Distributed Hydrology Soil Vegetation Model (DHSVM) driven by (1) 1981–2012 Daymet meteorological observations and (2) 11 sets of downscaled global climate models (GCMs) during the 1966–2005 historical and 2011–2050 future periods. Surface inundation was simulated using a GPU-accelerated Two-dimensional Runoff Inundation Toolkit for Operational Needs (TRITON) hydrodynamic model. A total of 9 out of the 11 GCMs exhibit an increase in the mean ensemble flood inundation areas. Moreover, at the 1 % annual exceedance probability level, the flood inundation frequency curves indicate a ∼ 16 km2 increase in floodplain area. The assessment also shows that even after flood-proofing, four of the substations could still be affected in the projected future period. The increase in floodplain area and substation vulnerability highlights the need to account for climate change in floodplain management. Overall, this study provides a proof-of-concept demonstration of how the computationally intensive hydrodynamic inundation modeling can be used to enhance flood frequency maps and vulnerability assessment under the changing climatic conditions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗