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At least 199 records · Page 11

WRF-ELM v1.0: a regional climate model to study land–atmosphere interactions over heterogeneous land use regions

Abstract. The Energy Exascale Earth System Model (E3SM) Land Model (ELM) is a state-of-the-art land surface model that simulates the intricate interactions between the terrestrial land surface and other components of the Earth system. Originating from the Community Land Model (CLM) version 4.5, ELM has been under active development, with added new features and functionality, including plant hydraulics, radiation–topography interaction, subsurface multiphase flow, and more explicit land use and management practices. This study integrates ELM v2.1 with the Weather Research and Forecasting (WRF; WRF-ELM) model through a modified Lightweight Infrastructure for Land Atmosphere Coupling (LILAC) framework, enabling affordable high-resolution regional modeling by leveraging ELM's innovative features alongside WRF's diverse atmospheric parameterization options. This framework includes a top-level driver for variable communication between WRF and ELM and Earth System Modeling Framework (ESMF) caps for the WRF atmospheric component and ELM workflow control, encompassing initialization, execution, and finalization. Importantly, this LILAC–ESMF framework demonstrates a more modular approach compared to previous coupling efforts between WRF and land surface models. It maintains the integrity of ELM's source code structure and facilitates the transfer of future developments in ELM to WRF-ELM. To test the ability of the coupled model to capture land–atmosphere interactions over regions with a variety of land uses and land covers, we conducted high-resolution (4 km) WRF-ELM ensemble simulations over the Great Lakes region (GLR) in the summer of 2018 and systematically compared the results against observations, reanalysis data, and WRF-CTSM (WRF coupled with the Community Terrestrial Systems Model). In general, the coupled WRF-ELM model has reasonably captured the spatial distribution of surface state variables and fluxes across the GLR, particularly over the natural vegetation areas. The evaluation results provide a baseline reference for further improvements in ELM in the regional application of high-resolution weather and climate predictions. Our work serves as an example to the model development community for expanding an advanced land surface model's capability to represent fully-coupled land–atmosphere interactions at fine spatial scales. The development and release of WRF-ELM marks a significant advancement for the ELM user community, providing opportunities for fine-scale regional representation, parameter calibration in coupled mode, and examination of new schemes with atmospheric feedback.

54 ENVIRONMENTAL SCIENCES↗

Metrics for evaluating tropical cyclones in climate data

This manuscript describes a software suite that can be used for objective evaluation of tropical cyclones (TCs) in gridded climate data. Using cyclone trajectories derived from 6-hourly data, a comprehensive set of metrics is defined to systematically compare and contrast products to one another. In addition to annual TC climatologies, attention is paid to spatial and temporal patterns of storm occurrence and intensity. Assessment can be performed either on the global scale or regional domains. Simple to visualize ‘scorecards’ allow for rapid credibility assessment. We showcase three key findings enabled by this suite. First, we compare the representation of TCs in seven current-generation global reanalyses and conclude that higher resolution models and those with TC-specific assimilation contain more accurate storm climatologies. Second, using a free-running Earth system model (ESM) we find that full basin refinement is required in variable-resolution configurations to adequately simulate North Atlantic TC frequency. Furthermore, upstream refinement over northern Africa offers little benefit in simulating storm occurrence but spatial genesis patterns are improved. Finally, we show that TCs simulated by ESMs can be highly sensitive to individual parameterizations in climate models, with North Atlantic TC metrics varying greatly depending on version of the Morrison-Gettelman microphysics package.

54 ENVIRONMENTAL SCIENCES↗

The DOE E3SM v1.2 Cryosphere Configuration: Description and Simulated Antarctic Ice‐Shelf Basal Melting

Abstract The processes responsible for freshwater flux from the Antarctic Ice Sheet (AIS), ice‐shelf basal melting and iceberg calving, are generally poorly represented in current Earth System Models (ESMs). Here we document the cryosphere configuration of the U.S. Department of Energy's Energy Exascale Earth System Model (E3SM) v1.2. This includes simulating Antarctic ice‐shelf basal melting, which has been implemented through simulating the ocean circulation within static Antarctic ice‐shelf cavities, allowing for the ability to calculate ice‐shelf basal melt rates from the associated heat and freshwater fluxes. In addition, we added the capability to prescribe forcing from iceberg melt, allowing for realistic representation of the other dominant mass loss process from the AIS. In standard resolution simulations (using a noneddying ocean) under preindustrial climate forcing, we find high sensitivity of modeled ocean/ice shelf interactions to the ocean state, which can result in a transition to a high basal melt regime under the Filchner‐Ronne Ice Shelf (FRIS), presenting a significant challenge to representing the ocean/ice shelf system in a coupled ESM. We show that inclusion of a spatially dependent parameterization of eddy‐induced transport reduces biases in water mass properties on the Antarctic continental shelf. With these improvements, E3SM produces realistic ice‐shelf basal melt rates across the continent that are generally within the range inferred from observations. The accurate representation of ice‐shelf basal melting within a coupled ESM is an important step toward reducing uncertainties in projections of the Antarctic response to climate change and Antarctica's contribution to global sea‐level rise.

54 ENVIRONMENTAL SCIENCES↗

An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion

We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for example, for magnetic confinement fusion. The new discretization is based on a mixed formulation, introducing a form of the directional derivative along the magnetic field as an auxiliary variable and discretizing both the temperature and auxiliary fields in a continuous Galerkin (CG) space. Both the temperature and auxiliary variable equations are stabilized using the streamline upwind Petrov–Galerkin (SUPG) method, ensuring a better representation of the directional derivatives and therefore an overall more accurate solution. This approach can be seen as the CG-based version of our previous work (Wimmer, Southworth, Gregory, Tang, 2024), where we considered a mixed discontinuous Galerkin (DG) spatial discretization including DG-upwind stabilization. We prove consistency of the novel discretization, and demonstrate its improved accuracy over existing CG-based methods in test cases relevant to magnetic confinement fusion. This includes a long-run tokamak equilibrium sustainment scenario, demonstrating a 35% and 32% spurious heat loss for existing primal and mixed CG-based formulations versus 4% for our novel SUPG-stabilized discretization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints

This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.

97 MATHEMATICS AND COMPUTING↗

Advancing the Understanding of Cloud Microphysical Processes and Aerosol Indirect Effects in High-Latitude Mixed-Phase Clouds by Linking ARM Measurements with Climate Model Simulations (Final Report)

The key objectives of this project were to advance our understanding of cloud microphysical characteristics and aerosol indirect effects on mixed-phase clouds in high latitudes. To improve the representation of ice and mixed-phase clouds in Earth System Models (ESMs), we propose an integrated observation and modeling study of cloud macro- and microphysical properties, including spatial heterogeneities, mass partitioning between ice crystals and supercooled liquid water, effects of ice nucleating particles (INPs), and efficiency of secondary ice production (SIP), etc. Specifically, we took four main approaches in this project: (1) examining macro- and microphysical properties of ice and mixed-phase clouds based on in-situ and ground-based observations from multiple field campaigns funded by the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program, including the Mixed-Phase Arctic Cloud Experiment (M-PACE), Indirect and Semi-Direct Aerosol Campaign (ISDAC), Ice Nucleating Particle Sources at Oliktok Point (INPOP), ARM West Antarctic Radiation Experiment (AWARE), Measurements of Aerosols, Radiation, and Clouds over the Southern Ocean (MARCUS), and Macquarie Island Cloud and Radiation Experiment (MICRE); (2) evaluating the DOE Energy Exascale Earth System Model (E3SM) simulations based on observations, particularly for ice and mixed-phase cloud microphysical properties; (3) examining the impacts of INPs on ice and mixed-phase clouds. Specifically, a series of comparisons were conducted using observations over the Arctic, Southern Ocean, and Antarctica, including comparisons between the lower and higher southern latitudes as well as comparisons between the northern and southern hemispheres. In addition, aerosol indirect effects from distinct sources of dust particles were examined; and (4) investigating the impacts of SIP. Ultimately, these results helped to improve cloud microphysics and aerosol-cloud interaction parameterizations in the E3SM model. Overall, the project provided improved understanding regarding various factors, including thermodynamic, dynamic, and aerosol conditions, on the micro- and macrophysical properties of ice and mixed-phase clouds in the high latitudes. Resulting analysis helped to provide an improved physical basis for refining the current cloud microphysics parameterizations related to ice and mixed-phase clouds in E3SM.

54 ENVIRONMENTAL SCIENCES↗

Environmental controls on observed spatial variability of soil pore water geochemistry in small headwater catchments underlain with permafrost

Abstract. Soil pore water (SPW) chemistry can vary substantially across multiple scales in Arctic permafrost landscapes. The magnitude of these variations and their relationship to scale are critical considerations for understanding current controls on geochemical cycling and for predicting future changes. These aspects are especially important for Arctic change modeling where accurate representation of sub-grid variability may be necessary to predict watershed-scale behaviors. Our research goal is to characterize intra- and inter-watershed soil water geochemical variations at two contrasting locations in the Seward Peninsula of Alaska, USA. We then attempt to identify the key factors controlling concentrations of important pore water solutes in these systems. The SPW geochemistry of 18 locations spanning two small Arctic catchments was examined for spatial variability and its dominant environmental controls. The primary environmental controls considered were vegetation, soil moisture and/or redox condition, water–soil interactions and hydrologic transport, and mineral solubility. The sampling locations varied in terms of vegetation type and canopy height, presence or absence of near-surface permafrost, soil moisture, and hillslope position. Vegetation was found to have a significant impact on SPW NO3- concentrations, associated with the localized presence of nitrogen-fixing alders and mineralization and nitrification of leaf litter from tall willow shrubs. The elevated NO3- concentrations were, however, frequently equipoised by increased microbial denitrification in regions with sufficient moisture to support it. Vegetation also had an observable impact on soil-moisture-sensitive constituents, but the effect was less significant. The redox conditions in both catchments were generally limited by Fe reduction, seemingly well-buffered by a cache of amorphous Fe hydroxides, with the most reducing conditions found at sampling locations with the highest soil moisture content. Non-redox-sensitive cations were affected by a wide variety of water–soil interactions that affect mineral solubility and transport. Identification of the dominant controls on current SPW hydrogeochemistry allows for qualitative prediction of future geochemical trends in small Arctic catchments that are likely to experience warming and permafrost thaw. As source areas for geochemical fluxes to the broader Arctic hydrologic system, geochemical processes occurring in these environments are particularly important to understand and predict with regards to such environmental changes.

Conroy, Nathan Alec (ORCID:0000000305973373)↗

Seasonal representation of extreme precipitation indices over the United States in CMIP6 present-day simulations

Realistically representing the present-day characteristics of extreme precipitation has been a challenge for global climate models, which is due in part to deficiencies in model resolution and physics, but is also due to a lack of consistency in gridded observations. In this study, we use three observation datasets, including gridded rain gauge and satellite data, to assess historical simulations from sixteen Coupled Model Intercomparison Project Phase 6 (CMIP6) models. We separately evaluate summer and winter precipitation over the United States (US) with a comprehensive set of extreme precipitation indices, including an assessment of precipitation frequency, intensity and spatial structure. The observations exhibit significant differences in their estimates of area-average intensity distributions and spatial patterns of the mean and extremes of precipitation over the US. In general, the CMIP6 multi-model mean performs better than most individual models at capturing daily precipitation distributions and extreme precipitation indices, particularly in comparison to gauge-based data. Also, the representation of the extreme precipitation indices by the CMIP6 models is better in the summer than winter. Although the ‘standard’ horizontal-resolution can vary significantly across CMIP6 models, from ~0.7° to ~2.8°, we find that resolution is not a good indicator of model performance. Overall, our results highlight common biases in CMIP6 models and demonstrate that no single model is consistently the most reliable across all indices.

54 ENVIRONMENTAL SCIENCES↗

Generalized representative structures for atomistic systems

A new method is presented to generate atomic structures that reproduce the essential characteristics of arbitrary material systems, phases, or ensembles. Previous methods allow one to reproduce the essential characteristics (e.g. the chemical disorder) of a large random alloy within a small crystal structure. The ability to generate small representations of random alloys, along with the restriction to crystal systems, results from using the fixed-lattice cluster correlations to describe structural characteristics. A more general description of the structural characteristics of atomic systems is obtained using complete sets of atomic environment descriptors. These are used within for generating representative atomic structures without restriction to fixed lattices. A general data-driven approach is provided here utilizing the atomic cluster expansion (ACE) basis. The N-body ACE descriptors are a complete set of atomic environment descriptors that span both chemical and spatial degrees of freedom and are used within for describing atomic structures. The generalized representative structure (GRS) method presented within generates small atomic structures that reproduce ACE descriptor distributions corresponding to arbitrary structural and chemical complexity. It is shown that systematically improvable representations of crystalline systems on fixed parent lattices, amorphous materials, liquids, and ensembles of atomic structures may be produced efficiently through optimization algorithms. With the GRS method, we highlight reduced representations of atomistic machine-learning training datasets that contain similar amounts of information and small 40–72 atom representations of liquid phases. The ability to use GRS methodology as a driver for informed novel structure generation is also demonstrated. The advantages over other data-driven methods and state-of-the-art methods restricted to high-symmetry systems are highlighted.

atomic cluster expansion↗

Potential Benefits in Remapping the Special Flood Hazard Area: Evidence from the U.S. Housing Market

A typical U.S. homebuyer's understanding of whether a property faces flood risk is based on whether the property is located inside the National Flood Insurance Program's (NFIP) Special Flood Hazard Area (SFHA). The SFHA boundary, however, may bias homebuyers’ perceptions of flood risk relative to unobserved true risk because the SFHA is an incomplete, and sometimes inaccurate, representation of flood hazards. Using a national dataset of property transactions, flood hazard data from the First Street Foundation, state-level measures of flood disclosure laws, and a spatially restricted triple-difference design, we distinguish capitalization effects of policy-driven (SFHA) versus quasi-objective (First Street) indicators of flood hazard. We identify these effects by assessing thousands of local spatial interactions between property SFHA designations, measures of quasi-objective flood hazard, and being in a state that mandates flood history disclosures. Being inside the SFHA generates a risk discount, but the signal is muted relative to underlying hazard exposure. Further, the SFHA signal can result in inefficient discounts for properties erroneously mapped in the SFHA. Disclosure requirements about flood history accentuate price effects for hazardous properties and result in more adequate risk internalization. In the absence of disclosures, however, we find either no or a weak risk signal for houses outside the SFHA that face flood hazard. Our results highlight potential benefits of updating SFHA boundaries to include all houses that may experience flooding, and argue in favor of requiring flood-related disclosures from sellers to improve the market's ability to internalize flood risk.

54 ENVIRONMENTAL SCIENCES↗

Sensitivity of mesoscale modeling to urban morphological feature inputs and implications for characterizing urban sustainability

We examine the differences in meteorological output from the Weather Research and Forecasting (WRF) model run at 270 m horizontal resolution using 10 m, 100 m and 1 km resolution 3D neighborhood morphological inputs and with no morphological inputs. We find that the spatial variability in temperature, humidity, and other meteorological variables across the city can vary with the resolution and the coverage of the 3D urban morphological input, and that larger differences occur between simulations run without 3D morphological input and those run with some type of 3D morphology. We also find that the inclusion of input-building-defined roughness length calculations would improve simulation results further. We show that these inputs produce different patterns of heat wave spatial heterogeneity across the city of Washington, DC. These findings suggest that understanding neighborhood level urban sustainability under extreme heat waves, especially for vulnerable neighborhoods, requires attention to the representation of surface terrain in numerical weather models.

54 ENVIRONMENTAL SCIENCES↗

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Peatland hydrology across scale: a probabilistic framework for confronting variability, heterogeneity, and uncertainty (Final Report)

Our project aimed to guide the representations of peatland hydrology and water-carbon feedbacks within Earth System Models, by improving process understanding and developing parsimonious models that elucidate the effects of hydroclimatic variability and spatial heterogeneity. Our research questions centered on the three key drivers of peatland hydrology: (1) seasonal and interannual hydroclimatic fluctuations, (2) spatial heterogeneity of peatland microtopography, and (3) hydrological connectivity across landscape units within a peatland watershed. Our analyses and model testing used existing long-term datasets within the Marcell Experimental Forest (MEF), with new data collected whenever necessary. To date, we have demonstrated the strong influence of water table elevations on the temperature sensitivity of CH 4 emissions, using a newly developed eddy covariance dataset spanning eleven years at MEF. Specifically, higher water tables dampen the increase in CH 4 emissions in the spring as well as their decrease in the fall, resulting in hysteresis. These results imply that any hydroclimatological changes in peatlands that shift seasonal water availability from winter to summer will increase annual CH 4 emissions, even if soil temperature remains unchanged. To further investigate water table elevation change within the peatland microtopography, we installed automated water table gauges across four bog-forest transects (the “lagg”) in two peatland watersheds at MEF, which are hotspots of intense biogeochemical activity. These measurements will give us new information about the extent of lagg expansion and contraction during snowmelt and high intensity rainfall events, as well as the directionality of water and nutrient flow into the bog from the surrounding forests. Finally, we investigated the hydrological connectivity across the peatland watershed complex during early spring – a critical period where water table is elevated from snowmelt – using extended hydrological records from MEF (e.g., snow and frost depths, water table elevations, streamflow). The importance of thermal and wintertime processes within the Energy Exascale Earth System Model (E3SM) was determined through sensitivity analyses. Results from data analyses show that (i) streamflow has decreased over decades likely due to increased evapotranspiration rates (despite no detectable trends in precipitation), (ii) spring streamflow generation is controlled by a sequence of fill-and-spill pathways from the snowpack to the stream through peatland water stores, and (iii) frost depth is a key explanatory variable for the timing and magnitude of streamflow. These results suggest that frost plays an important role in connecting surface water storage in peatlands to stream outlets, and that the hydrological connectivity across the peatland watershed complex can mediate the sensitivity of hydrological responses to climate variations.

54 ENVIRONMENTAL SCIENCES↗

Deep medical image analysis with representation learning and neuromorphic computing

Deep learning is increasingly used in medical imaging, improving many steps of the processing chain, from acquisition to segmentation and anomaly detection to outcome prediction. Yet significant challenges remain: (i) image-based diagnosis depends on the spatial relationships between local patterns, something convolution and pooling often do not capture adequately; (ii) data augmentation, the de facto method for learning three-dimensional pose invariance, requires exponentially many points to achieve robust improvement; (iii) labelled medical images are much less abundant than unlabelled ones, especially for heterogeneous pathological cases; and (iv) scanning technologies such as magnetic resonance imaging can be slow and costly, generally without online learning abilities to focus on regions of clinical interest. To address these challenges, novel algorithmic and hardware approaches are needed for deep learning to reach its full potential in medical imaging.

60 APPLIED LIFE SCIENCES↗

A high accuracy/resolution spectral element/Fourier–Galerkin method for the simulation of shoaling non-linear internal waves and turbulence in long domains with variable bathymetry

A high-order hybrid continuous-Galerkin numerical method, designed for the simulation of non-linear, non -hydrostatic internal waves and turbulence in long computational domains with complex bathymetry, is presented. The spatial discretization in the non-periodic wave-propagating directions, utilizes the nodal spectral element method. Such a high-order element-based discretization allows the highly accurate representation of complex domain geometry along with the flexibility of concentrating resolution in areas of interest. Under the assumption of the normal-to-isobath propagation of non-linear internal waves, a third periodic direction is incorporated via a Fourier-Galerkin discretization. The distinct non-hydrostatic nature of non-linear internal waves and, any instabilities and turbulence therein, necessitates the numerically challenging solution of the pressure Poisson problem. A defining feature of this work is the application of a domain decomposition approach, combined with block-Jacobi/deflation-based preconditioning to the pressure Poisson problem. Such a combined approach is particularly suitable for the long high aspect-ratio complex domains of interest and enables the efficient high-accuracy reproduction of the non-hydrostatic dynamics of non-linear internal waves. Implementation details are also described in the context of the stability of the solver and its parallelization strategy. A series of benchmarks of increasing complexity demonstrate the robustness of the flow solver. The benchmarks culminate with the three-dimensional simulation of a convectively breaking mode-one non-linear internal wave over a realistic South-China-Sea bathymetric transect and background current/stratification profiles.

Deflation↗

Implementation and Evaluation of Emission‐Driven Land‐Atmosphere Coupled Simulation in E3SMv2.1

Emissions-driven (prognostic CO 2 ) simulations are essential for representing two-way carbon-climate feedback in Earth System Models. We present an emissions-driven land–atmosphere coupled biogeochemistry (BGC) configuration (BGCLNDATM_progCO2) in version 2.1 of the Energy Exascale Earth System Model (E3SMv2.1). This is the first E3SM configuration that performs land-atmosphere emission-hindcasts. Here, we document its implementation, evaluate the model's performance against observations and other models, and propose a structured evaluation protocol for such emissions-driven simulations. We conducted transient historical simulations (1850–2014) with BGCLNDATM_progCO2 and compare them to reference simulations—a land-atmosphere coupled simulation without BGC and a standalone land simulation with BGC, both using prescribed CO 2 concentrations—and to observations. BGCLNDATM_progCO2 overestimates atmospheric CO 2 concentrations by 11–23 ppm yet stays within the 40-ppm spread CMIP6 emission-driven models and retains physical climate properties comparable to the reference runs. The CO 2 biases are partly attributed to underrepresented oceanic CO 2 uptake and inadequate representations of some terrestrial processes. In general, introducing prognostic CO 2 did not change physical climate metrics at the global scale but had larger regional effects, particularly over land where spatially heterogeneous CO 2 and prognostic leaf area index influenced surface energy balance. Finally, we propose a general evaluation protocol including spin-up assessment, atmospheric CO 2 benchmarking, physical climate evaluation, and land biogeochemical analysis to support scientific rigor and facilitate inter-model comparisons. The new configuration lays the groundwork for future enhancements, including improved terrestrial biogeochemical processes, integrated marine biogeochemistry, and additional human–Earth system interactions. These developments advance E3SM toward fully coupled emissions-driven simulations, enabling more accurate carbon–climate feedback projections and informing mitigation policy by providing physically consistent carbon-budget metrics for mitigation scenarios.

54 ENVIRONMENTAL SCIENCES↗

A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations

Here, in this paper, we present a predictor-corrector strategy for constructing rank-adaptive, dynamical low-rank approximations (DLRAs) of matrix-valued ODE systems. The strategy is a compromise between (i) low-rank step-truncation approaches that alternately evolve and compress solutions and (ii) strict DLRA approaches that augment the low-rank manifold using subspaces generated locally in time by the DLRA integrator. The strategy is based on an analysis of the error between a forward temporal update into the ambient full-rank space, which is typically computed in a step-truncation approach before recompressing, and the standard DLRA update, which is forced to live in a low-rank manifold. We use this error, without requiring its full-rank representation, to correct the DLRA solution. A key ingredient for maintaining a low-rank representation of the error is a randomized SVD, which introduces some degree of stochastic variability into the implementation. The strategy is formulated and implemented in the context of discontinuous Galerkin spatial discretizations of PDEs and applied to several versions of DLRA methods found in the literature as well as a new variant. Numerical experiments comparing the predictor-corrector strategy to other methods demonstrate robustness to overcome shortcomings of step truncation or strict DLRA approaches: The former may require more memory than is strictly needed, while the latter may miss transients solution features that cannot be recovered. The effect of randomization, tolerances, and other implementation parameters is also explored.

97 MATHEMATICS AND COMPUTING↗

MLMOD: Machine Learning Methods for Data-Driven Modeling in LAMMPS

MLMOD is a software package for incorporating machine learning approaches and models into simulations of microscale mechanics and molecular dynamics in LAMMPS. Recent machine learning approaches provide promising data-driven approaches for learning representations for system behaviors from experimental data and high fidelity simulations. The package facilitates learning and using data-driven models for (i) dynamics of the system at larger spatial-temporal scales (ii) interactions between system components, (iii) features yielding coarser degrees of freedom, and (iv) features for new quantities of interest characterizing system behaviors. MLMOD provides hooks in LAMMPS for (i) modeling dynamics and time-step integration, (ii) modeling interactions, and (iii) computing quantities of interest characterizing system states. The package allows for use of machine learning methods with general model classes including Neural Networks, Gaussian Process Regression, Kernel Models, and other approaches. Here we discuss our prototype C++/Python package, aims, and example usage. For related papers, examples, updates, and additional information see https://github.com/atzberg/mlmod and http://atzberger.org/.

97 MATHEMATICS AND COMPUTING↗