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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Neuromorphic intermediate representation: A unified instruction set for interoperable brain-inspired computing

Abstract Spiking neural networks and neuromorphic hardware platforms that simulate neuronal dynamics are getting wide attention and are being applied to many relevant problems using Machine Learning. Despite a well-established mathematical foundation for neural dynamics, there exists numerous software and hardware solutions and stacks whose variability makes it difficult to reproduce findings. Here, we establish a common reference frame for computations in digital neuromorphic systems, titled Neuromorphic Intermediate Representation (NIR). NIR defines a set of computational and composable model primitives as hybrid systems combining continuous-time dynamics and discrete events. By abstracting away assumptions around discretization and hardware constraints, NIR faithfully captures the computational model, while bridging differences between the evaluated implementation and the underlying mathematical formalism. NIR supports an unprecedented number of neuromorphic systems, which we demonstrate by reproducing three spiking neural network models of different complexity across 7 neuromorphic simulators and 4 digital hardware platforms. NIR decouples the development of neuromorphic hardware and software, enabling interoperability between platforms and improving accessibility to multiple neuromorphic technologies. We believe that NIR is a key next step in brain-inspired hardware-software co-evolution, enabling research towards the implementation of energy efficient computational principles of nervous systems. NIR is available atneuroir.org

Science & Technology - Other Topics↗
DOE OSTI2026

Optimal binning of correlated measurements

Experimental measurements are commonly represented on a discrete grid, requiring a balance between granularity and statistical noise. Two strategies have traditionally been used to improve such representations: selecting an appropriate bin width to control discretization error and applying kernel-based smoothing to suppress fluctuations. Despite their shared goal, these approaches have largely developed independently, without a unified statistical description of how discretization and correlation jointly determine measurement precision. Here, we extend the discussion of optimal interval averaging to a correlation-aware setting by Gaussian process regression, which explicitly accounts for correlations among neighboring bins. Starting from first principles, we derive the mean-squared error of discretized measurements and obtain closed-form asymptotic expressions for the optimal bin width and correlation length. When recast in reduced variables, the theory reveals distinct universal scaling laws governing the error in the correlation-free and correlation-controlled regimes. Characterized by intrinsically smooth intensity profiles and counting-based statistics, neutron scattering measurements are well suited for demonstrating the enhanced error contraction enabled by inter-bin correlations. We show that such improvement is achievable over the experimentally accessible Q-range and across multiple instruments and material systems. These results show that explicitly accounting for correlations systematically reshapes the limits of precision in discretized, noise-limited measurements. More broadly, the framework provides a transferable statistical foundation for optimizing data representation, inference, and experimental design across the physical and data sciences.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗
DOE OSTI2022

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↗
DOE OSTI2022

Combining shallow-water and analytical wake models for tidal array micro-siting

For tidal-stream energy to become a competitive renewable energy source, clustering multiple turbines into arrays is paramount. Array optimisation is thus critical for achieving maximum power performance and reducing cost of energy. However, ascertaining an optimal array layout is a complex problem, subject to specific site hydrodynamics and multiple inter-disciplinary constraints. In this work, we present a novel optimisation approach that combines an analytical-based wake model, FLORIS, with an ocean model, Thetis. The approach is demonstrated through applications of increasing complexity. By utilising the method of analytical wake superposition, the addition or alteration of turbine position does not require re-calculation of the entire flow field, thus allowing the use of simple heuristic techniques to perform optimisation at a fraction of the computational cost of more sophisticated methods. Using a custom condition-based placement algorithm, this methodology is applied to the Pentland Firth for arrays with turbines of 3.05 m/s rated speed, demonstrating practical implications whilst considering the temporal variability of the tide. For a 24-turbine array case, micro-siting using this technique delivered an array 15.8% more productive on average than a staggered layout, despite flow speeds regularly exceeding the rated value. Performance was evaluated through assessment of the optimised layout within the ocean model that treats turbines through a discrete turbine representation. Used iteratively, this methodology could deliver improved array configurations in a manner that accounts for local hydrodynamic effects.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

Modeling rarefied gas chemistry with QuiPS, a novel quasi-particle method

The goal of this work is to build up the capability of quasi-particle simulation (QuiPS), a novel flow solver, such that it can adequately model the rarefied portion of an atmospheric reentry trajectory. Direct simulation Monte Carlo (DSMC) is the conventional solver for such conditions, but struggles to resolve transient flows, trace species, and high-level internal energy states due to stochastic noise. Quasi-particle simulation (QuiPS) is a novel Boltzmann solver that describes a system with a discretized, truncated velocity distribution function. The resulting fixed-velocity, variable weight quasi-particles enable smooth variation of macroscopic properties. The distribution function description enables the use of a variance-reduced collision model, greatly minimizing expense near equilibrium. This work presents the addition of a neutral air chemistry model to QuiPS and some demonstrative 0D simulations. The explicit representation of internal distributions in QuiPS reveals some of the flaws in existing physics models. Overall, variance reduction, a key feature of QuiPS, can greatly reduce expense of multi-dimensional calculations, but is only cheaper when the gas composition is near chemical equilibrium.

42 ENGINEERING↗
DOE OSTI2021

Scalable Techniques for Stochastic Power Flow Problems (Final Report)

The proposed research focuses on developing scalable algorithms for two-stage security-constrained OPF problems with AC power flow constraints, a class of problems complicated by (i) scale arising from a scenario representation; and (ii) the presence of nonlinearity, nonconvexity, and possibly second-stage discreteness or complementarity. Unfortunately, most existing solvers cannot contend with both challenges simultaneously; accordingly, the proposed research focuses on developing solution techniques that can both scale with the number of scenarios and contend with nonconvexity and second-stage complementarity. We consider three avenues for addressing such problems: (i) Variable sample-size SQP (VS-SQP) methods that combine sparse Quasi-Newton updates with a scalable variance-reduced stochastic gradient scheme for stochastic QP subproblems, allowing for contending with second-stage complementarity via regularization; (ii) Variable sample-size stochastic Interior-point (VS-sIP) schemes that propose a sampling-based regularized (to allow for contending with complementarity) interior-point schemes in which a Schur-complement technique is employed for decomposing the Newton direction computation step; (iii) Variable sample-size tractable ADMM (VS-tADMM) schemes combine variable sample-sizes with carefully designed techniques for resolving each of the nonconvex updates (by leveraging the QCQP structures). We intend to compare the three schemes using performance profiles in terms of solution quality, scalability, etc. and then select one scheme which will then be developed and further refined in Python for purposes of the GO competition.

42 ENGINEERING↗
DOE OSTI2023

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

thornado+FLASH-X: A Hybrid Discontinuous Galerkin–Implicit-explicit and Finite-volume Framework for Neutrino-radiation Hydrodynamics in Core-collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement–based multiphysics simulation framework FLASH-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $\mathcal{O}(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino–matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino–electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved through a hybrid DG-FV representation of the fluid variables and operator-split evolution within FLASH-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within FLASH-X. thornado’s neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

Endeve, Eirik [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2024

Barrier penetration in a discrete-basis formalism

The dynamics of a many-particle system are often modeled by mapping the Hamiltonian into a Schrödinger equation. An alternative approach is to solve the Hamiltonian equations directly in a model space of many-body configurations. In a previous paper the numerical convergence of the two approaches was compared with a simplified treatment of the Hamiltonian representation. Here, we extend the comparison to the nonorthogonal model spaces that would be obtained by the generator-coordinate method. With a suitable choice of the collective-variable grid, a configuration-interaction Hamiltonian can reproduce the Schrödinger dynamics very well. Furthermore, the method as implemented here requires that the barrier height is not much larger than the zero-point energy in the collective coordinates of the configurations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

The importance of explicitly representing the streambed in watershed models

Abstract The streambed is the critical interface between the aquatic and terrestrial systems and hosts important biogeochemical hot spots within river corridors. Although the streambed characteristics are significantly different from those of its surrounding soil, the streambed itself has not been explicitly represented in watershed models. Here, we explicitly incorporated a streambed layer into an integrated hydrologic model through model parameterization and discretization. We examined the hydrological effects of streambed characteristics, including hydraulic conductivity ( K ), layer thickness, and resolution, on the exchange fluxes across the streambed as well as the streamflow at the watershed outlet. The numerical experiments were performed in the American River Watershed, a headwater, mountainous watershed within the Yakima River Basin in central Washington. Despite having a negligible effect on the watershed streamflow, an explicit representation of the streambed with distinctive properties dramatically changed the magnitude and variability of the exchange flux. In general, a larger streambed K along with a thicker streambed layer induced larger exchange fluxes. The exchange flux was most sensitive to the streambed resolution. A finer streambed resolution increased exchange fluxes per unit area while reducing the overall exchange volumes across the entire streambed. The amount of baseflow decreased by 6% as the streambed resolution increased from 250 to 50 m. This finding is important because these hydrological changes may, in turn, affect the exchange of nutrients and contaminants between surface water and groundwater and the associated biogeochemical processes. Our work demonstrated the importance of representing streambeds in fully distributed, process‐based watershed models to better capture the exchange flow dynamics in river corridors.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Connecting Large‐Scale Meteorological Patterns to Extratropical Cyclones in CMIP6 Climate Models Using Self‐Organizing Maps

Abstract Extratropical cyclones (ETCs) are responsible for the majority of cool‐season extreme events in the northeastern United States (NEUS), often leading to high‐impact weather conditions that can have wide‐ranging socioeconomic impacts. Evaluating the ability of climate models to adequately simulate ETC dynamics is essential for improving model performance and increasing confidence in future projections used by stakeholders and policymakers. ETCs are traditionally studied using techniques such as case studies and synoptic typing, however, these approaches can be time‐consuming, require subjective analysis, and do not necessarily identify the coincident large‐scale meteorological patterns (LSMPs). Here, we apply self‐organizing maps (SOMs) as an automated machine‐learning approach to characterize the LSMPs and associated frequency and intensity of discrete ETC events over NEUS. The dominant patterns of geopotential height variability are identified through SOM analysis of five reanalysis products during the last four decades. ETC events are tracked using TempestExtremes and are integrated with SOMs to classify the accumulated cyclone activity (ACA) associated with each pattern. We then evaluate the skill of CMIP6 historical experiments in simulating the LSMPs and ETC events identified in the SOM. Our results identify a robust bias toward more zonal patterns, with models struggling to reproduce the more amplified patterns typically associated with the highest cyclone activity. While model resolution has some impact on simulation credibility, model configuration appears to be more important in LSMP representation. The vast majority of CMIP6 models produce too few ETCs, although model errors are distributed around historical reanalyses when ACA is normalized by storm frequency.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A robust estimator of mutual information for deep learning interpretability

Abstract We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning (DL) models. To accurately estimate MI from a finite number of samples, we present GMM-MI (pronounced ‘Jimmie’), an algorithm based on Gaussian mixture models that can be applied to both discrete and continuous settings. GMM-MI is computationally efficient, robust to the choice of hyperparameters and provides the uncertainty on the MI estimate due to the finite sample size. We extensively validate GMM-MI on toy data for which the ground truth MI is known, comparing its performance against established MI estimators. We then demonstrate the use of our MI estimator in the context of representation learning, working with synthetic data and physical datasets describing highly non-linear processes. We train DL models to encode high-dimensional data within a meaningful compressed (latent) representation, and use GMM-MI to quantify both the level of disentanglement between the latent variables, and their association with relevant physical quantities, thus unlocking the interpretability of the latent representation. We make GMM-MI publicly available in this GitHub repository.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Quantum simulation of QED in Coulomb gauge

A recent work considered quantum simulation of Quantum Electrodynamics on a lattice in the Coulomb gauge with gauge degrees of freedom represented in the occupation basis in momentum space. In this work, we consider the more efficient representation of the gauge degrees of freedom in field basis in position space and develop a quantum algorithm for real-time simulation. We show that the continuum Coulomb gauge Hamiltonian is equivalent to the temporal gauge Hamiltonian when acting on physical states consisting of fermion and transverse gauge fields. The Coulomb gauge Hamiltonian is discretized by using the Green’s function of the discrete Laplacian operator under the Dirichlet boundary conditions. Both the continuum Coulomb gauge Hamiltonian and the discretized one proposed here guarantee that the unphysical longitudinal gauge fields are decoupled and commute with the corresponding Hamiltonian. Thus there is no need to impose any constraint. The local gauge field basis and the canonically conjugate variable basis are swapped efficiently using the quantum Fourier transform. We prove that the qubit cost to represent physical states and the gate count for real-time simulation scale polynomially with the lattice size, energy, time, accuracy, and Hamiltonian parameters in lattice units. The gate cost here for implementing the time evolution of the gauge field is reduced at least by a factor on the order of 10 8 for modest lattice size and accuracy level compared with the previous work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Discrete versus continuous: Enhancing battery optimization in capacity expansion models

This study compares two battery modeling approaches for capacity expansion models: discrete-duration and continuous-duration formulations. In the discrete approach, battery duration is fixed, and power capacity is optimized. In the continuous approach, both power and energy capacities are decision variables, allowing storage duration to be optimized endogenously. Although both discrete-duration and continuous-duration battery formulations are used in long-term power system planning models, the literature has provided limited direct, systematic comparisons of their implications within a common modeling framework. To address this gap, this study implements both approaches in the Regional Energy Deployment System (ReEDS TM ) capacity expansion model using two resource adequacy methods, across a range of future system conditions, and with varying battery cost projections. Results show continuous-duration and high-resolution discrete approaches produce similar capacity expansion outcomes. The continuous formulation achieves faster runtimes compared to discrete-duration runs with many discrete-duration options. However, the discrete-duration approach allows users to choose to have limited fidelity for storage duration options, which in some cases can outperform the continuous formulation. The continuous formulation has the lowest overall system costs, indicating its ability to fine-tune storage duration to better meet specific system needs. This study's findings provide a side-by-side evaluation of discrete and continuous battery modeling approaches and offer guidance for improving the representation of real-world systems, flexibility, and computational efficiency for representing energy storage in long-term power system planning models.

25 ENERGY STORAGE↗
DOE OSTI2020

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Finding simplicity: unsupervised discovery of features, patterns, and order parameters via shift-invariant variational autoencoders *

Abstract Recent advances in scanning tunneling and transmission electron microscopies (STM and STEM) have allowed routine generation of large volumes of imaging data containing information on the structure and functionality of materials. The experimental data sets contain signatures of long-range phenomena such as physical order parameter fields, polarization, and strain gradients in STEM, or standing electronic waves and carrier-mediated exchange interactions in STM, all superimposed onto scanning system distortions and gradual changes of contrast due to drift and/or mis-tilt effects. Correspondingly, while the human eye can readily identify certain patterns in the images such as lattice periodicities, repeating structural elements, or microstructures, their automatic extraction and classification are highly non-trivial and universal pathways to accomplish such analyses are absent. We pose that the most distinctive elements of the patterns observed in STM and (S)TEM images are similarity and (almost-) periodicity, behaviors stemming directly from the parsimony of elementary atomic structures, superimposed on the gradual changes reflective of order parameter distributions. However, the discovery of these elements via global Fourier methods is non-trivial due to variability and lack of ideal discrete translation symmetry. To address this problem, we explore the shift-invariant variational autoencoders (shift-VAEs) that allow disentangling characteristic repeating features in the images, their variations, and shifts that inevitably occur when randomly sampling the image space. Shift-VAEs balance the uncertainty in the position of the object of interest with the uncertainty in shape reconstruction. This approach is illustrated for model 1D data, and further extended to synthetic and experimental STM and STEM 2D data. We further introduce an approach for training shift-VAEs that allows finding the latent variables that comport to known physical behavior. In this specific case, the condition is that the latent variable maps should be smooth on the length scale of the atomic lattice (as expected for physical order parameters), but other conditions can be imposed. The opportunities and limitations of the shift VAE analysis for pattern discovery are elucidated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Non-Gaussian photonic state engineering with the quantum frequency processor

Non-Gaussian quantum states of light are critical resources for optical quantum information processing, but methods to generate them efficiently remain challenging to implement. Here we introduce a generic approach for non-Gaussian state production from input states populating discrete frequency bins. Based on controllable unitary operations with a quantum frequency processor, followed by photon-number-resolved detection of ancilla modes, our method combines recent developments in both frequency-based quantum information and non-Gaussian state preparation. Leveraging and refining the K-function representation of quantum states in the coherent basis, we develop a theoretical model amenable to numerical optimization and, as specific examples, design quantum frequency processor circuits for the production of Schrödinger cat states, exploring the performance tradeoffs for several combinations of ancilla modes and circuit depth. Our scheme provides a valuable framework for producing complex quantum states in frequency bins, paving the way for single-spatial-mode, fiber-optic-compatible non-Gaussian resources.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantifying the Impact of Vertical Resolution on the Representation of Marine Boundary Layer Physics for Global-Scale Models

Abstract While GCM horizontal resolution has received the majority of scale improvements in recent years, ample evidence suggests that a model’s vertical resolution exerts a strong control on its ability to accurately simulate the physics of the marine boundary layer. Here we show that, regardless of parameter tuning, the ability of a single-column model (SCM) to simulate the subtropical marine boundary layer improves when its vertical resolution is improved. We introduce a novel objective tuning technique to optimize the parameters of an SCM against profiles of temperature and moisture and their turbulent fluxes, horizontal winds, cloud water, and rainwater from large-eddy simulations (LES). We use this method to identify optimal parameters for simulating marine stratocumulus and shallow cumulus. The novel tuning method utilizes an objective performance metric that accounts for the uncertainty in the LES output, including the covariability between model variables. Optimization is performed independently for different vertical grid spacings and value of time step, ranging from coarse scales often used in current global models (120 m, 180 s) to fine scales often used in parameterization development and large-eddy simulations (10 m, 15 s). Uncertainty-weighted disagreement between the SCM and LES decreases by a factor of ∼5 when vertical grid spacing is improved from 120 to 10 m, with time step reductions being of secondary importance. Model performance is shown to converge at a vertical grid spacing of 20 m, with further refinements to 10 m leading to little further improvement. Significance Statement In successive generations of computer models that simulate Earth’s atmosphere, improvements have been mainly accomplished by reducing the horizontal sizes of discretized grid boxes, while the vertical grid spacing has seen comparatively lesser refinements. Here we advocate for additional attention to be paid to the number of vertical layers in these models, especially in the model layers closest to Earth’s surface where climatologically important marine stratocumulus and shallow cumulus clouds reside. Our experiments show that the ability of a one-dimensional model to represent physical processes important to these clouds is strongly dependent on the model’s vertical grid spacing.

Meteorology & Atmospheric Sciences↗