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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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At least 37 records · Page 2

Mitigation of nitrogen vacancy photoluminescence quenching from material integration for quantum sensing

The nitrogen-vacancy (NV) color center in diamond has demonstrated great promise in a wide range of quantum sensing. Recently, there have been a series of proposals and experiments using NV centers to detect spin noise of quantum materials near the diamond surface. This is a rich complex area of study with novel nano-magnetism and electronic behavior, that the NV center would be ideal for sensing. However, due to the electronic properties of the NV itself and its host material, getting high quality NV centers within nanometers of such systems is challenging. Band bending caused by space charges formed at the metal-semiconductor interface force the NV center into its insensitive charge states. Here, we investigate optimizing this interface by depositing thin metal films and thin insulating layers on a series of NV ensembles at different depths to characterize the impact of metal films on different ensemble depths. We find an improvement of coherence and dephasing times we attribute to ionization of other paramagnetic defects. The insulating layer of alumina between the metal and diamond provide improved photoluminescence and higher sensitivity in all modes of sensing as compared to direct contact with the metal, providing as much as a factor of 2 increase in sensitivity, decrease of integration time by a factor of 4, for NV T 1 relaxometry measurements.

36 MATERIALS SCIENCE↗

Decadal Spiciness Variability in the Subtropical-Tropical Pacific in the CESM2 Large Ensemble

Tropical Pacific decadal variations impact weather and climate around the world and are also connected to variations in the global warming trend. The mechanisms driving these long-term modulations, particularly the role of subsurface ocean dynamics, are still debated. Here, we investigate the dynamics of spiciness (density-compensated temperature and salinity) anomalies in the tropical and subtropical Pacific, which are hypothesized as a possible driving mechanism of decadal climate variability. Based on the analysis of 100 realizations from the Community Earth System Model Version 2 Large Ensemble (CESM2-LE), we demonstrate a coupling between the subtropics and the equatorial Pacific by propagating spiciness anomalies at decadal time scales. The CESM2-LE simulates spiciness variability along a subduction path from the subtropics to the equator with frequency spectra that show the highest power at low frequencies and a power decay proportional to a −4 slope for frequencies greater than 0.01 cycles per months, corresponding to periods smaller than ∼8.5 years. Signals that originate in the Southern Hemisphere (SH) dominate and arrive with a larger magnitude at the equator compared to spiciness anomalies from the Northern Hemisphere (NH). Spiciness anomalies from the SH have shorter propagation times and are strengthened along their pathway as stochastic wind stress curl forcing generates anomalous baroclinic ocean pressure gradients. These pressure gradients generate spiciness anomalies via anomalous advection across climatological spiciness gradients in the SH. We conclude that the observed spiciness variance at decadal time scales is consistent with a forcing by stochastic wind variations that are low-pass filtered by ocean dynamics.

54 ENVIRONMENTAL SCIENCES↗

Electrocatalytic alkene epoxidation at disrupted metal ensembles in blended electrolytes

The project aims to achieve a molecular understanding of oxygen-atom transfer from water to alkenes at electrocatalytic interfaces. Molecular oxygen is the most common oxygen-atom source for epoxidations, and our group is developing sustainable routes through which epoxidation of olefins is achieved using water as the oxygen source. This route can improve the safety of the reaction while also co-producing hydrogen, demonstrating the relevance of this reaction to the energy transition. If successful in our efforts, we may enable oxygen-atom transfer reactions at the anode of water electrolyzers in the place of conventional oxygen evolution, allowing for the synthesis of sustainable value-added co-products. In this vein, we explore several approaches to acquiring high selectivity toward epoxidation over competing reactions, such as oxygen evolution. One of our aims is to allow for rational control of epoxide selectivity by disrupting contiguous metal ensembles at the surface of catalytic metal oxide nanoparticles. Specifically, we aim to synthesize single-atom, few-atom, and many-atom clusters supported on metal oxides and study the mechanism of oxygen evolution and alkene epoxidation on these materials. Thus, this approach will determine the impact of disrupting metal ensembles on the selectivity for alkene epoxidation versus oxygen evolution in blended electrolytes. Another aim is to develop a molecular-level understanding of how a blended electrolyte (i.e., a mixture of aqueous and organic solvents) influences rates of alkene epoxidation versus oxygen evolution. In other words, we are interested in understanding the catalytic influence of the solvent, as our preliminary work shows that the selectivity and reactivity of epoxidation depend strongly on the solvent composition. This investigation includes blended electrolytes and electrolytes containing redox mediator species that improve selectivity toward the desired epoxidation reaction. Overall, our proposed work will help to provide a detailed molecular-level picture of how solvents interact with substrates at the electrode-electrolyte interface, including their involvement in proton transfer reactions and screening of electric fields.

14 SOLAR ENERGY↗

Advancing research on compound weather and climate events via large ensemble model simulations

Societally relevant weather impacts typically result from compound events, which are rare combinations of weather and climate drivers. Focussing on four event types arising from different combinations of climate variables across space and time, here we illustrate that robust analyses of compound events — such as frequency and uncertainty analysis under present-day and future conditions, event attribution to climate change, and exploration of low-probability-high-impact events — require data with very large sample size. In particular, the required sample is much larger than that needed for analyses of univariate extremes. We demonstrate that Single Model Initial-condition Large Ensemble (SMILE) simulations from multiple climate models, which provide hundreds to thousands of years of weather conditions, are crucial for advancing our assessments of compound events and constructing robust model projections. Combining SMILEs with an improved physical understanding of compound events will ultimately provide practitioners and stakeholders with the best available information on climate risks.

54 ENVIRONMENTAL SCIENCES↗

Large Ensemble Exploration of Global Energy Transitions Under National Emissions Pledges

Global climate goals require a transition to a deeply decarbonized energy system. Meeting the objectives of the Paris Agreement through countries' nationally determined contributions and long-term strategies represents a complex problem with consequences across multiple systems shrouded by deep uncertainty. Robust, large-ensemble methods and analyses mapping a wide range of possible future states of the world are needed to help policymakers design effective strategies to meet emissions reduction goals. This study contributes a scenario discovery analysis applied to a large ensemble of 5,760 model realizations generated using the Global Change Analysis Model. Eleven energy-related uncertainties are systematically varied, representing national mitigation pledges, institutional factors, and techno-economic parameters, among others. The resulting ensemble maps how uncertainties impact common energy system metrics used to characterize national and global pathways toward deep decarbonization. Results show globally consistent but regionally variable energy transitions as measured by multiple metrics, including electricity costs and stranded assets. Larger economies and developing regions experience more severe economic outcomes across a broad sampling of uncertainty. The scale of CO 2 removal globally determines how much the energy system can continue to emit, but the relative role of different CO 2 removal options in meeting decarbonization goals varies across regions. Previous studies characterizing uncertainty have typically focused on a few scenarios, and other large-ensemble work has not (to our knowledge) combined this framework with national emissions pledges or institutional factors. Our results underscore the value of large-ensemble scenario discovery for decision support as countries begin to design strategies to meet their goals.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Storylines for the 1997 New Year’s Flood: The role of watershed antecedent conditions and future warming in shaping discharge in the Truckee River watershed

The 1997 New Year’s flood was among the most devastating floods in the Truckee River watershed located in western Nevada. This event resulted from complex interactions of flood drivers, such as extreme precipitation, wet antecedent watershed conditions, warm temperatures and rapid snowmelt. We leveraged simulated forcings from the regionally refined mesh capabilities of the Energy Exascale Earth System Model (RRM-E3SM) and a process-based hydrological model to recreate the 1997 New Year’s flood for the Truckee River watershed across four climate warming levels ranging from the current temperatures to + 4° C. For each scenario, we conducted ensemble simulations with the same forcing but with 100 different seasonal watershed antecedent conditions, which were randomly sampled from long-term hydrological simulations. The results show that the 1997 New Year’s flood can be reproduced or exceeded consistently only when the antecedent watershed conditions are wet, specifically when streamflows are above the 75th percentile of the climatological value. There is negligible change in ensemble mean peakflows for Truckee River near Reno; however, there are increases of 18% and 14% under the warming levels of + 3° C and + 4° C, respectively. The increases in peakflows under future climate warming are attributed to wetter antecedent watershed conditions and enhanced snowmelt. Furthermore, the largest increases in peakflows occur at small, high-elevation headwater basins along the Sierra Nevada crest. This study highlights that changes in extreme flood events will result from the complex interplay of multiple flood drivers. It also demonstrates the potential of storyline approaches to analyze future realizations of these extreme events under different climate scenarios.

Climate change impact study↗

The Influence of African Easterly Waves on Atlantic Tropical Cyclone Tracks and Landfall in Large Ensembles

African easterly waves (AEWs) are an important precursor or “seed” for Atlantic tropical cyclones (TCs), with 60%–80% of major hurricanes observed to originate from AEWs. However, climate model simulations indicate that AEWs are not necessary to maintain annual Atlantic TC frequency. Furthermore, small ensembles suggest that AEWs may impact the spatial distribution and landfall of Atlantic TCs. Here, we investigated the influence of AEWs on the spatial distribution of Atlantic TC tracks and landfall using 50-member ensembles of TC-permitting regional model simulations for five hurricane seasons characterized by different levels of TC activity. The control simulations are seasonal hindcasts in which AEWs were prescribed through the eastern lateral boundary condition using reanalysis. In the experiments, we suppressed AEWs by applying a 2–10 day filter to the eastern lateral boundary condition. In response to AEW suppression, we discovered statistically significant increases in Atlantic TC frequency (10%–26%) and landfall (16%–44%), a westward shift in TC genesis location and tracks with increased landfall over the Caribbean Islands, southwestern Gulf Coast, and southeastern US coast, and increases in mid-tropospheric relative humidity in the main development region. In addition, we evaluated TC genesis mechanisms in the absence of AEWs and found evidence that the intertropical convergence zone (ITCZ) intensified and extended northward, resulting in ITCZ wave-breaking that shed vortices which served as TC seeds. By uncovering the connections between TC seed types and the likelihood of TC landfall, this research can provide Atlantic coastal and island communities with useful information to prepare for TC impacts.

African easterly waves↗

Projected changes in cross-equatorial northerly surges and their hydrological impacts in the near future

Recent decades have witnessed unprecedented extreme precipitation and catastrophic flooding in some of the most populated regions in Southeast Asia during boreal winter. These extreme events are often influenced by the cross-equatorial northerly surge (CENS), characterized by a strengthening of northerly moist monsoon winds south of the equator in the western Maritime Continent. However, the potential future changes in CENS and its hydrological impacts remain underexplored. Here, using an ensemble of high-resolution climate model simulations (CMIP6 HighResMIP), we show that the regional impacts of CENS on the intensity and frequency of extreme precipitation events are projected to significantly increase in the near future (2030–2050), particularly over the adjacent coastal regions of southern Indonesia and northwestern Australia. More specifically, the risk of CENS-related extreme precipitation is projected to increase by up to 39 ± 1.2% relative to the seasonal probability, despite no apparent changes in the CENS characteristics in the near future. Such stronger impact is attributed to the enhanced moistening efficiency and moist static instability due to a more humid and warmer environment, which leads to more intense CENS convection. Our results suggest the need for effective monitoring and disaster managements to respond to the increasing severity of such events in the near future.

Climate sciences↗

Land Processes Can Substantially Impact the Mean Climate State

Terrestrial processes influence the atmosphere by controlling land-to-atmosphere fluxes of energy, water, and carbon. Prior research has demonstrated that parameter uncertainty drives uncertainty in land surface fluxes. However, the influence of land process uncertainty on the climate system remains underexplored. Here, we quantify how assumptions about land processes impact climate using a perturbed parameter ensemble for 18 land parameters in the Community Earth System Model version 2 under preindustrial conditions. We find that an observationally-informed range of land parameters generate biogeophysical feedbacks that significantly influence the mean climate state, largely by modifying evapotranspiration. Global mean land surface temperature ranges by 2.2°C across our ensemble (σ = 0.5°C) and precipitation changes were significant and spatially variable. Our analysis demonstrates that the impacts of land parameter uncertainty on surface fluxes propagate to the entire Earth system, and provides insights into where and how land process uncertainty influences climate.

54 ENVIRONMENTAL SCIENCES↗

Quancorde: Boosting fidelity with Quantum Canary Ordered Diverse Ensembles

On today's noisy imperfect quantum devices, execution fidelity tends to collapse dramatically for most applications beyond a handful of qubits. It is therefore imperative to employ novel techniques that can boost quantum fidelity in new ways. Here, this paper aims to boost quantum fidelity with Clifford canary circuits by proposing Quancorde: Quantum Canary Ordered Diverse Ensembles, a fundamentally newapproach to identifying the correct outcomes of extremely low-fidelity quantum applications. It is based on the key idea of diversity in quantum devices - variations in noise sources, make each (portion of a) device unique, and therefore, their impact on an application's fidelity, also unique. Quancorde utilizes Clifford canary circuits (which are classically simulable, but also resemble the target application structure and thus suffer similar structural noise impact) to order a diverse ensemble of devices or qubits/mappings approximately along the direction of increasing fidelity of the target application. Quancorde then estimates the correlation of the ensemble-wide probabilities of each output string of the application, with the canary ensemble ordering, and uses this correlation to weight the application's noisy probability distribution. The correct application outcomes are expected to have higher correlation with the canary ensemble order, and thus their probabilities are boosted in this process. Doing so, Quancorde improves the fidelity of evaluated quantum applications by a mean of 8.9x/4.2x (wrt. different baselines) and up to a maximum of 34x.

clifford↗

Impact of Model Resolution on Tropical Cyclone Simulation Using the HighResMIP–PRIMAVERA Multimodel Ensemble

A multimodel, multiresolution set of simulations over the period 1950–2014 using a common forcing protocol from CMIP6 HighResMIP have been completed by six modeling groups. Analysis of tropical cyclone performance using two different tracking algorithms suggests that enhanced resolution toward 25 km typically leads to more frequent and stronger tropical cyclones, together with improvements in spatial distribution and storm structure. Both of these factors reduce typical GCM biases seen at lower resolution. Using single ensemble members of each model, there is little evidence of systematic improvement in interannual variability in either storm frequency or accumulated cyclone energy as compared with observations when resolution is increased. Changes in the relationships between large-scale drivers of climate variability and tropical cyclone variability in the Atlantic Ocean are also not robust to model resolution. However, using a larger ensemble of simulations (of up to 14 members) with one model at different resolutions does show evidence of increased skill at higher resolution. The ensemble mean correlation of Atlantic interannual tropical cyclone variability increases from ~0.5 to ~0.65 when resolution increases from 250 to 100 km. In the northwestern Pacific Ocean the skill keeps increasing with 50-km resolution to 0.7. These calculations also suggest that more than six members are required to adequately distinguish the impact of resolution within the forced signal from the weather noise.

54 ENVIRONMENTAL SCIENCES↗

Structural basis of differential gene expression at eQTLs loci from high-resolution ensemble models of 3D single-cell chromatin conformations

Abstract Motivation Techniques such as high-throughput chromosome conformation capture (Hi-C) have provided a wealth of information on nucleus organization and genome important for understanding gene expression regulation. Genome-Wide Association Studies have identified numerous loci associated with complex traits. Expression quantitative trait loci (eQTL) studies have further linked the genetic variants to alteration in expression levels of associated target genes across individuals. However, the functional roles of many eQTLs in noncoding regions remain unclear. Current joint analyses of Hi-C and eQTLs data lack advanced computational tools, limiting what can be learned from these data. Results We developed a computational method for simultaneous analysis of Hi-C and eQTL data, capable of identifying a small set of nonrandom interactions from all Hi-C interactions. Using these nonrandom interactions, we reconstructed large ensembles (×105) of high-resolution single-cell 3D chromatin conformations with thorough sampling, accurately replicating Hi-C measurements. Our results revealed many-body interactions in chromatin conformation at the single-cell level within eQTL loci, providing a detailed view of how 3D chromatin structures form the physical foundation for gene regulation, including how genetic variants of eQTLs affect the expression of associated eGenes. Furthermore, our method can deconvolve chromatin heterogeneity and investigate the spatial associations of eQTLs and eGenes at subpopulation level, revealing their regulatory impacts on gene expression. Together, ensemble modeling of thoroughly sampled single-cell chromatin conformations combined with eQTL data, helps decipher how 3D chromatin structures provide the physical basis for gene regulation, expression control, and aid in understanding the overall structure-function relationships of genome organization. Availability and implementation It is available at https://github.com/uic-liang-lab/3DChromFolding-eQTL-Loci.

Du, Lin (ORCID:0009000289869812)↗

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↗

Increased Asian aerosols drive a slowdown of Atlantic Meridional Overturning Circulation

Observational evidence and climate model experiments suggest a slowdown of the Atlantic Meridional Overturning Circulation (AMOC) since the mid-1990s. Increased greenhouse gases and the declined anthropogenic aerosols (AAs) over North America and Europe are believed to contribute to the AMOC slowdown. Asian AAs continue to increase but the associated impact has been unclear. Using ensembles of climate simulations, here we show that the radiative cooling resulting from increased Asian AAs drives an AMOC reduction. The increased AAs over Asia generate circumglobal stationary Rossby waves in the northern midlatitudes, which shift the westerly jet stream southward and weaken the subpolar North Atlantic westerlies. Consequently, reduced transport of cold air from North America hinders water mass transformation in the Labrador Sea and thus contributes to the AMOC slowdown. The link between increased Asian AAs and an AMOC slowdown is supported by different models with different configurations. Thus, reducing emissions of Asian AAs will not only lower local air pollution, but also help stabilize the AMOC.

54 ENVIRONMENTAL SCIENCES↗

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↗

Prescreening-Based Subset Selection for Improving Predictions of Earth System Models With Application to Regional Prediction of Red Tide

We present the ensemble method of prescreening-based subset selection to improve ensemble predictions of Earth system models (ESMs). In the prescreening step, the independent ensemble members are categorized based on their ability to reproduce physically-interpretable features of interest that are regional and problem-specific. The ensemble size is then updated by selecting the subsets that improve the performance of the ensemble prediction using decision relevant metrics. We apply the method to improve the prediction of red tide along the West Florida Shelf in the Gulf of Mexico, which affects coastal water quality and has substantial environmental and socioeconomic impacts on the State of Florida. Red tide is a common name for harmful algal blooms that occur worldwide, which result from large concentrations of aquatic microorganisms, such as dinoflagellate Karenia brevis, a toxic single celled protist. We present ensemble method for improving red tide prediction using the high resolution ESMs of the Coupled Model Intercomparison Project Phase 6 (CMIP6) and reanalysis data. The study results highlight the importance of prescreening-based subset selection with decision relevant metrics in identifying non-representative models, understanding their impact on ensemble prediction, and improving the ensemble prediction. These findings are pertinent to other regional environmental management applications and climate services. Additionally, our analysis follows the FAIR Guiding Principles for scientific data management and stewardship such that data and analysis tools are findable, accessible, interoperable, and reusable. As such, the interactive Colab notebooks developed for data analysis are annotated in the paper. This allows for efficient and transparent testing of the results’ sensitivity to different modeling assumptions. Moreover, this research serves as a starting point to build upon for red tide management, using the publicly available CMIP, Coordinated Regional Downscaling Experiment (CORDEX), and reanalysis data.

54 ENVIRONMENTAL SCIENCES↗

Machine-learning-assisted deciphering of microstructural effects on ionic transport in composite materials: A case study of Li 7 La 3 Zr 2 O 12 -LiCoO 2

The effective diffusivity of ionic species in multiphase materials is critical for the design and function of composite materials for electrochemical energy storage. In practice, effective diffusivity depends sensitively not only on the intrinsic diffusivities of constituting materials but also on their topological arrangement; nevertheless, these coupled contributions are oversimplified in most analytical models. Here, we combine atomistically informed mesoscale modeling and machine learning (ML) analysis to unravel how such features affect effective diffusivity in two-phase composites. Using the Li 7 La 3 Zr 2 O 12 -LiCoO 2 composite solid-state battery cathode as a model system, we compute effective diffusivity for 600 distinct dense polycrystalline microstructures with different topological configurations of grains, grain boundaries, and heterointerfaces. We verify that in addition to atomic-scale variabilities, microstructural feature diversity can significantly impact effective transport properties. Across the ensemble of test microstructures, this often results in bimodal distributions of effective diffusivity that encompass two qualitatively distinct operating mechanisms, which we identify via flux analysis. An ML approach reveals that the most critical determining factors for effective diffusivity are the connectivity of bulk phases and their heterointerfaces. The role of ionic mobility at the heterointerfaces is also discussed. These insights highlight the combined importance of microstructure and interface engineering in tuning the transport properties of ionic species in composite materials. In conclusion, our framework can also be extended for understanding generic microstructure-property relationships in other complex multiphase materials.

25 ENERGY STORAGE↗

Accelerated Depth Computation for Surface Boxplots with Deep Learning

Functional depth is a well-known technique used to derive descriptive statistics (e.g., median, quartiles, and outliers) for 1D data. Surface boxplots extend this concept to ensembles of images, helping scientists and users identify representative and outlier images. However, the computational time for surface boxplots increases cubically with the number of ensemble members, making it impractical for integration into visualization tools. In this paper, we propose a deep-learning solution for efficient depth prediction and computation of surface boxplots for time-varying ensemble data. Our deep learning framework accurately predicts member depths in a surface boxplot, achieving average speedups of 6X on a CPU and 15X on a GPU for the 2D Red Sea dataset with 50 ensemble members compared to the traditional depth computation algorithm. Our approach achieves at least a 99% level of rank preservation, with order flipping occurring only at pairs with extremely similar depth values that pose no statistical differences. This local flipping does not significantly impact the overall depth order of the ensemble members.

Han, Mengjiao↗