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At least 343 records · Page 19

Systematic Evaluation of Atmospheric Forcing, Surface Datasets, and Mesh Effects on Kilometer-Scale Land Surface and River Modeling

Earth system models are advancing toward kilometer-scale resolution to capture local climate impacts and extremes. High-resolution land and river modeling depends on multiple factors, including mesh, surface datasets, and atmospheric forcing, but their relative effects at kilometer scales remain unquantified. We evaluated five Energy Exascale Earth System Model land and river configurations over the Mid-Atlantic region using two mesh (1/8° structured versus variable-resolution unstructured mesh), two surface datasets (default versus newly developed), and three atmospheric forcings (NLDAS2, MSWX, GSWP). Evaluation against satellite, reanalysis, and in situ benchmarks across water, energy, and carbon cycles quantifies how these factors affect model performance. Forcing selection produces the largest bias reductions (12-99% across variables), followed by surface datasets (7-75%) and mesh (up to 21%). Forcing effects vary by variable, with MSWX reducing biases for snow water equivalent, evapotranspiration, albedo, temperature, and gross primary productivity, GSWP for snow cover and runoff, and NLDAS for soil moisture and streamflow. The use of newly developed surface datasets improves gross primary productivity (58% bias reduction) and evapotranspiration but increase soil moisture and albedo biases due to current modeling limitations. Variable-resolution unstructured mesh improves the simulation of small-basin streamflow through better capturing drainage networks, though mesh minimally affects other land variables. These findings provide important guidance for high-resolution modeling development and actionable science.

Land and River modeling↗

Standardizing an Intermediate-Scale High Explosive Safety Test Suite

Small-scale safety testing, while successful in screening out extremely dangerous explosive compositions, does not fully characterize the explosive hazards associated with handling larger, consolidated or bare charges. It is proposed that intermediate-scale tests using consolidated charges in the range 25 mg – 1 kg are warranted to satisfactorily address the hazards. A standard for this intermediate-scale testing should be developed, proofed, peer-reviewed and adopted to assist in the development of safe new high explosive compositions across the complex. This whitepaper explains why current small-scale safety testing is insufficient to characterize the handling hazard, identifies the guiding aspects of explosive response that drive the handling hazards associated with larger consolidated charges, and proposes a suite of tests/experiments that can serve as a starting point for an intermediate-scale safety standard.

42 ENGINEERING↗

Northern Hemisphere Extratropical Cyclone Activity in the Twentieth Century Reanalysis Version 3 (20CRv3) and Its Relationship with Continental Extreme Temperatures

In this study, we detect and track extratropical cyclones using 6-hourly mean sea level pressure data taken from the Twentieth Century Reanalysis version 3 (20CRv3) over the period 1951–2015 and compare them with those in the Interim and fifth generation of ECMWF reanalyses over the period 1979–2018. Three indices were employed to characterize cyclone activity, including cyclone count, cyclone intensity, and a cyclone activity index (CAI) that combines the count and intensity. The results show that the cyclone indices in the three datasets have comparable annual climatologies and seasonal evolution over the northern extratropical land and ocean in recent decades. Based on the cyclone indices over the period 1951–2010 in 80 ensemble members of 20CRv3, cyclone count and intensity are negatively correlated in winter and tend to be positively and weakly correlated in summer. The interannual CAI variability is dominated by the cyclone count variability. Regional mean cyclone activity can be well represented using the ensemble average cyclone index. We then examined the linkage of the cyclone activity in 20CRv3 and observed cold and warm extremes over Eurasia and North America over the period 1951–2010. In winter, the principal components of interannual cold and warm extreme anomalies are more correlated with the regional mean cyclone count index over Eurasia, while they are more correlated with the cyclone intensity index over North America. The temperature anomalies associated with the regional and ensemble mean cyclone count index explain about 10% (20%) of interannual cold (warm) extreme variances averaged over Eurasia. The temperature anomalies associated with the mean cyclone intensity explain about 10% of interannual cold and warm extreme variances over North America. Large-scale atmospheric circulation anomalies in association with cyclone activity and the induced temperature advection drive temperature anomalies over Eurasia and North America. In summer, circulation and thermal advection anomalies associated with cyclone activity are weak over the two continents. Hence, that season’s relationship between cyclone activity and extreme temperature variability is weak.

20CRv3↗

An Intelligent Distributed Ledger Construction Algorithm for IoT

Blockchain is the next generation of secure data management that creates near-immutable decentralized storage. Secure cryptography created a niche for blockchain to provide alternatives to well-known security compromises. However, design bottlenecks with traditional blockchain data structures scale poorly with increased network usage and are extremely computation-intensive. This made the technology difficult to combine with limited devices, like those in Internet of Things networks. In protocols like IOTA, replacement of blockchain's linked-list queue processing with a lightweight dynamic ledger showed remarkable throughput performance increase. However, current stochastic algorithms for ledger construction suffer distinct trade-offs between efficiency and security. This work proposed a machine-learning approach with a multi-arm bandit that resolved these issues and was designed for auditing on limited devices. This algorithm was tested in a reinforcement-learning environment simulating the IOTA ledger's construction with a decision tree. This study showed through regret analysis and experimentation that this approach was secure against impulse manipulation attacks while remaining energy-efficient. Although the IOTA protocol was a pioneer for lightweight distributed ledgers, it is expected that future blockchain protocols will adopt techniques similar to those presented in this work.

multi-arm bandit↗

High-Resolution Fire Weather Index Data for the Conterminous US (1980–2099), Version 1

This dataset presents a suite of high-resolution fire weather index datasets calculated from observation (gridMet, Livneh, Daymet V4), reanalysis (AgERA5), downscaled hydro-climate projections over the conterminous United States (CONUS) based on multiple selected Global Climate Models (GCMs) from the Coupled Model Intercomparison Project Phase 6 (CMIP6). Aside from the daily FWI datasets, we also include a set of FWI extreme indicators at annual, seasonal, and monthly scales, including 1) fwixx: maximum FWI; 2) fwisa: mean FWI. For annual fwisa, it refers to the season with the maximum seasonal average; 3) fwils: Length of fire season over a specified period, where fire season is defined as the days exceeding the median value of the normalized FWI during the reference period (1980-1984); 4) fwixd: Number of extreme fire weather days over a specified period, where extreme day is defined as the day with FWI > the 95th percentile of the FWI during the reference period (1980-1984). All FWI datasets cover 1980-2020 baseline and the model simulated products including the downscaled products additionally include 2021-2099 near-future periods under the high-end (SSP585) emission scenario.

54 ENVIRONMENTAL SCIENCES↗

Learning from learning machines: improving the predictive power of energy-water-land nexus models with insights from complex measured and simulated data

Focal Area(s): Insights gleaned from complex data (observed and simulated) using AI; Predictive modeling through the use of AI techniques and AI-derived model components, including physics- and knowledge-informed models; Energy-water-land nexus and integrated energy systems – models of MultiSector dynamics. Science Challenge: Scientific communities are in need of tools for the computational integration of physics-based models, experimental data, and empirical/observational studies across a broad range of temporal and spatial scales to explore and meet EESSD grand challenges. We require AI algorithms for the discovery of process-drivers in the Earth-energy-human system and to link them with complex measured and simulated data. We aim to understand the energy-water-land nexus, particularly under extreme forcing scenarios and rare events, leveraging scale-aware AI process models, including probabilistic uncertainties, and benefiting from the emerging 5G-enabled landscape-scale sensing and edge computing capabilities. These models are needed to identify instabilities and tipping points that manifest extreme system behaviors with consequences for integrated energy systems and the environment. This work requires fundamental advances in uncertainty quantification, in particular, to identify and model unlikely but catastrophic outliers. Specifically, we need models that are interpretable to domain scientists and, essentially, explainable to public and private stake holders.

54 ENVIRONMENTAL SCIENCES↗

Intercomparison of Dynamically and Statistically Downscaled Climate Change Projections over the Midwest and Great Lakes Region

Downscaling of global climate model (GCMs) simulations is a key element of regional-to-local-scale climate change projections that can inform impact assessments, long-term planning, and resource management in different sectors. Here, we conduct an intercomparison between statistically and dynamically downscaled GCMs simulations using the hybrid delta (HD) and the Weather Research and Forecast (WRF) Model, respectively, over the Midwest and Great Lakes region to 1) validate their performance in reproducing extreme daily precipitation (P) and daily maximum temperature (T max ) for summer and winter and 2) evaluate projections of extremes in the future. Our results show the HD statistical downscaling approach, which includes large-scale bias correction of GCM inputs, can reproduce observed extreme P and T max reasonably well for both summer and winter. However, raw historical WRF simulations show significant bias in both extreme P and T max for both seasons. Interestingly, the convection-permitting WRF simulation at 4-km grid spacing does not produce better results for seasonal extremes than the WRF simulation at 12 km using a parameterized convection scheme. Despite a broad similarity for winter extreme P projections, the projected changes in the future summer storms are quite different between downscaling methods; WRF simulations show substantial increases in summer extreme precipitation, while the changes projected by the HD approach exhibit moderate decreases overall. The WRF simulations at 4 km also show a pronounced decoupling effect between seasonal totals and extreme daily P for summer, which suggests that there could be more intense summer extremes at two different time scales, with more severe individual convective storms combined with longer summer droughts at the end of the twenty-first century.

54 ENVIRONMENTAL SCIENCES↗

Extreme Antiscaling Performance of Slippery Omniphobic Covalently Attached Liquids

Scale formation presents an enormous cost to the global economy. Classical nucleation theory dictates that to reduce the heterogeneous nucleation of scale, the surface should have low surface energy and be as smooth as possible. Past approaches have focused on lowering surface energy via the use of hydrophobic coatings and have created atomically smooth interfaces to eliminate nucleation sites, or both, via the infusion of low-surface-energy lubricants into rough superhydrophobic substrates. Although lubricant-based surfaces are promising candidates for antiscaling, lubricant drainage inhibits their utilization. Here, we develop methodologies to deposit slippery omniphobic covalently attached liquids (SOCAL) on arbitrary substrates. Similar to lubricant-based surfaces, SOCAL has ultralow roughness and surface energy, enabling low nucleation rates and eliminating the need to replenish the lubricant. To enable SOCAL coating on metals, we investigated the surface chemistry required to ensure high-quality functionalization as measured by ultralow contact angle hysteresis (<3°). Using a multilayer deposition approach, we first electrophoretically deposit (EPD) silicon dioxide (SiO 2 ) as an intermediate layer between the metallic substrate and SOCAL. The necessity of EPD SiO 2 is to smooth (<10 nm roughness) as well as to enable the proper surface chemistry for SOCAL bonding. To characterize antiscaling performance, we utilized calcium sulfate (CaSO 4 ) scale tests, showing a 20× reduction in scale deposition rate than untreated metallic substrates. Descaling tests revealed that SOCAL dramatically decreases scale adhesion, resulting in rapid removal of scale buildup. Furthermore, our work not only demonstrates a robust methodology for depositing antiscaling SOCAL coatings on metals but also develops design guidelines for the creation of antifouling coatings for alternate applications such as biofouling and high-temperature coking.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Impacts of the boreal summer intraseasonal oscillation on precipitation extremes in Indonesia

The relationship between boreal summer intraseasonal oscillation (BSISO) and precipitation extremes over Indonesia is investigated using observational datasets from 30 years (1987–2016) of rain gauge measurements and the gridded Asian Precipitation–Highly Resolved Observational Data Integration Towards Evaluation of Water Resources from 1998 to 2015. The results indicate that the frequency of daily extreme precipitation events in Indonesia (defined as total precipitation above the 95th percentile) during extended boreal summer (May–August) is significantly modulated by BSISO, especially over the western and northern regions. Under the influences of BSISO1, the probability of the precipitation extremes over Sumatra and Borneo increases by 20–120% (relative to the seasonal probability) during phases 1–3 and approximately 50–80% over the eastern part of Borneo and Sulawesi during phase 4. Under BSISO2, the probability of the extremes increases up to 40% over Sumatra during phases 1 and 2 and up to 140% over Borneo and Sulawesi during phases 2 and 3. The increase in the probability of extreme summer precipitation is associated with enhanced large–scale moisture flux convergence and upward moisture transport induced by the active phases of BSISO. Finally, these results provide potential information for medium–to extended–range predictions of summer precipitation extremes in Indonesia.

54 ENVIRONMENTAL SCIENCES↗

Implicit learning of convective organization explains precipitation stochasticity

Accurate prediction of precipitation intensity is crucial for both human and natural systems, especially in a warming climate more prone to extreme precipitation. Yet, climate models fail to accurately predict precipitation intensity, particularly extremes. One missing piece of information in traditional climate model parameterizations is subgrid-scale cloud structure and organization, which affects precipitation intensity and stochasticity at coarse resolution. Here, using global storm-resolving simulations and machine learning, we show that, by implicitly learning subgrid organization, we can accurately predict precipitation variability and stochasticity with a low-dimensional set of latent variables. Using a neural network to parameterize coarse-grained precipitation, we find that the overall behavior of precipitation is reasonably predictable using large-scale quantities only; however, the neural network cannot predict the variability of precipitation (R 2 ~ 0.45) and underestimates precipitation extremes. The performance is significantly improved when the network is informed by our organization metric, correctly predicting precipitation extremes and spatial variability (R 2 ~ 0.9). The organization metric is implicitly learned by training the algorithm on a high-resolution precipitable water field, encoding the degree of subgrid organization. The organization metric shows large hysteresis, emphasizing the role of memory created by subgrid-scale structures. We demonstrate that this organization metric can be predicted as a simple memory process from information available at the previous time steps. These findings stress the role of organization and memory in accurate prediction of precipitation intensity and extremes and the necessity of parameterizing subgrid-scale convective organization in climate models to better project future changes of water cycle and extremes.

54 ENVIRONMENTAL SCIENCES↗

Dynamics and drivers of land use and land cover changes in Bangladesh

Abstract Bangladesh has undergone dramatic land use and land cover changes (LULCC) in recent years, but no quantitative analysis of LULCC drivers at the national scale exists so far. Here, we quantified the drivers of major LULCC in combination with biophysical and socioeconomic observations at the sub-district level. We used Landsat satellite data to interpret LULCC from 2000 to 2010 and employed a Global Surface Water Dataset to account for the influences of water seasonality. The results suggest that major LULCC in Bangladesh occur between agricultural land and waterbodies and between forest and shrubland. Exclusion of seasonal waterbodies can improve the accuracy of our LULCC results and driver analysis. Although the gross gain and loss of agricultural land are large on the local scale, the net change (gross gain minus gross loss) at a country scale is almost negligible. Climate dynamics and extreme events and changes in urban and rural households were driving the changes from forest to shrubland in the southeast region. The conversion from agricultural land to standing waterbodies in the southwest region was mainly driven by urban household dynamics, population growth, distance to cities and major roads, and precipitation dynamics. This study, which is the first effort accounting for water seasonality and quantifying biophysical and socioeconomic drivers of LULCC at the national scale, provides a perspective on overall LULCC and underlying drivers over a decadal time scale and national spatial scale and can serve as a scientific basis for developing land policies in Bangladesh.

54 ENVIRONMENTAL SCIENCES↗

Extreme ultraviolet transient gratings: A tool for nanoscale photoacoustics

Collective lattice dynamics determine essential aspects of condensed matter, such as elastic and thermal properties. These exhibit strong dependence on the length-scale, reflecting the marked wavevector dependence of lattice excitations. The extreme ultraviolet transient grating (EUV TG) approach has demonstrated the potential of accessing a wavevector range corresponding to the 10s of nm length-scale, representing a spatial scale of the highest relevance for fundamental physics and forefront technology, previously inaccessible by optical TG and other inelastic scattering methods. In this manuscript we report on the capabilities of this technique in the context of probing thermoelastic properties of matter, both in the bulk and at the surface, as well as discussing future developments and practical considerations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Visualization of shocked material instabilities using a fast-framing camera and XFEL four-pulse train

Many questions regarding dynamic materials could be answered by using time-resolved ultra-fast imaging techniques to characterize the physical and chemical behavior of materials in extreme conditions and their evolution on the nanosecond scale. In this work, we perform multi-frame phase-contrast imaging (PCI) of micro-voids in low density polymers under laser-driven shock compression. At the Matter in Extreme Conditions (MEC) Instrument at the Linac Coherent Light Source (LCLS), we used a train of four x-ray free electron laser (XFEL) pulses to probe the evolution of the samples. To visualize the void and shock wave interaction, here, we deployed the Icarus V2 detector to record up to four XFEL pulses, separated by 1-3 nanoseconds. In this work, we image elastic waves interacting with the micro-voids at a pressure of several GPa. Monitoring how the material’s heterogeneities, like micro-voids, dictate its response to a compressive wave is important for benchmarking the performances of inertial confinement fusion energy materials. For the first time in a single sample, we have combined an ultrafast x-ray framing camera and four XFEL pulse train to create an ultrafast movie of micro-void evolution under laser-driven shock compression. Eventually, we hope this technique will resolve the material density as it evolves dynamically under laser shock compression.

fusion↗

Attosecond Transient Grating Spectroscopy with Near-Infrared Grating Pulses and an Extreme Ultraviolet Diffracted Probe

Transient grating spectroscopy has become a mainstay among metal and semiconductor characterization techniques. Here, we extend the technique toward the shortest achievable time scales by using tabletop high-harmonic generation of attosecond extreme ultraviolet (XUV) pulses that diffract from transient gratings generated with sub-5 fs near-infrared (NIR) pulses. We demonstrate the power of attosecond transient grating spectroscopy (ATGS) by investigating the ultrafast photoexcited dynamics in an Sb semimetal thin film. ATGS provides an element-specific, background-free signal unfettered by spectral congestion, in contrast to transient absorption spectroscopy. With ATGS measurements in Sb polycrystalline thin films, we observe the generation of coherent phonons and investigate the lattice and carrier dynamics. Among the latter processes, we extract carrier thermalization, hot carrier cooling, and electron-hole recombination, which are on the order of 20 fs, 50 fs, and 2 ps time scales, respectively. Furthermore, the simultaneous collection of transient absorption and transient grating data allows us to extract the total complex dielectric constant in the sample dynamics with a single measurement, including the real-valued refractive index, from which we are also able to investigate carrier-phonon interactions and longer-lived phonon dynamics. The outlined experimental technique expands the capabilities of transient grating spectroscopy and attosecond spectroscopies by providing a wealth of information concerning carrier and lattice dynamics with an element-selective technique at the shortest achievable time scales.

Quintero-Bermudez, Rafael↗

Global teleconnections influencing large-scale drought in the United States using SVDI

Understanding recent large-scale drought patterns and the mechanisms producing extreme drought events is vital for future drought forecasts and understanding future drought risks. Increasingly, vapor pressure deficit (VPD) has been used as an important measure of evaporative demand and proxy for drought detection. In this study, VPD is used to calculate the new Standardized VPD Drought Index (SVDI) with NASA North American Land Data Assimilation System (NLDAS) data. Previous studies have shown that SVDI accurately identifies the timing and magnitude short-term droughts in the United States (U.S). In the present study, SVDI is now used to identify large-scale drought patterns between 1980 and 2021 and drought variability driven by selected global teleconnections originating in the Pacific and Atlantic Oceans. Spatial drought characteristics were extracted from SVDI using empirical orthogonal function (EOF) analysis. Then a k-means clustering algorithm was applied to both EOF principal components and primary teleconnections, including the El Nino-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) to identify drought events driven by the Pacific Ocean. Results show that the SVDI is useful in evaluating large-scale drought variability in the U.S. related to global teleconnections, and that mechanisms influencing summer drought patterns in the Western and Southwestern U.S. are driven by a tropical-extratropical interactions originating in the equatorial Pacific Ocean related to ENSO dynamics with interdecadal variability modulated by PDO. The large-scale droughts in the Central and Southern U.S., like those in 2011 and 2012, on the other hand, are driven by the North Pacific Ocean warm pool during a strong negative PDO, which subsequently influenced variability in the Bermuda-Azores High in the Atlantic Ocean. In summer 2011, the Bermuda-Azores High weakened, reducing the onshore winds and moisture transport along the eastern Gulf of Mexico and contributing to ongoing drought in the region. The Northern Pacific and Atlantic Ocean sea surface temperatures (SSTs) have increased between 1980 and 2021. In conclusion, as SSTs continue to rise in the Northern Pacific Ocean, one consequence of the coupled North Pacific warm pool and atmospheric dynamics, is to increase summer drought variability over a large region in the southern and midwestern U.S. under global warming.

54 ENVIRONMENTAL SCIENCES↗

Determining Spatial Scales of Soil Moisture—Cloud Coupling Pathways Using Semi-Idealized Simulations

The spatial scales of land-atmosphere interactions over heterogeneous, realistic soil moisture patterns are critical to improve our understanding of land-atmosphere interactions. However, these scales are poorly quantified. We use high-resolution numerical experiments to quantify the spatial scales for a selected day during the Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems (HI-SCALE) campaign in Oklahoma. A semi-idealized approach (removing background winds and surface topography while retaining the real-world data for other boundary conditions) enables examination of the local influence from the surface. Simulations that apply uniform surface, variable land cover with uniform soil moisture, and variable land cover with variable soil moisture are then compared. Land cover variations, especially water and urban surfaces, create two variance peaks in the surface sensible heat flux in the scales >10 km (meso-β) and <6 km (meso-γ). Both peaks are enhanced by the observation-based soil moisture distribution that has most of its variance in the meso-β scale. Atmospheric response in the meso-β scale is hydrostatic with weak vertical motion. The land cover variations induce secondary circulations in the scales of 2.5–6 km. The additional soil moisture variability intensifies extreme circulations over dry soil patches and sharp sensible heat flux gradients, slightly extending the characteristic scales to 2.5–9 km. While their areal coverage is small, soil moisture variations on such “hotspots” lead to substantially larger convective cloud structure and domain-mean rainfall, calling for a consideration of their non-linear effect in large-scale models.

54 ENVIRONMENTAL SCIENCES↗

Bayesian model updating with finite element vs surrogate models: Application to a miter gate structural system

Bayesian finite element (FE) model updating using direct model evaluations of large-scale high-fidelity FE models is extremely computationally expensive. Surrogate models can be used as fast emulators of FE models to accelerate the model calibration process. The physics/mechanics-based FE models are still the underpinning behind the surrogate models. Here, this paper evaluates the loss in accuracy and the gain in computational time while performing Bayesian model updating by using surrogate model evaluations compared to using direct FE model evaluations. This evaluation is crucial before entirely relying on surrogate models in model updating for structural health monitoring (SHM) and damage prognosis (DP) purposes. This paper also demonstrates Bayesian updating and surrogate model construction of large-scale high-fidelity FE models of infrastructure systems. In this regard, the miter gate structural system is considered as the testbed structure. Three predominant damage modes (loss of contact between gate and wall, loss of thickness due to corrosion, and loss of tension in the diagonal rods) are considered for model updating purposes. Bayesian model updating is performed using direct FE evaluations by leveraging parallel computing. Two types of surrogates, namely polynomial chaos expansion (PCE) and Gaussian process regression (GPR), are developed for the miter gate. Model updating is performed again using the trained surrogate models, and the updating results are compared with their counterparts obtained using the direct FE evaluation results. The posterior distribution of the FE model parameters obtained using the trained surrogates are sufficiently accurate with respect to the posterior obtained utilizing the direct FE evaluations. In addition, an approximate 4-fold decrease in the computational time was observed when using surrogate model evaluations instead of direct FE evaluations for model updating.

42 ENGINEERING↗

A Fast Algorithm for Scanning Transmission Electron Microscopy Imaging and 4D-STEM Diffraction Simulations

Scanning transmission electron microscopy (STEM) is an extremely versatile method for studying materials on the atomic scale. Many STEM experiments are supported or validated with electron scattering simulations. However, using the conventional multislice algorithm to perform these simulations can require extremely large calculation times, particularly for experiments with millions of probe positions as each probe position must be simulated independently. Recently, the plane-wave reciprocal-space interpolated scattering matrix (PRISM) algorithm was developed to reduce calculation times for large STEM simulations. Here, we introduce a new method for STEM simulation: partitioning of the STEM probe into “beamlets,” given by a natural neighbor interpolation of the parent beams. This idea is compatible with PRISM simulations and can lead to even larger improvements in simulation time, as well requiring significantly less computer random access memory (RAM). We have performed various simulations to demonstrate the advantages and disadvantages of partitioned PRISM STEM simulations. We find that this new algorithm is particularly useful for 4D-STEM simulations of large fields of view. We also provide a reference implementation of the multislice, PRISM, and partitioned PRISM algorithms.

97 MATHEMATICS AND COMPUTING↗