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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Multiscale and Machine Learning Modeling for Process-informed Microstructure Prediction in Additively Manufactured Materials Using MALAMUTE

Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy, aims to develop and qualify additively-manufactured materials for nuclear applications. The key challenges to these efforts are the microstructural variabilities observed on the AM products and their impact on the properties and performance of the material in extreme environments. AMMT is using a combination of high-through-put experimental and modeling techniques to accelerate the qualification efforts. Conventionally, in-situ and ex-situ characterizations and testing are performed to correlate different aspects of the AM process to the final product and its performance. However, adopting a trial-and-error approach to experimentally evaluate the vast range of process parameters required to capture the microstructural variabilities is cost-prohibitive. Modeling and simulation provide a comparatively inexpensive way to understand and correlate the microstructural evolution to the processing conditions. The modeling and simulation work-packages within the AMMT program aims to use physics-based and machine learning modeling capabilities to develop a digital twin for AM that can correlate the process conditions to the final product and establish a process-structure-property-performance (PSPP) correlation for AM materials. The melting and subsequent solidification that occurs during the AM process is a complex phenomenon that requires multiscale multiphysics analysis. Idaho National Laboratory’s (INL) Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) software, provides an ideal platform for developing the multiphysics multiscale model to explore the intricacies of the microstructural evolution during the AM processes within a single framework. Furthermore, given that such full-fidelity simulations can be computationally intensive, reduced order models are necessary to explore the PSPP space for AM materials in an efficient, reliable, and cost-effective way. This work package focuses on understanding the role of process variabilities on the various microstructural characteristics of the AM materials. Microstructures unique to AM materials, such as compositional micro-heterogeneity and dislocation cells, are of particular interest here since they can influence the creep properties and radiation performance. In fiscal year (FY) 24, we significantly advanced upon our work in the last fiscal year, both on physics-based and ML models. The alloy solidification model available in MOOSE has been extended to incorporate the thermodynamic properties and free energy relevant to 316SS. The model demonstrates the Cr segregation that occurs during solidifcation. It is demonstrated that rate of solidification and solute segregation is primarily influence by the cooling rate dictating the level of freezing. This work captures the microstructural variabilities at the subgrain level that are often missing in the part-scale models. With an aim to connect the microstructural evolution model to realistic process conditions, a reduced order model is developed for predicting the thermal conditions around meltpool from high-fidelity process simulations. Furthermore, machine learning approach is used to accelerate the temperature prediction during the AM process. In the following years, MALAMUTE will be used to connect different aspects of the models and quantitatively predict the microstructural evolution. The developed ML-based surrogate model will consider the process conditions as the input to predict the microstructural features in a cost-effective way. The generated microstructures can be used by other work packages under AMMT to evaluate the properties and environmental response of the material at the mesoscale. Thus, this work help identify the key microstructural features at the subgrain level that are significant in property/performance prediction of the AM products. This work will provide inputs to the large-scale process variability models to reevaluate and validate assumptions/simplifications made in the part-scale models. Furthermore, through active learning this work will help identify the data need from both modeling and experimental sides for development of a robust digital twin for AM.

36 MATERIALS SCIENCE↗
DOE OSTI2022

VA EDH Data Curation Documentation (FY22-Q3, Rev.2)

The health and well-being of the Nation’s men and women who have served in uniform is the highest priority for the U.S. Department of Veterans Affairs (VA). VA is committed to providing timely access to high-quality, recovery-oriented, evidence-based mental health care that anticipates and responds to Veterans’ needs and supports the reintegration of returning Service members into their communities. VA is working to eliminate suicide among all Veterans by developing and implementing innovative suicide prevention approaches and resources. Health outcomes, such as suicide are typically modeled as a function of genetics and environment, where environment refers to factors beyond medical, e.g., air quality, access to transportation and food, homelessness status, etc. Mental health outcomes for each individual are considered to be associated with multiple stressors that fall under a variety of categories socioeconomic, economic, physical environment. Understanding the relationships between these stressors, covariates and health outcomes, requires curated, standardized data that can be input into the VA’s Recovery Engagement and Coordination for Health - Veterans Enhanced Treatment (REACH VET) or other health outcomes model. Environmental Determinants of Health (EDH) as defined by the World Health Organization (WHO) is clean air, stable climate, adequate water, sanitation and hygiene, safe use of chemicals, protection from radiation, healthy and safe workplaces, sound agricultural practices, health-supportive cities and built environments, and a preserved nature are all prerequisites for good health.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

CRCNS21 Computational Models of Multisensory Integration by Upper Limb in Humanoids and Amputees

This international collaborative research project between Johns Hopkins University (JHU) and the Technical University of Munich (TUM) investigated how the human brain processes and integrates multiple types of sensory information, such as touch and force, with the goal of improving prosthetic limbs for amputees and advancing sensory capabilities in humanoid robots. The research advanced our understanding of how the brain responds to sensory feedback in upper-limb amputees. Through experiments in which amputees received electrical stimulation while performing phantom hand movements, we demonstrated that sensory feedback activates the cortical sensorimotor and multisensory regions, and that these regions communicate dynamically during stimulation. Experiments with intact-limb participants explored the integration of visual, haptic, and force feedback, as well as in virtual reality motor training, further showing how the brain processes multimodal sensory information. In addition, this research inspired work on examining the reliability of where amputees perceive sensations over time, which contributed to a successful doctoral fellowship for continued investigation. Our collaborators at TUM improved multimodal sensor technology combining tactile and thermal feedback for humanoid robots, demonstrating the feasibility of integrating multiple sensor types into a unified system for detecting and responding to environmental stimuli. The experimental methods and analysis techniques developed across both teams, including functional network analysis and multimodal sensor integration, provide a foundation for future research in prosthetics and robotics. This research benefits the public by generating knowledge about how amputees process restored sensory information. Advances in humanoid sensing contribute to safer human-robot interaction. The project also fostered international collaboration and cross-disciplinary training: one TUM doctoral student spent a summer at JHU working on multimodal sensor integration, while two JHU students traveled to TUM to host workshops on neuromorphic sensory encoding and sensory integration.

42 ENGINEERING↗
DOE OSTI2020

A Comparison of RESRAD and GoldSim Models for Assessing Radiological Dose for a RCRA Landfill - 20418

US Ecology Idaho (USEI) operates a Resource Conservation and Recovery Act (RCRA) Subtitle C, Hazardous Waste Treatment, Storage, and Disposal (TSD) Facility on a 640-acre property in Owyhee County, Idaho. USEI accepts a wide variety of RCRA-exempt low activity radioactive wastes, including naturally occurring radioactive material (NORM) and technologically enhanced NORM (TENORM) (USEI 2009). The performance of the landfill with regard to radiological operating permit requirements was previously assessed using a model constructed with the residual radioactivity (RESRAD) computer program, developed by Argonne National Laboratory for the U.S. Department of Energy (DOE). RESRAD supports the evaluation of several environmental transport pathways related to a radionuclide-contaminated soil source term, but it was not conceived as a model for the evaluation of landfill radiological performance. A more comprehensive and realistic model is desired in order to better support submissions to both the State of Idaho's Department of Environmental Quality as well as the U.S. Nuclear Regulatory Commission. A Performance Assessment (PA) computer model was developed using GoldSim software for the USEI RCRA Subtitle C landfill. The RESRAD computer model was specifically developed for calculating soil cleanup criteria and radiological dose and cancer risk from residual radioactive material in soil. To evaluate site-specific conditions, users may select from among a number of available environmental transport and exposure pathways and modify 'default' parameter values. In GoldSim, a user must construct the model 'from scratch.' However, this modeling is facilitated by a number of specialized elements available in GoldSim to support a radiological mass transport model. These include elements for defining radiological decay and ingrowth, container failure and radiological release, advective and diffusive transport, and other processes. Advantages afforded by the use of RESRAD for modeling radiological dose for a RCRA Subtitle C landfill include ease of use and reasonable flexibility in specifying site-specific conditions. GoldSim allows for considerably more flexibility and site-specificity than RESRAD, including evaluation of potentially relevant environmental transport processes not supported in RESRAD. The probabilistic modeling capabilities of GoldSim also far exceed those of RESRAD. The pros and cons of RESRAD and GoldSim for this modeling problem are explored with a focus on identifying approaches and critical factors in identifying the appropriate platform. The capabilities of RESRAD and GoldSim for mathematically modeling the disposal system will be contrasted and compared. For example, the existing RESRAD radiological safety assessment evaluated potentially complete exposure pathways related to infiltration to groundwater and upwards diffusion of radon. Additional transport pathways identified in the USEI Idaho facility Conceptual Site Model include deposition of radon decay products in cover material, root uptake of radionuclides in disposed wastes by native plants, and mixing of cover material by burrowing animals. Results of the two models and how the different transport and dose pathways affect results will be discussed. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Multiple Degradation Mechanisms in Reinforced Concrete Structures, Modeling and Risk Analysis

The overarching goal of this project is to complement ongoing Department of Energy (DOE) Light Water Reactor Sustainability (LWRS)-funded Grizzly concrete modeling development efforts by providing improved multi-physics models for incorporation into the Grizzly and BlackBear codes. Objectives of this work identified at the outset of this project include: 1. Coupling between mechanical damage and transport processes. The mechanical damage will be characterized by nonlinear mechanical constitutive models appropriate for concrete used in nuclear power plants (NPPs). 2. Improved representation of the coupling among the transport process, building on the current moisture and thermal transport models in Grizzly. The parameters for coupling among heat and mass transport in the multi-physics model will be experimentally determined. 3. Coupling among different scale levels of concrete constituents, fine and coarse aggregates, cement paste, hydration products, and pore structure. 4. Probabilistic analysis of the random nature of the heterogeneous concrete structure and the environmental factors (ambient temperature and humidity) and their multiple effects on concrete deterioration. 5. Benchmark verification, validation and uncertainty quantification of the thermo-hygro- chemo-mechanical (THCM) concrete formulation. The end goal of this work was to provide a comprehensive and robust simulation capability that can be applied at the engineering scale for analysis of realistic deterioration scenarios in NPP concrete structures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Can machine learning accelerate process understanding and decision‐relevant predictions of river water quality?

Abstract The global decline of water quality in rivers and streams has resulted in a pressing need to design new watershed management strategies. Water quality can be affected by multiple stressors including population growth, land use change, global warming, and extreme events, with repercussions on human and ecosystem health. A scientific understanding of factors affecting riverine water quality and predictions at local to regional scales, and at sub‐daily to decadal timescales are needed for optimal management of watersheds and river basins. Here, we discuss how machine learning (ML) can enable development of more accurate, computationally tractable, and scalable models for analysis and predictions of river water quality. We review relevant state‐of‐the art applications of ML for water quality models and discuss opportunities to improve the use of ML with emerging computational and mathematical methods for model selection, hyperparameter optimization, incorporating process knowledge into ML models, improving explainablity, uncertainty quantification, and model‐data integration. We then present considerations for using ML to address water quality problems given their scale and complexity, available data and computational resources, and stakeholder needs. When combined with decades of process understanding, interdisciplinary advances in knowledge‐guided ML, information theory, data integration, and analytics can help address fundamental science questions and enable decision‐relevant predictions of riverine water quality.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Reference-free structural variant detection in microbiomes via long-read co-assembly graphs

Motivation: The study of bacterial genome dynamics is vital for understanding the mechanisms underlying microbial adaptation, growth, and their impact on host phenotype. Structural variants (SVs), genomic alterations of 50 base pairs or more, play a pivotal role in driving evolutionary processes and maintaining genomic heterogeneity within bacterial populations. While SV detection in isolate genomes is relatively straightforward, metagenomes present broader challenges due to the absence of clear reference genomes and the presence of mixed strains. In response, our proposed method rhea, forgoes reference genomes and metagenome-assembled genomes (MAGs) by encompassing all metagenomic samples in a series (time or other metric) into a single co-assembly graph. The log fold change in graph coverage between successive samples is then calculated to call SVs that are thriving or declining. Results: We show rhea to outperform existing methods for SV and horizontal gene transfer (HGT) detection in two simulated mock metagenomes, particularly as the simulated reads diverge from reference genomes and an increase in strain diversity is incorporated. We additionally demonstrate use cases for rhea on series metagenomic data of environmental and fermented food microbiomes to detect specific sequence alterations between successive time and temperature samples, suggesting host advantage. Our approach leverages previous work in assembly graph structural and coverage patterns to provide versatility in studying SVs across diverse and poorly characterized microbial communities for more comprehensive insights into microbial gene flux.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Total Effective Dose from Radiologic Emissions from INL Facilities for Calculation of Population Dose for the INL 2024 Annual Site Environmental Report

Total effective radiation dose from airborne releases was calculated using air dispersion modeling performed by the National Oceanic and Atmospheric Administration (NOAA) Idaho Falls Office using their HYSPLIT computer model (Stein et al. 2015; Draxler et al. 2013), and the Dose Multi-Media (DOSEMM) dose assessment model (Rood 2019) . The objective of these calculations was to provide a grid of total effective dose across a model domain that encompasses a 50-mile (80-km) radius from any Idaho National Laboratory (INL) Site source. In addition to INL Site sources, releases from the Radiological and Environmental Sciences Laboratory (RESL) (IF-683) and IF-603 located at the INL Research Center (IRC) within the Idaho Falls city limits were also included. Due to tracking limitations, radionuclides released from IF-611 and IF-603 are modeled as released from IF-603. The dose results will be combined with GIS software to compute a total population dose for the calendar year (CY) 2024 and will be reported in the INL Annual Site Environmental Report (ASER). This report does not cover the population dose calculation and only documents generation of the gridded dose file.

42 - ENGINEERING↗
NASA NTRS2009

Complexity Science Applications to Dynamic Trajectory Management: Research Strategies

The promise of the Next Generation Air Transportation System (NextGen) is strongly tied to the concept of trajectory-based operations in the national airspace system. Existing efforts to develop trajectory management concepts are largely focused on individual trajectories, optimized independently, then de-conflicted among each other, and individually re-optimized, as possible. The benefits in capacity, fuel, and time are valuable, though perhaps could be greater through alternative strategies. The concept of agent-based trajectories offers a strategy for automation of simultaneous multiple trajectory management. The anticipated result of the strategy would be dynamic management of multiple trajectories with interacting and interdependent outcomes that satisfy multiple, conflicting constraints. These constraints would include the business case for operators, the capacity case for the Air Navigation Service Provider (ANSP), and the environmental case for noise and emissions. The benefits in capacity, fuel, and time might be improved over those possible under individual trajectory management approaches. The proposed approach relies on computational agent-based modeling (ABM), combinatorial mathematics, as well as application of "traffic physics" concepts to the challenge, and modeling and simulation capabilities. The proposed strategy could support transforming air traffic control from managing individual aircraft behaviors to managing systemic behavior of air traffic in the NAS. A system built on the approach could provide the ability to know when regions of airspace approach being "full," that is, having non-viable local solution space for optimizing trajectories in advance.

Sawhill, Bruce↗
DOE OSTI2021

Repository scale classification and decomposition of tandem mass spectral data

Various studies have shown associations between molecular features and phenotypes of biological samples. These studies, however, focus on a single phenotype per study and are not applicable to repository scale metabolomics data. Here we report MetSummarizer, a method for predicting (i) the biological phenotypes of environmental and host-oriented samples, and (ii) the raw ingredient composition of complex mixtures. We show that the aggregation of various metabolomic datasets can improve the accuracy of predictions. Since these datasets have been collected using different standards at various laboratories, in order to get unbiased results it is crucial to detect and discard standard-specific features during the classification step. We further report high accuracy in prediction of the raw ingredient composition of complex foods from the Global Foodomics Project.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Using Complex Probability Amplitudes to Simulate Solute Transport in Composite Porous Media

Probability amplitudes are fundamental to quantum mechanics and offer robust descriptions of complicated systems, which have allowed physicists to explain behaviors inaccessible to classical physics. This article ponders how some of the same conceptual underpinnings of the mathematics used for modeling quantum systems might be applied to subsurface water resources problems and speculates how these tools could facilitate applications on quantum computers. A probability amplitude-based model for describing advective-dispersive transport in porous media using linear operators is investigated. The proposed complex valued model decomposes spreading into two “sub-continuum partial dispersion” coefficients, and this recovers classical spreading when the sum of these coefficients is the Fickian dispersion coefficient. However, the probability amplitudes have a manyto-one relationship to a probability distribution, so it embeds a level of heterogeneity into seemingly equivalent functions. Two propagators with different sub-continuum coefficients may have the same macroscopic behavior when either is considered in isolation, but when they act on the other the system’s behavior changes. Additionally, differences in the amplitudes cause a reduction in spreading as velocity correlations are disrupted, despite both propagators having identical dispersion coefficients, and this cannot be achieved using classical methods without changing the dispersion coefficient. The main point is that these amplitude-based models offer a way to embed information about the system into the propagators, instead of just “averaging it out” when making an upscaled model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

EcoPLOT: dynamic analysis of biogeochemical data

Motivation: We have created EcoPLOT (parameterized linkage of omics-driven technologies), a web-app for the dynamic, interactive analysis of biogeochemical datasets that combines state-of-the-art analysis tools to statistically and graphically explore environmental, geochemical and microbiome datasets. Using the iterative random forest, a machine learning algorithm, EcoPLOT allows for the de novo discovery of drivers which exhibit significant impact on plant, microbial or soil dynamics. Availability and implementation: EcoPLOT is built entirely within the R language. It can be accessed through any system where R is installed, including Windows, Mac and most Linux systems. EcoPLOT is free to use and can be accessed at https://github.com/cdsanchez18/EcoPLOT.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Opportunities and Challenges from Artificial Intelligence and Machine Learning for the Advancement of Science, Technology, and the Office of Science Missions

In February 2019, the President signed Executive Order 13859, Maintaining American Leadership in Artificial Intelligence. This order launched the American Artificial Intelligence Initiative, a concerted effort to promote and protect AI technology and innovation in the United States. The Initiative implements a government-wide strategy in collaboration and engagement with the private sector, academia, the public, and like-minded international partners. Among other actions, key directives in the Initiative called for Federal agencies to: Prioritize AI research and development investments, Enhance access to high-quality cyberinfrastructure and data, Ensure that the US maintains an international leadership role in the development of technical standards for AI, and Provide education and training opportunities to prepare the American workforce for the new era of AI. The mission of the Department of Energy (DOE) is to ensure America’s security and prosperity by addressing its energy, environmental, and nuclear challenges through transformative science and technology solutions. In terms of Science and Innovation, the DOE’s mission is to maintain a vibrant US effort in science and engineering as a cornerstone of our economic prosperity with clear leadership in strategic areas. From July to October in 2019, the Argonne, Oak Ridge, and Berkeley National Laboratories hosted a series of four AI for Science Town Hall meetings in Chicago, Oak Ridge, Berkeley, and Washington DC. The four meetings were attended by over 1300 scientists from the 17 DOE Labs, 39 companies, and over 90 universities. The goal of the Town Hall series was ‘to examine scientific opportunities in the areas of artificial intelligence, Big Data, and high-performance computing (HPC) in the next decade, and to capture the big ideas, grand challenges, and next steps to realizing these.’ The discussions at the meetings were captured in the final report of the AI for Science Town Hall meetings.

42 ENGINEERING↗
DOE OSTI2024

Feasibility of Formulating Ecosystem Biogeochemical Models From Established Physical Rules

Abstract To improve the predictive capability of ecosystem biogeochemical models (EBMs), we discuss the feasibility of formulating biogeochemical processes using physical rules that have underpinned the many successes in computational physics and chemistry. We argue that the currently popular empirically based approaches, such as multiplicative empirical response functions and the law of the minimum, will not lead to EBM formulations that can be continuously refined to incorporate improved mechanistic understanding and empirical observations of biogeochemical processes. Instead, we propose that EBM parameterizations, as a lossy data compression problem, can be better formulated using established physical rules widely used in computational physics and chemistry, and different biogeochemical processes can be more robustly integrated within a reactive‐transport framework. Through several examples, we demonstrate how mathematical representations derived from physical rules can improve understanding of relevant biogeochemical processes and enable more effective communication between modelers, observationalists, and experimentalists regarding essential questions, such as what measurements are needed to meaningfully inform models and how can models generate new process‐level hypotheses to test in empirical studies. Finally, while empirical models with more parameters are often less robust, physical rules‐based models can be more robust and show lower predictive equifinality, stemming from their enhanced consistency in representations of processes, interactions and spatial scaling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Optimal Transport as a Tool for Scientific Discovery in Radiation Biology

This report summarizes findings from research conducted for the “Exploration of the Poten tial for Artificial Intelligence and Machine Learning to Advance Low-Dose Radiation Biology Re search” (RadBio-AI) program, supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, under Awards KP1601011/FWP CC121 and KP1601017/FWP CC121. The research reported here was undertaken in an effort to assess the potential of optimal measure transport methods as components within the larger scope of a com putational framework envisioned to support research in the radiation biology domain. Within this effort, our interest centered on enabling a unified generic framework where probabilistic modeling, inference, and statistical learning can be carried out for a wide range of data distributions. As described next in Section 1 (and in more detail in our original publication), optimal measure transport offers the possibility of such unified approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Development of a Versatile Analysis Method for the Isotopic Characterization of Alpha Spectra

Over the past several years significant work has been performed at Idaho National Laboratory to build an alpha-particle spectrometry capability and expertise for a wide range of applications that include technical nuclear forensics, nuclear safeguards, and environmental monitoring. This development has led to a diverse collection of sample types and preparations measured with varied solid-state detector materials and configurations. Several characteristics of a measured alpha pulse height spectrum make performing localized fits of individual peak shapes unfeasible. Alternatively, the entirety of the spectrum must be fit concurrently to extract isotopic information. An analysis tool has been developed to perform isotopic characterization of alpha spectra. This process included a study of both the mathematical model used to represent the detector response of an alpha-particle as well as the algorithm used to fit the spectrum.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

5G Enabled Energy Innovation: Advanced Wireless Networks for Science

Digital wireless communication has become a foundational technology for the nation. The U.S. Department of Energy’s Office of Science (DOE-SC) is the Nation’s largest supporter of basic research in the physical sciences discovering new materials, designing advanced microelectronics, and understanding the physics of radio frequency signaling. The expanding national rollout of a new fifth-generation (5G) mobile network, coupled with the torrent of scientific data generated by next-generation devices such as battery-powered Internet of Things (IoT) sensors, has created an urgent need to enhance cutting-edge wireless technology. Breakthroughs in the deployment, integration, security, and operational range of wireless networking can provide new scientific capabilities for the next decade - from autonomous mobile instruments for scientific user facilities to intelligent sensors networks distributed over thousands of kilometers to study environmental processes. To realize this promise, however, we must continue to drive innovations in computing, artificial intelligence (AI), advanced materials, high-speed networking, and microelectronics. In March 2020, the DOE-SC convened a workshop to identify the potential opportunities and explore the scientific challenges of advanced wireless technologies.

42 ENGINEERING↗
NASA NTRS2010

Solar Radiation Transport in the Cloudy Atmosphere: A 3D Perspective on Observations and Climate Impacts

The interplay of sunlight with clouds is a ubiquitous and often pleasant visual experience, but it conjures up major challenges for weather, climate, environmental science and beyond. Those engaged in the characterization of clouds (and the clear air nearby) by remote sensing methods are even more confronted. The problem comes, on the one hand, from the spatial complexity of real clouds and, on the other hand, from the dominance of multiple scattering in the radiation transport. The former ingredient contrasts sharply with the still popular representation of clouds as homogeneous plane-parallel slabs for the purposes of radiative transfer computations. In typical cloud scenes the opposite asymptotic transport regimes of diffusion and ballistic propagation coexist. We survey the three-dimensional (3D) atmospheric radiative transfer literature over the past 50 years and identify three concurrent and intertwining thrusts: first, how to assess the damage (bias) caused by 3D effects in the operational 1D radiative transfer models? Second, how to mitigate this damage? Finally, can we exploit 3D radiative transfer phenomena to innovate observation methods and technologies? We quickly realize that the smallest scale resolved computationally or observationally may be artificial but is nonetheless a key quantity that separates the 3D radiative transfer solutions into two broad and complementary classes: stochastic and deterministic. Both approaches draw on classic and contemporary statistical, mathematical and computational physics.

Davis, Anthony B.↗