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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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
DOE OSTI2025

Solving sparse finite element problems on neuromorphic hardware

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

Applied mathematics↗
DOE OSTI2023

Strictly Enforcing Invertibility and Conservation in CNN-Based Super Resolution for Scientific Datasets

Abstract Recently, deep convolutional neural networks (CNNs) have revolutionized image “super resolution” (SR), dramatically outperforming past methods for enhancing image resolution. They could be a boon for the many scientific fields that involve imaging or any regularly gridded datasets: satellite remote sensing, radar meteorology, medical imaging, numerical modeling, and so on. Unfortunately, while SR-CNNs produce visually compelling results, they do not necessarily conserve physical quantities between their low-resolution inputs and high-resolution outputs when applied to scientific datasets. Here, a method for “downsampling enforcement” in SR-CNNs is proposed. A differentiable operator is derived that, when applied as the final transfer function of a CNN, ensures the high-resolution outputs exactly reproduce the low-resolution inputs under 2D-average downsampling while improving performance of the SR schemes. The method is demonstrated across seven modern CNN-based SR schemes on several benchmark image datasets, and applications to weather radar, satellite imager, and climate model data are shown. The approach improves training time and performance while ensuring physical consistency between the super-resolved and low-resolution data. Significance Statement Recent advancements in using deep learning to increase the resolution of images have substantial potential across the many scientific fields that use images and image-like data. Most image super-resolution research has focused on the visual quality of outputs, however, and is not necessarily well suited for use with scientific data where known physics constraints may need to be enforced. Here, we introduce a method to modify existing deep neural network architectures so that they strictly conserve physical quantities in the input field when “super resolving” scientific data and find that the method can improve performance across a wide range of datasets and neural networks. Integration of known physics and adherence to established physical constraints into deep neural networks will be a critical step before their potential can be fully realized in the physical sciences.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

WFSUITE: A PYTHON SOFTWARE SUITE FOR X-RAY WAVEFRONT SENDING AND AT-WAVELENGTH METROLOGY

SF-26-025 WFSuite is a graphical and command-line toolkit for coded-mask-based X-ray wavefront sensing and phase reconstruction at synchrotron beamlines. It integrates analysis tools for both relative and absolute speckle-based measurements. In the relative metrology module, WFSuite implements Wavelet-transform-based X-ray Speckle Tracking (WXST) and Wavelet-transform-based Speckle Vector Tracking (WSVT) methods to retrieve differential phase and wavefront distortions by comparing speckle patterns recorded with and without the test sample. In the absolute phase module, WFSuite uses coded-mask speckle patterns and replaces the measured reference with a numerically simulated one, enablingsingle-shot wavefront reconstruction using either WXST or a neural-network-based method (SPINNet).

Rebuffi, Luca [Argonne National Laboratory (ANL), ↗
DOE OSTI2025

High‐Resolution National‐Scale Water Modeling Is Enhanced by Multiscale Differentiable Physics‐Informed Machine Learning

Abstract The National Water Model (NWM) is a key tool for flood forecasting, planning, and water management. Key challenges facing the NWM include calibration and parameter regionalization when confronted with big data. We present two novel versions of high‐resolution (∼37 km 2 ) differentiable models (a type of hybrid model): one with implicit, unit‐hydrograph‐style routing and another with explicit Muskingum‐Cunge routing in the river network. The former predicts streamflow at basin outlets whereas the latter presents a discretized product that seamlessly covers rivers in the conterminous United States (CONUS). Both versions use neural networks to provide a multiscale parameterization and process‐based equations to provide a structural backbone, which were trained simultaneously (“end‐to‐end”) on 2,807 basins across the CONUS and evaluated on 4,997 basins. Both versions show great potential to elevate future NWM performance for extensively calibrated as well as ungauged sites: the median daily Nash‐Sutcliffe efficiency of all 4,997 basins is improved to around 0.68 from 0.48 of NWM3.0. As they resolve spatial heterogeneity, both versions greatly improved simulations in the western CONUS and also in the Prairie Pothole Region, a long‐standing modeling challenge. The Muskingum‐Cunge version further improved performance for basins >10,000 km 2 . Overall, our results show how neural‐network‐based parameterizations can improve NWM performance for providing operational flood predictions while maintaining interpretability and multivariate outputs. The modeling system supports the Basic Model Interface (BMI), which allows seamless integration with the next‐generation NWM. We also provide a CONUS‐scale hydrologic data set for further evaluation and use.

Song, Yalan [Civil and Environmental Engineering T↗
DOE OSTI2025

Towards AI Based Data Classification for Decision Making During Testing

During the development of high-consequence items, test systems should be capable of differentiating between test failures resulting from narrowly missing requirements versus those indicating potentially catastrophic faults. In many instances, classifying the data corresponds to simply identifying whether measured waveforms have approximately the anticipated shape. Cast in this light, the problem reduces to converting raw data into a form optimal for use with neural network classifiers. This manuscript investigates different means of representing raw data for image classification. Raw data plots and Short Time Fourier Transform (STFT) spectrograms are classified by both custom built, small-scale, Convolution Neural Networks (CNN) and open-source, multi-million parameter, pre-trained deep CNNs. In the case of time varying frequency content, the STFTs provide images with greater detail and can be accurately classified with simpler networks. This requires less memory and runs faster than classifying the raw data using the more sophisticated options—making STFTs optimal for applications with memory constraints. STFTs are not a panacea. In some cases the time-domain signal contains useful information that should not be discarded. Rather than using raw data or STFTs, the images can be constructed from both by using red and green channels of an RGB image to visualize the real and imaginary components of the transform, with the raw data occupying the blue channel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Long–short-term memory encoder–decoder with regularized hidden dynamics for fault detection in industrial processes

The ability of recurrent neural networks (RNN) to model nonlinear dynamics of high dimensional process data has enabled data-driven RNN-based fault detection algorithms. Previous studies have focused on detecting faults by identifying the discrepancies in data distribution between the faulty and normal data, as reflected in prediction errors generated by RNN models. However, in industrial processes, variations in data distribution can also result from changes in normal control setpoints and compensatory control adjustments in response to disturbances, making it hard to differentiate between normal and faulty conditions. This paper proposes a fault detection method utilizing a long short-term memory (LSTM) encoder–decoder structure with regularized hidden dynamics and reversible instance normalization (RevIN) to compactly represent high-dimensional measurements for effective monitoring. During training, the hidden states of the model are regularized to form a low-dimensional latent space representation of the original multivariate time series data. As a result, the prediction errors of the latent states can be used to monitor the abnormal dynamic variations, while the reconstruction errors of the measured variables are used to monitor the abnormal static variations. Furthermore, the proposed indices can reflect operating conditions, even when the distribution of test data changes, which helps distinguish faults from normal adjustments and disturbances that controllers can settle. Here, data from numerical simulation and the Tennessee Eastman process are used to illustrate the effectiveness of the proposed fault detection method.

42 ENGINEERING↗
DOE OSTI2022

Performance of New Near-Real-Time PERSIANN Product (PDIR-Now) for Atmospheric River Events over the Russian River Basin, California

Most heavy precipitation events and extreme flooding over the U.S. Pacific coast can be linked to prevalent atmospheric river (AR) conditions. Thus, reliable quantitative precipitation estimation with a rich spatiotemporal resolution is vital for water management and early warning systems of flooding and landslides over these regions. At the same time, high-quality near-real-time measurements of AR precipitation remain challenging due to the complex topographic features of land surface and meteorological conditions of the region: specifically, orographic features occlude radar measurements while infrared-based algorithms face challenges, differentiating between both cold brightband (BB) precipitation and the warmer nonbrightband (NBB) precipitation. It should be noted that the latter precipitation is characterized by greater orographic enhancement. In this study, we evaluate the performance of a recently developed near-real-time satellite precipitation algorithm: Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN) Dynamic Infrared–Rain Rate-Now (PDIR-Now). This model is primarily dependent on infrared information from geostationary satellites as input; consequently, PDIR-Now has the advantage of short data latency, 15–60-min delay between observation to precipitation product delivery. The performance of PDIR-Now is analyzed with a focus on AR-related events for cases dominated by NBB and BB precipitation over the Russian River basin. In our investigations, we utilize S-band (3-GHz) precipitation profilers with Joss/Parsivel disdrometer measurements at the Middletown and Santa Rosa stations to classify BB and NBB precipitation events. In general, our analysis shows that PDIR-Now is more skillful in retrieving precipitation rates over both BB and NBB events across the topologically complex study area as compared to PERSIANN-Cloud Classification System (CCS). Also, we discuss the performance of well-known operational near-real-time precipitation products from 2017 to 2019. Conventional categorical and volumetric categorical indices, as well as continuous statistical metrics, are used to show the differences between various high-resolution precipitation products such as Multi-Radar Multi-Sensor (MRMS).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries

Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from $O(N^d)$ to $O(N^{d-1}$), where $d$ is the domain’s dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Finally, our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

Feedback Linearized Aircraft Control Using Dynamic Cell Structure

A Dynamic Cell Structure (DCS ) Neural Network was developed which learns a topology representing network (TRN) of F-15 aircraft aerodynamic stability and control derivatives. The network is combined with a feedback linearized tracking controller to produce a robust control architecture capable of handling multiple accident and off-nominal flight scenarios. This paper describes network and its performance for accident scenarios including differential stabilator lock, soft sensor failure, control, stability derivative variation, and turbulence.

Jorgensen, C. C.↗
NASA NTRSDate not supplied

Application of ML/AI for Identifying Earth Science Datasets in Research Publications

NASA Data Active Archive Centers, or DAACs, ingest, store and distribute data acquired from satellites, ground systems as well as modelling data. These data are organized by the datasets, each presenting collection of files usually associated with the certain mission, instrument, processing level, parameter(s), algorithm and/or model. The number of datasets offered by a single DAAC to the public varies. GES DISC, for example, currently offers for public use approximately ~1,300 datasets. While each publicly offered dataset comes with supporting documentation, it is challenging for novice and even experienced scientists to navigate among the datasets that offer similar parameters to find the datasets for their particular research application. Supplying dataset documentation with the scientific paper citations that refer to that dataset provides means for the dataset users to educate themselves with the application research that dataset is being used in. Collecting citations of the papers that use the datasets for their research yield valuable insights into application areas of those datasets, information about usage of the dataset groups for specific applications and those application topics. It also gives insights into the “deep metrics” of the dataset usage, as opposed to the common metrics of the dataset usage such as number of users who downloaded the dataset files and volumes of downloaded data. Association of a certain scientific paper with the dataset(s) presents a challenge because most of the paper authors do not properly cite the datasets, datasets usually have cryptic names and Digital Object Identifiers (DOIs) that are used for dataset identification were assigned to the datasets only few years ago. Simple Google or online library search do not provide even meaningful fraction of the results when performed by the dataset name or DOI, however they provide too many results when the search is done by more broader terms such as mission and instrument names. Attempts to create an AI system capable to identify dataset in the scientific papers have already been made using neural networks classifiers on the basis of the dataset mission, instrument and variable name. This method was applied to NASA SEDAC, which has 41 datasets in total. In GES DISC there can be as many as ~100 datasets per mission/instrument with some of the datasets consisting of multiple variables so there is a need for more differentiating parameters for dataset identification in the paper. The approach we are currently investigating is creating AI classifiers that are based on multiple dataset features, or keywords, extracted from the NASA Earthdata Common Dataset Repository (CMR). The features are weighted based on how precisely they can identify a dataset. The classifier uses preprocessed paper text as input and searches for the CMR datasets whose feature sets are the closest to the feature sets contained in the paper. The challenges of dataset identification include variety of ways the paper authors describe the datasets in their papers and incomplete tagging of the CMR dataset description (DIFs).

Irina Gerasimov↗
DOE OSTI2023

Machine-learning-based spectral methods for partial differential equations

Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Model reduction for the dynamics and control of large structural systems via neutral network processing direct numerical optimization

Three neural network processing approaches in a direct numerical optimization model reduction scheme are proposed and investigated. Large structural systems, such as large space structures, offer new challenges to both structural dynamicists and control engineers. One such challenge is that of dimensionality. Indeed these distributed parameter systems can be modeled either by infinite dimensional mathematical models (typically partial differential equations) or by high dimensional discrete models (typically finite element models) often exhibiting thousands of vibrational modes usually closely spaced and with little, if any, damping. Clearly, some form of model reduction is in order, especially for the control engineer who can actively control but a few of the modes using system identification based on a limited number of sensors. Inasmuch as the amount of 'control spillover' (in which the control inputs excite the neglected dynamics) and/or 'observation spillover' (where neglected dynamics affect system identification) is to a large extent determined by the choice of particular reduced model (RM), the way in which this model reduction is carried out is often critical.

Becus, Georges A.↗
DOE OSTI2021

Parallel physics-informed neural networks via domain decomposition

Here we develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation capacity, efficient hyperparameter tuning, and is particularly effective for multi-scale and multi-physics problems. Here, we present a parallel algorithm for cPINNs and XPINNs constructed with a hybrid programming model described by MPI + X, where X ∈ {CPUs, GPUs}. The main advantage of cPINN and XPINN over the more classical data and model parallel approaches is the flexibility of optimizing all hyperparameters of each neural network separately in each subdomain. We compare the performance of distributed cPINNs and XPINNs for various forward problems, using both weak and strong scalings. Our results indicate that for space domain decomposition, cPINNs are more efficient in terms of communication cost but XPINNs provide greater flexibility as they can also handle time-domain decomposition for any differential equations, and can deal with any arbitrarily shaped complex subdomains. To this end, we also present an application of the parallel XPINN method for solving an inverse diffusion problem with variable conductivity on the United States map, using ten regions as subdomains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

Continuous system modeling

A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.

Cellier, Francois E.↗
DOE OSTI2026

Measurement of the muon neutrino charged-current mesonless cross section in the NOvA near detector

NOvA is a long-baseline accelerator neutrino experiment at Fermilab. Its physics goals include precision neutrino oscillation measurements, neutrino interaction cross-section measurements and beyond Standard Model explorations. We present a measurement of muon neutrino charged-current cross section with zero mesons in the final state at the NOvA near detector. This measurement is performed as a function of the kinematics of the final state muon. Our chosen interaction channel is especially sensitive to quasielastic and meson exchange current interactions and it provides handles for constraining the cross section systematic uncertainties in oscillation analyses in present and future experiments. For particle identification, we use a convolutional neural network (CNN) trained on individual particles simulated in the NOvA Near detector. This allows us to select the desired signal while reducing the potential bias from neutrino interaction modeling. We study strategies for constraining the remaining charged-pion background via Michel electron information in a template fitting approach. The main experimental result is a two-dimensional differential cross section as a function of final-state muon kinetic energy and polar angle. The parameters of this measurement, including binning and unfolding, were optimized to reduce the expected systematic uncertainty in the total cross section. The final result shows good agreement with the main GENIE-based simulation framework that was independently fine-tuned in NOvA. We finally propose improvements and subsequent steps that build on this analysis and further dissect the final states of neutrino interactions. This work has been supported by US DOE grant DE-SC0015684.

Sánchez Falero, Sebastián Jesús [Iowa State U.]↗
NASA NTRS2020

Neural Network Reflectance Prediction Model for Both Open Ocean and Coastal Waters

Remote sensing of global ocean color is a valuable tool for understanding the ecology and biogeochemistry of the worlds oceans, and provides critical input to our knowledge of the global carbon cycle and the impacts of climate change. Ocean polarized reflectance contains information about the constituents of the upper ocean euphotic zone, such as colored dissolved organic matter (CDOM), sediments, phytoplankton, and pollutants. In order to retrieve the information on these constituents, remote sensing algorithms typically rely on radiative transfer models to interpret water color or remote-sensing reflectance; however, this can be resource-prohibitive for operational use due to the extensive CPU time involved in radiative transfer solutions. In this work, we report a fast model based on machine learning techniques, called Neural Network Reflectance Prediction Model (NNRPM), which can be used to predict ocean bidirectional polarized reflectance given inherent optical properties of ocean waters. This supervised model is trained using a large volume of data derived from radiative transfer simulations for coupled atmosphere and ocean systems using the successive order of scattering technique (SOS-CAOS). The performance of the model is validated against another large independent test dataset generated from SOS-CAOS. The model is able to predict both polarized and unpolarized reflectances with an absolute error (AE) less than 0.004 for 99% of test cases. We have also shown that the degree of linear polarization (DoLP) for unpolarized incident light can be predicted with an AE less than 0.002 for 99% of test cases. In general, the simulation time of SOS-CAOS depends on optical depth, and required accuracy. When comparing the average speeds of the NNRPM against the SOS-CAOS model for the same parameters, we see that the NNRPM is able to predict the Ocean BRDF 6000 times faster than SOS-CAOS. Both ultraviolet and visible wavelengths are included in the model to help differentiate between dissolved organic material and chlorophyll in the study of the open ocean and the coastal zone. The incorporation of this model into the retrieval algorithm will make the retrieval process more efficient, and thus applicable for operational use with global satellite observations.

radiative transfer↗