Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Generative models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

Structured Neural Network Modeling for Developing Digital Twins Models of Hydropower Generation Units

Dynamic modeling is a key part in the development of digital twin (DT) for dynamic systems. This is true for hydropower systems, where whole system modeling including penstock, turbine and generators, etc is important in realizing actuate modeling for the real systems. On the other hand, in response to the large variations of the power demand due to increased penetration of renewables such as wind and solar, hydropower systems are now required to operate in a large power generation range. This situation triggers the nonlinear characteristics of the generation unit with respect to its models. As such, it is imperative to use data driven modeling such as neural networks to learn the nonlinear dynamics of the hydropower generation unit. To achieve this objective, this study constructs a modeling and learning algorithm integrated with multiple structured neural network models for the modeling of turbine shaft speed, penstock pressure, and generator power output based on the generator power control setpoint, field current, and field voltage. In addition, the study uses the hydropower data from Tacoma Public Utilities to train and validate the proposed neural network algorithm. The results have shown that this structured neural network modeling approach can learn the system dynamics effectively by using the real-time data collected from the hydropower system with the desired modeling results.

Wang, Hong↗

Discrete generative diffusion models without stochastic differential equations: A tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025

Causer, Luke (ORCID:0000000194243473)↗

Observational Data for Next-Generation Climate Model Evaluation: Requirements, Considerations, and Best Practices

Climate model simulations are an important source of information about our planet’s climate system and also enable informed decision-making under different future scenarios. As a new archive of results from the next generation of climate models is anticipated to become available with the Coupled Model Intercomparison Project phase 7 (CMIP7), the need to develop efficient and robust methods to evaluate models is paramount. Observations are an integral part of model evaluation, providing a means to quantify and understand the degree to which climate models can faithfully reproduce Earth system processes. Such analysis is critical for constraining climate projections, identifying areas of focus for model development, and assisting analysts in deciphering the utility of models for specific applications. Observations of Earth system come from a diversity of sources, span different space–time domains, and are produced by different communities, and each dataset features different data structures and formats, metadata standards, and its own unique uncertainties. Uncertainties in an observational dataset may stem from gaps in temporal and spatial coverage, instrumentation errors, or assumptions in retrieval and processing methods. How then does one ensure that observational data are ready for use and utilized in the most appropriate way for robust, rapid, and routine climate model evaluation? The CMIP7 Model Benchmarking Task Team with input from the broader climate modeling, model evaluation, and observational data communities present a vision and considerations for best practices toward the optimal and appropriate use of observational data to support next-generation climate model evaluation.

Climate models↗

Search for vector-like leptons coupling to first- and second-generation Standard Model leptons in pp collisions at s = 13 TeV with the ATLAS detector

A search for pair production of vector-like leptons coupling to first- and second-generation Standard Model leptons is presented. The search is based on a dataset of proton-proton collisions at s$$ \sqrt{s} $$ = 13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb−1. Events are categorised depending on the flavour and multiplicity of leptons (electrons or muons), as well as on the scores of a deep neural network targeting particular signal topologies according to the decay modes of the vector-like leptons. In each of the signal regions, the scalar sum of the transverse momentum of the leptons and the missing transverse momentum is analysed. The main background processes are estimated using dedicated control regions in a simultaneous fit with the signal regions to data. No significant excess above the Standard Model background expectation is observed and limits are set at 95% confidence level on the production cross-sections of vector-like electrons and muons as a function of the vector-like lepton mass, separately for SU(2) doublet and singlet scenarios. The resulting mass lower limits are 1220 GeV (1270 GeV) and 320 GeV (400 GeV) for vector-like electrons (muons) in the doublet and singlet scenarios, respectively.

Aad, G↗

LLNL Kimberlina 1.2 NUFT Simulations June 2018 (v2)

This dataset contains the output 6,000, 3-dimensional reactive multi-phase flow and transport aquifer simulations of brine and CO2 leakage into a protective aquiver in California’s San Joaquin Valley and input data files detailing the geologic mesh, aquifer physical properties and CO2 and brine injection rates. This data set was generated as an ongoing effort with the US DOE National Risk Assessment Partnership (NRAP) to evaluate the effectiveness of monitoring techniques to detect brine and CO2 leakage from legacy wells into underground sources of drinking water overlaying a CO2 storage reservoir. Each simulation contains a unique set of input parameters, generated stochastically. The outputs consist of these upper three geologic layers (from top): the Etchegoin, Macoma-Chanac, Santa Margarita-McLure formations. These simulations span the several distances (1, 3 and 6 km or wells W31-0.2, W31-0.5 and W31-1.0, respectively) from the CO2 injector, initiated from bottom hole pressure and saturation to calculate wellbore leakage from the storage reservoir, with low and high regional groundwater gradients and wellbore leakage into 5 leaky nodes. The dataset includes 1,000 unique simulations for each distance, which each contain a unique aquifer heterogeneity, aquifer and caprock permeability, and two model generations are included with a high permeability (prod07) and hybrid permeability (prod09). The range of permeability distributions is listed in Table 1. Each model generation consists of 3,000 simulations. Included in the dataset are the leakage rates determined from 2D wellbore models which utilize the pressure and CO2 saturation from LBL's reservoir simulations, NUFT mesh files with distributed lithology, NUFT rocktab files which describe the material properties for the geologic layers and the NUFT input files and post-processed output 'ntab' files. Each ntab file contains spatial (rows) and temporal (columns) model output tables for each model cell, the locations (x,y,z) and dimensions for each cells (dx, dy, dz). Table 1. Permeability distribution ranges for prod07 and prod09 model generations Geologic Layer: Permeability Range (log10 m^2) prod07 prod09 Etchegoin -12.92 to -10.92 -13.70 to -11.44 Macoma-Chanac -12.72 to -10.72 -13.50 to -11.24 Santa Margarita-McLure -12.70 to -10.70 -13.48 to -11.22 The input files used to generate the model include which are included in the dataset are: Time series of CO2 leakage input into the model (ex: Q_brn.W31-0.2.sim1000.layers123.tab) Time series of CO2 leakage input into the model (ex: Q_CO2.W31-0.2.sim1000.layers123.tab) Physical properties of the aquifer materials detailing the aquifer porosity, solid density, partitioning coefficients, permeabilities and van-Genuchten parameters detailed in a NUFT rocktab file: (ex: sim1000.usnt.rocktab) Numerical mesh and geologic data assigned to each model cell detailed in a NUFT genmsh format (ex: sim1000.mesh_k16.prod07.trans.genmsh) The primary output parameters are: pH (use absolute value) Change in TDS (mg/kg) Change in Pressure (Pa) Change CO2 gas saturation (fraction range 0.0-1.0) for example, the directory /p/lscratchh/mansoor1/nrap/kimberlina/prod09/mainfiles/sim1000/W31- 0.2 contains: sim1000.W31-0.2.trans.pH.red.ntab sim1000.W31-0.2.no_bg.trans.TDS.red.ntab sim1000.W31-0.2.usnt.P.deltabg.red.ntab sim1000.W31-0.2.usnt.CO2_sat.deltabg.red.ntab Each row in the NTAB files consist of model output per numerical grid cell. Each output file contains 33 columns (variables), including the information of numerical records, geologic location and sizes and the simulated parameter values over time. The first 13 variables are about numerical records and relative geologic information for a simulation grid: 1. index: simulation index 2. i: the ith grid of x-axis 3. j: the ith grid of y-axis 4. k: the ith grid of z-axis 5. element_ref: element reference 6. nuft_ind: nuft index 7. x: grid location in the x axis direction 8. y: grid location in the y axis direction 9. z: grid location in the z axis direction 10. dx: grid length in the x axis direction 11. dy: grid length in the y axis direction 12. dz: grid length in the z axis direction 13. volume: volume of the simulation grid The remainder (14, 15, 16...) variables are the simulated parameter values over time, take Pressure as an example, are: 14. 0.0y: initial pressure per cell. 15. 10.0y: simulated pressure at the end of the 10th year. 16. 20.0y: simulated pressure at the end of the 20th year. ... (repeated for every 10 years until 200 years)... The model extends 10,000 m, 5,000 m and 1,411 m in the x,y and z dimensions, respectively. The mesh consists of 164,832 cells with mesh dimensions of 101 x 51 x 32 (nx, ny, nz), with cell dimensions ranging from 100 m laterally (along x and y-axis) and model layers are as designated in the z-axis: Layer 1: atmosphere (1e-30 m thick) Layer 2: upper caprock (10 m thick) Layers 3-13: Etchegoin (536.23 m thck) Layers 14-27: Macoma-Chanac (679.04 m thick) Layers 28-32: Santa Margarita-McLure (185.94 m thick) The wellbore is placed along node i=51, j=26, and extends vertically along 5 nodes from the top to the bottom of the model. Special instructions when extracting files: Each Gzip archive (ex: prod07.sim1000-sim00099.tar.gz) contains 100 simulations. Gzip archives should be transferred into base directories (ie. In Linux: mkdir prod07; mv prod07.*.tar.gz prod07/.) before extracting, or files will be overwritten. Each sub-simulation tree should have the following file structure pattern (using the linux 'tree' command): |-- prod07 | |-- sim0001 | |-- W31-0.2 | | |-- Q_brn.W31-0.2.sim0001.layers123.tab | | |-- Q_co2.W31-0.2.sim0001.layers123.tab | | |-- sim0001.W31-0.2.no_bg.trans.TDS.red.ntab | | |-- sim0001.W31-0.2.trans.pH.red.ntab | | |-- sim0001.W31-0.2.usnt.CO2_sat.deltabg.red.ntab | | |-- sim0001.W31-0.2.usnt.P.deltabg.red.ntab | |-- W31-0.5 | | |-- Q_brn.W31-0.5.sim0001.layers123.tab | | |-- Q_co2.W31-0.5.sim0001.layers123.tab | | |-- sim0001.W31-0.5.no_bg.trans.TDS.red.ntab | | |-- sim0001.W31-0.5.trans.pH.red.ntab | | |-- sim0001.W31-0.5.usnt.CO2_sat.deltabg.red.ntab | | |-- sim0001.W31-0.5.usnt.P.deltabg.red.ntab | |-- W31-1.0 | | |-- Q_brn.W31-1.0.sim0001.layers123.tab | | |-- Q_co2.W31-1.0.sim0001.layers123.tab | | |-- sim0001.W31-1.0.no_bg.trans.TDS.red.ntab | | |-- sim0001.W31-1.0.trans.pH.red.ntab | | |-- sim0001.W31-1.0.usnt.CO2_sat.deltabg.red.ntab | | |-- sim0001.W31-1.0.usnt.P.deltabg.red.ntab | |-- sim0001.mesh_k16.prod07.trans.genmsh Disclaimer This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344. This report was reviewed and released as LLNL-MI-753464.

aquifer↗

Clustering, randomness and regularity in cloud fields. I - Theoretical considerations. II - Cumulus cloud fields

The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.

Weger, R. C.↗

Modelling Aerodynamically Generated Sound: Recent Advances in Rotor Noise Prediction

A great deal of progress has been made in the modeling of aerodynamically generated sound for rotors over the past decade. The Ffowcs Williams-Hawkings (FW-H ) equation has been the foundation for much of the development. Both subsonic and supersonic quadrupole noise formulations have been developed for the prediction of high-speed impulsive noise. In an effort to eliminate the need to compute the quadrupole contribution, the FW-H has also been utilized on permeable surfaces surrounding all physical noise sources. Comparison of the Kirchhoff formulation for moving surfaces with the FW-H equation have shown that the Kirchhoff formulation for moving surfaces can give erroneous results for aeroacoustic problems.

Brentner, Kenneth S.↗

Unsupervised quantum circuit learning in high energy physics

Unsupervised training of generative models is a machine learning task that has many applications in scientific computing. Here, in this work, we evaluate the efficacy of using quantum circuit-based generative models to generate synthetic data of high energy physics processes. We use nonadversarial, gradient-based training of quantum circuit Born machines to generate joint distributions over two and three variables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian deep learning

The goal of generative models is to learn the intricate relations between the data to create new simulated data, but current approaches fail in very high dimensions. When the true data-generating process is based on physical processes, these impose symmetries and constraints, and the generative model can be created by learning an effective description of the underlying physics, which enables scaling of the generative model to very high dimensions. In this work, we propose Lagrangian deep learning (LDL) for this purpose, applying it to learn outputs of cosmological hydrodynamical simulations. The model uses layers of Lagrangian displacements of particles describing the observables to learn the effective physical laws. The displacements are modeled as the gradient of an effective potential, which explicitly satisfies the translational and rotational invariance. The total number of learned parameters is only of order 10, and they can be viewed as effective theory parameters. Further, we combine N-body solver fast particle mesh (FastPM) with LDL and apply it to a wide range of cosmological outputs, from the dark matter to the stellar maps, gas density, and temperature. The computational cost of LDL is nearly four orders of magnitude lower than that of the full hydrodynamical simulations, yet it outperforms them at the same resolution. We achieve this with only of order 10 layers from the initial conditions to the final output, in contrast to typical cosmological simulations with thousands of time steps. This opens up the possibility of analyzing cosmological observations entirely within this framework, without the need for large dark-matter simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

The 3D Recognition, Generation, Fusion, Update and Refinement (RG4) Concept

This paper describes an active (real time) recognition strategy whereby information is inferred iteratively across several viewpoints in descent imagery. We will show how we use inverse theory within the context of parametric model generation, namely height and spectral reflection functions, to generate model assertions. Using this strategy in an active context implies that, from every viewpoint, the proposed system must refine its hypotheses taking into account the image and the effect of uncertainties as well. The proposed system employs probabilistic solutions to the problem of iteratively merging information (images) from several viewpoints. This involves feeding the posterior distribution from all previous images as a prior for the next view. Novel approaches will be developed to accelerate the inversion search using novel statistic implementations and reducing the model complexity using foveated vision. Foveated vision refers to imagery where the resolution varies across the image. In this paper, we allow the model to be foveated where the highest resolution region is called the foveation region. Typically, the images will have dynamic control of the location of the foveation region. For descent imagery in the Entry, Descent, and Landing (EDL) process, it is possible to have more than one foveation region. This research initiative is directed towards descent imagery in connection with NASA's EDL applications. Three-Dimensional Model Recognition, Generation, Fusion, Update, and Refinement (RGFUR or RG4) for height and the spectral reflection characteristics are in focus for various reasons, one of which is the prospect that their interpretation will provide for real time active vision for automated EDL.

Maluf, David A.↗

The QBO in Two GISS Global Climate Models: 1. Generation of the QBO

The adjustment of parameterized gravity waves associated with model convection and finer vertical resolution has made possible the generation of the quasi-biennial oscillation (QBO) in two Goddard Institute for Space Studies (GISS) models, GISS Middle Atmosphere Global Climate Model III and a climate/middle atmosphere version of Model E2. Both extend from the surface to 0.002 hPa, with 2deg × 2.5deg resolution and 102 layers. Many realistic features of the QBO are simulated, including magnitude and variability of its period and amplitude. The period itself is affected by the magnitude of parameterized convective gravity wave momentum fluxes and interactive ozone (which also affects the QBO amplitude and variability), among other forcings. Although varying sea surface temperatures affect the parameterized momentum fluxes, neither aspect is responsible for the modeled variation in QBO period. Both the parameterized and resolved waves act to produce the respective easterly and westerly wind descent, although their effect is offset in altitude at each level. The modeled and observed QBO influences on tracers in the stratosphere, such as ozone, methane, and water vapor are also discussed. Due to the link between the gravity wave parameterization and the models' convection, and the dependence on the ozone field, the models may also be used to investigate how the QBO may vary with climate change.

middle atmosphere dynamics↗

Modeling Images of Natural 3D Surfaces: Overview and Potential Applications

Generative models of natural images have long been used in computer vision. However, since they only describe the of 2D scenes, they fail to capture all the properties of the underlying 3D world. Even though such models are sufficient for many vision tasks a 3D scene model is when it comes to inferring a 3D object or its characteristics. In this paper, we present such a generative model, incorporating both a multiscale surface prior model for surface geometry and reflectance, and an image formation process model based on realistic rendering, the computation of the posterior model parameter densities, and on the critical aspects of the rendering. We also how to efficiently invert the model within a Bayesian framework. We present a few potential applications, such as asteroid modeling and Planetary topography recovery, illustrated by promising results on real images.

Jalobeanu, Andre↗

Magnetic Gears for a Marine Hydrokinetic Generator Component Model

The goal of this project is to design, fabricate, and test a hermetically sealed 50 kilowatt (kW) multistage magnetically geared generator (MGG). The Component Content Model provides data submitters with an easy and consistent means of uploading data and associated meta data about a component that is currently under development. The data fields include generic information about the component, technology classifications, current costs and performance, proposed target goals, and the environment that the component is operated in. These data are important to DOE and will be used to develop data products that provide quantitative information to guide and support programmatic decisions. Data will also be used by DOE in general assessments of MHK component readiness, performance, costs, and proposed plans. The ultimate goal is to use these data to perform research and tailor programs to best benefit the industry.

16 TIDAL AND WAVE POWER↗

Applying Particle Swarm Optimization and Extended Kalman Filtering to Model Kaplan Generation Dynamics for Hydropower Systems

Variable renewable generation is increasing the need for hydropower plants to provide fast and flexible grid support, which places new demands on plant-level dynamic models used for monitoring, control, and operational decision-making. This need is especially important for hydroelectric systems, where turbine and generator dynamics are strongly coupled, nonlinear, and time-varying, making accurate real-time representation difficult. To address this problem, this paper develops a digital twin (DT) framework for a synchronous generator–Kaplan turbine system using an explicit separation of slow turbine dynamics and fast generator dynamics. The turbine subsystem is represented by a six-coefficient model, whose parameters are identified offline using particle swarm optimization, while the generator subsystem is updated online through an extended Kalman filter for real-time state and parameter estimation. These models are integrated within a closed-loop simulation that includes a proportional–integral–derivative–double-derivative governor and excitation system, allowing the DT to track plant behavior under realistic operating conditions. Unlike prior studies that treat turbine and generator modeling separately or rely mainly on simulated inputs, the proposed framework is validated using real operational data from a hydropower plant. Results show that the DT reproduces terminal voltage, active power, and reactive power with a normalized root mean square error of approximately 5%. This hybrid offline–online formulation constitutes the main contribution of the work, providing an adaptive and practically deployable DT for hydropower systems with direct relevance to control improvement, performance monitoring, and grid-support applications under high renewable penetration.

13 HYDRO ENERGY↗

Active learning for the design of polycrystalline textures using conditional normalizing flows

Generative modeling has opened new avenues for solving previously intractable materials design problems. However, these new opportunities are accompanied by a drastic increase in the required amount of training data. This is in stark juxtaposition to the high expense and difficulty in curating such large materials datasets. In this work, we propose a novel framework for integrating generative models within an active learning loop. Further, this enables the training of generative models with datasets significantly smaller than what has previously been demonstrated, providing a direct route for their application in data constrained environments. The functionality of this framework is then demonstrated by addressing the challenge of designing polycrystalline textures associated with target anisotropic mechanical properties. The developed protocol exhibited a cost reduction between 14 to 18 times over a randomly sampled experimental design.

36 MATERIALS SCIENCE↗

Hierarchical Conditioning of Diffusion Models Using Tree-of-Life for Studying Species Evolution

A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of large-scale image repositories in biology and recent advances in generative modeling, there is an opportunity to accelerate the discovery of evolutionary traits automatically from images. Toward this goal, we introduce Phylo-Diffusion, a novel framework for conditioning diffusion models with phylogenetic knowledge represented in the form of HIERarchical Embeddings (HIER-Embeds). We also propose two new experiments for perturbing the embedding space of Phylo-Diffusion: trait masking and trait swapping, inspired by counterpart experiments of gene knockout and gene editing/swapping. Our work represents a novel methodological advance in generative modeling to structure the embedding space of diffusion models using tree-based knowledge. Our work also opens a new chapter of research in evolutionary biology by using generative models to visualize evolutionary changes directly from images. We empirically demonstrate the usefulness of Phylo-Diffusion in capturing meaningful trait variations for fishes and birds, revealing novel insights about the biological mechanisms of their evolution. (Model and code can be found at imageomics.github.io/phylo-diffusion)

Khurana, Mridul↗

Integrated Control Modeling for Propulsion Systems Using NPSS

The Numerical Propulsion System Simulation (NPSS), an advanced engineering simulation environment used to design and analyze aircraft engines, has been enhanced by integrating control development tools into it. One of these tools is a generic controller interface that allows NPSS to communicate with control development software environments such as MATLAB and EASY5. The other tool is a linear model generator (LMG) that gives NPSS the ability to generate linear, time-invariant state-space models. Integrating these tools into NPSS enables it to be used for control system development. This paper will discuss the development and integration of these tools into NPSS. In addition, it will show a comparison of transient model results of a generic, dual-spool, military-type engine model that has been implemented in NPSS and Simulink. It will also show the linear model generator s ability to approximate the dynamics of a nonlinear NPSS engine model.

Parker, Khary I.↗

Troposphere-stratosphere (surface-55 km) monthly winter general circulation statistics for the Northern Hemisphere Four year averages

In response to theoretically predicted anthropogenic depletion of stratospheric ozone, there has been, in recent years, an increased effort in stratospheric modeling. For comparison between models and observations, it is not sufficient to only compare the morphology of model-generated parameters with observed parameter values. Model-generated statistics should also be compared with observation. It is one of the objectives of the present investigation to discuss a data set which can be used for this purpose for the Northern Hemisphere troposphere and stratosphere. However, the investigation is mainly concerned with a presentation of some of the general circulation statistics derived with the aid of the data set. Attention is given to winter monthly general circulation statistics which were derived from four years of daily 1200 GMT NOAA/NMC Northern Hemisphere analyses.

Geller, M. A.↗