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NASA NTRS1989

A Storage-Efficient WY Representation for Products of Householder Transformations

A product Q=P1 ... P(sub r) of m x m Householder matrices can be written in the form Q = I + WY(sup T), where W and Y are each m x r. This is called the WY representation of Q. It is of interest when implementing Householder techniques in high-performance computing environments that are especially good at matrix-matrix multiplication. In this note a storage-efficient way to implement the WY representation is described. In particular, it is shown how the matrix Q can be expressed in the form Q = I + YTY(sup T). Usually r much less than m and so this 'compact' WY representation requires less storage. When compared with the recent block-reflector strategy the new technique still has a storage advantage and involves a comparable amount of work.

Schreiber, Robert↗

NASA NTRS1997

Distortion Representation of Forecast Errors for Model Skill Assessment and Objective Analysis

We proposed a novel characterization of errors for numerical weather predictions. In its simplest form we decompose the error into a part attributable to phase errors and a remainder. The phase error is represented in the same fashion as a velocity field and is required to vary slowly and smoothly with position. A general distortion representation allows for the displacement and amplification or bias correction of forecast anomalies. Characterizing and decomposing forecast error in this way has two important applications, which we term the assessment application and the objective analysis application. For the assessment application, our approach results in new objective measures of forecast skill which are more in line with subjective measures of forecast skill and which are useful in validating models and diagnosing their shortcomings. With regard to the objective analysis application, meteorological analysis schemes balance forecast error and observational error to obtain an optimal analysis. Presently, representations of the error covariance matrix used to measure the forecast error are severely limited. For the objective analysis application our approach will improve analyses by providing a more realistic measure of the forecast error. We expect, a priori, that our approach should greatly improve the utility of remotely sensed data which have relatively high horizontal resolution, but which are indirectly related to the conventional atmospheric variables. In this project, we are initially focusing on the assessment application, restricted to a realistic but univariate 2-dimensional situation. Specifically, we study the forecast errors of the sea level pressure (SLP) and 500 hPa geopotential height fields for forecasts of the short and medium range. Since the forecasts are generated by the GEOS (Goddard Earth Observing System) data assimilation system with and without ERS 1 scatterometer data, these preliminary studies serve several purposes. They (1) provide a testbed for the use of the distortion representation of forecast errors, (2) act as one means of validating the GEOS data assimilation system and (3) help to describe the impact of the ERS 1 scatterometer data.

Hoffman, Ross N.↗

NASA NTRS1999

Spacecraft Attitude Representations

The direction cosine matrix or attitude matrix is the most fundamental representation of the attitude, but it is very inefficient: It has six redundant parameters, it is difficult to enforce the six (orthogonality) constraints. the four-component quaternion representation is very convenient: it has only one redundant parameter, it is easy to enforce the normalization constraint, the attitude matrix is a homogeneous quadratic function of q, quaternion kinematics are bilinear in q and m. Euler angles are extensively used: they often have a physical interpretation, they provide a natural description of some spacecraft motions (COBE, MAP), but kinematics and attitude matrix involve trigonometric functions, "gimbal lock" for certain values of the angles. Other minimum (three-parameter) representations: Gibbs vector is infinite for 180 deg rotations, but useful for analysis, Modified Rodrigues Parameters are nonsingular, no trig functions, Rotation vector phi is nonsingular, but requires trig functions.

Markley, F. Landis↗

NASA NTRS2001

Attitude Representations for Kalman Filtering

The four-component quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation, it represents the attitude matrix as a homogeneous quadratic function, and its dynamic propagation equation is bilinear in the quaternion and the angular velocity. The quaternion is required to obey a unit norm constraint, though, so Kalman filters often employ a quaternion for the global attitude estimate and a three-component representation for small errors about the estimate. We consider these mixed attitude representations for both a first-order Extended Kalman filter and a second-order filter, as well for quaternion-norm-preserving attitude propagation.

Markley, F. Landis↗

NASA NTRS2000

Wavelet-Based Interpolation and Representation of Non-Uniformly Sampled Spacecraft Mission Data

A well-documented problem in the analysis of data collected by spacecraft instruments is the need for an accurate, efficient representation of the data set. The data may suffer from several problems, including additive noise, data dropouts, an irregularly-spaced sampling grid, and time-delayed sampling. These data irregularities render most traditional signal processing techniques unusable, and thus the data must be interpolated onto an even grid before scientific analysis techniques can be applied. In addition, the extremely large volume of data collected by scientific instrumentation presents many challenging problems in the area of compression, visualization, and analysis. Therefore, a representation of the data is needed which provides a structure which is conducive to these applications. Wavelet representations of data have already been shown to possess excellent characteristics for compression, data analysis, and imaging. The main goal of this project is to develop a new adaptive filtering algorithm for image restoration and compression. The algorithm should have low computational complexity and a fast convergence rate. This will make the algorithm suitable for real-time applications. The algorithm should be able to remove additive noise and reconstruct lost data samples from images.

Bose, Tamal↗

NASA NTRS2002

Attitude Error Representations for Kalman Filtering

The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.

Markley, F. Landis↗

NASA NTRS2003

Generative Representations for Evolving Families of Designs

Since typical evolutionary design systems encode only a single artifact with each individual, each time the objective changes a new set of individuals must be evolved. When this objective varies in a way that can be parameterized, a more general method is to use a representation in which a single individual encodes an entire class of artifacts. In addition to saving time by preventing the need for multiple evolutionary runs, the evolution of parameter-controlled designs can create families of artifacts with the same style and a reuse of parts between members of the family. In this paper an evolutionary design system is described which uses a generative representation to encode families of designs. Because a generative representation is an algorithmic encoding of a design, its input parameters are a way to control aspects of the design it generates. By evaluating individuals multiple times with different input parameters the evolutionary design system creates individuals in which the input parameter controls specific aspects of a design. This system is demonstrated on two design substrates: neural-networks which solve the 3/5/7-parity problem and three-dimensional tables of varying heights.

Hornby, Gregory S.↗

NASA NTRS2003

Generative Representations for the Automated Design of Modular Physical Robots

We will begin with a brief background of evolutionary robotics and related work, and demonstrate the scaling problem with our own prior results. Next we propose the use of an evolved generative representation as opposed to a non-generative representation. We describe this representation in detail as well as the evolutionary process that uses it. We then compare progress of evolved robots with and without the use of the grammar, and quantify the obtained advantage. Working two- dimensional and three-dimensional physical robots produced by the system are shown.

Hornby, Gregory S.↗

NASA NTRS2002

The effects of mental representation on performance in a navigation task

In three experiments, we investigated the mental representations employed when instructions were followed that involved navigation in a space displayed as a grid on a computer screen. Performance was affected much more by the number of instructional units than by the number of words per unit. Performance in a three-dimensional space was independent of the number of dimensions along which participants navigated. However, memory for and accuracy in following the instructions were reduced when the task required mentally representing a three-dimensional space, as compared with representing a two-dimensional space, although the words used in the instructions were identical in the two cases. These results demonstrate the interdependence of verbal and spatial memory representations, because individuals' immediate memory for verbal navigation instructions is affected by their mental representation of the space referred to by the instructions.

Imagination↗

NASA NTRS2005

Knowledge Representation Standards and Interchange Formats for Causal Graphs

In many domains, automated reasoning tools must represent graphs of causally linked events. These include fault-tree analysis, probabilistic risk assessment (PRA), planning, procedures, medical reasoning about disease progression, and functional architectures. Each of these fields has its own requirements for the representation of causation, events, actors and conditions. The representations include ontologies of function and cause, data dictionaries for causal dependency, failure and hazard, and interchange formats between some existing tools. In none of the domains has a generally accepted interchange format emerged. The paper makes progress towards interoperability across the wide range of causal analysis methodologies. We survey existing practice and emerging interchange formats in each of these fields. Setting forth a set of terms and concepts that are broadly shared across the domains, we examine the several ways in which current practice represents them. Some phenomena are difficult to represent or to analyze in several domains. These include mode transitions, reachability analysis, positive and negative feedback loops, conditions correlated but not causally linked and bimodal probability distributions. We work through examples and contrast the differing methods for addressing them. We detail recent work in knowledge interchange formats for causal trees in aerospace analysis applications in early design, safety and reliability. Several examples are discussed, with a particular focus on reachability analysis and mode transitions. We generalize the aerospace analysis work across the several other domains. We also recommend features and capabilities for the next generation of causal knowledge representation standards.

Throop, David R.↗

NASA NTRS2010

The Graphical Representation of the Digital Astronaut Physiology Backbone

This report summarizes my internship project with the NASA Digital Astronaut Project to analyze the Digital Astronaut (DA) physiology backbone model. The Digital Astronaut Project (DAP) applies integrated physiology models to support space biomedical operations, and to assist NASA researchers in closing knowledge gaps related to human physiologic responses to space flight. The DA physiology backbone is a set of integrated physiological equations and functions that model the interacting systems of the human body. The current release of the model is HumMod (Human Model) version 1.5 and was developed over forty years at the University of Mississippi Medical Center (UMMC). The physiology equations and functions are scripted in an XML schema specifically designed for physiology modeling by Dr. Thomas G. Coleman at UMMC. Currently it is difficult to examine the physiology backbone without being knowledgeable of the XML schema. While investigating and documenting the tags and algorithms used in the XML schema, I proposed a standard methodology for a graphical representation. This standard methodology may be used to transcribe graphical representations from the DA physiology backbone. In turn, the graphical representations can allow examination of the physiological functions and equations without the need to be familiar with the computer programming languages or markup languages used by DA modeling software.

Briers, Demarcus↗

NASA NTRS2016

On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time- frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and nonstationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

Huang, Norden E.↗

NASA NTRS2018

Explicit Cloud Representation in the Atmos 1D Climate Model for Earth and Rocky Planet Applications

1D climate models are less sophisticated than 3D global circulation models (GCMs), however their computational time is much less expensive, allowing a large number of runs in a short period of time to explore a wide parameter space. Exploring parameter space is particularly important for predicting the observable properties of exoplanets, for which few parameters are known with certainty. Therefore, 1D climate models are still very useful tools for planetary studies. In most of these 1D models, clouds are not physically represented in the atmosphere, despite having a well-known, significant impact on a planetary radiative budget. This impact is simulated by artificially raising surface albedo, in order to reproduce the observed-averaged surface temperature (i.e. 288 K for modern Earth) and a radiative balance at the top of the atmosphere. This non-physical representation of clouds, causes atmospheric long wave and shortwaves fluxes to not match observational data. Additionally, this technique represents a parameter that is highly-tuned to modern Earth’s climate, and may not be appropriate for planets that deviate from modern Earth’s climate conditions. In this paper, we present an update to the climate model within the Atmos 1D atmospheric modeling package with a physical representation of clouds. We show that this physical representation of clouds in the atmosphere allows both long wave and shortwave fluxes to match observational data. This improvement will allow us to study the energy fluxes for a variety of cloudy rocky planets, and increase our confidence in future simulations of temperature profile and net energy balance.

Thomas Fauchez↗

NASA NTRS2020

Understanding and Improving Model Representation of Aerosol Optical Properties for a Chinese Haze Event Measured During KORUS-AQ

KORUS-AQ was an international cooperative air quality field study in South Korea that measured local and remote sources of air pollution affecting the Korean Peninsula during May–June 2016. Some of the largest aerosol mass concentrations were measured during a Chinese haze transport event (24 May). Air quality forecasts using the WRF-Chem model with aerosol optical depth (AOD) data assimilation captured AOD during this pollution episode but overpredicted surface particulate matter concentrations in South Korea, especially PM2.5, often by a factor of 2 or larger. Analysis revealed multiple sources of model deficiency related to the calculation of optical properties from aerosol mass that explain these discrepancies. Using in situ observations of aerosol size and composition as inputs to the optical properties calculations showed that using a low-resolution size bin representation (four bins) underestimates the efficiency with which aerosols scatter and absorb light (mass extinction efficiency). Besides using finer-resolution size bins (8–16 bins), it was also necessary to increase the refractive indices and hygroscopicity of select aerosol species within the range of values reported in the literature to achieve better consistency with measured values of the mass extinction efficiency (6.7 m2 g−1 observed average) and light-scattering enhancement factor (f(RH)) due to aerosol hygroscopic growth (2.2 observed average). Furthermore, an evaluation of the optical properties obtained using modeled aerosol properties revealed the inability of sectional and modal aerosol representations in WRF-Chem to properly reproduce the observed size distribution, with the models displaying a much wider accumulation mode. Other model deficiencies included an underestimate of organic aerosol density (1.0 g cm−3 in the model vs. observed average of 1.5 g cm−3) and an overprediction of the fractional contribution of submicron inorganic aerosols other than sulfate, ammonium, nitrate, chloride, and sodium corresponding to mostly dust (17 %–28 % modeled vs. 12 % estimated from observations). These results illustrate the complexity of achieving an accurate model representation of optical properties and provide potential solutions that are relevant to multiple disciplines and applications such as air quality forecasts, health impact assessments, climate projections, solar power forecasts, and aerosol data assimilation.

Pablo E. Saide↗

NASA NTRS2024

Influence of More Mechanistic Representation of Particle Dry Deposition on 1850–2000 Changes in Global Aerosol Burdens and Radiative Forcing

Robust estimates of historical changes in aerosols are key for accurate constraints on climate sensitivity. Dry deposition is a primary sink of aerosols from the atmosphere. However, most global climate models do not accurately represent observed strong dependencies of dry deposition following turbulent transport on aerosol size. It is unclear whether there is a substantial impact of mischaracterized aerosol deposition velocities on historical aerosol changes. Here we describe improved mechanistic representation of aerosol dry deposition in the NASA Goddard Institute for Space Studies (GISS) global climate model, ModelE, and illustrate the impact on 1850–2000 changes in global aerosol burdens as well as aerosol direct and cloud albedo effects using a set of 1850 and 2000 time slice simulations. We employ two aerosol configurations of ModelE (a “bulk” mass-based configuration and a configuration that more explicitly represents aerosol size distributions, internal mixing, and microphysics) to explore how model structural differences in aerosol representation alter the response to representation of dry deposition. Both configurations show larger historical increases in the global burdens of non-dust aerosols with the new dry deposition scheme, by 11% in the simpler mass-based configuration and 23% in the more complex microphysical configuration. Historical radiative forcing responses, which vary in magnitude from 5% to 12% as well as sign, depend on the aerosol configuration.

aerosol↗

NASA NTRSDate not supplied

Trade-Offs of Simplified Versus Comprehensive Representation of Mineralogy When Studying Dust Impacts on Earth’s Climate Systems

The intensity and direction of dust impacts on Earth’s climate systems depend on mineral composition. For example, the presence or absence of a few percent of iron oxides in dust will determine if dust is warming or cooling the atmosphere. Similarly, feldspar will enhance ice cloud formation, while acid gases in the atmosphere will react on the surface of dust calcite limiting acid rain. Still, most climate models use a simplified representation of dust mineralogy. They assume a fixed composition at emission which stays invariant during transport and removal. Such simplification assumes spatially and temporally constant physical and chemical properties of dust, and appears to provide satisfactory results when comparing some properties with observations. The trade-off is their lack of spatial gradients, which will fail to induce circulation, cloud and precipitation changes. The two reasons to omit mineral variations are the uncertainty of current atlases of soil mineral composition in arid regions, and, more practically, an improved runtime efficiency. The former reason is losing ground with the recent launch (July 2022) of a dedicated mission (NASA/JPL EMIT) to retrieve global soil mineralogy of dust sources at high spatial resolution. While the EMIT science team is finalizing a satisfactory global map of mineral composition of dust sources, we analyzed the interaction of dust mineralogy on radiation and its impact on the fast temperature response using different representations of mineral composition from detailed and spatially varying to simplified and globally uniform, assuming different hematite contents and methods to calculate optical properties. Our results show that resolving dust mineralogy reduces dust absorption, and results in improved agreement with observation-based single scattering albedo (SSA), radiative fluxes from CERES (the Clouds and the Earth’s Radiant Energy System), and land surface temperature from CRU (Climatic Research Unit), compared to the baseline bulk dust model version. It also results in distinct radiative impacts on Earth’s climate over North Africa. From our 19-year simulation, we will show that it leads to a reduction of over 50% in net downward radiation at top of atmosphere (TOA) across the Sahara and an approximately 20% reduction over the Sahel. We will explain how the surface temperature response affects the monsoon flow from the Gulf of Guinea. Interestingly, we find similar results by simply fixing the hematite content of dust to a globally uniform value of 0.9% by volume. We will discuss the underlying reasons for such results and show that they may be unrelated to the distribution of soil mineralogy. Still, an accurate representation of soil mineralogy is necessary to better understand dust impacts on the Earth’s climate systems.

dust impacts↗

DOE OSTI2020

Anomaly Detection in Sequential Health Care Data using Higher-Order Network Representation

The ever-increasing use of information technology (IT) in health care presents new challenges to patient care. Information errors arising from the use of Health IT and their implications on care delivery and patient outcomes have been widely reported. Information errors can lead to changes in clinical decisions, care processes, and care outcomes, among others. An altered care process, for example, could interrupt the sequence of care, which could lead to changes in care decisions and/or changes in care outcomes. We define interruptions in the care process as anomalies in the care sequence. In this paper, we present a new approach based on the higher-order network (HON) representation to detect anomalies in sequential health care data using electronic health records. The results show that there are higher-order dependencies in health care data; and that the use of HON representation is more effective than the first-order network representation for detecting anomalies in sequential health care data.

Niu, Haoran↗

DOE OSTI2021

Geothermal Representation in Power System Models

Power system models generally fail to capture the range of characteristics geothermal resources provide and the value they potentially contribute to decarbonization and reliability of future electricity grids as firm, dispatchable, non-combustion power resources. This study reviews the results of power system modeling efforts to investigate geothermal deployment potential in the United States, including the U.S. DOE GeoVision analysis and ongoing modeling and analysis efforts to support planning and development of future grids with 100% renewable energy in California. Several themes are identified that could be implemented immediately to improve the accuracy of geothermal representation in power system models: consistency of model inputs, modeling of baseload and dispatchable geothermal resources, accurate valuation of grid services, improved representation of capacity factor, use of contemporary LCOE estimates, improved understanding of the evolution of geothermal value, and use of accurate resource potential constraints. Many of the models reviewed produced significantly different amounts of geothermal resource selection - even when modeling the same region and time period. This highlights the variability of inputs and assumptions among models, so creating a consistent set of geothermal inputs is a first step toward more accurate representation of geothermal in models. Research opportunities are identified that could help improve geothermal data inputs in modeling efforts, including analyses of historical data, sensitivity to model inputs, and comparative value of geothermal generators as baseload or dispatchable resources. Outcomes of such research can inform the geothermal community about how best to guide geothermal development toward wider deployment in support of future electricity grids through improved understanding of the evolution of geothermal value over time and the characteristics that contribute to that value.

capacity expansion models↗