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All sourcesNASA NTRSDOE OSTI
NASA NTRS2023

Solar Activity Relations in Energetic Electron Events Measured By the MESSENGER Mission

Aims. We perform a statistical study of the relations between the properties of solar energetic electron (SEE) events measured by the MESSENGER mission from 2010 to 2015 and the parameters of the respective parent solar activity phenomena in order to identify the potential correlations between them. During the time of analysis, the MESSENGER heliocentric distance varied between 0.31 and 0.47 au. Methods. We used a published list of 61 SEE events measured by MESSENGER, which includes information on the near-relativistic electron peak intensities, the peak-intensity energy spectral indices, and the measured X-ray peak intensity of the flares related to the SEE events. Taking advantage of multi-viewpoint remote-sensing observations, we reconstructed, whenever possible, the associated coronal mass ejections (CMEs) and shock waves; and we determined the three-dimensional (3D) properties (location, speed, and width) of the CMEs and the maximum speed of the 3D CME-driven shocks in the corona. We used different methods (Spearman, Pearson, and a Bayesian approach, namely the Kelly method to linear regression) to estimate the correlation coefficients between the flare intensity, maximum speed at the apex of the CME-driven shock, CME speed at the apex, and CME width with the electron peak intensities and with the energy spectral indices. In this statistical study, we considered and addressed the limitations of the particle instrument on board MESSENGER (elevated background intensity level, anti-Sun pointing). Results. There is an asymmetry to the east in the range of connection angles (CAs) for which the SEE events present the highest peak intensities, where the CA is the longitudinal separation between the footpoint of the magnetic field connecting to the spacecraft and the flare location. Based on this asymmetry, we define a subsample of well-connected events as when −65° ≤ CA ≤ +33°. For the well-connected sample, we find moderate to strong correlations between the near-relativistic electron peak intensity and the 3D CME-driven shock maximum speed at the apex (Spearman: cc = 0.53 ± 0.05; Pearson: cc = 0.65 ± 0.04; Kelly: cc = 0.87 ± 0.20), the flare peak intensity (Spearman: cc = 0.63 ± 0.03; Pearson: cc = 0.59 ± 0.03; Kelly: cc = 0.74 ± 0.30), and the 3D CME speed at the apex (Spearman: cc = 0.50 ± 0.04; Pearson: cc = 0.46 ± 0.03; Kelly: cc = 0.60 ± 0.39). When including poorly connected events (full sample), the relations between the peak intensities and the solar-activity phenomena are blurred, showing lower correlation coefficients. Conclusions. Based on the comparison of the correlation coefficients presented in this study using near 0.4 au data, (1) both flare and shock-related processes may contribute to the acceleration of near relativistic electrons in large SEE events, in agreement with previous studies based on near 1 au data; and (2) the maximum speed of the CME-driven shock is a better parameter to investigate particle-acceleration-related mechanisms than the average CME speed, as suggested by the stronger correlation with the SEE peak intensities.

Sun↗
NASA NTRS2024

Low-Cost Sensor Performance Intercomparison, Correction Factor Development, and 2+ Years of Ambient PM2.5 Monitoring in Accra, Ghana

Particulate matter air pollution is a leading cause of global mortality, particularly in Asia and Africa. Addressing the high and wide-ranging air pollution levels requires ambient monitoring, but many low- and middle-income countries (LMICs) remain scarcely monitored. To address these data gaps, recent studies have utilized low-cost sensors. These sensors have varied performance, and little literature exists about sensor intercomparison in Africa. By colocating 2 QuantAQ Modulair-PM, 2 PurpleAir PA-II SD, and 16 Clarity Node-S Generation II monitors with a reference-grade Teledyne monitor in Accra, Ghana, we present the first intercomparisons of different brands of low-cost sensors in Africa, demonstrating that each type of low-cost sensor PM2.5 is strongly correlated with reference PM2.5, but biased high for ambient mixture of sources found in Accra. When compared to a reference monitor, the QuantAQ Modulair-PM has the lowest mean absolute error at 3.04 μg/m3, followed by PurpleAir PA-II (4.54 μg/m3) and Clarity Node-S (13.68 μg/m3). We also compare the usage of 4 statistical or machine learning models (Multiple Linear Regression, Random Forest, Gaussian Mixture Regression, and XGBoost) to correct low-cost sensors data, and find that XGBoost performs the best in testing (R2: 0.97, 0.94, 0.96; mean absolute error: 0.56, 0.80, and 0.68 μg/m3 for PurpleAir PA-II, Clarity Node-S, and Modulair-PM, respectively), but tree-based models do not perform well when correcting data outside the range of the colocation training. Therefore, we used Gaussian Mixture Regression to correct data from the network of 17 Clarity Node-S monitors deployed around Accra, Ghana, from 2018 to 2021. We find that the network daily average PM2.5 concentration in Accra is 23.4 μg/m3, which is 1.6 times the World Health Organization Daily PM2.5 guideline of 15 μg/m3. While this level is lower than those seen in some larger African cities (such as Kinshasa, Democratic Republic of the Congo), mitigation strategies should be developed soon to prevent further impairment to air quality as Accra, and Ghana as a whole, rapidly grow.

Humidity↗
NASA NTRSDate not supplied

On the Integration of Loudness Over Time for the Prediction of Single-Event Annoyance

Loudness is the quality of human perception that is most related to acoustic intensity and energy, however there is no agreed-upon way of integrating loudness over time for the prediction of noise-induced annoyance. Most noise metrics used today for aircraft certification and regulation employ the “Equal-Energy Hypothesis” (EEH) and sum the acoustical energy of one or more noise events over time to create a single metric value that represents the entire exposure. Using the EEH creates a natural tradeoff between the peak energy and the duration of a single noise event, the “hypothesis” being that this tradeoff optimally predicts annoyance in a wide variety of situations. This work proposes a strategy for integrating a loudness-like time series which is flexible in two ways: First, it includes a parameter b ∈ [0,1]. When b = 0, the metric will return the peak of the time series. At b = .5, the metric will behave in accordance with the EEH. At b = 1, the metric will penalize the duration of the sound more than the EEH would. Second, transformations are given so that the strategy can be computed from, or generate quantities in units analogous to, decibels (or phon), physical units (acoustic pressure/power), or perceptually-scaled units (sone). This approach is demonstrated on a dataset of annoyance responses to single events of UAV and road vehicle noise that is fit with an augmented linear regression. Analyses based on this integration of A-weighted level and the output of the “Zwicker” loudness model yield similar results: that subjects may have been slightly more sensitive to the durations of the events than the EEH would suppose, but that the EEH cannot be disproven using these data. The time-integrated metrics outperform both time-averaged and centile-based metrics.

Psychoacoustics↗
NASA NTRSDate not supplied

On the Integration of Loudness Over Time for the Prediction of Single-Event Annoyance

Loudness is the quality of human perception that is most related to acoustic intensity and energy, however there is no agreed-upon way of integrating loudness over time for the prediction of noise-induced annoyance. Most noise metrics used today for aircraft certification and regulation employ the “Equal-Energy Hypothesis” (EEH) and sum the acoustical energy of one or more noise events over time to create a single metric value that represents the entire exposure. Using the EEH creates a natural tradeoff between the peak energy and the duration of a single noise event, the “hypothesis” being that this tradeoff optimally predicts annoyance in a wide variety of situations. This work proposes a strategy for integrating a loudness-like time series which is flexible in two ways: First, it includes a parameter b ∈ [0,1]. When b = 0, the metric will return the peak of the time series. At b = .5, the metric will behave in accordance with the EEH. At b = 1, the metric will penalize the duration of the sound more than the EEH would. Second, transformations are given so that the strategy can be computed from, or generate quantities in units analogous to, decibels (or phon), physical units (acoustic pressure/power), or perceptually-scaled units (sone). This approach is demonstrated on a dataset of annoyance responses to single events of UAV and road vehicle noise that is fit with an augmented linear regression. Analyses based on this integration of A-weighted level and the output of the “Zwicker” loudness model yield similar results: that subjects may have been slightly more sensitive to the durations of the events than the EEH would suppose, but that the EEH cannot be disproven using these data. The time-integrated metrics outperform both time-averaged and centile-based metrics.

Psychoacoustics↗
NASA NTRS2025

Jemez Pueblo Agriculture: Monitoring Rangeland Conditions to Inform Drought and Land Management in New Mexico

The Jemez Pueblo, a community located in the semi-arid high desert region of northcentral New Mexico, faces challenges with drought mitigation and livestock management. NASA DEVELOP partnered with the Pueblo of Jemez Natural Resources Department and The Nature Conservancy to provide recent and historical rangeland conditions to aid present decision-making, which relies on cultural practices, site familiarity, available resources, and physical data. This partnership offers the opportunity to support management practices by leveraging remote sensing and virtual fencing technologies. Our project explored Rangeland Analysis Platform (RAP) products incorporating NASA Earth observation Landsat 5 TM, Landsat 7 ETM+, Landsat 8 OLI, and Landsat 9 OLI-2 remote-sensed imagery as an agricultural land management tool. We performed linear regression analysis to evaluate RAP data to field data and explored RAP annual herbaceous biomass, ground cover trends, and climatic factors at the pasture level. We then computed study area summary statistics, performed pixel-by-pixel trend analysis across the study period, and evaluated ground cover trends near water sources. Based on available data, RAP was poorly correlated to bare ground and herbaceous biomass, generally underestimating the former and overestimating the latter. To improve the evaluation of RAP products, we suggest increasing the spatiotemporal distribution of the field dataset. According to RAP, from 1986 to 2023, the site became hotter and drier, bare ground increased, and annual forbs and grasses increased while perennials decreased. RAP products did not agree with field-collected data; however, the trends over time may be useful for informing rangeland management actions.

cattle grazing management↗
NASA NTRS2024

Urban Air Quality Management at Low-Cost Using Micro Air Sensors: A Case Study From Accra, Ghana

Urban air quality management is dependent on the availability of local air pollution data. In many major urban centers of Africa, there is limited to non-existent information on air quality. This is gradually changing in part due to the increasing use of micro air sensors which have the potential to enable the generation of ground-based air quality data at fine scales for understanding local emission trends. Regional literature on the application of the high-resolution data for emission source identification in this region is limited. In this study a micro air sensor was co-located at the Physics Department, University of Ghana with a reference grade instrument to evaluate its performance for estimating PM2.5 pollution accurately at fine scales and the value of this data in identification of local sources and their behavior over time. For this study 15 weeks of data at hourly resolution with approximately 2500 data pairs are generated and analyzed (June 01, 2023, to September 15, 2023). For this time period a coefficient of determination (r 2 ) of 0.83 was generated with a mean absolute error (MAE) of 5.44 μgm -3 between the pre local calibration micro air sensor (i.e. out of box) and the reference-grade instrument. Following currently accepted best practice methods (see e.g., PAS4023) a domain specific (i.e. local) calibration factor was generated using a multi-linear regression model and when this factor is applied to the micro air sensor data, a reduction i.e., improvement in MAE to 1.43 μgm -3 was found. Daily variation was calculated, a receptor model was applied, and time series plots as a function of wind direction were generated, including PM2.5/PM10 ratio scatter and count plots to explore the utility of this observational approach for local source identification. The 3 data sets were compared (out of box, domain calibrated and reference-grade) and it was found that although there were variations in the data reported, source areas highlighted based on these data were similar, with input from local sources such as traffic emissions and biomass burning. As the temporal resolution of observational data associated with these micro air sensors is higher than for reference grade instruments (primarily due to costs and logistics limitations), they have the potential to provide insight into the complex, often hyper localized sources associated with urban areas, such as those found in major African cities.

Source apportionment↗
NASA NTRS1975

Comparison of some biased estimation methods (including ordinary subset regression) in the linear model

Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.

Sidik, S. M.↗
NASA NTRS1976

Linear feedback rate bounds for regressive channels

Bounds for the linear feedback capacity of m-th order Gaussian autoregressive channels are derived. The upper bound is tighter than that found by Tiernan and Schalwijk (1974) for the feedback capacity of a first-order autoregressive Gaussian channel with not necessarily linear processing. The separation between the upper and lower bounds is small, and it is conjectured that the lower bound converges to the feedback capacity of the first-order channel as the number of signals tends to infinity.

Butman, S. A.↗
NASA NTRS2005

A Note on the Relationship between Temperature and Water Vapor in Quasi-Equilibrium and Climate States

An ideal and simple formulation is successfully derived that well represents a quasi-linear relationship found between the domain-averaged water vapor, q (mm), and temperature, T (K), fields obtained from a series of quasi-equilibrium (long-term) simulations for the Tropics using the two-dimensional Goddard Cumulus Ensemble (GCE) model. Earlier model work showed that the forced maintenance of two different wind profiles in the Tropics leads to two different equilibrium states. Investigating this finding required investigation of the slope of the moisture-temperature relations, which turns out to be linear in the Tropics. The extra-tropical climate equilibriums become more complex, but insight on modeling sensitivity can be obtained by linear stepwise regression of the integrated temperature and humidity. A globally curvilinear moisture-temperature distribution, similar to the famous Clausius-Clapeyron curve (i.e., saturated water vapor pressure versus temperature), is then found in this study. Such a genuine finding clarifies that the dynamics are crucial to the climate (shown in the earlier work) but the thermodynamics adjust. The range of validity of this result is further examined herein. The GCE-modeled tropical domain-averaged q and T fields form a linearly-regressed "q-T" slope that genuinely resides within an ideal range of slopes obtained from the aforementioned formulation. A quantity (denoted as dC2/dC1) representing the derivative between the static energy densities due to temperature (C2) and water vapor (C1) for various quasi-equilibrium states can also be obtained. A dC2/dC1 value near unity obtained for the GCE-modeled tropical simulations implies that the static energy densities due to moisture and temperature only differ by a pure constant for various equilibrium states. An overall q-T relation also including extra-tropical regions is, however, found to have a curvilinear relationship. Accordingly, warm/moist regions favor change in water vapor faster than temperature, while cold/dry regions favor an increase in temperature quicker than water vapor.

Shie, C.-L.↗
NASA NTRS1993

On neural networks in identification and control of dynamic systems

This paper presents a discussion of the applicability of neural networks in the identification and control of dynamic systems. Emphasis is placed on the understanding of how the neural networks handle linear systems and how the new approach is related to conventional system identification and control methods. Extensions of the approach to nonlinear systems are then made. The paper explains the fundamental concepts of neural networks in their simplest terms. Among the topics discussed are feed forward and recurrent networks in relation to the standard state-space and observer models, linear and nonlinear auto-regressive models, linear, predictors, one-step ahead control, and model reference adaptive control for linear and nonlinear systems. Numerical examples are presented to illustrate the application of these important concepts.

Phan, Minh↗
NASA NTRS1983

Advanced microwave soil moisture studies

Comparisons of low level L-band brightness temperature (TB) and thermal infrared (TIR) data as well as the following data sets: soil map and land cover data; direct soil moisture measurement; and a computer generated contour map were statistically evaluated using regression analysis and linear discriminant analysis. Regression analysis of footprint data shows that statistical groupings of ground variables (soil features and land cover) hold promise for qualitative assessment of soil moisture and for reducing variance within the sampling space. Dry conditions appear to be more conductive to producing meaningful statistics than wet conditions. Regression analysis using field averaged TB and TIR data did not approach the higher sq R values obtained using within-field variations. The linear discriminant analysis indicates some capacity to distinguish categories with the results being somewhat better on a field basis than a footprint basis.

Dalsted, K. J.↗
NASA NTRS2010

The Prediction Properties of Inverse and Reverse Regression for the Simple Linear Calibration Problem

The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions.

Parker, Peter A.↗
NASA NTRS2005

Tools for Basic Statistical Analysis

Statistical Analysis Toolset is a collection of eight Microsoft Excel spreadsheet programs, each of which performs calculations pertaining to an aspect of statistical analysis. These programs present input and output data in user-friendly, menu-driven formats, with automatic execution. The following types of calculations are performed: Descriptive statistics are computed for a set of data x(i) (i = 1, 2, 3 . . . ) entered by the user. Normal Distribution Estimates will calculate the statistical value that corresponds to cumulative probability values, given a sample mean and standard deviation of the normal distribution. Normal Distribution from two Data Points will extend and generate a cumulative normal distribution for the user, given two data points and their associated probability values. Two programs perform two-way analysis of variance (ANOVA) with no replication or generalized ANOVA for two factors with four levels and three repetitions. Linear Regression-ANOVA will curvefit data to the linear equation y=f(x) and will do an ANOVA to check its significance.

Luz, Paul L.↗
NASA NTRS1980

Predicting major element mineral/melt equilibria - A statistical approach

Empirical equations have been developed for calculating the mole fractions of NaO0.5, MgO, AlO1.5, SiO2, KO0.5, CaO, TiO2, and FeO in a solid phase of initially unknown identity given only the composition of the coexisting silicate melt. The approach involves a linear multivariate regression analysis in which solid composition is expressed as a Taylor series expansion of the liquid compositions. An internally consistent precision of approximately 0.94 is obtained, that is, the nature of the liquidus phase in the input data set can be correctly predicted for approximately 94% of the entries. The composition of the liquidus phase may be calculated to better than 5 mol % absolute. An important feature of this 'generalized solid' model is its reversibility; that is, the dependent and independent variables in the linear multivariate regression may be inverted to permit prediction of the composition of a silicate liquid produced by equilibrium partial melting of a polymineralic source assemblage.

Hostetler, C. J.↗
NASA NTRS1976

A method for the selection of a functional form for a thermodynamic equation of state using weighted linear least squares stepwise regression

A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.

Jacobsen, R. T.↗
NASA NTRS1973

Multiple regression technique for Pth degree polynominals with and without linear cross products

A multiple regression technique was developed by which the nonlinear behavior of specified independent variables can be related to a given dependent variable. The polynomial expression can be of Pth degree and can incorporate N independent variables. Two cases are treated such that mathematical models can be studied both with and without linear cross products. The resulting surface fits can be used to summarize trends for a given phenomenon and provide a mathematical relationship for subsequent analysis. To implement this technique, separate computer programs were developed for the case without linear cross products and for the case incorporating such cross products which evaluate the various constants in the model regression equation. In addition, the significance of the estimated regression equation is considered and the standard deviation, the F statistic, the maximum absolute percent error, and the average of the absolute values of the percent of error evaluated. The computer programs and their manner of utilization are described. Sample problems are included to illustrate the use and capability of the technique which show the output formats and typical plots comparing computer results to each set of input data.

Davis, J. W.↗
NASA NTRS2002

Comparison of Total Solar Irradiance with NASA/NSO Spectromagnetograph Data in Solar Cycles 22 and 23

An earlier study compared NASA/NSO Spectromagnetograph (SPM) data with spacecraft measurements of total solar irradiance (TSI) variations over a 1.5 year period in the declining phase of solar cycle 22. This paper extends the analysis to an eight-year period which also spans the rising and early maximum phases of cycle 23. The conclusions of the earlier work appear to be robust: three factors (sunspots, strong unipolar regions, and strong mixed polarity regions) describe most of the variation in the SPM record, but only the first two are associated with TSI. Additionally, the residuals of a linear multiple regression of TSI against SPM observations over the entire eight-year period show an unexplained, increasing, linear time variation with a rate of about 0.05 W m(exp -2) per year. Separate regressions for the periods before and after 1996 January 01 show no unexplained trends but differ substantially in regression parameters. This behavior may reflect a solar source of TSI variations beyond sunspots and faculae but more plausibly results from uncompensated non-solar effects in one or both of the TSI and SPM data sets.

Jones, Harrison P.↗
NASA NTRS2008

Sparse Regression as a Sparse Eigenvalue Problem

We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization

Exact Sparse Least Squares (ESLS)↗