Search NASA⌕ Search

SEARCH · Search NASA

Results for “VARIANCE”

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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Crop acreage estimation using a Landsat-based estimator as an auxiliary variable

The problem of improving upon the ground survey estimates of crop acreages by utilizing Landsat data is addressed. Three estimators, called regression, ratio, and stratified ratio, are studied for bias and variance, and their relative efficiencies are compared. The approach is to formulate analytically the estimation problem that utilizes ground survey data, as collected by the U.S. Department of Agriculture, and Landsat data, which provide complete coverage for an area of interest, and then to conduct simulation studies. It is shown over a wide range of parametric conditions that the regression estimator is the most efficient unless there is a low correlation between the actual and estimated crop acreages in the sampled area segments, in which case the ratio and stratified ratio estimators are better. Furthermore, it is seen that the regression estimator is potentially biased due to estimating the regression coefficient from the training sample segments. Estimation of the variance of the regression estimator is also investigated. Two variance estimators are considered, the large sample variance estimator and an alternative estimator suggested by Cochran. The large sample estimate of variance is found to be biased and inferior to the Cochran estimate for small sample sizes.

Chhikara, R. S.↗
NASA NTRS1989

Data structure characterization of miltispectral data using principal component and principal factor analysis

Both principal component analysis (PCA) and principal factor analysis (PFA) were used to analyze an experimental multispectral data structure in terms of common and unique variance. Only the common variance of the multispectral data was associated with the principal factor, while higher-order principal components were associated with both common and unique variance. The unique variance was found to represent small spectral variations within each cover type as well as noise vectors, and was most abundant in the lower-order principal components. The lower-order principal components can be useful in research designed to discriminate minor physical variations within features, and to highlight localized change when using multitemporal-multispectral data. Conversely, PFA of the multispectral data provided an insight into a great potential for discriminating basic land-cover types by excluding the unique variance which was related to the noise and minor spectral variations.

Lee, Jae K.↗
NASA NTRS1994

Atmospheric pressure loading effects on Global Positioning System coordinate determinations

Earth deformation signals caused by atmospheric pressure loading are detected in vertical position estimates at Global Positioning System (GPS) stations. Surface displacements due to changes in atmospheric pressure account for up to 24% of the total variance in the GPS height estimates. The detected loading signals are larger at higher latitudes where pressure variations are greatest; the largest effect is observed at Fairbanks, Alaska (latitude 65 deg), with a signal root mean square (RMS) of 5 mm. Out of 19 continuously operating GPS sites (with a mean of 281 daily solutions per site), 18 show a positive correlation between the GPS vertical estimates and the modeled loading displacements. Accounting for loading reduces the variance of the vertical station positions on 12 of the 19 sites investigated. Removing the modeled pressure loading from GPS determinations of baseline length for baselines longer than 6000 km reduces the variance on 73 of the 117 baselines investigated. The slight increase in variance for some of the sites and baselines is consistent with expected statistical fluctuations. The results from most stations are consistent with approximately 65% of the modeled pressure load being found in the GPS vertical position measurements. Removing an annual signal from both the measured heights and the modeled load time series leaves this value unchanged. The source of the remaining discrepancy between the modeled and observed loading signal may be the result of (1) anisotropic effects in the Earth's loading response, (2) errors in GPS estimates of tropospheric delay, (3) errors in the surface pressure data, or (4) annual signals in the time series of loading and station heights. In addition, we find that using site dependent coefficients, determined by fitting local pressure to the modeled radial displacements, reduces the variance of the measured station heights as well as or better than using the global convolution sum.

Vandam, Tonie M.↗
NASA NTRS1995

A new model for Mars atmospheric dust based upon analysis of ultraviolet through infrared observations from Mariner 9, Viking, and Phobos

We propose key modifications to the Toon et al. (1977) model of the particle size distribution and composition of Mars atmospheric dust, based on a variety of spacecraft and wavelength observations of the dust. A much broader (r(sub eff) variance approximately 0.8 micrometers), smaller particle size (r(sub mode) approximately 0.02 micrometers) distribution coupled with a 'palagonite-like' composition is argued to fit the complete ultraviolet-to-30-micrometer absorption properties of the dust better than the montmorillonite-basalt, r(sub eff) variance = 0.4 micrometers, r(sub mode) = 0.40 dust model of Toon et al. Mariner 9 (infrared interferometer spectrometer) IRIS spectra of high atmospheric dust opacities during the 1971-1972 Mars global dust storm are analyzed in terms of the Toon et al. dust model, and a Hawaiian palagonite sample (Rousch et al., 1991) with two different size distribution models incorporating smaller dust particle sizes. Viking Infrared Thermal Mapper (IRTM) emmission-phase-function (EPF) observations at 9 micrometers are analyzed to retrieve 9-micrometer dust opacities coincident with solar band dust opacities obtained from the same EPF sequences (Clancy and Lee, 1991). These EPF dust opacities provide an independent measurement of the visible/9-micrometer extinction opacity ratio (greater than or = 2) for Mars atmospheric dust, which is consistent with a previous measurement by Martin (1986). Model values for the visible/9-micrometer opacity ratio and the ultraviolet and visible single-scattering albedos are calculated for the palagonite model with the smaller particle size distributions compared to the same properties for the Toon et al. model of dust. The montmorillonite model of the dust is found to fit the detailed shape of the dust 9-micrometer absorption well. However, it predicts structured, deep aborptions at 20 micrometers which are not observed and requires a separate ultraviolet-visible absorbing component to match the observed behavior of the dust in this wavelength region. The modeled palagonite does not match the 8-to 9-micrometer absorption presented by the dust in the IRIS spectra, probably due to its low SiO2 content (31%). However, it does provide consistent levels of ultraviolet/visible absorption, 9-to 12-micrometer absorption, and a lack of structured absorption at 20 micrometers. The ratios of dust extinction opacities at visible, 9 micrometers, and 30 micrometers are strongly affected by the dust particle size distribution. The Toon et al. dust size distribution (r(sub mode) = 0.40,r(sub eff) variance = 0.4 micrometers, r(sub cwmu) = 2.7 micrometers) predicts the correct ratio of the 9- to 30-micrometer opacity, but underpredicts the visible/9-micrometer opacity ratio considerably (1 versus greater than or = 2). A similar particle distribution width with smaller particle sizes (r(sub mode) = 0.17, r(sub eff) variance = 0.4 micrometers, r(sub cwmu) = 1.2 micrometers) will fit the observed visible/9-micrometer opacity ratio, but overpredicts the observed 9-micrometer/30-micrometer opacity ratio. A smaller and much broader particle size distribution (r(sub mode) = 0.002, r(sub eff) variance = 0.8 micrometers, r(sub cwmu) = 1.8 micrometers) can fit both dust opacity ratios. Overall, the nanocrystalline structure of palagonite coupled with a smaller, broader distribution of dust particle sizes provides a more consistent fit than the Toon et al. model of the dust to the IRIS spectra, the observed visible/9-micrometer dust opacity ratio, the Phobos occulation measurements of the dust particle sizes (Chassefiere et al., 1992), and the weakness of surface near IR absorptions expected for clay minerals (Clark, 1992; Bell and Crisp, 1993).

Clancy, R. T.↗
NASA NTRS1995

A new model for Mars atmospheric dust based upon analysis of ultraviolet through infrared observations from Mariner 9, Viking, and Phobos

We propose key modifications to the Toon et al. (1977) model of the particle size distribution and composition of Mars atmospheric dust, based on a variety of spacecraft and wavelength observations of the dust. A much broader (r(sub eff)variance-0.8 micron), smaller particle size (r(sub mode)-0.02 microns) distribution coupled with a "palagonite-like" composition is argued to fit the complete ultraviolet-to-30-micron absorption properties of the dust better than the montmorillonite-basalt r(sub eff)variance= 0.4 micron, r(sub mode)= 0.40 micron dust model of Toon et al. Mariner 9 (infrared interferometer spectrometer) IRIS spectra of high atmospheric dust opacities during the 1971 - 1972 Mars global dust storm are analyzed in terms of the Toon et al. dust model, and a Hawaiian palagonite sample with two different size distribution models incorporating smaller dust particle sizes. Viking Infrared Thermal Mapper (IRTM) emission-phase-function (EPF) observations at 9 microns are analyzed to retrieve 9-micron dust opacities coincident with solar band dust opacities obtained from the same EPF sequences. These EPF dust opacities provide an independent measurement of the visible/9-microns extinction opacity ratio (> or equal to 2) for Mars atmospheric dust, which is consistent with a previous measurement by Martin (1986). Model values for the visible/9-microns opacity ratio and the ultraviolet and visible single-scattering albedos are calculated for the palagonite model with the smaller particle size distributions and compared to the same properties for the Toon et al. model of dust. The montmorillonite model of the dust is found to fit the detailed shape of the dust 9-micron absorption well. However, it predicts structured, deep absorptions at 20 microns which are not observed and requires a separate ultraviolet-visible absorbing component to match the observed behavior of the dust in this wavelength region. The modeled palagonite does not match the 8- to 9-micron absorption presented by the dust in the IRIS spectra, probably due to its low SiO2 content (31%). However, it does provide consistent levels of ultraviolet/visible absorption, 9- to 12-micron absorption, and a lack of structured absorption at 20 microns. The ratios of dust extinction opacities at visible, 9 microns, and 30 microns are strongly affected by the dust particle size distribution. The Toon et al. dust size distribution (r(sub mode)= 0.40, r(sub eff)variance= 0.4 microns, r(sub cw mu)= 2.7 microns) predicts the correct ratio of the 9- to 30-micron opacity, but underpredicts the visible/9-micron opacity ratio considerably (1 versus > or equal to 2). A similar particle distribution width with smaller particle sizes (r(sub mode)= 0.17, r(sub eff)variance= 0.4 microns, r(sub cw mu)=1.2 microns) will fit the observed visible/9-micron opacity ratio, but overpredicts the observed 9-micron/30-micron opacity ratio. A smaller and much broader particle size distribution (r(sub mode)= 0.02, r(sub eff)variance= 0.8 microns, r(sub cw mu)= 1.8 microns) can fit both dust opacity ratios. Overall, the nanocrystalline structure of palagonite coupled with a smaller, broader distribution of dust particle sizes provides a more consistent fit than the Toon et al. model of the dust to the IRIS spectra, the observed visible/9-micron dust opacity ratio, the Phobos occultation measurements of dust particle sizes, and the weakness of surface near IR absorptions expected for clay minerals.

Clancy, R. T.↗
NASA NTRS2012

The Transport of Density Fluctuations Throughout the Heliosphere

The solar wind is recognized as a turbulent magnetofluid, for which the properties of the turbulent velocity and magnetic field fluctuations are often described by the equations of incompressible magnetohydrodynamics (MHD). However, low-frequency density turbulence is also ubiquitous. On the basis of a nearly incompressible formulation of MHD in the expanding inhomogeneous solar wind, we derive the transport equation for the variance of the density fluctuations (Rho(exp 2)). The transport equation shows that density fluctuations behave as a passive scalar in the supersonic solar wind. In the absence of sources of density turbulence, such as within 1AU, the variance (Rho(exp 2)) approximates r(exp -4). In the outer heliosphere beyond 1 AU, the shear between fast and slow streams, the propagation of shocks, and the creation of interstellar pickup ions all act as sources of density turbulence. The model density fluctuation variance evolves with heliocentric distance within approximately 300 AU as (Rho(exp 2)) approximates r(exp -3.3) after which it flattens and then slowly increases. This is precisely the radial profile for the density fluctuation variance observed by Voyager 2. Using a different analysis technique, we confirm the radial profile for Rho(exp 2) of Bellamy, Cairns, & Smith using Voyager 2 data. We conclude that a passive scalar description for density fluctuations in the supersonic solar wind can explain the density fluctuation variance observed in both the inner and the outer heliosphere.

Zank, G. P.↗
NASA NTRS2015

The Pattern Across the Continental United States of Evapotranspiration Variability Associated with Water Availability

The spatial pattern across the continental United States of the interannual variance of warm season water-dependent evapotranspiration, a pattern of relevance to land-atmosphere feedback, cannot be measured directly. Alternative and indirect approaches to estimating the pattern, however, do exist, and given the uncertainty of each, we use several such approaches here. We first quantify the water dependent evapotranspiration variance pattern inherent in two derived evapotranspiration datasets available from the literature. We then search for the pattern in proxy geophysical variables (air temperature, stream flow, and NDVI) known to have strong ties to evapotranspiration. The variances inherent in all of the different (and mostly independent) data sources show some differences but are generally strongly consistent they all show a large variance signal down the center of the U.S., with lower variances toward the east and (for the most part) toward the west. The robustness of the pattern across the datasets suggests that it indeed represents the pattern operating in nature. Using Budykos hydroclimatic framework, we show that the pattern can largely be explained by the relative strength of water and energy controls on evapotranspiration across the continent.

Air Temperature↗
NASA NTRS2017

Sensitivity Analysis and Uncertainty Quantification of a Mars Ascent Vehicle Concept

The design of a conceptual Mars ascent vehicle is a challenging problem. In order to aid the vehicle and mission concept design it is important to understand the driving design parameters and the expected performance in the presence of model errors and uncertainties. An existing six degree of freedom simulation model is analyzed on a statistical basis using the methods available in the Design Analysis Kit for Optimization and Terascale Applications toolkit. The methods utilized include conventional Monte Carlo techniques, metamodeling via polynomial chaos expansions, and global variance-based sensitivity analyses. Two additional analysis methods referred to as “Monte Carlo filtering” and ”Classification trees” are used to determine which uncertain parameters are driving the performance of the vehicle. Monte Carlo filtering provides a methodology to determine which parameters cause qualitatively different behavior while the classification trees use heuristics to partition the input space and assign probabilities to each partition. These methods serve as qualitative descriptors of model sensitivity while variance-based global sensitivity analysis seeks a quantitative mapping from total output variance to the variance of individual inputs. Application of these techniques to several outputs of a Mars ascent vehicle concept simulation indicates that only a select few input factors dominate their variance.

Noyes, Connor↗
NASA NTRS1979

Large Area Crop Inventory Experiment (LACIE). Evaluation of three-category classification

The author has identified the following signficant results. Examination of both machine estimates and stratified areal estimates produced by clustering and classification reveal no significant differences between the proportion estimates and ground truth estimates. When testing the variances of the machine estimates, a significant reduction in the variances was found when the number of starting dots was increased from 30 to 45. The variances were again reduced, although not significantly, when the number of starting dots was increased from 45 to 60. From these results, 60 starting dots are recommended for a three-category classifier. When examining the variances of the estimates for the four estimation procedures (using 60 dots), no significant differences were found between procedures. Thus, only the machine clustering may be used to produce an estimate, and the stratified areal estimate computations and maximum likelihood classification can be deleted.

Havens, K. A.↗
NASA NTRS1980

Microstructure of the interplanetary magnetic field near 4 and 5 AU

Interplanetary magnetic field fluctuations near 4 and 5 AU are investigated on the basis of Pioneer 10 and 11 vector magnetic field measurements in order to identify extant wave modes and propagation directions as functions of frequency in the range 0.00004 to 0.009 Hz. Analysis of the approximately 500 spectral matrices as functions of frequency obtained from each spacecraft indicates the distributions of maximum variance directions to be peaked along the normal to the plane of the minimum variance direction and the mean magnetic field, as would be expected for a planar, small-amplitude Alfven wave with a minimum variance direction close to the wave vector. It is thus inferred that single small-amplitude Alfven waves are occasionally present in the temporal and frequency bands analyzed, however waves with wave vectors not well approximated by the minimum variance direction, Alfven wave ensembles, finite-amplitude waves and nonplanar fluctuations may also be present. Observations are also noted to suggest the predominance of the Alfven mode over the fast and slow modes, however do not support theoretical models of outward propagating plane Alfven waves of solar origin.

Parker, G. D.↗
NASA NTRS1982

The effects of multiplicative motor noise on the optimal human operator model

The effects of a multiplicative motor noise model on the optimal-control human operator model were analyzed. A study of the interaction between multiplicative motor noise variance, plant dynamics, and predicted operator response behavior shows that, in general, an increase in motor noise variance produces a decrease in operator gain and a decrease in high-frequency remnant. An increase in multiplicative motor noise variance is also reflected by an increase in the effective motor time constant; in the absence of a cost penalty on commanded control, the motor time constant equals the motor noise variance.

Caglayan, A. K.↗
NASA NTRS1982

Factors controlling degree of correlation between ISEE 1 and ISEE 3 interplanetary magnetic field measurements

Correlation variability between ISEE 1 and 3 IMF measurements is investigated, and factors governing the variability are discussed. About 200 two-hour periods when correlation was good, and 200 when correlation was poor, are examined, and both IMF variance and spacecraft separation distance in the plane perpendicular to the earth-sun line exert substantial control. The scale size of magnetic features is larger when variance is high, and abrupt changes in the correlation coefficient from poor to good or good to poor in adjacent two-hour intervals appear to be governed by the sense of change of IMF variance and vice versa. During periods of low variance, good correlations are most likely to occur when the distance between ISEE 1 and 3 perpendicular to the IMF is less than 20 earth radii.

Crooker, N. U.↗
NASA NTRS1983

On the error in crop acreage estimation using satellite (LANDSAT) data

The problem of crop acreage estimation using satellite data is discussed. Bias and variance of a crop proportion estimate in an area segment obtained from the classification of its multispectral sensor data are derived as functions of the means, variances, and covariance of error rates. The linear discriminant analysis and the class proportion estimation for the two class case are extended to include a third class of measurement units, where these units are mixed on ground. Special attention is given to the investigation of mislabeling in training samples and its effect on crop proportion estimation. It is shown that the bias and variance of the estimate of a specific crop acreage proportion increase as the disparity in mislabeling rates between two classes increases. Some interaction is shown to take place, causing the bias and the variance to decrease at first and then to increase, as the mixed unit class varies in size from 0 to 50 percent of the total area segment.

Chhikara, R.↗
NASA NTRS1983

A comparison of coronal and interplanetary current sheet inclinations

The HAO white light K-coronameter observations show that the inclination of the heliospheric current sheet at the base of the corona can be both large (nearly vertical with respect to the solar equator) or small during Cararington rotations 1660 - 1666 and even on a single solar rotation. Voyager 1 and 2 magnetic field observations of crossing of the heliospheric current sheet at distances from the Sun of 1.4 and 2.8 AU. Two cases are considered, one in which the corresponding coronameter data indicate a nearly vertical (north-south) current sheet and another in which a nearly horizontal, near equatorial current sheet is indicated. For the crossings of the vertical current sheet, a variance analysis based on hour averages of the magnetic field data gave a minimum variance direction consistent with a steep inclination. The horizontal current sheet was observed by Voyager as a region of mixed polarity and low speeds lasting several days, consistent with multiple crossings of a horizontal but irregular and fluctuating current sheet at 1.4 AU. However, variance analysis of individual current sheet crossings in this interval using 1.92 see averages did not give minimum variance directions consistent with a horizontal current sheet.

Behannon, K. W.↗
NASA NTRS1983

A comparison of coronal and interplanetary current sheet inclinations

The HAO white light K-coronameter observations show that the inclination of the heliospheric current sheet at the base of the corona can be both large (nearly vertical with respect to the solar equator) or small during Cararington rotations 1660 - 1666 and even on a single solar rotation. Voyager 1 and 2 magnetic field observations of crossing of the heliospheric current sheet at distances from the sun of 1.4 and 2.8 AU. Two cases are considered, one in which the corresponding coronameter data indicate a nearly vertical (north-south) current sheet and another in which a nearly horizontal, near equatorial current sheet is indicated. For the crossings of the vertical current sheet, a variance analysis based on hour averages of the magnetic field data gave a minimum variance direction consistent with a steep inclination. The horizontal current sheet was observed by Voyager as a region of mixed polarity and low speeds lasting several days, consistent with multiple crossings of a horizontal but irregular and fluctuating current sheet at 1.4 AU. However, variance analysis of individual current sheet crossings in this interval using 1.92 see averages did not give minimum variance directions consistent with a horizontal current sheet. Previously announced in STAR as N83-31566

Behannon, K. W.↗
NASA NTRS1983

Interannual variability and predictability of 500 mb geopotential heights over the Northern Hemisphere

The interannual variability of monthly mean 500 mb heights in a 15-year sample of observed data is compared to the variance expected from sampling errors associated with high-frequency fluctuations using the analysis of variance approach. The monthly mean 'signal' stands out significantly from the 'noise' over a substantial fraction of the Northern Hemisphere during the winter. The expected spectrum of variance at very low frequencies is assumed to be white at frequencies lower than per (30 days) rather than the per (96 days) cutoff used by Madden. This difference is justified by observing that the effective time between independent samples T(0) is relatively insensitive to changes in the maximum lag over which the local autocorrelation is integrated to calculate T(0). Further non-randomness in the variance of 500 mb heights is evidenced by the correlation between monthly mean height and contemporaneous daily variability.

Shukla, J.↗
NASA NTRS1984

Estimating optimal sampling unit sizes for satellite surveys

This paper reports on an approach for minimizing data loads associated with satellite-acquired data, while improving the efficiency of global crop area estimates using remotely sensed, satellite-based data. Results of a sampling unit size investigation are given that include closed-form models for both nonsampling and sampling error variances. These models provide estimates of the sampling unit sizes that effect minimal costs. Earlier findings from foundational sampling unit size studies conducted by Mahalanobis, Jessen, Cochran, and others are utilized in modeling the sampling error variance as a function of sampling unit size. A conservative nonsampling error variance model is proposed that is realistic in the remote sensing environment where one is faced with numerous unknown nonsampling errors. This approach permits the sampling unit size selection in the global crop inventorying environment to be put on a more quantitative basis while conservatively guarding against expected component error variances.

Hallum, C. R.↗
NASA NTRS1984

Effect of mixed (boundary) pixels on crop proportion estimation

In estimating acreage proportions of crop types in a segment using Landsat data, considerable problem is caused by the presence of mixed pixels. Due to lack of understanding of their spectral characteristics, mixed pixels have been treated in the past as pure while clustering and classifying the segment data. This paper examines this approach of treating mixed pixels as pure pixels and the effect of mixed pixels on the bias and variance of a crop type proportion estimate. First, the spectral response of a boundary pixel is modeled and an analytical expression for the bias and variance of a proportion estimate is obtained. This is followed by a numerical illustration of the effect of mixed pixels on bias and variance. It is shown that as the size of the mixed pixel class increases in a segment, the variance increases, however, such increase does not always affect the bias of the proportion estimate.

Chhikara, R. S.↗