SEARCH · Search NASA
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.
Report discusses formulas for estimation of Allan variances. Presents algorithms for closed-form approximations of numbers of degrees of freedom characterizing results obtained when various estimators applied to five power-law components of classical mathematical model of clock noise.
An investigation of the Allan variance method as a possible means for characterizing fluctuations in radiometric noise diodes has been performed. The goal is to separate fluctuation components into white noise, flicker noise, and random-walk noise. The primary means is by discrete-time processing, and the study focused primarily on the digital processes involved. Noise satisfying the requirements was generated by direct convolution, fast Fourier transformation (FFT) processing in the time domain, and FFT processing in the frequency domain. Some of the numerous results obtained are presented along with the programs used in the study.
Cosmic anisotrophy produces an excess variance sq sigma(sub sky) in the Delta maps produced by the Differential Microwave Radiometer (DMR) on cosmic background explorer (COBE) that is over and above the instrument noise. After smoothing to an effective resolution of 10 deg, this excess sigma(sub sky)(10 deg), provides an estimate for the amplitude of the primordial density perturbation power spectrum with a cosmic uncertainty of only 12%. We employ detailed Monte Carlo techniques to express the amplitude derived from this statistic in terms of the universal root mean square (rms) quadrupole amplitude, (Q sq/RMS)(exp 0.5). The effects of monopole and dipole subtraction and the non-Gaussian shape of the DMR beam cause the derived (Q sq/RMS)(exp 0.5) to be 5%-10% larger than would be derived using simplified analytic approximations. We also investigate the properties of two other map statistics: the actual quadrupole and the Boughn-Cottingham statistic. Both the sigma(sub sky)(10 deg) statistic and the Boughn-Cottingham statistic are consistent with the (Q sq/RMS)(exp 0.5) = 17 +/- 5 micro K reported by Smoot et al. (1992) and Wright et al. (1992).
We summarize recent Ulysses observations of the variances over large temporal scales in the interplanetary magnetic field components and their increase as Ulysses approached the South Solar Pole. A model of these fluctuations is shown to provide a very good fit to the observed amplitude and temporal variation of the fluctuations. In addition, the model predicts that the transport of cosmic rays in the heliosphere will be significantly altered by this level of fluctuations. In addition to altering the inward diffusion and drift access of cosmic rays over the solar poles, we find that the magnetic fluctuations also imply a large latitudinal diffusion, caused primarily by the associated field-line random walk.
We evaluate with simulated data a new type of sample variance for the characterization of frequency stability. The new statistic (referred to as TOTALVAR and its square root TOTALDEV) is a better predictor of long-term frequency variations than the present sample Allan deviation. The statistical model uses the assumption that a time series of phase or frequency differences is wrapped (periodic) with overall frequency difference removed. We find that the variability at long averaging times is reduced considerably for the five models of power-law noise commonly encountered with frequency standards and oscillators.
Unique and innovative system programmatic estimation is conducted using the variance of the packaged technologies. Covariance analysis is performed on the subsystems and components comprising the system of interest. Technological "return" and "variation" parameters are estimated. These parameters are combined with the model error to arrive at a measure of system development stability. The resulting estimates provide valuable information concerning the potential cost growth of the system under development.
Unique and innovative system programmatic estimation is conducted using the variance of the packaged technologies. Covariance analysis is performed oil the subsystems and components comprising the system of interest. Technological "returns" and "variation" parameters, are estimated. These parameters are combined with the model error to arrive at a measure of system development stability. The resulting estimates provide valuable information concerning the potential cost growth of the system under development.
Data assimilation is all about understanding the error characteristics of the data and models that are used in the assimilation process. Reliable error estimates are needed to implement observational quality control, bias correction of observations and model fields, and intelligent data selection. Meaningful covariance specifications are obviously required for the analysis as well, since the impact of any single observation strongly depends on the assumed structure of the background errors. Operational atmospheric data assimilation systems still rely primarily on climatological background error covariances. To obtain error estimates that reflect both the character of the flow and the current state of the observing system, it is necessary to solve three problems: (1) how to account for the short-term evolution of errors in the initial conditions; (2) how to estimate the additional component of error caused by model defects; and (3) how to compute the error reduction in the analysis due to observational information. Various approaches are now available that provide approximate solutions to the first and third of these problems. However, the useful accuracy of these solutions very much depends on the size and character of the model errors and the ability to account for them. Model errors represent the real-world forcing of the error evolution in a data assimilation system. Clearly, meaningful model error estimates and/or statistics must be based on information external to the model itself. The most obvious information source is observational, and since the volume of available geophysical data is growing rapidly, there is some hope that a purely statistical approach to model error estimation can be viable. This requires that the observation errors themselves are well understood and quantifiable. We will discuss some of these challenges and present a new sequential scheme for estimating model error variances from observations in the context of an atmospheric data assimilation system.
The accuracy of traditional multispectral maximum-likelihood image classification is limited by the skewed statistical distributions of reflectances from the complex heterogenous mixture of land cover types in urban areas. This work examines the utility of local variance, fractal dimension and Moran's I index of spatial autocorrelation in segmenting multispectral satellite imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze Landsat 7 imagery of Atlanta, Georgia. Although segmentation of panchromatic images is possible using indicators of spatial complexity, different land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification. The addition of fractal dimension measures is particularly effective at resolving land cover classes within urbanized areas, as compared to per-pixel spectral classification techniques.
Proposed method of total observation and forecast error variance correction is based on the assumption about normal distribution of "observed-minus-forecast" residuals (O-F), where O is an observed value and F is usually a short-term model forecast. This assumption can be accepted for several types of observations (except humidity) which are not grossly in error. Degree of nearness to normal distribution can be estimated by the symmetry or skewness (luck of symmetry) a(sub 3) = mu(sub 3)/sigma(sup 3) and kurtosis a(sub 4) = mu(sub 4)/sigma(sup 4) - 3 Here mu(sub i) = i-order moment, sigma is a standard deviation. It is well known that for normal distribution a(sub 3) = a(sub 4) = 0.
We give results of recent work on a newly developed frequency stability characterization, called Total variance, whose main advantages are improved confidence at and near the longest averaging time of half the data duration, and lower sensitivity to drift removal.
Magnetic field fluctuations at high heliographic latitudes are discussed in terms of the latitude and radial dependence of their variances, as observed by the Ulysses spacecraft.
This paper is a tutorial introduction to the analysis of variance (ANOVA), intended as a reference for aerospace researchers who are being introduced to the analytical methods of the Modern Design of Experiments (MDOE), or who may have other opportunities to apply this method. One-way and two-way fixed-effects ANOVA, as well as random effects ANOVA, are illustrated in practical terms that will be familiar to most practicing aerospace researchers.
The realism of ray-based spectral parameterization of convective gravity wave drag, which considers the updated moving speed of the convective source and multiple wave propagation directions, is tested against the Atmospheric Infrared Sounder (AIRS) onboard the Aqua satellite. Offline parameterization calculations are performed using the global reanalysis data for January and July 2005, and gravity wave temperature variances (GWTVs) are calculated at z = 2.5 hPa (unfiltered GWTV). AIRS-filtered GWTV, which is directly compared with AIRS, is calculated by applying the AIRS visibility function to the unfiltered GWTV. A comparison between the parameterization calculations and AIRS observations shows that the spatial distribution of the AIRS-filtered GWTV agrees well with that of the AIRS GWTV. However, the magnitude of the AIRS-filtered GWTV is smaller than that of the AIRS GWTV. When an additional cloud top gravity wave momentum flux spectrum with longer horizontal wavelength components that were obtained from the mesoscale simulations is included in the parameterization, both the magnitude and spatial distribution of the AIRS-filtered GWTVs from the parameterization are in good agreement with those of the AIRS GWTVs. The AIRS GWTV can be reproduced reasonably well by the parameterization not only with multiple wave propagation directions but also with two wave propagation directions of 45 degrees (northeast-southwest) and 135 degrees (northwest-southeast), which are optimally chosen for computational efficiency.
The bispectral method retrieves cloud optical thickness (τ) and cloud droplet effective radius (re) simultaneously from a pair of cloud reflectance observations, one in a visible or near-infrared (VIS/NIR) band and the other in a shortwave infrared (SWIR) band. A cloudy pixel is usually assumed to be horizontally homogeneous in the retrieval. Ignoring subpixel variations of cloud reflectances can lead to a significant bias in the retrieved τ and re. In the literature, the retrievals of τ and re are often assumed to be independent and considered separately when investigating the impact of subpixel cloud reflectance variations on the bispectral method. As a result, the impact on τ is contributed only by the subpixel variation of VIS/NIR band reflectance and the impact on re only by the subpixel variation of SWIR band reflectance. In our new framework, we use the Taylor expansion of a two-variable function to understand and quantify the impacts of subpixel variances of VIS/NIR and SWIR cloud reflectances and their covariance on the τ and re retrievals. This framework takes into account the fact that the retrievals are determined by both VIS/NIR and SWIR band observations in a mutually dependent way. In comparison with previous studies, it provides a more comprehensive understanding of how subpixel cloud reflectance variations impact the τ and re retrievals based on the bispectral method. In particular, our framework provides a mathematical explanation of how the subpixel variation in VIS/NIR band influences the re retrieval and why it can sometimes outweigh the influence of variations in the SWIR band and dominate the error in re retrievals, leading to a potential contribution of positive bias to the re retrieval. We test our framework using synthetic cloud fields from a large-eddy simulation and real observations from Moderate Resolution Imaging Spectroradiometer. The predicted results based on our framework agree very well with the numerical simulations. Our framework can be used to estimate the retrieval uncertainty from subpixel reflectance variations in operational satellite cloud products and to help understand the differences in τ and re retrievals between two instruments.
The so-called bi-spectral method retrieves cloud optical thickness (τ) and cloud droplet effective radius (re) simultaneously from a pair of cloud reflectance observations, one in a visible or near infrared (VIS/NIR) band and the other in a shortwave-infrared (SWIR) band. A cloudy pixel is usually assumed to be horizontally homogeneous in the retrieval. Ignoring sub-pixel variations of cloud reflectances can lead to a significant bias in the retrieved τ and re. In this study, we use the Taylor expansion of a two-variable function to understand and quantify the impacts of sub-pixel variances of VIS/NIR and SWIR cloud reflectances and their covariance on the τ and re retrievals. This framework takes into account the fact that the retrievals are determined by both VIS/NIR and SWIR band observations in a mutually dependent way. In comparison with previous studies, it provides a more comprehensive understanding of how sub-pixel cloud reflectance variations impact the τ and re retrievals based on the bi-spectral method. In particular, our framework provides a mathematical explanation of how the sub-pixel variation in VIS/NIR band influences the re retrieval and why it can sometimes outweigh the influence of variations in the SWIR band and dominate the error in re retrievals, leading to a potential contribution of positive bias to the re retrieval.
A new variant of the multilevel Monte Carlo estimator [5, 3, 9, 12] is presented for the estimation of expectation statistics that utilizes sample reuse in specified levels, explicitly removes approximation error bias associated with numerically computed output quantities of interest that have an asymptotic limit behavior, and permits a low variance estimate of the asymptotic rate of convergence to that limit. In addition, it is shown that this new multilevel Monte Carlo variant can yield a computational cost savings. A review of Monte Carlo and multilevel Monte Carlo estimators is presented that includes analysis of expected value, expected mean squared error, and the calculation of optimized multilevel sample size parameters. The multilevel Monte Carlo estimator produces estimates of expectation for numerically approximated output quantities of interest that are biased by approximation error. When the quantity of interest can be modeled as the asymptotic limit of numerically approximated output quantities of interest, it is theoretically possible to remove this approximation error bias in the multilevel Monte Carlo estimator. In actual implementations, however, this procedure is unreliable due to statistical variability and inaccuracy in estimating the needed asymptotic limit. Analysis and numerical experiment show that the proposed variant of the multilevel Monte Carlo method greatly reduces (in some cases eliminates) the statistical variability in this limit estimation.
This work gives an algorithm for computing the degrees of freedom of estimators of Allan and Hadamard variances, including their modified versions. A consistent aproach is used throughout.