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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Applications of non-parametric statistics and analysis of variance on sample variances

Nonparametric methods that are available for NASA-type applications are discussed. An attempt will be made here to survey what can be used, to attempt recommendations as to when each would be applicable, and to compare the methods, when possible, with the usual normal-theory procedures that are avavilable for the Gaussion analog. It is important here to point out the hypotheses that are being tested, the assumptions that are being made, and limitations of the nonparametric procedures. The appropriateness of doing analysis of variance on sample variances are also discussed and studied. This procedure is followed in several NASA simulation projects. On the surface this would appear to be reasonably sound procedure. However, difficulties involved center around the normality problem and the basic homogeneous variance assumption that is mase in usual analysis of variance problems. These difficulties discussed and guidelines given for using the methods.

Myers, R. H.↗
NASA NTRS2008

Global Gravity Wave Variances from Aura MLS: Characteristics and Interpretation

The gravity wave (GW)-resolving capabilities of 118-GHz saturated thermal radiances acquired throughout the stratosphere by the Microwave Limb Sounder (MLS) on the Aura satellite are investigated and initial results presented. Because the saturated (optically thick) radiances resolve GW perturbations from a given altitude at different horizontal locations, variances are evaluated at 12 pressure altitudes between 21 and 51 km using the 40 saturated radiances found at the bottom of each limb scan. Forward modeling simulations show that these variances are controlled mostly by GWs with vertical wavelengths z 5 km and horizontal along-track wavelengths of y 100-200 km. The tilted cigar-shaped three-dimensional weighting functions yield highly selective responses to GWs of high intrinsic frequency that propagate toward the instrument. The latter property is used to infer the net meridional component of GW propagation by differencing the variances acquired from ascending (A) and descending (D) orbits. Because of improved vertical resolution and sensitivity, Aura MLS GW variances are 5?8 times larger than those from the Upper Atmosphere Research Satellite (UARS) MLS. Like UARS MLS variances, monthly-mean Aura MLS variances in January and July 2005 are enhanced when local background wind speeds are large, due largely to GW visibility effects. Zonal asymmetries in variance maps reveal enhanced GW activity at high latitudes due to forcing by flow over major mountain ranges and at tropical and subtropical latitudes due to enhanced deep convective generation as inferred from contemporaneous MLS cloud-ice data. At 21-28-km altitude (heights not measured by the UARS MLS), GW variance in the tropics is systematically enhanced and shows clear variations with the phase of the quasi-biennial oscillation, in general agreement with GW temperature variances derived from radiosonde, rocketsonde, and limb-scan vertical profiles.

MLS (MICROWAVE LIMB SOUNDER)↗
NASA NTRS1996

Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation

The Global Positioning System (GPS) Master Control Station (MCS) currently makes significant use of the Allan Variance. This two-sample variance equation has proven excellent as a handy, understandable tool, both for time domain analysis of GPS cesium frequency standards, and for fine tuning the MCS's state estimation of these atomic clocks. The Allan Variance does not explicitly converge for the nose types of alpha less than or equal to minus 3 and can be greatly affected by frequency drift. Because GPS rubidium frequency standards exhibit non-trivial aging and aging noise characteristics, the basic Allan Variance analysis must be augmented in order to (a) compensate for a dynamic frequency drift, and (b) characterize two additional noise types, specifically alpha = minus 3, and alpha = minus 4. As the GPS program progresses, we will utilize a larger percentage of rubidium frequency standards than ever before. Hence, GPS rubidium clock characterization will require more attention than ever before. The three sample variance, commonly referred to as a renormalized Hadamard Variance, is unaffected by linear frequency drift, converges for alpha is greater than minus 5, and thus has utility for modeling noise in GPS rubidium frequency standards. This paper demonstrates the potential of Hadamard Variance analysis in GPS operations, and presents an equation that relates the Hadamard Variance to the MCS's Kalman filter process noises.

Hutsell, Steven T.↗
NASA NTRSDate not supplied

Continuum covariance propagation for understanding variance loss in advective systems

At the heart of modern data assimilation schemes is covariance propagation.Loss of variance experienced in large-scale applications such as numerical weather prediction is problematic, and the development of auxiliary methods to mitigate this issue is an active research area. The focus of this work is to understand the root causes of variance loss and show that for advective dynamics, the covariance propagation by itself typically causes significant, spurious loss of variance, even at full rank. To demonstrate this, we first study continuum covariance propagation by analyzing the covariance evolution equation for advective dynamics. The behavior of this evolution equation changes abruptly as the correlation length tends to zero, for example in the vicinity of sharp gradients in the advection field. This happens because the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments then confirm that the variance lost during numerical propagation greatly exceeds that due to numerical dissipation alone. The variance loss is driven primarily by inaccurate variance propagation resulting from standard, full-rank covariance propagation schemes, which have difficulty capturing the abrupt change in dynamics as the correlation length tends to zero. These results suggest that developing local covariance propagation methods may prove useful in ameliorating the variance loss observed in data assimilation schemes

Covariance Propagation↗
NASA NTRS1982

The latitude dependence of the variance of zonally averaged quantities

Geometric characteristics of the spherical earth are shown to be responsible for the increase of variance with latitude of zonally averaged meteorological statistics. An analytic model is constructed to display the effect of a spherical geometry on zonal averages, employing a sphere labeled with radial unit vectors in a real, stochastic field expanded in complex spherical harmonics. The variance of a zonally averaged field is found to be expressible in terms of the spectrum of the vector field of the spherical harmonics. A maximum variance is then located at the poles, and the ratio of the variance to the zonally averaged grid-point variance, weighted by the cosine of the latitude, yields the zonal correlation typical of the latitude. An example is provided for the 500 mb level in the Northern Hemisphere compared to 15 years of data. Variance is determined to increase north of 60 deg latitude.

North, G. R.↗
NASA NTRS1998

Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter: Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics - Pt. 2

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

Menard, Richard↗
NASA NTRS2006

The Variance of Solar Wind Magnetic Fluctuations: Solutions and Further Puzzles

We study the dependence of the variance directions of the magnetic field in the solar wind as a function of scale, radial distance, and Alfvenicity. The study resolves the question of why different studies have arrived at widely differing values for the maximum to minimum power (approximately equal to 3:1 up to approximately equal to 20:1). This is due to the decreasing anisotropy with increasing time interval chosen for the variance, and is a direct result of the "spherical polarization" of the waves which follows from the near constancy of |B|. The reason for the magnitude preserving evolution is still unresolved. Moreover, while the long-known tendency for the minimum variance to lie along the mean field also follows from this view (as shown by Barnes many years ago), there is no theory for why the minimum variance follows the field direction as the Parker angle changes. We show that this turning is quite generally true in Alfvenic regions over a wide range of heliocentric distances. The fact that nonAlfvenic regions, while still showing strong power anisotropies, tend to have a much broader range of angles between the minimum variance and the mean field makes it unlikely that the cause of the variance turning is to be found in a turbulence mechanism. There are no obvious alternative mechanisms, leaving us with another intriguing puzzle.

Roberts, D. A.↗
NASA NTRS2010

Integrating Variances into an Analytical Database

For this project, I enrolled in numerous SATERN courses that taught the basics of database programming. These include: Basic Access 2007 Forms, Introduction to Database Systems, Overview of Database Design, and others. My main job was to create an analytical database that can handle many stored forms and make it easy to interpret and organize. Additionally, I helped improve an existing database and populate it with information. These databases were designed to be used with data from Safety Variances and DCR forms. The research consisted of analyzing the database and comparing the data to find out which entries were repeated the most. If an entry happened to be repeated several times in the database, that would mean that the rule or requirement targeted by that variance has been bypassed many times already and so the requirement may not really be needed, but rather should be changed to allow the variance's conditions permanently. This project did not only restrict itself to the design and development of the database system, but also worked on exporting the data from the database to a different format (e.g. Excel or Word) so it could be analyzed in a simpler fashion. Thanks to the change in format, the data was organized in a spreadsheet that made it possible to sort the data by categories or types and helped speed up searches. Once my work with the database was done, the records of variances could be arranged so that they were displayed in numerical order, or one could search for a specific document targeted by the variances and restrict the search to only include variances that modified a specific requirement. A great part that contributed to my learning was SATERN, NASA's resource for education. Thanks to the SATERN online courses I took over the summer, I was able to learn many new things about computers and databases and also go more in depth into topics I already knew about.

Sanchez, Carlos↗
NASA NTRSDate not supplied

Variance Decomposition of MEDLI2 Reconstructed Heating Using Neural Networks

The Mars Entry, Descent, and Landing Instrumentation (MEDLI2) sensor suite collected data during entry of the Mars 2020 Perseverance rover into Mars’ atmosphere. This suite included a network of MEDLI2 Instrumented Sensor Plugs (MISPs). Each MISP was comprised of a cylinder made of Thermal Protection System (TPS) material with 1-3 embedded thermocouples (TCs), and it was flush mounted into the heatshield or backshell. Data from these in-depth TCs were used to reconstruct the aeroheating environment of the vehicle throughout entry. Surface heating was posed as an inverse problem, with the goal of estimating the surface heating by minimizing an objective function of the difference between MISP temperature measurements during flight and the temperature predictions derived from the Fully Implicit Ablation and Thermal response (FIAT) program. Given an aerothermal environment, FIAT calculates the material response and provides in-depth temperatures throughout the TPS material. To achieve the reverse, an internal tool called FIAT_Opt runs through multiple different environments until the output temperature at the TC depth closely matches the flight data. 95% confidence intervals on the reconstructed surface heating were obtained using Monte Carlo analysis, in which uncertainties in the thermocouple depth and the TPS material properties (e.g., density, thermal conductivity, heat capacity, emissivity) based on flight-lot material testing were included. A variance decomposition method using Sobol indices was employed to assess the sensitivity of the reconstructed peak heating to the TC placement and material property uncertainties. Variance decomposition was found to require tens of thousands of FIAT_Opt runs in order for the Sobol indices to converge. With a single FIAT_Opt run taking on the order of 40 minutes, the required number of computations would take months to complete, even if using multiple CPUs. To mitigate this problem, three machine learning models (ridge regression with cross-validation, random forest regression, and a deep neural network) were trained and tested using the 2000 Monte Carlo runs that were already completed. A subset of 1600 runs were used to train the model (i.e., training set), while the remaining 400 runs were used as the test set. The predictions from the deep neural network (DNN) on the test set showed nearly perfect agreement to the actual values computed with FIAT_Opt (R2 > 0.99). Using the DNN as a surrogate model, the variance decomposition using 50,000 runs was completed within minutes. The resulting Sobol indices showed that the reconstructed peak surface heating was most sensitive to the uncertainties in the thermal conductivity (ST = 0.37) and heat capacity (ST = 0.26). This method can be leveraged to provide requirements for material property measurements needed to improve the accuracy of surface heating prediction and ultimately lead to the reduction of design margins in the future. This presentation will include background on the MEDLI2 suite; the method used for inverse heating estimation; the way that material property uncertainties were accounted for using Monte Carlo analysis; a brief background on variance decomposition; the motivation for using machine learning in this context; how a neural network was trained on the data to enable variance decomposition in a fraction of the time; and the variance decomposition results for one of the MISPs.

Hannah Alpert↗
DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗
NASA NTRS2012

Gravity Wave Variances and Propagation Derived from AIRS Radiances

As the first gravity wave (GW) climatology study using nadir-viewing infrared sounders, 50 Atmospheric Infrared Sounder (AIRS) radiance channels are selected to estimate GW variances at pressure levels between 2-100 hPa. The GW variance for each scan in the cross-track direction is derived from radiance perturbations in the scan, independently of adjacent scans along the orbit. Since the scanning swaths are perpendicular to the satellite orbits, which are inclined meridionally at most latitudes, the zonal component of GW propagation can be inferred by differencing the variances derived between the westmost and the eastmost viewing angles. Consistent with previous GW studies using various satellite instruments, monthly mean AIRS variance shows large enhancements over meridionally oriented mountain ranges as well as some islands at winter hemisphere high latitudes. Enhanced wave activities are also found above tropical deep convective regions. GWs prefer to propagate westward above mountain ranges, and eastward above deep convection. AIRS 90 field-of-views (FOVs), ranging from +48 deg. to −48 deg. off nadir, can detect large-amplitude GWs with a phase velocity propagating preferentially at steep angles (e.g., those from orographic and convective sources). The annual cycle dominates the GW variances and the preferred propagation directions for all latitudes. Indication of a weak two-year variation in the tropics is found, which is presumably related to the Quasi-biennial oscillation (QBO). AIRS geometry makes its out-tracks capable of detecting GWs with vertical wavelengths substantially shorter than the thickness of instrument weighting functions. The novel discovery of AIRS capability of observing shallow inertia GWs will expand the potential of satellite GW remote sensing and provide further constraints on the GW drag parameterization schemes in the general circulation models (GCMs).

AIRS↗
NASA NTRS1996

Spectral Ambiguity of Allan Variance

We study the extent to which knowledge of Allan variance and other finite-difference variances determines the spectrum of a random process. The variance of first differences is known to determine the spectrum. We show that, in general, the Allan variance does not. A complete description of the ambiguity is given.

Allan Variance variances finite-difference varianc↗
DOE OSTI2025

Moist Energy Constraints on Surface Temperature Variance Under Climate Warming

Understanding the factors controlling surface temperature variance is crucial for predicting temperature extremes. Previous investigations have examined individual impacts of temperature advection and surface turbulent fluxes on temperature fluctuations. Here, we explore the constraints on temperature variance from the moist static energy (MSE) balance and introduce a new scaling relation that connects the generation of temperature variance through moist energy transport with its dissipation due to the net energetic forcing of the atmosphere. This theory is evaluated in an idealized aquaplanet model. We find that surface temperature variance is influenced by eddy (sensible) heat flux, MSE gradient, and the Clausius‐Clapeyron relation for evaporative cooling. Under global warming, the reduced temperature variance in the aquaplanet model is dominated by the weakening in eddy heat flux, but it is also affected by changes in evaporative cooling and MSE gradient, which may be more important in realistic, moisture‐limited regions over land.

Eddy heat flux↗
NASA NTRS1974

NASTRAN variance analysis and plotting of HBDY elements

The NASTRAN Thermal Analyzer has been intended to do variance analysis and plot the thermal boundary elements. The objective of the variance analysis addition is to assess the sensitivity of temperature variances resulting from uncertainties inherent in input parameters for heat conduction analysis. The plotting capability provides the ability to check the geometry (location, size and orientation) of the boundary elements of a model in relation to the conduction elements. Variance analysis is the study of uncertainties of the computed results as a function of uncertainties of the input data. To study this problem using NASTRAN, a solution is made for both the expected values of all inputs, plus another solution for each uncertain variable. A variance analysis module subtracts the results to form derivatives, and then can determine the expected deviations of output quantities.

Harder, R. L.↗
NASA NTRS1980

Stratum variance estimation for sample allocation in crop surveys

The problem of determining stratum variances needed in achieving an optimum sample allocation for crop surveys by remote sensing is investigated by considering an approach based on the concept of stratum variance as a function of the sampling unit size. A methodology using the existing and easily available information of historical crop statistics is developed for obtaining initial estimates of tratum variances. The procedure is applied to estimate stratum variances for wheat in the U.S. Great Plains and is evaluated based on the numerical results thus obtained. It is shown that the proposed technique is viable and performs satisfactorily, with the use of a conservative value for the field size and the crop statistics from the small political subdivision level, when the estimated stratum variances were compared to those obtained using the LANDSAT data.

Perry, C. R., Jr.↗
NASA NTRS1995

Variances of the components and magnitude of the polar heliospheric magnetic field

The heliolatitude dependences of the variances in the components and the magnitude of the heliospheric magnetic field have been analysed, using the Ulysses magnetic field observations from close to the ecliptic plane to 80 southern solar latitude. The normalized variances in the components of the field increased significantly (by a factor about 5) as Ulysses entered the purely polar flows from the southern coronal hole. At the same time, there was at most a small increase in the variance of the field magnitude. The analysis of the different components indicates that the power in the fluctuations is not isotropically distributed: most of the power is in the components of the field transverse to the radial direction. Examining the variances calculated over different time scales from minutes to hours shows that the anisotropy of the field variances is different on different scales, indicating the influence of the two distinct populations of fluctuations in the polar solar wind which have been previously identified. We discuss these results in terms of evolutionary, dynamic processes as a function of heliocentric distance and as a function of the large scale geometry of the magnetic field associated with the polar coronal hole.

Balogh, A.↗