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NASA NTRS1985

The Seasonal Cycle of Storminess as Measured by Band-Pass Fluctuations

A sample of statistics, namely the seasonal cycle of baroclinic storms, as represented by bandpass filtered geopotential height variances at 850 mb is presented. The particular filter used is that suggested by Blackmon and White (1982), and retains periods of approximately 2.5 to 10 days. The time series of height (at each grid point) were filtered by removing the annual and semiannual cycles for that point, and by removing zonal wavenumbers higher than 20. The bandpass filter was then applied. The height variances of the filtered fields were then computed for each winter season, each spring, each summer season, and each fall season. These variances were then averaged by season. Maps of the standard deviation are shown. Figures show clearly the seasonal cycle of bandpass fluctuations. The major seasonal variation is seen to consist mostly of a summertime weakening and shift; spring and fall appear nearly identical to winter. The corresponding results at 500 mb are similar, but with the stormtrack variance being slightly larger in spring and fall compared to winter.

Straus, D. M.↗

NASA NTRS1986

On the design of classifiers for crop inventories

Crop proportion estimators that use classifications of satellite data to correct, in an additive way, a given estimate acquired from ground observations are discussed. A linear version of these estimators is optimal, in terms of minimum variance, when the regression of the ground observations onto the satellite observations in linear. When this regression is not linear, but the reverse regression (satellite observations onto ground observations) is linear, the estimator is suboptimal but still has certain appealing variance properties. In this paper expressions are derived for those regressions which relate the intercepts and slopes to conditional classification probabilities. These expressions are then used to discuss the question of classifier designs that can lead to low-variance crop proportion estimates. Variance expressions for these estimates in terms of classifier omission and commission errors are also derived.

Heydorn, R. P.↗

NASA NTRS1987

The response of SAR imagery to azimuth travelling ocean surface waves as determined from shuttle SAR imagery

Comparisons between two-dimensional ocean wave spectra, derived from synthetic aperture radar (SAR) imagery, and two-dimensional wave spectra from independent instruments have shown good agreement. The procedure by which raw SAR image intensity-variance spectra are converted to estimates of wave spectra is dependent upon models of how a SAR is able to image ocean waves. The greatest uncertainty exists about the mechanism by which azimuth (along track) traveling waves are imaged. In this paper, independent wave spectra from an airborne, radar ocean wave spectrometer (ROWS) are systematically compared with spatially and temporally coincident shuttle SAR image intensity-variance spectra to determine an optimum description of the relationship between the two. The result of these comparisons is to demonstrate that a SAR image intensity-variance spectrum is nearly proportional to the ocean wave slope-variance spectrum for azimuth traveling waves.

Monaldo, Frank M.↗

NASA NTRS1989

Gravity wave structure between 60 and 90 km inferred from Space Shuttle reentry data

Density fluctuations obtained along seven Space Shuttle reentry tracks are used to examine the horizontal structure and the vertical distribution of density variance in the mesosphere and lower thermosphere. The tracks lie primarily over open ocean at middle and low latitudes and represent the only measurements of horizontal atmospheric structure at these heights available to date. The density fluctuations are interpreted in terms of gravity-wave motions and reveal significant density (and velocity) variance at horizontal scales ranging from about 10 to 1000 km. Fluctuation amplitudes are used to infer corresponding velocity perturbations and characteristic vertical scales and frequencies of the wave spectrum. Results suggest that the mean velocity variance is smaller over the Pacific ocean than over major land masses, and that the variance increases with height in a manner consistent with that expected in the present of wave saturation processes.

Fritts, David C.↗

NASA NTRS1990

Further study of terrain effects on the mesoscale spectrum of atmospheric motions

Wind and temperature data collected on commercial airliners are used to investigate the effects of underlying terrain on mesoscale variability. These results expand upon those of Nastrom et al., by including all available data from the Global Atmospheric Sampling Program (GASP) and by more closely focusing on the coupling of variance with the roughness of the underlying terrain over mountainous regions. The earlier results, showing that variances are larger over mountains than over oceans or plains, with greatest increases at wavelengths below about 80 km, are confirmed. Statistical tests are used to confirm that these differences are highly significant. Over mountainous regions the roughness of the underlying terrain was parameterized from topographic data and it was found that variances are highly correlated with roughness and, in the troposphere, with background windspeed. Average variances over the roughest terrain areas range up to about ten times larger than those over the oceans. These results are found to follow the scaling with stability predicted in the framework of linenar gravity wave theory. The implications of these results for vertical transports of momentum and energy, assuming they are due to gravity waves and considering the effects of intermittency and anisotroy, are also discussed.

Jasperson, W. H.↗

NASA NTRS1994

An analysis of carrier phase jitter in an MPSK receiver utilizing map estimation

The use of 8 and 16 PSK TCM to support satellite communications in an effort to achieve more bandwidth efficiency in a power-limited channel has been proposed. This project addresses the problem of carrier phase jitter in an M-PSK receiver utilizing the high SNR approximation to the maximum aposteriori estimation of carrier phase. In particular, numerical solutions to the 8 and 16 PSK self-noise and phase detector gain in the carrier tracking loop are presented. The effect of changing SNR on the loop noise bandwidth is also discussed. These data are then used to compute variance of phase error as a function of SNR. Simulation and hardware data are used to verify these calculations. The results show that there is a threshold in the variance of phase error versus SNR curves that is a strong function of SNR and a weak function of loop bandwidth. The M-PSK variance thresholds occur at SNR's in the range of practical interest for the use of 8 and 16-PSK TCM. This suggests that phase error variance is an important consideration in the design of these systems.

Osborne, William P.↗

NASA NTRS1993

Stochastic dynamics of baroclinic waves

The maintenance of variance and attendant heat flux in linear, forced dissipative baroclinic shear flows subject to stochastic excitation is examined. The baroclinic problem, is intrinsically nonnormal and its stochastic dynamics is found to differ significantly from the more familiar stochastic dynamics of normal systems. When the shear is sufficiently great in comparison to dissipative effects, stochastic excitation supports highly enhanced variance levels in these nonnormal systems compared to variance levels supproted by the same forcing and dissipation in related normal systems. The eddy variance and associated heat flux are found to arise in response to transient amplification of a subset of forcing functions that obtain energy from the mean flow and project this energy on a distinct subset of response functions (EOFs) that are in turn distinct from the set of normal modes of the system. A method for obtaining the dominant forcing and response functions as well as the distribution of heat flux for a given flow is described.

Farrell, Brian F.↗

NASA NTRS1996

An Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance

Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system.

Keel, Byron M.↗

NASA NTRS2000

Precision of Four Acoustic Bone Measurement Devices

Though many studies have quantified the precision of various acoustic bone measurement devices, it is difficult to directly compare the results among the studies, because they used disparate subject pools, did not specify the estimation methodology, or did not use consistent definitions for various precision characteristics. In this study, we used a repeated measures design protocol to directly determine the precision characteristics of four acoustic bone measurement devices: the Mechanical Response Tissue Analyzer (MRTA), the UBA-575+, the SoundScan 2000 (S2000), and the Sahara Ultrasound Done Analyzer. Ten men and ten women were scanned on all four devices by two different operators at five discrete time points: Week 1, Week 2, Week 3, Month 3 and Month 6. The percent coefficient of variation (%CV) and standardized coefficient of variation were computed for the following precision characteristics: interoperator effect, operator-subject interaction, short-term error variance, and long-term drift, The MRTA had high interoperator errors for its ulnar and tibial stiffness measures and a large long-term drift in its tibial stiffness measurement. The UBA-575+ exhibited large short-term error variances and long-term drift for all three of its measurements. The S2000's tibial speed of sound measurement showed a high short-term error variance and a significant operator-subject interaction but very good values ( < 1%) for the other precision characteristics. The Sahara seemed to have the best overall performance, but was hampered by a large %CV for short-term error variance in its broadband ultrasound attenuation measure.

Miller, Christopher↗

NASA NTRS2000

Precision of Four Acoustic Bone Measurement Devices

Though many studies have quantified the precision of various acoustic bone measurement devices, it is difficult to directly compare the results among the studies, because they used disparate subject pools, did not specify the estimation methodology, or did not use consistent definitions for various precision characteristics. In this study, we used a repeated measures design protocol to directly determine the precision characteristics of four acoustic bone measurement devices: the Mechanical Response Tissue Analyzer (MRTA), the UBA-575+, the SoundScan 2000 (S2000), and the Sahara Ultrasound Bone Analyzer. Ten men and ten women were scanned on all four devices by two different operators at five discrete time points: Week 1, Week 2, Week 3, Month 3 and Month 6. The percent coefficient of variation (%CV) and standardized coefficient of variation were computed for the following precision characteristics: interoperator effect, operator-subject interaction, short-term error variance, and long-term drift. The MRTA had high interoperator errors for its ulnar and tibial stiffness measures and a large long-term drift in its tibial stiffness measurement. The UBA-575+ exhibited large short-term error variances and long-term drift for all three of its measurements. The S2000's tibial speed of sound measurement showed a high short-term error variance and a significant operator-subject interaction but very good values (less than 1%) for the other precision characteristics. The Sahara seemed to have the best overall performance, but was hampered by a large %CV for short-term error variance in its broadband ultrasound attenuation measure.

Miller, Christopher↗

NASA NTRS2002

Reproducibility and Repeatability of Tensile and Low-Cycle Fatigue Properties in Propulsion Grade Hydrogen

Hydrogen has the potential of increased use in the future as an environmentally friendly fuel. It has, however, shown a tendency to embrittle some materials. To be used in a safe manner and to exploit its full potential, it will be necessary to develop a database of material properties in hydrogen environment. The tests needed to produce this data are costly to perform (tensile test cost 25 times more and low cycle fatigue test are 55 times as expensive). Moreover, there is presently a lack of universal test methods to ensure standardized data within the hydrogen community. Each of the industries that work with hydrogen (aerospace, petroleum, fuel cells, etc.) performs tests by their own laboratory-developed methods, thus rendering cross- comparisons of material property data highly questionable. It is extremely important that data generated in a hydrogen environment be done to a standard that reduces variance to a minimum and allows direct comparison of test results from different laboratories. Doing so will assure that all data generated can be used to further our understanding of the hydrogen effects and to make sure components/products designed for hydrogen are the safest and most reliable possible. This paper reviews the results of two 'round-robin' programs conducted by NASA-MSFC. These two programs examined the reproducibility and repeatability of tensile and low-cycle fatigue test results in high-pressure hydrogen environments. The studies indicated that even with the tightest controls available from current commercial standards, the reproducibility (between different laboratories) and repeatability (within a laboratory) results of the tensile tests exhibited five times the variance as in standard ambient air tests. The variance with the LCF tests were on the same order as with air tests, but that was due to the large variation present in the last Interlaboratory air program. The paper concludes with a recommendation for a program that would allow the development of improved test methods, leading to lower variance in the generation of mechanical property data in the future.

Vesely, E. J.↗

NASA NTRS2002

Causes of Long-Term Drought in the United States Great Plains

The United States Great Plains (USGP) experienced a number of multi-year droughts during the last century, most notably the droughts of the 1930s and 1950s. This study examines the causes of such droughts using ensembles of long term (1930-1999) simulations carried out with the NASA Seasonal-to-Interannual Prediction Project (NSIPP-1) atmospheric general circulation model (AGCM) forced with observed sea surface temperatures (SSTs). The results show that the model produces long-term (multi-year) variations in the USGP precipitation that are similar to those observed. A correlative analysis suggests that the ensemble mean low frequency (time scales longer than about 6 years) rainfall variations in the USGP are linked to a pan-Pacific pattern of SST variability that is the leading empirical orthogonal function (EOF) in the low frequency SST data. The link between the SST and the Great Plains precipitation is confirmed in idealized AGCM simulations, in which the model is forced by the 2 polarities of the pan-Pacific SST pattern. The idealized simulations further show that it is primarily the tropical part of the SST anomalies that influence the USGP. As such, the USGP tend to have above normal precipitation when the tropical Pacific SSTs are above normal, while there is a tendency for drought when the tropical SSTs are cold. The upper tropospheric response to the pan-Pacific SST EOF shows a global-scale pattern with a strong wave response in the Pacific and a substantial zonally-symmetric component in which USGP pluvial (drought) conditions are associated with reduced (enhanced) heights throughout the extra-tropics. The potential predictability of rainfall in the USGP associated with SSTs is rather modest, with on average about 1/3 of the total low frequency rainfall variance forced by SST anomalies. Further idealized experiments with climatological SST, suggest that the remaining low frequency variance in the USGP precipitation is the result of interactions with soil moisture. In particular, simulations with soil moisture feedback show a six-fold increase in the variance in annual USGP precipitation compared with simulations in which the soil feedback is excluded. In addition to increasing variance, the interactions with the soil introduce year-to-year memory in the hydrological cycle that is consistent with a red noise process, in which the low frequencies in the deep soil are the result of integrating a net forcing (precipitation-evaporation-runoff) that is white noise on interannual time scales. As such, the role of low frequency SST variability is to introduce a bias to the net forcing on the soil moisture that drives the random process preferentially to either wet or dry conditions.

Schubert, Siegfried D.↗

NASA NTRS2003

Causes of Long-Term Drought in the United States Great Plains

This study examines the causes of long term droughts in the United States Great Plains (USGP). The focus is on the relative roles of slowly varying SSTs and interactions with soil moisture. The results from ensembles of long term (1930-1999) simulations carried out with the NASA Seasonal-to- Interannual Prediction Project (NSIPP-1) atmospheric general circulation model (AGCM) show that the SSTs account for about 1/3 of the total low frequency rainfall variance in the USGP. Results from idealized experiments with climatological SST suggest that the remaining low frequency variance in the USGP precipitation is the result of interactions with soil moisture. In particular, simulations with soil moisture feedback show a five-fold increase in the variance in annual USGP precipitation compared with simulations in which the soil feedback is excluded. In addition to increasing variance, the interactions with the soil introduce year-to-year memory in the hydrological cycle that is consistent with a red noise process, in which the deep soil is forced by white noise and damped with a time scale of about 2 years. As such, the role of low frequency SST variability is to introduce a bias to the net forcing on the soil moisture that drives the random process preferentially to either wet or dry conditions.

Schubert, Siegfried D.↗

NASA NTRS2004

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Number

Present simulation of turbulent flows involving shock wave/boundary layer interaction invariably overestimates heat flux by almost a factor of two. One possible reason for such a performance is a result of the fact that the turbulence models employed make use of Morkovin's hypothesis. This hypothesis is valid for non-hypersonic Mach numbers and moderate rates of heat transfer. At hypersonic Mach numbers, high rates of heat transfer exist in regions where shock wave/boundary layer interactions are important. As a result, one should not expect traditional turbulence models to yield accurate results. The goal of this investigation is to explore the role of a variable Prandtl number formulation in predicting heat flux in flows dominated by strong shock wave/boundary layer interactions. The intended applications involve external flows in the absence of combustion such as those encountered in supersonic inlets. This can be achieved by adding equations for the temperature variance and its dissipation rate. Such equations can be derived from the exact Navier-Stokes equations. Traditionally, modeled equations are based on the low speed energy equation where the pressure gradient term and the term responsible for energy dissipation are ignored. It is clear that such assumptions are not valid for hypersonic flows. The approach used here is based on the procedure used in deriving the k-zeta model, in which the exact equations that governed k, the variance of velocity, and zeta, the variance of vorticity, were derived and modeled. For the variable turbulent Prandtl number, the exact equations that govern the temperature variance and its dissipation rate are derived and modeled term by term. The resulting set of equations are free of damping and wall functions and are coordinate-system independent. Moreover, modeled correlations are tensorially consistent and invariant under Galilean transformation. The final set of equations will be given in the paper.

Xiao, X.↗

NASA NTRS2003

Estimation and Simulation of Slow Crack Growth Parameters from Constant Stress Rate Data

Closed form, approximate functions for estimating the variances and degrees-of-freedom associated with the slow crack growth parameters n, D, B, and A(sup *) as measured using constant stress rate ('dynamic fatigue') testing were derived by using propagation of errors. Estimates made with the resulting functions and slow crack growth data for a sapphire window were compared to the results of Monte Carlo simulations. The functions for estimation of the variances of the parameters were derived both with and without logarithmic transformation of the initial slow crack growth equations. The transformation was performed to make the functions both more linear and more normal. Comparison of the Monte Carlo results and the closed form expressions derived with propagation of errors indicated that linearization is not required for good estimates of the variances of parameters n and D by the propagation of errors method. However, good estimates variances of the parameters B and A(sup *) could only be made when the starting slow crack growth equation was transformed and the coefficients of variation of the input parameters were not too large. This was partially a result of the skewered distributions of B and A(sup *). Parametric variation of the input parameters was used to determine an acceptable range for using closed form approximate equations derived from propagation of errors.

Salem, Jonathan A.↗

NASA NTRS2006

Annual Cycles of Surface Shortwave Radiative Fluxes

The annual cycles of surface shortwave flux are investigated using the 8-yr dataset of the surface radiation budget (SRB) components for the period July 1983-June 1991. These components include the downward, upward, and net shortwave radiant fluxes at the earth's surface. The seasonal cycles are quantified in terms of principal components that describe the temporal variations and empirical orthogonal functions (EOFs) that describe the spatial patterns. The major part of the variation is simply due to the variation of the insolation at the top of the atmosphere, especially for the first term, which describes 92.4% of the variance for the downward shortwave flux. However, for the second term, which describes 4.1% of the variance, the effect of clouds is quite important and the effect of clouds dominates the third term, which describes 2.4% of the variance. To a large degree the second and third terms are due to the response of clouds to the annual cycle of solar forcing. For net shortwave flux at the surface, similar variances are described by each term. The regional values of the EOFs are related to climate classes, thereby defining the range of annual cycles of shortwave radiation for each climate class.

Wilber, Anne C.↗

NASA NTRS2008

Constraining Particle Variation in Lunar Regolith for Simulant Design

Simulants are used by the lunar engineering community to develop and test technologies for In Situ Resource Utilization (ISRU), excavation and drilling, and for mitigation of hazards to machinery and human health. Working with the United States Geological Survey (USGS), other NASA centers, private industry and academia, Marshall Space Flight Center (MSFC) is leading NASA s lunar regolith simulant program. There are two main efforts: simulant production and simulant evaluation. This work requires a highly detailed understanding of regolith particle type, size, and shape distribution, and of bulk density. The project has developed Figure of Merit (FoM) algorithms to quantitatively compare these characteristics between two materials. The FoM can be used to compare two lunar regolith samples, regolith to simulant, or two parcels of simulant. In work presented here, we use the FoM algorithm to examine the variance of particle type in Apollo 16 highlands regolith core and surface samples. For this analysis we have used internally consistent particle type data for the 90-150 m fraction of Apollo core 64001/64002 from station 4, core 60009/60010 from station 10, and surface samples from various Apollo 16 stations. We calculate mean modal compositions for each core and for the group of surface samples and quantitatively compare samples of each group to its mean as a measurement of within-group variance; we also calculate an FoM for every sample against the mean composition of 64001/64002. This gives variation with depth at two locations and between Apollo 16 stations. Of the tested groups, core 60009/60010 has the highest internal variance with an average FoM score of 0.76 and core 64001/64002 has the lowest with an average FoM of 0.92. The surface samples have a low but intermediate internal variance with an average FoM of 0.79. FoM s calculated against the 64001/64002 mean reference composition range from 0.79-0.97 for 64001/64002, from 0.41-0.91 for 60009/60010, and from 0.54-0.93 for the surface samples. Six samples fall below 0.70, and they are also the least mature (i.e., have the lowest I(sub s)/FeO). Because agglutinates are the dominant particle type and the agglutinate population increases with sample maturity (I(sub s)/FeO), the maturity of the sample relative to the reference is a prime determinant of the particle type FoM score within these highland samples.

Schrader, Christian M.↗

NASA NTRS2009

Evaluation of TRMM Ground-Validation Radar-Rain Errors Using Rain Gauge Measurements

Ground-validation (GV) radar-rain products are often utilized for validation of the Tropical Rainfall Measuring Mission (TRMM) spaced-based rain estimates, and hence, quantitative evaluation of the GV radar-rain product error characteristics is vital. This study uses quality-controlled gauge data to compare with TRMM GV radar rain rates in an effort to provide such error characteristics. The results show that significant differences of concurrent radar-gauge rain rates exist at various time scales ranging from 5 min to 1 day, despite lower overall long-term bias. However, the differences between the radar area-averaged rain rates and gauge point rain rates cannot be explained as due to radar error only. The error variance separation method is adapted to partition the variance of radar-gauge differences into the gauge area-point error variance and radar rain estimation error variance. The results provide relatively reliable quantitative uncertainty evaluation of TRMM GV radar rain estimates at various times scales, and are helpful to better understand the differences between measured radar and gauge rain rates. It is envisaged that this study will contribute to better utilization of GV radar rain products to validate versatile spaced-based rain estimates from TRMM, as well as the proposed Global Precipitation Measurement, and other satellites.

Wang, Jianxin↗