Variance of lunar slopes
Deriving root-mean-square slope of lunar surface from Ranger 7 observations
Marcus, A. H.↗
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Evaluating the radiance transformation for normalizing Landsat data
A technique is examined for improving the comparability of Landsat multisppectral scanner (MSS) data acquired on different dates. The technique involves conversion of digital brightness counts to relative radiance values measured in energy units (milliwatts per square centimeter-steradian). The statistical data of signature from 23 land cover (or biomass) classifications derived from all three Landsats were compared before and after the radiance normalization. Significant convergence occurred among the data sets for mean spectral values and the variances associated with each of seven major land cover types for MSS bands 4, 5, and 7. Overall, the variance attributed to the sensor component was reduced from 5.39 to 2.69 percent, with the largest decrease occurring in band 4 (14.4 percent to 3.7 percent).
Middleton, E. M.↗
A general form for the dissipation length scale in turbulent shear flows
It has been found that, for a wide range of turbulent wall-bounded shear flows with mean velocity profile U(y), the scale length L-epsilon determining the dissipation is approximately described in terms of distance from the wall (y), the mean shear (dU/dy), and the variance of the normal component of turbulence (bar u-squared), by the formula: L-epsilon to the -1 power is approximately equal to (A sub B / y) + A sub S (dU/dy / square root of bar u-squared) where L-epsilon = epsilon/(bar u-squared) to the 3/2 power. To match with shear-free boundary layers, A sub B is approximately 0.27, and to match with the log layer, A sub S is approximately 0.46. The shear flows tested here were: boundary layers over a flat plate, sink flow, oscillatory flow, and channel flow. The use of the square root of bar u-squared as a velocity scale minimizes the effects of Reynolds number. However, the formula fails within a distance of order L-epsilon for the regions where dU/dy = 0.
Hunt, J. C. R.↗
Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model
A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies.
Sommer, T. P.↗
Investigation of Allan variance for determining noise spectral forms with application to microwave radiometry
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.
Stanley, William D.↗
Seasonal-to-Interannual Variability in Antarctic Sea-Ice Dynamics, and Its Impact on Surface Fluxes and Water Mass Production
Strong seasonal and interannual signals in Antarctic bottom-water outflow remain unexplained yet are highly correlated with anomalies in net sea-ice growth in coastal polynyas. The mechanisms responsible for driving salination and replenishment and rejuvenation of the dense shelf "source" waters likely also generate pulses of bottom water outflow. The objective of this research is to investigate time-scales of variability in the dynamics of sea-ice in the Southern Ocean in order to determine the primary sites for production of dense shelf waters. We are using a merged satellite/buoy sea-ice motion data set for the period 1978-present day to compute the dynamics of opening and closing of coastal polynyas over the continental shelf. The Ocean Circulation and Climate Advanced Model (OCCAM) ocean general circulation model with coupled sea-ice dynamics is presently forced using National Center for Environmental Prediction (NCEP) data to simulate fluxes and the salination impact of the ocean shelf regions. This work is relevant in the context of measuring the influence of polar sea-ice dynamics upon polar ocean characteristics, and thereby upon global thermohaline ocean circulation. Interannual variability in simulated net freezing rate in the Southern Weddell Sea is shown for the period 1986-1993. There is a pronounced maximum of ice production in 1988 and minimum in 1991 in response to anomalies in equatorward meridional wind velocity. This follows a similar approximate 8-year interannual cycle in Sea Surface Temperature (SST) and satellite-derived ice-edge anomalies reported elsewhere as the "Antarctic Circumpolar Wave." The amplitude of interannual fluctuations in annual net ice production are about 40% of the mean value, implying significant interannual variance in brine rejection and upper ocean heat loss. Southward anomalies in wind stress induce negative anomalies in open water production, which are observed in passive microwave satellite images. Thus, cycles of enhanced poleward wind stress reduce ice growth by compacting the ice along the coastline and closing open water in leads and polynyas. Model simulations confirm that years of low ice production, such as 1991, coincide with years of lower than normal bottom water outflow. Future plans include the assimilation of satellite ice concentrations and ice drift dynamics to more accurately constrain boundary conditions in the model.
Drinkwater, Mark R.↗
Measuring Greenland Ice Mass Variation With Gravity Recovery and the Climate Experiment Gravity and GPS
The response of the Greenland ice sheet to climate change could significantly alter sea level. The ice sheet was much thicker at the last glacial maximum. To gain insight into the global change process and the future trend, it is important to evaluate the ice mass variation as a function of time and space. The Gravity Recovery and Climate Experiment (GRACE) mission to fly in 2001 for 5 years will measure gravity changes associated with the current ice variation and the solid earth's response to past variations. Our objective is to assess the separability of different change sources, accuracy and resolution in the mass variation determination by the new gravity data and possible Global Positioning System (GPS) bedrock uplift measurements. We use a reference parameter state that follows a dynamic ice model for current mass variation and a variant of the Tushingham and Peltier ICE-3G deglaciation model for historical deglaciation. The current linear trend is also assumed to have started 5 kyr ago. The Earth model is fixed as preliminary reference Earth model (PREM) with four viscoelastic layers. A discrete Bayesian inverse algorithm is developed employing an isotropic Gaussian a priori covariance function over the ice sheet and time. We use data noise predicted by the University of Texas and JPL for major GRACE error sources. A 2 mm/yr uplift uncertainty is assumed for GPS occupation time of 5 years. We then carry out covariance analysis and inverse simulation using GRACE geoid coefficients up to degree 180 in conjunction with a number of GPS uplift rates. Present-day ice mass variation and historical deglaciation are solved simultaneously over 146 grids of roughly 110 km x 110 km and with 6 time increments of 3 kyr each, along with a common starting epoch of the current trend. For present-day ice thickness change, the covariance analysis using GRACE geoid data alone results in a root mean square (RMS) posterior root variance of 2.6 cm/yr, with fairly large a priori uncertainties in the parameters and a Gaussian correlation length of 350 km. Simulated inverse can successfully recover most features in the reference present-day change. The RMS difference between them over the grids is 2.8 cm/yr. The RMS difference becomes 1.1 cm/yr when both are averaged with a half Gaussian wavelength of 150 km. With a fixed Earth model, GRACE alone can separate the geoid signals due to past and current load fairly well. Shown are the reference geoid signatures of direct and elastic effects of the current trend, the viscoelastic effect of the same trend starting from 5 kyr ago, the Post Glacial Rebound (PGR), and the predicted GRACE geoid error. The difference between the reference and inverse modeled total viscoelastic signatures is also shown. Although past and current ice mass variations are allowed the same spatial scale, their geoid signals have different spatial patterns. GPS data can contribute to the ice mass determination as well. Additional information is contained in the original.
Wu, Xiao-Ping↗
Long-Term Global Morphology of Gravity Wave Activity Using UARS Data
This report provides a broad outline of the total body of research conducted during the past three years. We report on detailed model studies of the precise way in which infrared limb scanning satellites explicitly detect gravity waves, and use these insights to resolve earlier discrepant zonal mean estimates of gravity wave variances from satellite limb scanners. Detailed analysis of CRISTA temperature fluctuations are outlined, which provide new global information on long-wavelength stratospheric gravity waves generated by mountains, tropical convection and the mid-latitude jet stream-vortex system, as well as interactions higher in the mesosphere with the diurnal tide. The detailed insights gained from analyzing CRISTA data are applied to provide a multiyear analysis of stratospheric mountain waves over the Andes evident in MLS limb-track data. We also demonstrate for the first time that stratospheric temperature data from the CLAES instrument on UARS resolved gravity waves, and we highlight mountain wave information in a subset of these data. Final conclusions and recommendations are set forth, and the present findings are directly related to the original goals of the research contract. A full list of publications that resulted from this research is provided.
Eckermann, Stephen D.↗
Long-Term Global Morphology of Gravity Wave Activity Using UARS Data
This report provides a broad outline of the total body of research conducted during the past three years. We report on detailed model studies of the precise way in which infrared limb scanning satellites explicitly detect gravity waves, and use these insights to resolve earlier discrepant zonal mean estimates of gravity wave variances from satellite limb scanners. Detailed analysis of CRISTA temperature fluctuations are outlined, which provide new global information on long-wavelength stratospheric gravity waves generated by mountains, tropical convection and the mid-latitude jet stream- vortex system, as well as interactions higher in the mesosphere with the diurnal tide. The detailed insights gained from analyzing CRISTA data are applied to provide a multi- year analysis of stratospheric mountain waves over the Andes evident in MLS limb-track data. We also demonstrate for the first time that stratospheric temperature data from the CLAES instrument on UARS resolved gravity waves, and we highlight mountain wave information in a subset of these data. Final conclusions and recommendations are set forth, and the present findings are directly related to the original goals of the research contract. A full list of publications that resulted from this research is provided.
Eckermann, Stephen D.↗
Comparison Study of Machine Learning Techniques to Predict Flight Energy Consumption for Advanced Air Mobility
This paper addresses the need to predict the flight energy consumption of aerial vehicles in the presence of wind using machine learning techniques. The presented work is critical to achieving sustainable and efficient operations for Advanced Air Mobility (AAM) and to evaluating the readiness of the ground-supporting energy infrastructure, e.g., electric grid and AAM portals. The flight energy consumption is described using the "energy per meter" (EPM) metric. We present a comparison study of influential machine learning techniques in predicting EPM using real-world flight test data. We presented new results of using the Decision Tree, Random Forest, and linear regression techniques, along with our previous results using the Recurrent Neural Network and Feed Forward Neural Network techniques. The comparison results show that the Linear Regression method outperforms other methods on the basis of the Mean Squared Error and error variance.
Machine Learning↗
The Principle of Energetic Consistency
A basic result in estimation theory is that the minimum variance estimate of the dynamical state, given the observations, is the conditional mean estimate. This result holds independently of the specifics of any dynamical or observation nonlinearity or stochasticity, requiring only that the probability density function of the state, conditioned on the observations, has two moments. For nonlinear dynamics that conserve a total energy, this general result implies the principle of energetic consistency: if the dynamical variables are taken to be the natural energy variables, then the sum of the total energy of the conditional mean and the trace of the conditional covariance matrix (the total variance) is constant between observations. Ensemble Kalman filtering methods are designed to approximate the evolution of the conditional mean and covariance matrix. For them the principle of energetic consistency holds independently of ensemble size, even with covariance localization. However, full Kalman filter experiments with advection dynamics have shown that a small amount of numerical dissipation can cause a large, state-dependent loss of total variance, to the detriment of filter performance. The principle of energetic consistency offers a simple way to test whether this spurious loss of variance limits ensemble filter performance in full-blown applications. The classical second-moment closure (third-moment discard) equations also satisfy the principle of energetic consistency, independently of the rank of the conditional covariance matrix. Low-rank approximation of these equations offers an energetically consistent, computationally viable alternative to ensemble filtering. Current formulations of long-window, weak-constraint, four-dimensional variational methods are designed to approximate the conditional mode rather than the conditional mean. Thus they neglect the nonlinear bias term in the second-moment closure equation for the conditional mean. The principle of energetic consistency implies that, to precisely the extent that growing modes are important in data assimilation, this term is also important.
Cohn, Stephen E.↗
Fast Image Texture Classification Using Decision Trees
Texture analysis would permit improved autonomous, onboard science data interpretation for adaptive navigation, sampling, and downlink decisions. These analyses would assist with terrain analysis and instrument placement in both macroscopic and microscopic image data products. Unfortunately, most state-of-the-art texture analysis demands computationally expensive convolutions of filters involving many floating-point operations. This makes them infeasible for radiation- hardened computers and spaceflight hardware. A new method approximates traditional texture classification of each image pixel with a fast decision-tree classifier. The classifier uses image features derived from simple filtering operations involving integer arithmetic. The texture analysis method is therefore amenable to implementation on FPGA (field-programmable gate array) hardware. Image features based on the "integral image" transform produce descriptive and efficient texture descriptors. Training the decision tree on a set of training data yields a classification scheme that produces reasonable approximations of optimal "texton" analysis at a fraction of the computational cost. A decision-tree learning algorithm employing the traditional k-means criterion of inter-cluster variance is used to learn tree structure from training data. The result is an efficient and accurate summary of surface morphology in images. This work is an evolutionary advance that unites several previous algorithms (k-means clustering, integral images, decision trees) and applies them to a new problem domain (morphology analysis for autonomous science during remote exploration). Advantages include order-of-magnitude improvements in runtime, feasibility for FPGA hardware, and significant improvements in texture classification accuracy.
Thompson, David R.↗
An interplanetary magnetic field ensemble at 1 AU
A method for calculation ensemble averages from magnetic field data is described. A data set comprising approximately 16 months of nearly continuous ISEE-3 magnetic field data is used in this study. Individual subintervals of this data, ranging from 15 hours to 15.6 days comprise the ensemble. The sole condition for including each subinterval in the averages is the degree to which it represents a weakly time-stationary process. Averages obtained by this method are appropriate for a turbulence description of the interplanetary medium. The ensemble average correlation length obtained from all subintervals is found to be 4.9 x 10 to the 11th cm. The average value of the variances of the magnetic field components are in the approximate ratio 8:9:10, where the third component is the local mean field direction. The correlation lengths and variances are found to have a systematic variation with subinterval duration, reflecting the important role of low-frequency fluctuations in the interplanetary medium.
Matthaeus, W. H.↗
An interplanetary magnetic field ensemble at 1 AU
A method for calculation ensemble averages from magnetic field data is described. A data set comprising approximately 16 months of nearly continuous ISEE-3 magnetic field data is used in this study. Individual subintervals of this data, ranging from 15 hours to 15.6 days comprise the ensemble. The sole condition for including each subinterval in the averages is the degree to shich it represents a weakly time-stationary process. Averages obtained by this method are appropriate for a turbulence description of the interplanetary medium. The ensemble average correlation length obtained from all subintervals is found to be 4.9 x 10 to the 11th cm. The average value of the variances of the magnetic field components are in the approximate ratio 8:9:10, where the third component is the local mean field direction. The correlation lengths and variances are found to have a systematic variation with subinterval duration, reflecting the important role of low-frequency fluctuations in the interplanetary medium.
Matthaeus, W. H.↗
Influence of Thermophysical Property Variability on Thermal Predictions of Ti-6Al-4V
The additive manufacturing (AM) industry has experienced rapid growth in recent decades as industrial interest in the process has grown. Because of this, there are many groups interested in simulations of the AM process. However, the influence of thermophysical property variability on the melt pool geometry during processing of various AM alloys is unclear. The goal of my work at NASA Langley Research Center (LaRC) was to characterize this influence on Ti-6Al-4V during AM processing alongside developing a tool to enable equivalent studies on other AM materials. To facilitate this process, a database tool was developed to contain and organize thermophysical data previously reported by primary sources. The specific thermophysical properties of interest for this study were density, specific heat capacity, and conductivity. Thermal diffusivity was calculated using the other three properties. This data was then fit with a Gaussian distribution and then randomly sampled from using Monte Carlo random value sampling. Using the Rosenthal equation, this sample data was used to simulate the temperature field during additive manufacturing and extract the melt pool geometry. Specifically, the melt pool’s length, width, and depth. This process was repeated an arbitrary number of times, with the default being 1000. Once this information was obtained, histograms were made showing the distributions of the sizes of the melt pool’s length, width, and depth. Representative statistical metrics of the distributions were calculated (mean, standard deviation, and coefficient of variance). This work found that at the simulated processing values, the melt pool’s width and depth had a 5.7% variation while the length had a 3.2% variation. Additionally, a tool was constructed to graph a thermal color map representation of the melt pool for specific, arbitrary values of density, specific heat, and conductivity. This tool allowed for more efficient plotting of individual queries of the thermophysical properties. The results that were observed in the research were that values reported in literature vary and this variance can have a significant impact on the simulation. Predictions of the melt pool’s dimensions show that length has a standard deviation of approximately 6 μm, width has a standard deviation of approximately 5 μm, and depth can vary by approximately 3 μm. Considering the mean sizes of length, width, and depth are 185 μm, 88 μm, and 44 μm respectively, such a deviation is significant. This shows that depth, for example, could be more than 10% larger or smaller than expected. This demonstrates that variability in the reported thermophysical properties are not negligible and should be expected to have an influence on the results of the laser powder bed fusion additive manufacturing process. When simulating this process in the future, measures should be taken to account for this discrepancy and the uncertainty involved
Justin Martin↗
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.↗
A computationally efficient model for turbulent droplet dispersion in spray combustion
A novel model for turbulent droplet dispersion is formulated having significantly improved computational efficiency in comparison to the conventional point source stochastic sampling methodology. In the proposed model, a computational parcel representing a group of physical particles is considered to have a normal (Gaussian) probability density function (PDF) in three-dimensional space. The mean of each PDF is determined by Lagrangian tracking of each computational parcel, either deterministically or stochastically. The variance is represented by a turbulence-induced mean squared dispersion which is based on statistical inferences from the linearized direct modeling formulation for particle/eddy interactions. Convolution of the computational parcel PDF's produces a single PDF for the physical particle distribution profile. The validity of the new model is established by comparison with the conventional stochastic sampling method, where in each parcel is represented by a delta function distribution, for non-evaporating particles injected into simple turbulent air flows.
Litchford, Ron J.↗
A Bayesian approach to parameter and reliability estimation in the Poisson distribution.
For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.
Canavos, G. C.↗