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NASA standard: Trend analysis techniques

This Standard presents descriptive and analytical techniques for NASA trend analysis applications. Trend analysis is applicable in all organizational elements of NASA connected with, or supporting, developmental/operational programs. Use of this Standard is not mandatory; however, it should be consulted for any data analysis activity requiring the identification or interpretation of trends. Trend Analysis is neither a precise term nor a circumscribed methodology, but rather connotes, generally, quantitative analysis of time-series data. For NASA activities, the appropriate and applicable techniques include descriptive and graphical statistics, and the fitting or modeling of data by linear, quadratic, and exponential models. Usually, but not always, the data is time-series in nature. Concepts such as autocorrelation and techniques such as Box-Jenkins time-series analysis would only rarely apply and are not included in this Standard. The document presents the basic ideas needed for qualitative and quantitative assessment of trends, together with relevant examples. A list of references provides additional sources of information.

Source record↗

Is it possible to identify a trend in problem/failure data

One of the major obstacles in identifying and interpreting a trend is the small number of data points. Future trending reports will begin with 1983 data. As the problem/failure data are aggregated by year, there are just seven observations (1983 to 1989) for the 1990 reports. Any statistical inferences with a small amount of data will have a large degree of uncertainty. Consequently, a regression technique approach to identify a trend is limited. Though trend determination by failure mode may be unrealistic, the data may be explored for consistency or stability and the failure rate investigated. Various alternative data analysis procedures are briefly discussed. Techniques that could be used to explore problem/failure data by failure mode are addressed. The data used are taken from Section One, Space Shuttle Main Engine, of the Calspan Quarterly Report dated April 2, 1990.

Church, Curtis K.↗

Clustering, randomness and regularity in cloud fields. I - Theoretical considerations. II - Cumulus cloud fields

The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.

Weger, R. C.↗

Identification of the Hard X-Ray Source Dominating the E > 25 keV Emission of the Nearby Galaxy M31

We report the identification of a bright hard X-ray source dominating the M31 bulge above 25 kiloelectronvolts from a simultaneous NuSTAR-Swift observation. We find that this source is the counterpart to Swift J0042.6+4112, which was previously detected in the Swift BAT All-Sky Hard X-Ray Survey. This Swift BAT source had been suggested to be the combined emission from a number of point sources; our new observations have identified a single X-ray source from 0.5 to 50 kiloelectronvolts as the counterpart for the first time. In the 0.5-10 kiloelectronvolt band, the source had been classified as an X-ray Binary candidate in various Chandra and XMM-Newton studies; however, since it was not clearly associated with Swift J0042.6+4112, the previous E is less than 10 kiloelectronvolts observations did not generate much attention. This source has a spectrum with a soft X-ray excess (kT approximately equal to 0.2 kiloelectronvolts) plus a hard spectrum with a power law of gamma approximately equal to 1 and a cutoff around 15-20 kiloelectronvolts, typical of the spectral characteristics of accreting pulsars. Unfortunately, any potential pulsation was undetected in the NuSTAR data, possibly due to insufficient photon statistics. The existing deep HST (Hubble Space Telescope) images exclude high-mass (greater than 3 times the radius of the moon) donors at the location of this source. The best interpretation for the nature of this source is an X-ray pulsar with an intermediate-mass (less than 3 times the radius of the moon M) companion or a symbiotic X-ray binary. We discuss other possibilities in more detail.

galaxies: bulges – galaxies: individual (M31)↗

Statistics of Low-Mass Companions to Stars: Implications for Their Origin

One of the more significant results from observational astronomy over the past few years has been the detection, primarily via radial velocity studies, of low-mass companions (LMCs) to solar-like stars. The commonly held interpretation of these is that the majority are "extrasolar planets" whereas the rest are brown dwarfs, the distinction made on the basis of apparent discontinuity in the distribution of M sin i for LMCs as revealed by a histogram. We report here results from statistical analysis of M sin i, as well as of the orbital elements data for available LMCs, to rest the assertion that the LMCs population is heterogeneous. The outcome is mixed. Solely on the basis of the distribution of M sin i a heterogeneous model is preferable. Overall, we find that a definitive statement asserting that LMCs population is heterogeneous is, at present, unjustified. In addition we compare statistics of LMCs with a comparable sample of stellar binaries. We find a remarkable statistical similarity between these two populations. This similarity coupled with marked populational dissimilarity between LMCs and acknowledged planets motivates us to suggest a common origin hypothesis for LMCs and stellar binaries as an alternative to the prevailing interpretation. We discuss merits of such a hypothesis and indicate a possible scenario for the formation of LMCs.

Stepinski, T. F.↗

Interpreting forest and grassland biome productivity utilizing nested scales of image resolution and biogeographical analysis

Several hardware, software, and data collection problems encountered were conquered. The Geographic Information System (GIS) data from other systems were converted to ERDAS format for incorporation with the image data. Statistical analysis of the relationship between spectral values and productivity is being pursued. Several project sites, including Jackson, Pope, Boulder, Smokies, and Huntington Forest are evolving as the most intensively studied areas, primarily due to availability of data and time. Progress with data acquisition and quality checking, more details on experimental sites, and brief summarizations of research results and future plans are discussed. Material on personnel, collaborators, facilities, site background, and meetings and publications of the investigators are included.

Iverson, L. R.↗

Martian lineaments from Mariner 6 and 7 photographs

Mariner 6 and 7 photographs were used to investigate the nature and importance of linear surface trends on Mars. Cross correlations of frequency-azimuth distributions of linear trends from different Mariner frames indicate that lineations not recognized as topographic features have a component of pseudoforms, probably introduced during digital reconstruction of the pictures. Similar statistical tests may aid in the analysis of surface trends from future satellites and space probes. The most reliable data were separated into photometrically defined provinces. Meridiani Sinus and Margaritifer Sinus display five major trends in common, which are interpreted as extensions of crustal weaknesses related to the enormous equatorial canyon revealed in Mariner 6 and 9 pictures. Alignments of crater wall segments generally match these trends and suggest structural control of crater plan. Crater chains, however, do not match these trends and are interpreted as secondary impacts. Rose diagrams of lineations in Deucalionis Regio exhibit much more complexity and are believed to reflect a better preserved or more complex geologic history.

Schultz, P. H.↗

Clear air turbulence forecasting techniques

A method to improve clear air turbulence (CAT) forecasting by more effectively using the currently operational rawinsonde (RW) system is discussed. The method is called the Diagnostic Richardson Number Tendency (DRT) technique. The technique does not attempt to use the RW as a direct detector of the turbulent motion or even of the CAT mechanism structure but rather senses the synoptic scale centers of action which provide the energy to the CAT mechanism at the mesoscale level. The DRT algorithm is deterministic rather than statistical in nature, using the hydrodynamic equations (equations of motion) relevant to the synoptic scale. However, interpretation, by necessity, is probabilistic. What is most important with respect to its operational implementation is that this method uses the same input data as currently used by the operational National Meteorological Center prognostic models.

Keller, J. L.↗

Global CO2 Distributions over Land from the Greenhouse Gases Observing Satellite (GOSAT)

January 2009 saw the successful launch of the first space-based mission specifically designed for measuring greenhouse gases, the Japanese Greenhouse gases Observing SATellite (GOSAT). We present global land maps (Level 3 data) of column-averaged CO2 concentrations (X(sub CO2)) derived using observations from the GOSAT ACOS retrieval algorithm, for July through December 2009. The applied geostatistical mapping approach makes it possible to generate maps at high spatial and temporal resolutions that include uncertainty measures and that are derived directly from the Level 2 observations, without invoking an atmospheric transport model or estimates of CO2 uptake and emissions. As such, they are particularly well suited for comparison studies. Results show that the Level 3 maps for July to December 2009 on a lO x 1.250 grid, at six-day resolution capture much of the synoptic scale and regional variability of X(sub CO2), in addition to its overall seasonality. The uncertainty estimates, which reflect local data coverage, X(sub CO2) variability, and retrieval errors, indicate that the Southern latitudes are relatively well-constrained, while the Sahara Desert and the high Northern latitudes are weakly-constrained. A probabilistic comparison to the PCTM/GEOS-5/CASA-GFED model reveals that the most statistically significant discrepancies occur in South America in July and August, and central Asia in September to December. While still preliminary, these results illustrate the usefulness of a high spatiotemporal resolution, data-driven Level 3 data product for direct interpretation and comparison of satellite observations of highly dynamic parameters such as atmospheric CO2.

Hammerling, Dorit M.↗

Improvements in aircraft extraction programs

Flight data from an F-8 Corsair and a Cessna 172 was analyzed to demonstrate specific improvements in the LRC parameter extraction computer program. The Cramer-Rao bounds were shown to provide a satisfactory relative measure of goodness of parameter estimates. It was not used as an absolute measure due to an inherent uncertainty within a multiplicative factor, traced in turn to the uncertainty in the noise bandwidth in the statistical theory of parameter estimation. The measure was also derived on an entirely nonstatistical basis, yielding thereby also an interpretation of the significance of off-diagonal terms in the dispersion matrix. The distinction between coefficients as linear and non-linear was shown to be important in its implication to a recommended order of parameter iteration. Techniques of improving convergence generally, were developed, and tested out on flight data. In particular, an easily implemented modification incorporating a gradient search was shown to improve initial estimates and thus remove a common cause for lack of convergence.

Balakrishnan, A. V.↗

Use of ERTS data for a multidisciplinary analysis of Michigan resources

The author has identified the following significant results. The results of this investigation of ratioing simulated ERTS spectral bands and several non-ERTS bands (all collected by an airborne multispectral scanner) indicate that significant terrain information is available from band-ratio images. Ratio images, which are based on the relative spectral changes which occur from one band to another, are useful for enhancing differences and aiding the image interpreter in identifying and mapping the distribution of such terrain elements as seedling crops, all bare soil, organic soil, mineral soil, forest and woodlots, and marsh areas. In addition, the ratio technique may be useful for computer processing to obtain recognition images of large areas at lower costs than with statistical decision rules. The results of this study of ratio processing of aircraft MSS data will be useful for future processing and evaluation of ERTS-1 data for soil and landform studies. Additionally, the results of ratioing spectral bands other than those currently collected by ERTS-1 suggests that some other bands (particularly a thermal band) would be useful in future satellites.

Andersen, A. L.↗

Methods for trend analysis: Examples with problem/failure data

Statistics are emphasized as an important role in quality control and reliability. Consequently, Trend Analysis Techniques recommended a variety of statistical methodologies that could be applied to time series data. The major goal of the working handbook, using data from the MSFC Problem Assessment System, is to illustrate some of the techniques in the NASA standard, some different techniques, and to notice patterns of data. Techniques for trend estimation used are: regression (exponential, power, reciprocal, straight line) and Kendall's rank correlation coefficient. The important details of a statistical strategy for estimating a trend component are covered in the examples. However, careful analysis and interpretation is necessary because of small samples and frequent zero problem reports in a given time period. Further investigations to deal with these issues are being conducted.

Church, Curtis K.↗

Plasmaspheric Plumes: Occurrence Frequency and Quantification using Magnetospheric State Vector

Plasmaspheric drainage plumes appear in the aftermath of periods of enhanced convection/erosion and are interpreted as a near-equatorial signature of the redistribution of thermal plasma along streamlines. Analysis of IMAGE/EUV observations reveals that for Kp >3, there is an 84% probability of observing a plasmaspheric plume in EUV data. We present a statistical analysis of the geomagnetic conditions [Kp, Dst, and solar wind-induced electric field] associated with EUV plume observations. Additionally, statistical analysis of the a solar wind-induced convection electric field at Earth [Ey,sm] associated with EUV plume observations are presented. These results are then used to specify a single magnetospheric state vector to define the configuration of magnetosphere associated with the formation of this major plasmaspheric structure.

Adrian, Mark L.↗

Coronal Plumes in the Fast Solar Wind

The expansion of a coronal hole filled with a discrete number of higher density coronal plumes is simulated using a time-dependent two-dimensional code. A solar wind model including an exponential coronal heating function and a flux of Alfven waves propagating both inside and outside the structures is taken as a basic state. Different plasma plume profiles are obtained by using different scale heights for the heating rates. Remote sensing and solar wind in situ observations are used to constrain the parameter range of the study. Time dependence due to plume ignition and disappearance is also discussed. Velocity differences of the order of approximately 50 km/s, such as those found in microstreams in the high-speed solar wind, may be easily explained by slightly different heat deposition profiles in different plumes. Statistical pressure balance in the fast wind data may be masked by the large variety of body and surface waves which the higher density filaments may carry, so the absence of pressure balance in the microstreams should not rule out their interpretation as the extension of coronal plumes into interplanetary space. Mixing of plume-interplume material via the Kelvin-Helmholtz instability seems to be possible within the parameter ranges of the models defined here, only at large di stances from the Sun, beyond 0.2-0.3 AU. Plasma and composition measurements in the inner heliosphere, such as those which will become available with Solar Orbiter and Solar Probe Plus, should therefore definitely be able to identify plume remnants in the solar wind.

Velli, Marco↗

Martian ages

Four discussions are conducted: (1) the methodology of relative age determination by impact crater statistics, (2) a comparison of proposed Martian impact chronologies for the determination of absolute ages from crater frequencies, (3) a report on work dating Martian volcanoes and erosional features by impact crater statistics, and (4) an attempt to understand the main features of Martian history through a synthesis of crater frequency data. Two cratering chronology models are presented and used for inference of absolute ages from crater frequency data, and it is shown that the interpretation of all data available and tractable by the methodology presented leads to a global Martian geological history that is characterized by two epochs of activity. It is concluded that Mars is an ancient planet with respect to its surface features.

Neukum, G.↗

A search for anisotrophy in the cosmic microwave background on intermediate angular scales

The results of a search for anisotropy in the cosmic microwave background on angular scales near 1 deg are presented. Observations were simultaneously performed in bands centered at frequencies of 6, 9, and 12 per cm with a multifrequency bolometric receiver mounted on a balloon-borne telescope. The statistical sensitivity of the data is the highest reported to date at this angular scale, which is of critical importance for understanding the formation of structure in the universe. Signals in excess of random were observed in the data. The experiment, data analysis, and interpretation are described.

Alsop, D. C.↗

Mimas: Preliminary Evidence For Amorphous Water Ice from VIMS

We have conducted a statistical clustering analysis (1,2) on a mosaic of VIMS data cubes obtained on February 13, 2010, for Saturn s satellite Mimas. Seven VIMS cubes were geometrically projected and re-sampled to a common spatial resolution. The clustering technique consists of a partitioning algorithm coupled to a criterion that prevents sub-optimal solutions and tests for the influence of random noise in the measurements. The clustering technique is agnostic about the meaning of the clusters, and scientific interpretation requires their a posteriori evaluation. The preliminary results yielded five clusters, demonstrating that spectral variability across Mimas surface is statistically significant. The ratios of the means calculated for each of the clusters show structure within the 1.6- micron water ice band, as well as the shape and the central wavelength of the strong ice band at 2 micron, that map spatially in patterns apparently related to the topography of Mimas, in particular certain regions in and around Herschel crater. The mean spectra of the five clusters, show similarities with laboratory spectra of amorphous and crystalline H2O ice (3) that are suggestive of the presence of an amorphous ice component in certain regions of Mimas, notably on the central peak of Herschel, on the crater floor, and in faults surrounding the crater. This may represent a mixture of both ice phases, or perhaps a layer of amorphous ice on a base of crystalline ice. Another possible occurrence of amorphous ice appears southwest of Herschel, close to the south pole.

Cruikshank, Dale P.↗

Implementation of ILLIAC 4 algorithms for multispectral image interpretation

Research has focused on the design and partial implementation of a comprehensive ILLIAC software system for computer-assisted interpretation of multispectral earth resources data such as that now collected by the Earth Resources Technology Satellite. Research suggests generally that the ILLIAC 4 should be as much as two orders of magnitude more cost effective than serial processing computers for digital interpretation of ERTS imagery via multivariate statistical classification techniques. The potential of the ARPA Network as a mechanism for interfacing geographically-dispersed users to an ILLIAC 4 image processing facility is discussed.

Ray, R. M.↗