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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Windowed and Wavelet Analysis of Marine Stratocumulus Cloud Inhomogeneity

To improve radiative transfer calculations for inhomogeneous clouds, a consistent means of modeling inhomogeneity is needed. One current method of modeling cloud inhomogeneity is through the use of fractal parameters. This method is based on the supposition that cloud inhomogeneity over a large range of scales is related. An analysis technique named wavelet analysis provides a means of studying the multiscale nature of cloud inhomogeneity. In this paper, the authors discuss the analysis and modeling of cloud inhomogeneity through the use of wavelet analysis. Wavelet analysis as well as other windowed analysis techniques are used to study liquid water path (LWP) measurements obtained during the marine stratocumulus phase of the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment. Statistics obtained using analysis windows, which are translated to span the LWP dataset, are used to study the local (small scale) properties of the cloud field as well as their time dependence. The LWP data are transformed onto an orthogonal wavelet basis that represents the data as a number of times series. Each of these time series lies within a frequency band and has a mean frequency that is half the frequency of the previous band. Wavelet analysis combined with translated analysis windows reveals that the local standard deviation of each frequency band is correlated with the local standard deviation of the other frequency bands. The ratio between the standard deviation of adjacent frequency bands is 0.9 and remains constant with respect to time. This ratio defined as the variance coupling parameter is applicable to all of the frequency bands studied and appears to be related to the slope of the data's power spectrum. Similar analyses are performed on two cloud inhomogeneity models, which use fractal-based concepts to introduce inhomogeneity into a uniform cloud field. The bounded cascade model does this by iteratively redistributing LWP at each scale using the value of the local mean. This model is reformulated into a wavelet multiresolution framework, thereby presenting a number of variants of the bounded cascade model. One variant introduced in this paper is the 'variance coupled model,' which redistributes LWP using the local standard deviation and the variance coupling parameter. While the bounded cascade model provides an elegant two- parameter model for generating cloud inhomogeneity, the multiresolution framework provides more flexibility at the expense of model complexity. Comparisons are made with the results from the LWP data analysis to demonstrate both the strengths and weaknesses of these models.

Gollmer, Steven M.↗
NASA NTRS1998

Arctic Sea Ice Motion from Wavelet Analysis of Satellite Data

Wavelet analysis of DMSP SSM/I (Special Sensor Microwave/Imager) 85 GHz and 37 GHz radiance data, SMMR (Scanning Multichannel Microwave Radiometer) 37 GHz, and NSCAT (NASA Scatterometer) 13.9 GHZ data can be used to obtain daily sea ice drift information for both the northern and southern polar regions. The derived maps of sea ice drift provide both improved spatial coverage over the existing array of Arctic Ocean buoys and better temporal resolution over techniques utilizing data from satellite synthetic aperture radars (SAR). Examples of derived ice-drift maps in the Arctic illustrate large-scale circulation reversals within a period of a couple weeks. Comparisons with ice displacements derived from buoys show good quantitative agreement. NASA Scatterometer (NSCAT) 13.9 GHZ data have been also used for wavelet analysis to derive sea-ice drift. First, the 40' incidence-angle, sigma-zero (surface roughness) daily map of whole Arctic region with 25 km of pixel size from satellite's 600 km swath has been constructed. Then, the similar wavelet transform procedure to SSM/I data can be applied. Various scales of wavelet transform and threshold have been tested. By overlaying , neighbor filtering, and block-averaging the results of multiscale wavelet transforms, the final sea ice drift vectors are much smooth and representative to the sea ice motion. This wavelet analysis procedure is robust and can make a major contribution to the understanding of ice motion over large areas at relatively high temporal resolutions. The results of wavelet analysis of SSM/I and NSCAT images and buoy data can be merged by some data fusion techniques and will help to improve our current knowledge of sea ice drift and related processes through the data assimilation of ocean-ice numerical model.

Liu, Antony K.↗
NASA NTRS1997

Wavelet Analysis of Satellite Images for Coastal Watch

The two-dimensional wavelet transform is a very efficient bandpass filter, which can be used to separate various scales of processes and show their relative phase/location. In this paper, algorithms and techniques for automated detection and tracking of mesoscale features from satellite imagery employing wavelet analysis are developed. The wavelet transform has been applied to satellite images, such as those from synthetic aperture radar (SAR), advanced very-high-resolution radiometer (AVHRR), and coastal zone color scanner (CZCS) for feature extraction. The evolution of mesoscale features such as oil slicks, fronts, eddies, and ship wakes can be tracked by the wavelet analysis using satellite data from repeating paths. Several examples of the wavelet analysis applied to various satellite Images demonstrate the feasibility of this technique for coastal monitoring.

Liu, Antony K.↗
NASA NTRS2000

Sea Ice Motion from Wavelet Analysis of Satellite Data

Wavelet analysis of NASA scatterometer (NSCAT) backscatter and Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I) radiance data can be used to obtain daily sea ice drift information for the Arctic region. This technique provides improved spatial coverage over the existing array of Arctic Ocean buoys and better temporal resolution over techniques utilizing data from satellite synthetic aperture radars. Comparisons with ice motion derived from ocean buoys give good quantitative agreement. Both comparison results from NSCAT and SSM/I are compatible, and the results from NSCAT can definitely complement that from SSM/I when there are cloud or surface effects. Then three sea-ice drift daily results from NSCAT, SSM/I, and buoy data can be merged as a composite map by some data fusion techniques. The ice flow streamlines are highly correlated with surface air pressure contours. Examples of derived ice-drift maps in December 1996 illustrate large-scale circulation reversals over a period of four days. A method for deriving divergence and shear at the large-scale has been developed and comparison between buoys and satellite results shows a good agreement. These calibrated/validated results indicate that NSCAT, SSM/I merged daily ice motion are suitably accurate to identify and closely locate sea ice processes, and to improve our current knowledge of sea ice drift and related processes through the data assimilation of ocean-ice numerical model. For demonstration purpose, the ice velocities derived from satellite data are compared with the ice velocities derived from a coupled ice-ocean interaction model. The comparison reveals that the general circulation patterns of the two are quite similar but the ice velocity differences between the two are quite significant. In order to quantify the wind effects on ice motion, empirical orthogonal functions (EOF) are used in the principal component analysis for both ice motion and pressure field. Some preliminary results of sea-ice motion from QuikScat will also be presented.

Liu, Antony K.↗
NASA NTRS2019

Statistical Hypothesis Testing in Wavelet Analysis: Theoretical Developments and Applications to Indian Rainfall

Statistical hypothesis tests in wavelet analysis are methods that assess the degree to which a wavelet quantity(e.g., power and coherence) exceeds background noise. Commonly, a point-wise approach is adopted in which a wavelet quantity at every point in a wavelet spectrum is individually compared to the critical level of the point-wise test. However, because adjacent wavelet coefficients are correlated and wavelet spectra often contain many wavelet quantities, the point-wise test can produce many false positive results that occur in clusters or patches. To circumvent the point-wise test drawbacks, it is necessary to implement the recently developed area-wise, geometric, cumulative area-wise, and topological significance tests, which are reviewed and developed in this paper. To improve the computational efficiency of the cumulative area-wise test, a simplified version of the testing procedure is created based on the idea that its output is the mean of individual estimates of statistical significance calculated from the geometric test applied at a set of point-wise significance levels. Ideal examples are used to show that the geometric and cumulative area-wise tests are unable to differentiate wavelet spectral features arising from singularity-like structures from those associated with periodicities. A cumulative arc-wise test is therefore developed to strictly test for periodicities by using normalized arc length, which is defined as the number of points composing a cross section of a patch divided by the wavelet scale in question. A previously proposed topological significance test is formalized using persistent homology profiles (PHPs) measuring the number of patches and holes corresponding to the set of all point-wise significance values. Ideal examples show that the PHPs can be used to distinguish time series containing signal components from those that are purely noise. To demonstrate the practical uses of the existing and newly developed statistical methodologies, a first comprehensive wavelet analysis of Indian rainfall is also provided. An R software package has been written by the author to implement the various testing procedures.

Wind speed↗
NASA NTRS1997

Tracking of Ice Edges and Ice Floes by Wavelet Analysis of SAR Images

This paper demonstrates the use of wavelet transforms in the tracking of sequential ice features in the ERS-1 synthetic aperture radar (SAR) imagery, especially in situations where feature correlation techniques fail to yield reasonable results. Examples include the evolution of the St. Lawrence polynya and summer sea ice change in the Beaufort Sea. For the polynya, the evolution of the region of young ice growth surrounding a polynya can be easily tracked by wavelet analysis due to the large backscatter difference between the young and old ice. Also within the polynya, a 2D fast Fourier transform (FFT) is used to identify the extent of the Langmuir circulation region, which is coincident with the wave-agitated frazil ice growth region, where the sea ice experiences its fastest growth. Therefore, the combination of wavelet and FFT analysis of SAR images provides for the large-scale monitoring of different polynya features. For summer ice, previous work shows that this is the most difficult period for ice trackers due to the lack of features on the sea ice cover. The multiscale wavelet analysis shows that this method delineates the detailed floe shapes during this period, so that between consecutive images, the floe translation and rotation can be estimated.

Liu, Antony K.↗
NASA NTRS1998

Wavelet Analysis of SAR Images for Coastal Monitoring

The mapping of mesoscale ocean features in the coastal zone is a major potential application for satellite data. The evolution of mesoscale features such as oil slicks, fronts, eddies, and ice edge can be tracked by the wavelet analysis using satellite data from repeating paths. The wavelet transform has been applied to satellite images, such as those from Synthetic Aperture Radar (SAR), Advanced Very High-Resolution Radiometer (AVHRR), and ocean color sensor for feature extraction. In this paper, algorithms and techniques for automated detection and tracking of mesoscale features from satellite SAR imagery employing wavelet analysis have been developed. Case studies on two major coastal oil spills have been investigated using wavelet analysis for tracking along the coast of Uruguay (February 1997), and near Point Barrow, Alaska (November 1997). Comparison of SAR images with SeaWiFS (Sea-viewing Wide Field-of-view Sensor) data for coccolithophore bloom in the East Bering Sea during the fall of 1997 shows a good match on bloom boundary. This paper demonstrates that this technique is a useful and promising tool for monitoring of coastal waters.

Liu, Antony K.↗
NASA NTRS1993

An introduction to wavelet analysis in oceanography and meteorology - With application to the dispersion of Yanai waves

Wavelet analysis is a relatively new technique that is an important addition to standard signal analysis methods. Unlike Fourier analysis that yields an average amplitude and phase for each harmonic in a dataset, the wavelet transform produces an instantaneous estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of nonstationary spatial or time-dependent signal characteristics. The wavelet transform is discussed, examples are given, and some methods for preprocessing data for wavelet analysis are compared. By studying the dispersion of Yanai waves in a reduced gravity equatorial model, the usefulness of the transform is demonstrated. The group velocity is measured directly over a finite range of wavenumbers by examining the time evolution of the transform. The results agree well with linear theory at higher wavenumber but the measured group velocity is reduced at lower wavenumbers, possibly due to interaction with the basin boundaries.

Meyers, Steven D.↗
NASA NTRS2015

A Wavelet Analysis Approach for Categorizing Air Traffic Behavior

In this paper two frequency domain techniques are applied to air traffic analysis. The Continuous Wavelet Transform (CWT), like the Fourier Transform, is shown to identify changes in historical traffic patterns caused by Traffic Management Initiatives (TMIs) and weather with the added benefit of detecting when in time those changes take place. Next, with the expectation that it could detect anomalies in the network and indicate the extent to which they affect traffic flows, the Spectral Graph Wavelet Transform (SGWT) is applied to a center based graph model of air traffic. When applied to simulations based on historical flight plans, it identified the traffic flows between centers that have the greatest impact on either neighboring flows, or flows between centers many centers away. Like the CWT, however, it can be difficult to interpret SGWT results and relate them to simulations where major TMIs are implemented, and more research may be warranted in this area. These frequency analysis techniques can detect off-nominal air traffic behavior, but due to the nature of air traffic time series data, so far they prove difficult to apply in a way that provides significant insight or specific identification of traffic patterns.

wavelet analysis↗
NASA NTRS2007

Variability of Solar Irradiances Using Wavelet Analysis

We have used wavelets to analyze the sunspot number, F10.7 (the solar irradiance at a wavelength of approx.10.7 cm), and Ap (a geomagnetic activity index). Three different wavelets are compared, showing how each selects either temporal or scale resolution. Our goal is an envelope of solar activity that better bounds the large amplitude fluctuations form solar minimum to maximum. We show how the 11-year cycle does not disappear at solar minimum, that minimum is only the other part of the solar cycle. Power in the fluctuations of solar-activity-related indices may peak during solar maximum but the solar cycle itself is always present. The Ap index has a peak after solar maximum that appears to be better correlated with the current solar cycle than with the following cycle.

Pesnell, William D.↗
NASA NTRS2004

Reduced-Order Modeling and Wavelet Analysis of Turbofan Engine Structural Response Due to Foreign Object Damage (FOD) Events

The development of a wavelet-based feature extraction technique specifically targeting FOD-event induced vibration signal changes in gas turbine engines is described. The technique performs wavelet analysis of accelerometer signals from specified locations on the engine and is shown to be robust in the presence of significant process and sensor noise. It is envisioned that the technique will be combined with Kalman filter thermal/health parameter estimation for FOD-event detection via information fusion from these (and perhaps other) sources. Due to the lack of high-frequency FOD-event test data in the open literature, a reduced-order turbofan structural model (ROM) was synthesized from a finite element model modal analysis to support the investigation. In addition to providing test data for algorithm development, the ROM is used to determine the optimal sensor location for FOD-event detection. In the presence of significant noise, precise location of the FOD event in time was obtained using the developed wavelet-based feature.

Turso, James↗
NASA NTRS2007

Reduced-Order Modeling and Wavelet Analysis of Turbofan Engine Structural Response Due to Foreign Object Damage "FOD" Events

The development of a wavelet-based feature extraction technique specifically targeting FOD-event induced vibration signal changes in gas turbine engines is described. The technique performs wavelet analysis of accelerometer signals from specified locations on the engine and is shown to be robust in the presence of significant process and sensor noise. It is envisioned that the technique will be combined with Kalman filter thermal/ health parameter estimation for FOD-event detection via information fusion from these (and perhaps other) sources. Due to the lack of high-frequency FOD-event test data in the open literature, a reduced-order turbofan structural model (ROM) was synthesized from a finite-element model modal analysis to support the investigation. In addition to providing test data for algorithm development, the ROM is used to determine the optimal sensor location for FOD-event detection. In the presence of significant noise, precise location of the FOD event in time was obtained using the developed wavelet-based feature.

Turso, James A.↗
NASA NTRS1995

Pseudo-wavelet analysis of turbulence patterns in three vegetation layers

Ramp patterns in scalar traces such as temperature are the signature of coherent structures. A pseudo-wavelet analysis technique was developed in which ideal saw-tooth patterns of varying size were used as basis functions and fitted to temperature and velocity data. Data recorded from three very different vegetation stands were examined in this study. It was found that the most probable structure duration for the forest canopy was in the range 35-40 s, for the orchard canopy it was 20-25 s and for the maize it was 15-20 s. When expressed in non-dimensional form, the structure duration probability distribution for the maize canopy was about a decade larger than for the forest canopy, with the orchard canopy intermediate. The mean eddy duration versus wind shear relation falls on a narrow band for all three canopies, indicating that wind shear at the canopy top is the determining factor for the scale of the coherent eddies. The inverse of duration and intermittency of coherent structures exhibits a tendency of independence from wind shear at higher wind shear values. Coherent structures transport heat in a more efficient way than do smaller scale, less coherent motions. In all the canopies, the heat flux fractions associated with coherent structures are at least 10% higher than the corresponding time fraction.

Qiu, Jie↗
NASA NTRS1998

Wavelet Analysis of Turbulent Spots and Other Coherent Structures in Unsteady Transition

This is a secondary analysis of a portion of the Halstead data. The hot-film traces from an embedded stage of a low pressure turbine have been extensively analyzed by Halstead et al. In this project, wavelet analysis is used to develop the quantitative characterization of individual coherent structures in terms of size, amplitude, phase, convection speed, etc., as well as phase-averaged time scales. The purposes of the study are (1) to extract information about turbulent time scales for comparison with unsteady model results (e.g. k/epsilon). Phase-averaged maps of dominant time scales will be presented; and (2) to evaluate any differences between wake-induced and natural spots that might affect model performance. Preliminary results, subject to verification with data at higher frequency resolution, indicate that spot properties are independent of their phase relative to the wake footprints: therefore requirements for the physical content of models are kept relatively simple. Incidentally, we also observed that spot substructures can be traced over several stations; further study will examine their possible impact.

Lewalle, Jacques↗
NASA NTRS1994

Wavelet analysis applied to the IRAS cirrus

The structure of infrared cirrus clouds is analyzed with Laplacian pyramid transforms, a form of non-orthogonal wavelets. Pyramid and wavelet transforms provide a means to decompose images into their spatial frequency components such that all spatial scales are treated in an equivalent manner. The multiscale transform analysis is applied to IRAS 100 micrometer maps of cirrus emission in the north Galactic pole region to extract features on different scales. In the maps we identify filaments, fragments and clumps by separating all connected regions. These structures are analyzed with respect to their Hausdorff dimension for evidence of the scaling relationships in the cirrus clouds.

Langer, William D.↗
NASA NTRS1990

Continuous wavelet analysis of coherent structures

We perform an analysis of planar cuts through three dimensional turbulent fields (planar channel flow and mixing layer) using the 2D continuous wavelet transform. We propose two new diagnostics: (1) a measure of intermittency I(r, vector x), which is the ratio of local energy and average energy at a given scale r; and (2) a local Reynolds number, defined on the local velocity contribution at a given scale, computed from the wavelet transform of the three velocity components, the scale of the transform, and molecular viscosity; this gives a representation of the local non-linearity of the flow viewed in both space and scale. We find, for the analyzed flows, strong small-scale intermittency located in the ejection regions for the channel flow and in the vortex core of the mixing layer.

Farge, M.↗
NASA NTRS2001

Efficient hemodynamic event detection utilizing relational databases and wavelet analysis

Development of a temporal query framework for time-oriented medical databases has hitherto been a challenging problem. We describe a novel method for the detection of hemodynamic events in multiparameter trends utilizing wavelet coefficients in a MySQL relational database. Storage of the wavelet coefficients allowed for a compact representation of the trends, and provided robust descriptors for the dynamics of the parameter time series. A data model was developed to allow for simplified queries along several dimensions and time scales. Of particular importance, the data model and wavelet framework allowed for queries to be processed with minimal table-join operations. A web-based search engine was developed to allow for user-defined queries. Typical queries required between 0.01 and 0.02 seconds, with at least two orders of magnitude improvement in speed over conventional queries. This powerful and innovative structure will facilitate research on large-scale time-oriented medical databases.

NASA Discipline Cardiopulmonary↗