Analysis of convectively-generated gravity waves in mesoscale model simulations and wind profiler observations

The characteristics of convectively-generated gravity waves during an episode of deep convection near the coast of Wales are examined in both high resolution mesoscale simulations [with the (UK) Met Oce Unified Model] and in observations from a Mesosphere-Stratosphere-Troposphere (MST) wind profiling Doppler radar. Deep convection reached the tropopause and generated vertically propagating, high frequency waves in the lower stratosphere that produced vertical velocity perturbations O(1 m/s). Wavelet analysis is applied in order to determine the characteristic periods and wavelengths of the waves. In both the simulations and observations, the wavelet spectra contain several distinct preferred scales indicated by multiple spectral peaks. The peaks are most pronounced in the horizontal spectra at several wavelengths less than 50 km. Although these peaks are most clear and of largest amplitude in the highest resolution simulations (with 1 km horizontal grid length), they are also evident in coarser simulations (with 4 km horizontal grid length). Peaks also exist in the vertical and temporal spectra (between approximately 2.5 and 4.5 km, and 10 to 30 minutes, respectively) with good agreement between simulation and observation. Two-dimensional (wavenumber-frequency) spectra demonstrate that each of the selected horizontal scales contains peaks at each of preferred temporal scales revealed by the one- dimensional spectra alone.

Reconhecimento de padrões via Wavelets: aplicação no monitoramento de estruturas a partir do efeito do multicaminho proveniente de sinais de satélites GPS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Solar-Terrestrial Signal Record in Tree Ring Width Time Series from Brazil

This work investigates the behavior of the sunspot number and Southern Oscillation Index (SOI) signal recorded in the tree ring time series for three different locations in Brazil: Humaita in Amaznia State, Porto Ferreira in So Paulo State, and Passo Fundo in Rio Grande do Sul State, using wavelet and cross-wavelet analysis techniques. The wavelet spectra of tree ring time series showed signs of 11 and 22 years, possibly related to the solar activity, and periods of 2-8 years, possibly related to El Nio events. The cross-wavelet spectra for all tree ring time series from Brazil present a significant response to the 11-year solar cycle in the time interval between 1921 to after 1981. These tree ring time series still have a response to the second harmonic of the solar cycle (5.5 years), but in different time intervals. The cross-wavelet maps also showed that the relationship between the SOI x tree ring time series is more intense, for oscillation in the range of 4-8 years.

Classification of lactose and mandelic acid THz spectra using subspace and wavelet-packet algorithms

This work compares classification results of lactose, mandelic acid and dl-mandelic acid, obtained on the basis of their respective THz transients. The performance of three different pre-processing algorithms applied to the time-domain signatures obtained using a THz-transient spectrometer are contrasted by evaluating the classifier performance. A range of amplitudes of zero-mean white Gaussian noise are used to artificially degrade the signal-to-noise ratio of the time-domain signatures to generate the data sets that are presented to the classifier for both learning and validation purposes. This gradual degradation of interferograms by increasing the noise level is equivalent to performing measurements assuming a reduced integration time. Three signal processing algorithms were adopted for the evaluation of the complex insertion loss function of the samples under study; a) standard evaluation by ratioing the sample with the background spectra, b) a subspace identification algorithm and c) a novel wavelet-packet identification procedure. Within class and between class dispersion metrics are adopted for the three data sets. A discrimination metric evaluates how well the three classes can be distinguished within the frequency range 0. 1 - 1.0 THz using the above algorithms.

Optimal discrimination and classification of THz spectra in the wavelet domain

In rapid scan Fourier transform spectrometry, we show that the noise in the wavelet coefficients resulting from the filter bank decomposition of the complex insertion loss function is linearly related to the noise power in the sample interferogram by a noise amplification factor. By maximizing an objective function composed of the power of the wavelet coefficients divided by the noise amplification factor, optimal feature extraction in the wavelet domain is performed. The performance of a classifier based on the output of a filter bank is shown to be considerably better than that of an Euclidean distance classifier in the original spectral domain. An optimization procedure results in a further improvement of the wavelet classifier. The procedure is suitable for enhancing the contrast or classifying spectra acquired by either continuous wave or THz transient spectrometers as well as for increasing the dynamic range of THz imaging systems. (C) 2003 Optical Society of America.

Rapid Oscillations in the Solar Atmosphere: Spectra and Physical Effects

High-frequency fluctuations are observed with the Rapid Oscillations in the Solar Atmosphere (ROSA) instrument (Jess et al. 2010, Solar Phys, 261, 363) at the Dunn Solar Telescope. This can produce simultaneous observations in up to six channels, at different heights in the photosphere and chromosphere, at an unprecedentedly high cadence of 0.5 seconds, and at a spatial resolution of 100 km after photometrically correct speckle reconstruction. Here we concentrate on observations at two levels. The first is in the G-band of the CH radical at 4305.5Å, bandpass 9.2Å, with height of formation z <250 km at a cadence of 0.525 sec corresponding to Nyquist frequency 950 mHz. The second is in the Ca II K-line core at 3933.7Å, bandpass 1.0Å, with height of formation z <1300 km, and cadence 4.2 sec giving Nyquist frequency 120 mHz. The data span 53 min, and the maximum field of view is 45 Mm. The data were taken on 28 May 2009 in internetwork and network near disk center. Using both Fourier and Morlet wavelet methods we find evidence in the G-band spectra for intensity fluctuations above noise out to frequencies f >> 100 mHz. The K-line signal is noisier and is seen only for f <50 mHz. With wavelet techniques we find that G-band spectral power with 20 <f <100 mHz is clearly concentrated in the intergranular lanes and especially at the locations of magnetic elements indicated by G-band bright points. This wavelet power is highly intermittent in time. By cross-correlating the data we find that pulses of high-frequency G-band power in the photosphere tend to be followed by increases in K-line emission in the chromosphere with a time lag of about 2 min.

Wavelet based detection of changes in the composition of RLC networks

The current work discusses the compositional analysis of spectra that may be related to amorphous materials that lack discernible Lorentzian, Debye or Drude responses. We propose to model such response using a 3-dimensional random RLC network using a descriptor formulation which is converted into an input-output transfer function representation. A wavelet identification study of these networks is performed to infer the composition of the networks. It was concluded that wavelet filter banks enable a parsimonious representation of the dynamics in excited randomly connected RLC networks. Furthermore, chemometric classification using the proposed technique enables the discrimination of dielectric samples with different composition. The methodology is promising for the classification of amorphous dielectrics.

Application of two-dimensional wavelet transform in near-shore X-band radar images

Among existing remote sensing applications, land-based X-band radar is an effective technique to monitor the wave fields, and spatial wave information could be obtained from the radar images. Two-dimensional Fourier Transform (2-D FT) is the common algorithm to derive the spectra of radar images. However, the wave field in the nearshore area is highly non-homogeneous due to wave refraction, shoaling, and other coastal mechanisms. When applied in nearshore radar images, 2-D FT would lead to ambiguity of wave characteristics in wave number domain. In this article, we introduce two-dimensional Wavelet Transform (2-D WT) to capture the non-homogeneity of wave fields from nearshore radar images. The results show that wave number spectra by 2-D WT at six parallel space locations in the given image clearly present the shoaling of nearshore waves. Wave number of the peak wave energy is increasing along the inshore direction, and dominant direction of the spectra changes from South South West (SSW) to West South West (WSW). To verify the results of 2-D WT, wave shoaling in radar images is calculated based on dispersion relation. The theoretical calculation results agree with the results of 2-D WT on the whole. The encouraging performance of 2-D WT indicates its strong capability of revealing the non-homogeneity of wave fields in nearshore X-band radar images.

VELOCITY FIELD OF COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE: WAVELET DECOMPOSITION AND MODE SCALINGS

We study compressible magnetohydrodynamic turbulence, which holds the key to many astrophysical processes, including star formation and cosmic-ray propagation. To account for the variations of the magnetic field in the strongly turbulent fluid, we use wavelet decomposition of the turbulent velocity field into Alfven, slow, and fast modes, which presents an extension of the Cho & Lazarian decomposition approach based on Fourier transforms. The wavelets allow us to follow the variations of the local direction of the magnetic field and therefore improve the quality of the decomposition compared to the Fourier transforms, which are done in the mean field reference frame. For each resulting component, we calculate the spectra and two-point statistics such as longitudinal and transverse structure functions as well as higher order intermittency statistics. In addition, we perform a Helmholtz-Hodge decomposition of the velocity field into incompressible and compressible parts and analyze these components. We find that the turbulence intermittency is different for different components, and we show that the intermittency statistics depend on whether the phenomenon was studied in the global reference frame related to the mean magnetic field or in the frame defined by the local magnetic field. The dependencies of the measures we obtained are different for different components of the velocity; for instance, we show that while the Alfven mode intermittency changes marginally with the Mach number, the intermittency of the fast mode is substantially affected by the change.

Análise wavelet e modelo de manchas em curvas de luz estelares dos telescópios espaciais Kepler e CoRoT

Analogous to sunspots and solar photospheric faculae, which visibility is modulated by stellar rotation, stellar active regions consist of cool spots and bright faculae caused by the magnetic field of the star. Such starspots are now well established as major tracers used to estimate the stellar rotation period, but their dynamic behavior may also be used to analyze other relevant phenomena such as the presence of magnetic activity and its cycles. To calculate the stellar rotation period, identify the presence of active regions and investigate if the star exhibits or not differential rotation, we apply two methods: a wavelet analysis and a spot model. The wavelet procedure is also applied here to study pulsation in order to identify specific signatures of this particular stellar variability for different types of pulsating variable stars. The wavelet transform has been used as a powerful tool for treating several problems in astrophysics. In this work, we show that the time-frequency analysis of stellar light curves using the wavelet transform is a practical tool for identifying rotation, magnetic activity, and pulsation signatures. We present the wavelet spectral composition and multiscale variations of the time series for four classes of stars: targets dominated by magnetic activity, stars with transiting planets, those with binary transits, and pulsating stars. We applied the Morlet wavelet (6th order), which offers high time and frequency resolution. By applying the wavelet transform to the signal, we obtain the wavelet local and global power spectra. The first is interpreted as energy distribution of the signal in time-frequency space, and the second is obtained by time integration of the local map. Since the wavelet transform is a useful mathematical tool for nonstationary signals, this technique applied to Kepler and CoRoT light curves allows us to clearly identify particular signatures for different phenomena. In particular, patterns were identified for the temporal evolution of the rotation period and other periodicity due to active regions affecting these light curves. In addition, a beat-pattern vii signature in the local wavelet map of pulsating stars over the entire time span was also detected. The second method is based on starspots detection during transits of an extrasolar planet orbiting its host star. As a planet eclipses its parent star, we can detect physical phenomena on the surface of the star. If a dark spot on the disk of the star is partially or totally eclipsed, the integrated stellar luminosity will increase slightly. By analyzing the transit light curve it is possible to infer the physical properties of starspots, such as size, intensity, position and temperature. By detecting the same spot on consecutive transits, it is possible to obtain additional information such as the stellar rotation period in the planetary transit latitude, differential rotation, and magnetic activity cycles. Transit observations of CoRoT-18 and Kepler-17 were used to implement this model.

Análise wavelet da variabilidade do quasar 3C 273

Discovered in 1963, 3C 273 was the second quasar identified and cataloged in the Third Cambridge Catalog for radio sources, and the first one for which emission lines were identified with a hydrogen sequence redshifted. It is the brightest quasar of the celestial sphere, the most studied, analyzed, and with a resulting abundance of data available in a vast literature. The accurate analysis of the deviations of the spectral lines of quasars provides enough information to put in evidence the variation of fundamental constants of nature and similarly the universe expansion rate. The analysis of the variability of the light curves of these bodies, and the consequent accuracy of their periodicity, is of utmost importance as it provides an efficiency of their observations, enables a greater understanding of the physical phenomena, and makes it possible to conduct spectral observations on more accurate dates (when their light curves show pronounced peaks and therefore richer spectra information). In this master’s thesis twenty eight light curves from the quasar 3C 273 are studied, covering all the electromagnetic spectrum wavebands (radio emission to gamma rays), totaling in the analysis of four light curves for each waveband. We have applied the method of Continuous Wavelet Transform using the sixth-order (!0 = 6) Morlet wavelet function, and obtained excellent results in accordance with the literature.

Análise wavelet da variabilidade do quasar 3C 273

Discovered in 1963, 3C 273 was the second quasar identified and cataloged in the Third Cambridge Catalog for radio sources, and the first one for which emission lines were identified with a hydrogen sequence redshifted. It is the brightest quasar of the celestial sphere, the most studied, analyzed, and with a resulting abundance of data available in a vast literature. The accurate analysis of the deviations of the spectral lines of quasars provides enough information to put in evidence the variation of fundamental constants of nature and similarly the universe expansion rate. The analysis of the variability of the light curves of these bodies, and the consequent accuracy of their periodicity, is of utmost importance as it provides an efficiency of their observations, enables a greater understanding of the physical phenomena, and makes it possible to conduct spectral observations on more accurate dates (when their light curves show pronounced peaks and therefore richer spectra information). In this master’s thesis twenty eight light curves from the quasar 3C 273 are studied, covering all the electromagnetic spectrum wavebands (radio emission to gamma rays), totaling in the analysis of four light curves for each waveband. We have applied the method of Continuous Wavelet Transform using the sixth-order (!0 = 6) Morlet wavelet function, and obtained excellent results in accordance with the literature.

Análise wavelet em curvas de luz estelares de sistemas binários da missão espacial CoRoT

Binary systems are key environments to study the fundamental properties of stars. In this work, we analyze 99 binary systems identified by the CoRoT space mission. From the study of the phase diagrams of these systems, our sample is divided into three groups: those whose systems are characterized by the variability relative to the binary eclipses; those presenting strong modulations probably due to the presence of stellar spots on the surface of star; and those whose systems have variability associated with the expansion and contraction of the surface layers. For eclipsing binary stars, phase diagrams are used to estimate the classification in regard to their morphology, based on the study of equipotential surfaces. In this context, to determine the rotation period, and to identify the presence of active regions, and to investigate if the star exhibits or not differential rotation and study stellar pulsation, we apply the wavelet procedure. The wavelet transform has been used as a powerful tool in the treatment of a large number of problems in astrophysics. Through the wavelet transform, one can perform an analysis in time-frequency light curves rich in details that contribute significantly to the study of phenomena associated with the rotation, the magnetic activity and stellar pulsations. In this work, we apply Morlet wavelet (6th order), which offers high time and frequency resolution and obtain local (energy distribution of the signal) and global (time integration of local map) wavelet power spectra. Using the wavelet analysis, we identify thirteen systems with periodicities related to the rotational modulation, besides the beating pattern signature in the local wavelet map of five pulsating stars over the entire time span.