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Vidakovic, Brani

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Author: Katul, Gabriel ×

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    Assessing the Effects of Atmospheric Stability on the Inertial Subrange of Surface Layer Turbulence using Local and Global Multiscale Approaches
    (Georgia Institute of Technology, 2004-06-19) Shi, Bin ; Vidakovic, Brani ; Albertson, John D. ; Katul, Gabriel
    The conceptual framework for modeling the inertial subrange is strongly influenced by the Richardson cascade, now the subject of various reinterpretations. One apparent departure from the Richardson cascade is attributed to boundary conditions influencing large-scale motion, which in turn, can directly interact with smaller scales thereby destroying the universal statistical scaling attributes of the inertial subrange. Investigating whether boundary conditions and inertial subrange eddies interact continues to be an active research problem in contemporary turbulence research. Using longitudinal (u), lateral (v), and vertical (w) velocities co-located with temperature (T) time series measurements collected in the atmospheric surface layer (ASL), we evaluate whether the inertial subrange is influenced by different stability regimes. The different stability regimes are proxies for different boundary conditions, as upper boundary condition force the mechanical shear and lower boundary condition force surface heating and buoyancy. The novelty of the present work lies in its combined use of global and local scaling properties (e.g. quasi-Hurst exponent, distributional properties of the wavelet coefficients, and Tsallis's thermostatic entropy measures) to assess whether atmospheric stability impacts both local and global inertial subrange scaling.
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    Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence
    (Georgia Institute of Technology, 2004-05-20) Angelini, Claudia ; Cava, Daniela ; Katul, Gabriel ; Vidakovic, Brani
    There is a growing need for statistical methods that generate an ensemble of plausible realizations of a hierarchical process from a single run or experiment. The main challenge is how to construct such an ensemble in a manner that preserves the internal dynamics (e.g. intermittency) and temporal persistency of the hierarchical process. A popular hierarchical process often used as a case study in such problems is atmospheric turbulent flow. Analogies to turbulence are often called upon when information flow from large to small scales, non Gaussian statistics, and intermittency are inherent attributes of the process under consideration. These attributes are key defining syndromes of the turbulent cascade thereby making turbulence time series ideal for testing such ensemble generation schemes. In this study, we propose a wavelet based resampling scheme (WB) and compare it to the traditional Fourier based phase randomization bootstrap (FB) approach within the context of the turbulence energy cascade. The comparison between the two resampling methods and observed ensemble statistics constructed by clustering similar meteorological conditions demonstrate that the WB reproduces several features related to intermittency of the ensemble series when compared to FB. In particular, the WB exhibited an increase in wavelet energy activity and an increase in the wavelet flatness factor with increasing frequency consistent with the cluster of ensemble statistics. On the other hand, the FB yielded no increase in such energy activity with scale and resulted in near Gaussian wavelet coefficients at all frequencies within the inertial subrange. The extension of WB to the multivariate case is also demonstrated via the conservation of co-spectra between longitudinal and vertical velocity time series. Because the resampling strategy proposed here is conducted in the wavelet domain, gap-infected and uneven sampled time series can be readily accommodated within the WB. Finally, recommendations about the filter and block sizes are discussed.
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    Quantifying the Effects of Atmospheric Stability on the Multifractal Spectrum of Turbulence
    (Georgia Institute of Technology, 2004) Shi, Bin ; Vidakovic, Brani ; Katul, Gabriel
    Over the past decade, several studies suggested possible analogy between price dynamics in the foreign exchange market and atmospheric turbulent flows. Such analogies suggest that applications in business and industry can directly benefit from detailed quantification of the scale-hierarchy existing in fully developed turbulent flows. Numerous studies have already demonstrated the multifractal properties of rough-wall boundary layer turbulence. How atmospheric stability (i.e. boundary conditions) alters the multifractal spectrum (MFS) of turbulent velocity and temperature fluctuations in the atmospheric surface layer remains to be investigated. A challenge of estimating the MFS from time series via traditional regression approaches is the heteroskedastic problem because the variance of the error term are shown to depend on scale. Using a combination of Discrete Wavelet Transforms (DWT) and a Weighted Least Squares (WLS) scheme, heteroskedastic effects are minimized and robust estimation of the scaling parameters needed to compute the MFS is derived. Next, to quantify the effects of atmospheric stability on the MFS, discriminative measures that utilize the left slope (rise), Hurst exponent (maxima), and broadness are employed. Distributional property of the estimators for these discriminative measures are investigated based on Monte Carlo simulations. These summary measures are applied to the MFS of velocity and temperature time series collected in the atmospheric surface layer for a wide range of atmospheric stability conditions. The criteria for success in evaluating how atmospheric stability alters the MFS of a single flow variable time series is formulated as a statistical classification model that properly infers the stability regime when these three discriminative measures are used as input vectors.
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    Denoising Ozone Concentration Measurements with BAMS Filtering
    (Georgia Institute of Technology, 2001) Katul, Gabriel ; Ruggeri, Fabrizio ; Vidakovic, Brani
    We propose a method for filtering self-similar geophysical signals corrupted by an antoregressive noise using a combination of non-decimated wavelet transform and a Bayesian model. In the application part, we consider separating the instrumentation noise from high frequency ozone concentration measurements sampled in the atmospheric boundary layer. The elicitation of priors needed to specify the statistical model in this application is guided by the well-known Kolmogorov K41-theory, which describes the statistical structure of the high frequency scalar concentration fluctuations.