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Ning Wang and Chungu Lu

1. Introduction The wavelet transform has become an important diagnostic tool for analyzing nonstationary signals. In particular, the continuous wavelet transform (CWT) serves as a continuously sweeping “microscope” in examining the spectral components of the dataset. The name CWT refers, in general, to the integral transform of functions of L 2 ( R ) with a wavelet function as transformation kernel. However, in practice, we usually use the name CWT to refer to the wavelet transform that

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Likun Wang and Kenneth Sassen

underrepresentation of low-frequency components ( Meyers et al. 1993 ). The wavelet transform (WT), on the other hand, uses generalized local base functions (wavelets) that can be stretched and translated with a flexible resolution in both frequency and time, and has been successfully applied to study cirrus dynamic processes and structures ( Smith and Jonas 1997 ; Demoz et al. 1998 ; Quante et al. 2002 ; Wang and Sassen 2006 ; Sassen et al. 2007 ). The time and height variations of a high-resolution lidar

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Shun Liu, Ming Xue, and Qin Xu

(compared to the adjacent radar gate distance in the azimuth) or between regions can provide valuable information that can potentially be utilized to reduce the false alarm rate of detection. In this paper, we use the wavelet analysis technique for the quantification of velocity differences at different spatial scales and use these measures to help design or improve tornado detection algorithms. In particular, a set of wavelet basis functions will be used and each basis function describes the averaged

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Yonggang Liu, X. San Liang, and Robert H. Weisberg

1. Introduction Wavelet analysis may be advantageous over the classical Fourier analysis in that it unfolds a time series not only in frequency but also in time, which is especially useful when the signal is nonstationary. Because of this property, wavelet analysis has been widely applied across disciplines since its introduction in the early 1980s. See Daubechies (1992) , Chui (1992) , Meyer (1992) , Strang and Nguyen (1997) , Percival and Walden (2000) , and references therein, for a

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Bryan K. Woods and Ronald B. Smith

spatial information. Wavelet transforms can be used to simultaneously present location and wavelength information. Through the use of complex wavelets, the continuous wavelet transforms of two variables, such as p ′ and w ′, can be combined to create a cross-spectrum, in this case representing vertical energy flux. Wavelet energy flux calculations have not previously been employed in aircraft mountain-wave studies, although complex wavelet analysis of satellite brightness temperatures ( Alexander

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Olivier Pannekoucke

complex domains (e.g., in ocean modeling with coasts). But in their current formalism, neither the recursive filters nor the diffusion operator are able to represent the nonseparability of statistics. However, an improvement of the spectral formulation, designed with the spherical wavelets, has been proposed by Fisher and Andersson (2001 ; see also Fisher 2003) . This correlation model is heterogeneous and nonseparable. An equivalent wavelet diagonal assumption has been considered by Deckmyn and

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Samantha Stevenson, Baylor Fox-Kemper, Markus Jochum, Balaji Rajagopalan, and Stephen G. Yeager

Assessment Report (AR4)-class climate models at both fine and coarse resolutions ( Jochum et al. 2009 ). Although biases remain, this version of CCSM performs as well as the current generation of coupled models at a relatively low computational cost, and it has therefore been used as the primary coupled model for this study. This paper uses long integrations of the coarse-resolution CCSM3.5 to illustrate a new, wavelet-based probabilistic model validation method, capable of dealing with skewed and

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Antonio Turiel, Jordi Isern-Fontanet, and Emilio García-Ladona

problem, still on the frame of 2D turbulence, has been introduced through wavelet analysis of the vorticity field ( Siegel and Weiss 1997 ; Farge et al. 1999 ; Farge and Schneider 2001 ). Flow is decomposed as a coherent, inhomogeneous, non-Gaussian component formed by a set of vortices at different scales and an incoherent homogeneous Gaussian component characteristic of the background flow ( Farge et al. 1999 ). When applied to numerical simulations, this method has shown good performance for

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Ross N. Bannister

dependencies of the vertical covariances ( Lorenc et al. 2000 ). This scheme is reviewed in section 3 , as the new wavelet-based methods introduced here adopt some conventions used in the Met Office’s current scheme. A wavelet possesses a characteristic scale, and concurrently, occupies a position in space. It is this property that makes wavelets attractive for the modeling of spatial error covariances in VAR, which has been looked at in different contexts. Tangborn (2004) has examined this in a Kalman

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Nathan J. M. Laxague, Brian K. Haus, David G. Ortiz-Suslow, and Hans C. Graber

study. The early 1980s saw the development of the wavelet transform, a nonstationary signal processing technique ( Morlet et al. 1982 ; Grossmann and Morlet 1984 ). An expansion of its modes of application in the areas of image and signal processing during the 1990s brought some promising results related to the field of geophysical fluid dynamical analysis ( Liu et al. 1995a , b ; Peng et al. 1995 ; Donelan et al. 1996 ). However, these earlier works were limited in that their investigations were

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