Stochastic Multiresolution Models for Turbulence Brandon Whitcher ∗ Jeffrey B. Weiss † Douglas W. Nychka ∗ Timothy J. Hoar ∗ August 6, 2002 Abstract The efficient and accurate representation of two-dimensional turbulent fields is of interest in the geosciences because the fundamental equations that describe turbulence are difficult to handle directly. Rather than extract the coherent portion of the image from the background variation, as in the classical signal plus noise model, we present a statistical model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features we want to extract from the observed field. By transforming the vortex template into the wavelet domain specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the observed vorticity field in the wavelet domain. Key words. multivariate multiple linear regression, non-decimated discrete wavelet transform, pe- nalized likelihood, turbulence, vorticity. * Geophysical Statistics Project, National Center for Atmospheric Research, Boulder, Colorado 80307-3000. E- mail: whitcher@ucar.edu, nychka@ucar.edu, thoar@ucar.edu. † Program in Atmospheric and Oceanic Sciences, Department of Astrophysical, Planetary and Atmospheric Sci- ences, University of Colorado at Boulder, Boulder, Colorado 80309. E-mail: jweiss@colorado.edu.