Partner organizations:

National Center For Atmospheric Research : Facilities

NCAR provided computer resources for access to National Meteorological
Center analyses of Northern Hemispheric meteorological fields, for
analysis by new methods developed by Dr. Fournier.

Stanford University : Facilities

Stanford University Department of Statistics personnel Jonathan
Buckheit, Shaobing Chen, David Donoho, Iain M. Johnstone, Eric
Kolaczyk and Thomas P.-Y. Yu, with NASA-Ames personnel Jeffrey
Scargle, partially supported by NSF-DMS-92-09130, authored a MATLAB
program package, WaveLab, which was encorporated into some of Dr.
Fournier's original analysis software.  Prof. Donoho and Drs. Buckheit
and Yu also contributed technical support.

Other collaborators:

The following scientists were consulted by Dr. Fournier in respect to
the project research on more than one occasion: Profs. G. Veronis and
B.B. Mandelbrot and Dr. E.W. Bolton at Yale, Prof. G. Beylkin at U.
CO. Boulder, Prof. M.V. Wickerhauser at Washington U., St. Louis, Dr.
M. Farge at Laboratoire de Meteorologie Dynamique du C.N.R.S., Paris,
and Dr. D.E. Stevens, Lawrence Berkeley National Lab.

Activities and findings:

Research Activities:
Dr. Fournier developed new orthonormal wavelet-based representation
and energetics computation techniques, and applied them to atmospheric
flow data from numerical models of various complexities, and also from
Northern Hemispheric (NH) observations.

Dr. Fournier gave 30 scientific presentations, including five at
American Geophysical Union and six at European Geophysical Society
meetings, and the 30th Annual Canadian Meteorological & Oceanographic
Society Congress, Toronto and 21st Annual Conference on Mathematical
Geophysics, Santa Fe.
 

Research Findings: 
Orthonormal wavelet analysis (WA) is a mathematical technique that may
be applied to very efficiently represent atmospheric structures, and
to usefully diagnose the transfers of kinetic energy (KE) between
scales, localized in space.

Methods have been developed to compensate for the lack of symmetry and
translation invariance of WA.

For atmospheric ``blocking,'' and similar spatially localized
structures, WA offers some advantage over traditional Fourier
analysis. Analysis of 180 semi-daily observed NH flows introduces
quantification of energetic features which in the literature have only
been inferred qualitatively, such as straining of upstream eddies and
maintenance of blocking by localized up-scale KE cascade, although the
data are too short in time to provide statistical significance.

Research Training: 
Dr. Fournier was trained in Geophysical Fluid Dynamics, Dynamical
Meteorology, Climate Dynamics, Dynamical Systems, Turbulence,
Radiative Transfer, Partial Differential Equations, and Real, Fourier,
Wavelet, Fractal and Numerical Analysis methods, and other
disciplines, and programming in Fortran and MATLAB, and use of Earth
Resource Mapper, HTML, LaTeX, NCARGraphics, netCDF, Spyglass, and
other computational tools.

Education and Outreach: 
Dr. Fournier gave 30 scientific presentations related to this
project.

Concurrently but not funded by this project, Dr. Fournier participated
in or coordinated the Yale College Math & Science Tutoring Program,
Academic Mentor Program in the Sciences, Hillhouse HS Science Club,
SAT Mathematics Preparation, Union of Concerned Scientists Sound
Science Initiative, and taught Calculus.

Dr. Fournier has also written letters to Congress and the press to
increase public understanding of science.

Journal publications:

Fournier, A., "Introduction to orthonormal wavelet analysis with shift invariance: Application to blocking spatial structure", Bulletin of the American Meteorological Society, vol. ??, (????). Submitted

Fournier, A., "Atmospheric energetics in the wavelet domain Part I: Governing equations and interpretation for idealized flows", Journal of the Atmospheric Sciences, vol. ??, (????). Submitted

Fournier, A., "Atmospheric energetics in the wavelet domain Part II: Time-averaged blocking", Journal of the Atmospheric Sciences, vol. ??, (????). Submitted

Fournier, A., "Atmospheric energetics in the wavelet domain Part III: Instantaneous transfers between block and local eddies", Journal of the Atmospheric Sciences, vol. ??, (????). Submitted

Book(s) or other one-time publication(s):

Fournier, A. and Stevens, D.E., "Wavelet multiresolution analysis of numerically simulated 3d radiative convection" , bibl. SPIE, (1996). Book
Fournier, A., "Wavelet analysis of observed geopotential and wind: blocking and local energy coupling across scales" , bibl. SPIE, (1996). Book
Fournier, A., "Wavelet representation of lower-atmospheric long nonlinear wave dynamics, governed by the Benjamin-Davis-Ono-Burgers equation" , bibl. SPIE, (1995). Book
Fournier, A., "Wavelet Analysis of Atmospheric Blocking Dynamics and Energetics" , bibl. Yale University, (1998). Thesis
Fournier, A., "Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking" , bibl. Cambridge University Press 0-521-59311-5, (1998). Book , Accepted
Fournier, A., "Description of nonlinear triad interactions in fluid dynamics using trilinear coordinates" , bibl. Annales Geophysicae Part IV, Supplement IV to Volume 16, (1998). Other
Fournier, A., "Resolution of a nonlinear function of a signal into smooth and singular or intermittent parts, using wavelet paraproduct" , bibl. Annales Geophysicae Part IV, Supplement IV to Volume 16, (1998). Other
Fournier, A., "Efficient representation of coherent structures by translation-invariant orthonormal wavelet analysis" , bibl. Annales Geophysicae Part IV, Supplement IV to Volume 16, (1998). Other
Fournier, A., "Formulation of energetic triadic interactions in the orthonormal wavelet representation of fluid dynamics" , bibl. Annales Geophysicae Part IV, Supplement IV to Volume 16, (1998). Other
Fournier, A., "Triadic interaction of observed atmospheric blocking- and cyclonic-scale vortices in the orthonormal wavelet representation" , bibl. Annales Geophysicae Part IV, Supplement IV to Volume 16, (1998). Other

Contributions:

Contributions within Discipline: 
Dr. Fournier was informed by U. Tsukuba Institute of Geoscience Prof.
Hiroshi L. Tanaka (e-mail of 1996/9/14) that his graduate student,
Akira Hasegawa, presented a seminar introducing Dr. Fournier's work,
using materials downloaded from Dr. Fournier's website, that they
intended to also apply wavelet-based energetics to study atmospheric
blocking, and that they did ``already pay great attention to [Dr.
Fournier's] work.''

Prof. Saltzman had discussed Dr. Fournier's work with Prof. Tanaka at
an earlier date.

As of 1998/10/13 the following investigators have requested papers
related to this project from Dr. Fournier: Patrice Abry (ENS-Lyon),
Vasilios Alexiades (ORNL), Julio Bacmeister (NRL), Steven K. Baum
(Texas A&M U.), Stephen Bergeron (U. Montreal), Dale H. Boggs (NASA
JPL), Didier Boiteux (INSA-Lyon Scientific and Technical U.), Joseph
L. Breeden (Santa Fe Inst.), Christopher M. Brislawn (LANL), Margaret
K. Brown (PNL), Robert F. Cahalan (NASA GSFC), Carlos Castillo-Chavez
(Cornell U.), Philippe Charton (Laboratoire de Meteorologie Dynamique
du CNRS), Er-Woon Chiou (NASA Langley), Won Gyu Choe (POSTECH), David
Colella (Mitre), Jim Craft (NASA-LARC), Belay Demoz (NASA GSFC),
Dao-Qing Dai (Zhongshan University), Xingang Dai (U. Catholique de
Louvain), W.J. Decker (U. VA Reactor Facility), Margarete Oliveira
Domingues (U. Campinas), Mihai Dorobantu (KTH), John B. Drake (ORNL),
William J. Dupree (U. Colorado), Gunnar Eidmann (U. Wuppertal), Dieter
Eppel (GKSS), A. Fabrikant (Penn State U.), Edward P. Flinchem (U.
Washington), Chris E. Forest (MIT), Hans Fraaije (U. Groningen), Yoshi
Fujiwara (Yukawa Institute for Theoretical Physics), Langis Gagnon (U.
Montreal), Roberto O. Gandulfo (UNB), Amadou Thierno Gaye (LPA ENSUT),
Gertie Geertsema (KNMI), German Poveda J. (U. Nacional de Colombia),
Jochen Goettelmann (U. Mainz), T. R. Gowrishankar (U. Chicago), David
F Griffiths (U. Dundee), Ioan Grosu (Beckman Inst.), Emilio
Hernandez-Garcia (IMEDEA), P.J. Hinton (U. Notre Dame), John Hornstein
(NRL), Peter Houtekamer (U. Montreal), Zhenglin Hu (U. Cincinnati),
Mayer Humi (WPI), Ben H. Jansen (U. Houston), Harm Jonker (KNMI), Jim
Kadtke (UCSD), Kajdan Dimitry (Technion), Jan Gerrit Kootstra (RUG),
Kim Kwang (TAMU), David Lane (Mobil Exploration and Production
Technical Center), Jyh-hao Lee (Academia Sinica), Daniel Lemire (U.
Toronto), Jacques Lewalle (Syracuse U.), Bailian Li (Texas A&M U.),
Shu-Guang Li (Portland State U.), Marcel Liauw (U. Houston), Chao-Ting
Lin (Academia Sinica), Kent Lindquist (Fairbanks Geophysical Inst.),
Peter Lipa (Inst. fuer Hochenergiephysik), Hanli Liu (U. Michigan), R.
Llave (U. TX Austin), F.L. Ludwig (Stanford U.), Dan Luss (U.
Houston), H. Lustfeld (KFA-JFF), Glenn Martin (UCF), Hedley Morris
(SJSU), Vasudeva Murthy (Indian Inst. of Science), Ranjan Muttiah
(TAMU), Norberto Nigro (UNL), Ole M. Nielsen (Technical U. of
Denmark), R.M. Oba (Stennis Space Center), Jose Ochoa (CICESE), Efim
Pelinovsky (Inst. of Applied Physics, Nizhny Novogorod), Jon Perras
(NASA GSFC), Pfenniger Daniel (U. Geneva), John Polygiannakis (U.
Athens), Ying Qi (Atmospheric Environment Service), Xiaoshu Qian (U.
Rhode Island), Jonathon Ralston (Queensland U. of Technology),
Jayakumar Ramanathan (Eastern Michigan U.), Peter Read (Oxford U.),
Carolyn Reynolds (NRL), Ranzi Roberto (U. Brescia), A.J. Roberts (U.
Southern Queensland), Anita Ruedin (UBA), Paolo Ruti (ENEA), Ginette
Saracco (Geosciences Rennes), Kai Schneider (U. Kaiserslautern),
Thorston Schneider (Physik Inst.), Ben Wichers Schreur (Koninklijk
Nederlands Meteorologisch Instituut), Chris Schwab (UMBC), Scott
Shannon (Boston U.), Arthur David Snider (U. South Florida), Steve
Spangler (U. Toronto), Colin P. Stark, Adam Stephen (Oxford U.), Bob
Stockwell (UWO), Theodore C. Tanner Jr. (Crystal River Engineering,
Inc.), Todor Fabian (U. Montreal), Stathis Tompaidis (U. Toronto),
Rafael Torres (UPV), Juan Valdivia (UMCP), David Valls-Gabaud
(Observatoire de Strasbourg), Wim Verkley (KNMI), Bin Wang (Mobil R&D
Co.), Jingfeng Wang (MIT), Jeff Weissel (LDEO), Jeremy Winick
(Phillips Lab), Ralf Witterberg (Princeton U.), Mahn-Ling Woo (U.
British Columbia), Scott Zasadil (NRL), Michael G. Zeitlin (Russian
Academy of Sciences), Yan Zheng (TAMU), William B.J. Zimmerman
(UMIST)

Contributions to Other Disciplines: 
Many of the scientists noted under ``Contributions within Discipline''
requested papers from Dr. Fournier which related to their research in
other disciplines, such as numerical solution of partial differential
equations, and turbulence signal analysis.

Contributions to Education and Human Resources: 
In addition to scientific presentations, Dr. Fournier has consulted
with scientists and students, to explain his analytical techniques.