STATISTICS AND PHYSICAL OCEANOGRAPHY

Panel on Statistics and Oceanography

Committee on Applied and Theoretical Statistics

Board on Mathematical Sciences

Commission on Physical Sciences, Mathematics, and Applications

National Research Council

National Academy Press
Washington, D.C.
1993



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Statistics and Physical Oceanography STATISTICS AND PHYSICAL OCEANOGRAPHY Panel on Statistics and Oceanography Committee on Applied and Theoretical Statistics Board on Mathematical Sciences Commission on Physical Sciences, Mathematics, and Applications National Research Council National Academy Press Washington, D.C. 1993

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Statistics and Physical Oceanography NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Frank Press is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. Robert M.White is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I.Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy’s purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Frank Press and Dr. Robert M.White are chairman and vice chairman, respectively, of the National Research Council. Support for this project was provided by the Office of Naval Research. Copyright 1993 by the National Academy of Sciences. All rights reserved. Additional copies of this report are available from: Board on Mathematical Sciences National Research Council 2101 Constitution Avenue, N.W. Washington, D.C. 20418 Printed in the United States of America

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Statistics and Physical Oceanography PANEL ON STATISTICS AND OCEANOGRAPHY DUDLEY B. CHELTON, Oregon State University, Cochair WILLIAM F. EDDY, Carnegie Mellon University, Cochair RICHARD DEVEAUX, Princeton University RAISA FELDMAN, University of California at Santa Barbara ROMAN E. GLAZMAN, Jet Propulsion Laboratory, California Institute of Technology ANNALISA GRIFFA, University of Miami KATHRYN A. KELLY, Woods Hole Oceanographic Institution GORDON J. MACDONALD, University of California at San Diego MURRAY ROSENBLATT, University of California at San Diego BORIS ROZOVSKII, University of Southern California Staff JOHN R. TUCKER, Senior Program Officer COMMITTEE ON APPLIED AND THEORETICAL STATISTICS WILLIAM F. EDDY, Carnegie Mellon University, Chair YVONNE BISHOP, U.S. Department of Energy MARY ELLEN BOCK, Purdue University MARJORIE G. HAHN, Tufts University DOUGLAS M. HAWKINS, University of Minnesota DAVID G. HOEL, Medical University of South Carolina JON R. KETTENRING, Bellcore KARL E. PEACE, Biopharmaceutical Research Consultants STEPHEN M. POLLOCK, University of Michigan DARYL PREGIBON, AT&T Bell Laboratories Staff JOHN R. TUCKER, Senior Program Officer

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Statistics and Physical Oceanography BOARD ON MATHEMATICAL SCIENCES SHMUEL WINOGRAD, IBM T.J. Watson Research Center, Chair RONALD DOUGLAS, State University of New York at Stony Brook, Vice-Chair LAWRENCE D.BROWN, Cornell University SUN-YUNG A. CHANG, University of California at Los Angeles AVNER FRIEDMAN, University of Minnesota JOHN F. GEWEKE, University of Minnesota JAMES GLIMM, State University of New York at Stony Brook DIANE LAMBERT, AT&T Bell Laboratories GERALD J. LIEBERMAN, Stanford University PAUL S. MUHLY, University of Iowa RONALD F. PEIERLS, Brookhaven National Laboratory JEROME SACKS, National Institute of Statistical Sciences ROBERT J. ZIMMER, University of Chicago Ex Officio Member WILLIAM F. EDDY, Carnegie Mellon University Chair, Committee on Applied and Theoretical Statistics Staff JOHN E. LAVERY, Director RUTH E. O’BRIEN, Staff Associate HANS OSER, Senior Program Officer JOHN R. TUCKER, Senior Program Officer BARBARA WRIGHT, Administrative Assistant

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Statistics and Physical Oceanography COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS RICHARD N. ZARE, Stanford University, Chair JOHN A. ARMSTRONG, IBM Corporation (retired) PETER J. BICKEL, University of California at Berkeley GEORGE F. CARRIER, Harvard University (retired) GEORGE W. CLARK, Massachusetts Institute of Technology MARYE ANNE FOX, University of Texas-Austin AVNER FRIEDMAN, University of Minnesota SUSAN L. GRAHAM, University of California at Berkeley NEAL F. LANE, Rice University ROBERT W. LUCKY, Bellcore CLAIRE E. MAX, Lawrence Livermore Laboratory CHRISTOPHER F. MCKEE, University of California at Berkeley JAMES W. MITCHELL, AT&T Bell Laboratories RICHARD S. NICHOLSON, American Association for the Advancement of Science ALAN SCHRIESHEIM, Argonne National Laboratory A.RICHARD SEEBASS III, University of Colorado KENNETH G. WILSON, Ohio State University NORMAN METZGER, Executive Director

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Statistics and Physical Oceanography This page in the original is blank.

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Statistics and Physical Oceanography PREFACE This report was prepared in response to a request from the Office of Naval Research to the National Research Council’s Committee on Applied and Theoretical Statistics. It describes research opportunities in statistics and applied probability arising in physical oceanographic applications. The report is expository, with the intended audience being statisticians and quantitatively literate people with a background in statistical applications to science, as well as federal agency representatives interested in encouraging such cross-disciplinary research. In producing this report, the panel had to surmount communication and comprehension difficulties to truly understand, e.g., what someone from another discipline had expressed. One result was an appreciation of just how difficult it is to engage in truly collaborative, cross-disciplinary work. Another result was an insight into what strategies will (and will not) be likely to succeed in performing such work. The panel believes understanding and appreciating these matters are as important to the encouragement and accomplishment of statistical research in physical oceanography as are the descriptions of statistical research opportunities discussed in Chapters 2 through 8. Accordingly, Chapter 9 gives the panel’s conclusions, observations, and suggestions on encouraging successful collaborations between statisticians and oceanographers. The panel gratefully acknowledges the support of the Office of Naval Research in this project and expresses appreciation to all of the people who provided information that aided the panel in the preparation of this report. They include Mark Abbott, Andrew Bennett, Hans Graber, Greg Holloway, Ricardo Matano, Robert N.Miller, Leonid Piterbarg, Michael Schlax, P.Ted Strub, V.Zlotnicki, and four anonymous reviewers who offered insightful comments and suggestions. In particular, L.Piterbarg helped write Chapter 3, P.Strub helped write Chapter 4, M.Abbott helped write Chapter 5, R.Miller and V.Zlotnicki helped write Chapter 6, and H.Graber helped write Chapter 7. The panel also gratefully acknowledges the editorial help of John Tucker and Susan Maurizi in preparing the report. Comments on the report are welcome, as are suggestions for future topics on which similar reports might help to provide useful cross-disciplinary bridges. All such remarks should be directed to John Tucker at the Board on Mathematical Sciences, National Research Council, Washington, D.C.

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Statistics and Physical Oceanography CONTENTS 1   OVERVIEW   1     Introduction   1     Purpose and Scope of This Report   1     Oceanography—A Brief Sketch   3     Oceanographic Modeling, Data, and Noise   5     The Many Meanings of the Term “Model”   5     Diverse Definitions of the Term “Data”   10     Low Noise Is Good Noise   14 2   STATISTICAL ISSUES IN THE MULTIPLE-SCALE VARIABILITY OF OCEANOGRAPHIC FIELDS   17     Oceanographic Variability   17     Satellite Observations   19     Issues for Statistical Research   20 3   LAGRANGIAN AND EULERIAN DATA AND MODELS   23     Prospective Directions for Research   26 4   FEATURE IDENTIFICATION   27     Tracking of Fronts and Rings   27     Sea Ice Tracking   28     Estimation of Horizontal Velocities from Image Sequences   29     Prospective Directions for Research   31 5   VISUALIZATION   33     Uses of Visualization   33     Challenges for Visualization   34     Outstanding Statistical Issues   36 6   INTERPOLATION, NONLINEAR SMOOTHING, FILTERING, AND PREDICTION   37     Interpolation of Satellite Data Sets   37     Characteristics of Satellite Data   37     Mapping Satellite Data: Motivation and Methods   38     Data Assimilation: Use of Dynamical Models for Smoothing and Filtering   40     Inverse Methods   42     Prospective Directions for Research   43 7   MODEL AND DATA COMPARISONS   45

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Statistics and Physical Oceanography 8   NON-GAUSSIAN RANDOM FIELDS   47     Statistical Research Opportunities   49 9   ENCOURAGING COLLABORATION BETWEEN STATISTICIANS AND OCEANOGRAPHERS   51     Conclusions   51     Observations and Suggestions   52     BIBLIOGRAPHY   55