Data Assimilation: Tools for Modelling the Ocean in a Global Change Perspective

Data Assimilation: Tools for Modelling the Ocean in a Global Change Perspective

NATO ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences B Physics C Mathematical and Physical Sciences D Behavioural and Social Sciences E Applied Sciences F Computer and Systems Sciences G Ecological Sciences H Cell Biology I Global Environmental Change Plenum Publishing Corporation London and New York Kluwer Academic Publishers Dordrecht, Boston and London Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest NATo-peo DATABASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords and/or abstracts) to more than 30000 contributions from international scientists published in all sections of the NATO ASI Series. Access to the NATO-PCO DATABASE compiled by the NATO Publication Coordination Office is possible in two ways: - via online FILE 128 (NATO-PCO DATABASE) hosted by ESRIN, Via Galileo Galilei, 1-00044 Frascati, Italy. - via CD-ROM "NATO Science & Technology Disk" with user-friendly retrieval software in English, French and German ( WTV GmbH and DATAWARE Technologies Inc. 1992). The CD-ROM can be ordered through any member of the Board of Publishers or through NATO-PCO, Overijse, Belgium. Series I: Global Environmental Change, Vol. 19

Data Assimilation: Tools for Modelling the Ocean in a Global Change Perspective Edited by Pierre P Brasseur Jacques C. J. Nihoul University of Liege G. H. E. R. Sart Tilman B5 4000 Liege, Belgium Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest Published in cooperation with NATO Scientific Affairs Division

Proceedings of the NATO Advanced Research Workshop on Data Assimilation: Tools for Modelling the Ocean in a Global Change Perspective, held in Liege, Belgium, May 1993 ISBN-13: 978-3-642-78941-0 e-isbn-13: 978-3-642-78939-7 001: 10.1007/978-3-642-78939-7 Library of Congress Cataloging-in-Publication Data Data assimilation: tools for modelling the ocean in a global change perspective / edited by Pierre P. Brasseur, Jacques C. J. Nihoul. p. cm. - (NATO ASI series. Series I, Global environmental change; vol. 19) "Proceedings of the NATO Advanced Research Workshop on Data Assimilation: Tools for Modelling the Ocean in a Global Change Perspective, held in Liege, Belgium, May 1993" - Tp. verso. Includes bibliographical references and index. 1. Oceanography-Mathematical models. I. Brasseur, Pierre P., 1966-. II. Nihoul, Jacques C. J. III. NATO Advanced Research Workshop on Data Assimilation: Tools for Modelling the Ocean in a Global Change Perspective (1993: Liege, Belgium) IV. Series. GC10.4.M36D38 1994 551.46'001 '5118- dc20 94-15300 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1994 Softcover reprint of the hardcover 1 st edition 1994 Typesetting: Camera ready by authors SPIN 10089098 31/3130-543210 - Printed on acid-free paper

PREFACE Data Assimilation is considered as a key component of numerical ocean model development and new data acquisition strategies. The basic concept of data assimilation is to combine real observations (generally sparse and noisy) via estimation theory (involving statistics) with dynamical models. Related methodologies exist in meteorology, in geophysics and in engineering. Of growing importance in physical oceanography, data assimilation can also be usefully exploited in biological and chemical oceanography. Such techniques are now recognized as essential to understand the role of the Ocean in a Global Change perspective. Methodologies for oceanic data assimilation benefit from the extended theoretical and operational experience gained in atmospheric science, but several peculiarities make the ocean data assimilation issues unique and novel. This book is the outcome of the NATO Advanced Research Workshop held in Liege, Belgium, May 1993. The workshop was organized at the University of Liege as a follow-on meeting to the 25th International Liege Colloquium in Ocean Hydrodynamics, dedicated in 1993 to Data Assimilation in Marine Science. The book contains the synthesis of the lectures given by 9 main speakers during the NATO ARW. The major objective of the workshop was to investigate how existing methodologies can be implemented to progress in the global-scale, long~ term prediction of the ocean circulation. Different topics have been addressed during the ARW, with a special emphasis on : data processing algorithms for assimilation, relevance of current methods for the assimilation of biogeochemical data in multidisciplinary studies, strategy of model development and design of observational array to assimilation. Almost all contributions are concerned with the application and possible extensions of traditional data assimilation methods to the modelling of the marine systems, exemplified by real case studies. Some chapters also address more theoretical and advanced techniques in idealized situations. The critical questions of hindcasting, model initialization and sensitivity to initial conditions were also considered. Some studies indicated that traditional data assimilation approaches (like the variational adjoint method or the statistical Kalman filter) are not really adequate for assimilating biological or geochemical data. Indeed, the

VI statistics of such parameters are poorly known, at least in regard to the time and length scales characterizing their evolution. Work still has to be done in that direction. Finally, considering the data assimilation schemes as part of the model setup, various issues were related with the design of numerical codes for fast parallel computers. The main support for the Advanced Research Workshop was provided by NATO under the auspices of the Scientific and Environmental Affairs Division: we gratefully acknowledge the NATO panel for provinding us the opportunity of this ARW. We are indebted also to many other organizations for their efficient help and support : the Belgian Ministry of Education and Scientific Research, the National Science Foundation of Belgium, the Scientific Committee on Oceanographic Research (SCOR), the Intergovernmental Oceanographic Commission, the UNESCO Division of Marine Sciences, the Office of Naval Research and the University of Liege. Finally it is a great pleasure to thank all the speakers, participants and members of the Organizing Committee who contributed not only to the scientific experience but also to the exciting atmosphere of this meeting. Pierre BRASSEUR, January 1994

Table of Contents K.HAINES Dynamics and Data Assimilation in Oceanography 1 E.V.STANEV Assimilation of Sea Suiface Temperature Data in a Numerical Ocean Circulation Model. A Study of the Water Mass Formation 33 J. SCHROTER A Sensitivity Analysis of Variational Data Assimilation 59 P.DEMEY Optimal Interpolation in a model of the Azores Current in 1986-88 85 J.C.J. NIHOUL, P. ADAM and P. BRASSEUR Mathematical Visualisation of the Northern Bering Sea's Summer Ecohydrodynamics 107 E. OZSOY and H. GONGOR The Northern Levantine Sea Circulation Based on Combined Analyses ofctd and ADCP DATA 135 M. GHIL and K. IDE Extended Kalman Filtering for Vortex Systems: An Example of Observing-System Design 167 R.N. MILLER Perspectives on Advanced Data Assimilation in Strongly Nonlinear Systems 195 A.M. MOORE and B.F. FARRELL Using Adjoint Models for Stability and Predictability Analysis 217