Consists of refereed papers by the world's leading authorities on tidal hydrodynamics. Its forty-four papers, including nine review papers, cover all aspects of the subject and present, for the first time in one place, state of the art treatments of recent advances including tidal detection from satellite altimetry, global tide modeling, nonlinear tidal interactions and internal tidal phenomena.

This book is a direct result of the NATO Advanced Study Institute held in Banyuls-sur-mer, France, June 1985. The Institute had the same title as this book. It was held at Laboratoire Arago. Eighty lecturers and students from almost all NATO countries attended. The purpose was to review the state of the art of physical oceanographic numerical modelling including the parameterization of physical processes. This book represents a cross-section of the lectures presented at the ASI. It covers elementary mathematical aspects through large scale practical aspects of ocean circulation calculations. It does not encompass every facet of the science of oceanographic modelling. We have, however, captured most of the essence of mesoscale and large-scale ocean modelling for blue water and shallow seas. There have been considerable advances in modelling coastal circulation which are not included. The methods section does not include important material on phase and group velocity errors, selection of grid structures, advanced methods to conservation in highly nonlinear systems, inverse methods and other important ideas for modern ocean modelling. Hopefully, this book will provide a foundation of knowledge to support the growth of this emergent field of science. The NATO Advanced Study Institute was supported by many organi zations. The seed money, of course, was received from the NATO Science Commi ttee. Many national organizations provided travel money for partiCipants. In France, CNES, IFREMER, and CNRS provided funds to support the French participants. In the U. S.

A new hydrodynamical interpolation technique has been developed and tested to construct a model of global ocean tides with the support of empirical tidal constants collected around the world. The discrete tide model features a 1 deg by 1 deg graded grid system in connection with a hydrodynamically defined bathymetry. The Laplace tidal equations are augmented by turbulent friction terms with novel mesh-area (latitude and depth) dependent eddy-viscosity and bottom-friction coefficients. The well-known astronomical tide-generating forces are modified by effects due to solid earth tides and ocean-tidal loading. New averaged finite differences in time are used to enhance stability characteritics and to facilitate the hydrodynamical interpolation of empirical data. This unique interpolation is accomplished by a controlled adjustment of the bottom-friction coefficient and by redefining a more physical shoreline. Extensive computer experiments were conducted to study the characteristics of the novel friction laws and hydrodynamical interpolation methods. The computed M2 tide data along with all (specially labeled) empirical constants are tabulated in map form for four typical 30 by 50 deg ocean areas. A complete tabulation and discussion of the computed M2 tide will be published in Part II of this report. It is estimated that the tabulated tidal charts permit a prediction of the M2-tide elevation of the ocean surface over the geoidal level with an accuracy of better than 5 cm anywhere in the open ocean and with somewhat less accuracy near rough shorelines.

" ... as soon as one has traversed the greater part of the wild sea, one comes upon such a huge quantity of ice that nowhere in the whole world has the like been known." "This ice is of a wonderful nature. It lies at times quite still, as one would expect, with openings or large fjords in it; but sometimes its movement is so strong and rapid as to equal that of a ship running before the wind, and it drifts against the wind as often as with it." Kongespeilet - 1250 A.D. ("The Mirror of Kings") Modern societies require increasing amounts influence on the water mass and on the resulting of scientific information about the environment total environment of the region; therefore, cer tain of its characteristics will necessarily be in whieh they live and work. For the seas this information must describe the air above the sea, included.

This volume contains most of the papers which were presented at the Interdisciplinary Symposium No. 4 "Geodetic Features of the Ocean Surface and their Implications" during the XVIII. General Assembly of the International Union of Geodesy and Geophysics (IUGG) in Hamburg, August 1983. The symposium was jointly sponsored by the International Associ ation of Geodesy (lAG) and the International Association for the Physi cal Sciences of the Ocean (IAPSO), and was as such one further step in animpQrtant line of international and interdisciplinary symposia, re lated to the field of Marine Geodesy. Originally the term "Marine Geodesy" was widely understood as "Geodesy in the Marine Environment" and dealt primarily with two as pects: precise position determination at sea and determination of a fine structured marine geoid. However, mainly with the impact of satel lite radar altimeter measurements, a new understanding began to develop: it became evident that the field of Marine Geodesy could not be treated adequately from geodesists alone but that it needed close cooperation with related disciplines such as oceanography and marine geophysics. Symposium No. 4 at Hamburg could demonstrate that this coopera tion has already become a lively reality. The "geodetic features of the ocean surface" don't only reflect oceanographical but also marine geo physical aspects. As such scientists from geodesy, oceanography, marine geology and geophysics came together to present their ideas and to dis cuss questions of mutual interest.

In the four years which elapsed between our first workshop on .Tidal Friction and the Earth's Rotation and the second, the proceedings of which are presented here, many of the disciplines involved made ad vances which we felt should be exchanged. We were encouraged by the good reception our first report met with. Of course, more insight often means more problems. Therefore, this volume contains new results and revisions of matters which previously appeared settled. We are certainly far from "final answers". For this reason, differing opinions on some issues are to be found in this book. Moreover, we have refrained from making mathematical symbols uniform to avoid the risk of errors and non-compatibility with the earlier work of an author. The two workshops have stimulated collaboration between participants working in various fields. The final versions of the contributions have already profited from these discussions. We are convinced that they will also influence further investigations. This advancement of our past and future aims is based on the very existence of the Centre for Interdisciplinary Studies and on the support we have received from its leading members. The authors have agreed to dedicate this book to Dr. H. Gerstenkorn, who died in 1981. He contributed fundamental ideas to the scientific fields treated in the meeting. P. Brosche Daun, September 1982 J. Slindermann Contents * Julius Robert Mayer's Ideas on a Theory of Tidal Friction H.P. Miinzenmayer ...•••.•••..••.•..•...••..•...•.•••.••••....•..