CANADIAN TIDAL MANUAL CANADIAN TIDAL MANUAL i ii CANADIAN TIDAL MANUAL Prepared under contract by WARREN D. FORRESTER, PH.D.* DEPARTMENT OF FISHERIES AND OCEANS Ottawa 1983 *This manual was prepared under contract (FP 802-1-2147) funded by The Canadian Hydrographic Service. Dr. Forrester was Chief of Tides, Currents, and Water Levels (1975-1980). Mr. Brian J. Tait, presently Chief of Tides, Currents, and Water Levels, Canadian Hydrographic service, acted as the Project Authority for the contract. iii The Canadian Hydrographic Service produces and distributes Nautical Charts, Sailing Directions, Small Craft Guides, Tide Tables, and Water Levels of the navigable waters of Canada. Director General S.B. MacPhee Director, Navigation Publications H.R. Blandford and Maritime Boundaries Branch Chief, Tides, Currents and Water Levels B.J. Tait ©Minister of Supply and Services Canada 1983 Available by mail from: Canadian Government Publishing Centre, Supply and Services Canada, Hull, Que., Canada KIA OS9 or through your local bookseller or from Hydrographic Chart Distribution Office, Department of Fisheries and Oceans, P.O. Box 8080, 1675 Russell Rd., Ottawa, Ont. Canada KIG 3H6 Canada $20.00 Cat. No. Fs 75-325/1983E Other countries $24.00 ISBN 0-660-11341-4 Correct citation for this publication: FORRESTER, W.D. 1983. Canadian Tidal Manual. Department of Fisheries and Oceans, Canadian Hydrographic Service, Ottawa, Ont. 138 p. iv CONTENTS Preface ....................................................................................................................................... ix Part I Theory and Concepts Chapter 1. Tides as Waves ........................................................................................................... 1 1.1 What is the tide? ............................................................................................................ 1 1.2 Waves ............................................................................................................................ 1 1.3 Surface gravity waves .................................................................................................... 2 1.4 Long and short waves of small amplitude ........................................................................ 4 1.5 Particle motions in long waves ........................................................................................ 5 1.6 Basin Oscillations ........................................................................................................... 7 1.7 Internal waves ............................................................................................................... 8 1.8 Coriolis acceleration ..................................................................................................... 20 1.9 Inertial currents ............................................................................................................ 22 1.10 Amphidromic systems .................................................................................................. 22 1.11 Tides and tidal streams ................................................................................................. 23 1.12 Shallow water effects ................................................................................................... 24 Chapter 2. The Tide-Raising Forces .......................................................................................... 21 2.1 Introduction .................................................................................................................. 21 2.2 Sun's tide-raising force ................................................................................................. 21 2.3 Moon's tide-raising force .............................................................................................. 23 2.4 Tidal potential and the equilibrium tide ........................................................................... 24 2.5 Semidiurnal and diurnal equilibrium tides ....................................................................... 25 2.6 Long-period equilibrium tides ........................................................................................ 29 2.7 Mathematical analysis of the equilibrium tide ................................................................ 29 2.8 Spring and neap tides .................................................................................................... 30 2.9 Classification of tides .................................................................................................... 31 Chapter 3. Tidal Analysis and Prediction ................................................................................... 35 3.1 Introduction .................................................................................................................. 35 3.2 The Fourier Theorem ................................................................................................... 35 3.3 Harmonic analysis of tides ............................................................................................ 36 3.4 Nineteen-year modulation of lunar constituents ............................................................. 38 3.5 Shallow-water constituents ........................................................................................... 39 3.6 Record length and sampling interval .............................................................................. 39 3.7 Harmonic analysis of tidal streams ................................................................................ 40 3.8 Harmonic method of tidal prediction ............................................................................. 41 3.9 Prediction of tidal and current extrema ......................................................................... 42 3.10 Cotidal charts ............................................................................................................... 42 3.11 Numerical modelling of tides ......................................................................................... 48 v Chapter 4. Meteorological and Other Non-Tidal Influences ................................................... 50 4.1 Introduction .................................................................................................................. 50 4.2 Wind-driven currents .................................................................................................... 50 4.3 Wind set-up .................................................................................................................. 51 4.4 Atmospheric pressure effect ........................................................................................ 52 4.5 Storm Surges ................................................................................................................ 53 4.6 Seiches ........................................................................................................................ 53 4.7 Precipitation, evaporation, and runoff ............................................................................ 54 4.8 Effect of Coriolis force on currents ............................................................................... 55 4.9 Estuarine circulation ..................................................................................................... 56 4.10 Melting and freezing ..................................................................................................... 58 4.11 Tsunamis ...................................................................................................................... 59 Chapter 5. Datums and Vertical Control .................................................................................... 61 5.1 Vertical datums ............................................................................................................ 61 5.2 Equi-geopotential or level surfaces ................................................................................ 61 5.3 Geopotential, dynamic, and orthometric elevations ......................................................... 61 5.4 Geodetic datum ............................................................................................................ 62 5.5 International Great Lakes Datum (1955) ...................................................................... 63 5.6 Hydrographic charting datums ...................................................................................... 63 5.7 Special tidal surfaces .................................................................................................... 65 5.8 Land levelling and water transfers ................................................................................ 66 5.9 Purpose and importance of benchmarks ...................................................................... 67 Chapter 6. Establishment of Temporary Water Level Gauge .................................................. 70 6.1 Introduction .................................................................................................................. 70 6.2 Stilling wells ................................................................................................................. 70 6.3 Gauge shelters ............................................................................................................. 72 6.4 Float gauges ................................................................................................................. 73 6.5 Pressure gauges - diaphragm type ...............................................................................