GLOSS Training Workshop Course Japan Meteorological Agency May 15-26, 2006 Sea Level Data Processing with SLPR2 3. Tidal Analysis and Prediction

Background *Tidal Forces, general physics *Theory used in Foreman Routines Application

General Physics of the Tides * Response of mass (primarily water) to Earth-Sun-Moon system (harmonic tidal constituents defined astronomically) * Local coastal shoreline and basin shapes lead to additional tidal constituents (non-linear, shallow water tidal energy) Good Reference: Pugh, D.T., Tides, Surges, and Mean Sea Level, A Handbook for Engineers and Scientists. John Wiley & Sons., 472p.

Basic Tidal Physics Force = G (M 1 *M 2 ) / R 2 M 1 = Mass 1 (earth) M 2 = Mass 2 (sun or moon) R = distance between centers of mass Newton’s Gravitational Law

Two Forces: Atractive and Centrifugal centrifugal attractive Results: -Typically two tidal cycles per day -More declination: 1) more inequality in ranges of semi-diurnal tides, 2) more range of diurnal tide Variations: 1) angle of declination 2) proximity to earth “Equilibrium Tide” Results - “perigee” y “apogee” of the moon - “perihilion y “apihelion” of the sun When closer, stronger Sun or moon

Example of Semi-diurnal dominant Tide Example of Diurnal dominant Tide

Earth, Sun, Moon System Spring Tides Neap Tides

Dynamical Theory of the Tides

The earth, moon, and sun system makes the tides. The declination angle (of sun or moon) and the proximity (of sun or moon) give rise to the various frequencies and magnitudes, known as the “tidal species”. The shape of the ocean basins, coastlines, extent of continental shelf, and effects of rivers make for complex Good References: Godin, G., Tides. Centro de Investigaciones Cientifica y de Educacion Superior de Ensensada, Ensendad, BC. Mexico., p290 by mail: Mareografia, CICESE, Ave. Espinoza #843, APDO Postal 2732 Ensenada, Baja California, MEXICO Pugh, D.T., Tides, Surges, and Mean Sea Level, A Handbook for Engineers and Scientists. John Wiley & Sons., 472p. Basic Tidal Physics Summary

Foreman Tidal Analysis: Theory 1.Astronomical variables derived from Doodson tidal potential, from which constituent frequencies were determined 2.Time origin is 00UTC 01 January, There are 45 main astronomical constituents in this package. 4.Shallow water constituents determined using Rayleigh Comparison pairs. 5. Nodal modulation corrections applied to include satellite frequencies. 6. Analysis: least squares fit for constituent amplitude and phase. Details at: Foreman, M.G.G., Manual for Tidal Heights Analysis and Prediction. Pacific Marine Science Report 77-10, Institute of Ocean Sciences, Patricia Bay, Sidney, B.C., 58 pp.

Foreman Tidal Analysis: Application 1.Choose a time period for analysis a. Use plots of hourly data b. Select time period with fewest gaps or obvious errors. c. Ideally 366 consecutive days (may cross over year) days (13 month limit) gives 68 harmonic constants - 30 days yields 30 constants; 14 days; 11 constants (shorter analysis period, less constants, less quality) - time period can not cross over century mark 2.Run \slpr2\tide\anl\TIDEANL.BAT P1 (P1: 3-digit station ID) a. must be ran from MS DOS prompt (not windows) b. interactive input - time scheme of hours used for analysis period eg, enter for hour 00, day 01, month 01, year If consecutive values in hourly values have difference > 2500 mm (gross value) then TIDEANL aborts. Replace gross value with 9999 Manual Section 4.1

Output of Analysis: Harmonic Constants Appendices F and G 1.If one reruns TIDEANL for the same station, INPsss.PRD and HARMsss.PRD will be overwritten. Thus, if one wants to save the original ones, move them to a new directory or rename them. 2.HARMsss.LIS has a complete header including statistics 3.INPsss.PRD becomes the input file for Foreman Tidal Prediction 4.Both HARMsss.LIS and INPsss.PRD hold the same harmonic constants frequency span of A G AL GL (cycle/hour) analysis (cm) 1 Z / SA / AL: amplitude, GL: phase direct from least squares analysis A: G: are amplitude and phase after Nodal Corrections

Foreman Tidal Prediction: Notes Manual Section Method: resultant predicted tide is sum of all amplitudes and phases given in the harmonic constant file (INPsss.PRD).

Sum of individual tidal components gives the resultant predicted sea level

Foreman Tidal Prediction: Notes 2.Two output options: equally-spaced (hourly) or times/heights of hi/lo tide 3.Purpose of the SLPR2 package is QUALITY CONTROL (hourly output) 4. Each run of the Tide Prediction program produces one year of predicted tides.

Foreman Tidal Prediction: Application Manual Section If hourly data file units are not millimeters, then modify \slpr2\din\PRDVP.DIN 2.Run \slpr2\tide\prd\TIDEPRD.BAT p1 p2 p3 p4 p5 p6 - must be run from MS DOS Prompt window - see page 17 of manual for command line parameter description 3.Output placed in \slpr2\prd\ 4. Special case when running for 1899 and 1999 (page 18 of manual)

Assignment for Hands-On Training Session (HOTS) 1. Choose time period for Tidal Analysis 2. Run Tidal Analysis 3. Study Harmonic Constant files 4.Make predicted tides for year(s) of observed hourly data 5. Optional: make hi/lo tides table