GLOSS Training Workshop Course Japan Meteorological Agency May 15-26, 2006

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

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

3. 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., 1987. Tides, Surges, and Mean Sea Level, A Handbook • for Engineers and Scientists. John Wiley & Sons., 472p.

4. Basic Tidal Physics Newton’s Gravitational Law Force = G (M1*M2) / R2 M1 = Mass 1 (earth) M2 = Mass 2 (sun or moon) R = distance between centers of mass

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

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

7. Earth, Sun, Moon System Spring Tides Neap Tides

8. Dynamical Theory of the Tides

9. Basic Tidal Physics Summary • 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., 1988. 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., 1987. Tides, Surges, and Mean Sea Level, A Handbook • for Engineers and Scientists. John Wiley & Sons., 472p.

10. Foreman Tidal Analysis: Theory • Astronomical variables derived from Doodson tidal potential, from which • constituent frequencies were determined • Time origin is 00UTC 01 January, 1976. • There are 45 main astronomical constituents in this package. • 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: http://www.pac.dfo-mpo.gc.ca/sci/osap/projects/tidpack/tidpack_e.htm Foreman, M.G.G., 1977. Manual for Tidal Heights Analysis and Prediction. Pacific Marine Science Report 77-10, Institute of Ocean Sciences, Patricia Bay, Sidney, B.C., 58 pp.

11. Foreman Tidal Analysis: Application Manual Section 4.1 • 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) • - 366 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 • 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 01-24 used for analysis period • eg, enter 0101012004 for hour 00, day 01, month 01, year 2004 • If consecutive values in hourly values have difference > 2500 mm • (gross value) then TIDEANL aborts. Replace gross value with 9999

12. Output of Analysis: Harmonic Constants Appendices F and G • 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. • HARMsss.LIS has a complete header including statistics • INPsss.PRD becomes the input file for Foreman Tidal Prediction • Both HARMsss.LIS and INPsss.PRD hold the same harmonic constants • frequency span of A G AL GL • (cycle/hour) analysis (cm) • 1 Z0 .00000000 0 785/ 786 178.6955 .00 178.6955 .00 • 2 SA .00011407 0 785/ 786 3.7802 109.26 3.7802 112.59 • AL: amplitude, GL: phase direct from least squares analysis • A: G: are amplitude and phase after Nodal Corrections

13. Foreman Tidal Prediction: Notes Manual Section 4.2 1. Method: resultant predicted tide is sum of all amplitudes and phases given in the harmonic constant file (INPsss.PRD).

14. Sum of individual tidal components gives the resultant predicted sea level

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

16. Foreman Tidal Prediction: Application Manual Section 4.2 • If hourly data file units are not millimeters, then modify \slpr2\din\PRDVP.DIN • 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 • Output placed in \slpr2\prd\ • 4. Special case when running for 1899 and 1999 (page 18 of manual)

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