Tidal Datum Computation

1. Tidal Datum Computation January 8, 2009 Center for Operational Oceanographic Products and Services

2. Overview • Introduction of tidal datum • Choose control station • Benchmark and station stability • Tidal Datum computation methodology • Example of Monthly Mean Comparison • Example of Tide-By-Tide Comparison

4. TYPES OF TIDE STATIONS • Control • Long-term stations (several years) with accepted tidal datums • Primary and Long-term Secondary • Monitoring for sea level trends • Subordinate • Secondary stations (>=1 yr & <19 yrs) • Tertiary (<1 year)

5. Tide Station Hierarchy Primary (>=19 years) Secondary (>=1 yr & <19 yrs) Tertiary (< 1 year)

7. NATIONAL TIDAL DATUM EPOCH (NTDE) A common time period to which tidal datums are referenced • A specific 19 year period that includes the longest periodic tidal variations caused by the astronomic tide-producing forces. • Averages out seasonal meteorological, hydrologic, and oceanographic fluctuations. • Provides a nationally consistent tidal datum network (bench marks) by accounting for seasonal and apparent environmental trends in sea level that affect the accuracy of tidal datums. • The NWLON provides the data required to maintain the epoch and make primary and secondary determinations of tidal datums.

8. SEATTLE, PUGET SOUND, WA VARIATIONS IN MEAN RANGE OF TIDE: 1900 – 1996 Due to the 19-year cycle of “Regression of the Moon’s Nodes”

9. 1983-01 EPOCH ACTUAL IDEALIZED CHANGE OF TIDAL EPOCH

10. Tidal Datum Computation • Make observation • Tabulate the tide • Compute tidal datum • Stations with over 19 years data: average values over a 19-year National Tidal Datum Epoch (NTDE) • Stations with less than 19 years data: simultaneous comparison between Subordinate Station and Control Station

11. Choose Control Station Example • Subordinate Station ID: 8448725 • Subordinate Station Name: Menemsha Harbor, MA

12. Requirements for a Control Station • Close to the subordinate • Long term station (ideally 19 years) • Simultaneous water level data • Similar tidal characteristics Candidates for control • Providence, RI (8454000) • Newport, RI (8452660)

13. Providence Newport Menemsha Harbor

14. Water Level Data Availability Water level data available for datum computation • Menemsha Harbor: 06/2008 – Present • Newport: 10/1930 - Present • Providence: 06/1938 - Present

15. Tidal Characteristics Tide type (Harmonic Analysis) (K1+O1)/(M2+S2) indicates tide type • >1.5 Diurnal • <=1.5 Semidiurnal/Mix • <0.25 Semidiurnal • Menemsha Harbor: 0.245 • Newport: 0.181 • Providence: 0.165

16. Simultaneous Data Plot

17. Simultaneous Data Plot

18. ESTIMATING ACCURACIES OF TIDAL DATUMS FROM SHORT TERM OBSERVATIONS The Bodnar Report Bodnar (1981), drawing upon Swanson (1974) applied multiple curvilinear regression equations estimating the accuracy of computed datums Bodnar’s analyses determined which independent variables related to differences in tidal characteristics explain the variations in the Swanson standard deviations using Swanson’s standard deviations as the dependent variables. Bodnar developed formulas for Mean Low Water (MLW) and Mean High Water (MHW). The equations for Mean Low Water are presented below. S1M = 0.0068 ADLWI + 0.0053 SRGDIST + 0.0302 MNR + 0.029 S3M = 0.0043 ADLWI + 0.0036 SRGDIST + 0.0255 MNR + 0.029 S6M = 0.0019 ADLWI + 0.0023 SRGDIST + 0.0207 MNR + 0.030

19. Bodnar Analysis S3M = 0.0043 ADLWI + 0.0036 SRGDIST + 0.0255 MNR + 0.029

20. Newport is chosen for the following reasons • Long term observation • Simultaneous water level data • Similar tidal characteristics • Smaller Error - Bodnar value

21. Importance of Benchmark Network - Examples of Bench Mark Photos

22. Network Stability 1. Gauge to Primary Benchmark 2. Primary Benchmark to other benchmarks Tide Gauge Pier Primary Bench mark Orifice Station Datum

23. NOS BENCHMARK LEVELING Distances vary but usually several hundred meters.

24. Leveling and Benchmark Stability Gauge stability Benchmark Stability NOS requires <9 mm tolerance for stability

25. Stability Requirements • Minimum three stable benchmarks • Compute datum using water level time series that are bracketed by leveling.

26. Tidal Datum Computation Simultaneous Comparison • Monthly Mean Comparison: collected water level data is long enough to allow monthly mean to be computed • Tide-By-Tide Comparison: monthly mean is not available Datum Computation Method • Modified-Range Ratio: semidiurnal and diurnal tide • Standard method: mix tide • Direct method: full range tide is not available

27. Tidal Datum Computation • Monthly Mean Comparison • Modified Range Ratio • Standard • Direct • Tide-By-Tide Comparison • Modified Range Ratio • Standard • Direct

28. Modified-Range Ratio Method • MLW = MTL - (0.5 x Mn) • MHW = MLW + Mn • MLLW= DTL - (0.5 x Gt) • MHHW = MLLW + Gt Standard Method • MLW = MTL - (0.5 x Mn) • MHW = MLW + Mn • MLLW= MLW - DLQ • MHHW = MHW + DHQ

29. Classification of Tide Types at Water Level Stations with Accepted Datums

30. Semidiurnal signal Eastport, Maine (K1 + O1) / (M2 + S2) = 0.09

31. Transition between Semidiurnal and Mixed-Semidiurnal signals Duck, North Carolina (K1 + O1) / (M2 + S2) = 0.25

32. Mixed-Semidiurnal signal Arena Cove, California (K1 + O1) / (M2 + S2) = 0.85

33. Transition between Mixed-Semidiurnal and Mixed-Diurnal signals Port Manatee, Florida (K1 + O1) / (M2 + S2) = 1.43

34. Transition between Mixed-Diurnal and Diurnal signals Corpus Christi, Texas (K1 + O1) / (M2 + S2) = 3.07

35. Diurnal signal Dauphin Island, Alabama (K1 + O1) / (M2 + S2) = 12.68

36. Modified-Range Ratio Method: East and Gulf Coasts and Caribbean Island Stations • MLW = MTL – (0.5 * Mn) • MHW = MLW + Mn • MLLW = DTL – 0.5 * GT • MHHW = MLLW + GT Standard Method: West Coast and Pacific Island stations • MLW = MTL – (0.5 * Mn) • MHW = MLW + Mn • MLLW = MLW – DLQ • MHHW = MHW + DHQ

37. Computation Flow of Monthly Mean Comparison Monthly Mean of each datum at Subordinate Monthly Mean of each datum at Control Average difference/Ratios between Monthly Mean of each datum between subordinate and control Use the average difference/ratios as corrector to adjust accepted 19-year datums at control station to derive 19-year datums at subordinate

38. Modified-Range Ratio Method for Monthly Mean Comparison East Coast, Gulf Coast and Caribbean IslandSemidiurnal and Diurnal

39. Modified-Range Ratio Method • MLW = MTL - (0.5 x Mn) • MHW = MLW + Mn • MLLW= DTL - (0.5 x Gt) • MHHW = MLLW + Gt • MTL, MN, DTL and GT have to be determined before computing MLW, MHW, MLLW, and MHHW

40. Charleston Control Port Pulaski Subordinate

41. Computation Flow of Monthly Mean Comparison Monthly Mean of each datum at Subordinate Monthly Mean of each datum at Control Average difference/Ratios between Monthly Mean of each datum between subordinate and control Use the average difference/ratios as corrector to adjust accepted 19-year datums at control station to derive 19-year datums at subordinate

42. Monthly Mean for Subordinate

43. Monthly Mean for Control

44. Simultaneous Comparison of MTL

45. Computation Flow of Monthly Mean Comparison Monthly Mean of each datum at Subordinate Monthly Mean of each datum at Control Average difference/Ratios between Monthly Mean of each datum between subordinate and control Use the average difference/ratios as corrector to adjust accepted 19-year datums at control station to derive 19-year datums at subordinate

46. Presently Accepted 19-year Epoch Datum at Control Station

47. MTL 2.119 = 1.622 + 0.497

48. DTL 2.137 = 1.643 + 0.494

49. MN 2.146 = 1.606 x 1.337

50. GT 2.325 = 1.768 x 1.315