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

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Presentation on theme: "Tidal Datum Computation January 8, 2009 Center for Operational Oceanographic Products and Services."— Presentation transcript:

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

3

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)

6

7 6A specific 19 year period that includes the longest periodic tidal variations caused by the astronomic tide-producing forces. 6Averages out seasonal meteorological, hydrologic, and oceanographic fluctuations. 6 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. 6The NWLON provides the data required to maintain the epoch and make primary and secondary determinations of tidal datums. NATIONAL TIDAL DATUM EPOCH (NTDE) A common time period to which tidal datums are referenced

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 IDEALIZED CHANGE OF TIDAL EPOCH ACTUAL 1983-01 EPOCH

10 Tidal Datum Computation 1.Make observation 2.Tabulate the tide 3.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 Menemsha Harbor Newport Providence

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

18 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 ESTIMATING ACCURACIES OF TIDAL DATUMS FROM SHORT TERM OBSERVATIONS

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

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 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 Tidal Datum Computation

27  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 Standard Method: West Coast and Pacific Island stations 1.MLW = MTL – (0.5 * Mn) 2.MHW = MLW + Mn 3.MLLW = MLW – DLQ 4.MHHW = MHW + DHQ Modified-Range Ratio Method: East and Gulf Coasts and Caribbean Island Stations 1.MLW = MTL – (0.5 * Mn) 2.MHW = MLW + Mn 3.MLLW = DTL – 0.5 * GT 4.MHHW = MLLW + GT

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 Island Semidiurnal 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 Port Pulaski Charleston Subordinate Control

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

51 Results  MLW = MTL - (0.5 x Mn)  MHW = MLW + Mn  MLLW= DTL - (0.5 x Gt)  MHHW = MLLW + Gt

52 Standard Method for Monthly Mean Comparison West Coast and Pacific Island Mix Tide

53 Standard Method  MLW = MTL - (0.5 x Mn)  MHW = MLW + Mn  MLLW= MLW - DLQ  MHHW = MHW + DHQ  MTL, MN, DHQ and DLQ have to be determined before computing MLW, MHW, MLLW, and MHHW

54 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

55 San Francisco Alameda Control Subordinate

56 Monthly Mean for Subordinate

57 Monthly Mean for Control

58 Simultaneous Comparison of MTL

59 Presently Accepted 19-year Epoch Datum at Control

60 MTL 2.043 = 2.728 + (-0.685)

61 MN 1.479 = 1.250 x 1.183

62 DHQ 0.188 = 0.183 x 1.029

63 DLQ 0.339 = 0.344 x 0.987

64 Results  MLW = MTL - (0.5 x Mn)  MHW = MLW + Mn  MLLW= MLW - DLQ  MHHW = MHW + DHQ

65 Monthly Mean Comparison - Summary Accepted 19 year MTL at control station MTL CORRECTED FOR A 19 year MTL at subordinate is computed by correcting 19 year MTL at control using the monthly mean differences between subordinate and control over a given time period

66 Modified-Range Ratio Method (Semi/Diurnal)  MLW = MTL - (0.5 x Mn)  MHW = MLW + Mn  MLLW= DTL - (0.5 x Gt)  MHHW = MLLW + Gt Standard Method (Mix)  MLW = MTL - (0.5 x Mn)  MHW = MLW + Mn  MLLW= MLW - DLQ  MHHW = MHW + DHQ

67 Monthly Mean Comparison - Direct Method  Used when a full range of tidal values are not available

68 Difference between Direct Method and Modified Range Ratio Method Direct Method Modified Range Ratio Method  MLW = MTL - (0.5 x Mn)  MHW = MLW + Mn  MLLW= DTL - (0.5 x Gt)  MHHW = MLLW + Gt VS.

69 A station where direct method is used in datum computation

70 0.893 = 5.128 + (-4.235)

71 1.069 = 5.310 + (-4.241)

72 Tidal Datum Computation  Monthly Mean Comparison  Modified Range Ratio  Standard  Direct  Tide-By-Tide Comparison  Modified Range Ratio  Standard  Direct

73 Computation Flow of Tide-By-Tide Comparison Average differences of the Highs at the subordinate and control as well as the differences of their lows Use the differences/ratios as corrector to adjust accepted 19-year datums at control station to derive 19-year datums at subordinate Monthly Mean of each datum at Subordinate Monthly Mean of each datum at Control Differences/Ratios between Monthly Mean of each datum between subordinate and control Use the differences/ratios as corrector to adjust accepted 19-year datums at control station to derive 19-year datums at subordinate Monthly Mean Comparison Tide-By-Tide Comparison Averages differences/Ratios of each datum between subordinate and control Mean of each datum at Subordinate

74 Port Pulaski Charleston Subordinate Control

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

76 Computation Flow of Tide-By-Tide Comparison Use the differences/ratios as corrector to adjust accepted 19-year datums at control station to derive 19-year datums at subordinate Average difference/Ratios of each datum between subordinate and control Mean of each datum at Subordinate Average differences of the Highs at the subordinate and control as well as the differences of their lows

77 Highs and Lows for Subordinate

78 Highs and Lows for Control

79 Simultaneous Comparison of Highs and Lows

80 Average Difference between Every High and Low

81 Computation Flow of Tide-By-Tide Comparison Use the differences/ratios as corrector to adjust accepted 19-year datums at control station to derive 19-year datums at subordinate Average difference/Ratios of each datum between subordinate and control Mean of each datum at Subordinate Average differences of the Highs at the subordinate and control as well as the differences of their lows

82 Mean at Subordinate 2 = 2 =

83 Computation Flow of Tide-By-Tide Comparison Average difference between every Highs and Lows between subordinate and control Use the differences/ratios as corrector to adujst accepted 19-year datums at control station to derive 19-year datums at subordinate Average difference/Ratios of each datum between subordinate and control Mean of each datum at Subordinate

84 Average Difference between Every High and Low

85 Difference between Sub and Control

86 Ratios between Sub and Control

87 Computation Flow of Tide-By-Tide Comparison Use the differences/ratios as corrector to adjust accepted 19-year datums at control station to derive 19-year datums at subordinate Average difference/Ratios between subordinate and control Mean of each datum at Subordinate Average difference between every Highs and Lows between subordinate and control

88 Presently Accepted 19-year Epoch Datum at Control

89 Results – part 1

90 Modified-Range Ratio Method  MLW = MTL - (0.5 x Mn)  MHW = MLW + Mn  MLLW= DTL - (0.5 x Gt)  MHHW = MLLW + Gt

91 Results – part 2

92 Tide-By-Tide Comparison - Summary the Mean of the differences of high waters at the subordinate and control Accepted 19 year MTL at control station

93 Accepted 19 year Mn at control station Tide-By-Tide Comparison - Summary

94 http://tidesandcurrents.noaa.gov/pub.html References

95 The End Questions?

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