Tidal Datum Computation
January 8, 2009Center for Operational
Oceanographic Products and Services
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
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)
Tide Station Hierarchy
Primary (>=19 years)Secondary (>=1 yr & <19 yrs)Tertiary (< 1 year)
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.
NATIONAL TIDAL DATUM EPOCH (NTDE)A common time period to which tidal datums are
referenced
SEATTLE, PUGET SOUND, WAVARIATIONS IN MEAN RANGE OF TIDE: 1900 – 1996
Due to the 19-year cycle of “Regression of the Moon’s Nodes”
IDEALIZED CHANGE OF TIDAL EPOCHACTUAL
1983-01 EPOCH
Tidal Datum Computation
1. Make observation2. Tabulate the tide3. 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
Choose Control Station
Example Subordinate
Station ID: 8448725
Subordinate Station Name: Menemsha Harbor, MA
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)
Menemsha Harbor
Newport
Providence
Water Level Data Availability
Water level data available for datum computation
Menemsha Harbor: 06/2008 – Present
Newport: 10/1930 - Present Providence: 06/1938 - Present
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
Simultaneous Data Plot
Simultaneous Data Plot
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 + 0.029S3M = 0.0043 ADLWI + 0.0036 SRGDIST + 0.0255 MNR + 0.029S6M = 0.0019 ADLWI + 0.0023 SRGDIST + 0.0207 MNR + 0.030
ESTIMATING ACCURACIES OF TIDAL DATUMS FROM SHORT TERM OBSERVATIONS
Bodnar Analysis
S3M = 0.0043 ADLWI + 0.0036 SRGDIST + 0.0255 MNR + 0.029
Newport is chosen for the following reasons
Long term observation Simultaneous water level data Similar tidal characteristics Smaller Error - Bodnar value
Importance of Benchmark Network - Examples of Bench Mark Photos
Primary Bench mark
Station Datum
Orifice
TideGauge
Network Stability 1. Gauge to Primary Benchmark
2. Primary Benchmark to other benchmarks
Pier
NOS BENCHMARK LEVELING
Distances vary but usually several hundred meters.
Leveling and Benchmark Stability
Gauge stability
Benchmark Stability
NOS requires <9 mm tolerance for stability
Stability Requirements
Minimum three stable benchmarks Compute datum using water level time
series that are bracketed by leveling.
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
Tidal Datum Computation
Monthly Mean Comparison Modified Range Ratio Standard Direct
Tide-By-Tide Comparison Modified Range Ratio Standard Direct
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
Classification of Tide Types at Water Level Stations with Accepted Datums
Semidiurnal signal
Eastport, Maine(K1 + O1) / (M2 + S2) = 0.09
Transition between
Semidiurnal and Mixed-Semidiurnal signals
Duck, North Carolina(K1 + O1) / (M2 + S2) = 0.25
Mixed-Semidiurnal signal
Arena Cove, California(K1 + O1) / (M2 + S2) = 0.85
Transition between
Mixed-Semidiurnal and Mixed-Diurnal signals
Port Manatee, Florida(K1 + O1) / (M2 + S2) = 1.43
Transition between
Mixed-Diurnal and Diurnal signals
Corpus Christi, Texas(K1 + O1) / (M2 + S2) = 3.07
Diurnal signal
Dauphin Island, Alabama(K1 + O1) / (M2 + S2) = 12.68
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
Computation Flow of Monthly Mean Comparison
Monthly Mean of each datum at SubordinateMonthly 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
Modified-Range Ratio Method for Monthly Mean Comparison
East Coast, Gulf Coast and Caribbean IslandSemidiurnal and Diurnal
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
Port Pulaski
Charleston
Subordinate
Control
Computation Flow of Monthly Mean Comparison
Monthly Mean of each datum at SubordinateMonthly 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
Monthly Mean for Subordinate
Monthly Mean for Control
Simultaneous Comparison of MTL
Computation Flow of Monthly Mean Comparison
Monthly Mean of each datum at SubordinateMonthly 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
Presently Accepted 19-year Epoch Datum at Control Station
MTL
2.119 = 1.622 + 0.497
DTL
2.137 = 1.643 + 0.494
MN
2.146 = 1.606 x 1.337
GT
2.325 = 1.768 x 1.315
Results MLW = MTL - (0.5 x Mn) MHW = MLW + Mn MLLW= DTL - (0.5 x Gt) MHHW = MLLW + Gt
Standard Method for Monthly Mean Comparison
West Coast and Pacific Island Mix Tide
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
Computation Flow of Monthly Mean Comparison
Monthly Mean of each datum at SubordinateMonthly 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
San Francisco
Alameda
Control
Subordinate
Monthly Mean for Subordinate
Monthly Mean for Control
Simultaneous Comparison of MTL
Presently Accepted 19-year Epoch Datum at Control
MTL
2.043 = 2.728 + (-0.685)
MN
1.479 = 1.250 x 1.183
DHQ
0.188 = 0.183 x 1.029
DLQ
0.339 = 0.344 x 0.987
Results
MLW = MTL - (0.5 x Mn) MHW = MLW + Mn MLLW= MLW - DLQ MHHW = MHW + DHQ
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
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
Monthly Mean Comparison - Direct Method
Used when a full range of tidal values are not available
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.
A station where direct method is used in datum computation
0.893 = 5.128 + (-4.235)
1.069 = 5.310 + (-4.241)
Tidal Datum Computation
Monthly Mean Comparison Modified Range Ratio Standard Direct
Tide-By-Tide Comparison Modified Range Ratio Standard Direct
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 SubordinateMonthly 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
Port Pulaski
Charleston
Subordinate
Control
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
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
Highs and Lows for Subordinate
Highs and Lows for Control
Simultaneous Comparison of Highs and Lows
Average Difference between Every High and Low
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
Mean at Subordinate
2=
2=
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
Average Difference between Every High and Low
Difference between Sub and Control
Ratios between Sub and Control
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
Presently Accepted 19-year Epoch Datum at Control
Results – part 1
Modified-Range Ratio Method
MLW = MTL - (0.5 x Mn) MHW = MLW + Mn MLLW= DTL - (0.5 x Gt) MHHW = MLLW + Gt
Results – part 2
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
Accepted 19 year Mn at control station
Tide-By-Tide Comparison- Summary
http://tidesandcurrents.noaa.gov/pub.html
References
The End
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