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

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


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



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



MTL, MN, DTL and GT have to be determined before computing MLW, MHW, MLLW, and MHHW

Port Pulaski

Charleston

Subordinate

Control





Monthly Mean for Subordinate

Monthly Mean for Control

Simultaneous Comparison of MTL





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





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)


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


VS.

A station where direct method is used in datum computation

0.893 = 5.128 + (-4.235)

1.069 = 5.310 + (-4.241)


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


Differences/Ratios between Monthly Mean of each datum between subordinate and control


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



MTL, DTL, MN and GT have to be determined before computing MLW, MHW, MLLW, and MHHW



Average difference/Ratios of each datum between subordinate and control



Highs and Lows for Subordinate

Highs and Lows for Control

Simultaneous Comparison of Highs and Lows

Average Difference between Every High and Low






Mean at Subordinate

2=

2=


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 between Every High and Low

Difference between Sub and Control

Ratios between Sub and Control



Average difference/Ratios between subordinate and control


Average difference between every Highs and Lows between subordinate and control

Presently Accepted 19-year Epoch Datum at Control

Results – part 1



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

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