010912-02-geodeticverticaldatums-michalski -grayscale.pdf

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Michael Michalski, NOAA/National Ocean ServiceCenter for Operational Oceanographic Products and ServicesMonday, January 9 2012

Tidal Datums

Non-tidal Datum considerations

Datum Computations

Datums Relative to Benchmarks

Regional Variation in Tidal –Geodetic

Interpolation of Tidal – GeodeticRelationships

Application of VDatum

Tidal Theory

Station Configuration

Data Collection

Data Processing

Tidal Characteristics

NTDE (MTDE)

Relative Sea Level Trends

Caused by gravitational attraction between the Earth, Moon, & Sun

Periodic variation in the surface level of the oceansPeriodic variation in the surface level of the oceans

MeanSeaLevel

Tide : The alternating rise and fall of water levels withrespect to land

Tidal Current : Horizontal motion resulting from rise& fall of water levels

Tide Range : difference in height between highesthigh & lowest low

Tidal Period : Time between successive lows or highs(Average ~12.4hs)

Common TermsCommon Terms

Tidal Current

Tide curve

Time

Wa

ter

leve

lhe

igh

t

Cu

rren

tsp

eed

Time

Tidal Frequency : How often 1 tidal period occurs per day (Average ~1.9 cycles per day)

Mean Sea Level : Averageheight of sea surface

Astronomy - Tides are result of the

gravitational forces of the Earth, Moon & Sun

& the centrifugal forces of their rotations

Hydrodynamics - The range & timing of the tide& the speed, direction & timing of the tidalcurrent are also influenced by the configurationof the coastline, bottom topography & localwater depth

Astronomy & HydrodynamicsAstronomy & Hydrodynamics

Bay

Long WaveIn the Ocean

Both the moon & the sun affect the tides (sun’s effect is 0.46 times that of the Moon)

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Most important tide modulations result from phases of the Moon relative to SunMost important tide modulations result from phases of the Moon relative to Sun

- When moon & Sun align with earth – get larger more predominate tides = Spring Tides

- When moon & Sun at right angles – get smaller less predominate tides = Neap Tides

- These modulations occur once each lunar month - ~29 ½ days

Forces change with alignment- Strength of the gravitational force is strongest when Sun &Moon are aligned (Phase Inequality)

Tide producing force ofthe Moon is 2.5 times

that of the Sun

Force due to the moon isabout 2.5x greater thanthe force due to the sun

full moon

Spring tides, with higherhigh tides and lower lowtides

Gra

vita

tio

nal

pu

ll

Gravitational pullCentrifugal force

Gravitational pull Centrifugal force

Gra

vita

tio

nal

pu

llC

en

trif

uga

lfo

rce half moon

Neap tides – muted, withhigher lows and lowerhighs

new moon

Spring tides, with higherhigh tides and lower lowtides

Gravitational pull Centrifugal force

Spring and Neap tides

• Spring tide: sun and moonaligned

• Neap tide: sun and moon notaligned

Affects the amplitude of the tides (tidal range)Affects the amplitude of the tides (tidal range)

MoonPhases: NeapNeapNeapNeapSpringSpring SpringSpring

Less significant modulations result from the elliptical orbits of Earth & MoonLess significant modulations result from the elliptical orbits of Earth & Moon

Moon’s Orbit – Monthly modulation

Diurnal InequalityThe changing distance of the Moon aboveor below the equator causes a differencein amplitude of the two tides in the same

day & results in the various tide types(Semidiurnal, Mixed & Diurnal)

The two daily highs will be most similarwhen the declination is smallest

Forces change with angle - Strength of the gravitational force is strongest when angle is smallest(Declination Inequalities)

A longer period modulation results from the angled orbital paths of the Earth &A longer period modulation results from the angled orbital paths of the Earth &moon around the sunmoon around the sun

Ecliptic - Apparent path of Earth about the Sun, as seenfrom the Sun

Lunar Orbit - Apparent path of Moon about the Sun, asseen from the Sun

Nodes - Points where Moon’s path crosses the ecliptic.

Effects the amplitude of the Annual Mean Range(Difference in height between mean high & low)

Regression of the Moon’s Nodes – Variation in thepath of the Moon about the Sun, such that the angleof the moon’s orbital plane with the equatorial planevaries over 18.6 yrs

Forces change with angle - Strength of the gravitational force is strongest when angle is smallest(Regression of the Nodes)

Effects the amplitude of the annual mean rangeEffects the amplitude of the annual mean range

ANNUAL MEAN RANGE

MONTHLY MEAN RANGE

The time between peaks is the period of oscillation of the regression (~18.6yrs))

-- Basis for defining the National Tidal Datum Epoch (NTDE) as a 19yr periodBasis for defining the National Tidal Datum Epoch (NTDE) as a 19yr period

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National Water Level Observation Network (NWLON)National Water Level Observation Network (NWLON)

Remote Pacific Island Stations Not Shown

• Network of long-term and short-term water level stations

• 306 coastal stations recording 6-minute data

• Includes 53 stations in the Great lakes

• Includes 61 Short-term stations supportingprojects such as storm surge monitoring research,hydro / photo support, and habitat restoration

Control stationsControl stations are operated by NOS and disseminated over the internetare operated by NOS and disseminated over the internet

Primary Control Tide Station: Continuous observations over 19 yrs ormore & expected to continue- Data used for determining tidal datums

Secondary Control Tide Station: Subordinate station with continuousobservations over at least 1 yr, but less than 19 yrs, and has a planned finitelifetime- Data must be compared to a suitable control station for determining tidaldatums

Tertiary Control Tide Station: Subordinate station with continuousobservations over at least 30 days, but less than 1 yr, and has a plannedfinite lifetime- Data must be compared to a suitable control station for determining tidaldatums

Subordinate stations are usually installed by field teams prior to surveyoperations and removed after surveys are completed

Essential EquipmentEssential Equipment

• Automatic water level sensor

• Backup water level sensor

• Backup & Primary data

collection platform

• Protective well

• Shelter

• Solar Panel

• GOES satellite radios

• Telephone modem

• Ancillary geophysical instruments

• System of Bench Marks

• Data Collection Platform

• Acoustic or pressure sensor

• Solar Panel

• GOES Transmitter

Short term stations

Control Stations

• Water Level

• Wind Speed/Direction

• Barometric Pressure

• Air/Water Temp.

• Conductivity/Temp

• Chart Datum

• Tsunami/Storm Surge

Observations

Collected

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Water Level Measurement SystemsWater Level Measurement Systems

Primary Measurement System

Aquatrak® Air Acoustic water level sensor

• Self-calibrating measurement technique

• Directly Leveled to local benchmark network

Sutron Xpert data collection platform

• Multitasking Operating system

• 30 Days of Data Storage

• Satellite Data Telemetry

• Telephone Modem - Data retrieval andsoftware upgrades

Backup Measurement System

Pressure sensor based water level sensor

Sutron Data Collection Platform

• 60 Days of Data Storage

• Transfers data to Primary Measurement System

Vertical Datum ReferenceVertical Datum ReferenceVertical Datum Reference characteristics are:

• Water levels accurately known relative to the latest tidal datums on thelatest National Tidal Datum Epoch (NTDE)

• Water levels accurately known relative to the land and a local network ofrecoverable tidal bench marks

• Precise connections to the national geodetic datum (NAVD88) using levelconnections or GPS connections to the bench marks in the NationalSpatial Reference System(NSRS)

• NGS Accuracy Standards2nd Order, Class I for long-term stations3rd Order for short-term stations

• Annual leveling for NWLON

installation and removal

levels for short-term stations

• Emergency leveling

for storm events

Geodetic Benchmark(and its WGS84 value)

Relative to Tidal Datum

NO

AA

Tidal Bench mark4811 G 2004

Station Datum

Orifice0.7428m


3.150 m

MHW2.736 m

MLLW1.220 m

Bench markwith geodetic control

(NAVD88, WGS84,etc.)

TideGauge

1.150 m(example)

Pier

GPS Receivers collecting simultaneousdata over existing bench marks allowfor datum transformation.

2.000 m

GPSReceiver

NAVD88

Sent from stations via satelliteSent from stations via satellite

NESDISNational Environmental Satellite,

Data and Information Services

PORTS®® ServerNWLON Server

Data Analyst

CO-OPS Web Page

GOESSatellite

Continuous Operational RealContinuous Operational Real--Time Monitoring System (CORMS)Time Monitoring System (CORMS)

Real-Time 24x7 QA/QC•Human Analysis•Data Quality Flags (e.g. Rate of Change)•Corrective Action

Post-Processing•Error in Data (e.g. spikes, missing data)•Data Quality Flags: shifts, bias, changes•Tabulation & Product Generation•Backup Gain and Offset•Verification & Acceptance

Initial Automated ProcessingInitial Automated Processing

Data Processing & Analysis Subsystem (DPAS)

• NOS Database Management System

• Receives water level data from stations– Calls NESDIS to download new water level data every hour

• Performs automated QC checks

• Generates QC Reports

Monthly Product Generator (MPG)•Software system that activates on the first day of each month to process the rawsensor data for all active stations

– check to insure that no product data exists for the month

– fill data gaps using a hierarchy of techniques

– develop quality control metrics - tabulate highs and lows - calculate monthly means

– insert the generated product into the database.

Works well with semidiurnal/mixed tidal dataof significant range, or data without breaks

Doesn’t work well with diurnal, lowrange or noisy data

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Initial Automated ProcessingInitial Automated Processing

• When MPG doesn’t work well you will see:

Not designed toreplace analysts

• Double or missing tides• Overlapping time series

• Data spikes• Bad break fills

Data Processing ProceduresData Processing Procedures

1. Preliminary Analysis

• Check station parameters

• Examine data inventories

• Initialize Working Water Level data

– Move data from sensor areas into working WLTable

• Review 6-minute Data plots

– Data Gaps

– Large standard deviations indicate a problem

Check station parameters

Review data plots


1. Preliminary Analysis (Cont’d)

• Fill Breaks

– Fill-six program or QC Spreadsheet

– Use Backup WL data, compatible nearby stationdata, predictions, or curve fit for small breaks

• Perform Offline QC Checks

• Check and correct erroneous data using theQC Spreadsheet, nearby station checks

Fill with backup (B1) or nearby station

Curve fit

Backup Fill

Fill with predicted (PR)data

Fill Breaks

Perform Offline QC Checks Programmed into the computer algorithms.Programmed into the computer algorithms.

1. Two-hour rule: Adjacent high and low waters must be different by 2 hours or more intime in order to be counted as a tide.

2. One-tenth of a foot rule (same as 0.03 m rule): Adjacent high and low waters must bedifferent in elevation be one tenth of a foot (or 0.03 m) or more in order to be counted as atide for tabulation.

Criteria for determining a TideCriteria for determining a Tide

Difference inelevation

Difference in time

2. Tabulation

• Tabulate High and Low waters

– Select DIUR or EXHL

– Tide Check Report – summary & error messages

• Use QC Spreadsheet to edit Hourly Heights and Hi/Lo waters

• Plot WL w/ HI/LO picks and corrections

• Run Hi/Lo check option


Hi-Low Water

Hourly Heights

Hi-Low Picks

Tide Check Report

2. Tabulation (Cont’d)

• Compute Monthly Means

• Mark data Complete

• Make output reports

• Final Time Series Check

4.Verification

• Check by a senior analyst

5.Compute Datums


Monthly Means

Verified HI / LO

Verified WATERLEVEL HOURLY

ACCEPTED Datums

VerifiedMonthlyMeans

VerifiedSIX-MINUTE

WATER LEVEL

RAW SIX-MINUTEWATER LEVEL

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• 6 minute data values

• Hourly Heights

• Highs and Lows

• Monthly means

Final Water Level ProductsFinal Water Level Products

- Because we know which frequencies will have tidal energy,• we can predict the tide or tidal current• without really knowing anything about the hydrodynamics• Though, we can do a better job of prediction, if we do understand the hydrodynamics

- As long as we have a long enough data time series at a location,• we can analyze that data,• extracting amplitude and phase information for each tidal frequency,• and make reasonably good tidal predictions

* for (only) that specific location for anytime in the future or past

Tide Analysis & PredictionTide Analysis & Prediction

Portland, ME

Harmonic ConstituentsHarmonic Constituents

Principal components that make up tide signal, & are used to make tide predictionsPrincipal components that make up tide signal, & are used to make tide predictions

M2 - Principal lunar

S2 - Principal solar

N2 - Larger lunar elliptic

K1 - Luni-solar diurnal

O1 - Principal lunar diurnal

P1 - Principal solar diurnal

More than 1 component fromsun & moon

• due to their orbits beingelliptical

• and at angles to the plane

• both changing over time

Analysis & Prediction

• Observed tides areanalyzed for theirconstituents

• Constituents are then usedto create predicted tides

Need observations over asuitable period of time

• 1 – 10yrs depending onconstituent to analyze

COMPARISON OF TIDAL VS. NONCOMPARISON OF TIDAL VS. NON--TIDAL EFFECTSTIDAL EFFECTSREDUCTION OF VARIANCE STATISTICSREDUCTION OF VARIANCE STATISTICS

(FROM ONE(FROM ONE--YEAR HARMONIC ANALYSIS)YEAR HARMONIC ANALYSIS)

STATION TIDAL NON-TIDAL

BOSTON, MA 98.2% 1.8%

BALTIMORE, MD 44.8% 55.2%

CHARLESTON, SC 91.2% 8.8%

KEY WEST, FL 74.5% 25.5%

PENSACOLA, FL 45.4% 54.6%

GALVESTON, TX 39.5% 60.5%

SAN FRANCISCO, CA 98.6% 1.4%

SEATTLE, WA 98.8% 1.2%

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two daily highs & lows~ similar height

Most common

two daily highs & lows~ not similar height

one daily high & low

US Tide Types by RegionUS Tide Types by Region

East CoastPrimarily SemidiurnalSemidiurnal

West Coast & AlaskaPrimarily MixedMixed

Gulf CoastPrimarily DiurnalDiurnal

Ocean City, MD

San Francisco, CA

Panama City, FL

Tide Type Varies by Region due to Local HydrodynamicsTide Type Varies by Region due to Local Hydrodynamics Examples for East CoastExamples for East Coast

Primarily Semidiurnal

Eastport, MEEastport, MEEstablished in 1929Established in 1929

Mean Range = 5.59mMean High Water = 5.729m (MLLW)

Mean Low Water = 0.136m (MLLW)

(K1 + O1) / (M2 + S2) = 0.09(Semidiurnal = 0.0 - 0.24)

Examples for East CoastExamples for East Coast




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Effects the amplitude of the annual mean rangeEffects the amplitude of the annual mean range

ANNUAL MEAN RANGE

MONTHLY MEAN RANGE

The time between peaks is the period of oscillation of the regression (~18.6yrs))

-- Basis for defining the National Tidal Datum Epoch (NTDE) as a 19yr periodBasis for defining the National Tidal Datum Epoch (NTDE) as a 19yr period



Galveston Pleasure Pier, TXGalveston Pleasure Pier, TXEstablished in 1957Established in 1957

Mean Range = 1.46ftMean High Water = 1.85ft (MLLW)

Mean Low Water = 0.39ft (MLLW)

(K1 + O1) / (M2 + S2) = 1.92(Mixed – Diurnal = 1.5-2.99)

Examples for Gulf CoastExamples for Gulf Coast

Primarily Diurnal

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Primarily Diurnal


Primarily Diurnal


Primarily Diurnal


Primarily Diurnal


Primarily Diurnal


Primarily Diurnal

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Examples for West Coast & AlaskaExamples for West Coast & Alaska

Primarily Mixed

North Spit, CANorth Spit, CAEstablished in 1977Established in 1977

Mean Range = 4.89ftMean High Water = 6.15ftMean Low Water = 1.26ft

(K1 + O1) / (M2 + S2) = 0.74(Mixed – Semidiurnal = 0.25-1.49)


Primarily Mixed


Primarily Mixed


Primarily Mixed


Primarily Mixed


Primarily Mixed

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Primarily Mixed


Primarily Mixed

Alaska

Bering Sea Tidal Characteristics

feet

feet

feet

feet

Examples for Great LakesExamples for Great LakesLake Superior

Examples for Great LakesExamples for Great Lakes

Seiche (pronounced “saysh”)• Standing wave in an enclosed body of water

Oscillation and storm surge on Lake Erie 17-22 September 2003

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A specific 19 year period that includes the longest periodic tidalvariations caused by the astronomic tide-producing forces.

Averages out long term seasonal meteorological, hydrologic, andoceanographic fluctuations.

Provides a nationally consistent tidal datum network (bench marks) byaccounting for seasonal and apparent environmental trends in sealevel that affects the accuracy of tidal datums.

The NWLON provides the data required to maintain the epoch andmake primary and secondary determinations of tidal datums.

A common time period to which tidal datums are referencedA common time period to which tidal datums are referenced

National Tidal Datum Epoch (NTDE)National Tidal Datum Epoch (NTDE)

• Official time period of tidal observations that are used for primary datum calculations

– Time it takes the Earth, Moon, & Sun to complete an epoch tidal cycle

– 19 year time period (Present NTDE is 1983-2001)

– Considered for revision every ~20-25yrs

– Includes the longest period tidal variations (18.6 year node cycle)

– Averages out seasonal fluctuations

– Provides a nationally consistent tidal datum network by accounting for seasonal andapparent environmental trends in sea level that affect the accuracy of tidal datums

1983-2001 EPOCH

Mean Sea Level TrendsMean Sea Level Trends Mean Sea Level TrendsMean Sea Level Trends

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Mean Sea Level TrendsMean Sea Level Trends

There are areas of Louisiana, Texas, SE Alaska and SW Alaska wherethere are anomalous sea level trends compared to most othergeographic regions of the United States.

“New Procedures” have been developed to address these regions sothat published tidal and geodetic relationships are representative ofcurrent conditions

COMPUTING TIDAL DATUMS IN AREAS OF ANOMALOUS SEA LEVEL TRENDS

Tidal Datums

Base reference elevation from whichBase reference elevation from which locallocal water levels are measuredwater levels are measured

Vertical Datum: Base elevation used as a reference from which to reckon heightsor depths

Tidal Datum : Local standard elevation defined by a certain phase of the tide fromobserved data (i.e. MLW, MHW, MSL)

- Derived from continuous observations over time at specific tide stations

- Are referenced to fixed and stable points on land (Bench Marks)

- Are local references and should not be extended into areas with differentoceanographic characteristics

- Are also used as a basis for establishing legal boundaries and regulations

Chart Datum : Water level datum to which nautical chart soundings are referred

- USA chart datum is Mean Lower Low Water (MLLW) for tidal areas,

or a Low Water Datum (LWD) for non-tidal areas

Definitions of some commonly used DatumsDefinitions of some commonly used Datums

Station Datum: Unique to each water level station- Established at a lower elevation than the water is ever expected to reach.- Referenced to the primary bench mark at the station- Held constant regardless of changes to the water level gauge or tide staff

MHHW: Mean Higher High WaterThe average height of the higher high water of each tidal day observed over the NTDE

MHW: Mean High WaterThe average of all the high water heights observed over the NTDE

DTL: Diurnal Tide LevelThe arithmetic mean of mean higher high water and mean lower low water

MTL: Mean Tide LevelThe arithmetic mean of mean high water and mean low water

MSL: Mean Sea Level or LMSL: Local Mean Sea LevelThe arithmetic mean of hourly heights observed over the NTDE

MLW: Mean Low WaterThe average of all the low water heights observed over the NTDE

MLLW: Mean Lower Low WaterThe average of the lower low water height of each tidal day observed over the NTDE

Definitions of some commonly used Datums (cont’d)Definitions of some commonly used Datums (cont’d)

GT: Great Diurnal RangeThe difference in height between mean higher high water and mean lower low water

MN: Mean Range of TideThe difference in height between mean high water and mean low water

DHQ: Mean Diurnal High Water InequalityThe difference in height of the two high waters of each tidal day for a mixed or semidiurnal tide

DLQ: Mean Diurnal Low Water InequalityThe difference in height of the two low waters of each tidal day for a mixed or semidiurnal tide

HWI: Greenwich High Water Interval (Lunitidal Interval)The average interval (in hours) between the moon's transit over the Greenwich meridian andthe following high water at a location

LWI: Greenwich Low Water Interval (Lunitidal Interval)The average interval (in hours) between the moon's transit over the Greenwich meridian andthe following low water at a location

TcHHWI: Tropic higher high water intervalThe lunitidal interval pertaining to the higher high waters

TcLLWI: Tropic lower low water intervalThe lunitidal interval pertaining to the lower low waters

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Principal tidal datums related to a beach profilePrincipal tidal datums related to a beach profileThe intersection of tidal datums with land define marine boundariesThe intersection of tidal datums with land define marine boundaries

Chart Datum

The chart datum is the level of water that charted depths displayed on nauticalcharts are measured from. The chart datum is generally a tidal datum; that is, adatum derived from some phase of the tide. Common chart datums are lowestastronomical tide and mean lower low water.

Mean Lower Low Water

The United States' National Oceanic and Atmospheric Administration uses meanlower low water (MLLW), which is the average of the lowest tide recorded at a tidestation each day during the recording period. MLLW is generally located above LATand therefore some tidal states may have negative heights. The advantage of usingMean Lower Low Water is avoiding the costs and confusion that moving to LATwould involve.

Lowest Astronomical Tide

Many national charting agencies, including the United Kingdom Hydrographic Officeand other hydrographic services, such as those of Canada and Australia, thatoriginated with the British Admiralty use the Lowest astronomical tide (LAT), theheight of the water at the lowest possible theoretical tide, as chart datum. Theadvantage of using LAT is that all tidal heights must then be positive (or zero)avoiding possible ambiguity and the need to explicitly state sign. Calculation of theLAT only allows for gravitational effects so lower tides may occur in practice due toother factors (e.g. meteorological effects such as high pressure systems).

Tidal Datums from time series dataTidal Datums from time series data

LMSL (Local Mean Sea Level) = avg. of hourly levels (over 19yr Epoch)MTL (Mean Tide Level) = avg. of MHW and MLW (over 19yr Epoch)DTL (Diurnal Tide Level)= avg. of MHHW and MLLW (over 19yr Epoch)

Day 1 Day 2

Higher HighHigher High Higher HighHigher High

MHHWMHHW

MHWMHW

LowLow

Lower LowLower Low LowLow

Lower LowLower LowMLLWMLLW

MLWMLW

ObservedWater Level

HighHigh

Special DatumsSpecial Datums

(Non(Non--Tidal Regions)Tidal Regions)

Non-Tidal = GT < 0.3’



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West Bank 1, Bayou Gauche, LA



87624828762482

Columbia River, OR & WA



Great Lakes and IGLD

Datum ComputationDatum Computation

1. Make observations (NWLON Stations)2. Tabulate the tides (Data Processing)

3.3. Compute tidal datumsCompute tidal datums

A.A. Control StationsControl Stations -- Stations with over 19 years data

Primary determination (NTDE Tidal Datums)

Method: First Reduction or Arithmetic mean

= Average of observations over a 19-year National Tidal Datum Epoch (NTDE)

B.B. Subordinate StationsSubordinate Stations -- Stations with less than 19 years data

Secondary determination (NTDE Equivalent Tidal Datums)

Method: Simultaneous comparison - Subordinate Station with Control Station3 Methods for Simultaneous Comparison: (Depending on tide type)

Standard Method Modified-Range Ratio Method Direct Method

VerifiedMonthlyMeans

ACCEPTED Datums

Datum ComputationDatum Computation

A.A. Control StationsControl Stations –– Primary determination using First Reduction

• Average of observations over a 19-year NationalTidal Datum Epoch (NTDE)

• Mean of all tidal heights for a particular phase (ieHW or LW) over the epoch time period

• Accepted NTDE datum values for that station

• Available online at CO-OPS Tides & CurrentsWebsite

• Used as a reference for converting elevations takenin that area to a common datum(i.e. hydro survey depths to MLLW for charting)

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B.B. Subordinate StationsSubordinate Stations -- Secondary determination using Simultaneous Comparison

Method of Comparison of Simultaneous Observations is a twoMethod of Comparison of Simultaneous Observations is a two--step process:step process:

1. Compute the differences and/or ratiosCompute the differences and/or ratios in the tidal parameters and differences inmean values between short-term and control stations over the period ofsimultaneous comparison.

2. Apply the differences and ratiosApply the differences and ratios computed above to the NTDE Accepted Values atthe control station. This provides equivalent NTDE values for the short-term station.

Datum ComputationDatum Computation Methods for Subordinate StationsMethods for Subordinate Stations

Simultaneous Comparison – compare monthly means between control & subordinate station1. Choose an appropriate control station to compare with2. Choose an appropriate computation method for the tide type3. Compare values to the control stations to correct to NTDE equivalent

Standard Method: (mixed tide types) West Coast & Pacific Islands

Modified-Range Ratio Method: (semidiurnal & diurnal) East Coast, Gulf Coast, & Caribbean

Direct Method: Generally used when a full range of tidal values are not availableDatums determined by direct comparison with appropriate control station

The Bodnar Report

Bodnar (1981), drawing upon Swanson (1974) applied regressionequations estimating the accuracy of computed datums

Bodnar developed formulas forMean Low Water (MLW) and Mean High Water (MHW).

The 3 Month equation for Mean Low Water is presented below.

Error = 0.0043 ADLWI + 0.0036 SRGDIST + 0.0255 MNR + 0.029

ESTIMATING ACCURACIES OF TIDAL DATUMSFROM SHORT TERM OBSERVATIONS

ADLWI : average difference between low water intervalsSRGDIST: square root of the distance between stationsMNR: mean range of the tide signal

ADLWI : average difference between low water intervalsSRGDIST: square root of the distance between stationsMNR: mean range of the tide signal

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1. Make ObservationsWL Data collected at 6-minute intervals, downloaded toDMS, CORMS & Auto QC

2. Preliminary AnalysisCheck station parameters, initialize data into workingtable, fill gaps, QC

3. TabulationTabulate Highs & Lows, QC & edit Hourly Heights & Hi/Lopicks, Compute Monthly Means

4. Compute Datums - Subordinate Station with <19ys of dataMake secondary determinations using simultaneous comparison of Monthly Means

• Choose appropriate control station

Charleston, SCCharleston, SC

• Choose appropriate method(east coast=Semidiurnal)

ModifiedModified--Range Ratio MethodRange Ratio Method

East Coast Example 1East Coast Example 1 –– Comparison of Monthly MeansComparison of Monthly Means

Fort Pulaski, GAFort Pulaski, GA –– Subordinate StationSubordinate Station



Modified-Range Ratio MethodNeed corrected MTL, DTL, Mn, & GT from comparison to appropriate controlstation

MLW = MTL - (0.5*Mn) MHHW = MLLW + GTMHW = MLW + Mn DHQ = MHHW - MHWMLLW = DTL - (0.5*GT) DLQ = MLW - MLLW



• Calculate mean monthly difference between control and subordinate valuesfor each MTL, DTL, Mn, & GT over the length of the data set

• Then correct MTL, DTL, Mn, & GT for the subordinate station using the meandifference & accepted 19yr datum from the control station

Accepted 19yr Tidal Datums - control station (Charleston)(Charleston)

Accepted MTL 19yr datumfrom control station

Accepted19yr datumfrom control

station

Computedmean

monthlydifference

I.e. Corrected MTLMTL = MTL + MTL

= 1.622 + 0.497 = 2.1192.119

ComputedMTL meanmonthly

difference

MTL mean monthly difference(Sub. - control station)

Worksheet



Modified-Range Ratio Method

Ft. Pulaski NTDE Equivalent datumsMLW = 2.119 - (0.5*2.146) = 1.046 MHHW = 0.974 + 2.325 = 3.299MHW = 1.046 + 2.146 = 3.192 DHQ = 3.299 - 3.192 = 0.107MLLW = 2.137 - (0.5*2.325) = 0.974 DLQ = 1.046 - 0.974 = 0.072

B. Apply corrected MTL, DTL, Mn, & GT to formulas for Modified-Range RatioMethod to calculate remaining NTDE equivalent datums for the subordinate




4. Compute Datums - Subordinate Station with <19ys of dataMake secondary determinations using simultaneous comparison of Monthly Means

• Choose appropriate control station

San Francisco, CASan Francisco, CA

• Choose appropriate method(west coast=Mixed)

Standard MethodStandard Method

West Coast Example 1West Coast Example 1 –– Comparison of Monthly MeansComparison of Monthly Means

Alameda, CAAlameda, CA –– Subordinate StationSubordinate Station

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• Calculate mean monthly difference between control and subordinate valuesfor each MTL, Mn, DHQ, & DLQ over the length of the data set

• Then correct MTL, Mn, DHQ, & DLQ for the subordinate station using themean difference & accepted 19yr datum from the control station

Accepted 19yr Tidal Datums - control station (San Francisco)(San Francisco)

Accepted MTL 19yr datumfrom control station


station

Computedmean

monthlydifference

I.e. Corrected MTLMTL = MTL + MTL

= 2.728 + -0.685 = 2.0432.043

ComputedMTL meanmonthly

difference

MTL mean monthly difference(Sub. - control station)

Worksheet



B. Apply corrected MTL, Mn, DHQ, & DLQ to formulas for Standard Method tocalculate remaining NTDE equivalent datums for the subordinate

Standard Method:Need corrected MTL, Mn, DHQ, & DLQ from comparison with appropriate control station

MLW = MTL - (0.5*Mn) MHHW = MHW + DHQMHW = MLW + Mn DTL = 0.5*(MHHW + MLLW)MLLW = MLW - DLQ GT = MHHW - MLLW

Alameda NTDE Equivalent datumsMLW = 2.043 - (0.5*1.479) = 1.304 MHHW = 2.783 + 0.188 = 2.971MHW = 1.304 + 1.479 = 2.783 DTL = 0.5*(2.971 + 0.965) = 1.968MLLW = 1.304 – 0.339 = 0.965 GT = 2.971 - 0.965 = 2.006




*** This example*** This example -- Data series too short to compute monthly means, or data starts & ends in middleData series too short to compute monthly means, or data starts & ends in middleof monthsof months

4. Compute Datums - Subordinate Station with <1 month<1 month of dataMake secondary determinations using simultaneous comparison of High & Low waters

• Choose appropriate control stationCharleston, SCCharleston, SC

• Choose appropriate method(east coast=Semidiurnal)

ModifiedModified--Range Ratio MethodRange Ratio Method

East Coast Example 2East Coast Example 2 –– Tide by Tide ComparisonTide by Tide Comparison




A. Compare highs & lows between Subordinate & Control to calculate corrected MTL,DTL, Mn, & GT for subordinate that will be used to calculate remaining datums(MLW, MHW, MLLW, MHHW, DHQ, DLQ)

1. Plot highs and lows to ensure that designations agree– If they do not, a type conversion is done for the subordinate

(ie. If sub. value is designated as LL, where control is L, then sub. is changed from LLto L so that the pair remains matched in designation)



3. Using the above values calculated in step 2, and the accepted means from thecontrol station, calculate the corrected MTL, DTL, Mn, & GT for the subordinateto use in Modified-Range Ratio calculations

Accepted 19yr Tidal Datums - control station (Charleston)(Charleston)


station

Corrected MTLMTL = MTL + ∆MTL = 1.622 + 0.484 = 2.1062.106

AcceptedCorrected DTLDTL = DTL + ∆DTL = 1.643 + 0.482 = 2.1252.125

AcceptedCorrected MnMn = Mn * Mn ratio = 1.606 * 1.369 = 2.1982.198

AcceptedCorrected GTGT = Gt * Gt ratio = 1.768 * 1.339 = 2.3672.367

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Example 3Example 3 (West Coast)(West Coast) –– Direct MethodDirect Method

Hamilton AFB, CAHamilton AFB, CA –– Subordinate StationSubordinate Station

Compute Datums - Subordinate Station where full range of tidal values are not available(i.e. Upper reaches of a Marsh – low tides are cut off)

Make secondary determinations using simultaneous comparison of available data

• Choose appropriate control stationRichmond, CARichmond, CA

• Choose appropriate method(west coast=Mixed – full range of tidal values not available)

Direct MethodDirect Method

Types of HeightsTypes of Heights

Orthometric (H) - i.e. Leveling

• The distance between the geoid and apoint on the Earths surface measuredalong the plumb line

Ellipsoid (h) - i.e. GPS

• The distance along a perpendicular fromthe ellipsoid to a point on the Earth’ssurface

H

H = Orthometric Height (NAVD 88)

H = h - Nh = Ellipsoidal Height (NAD 83)

N = Geoid Height (Geoid03)

h

Ellipsoid

N

GeoidGEOID 03(Hi Res Model)

TOPOGRAPHICSURFACE

GPS-Derived Orthometric Heights

Tidal Datum : Local standard elevation defined by a certain phase of the tide from observed data (i.e. MLW,MHW, MSL)

- Derived from continuous observations over time at specific tide stations

- Are referenced to fixed and stable points on land (Bench Marks)

- Are local references and should not be extended into areas with different

oceanographic characteristics

- Are also used as a basis for establishing legal boundaries and regulations

GPS Connections Between BenchmarksGPS Connections Between Benchmarks

NO

AA


Station Datum

Orifice

0.7428 m


3.150 m

MHW2.736 m

MLLW1.220 m

Bench markwith geodetic control

(NAVD88, WGS84,etc.)

TideGauge

1.150 m(example)

Pier

Geodetic Benchmark(and its WGS84 value)

Relative to Tidal Datum

GPS Receivers collecting simultaneousdata over existing bench marks allow fordatum transformation.

2.000 m

GPSReceiver

Ellipsoid

NAVD88

• GPS-derived orthometric heights can be used for datum transfers (H = h – N)

• Not as limited as line of sight leveling for making benchmark connections

• Allows for connections over greater distances

Web Access to Benchmark DataWeb Access to Benchmark Datahttp://www.tidesandcurrents.noaa.govhttp://www.tidesandcurrents.noaa.gov

Data Available through OPenDAP andWeb Services

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Getting IDB datasheets from NGS websiteStart at: www.ngs.noaa.gov which is the NGS home page.

Getting OPUS datasheets from NGS websiteStart at: www.ngs.noaa.gov which is the NGS home page.

Online GPS Processing

Rapid Return on Ellipsoidal Solution

Lower accuracy than traditional leveling ~ cm

Currently ~ 1000 records in OPUS Database

CO-OPS Published benchmarksheet Elevations of individual

BM relative to tidaldatums.

Can identify the relativeelevation differencesbetween individual BM

Note the elevations arebased on a series (2 ormore) of levels.

BM identified as unstablebased on elevationsrelationships determinedby leveling will not beincluded.

Individual CO-OPS tidalbenchmarks with NGS IDBPID will be hyperlinked tothe data sheets.

Geodetic comps sheet CO-OPS Accepted Datumspage Published NAVD88 are

based on a minimum of2 published NGS IDBvalues.

Values are within in 9mmrelative to one anotherwhen set to local stationdatum.

Value are static Future alterations

Currently working onexpanding to includeOPUS-DB values

Publishing a singleNAVD88 value.

Including Ellipsoidalvalues.

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DatumDatumInformation onInformation onthe BM Sheetthe BM Sheet

Epoch, Series &Control Station

Tidal DatumsRelative to

MLLW

BenchmarksRelative toMLLW and

MHWThe NAVD 88 and the NGVD 29 elevations related to MLLW were computed from Bench Mark,941 1340 TIDAL 1, at the station. Displayed tidal datums are Mean Higher High Water(MHHW),Mean High Water (MHW), Mean Tide Level(MTL), Mean Sea Level (MSL), Mean Low Water(MLW),and Mean Lower Low Water(MLLW) referenced on 1983-2001 Epoch.

Get Orthometric heightsfrom NGS data sheets

(Links on CO-OPSBenchmark Sheet)

Seattle, WASeattle, WA

Unknown ?

NAVD 88 FromNGS Data Sheets

5.869m = 0.713m4.896m = 0.714m5.695m = 0.713m6.519m = 0.712m

= 0.713m

Calculate NAVDusing heights fromNGS data sheets

and MLLW datumfrom CO-OPSDatums Page

Seattle, WASeattle, WA

Unknown ?

NAVD88 FromNGS Data Sheets

3.996m = -0.024m5.029m = -0.016m

= -0.020m

Calculate NAVDusing heights fromNGS data sheets

and MLLW datumfrom CO-OPSDatums Page

San Francisco, CASan Francisco, CA

Connection Between Tide Datums & Geodetic DatumsConnection Between Tide Datums & Geodetic Datums

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The Georgia Anomaly???

???

Tidal Datums Relative to Geodetic Datum NAVD88Tidal Datums Relative to Geodetic Datum NAVD88

CA

Tidal Datums Relative to Geodetic Datum NAVD88Tidal Datums Relative to Geodetic Datum NAVD88 Tidal Datums Relative to Geodetic Datum NAVD88Tidal Datums Relative to Geodetic Datum NAVD88

AK

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OR

WA


Tidal Datums Relative to Geodetic Datum NAVD88Tidal Datums Relative to Geodetic Datum NAVD88 Tidal Datums Relative to Geodetic Datum NAVD88Tidal Datums Relative to Geodetic Datum NAVD88

FL


0.071

-0.090

-0.013

-0.108

0.109

-0.009

-0.102

0.034

-0.157

-0.009

-0.135

-0.278

-0.134

-0.240

-0.3000

-0.2500

-0.2000

-0.1500

-0.1000

-0.0500

0.0000

0.0500

0.1000

0.1500

MLL

WR

ela

tive

toN

AV

D8

82

00

6.8

1(m

)

NOAA Water Level Stations (East to West)

NAVD88 2006.81


0.220

0.035

0.0700.055

0.161

0.066

0.041

0.107

0.059

0.320

0.137

0.1060.092

0.128

0.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

0.3500

LMSL

Re

lati

veto

NA

VD

88

2006

.81

(m)

NOAA Water Level Stations (East to West)

NAVD88 2006.81NAVD88 2006.81NAVD88 2006.81NAVD88 2006.81

LMSL Relative to NAVD88 2006.81 (m)

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KNOWN(Charleston) MTL – NAVD88 = 1.253 – 0.152 = 1.101 m

(North Bend) MTL – NAVD88 = 1.387 – 0.295 = 1.092 m

AVE. MTL – NAVD88 = 1.101 + 1.092/ 2 = 1.097

UNKNOWNSitka Dock (9432879) MTL – X = AVE. MTL – NAVD88

NAVD88 = 1.270 (MTL) – 1.097 (MTL – NAVD88)Therefore NAVD88 @ Sitka Dock ~ 0.173 m

Sitka Dock ~ 0.173 m using interpolation, compare to published…..

Available Data / Differing DatumsAvailable Data / Differing Datums

BUT there are a many different vertical datums inuse around the nation

Ellipsoid Datums

Orthometric Datums

Tidal Datums

MHHW, MHW,MTL, DTL,LMSL,MLW, MLLW

NAVD 88,NGVD 29

WGS 84,NAD 83(NSRS), 17others

GeodeticDatums

For elevation data sets to be blendedtogether they must be referenced to samevertical datum.

All elevation data is referenced to a vertical datum.

7 TidalDatums

18 3-DDatums

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GEODETIC DATUMS

Geoid---the shape the ocean surface would haveif it were not in motion and only influenced bygravity.

● It is an equipotential surface of gravity.● Is the zero surface as defined by the Earth’s

surface.● May be approximated by MSL● Orthometric height ( dynamic height in

academia)

What is the Geoid?

Equipotential

Surface

of Gravity

GRACE Gravity Model 01- Released July 2003

Why do we need an ellipsoid?

This image depicts the earth’sshape without water and clouds.

Calculation of geographicposition on this irregular surfaceis very complex. A simplermodel is needed.

This simplified mathematical

surface is the ellipsoid.

GPS - Derived Ellipsoid Heights

Z Axis

X Axis

Y Axis

(X,Y,Z) = P (,,h)

h

Earth’sSurface

ZeroMeridian

Mean Equatorial Plane

Reference Ellipsoid

P

Ellipsoidal Height (NAD 83)

An ellipsoidal height (h) is the distance from a point on the Earth’s surface measured along aline perpendicular to a mathematically-defined reference ellipsoid.

(Reference) ellipsoidal surface: a mathematical (geometric) model which approximates theirregular shape of geoid.

H

H = Orthometric Height (NAVD 88)

H = h - N

TOPOGRAPHIC SURFACE

h = Ellipsoidal Height (NAD 83)

N = Geoid Height (GEOID 03)

h

Ellipsoid(NAD 83)

N

Geoid(NAVD 88)

Geoid Height(GEOID03)

Ellipsoid, Geoid,Ellipsoid, Geoid, and Orthometric Heights

AB

Orthometric Height (NAVD 88)

An orthometric height (H) is the distance from a point on the Earth’s surface measured along aline perpendicular to a geoid.

Tri office responsibilities Assessment:

• Existing Stations on 83-01 Epoch:• Connections to other datums• Ellipsoidal (NAD83)• Orthometric (NAVD88)

• Land usages:• Identify land types. (wetlands,developed areas, tidal flats).• Topographic heights

• Tidal and Geodetic Dynamics:• Tidal range change of 0.2 ft / mi orgreater• Datum relationships: Identifyorthometric (NAVD88) or ellipsoidal(NAD83) dynamic regions

• Marine analysis:• Bathy depths• Identify bottom types.• Identify dredged areas.• Identify commercial transit routes.

• Hydrodynamic model:• Infer tidal dynamics and currentdynamics.

CO-OPS Responsibilities:

Results:

• New geodetic survey onbenchmark that is connected toexisting stations with 83-01 epochdata to establish tidal geodeticconnection.

• Installations of a new CO-OPSwater level station.

• Reoccupation of historical CO-OPS water level station.

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Report:

Documentation of existing 83-01datums.

Definition of stations requiringsurveys or installations.

Survey work lists

Graphic:

Present data

Recommendations

Datum errors

Datum relationships

NWLON gaps

National VDatumNational VDatum

Vertical Datum Transformation Tool

• software tool to allow a seamless transform of elevations between approximately 27vertical datums of three categories: tidal (MSL), orthometric (NAVD88) and ellipsoidal(NAD83) vertical datums

• Data from many different resources can be be referenced to a common vertical datum

Bathy/Bathy/TopoTopoDigital Elevation ModelDigital Elevation Model

NOAANOAABathymetryBathymetry

USGSUSGSTopographyTopography

EllipsoidModel

TidalModel

GeoidModel

National VDatum( Vertical Datum Transform Tool )

Bathy/TopoDigital Elevation Model

Bathymetry

TopographyVDatum

VDatum and Creation of Digital Elevation Models

• Inundation modeling from storm surge,tsunamis, and sea level rise.

• Erosion, accretion, renourishment

• Analyzing storm impacts

• Determining setback lines

• Determining local, state, and nationalboundaries

• Navigation Products andServices

• Habitat restoration

• Shoreline Change Analysis

• Analyzing environmental andnatural resources

• Permitting

Applications for Seamless Bathy/Topo Datasets: NAD83 (NSRS) NAVD 88 LMSL

MHHW

MHW

MTL

DTL

MLW

MLLW

NGVD 29

GEOID99,GEOID03 TSS

(Topography ofthe Sea Surface)

WGS 84 (G873)

WGS 84 (G730)

WGS 84 (orig.)

ITRF97

ITRF94

ITRF96

ITRF93

ITRF92

ITRF91

ITRF90

ITRF89

ITRF88

SIO/MIT 92

NEOS 90

PNEOS 90

WGS 84 (G1150)

ITRF2000

3D Datums Tidal DatumsOrthometric

Datums

VERTCON

Tide Models

Calibrated HelmertTransformations

Vertical Datum Transformation “Roadmap”

Choose a horizontal datum

Choose a geoid model

Choose input andoutput vertical

datums:

Run as single point, batch, or insert into programming

Uncertainty has been calculated for transformationsacross the full process…

Ellipsoid Orthometric Tidal

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Current VDatum Availability

VDatum.noaa.gov

162

Questions?

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Michael Michalski, NOAA/National Ocean ServiceCenter for Operational Oceanographic Products and ServicesMonday, January 9 2012

010912-02-geodeticverticaldatums-michalski -grayscale.pdf

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