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12/20/2011
Tidal Theory
Tidal Datums
Station Configuration
Non-tidal Datum considerations
Data Collection
Datum Computations
Data Processing
Datums Relative to Benchmarks
Tidal Characteristics
Regional Variation in Tidal –
Geodetic
NTDE (MTDE)
Relative Sea Level Trends
Michael Michalski, NOAA/National Ocean Service
Center for Operational Oceanographic Products and Services
Monday, January 9 2012
Interpolation of Tidal – Geodetic
Relationships
Application of VDatum
Periodic variation in the surface level of the oceans
Caused by gravitational attraction between the Earth, Moon, & Sun
Astronomy & Hydrodynamics
Common Terms
Tide : The alternating rise and fall of water levels with
Tide curve
Tidal Current : Horizontal motion resulting from rise
& fall of water levels
Tide Range : difference in height between highest
high & lowest low
Water level height
respect to land
Both the moon & the sun affect the tides (sun’s effect is 0.46 times that of the Moon)
Mean
Sea
Level
Astronomy - Tides are result of the
gravitational forces of the Earth, Moon & Sun
& the centrifugal forces of their rotations
Tidal Period : Time between successive lows or highs
(Average ~12.4hs)
Time
Tidal Frequency : How often 1 tidal period occurs per day (Average ~1.9 cycles per day)
Mean Sea Level : Average
Tidal Current
Current speed
height of sea surface
Hydrodynamics - The range & timing of the tide
& the speed, direction & timing of the tidal
current are also influenced by the configuration
of the coastline, bottom topography & local
water depth
Bay
Long Wave
In the Ocean
Time
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Most important tide modulations result from phases of the Moon relative to Sun
Forces change with alignment- Strength of the gravitational force is strongest when Sun &
Moon are aligned (Phase Inequality)
• Spring tide: sun and moon
aligned
• Neap tide: sun and moon not
aligned
Centrifugal
force
Gravitational
pull
Spring and Neap tides
Gravitational pull
- 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
Affects the amplitude of the tides (tidal range)
Spring
tides,– with
with
higher
Spring
tides,
higher
Neap tides
muted,
with
high
tides
and
lower
low
high
tides
and
lower
low
higher
lows
and
lower
tides
tides
highs
Centrifugal force
Centrifugal force
Gravitational pull
Centrifugal
force
Gravitational
pull
Gravitational pull
Tide producing force of
the Moon is 2.5 times
that of the Sun
new
moon
full
halfmoon
moon
Force due to the moon is
about 2.5x greater than
the force due to the sun
Less significant modulations result from the elliptical orbits of Earth & Moon
Forces change with angle - Strength of the gravitational force is strongest when angle is smallest
(Declination Inequalities)
Moon’s Orbit – Monthly modulation
Diurnal Inequality
The changing distance of the Moon above
or below the equator causes a difference
in amplitude of the two tides in the same
day & results in the various tide types
(Semidiurnal, Mixed & Diurnal)
Moon
Phases:
The two daily highs will be most similar
when the declination is smallest
Spring
Neap
Spring
Neap
A longer period modulation results from the angled orbital paths of the Earth &
moon around the sun
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 range
ANNUAL MEAN RANGE
Ecliptic - Apparent path of Earth about the Sun, as seen
from the Sun
Lunar Orbit - Apparent path of Moon about the Sun, as
seen from the Sun
Nodes - Points where Moon’s path crosses the ecliptic.
Regression of the Moon’s Nodes – Variation in the
path of the Moon about the Sun, such that the angle
of the moon’s orbital plane with the equatorial plane
varies over 18.6 yrs
Effects the amplitude of the Annual Mean Range
(Difference in height between mean high & low)
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 period
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National Water Level Observation Network (NWLON)
• 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 supporting
projects such as storm surge monitoring research,
hydro / photo support, and habitat restoration
Remote Pacific Island Stations Not Shown
Essential Equipment
Control stations are operated by NOS and disseminated over the internet
Control Stations
Subordinate stations are usually installed by field teams prior to survey
operations and removed after surveys are completed
• 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
Primary Control Tide Station: Continuous observations over 19 yrs or
more & expected to continue
- Data used for determining tidal datums
Secondary Control Tide Station: Subordinate station with continuous
observations over at least 1 yr, but less than 19 yrs, and has a planned finite
lifetime
- Data must be compared to a suitable control station for determining tidal
datums
Tertiary Control Tide Station: Subordinate station with continuous
observations over at least 30 days, but less than 1 yr, and has a planned
finite lifetime
- Data must be compared to a suitable control station for determining tidal
datums
•
•
•
•
•
•
•
Water Level
Wind Speed/Direction
Barometric Pressure
Air/Water Temp.
Conductivity/Temp
Chart Datum
Tsunami/Storm Surge
Short term stations
Observations
Collected
•
•
•
•
Data Collection Platform
Acoustic or pressure sensor
Solar Panel
GOES Transmitter
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Water 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
Vertical Datum Reference
Vertical Datum Reference characteristics are:
• Water levels accurately known relative to the latest tidal datums on the
latest National Tidal Datum Epoch (NTDE)
• Water levels accurately known relative to the land and a local network of
recoverable tidal bench marks
• Precise connections to the national geodetic datum (NAVD88) using level
connections or GPS connections to the bench marks in the National
Spatial Reference System
(NSRS)
• NGS Accuracy Standards
Tidal Bench mark 3.150 m
4811 G 2004
2nd Order, Class I for long-term stations
3rd Order for short-term stations
Backup Measurement System
Pressure sensor based water level sensor
Sutron Data Collection Platform
• 60 Days of Data Storage
• Transfers data to Primary Measurement System
• Annual leveling for NWLON
installation and removal
levels for short-term stations
• Emergency leveling
for storm events
GPS
Receiver
Tide
Gauge
1.150 m
(example)
2.736 m
MHW
Geodetic Benchmark
2.000 m
(and its WGS84 value)
Relative to Tidal Datum
MLLW
Tidal Bench mark
4811 G 2004
1.220 m
NAVD88
0.7428 m
Station Datum
GPS Receivers collecting simultaneous
data over existing bench marks allow
for datum transformation.
Pier
NOAA
• Multitasking Operating system
• 30 Days of Data Storage
• Satellite Data Telemetry
• Telephone Modem - Data retrieval and
software upgrades
Bench mark
with geodetic control
(NAVD88, WGS84,etc.)
Orifice
Sent from stations via satellite
GOES
Satellite
NESDIS
National Environmental Satellite,
Data and Information Services
NWLON Server PORTS®
® Server
CO-OPS Web Page
Data Analyst
Continuous Operational Real
Real--Time Monitoring System (CORMS)
Real-Time 24x7 QA/QC
•Human Analysis
•Data Quality Flags (e.g. Rate of Change)
•Corrective Action
Initial 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 raw
sensor data for all active stations
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
–
–
–
–
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 data
of significant range, or data without breaks
Doesn’t work well with diurnal, low
range or noisy data
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Initial Automated Processing
Data Processing Procedures
Check station parameters
• When MPG doesn’t work well you will see:
• Data spikes
• Bad break fills
• Double or missing tides
• Overlapping time series
Not designed to
replace analysts
1. Preliminary Analysis
• Check station parameters
• Examine data inventories
• Initialize Working Water Level data
–
Move data from sensor areas into working WL
Table
• Review 6-minute Data plots
–
–
Data Gaps
Large standard deviations indicate a problem
Review data plots
1. Preliminary Analysis (Cont’d)
• Fill Breaks
–
–
Criteria for determining a Tide
Programmed into the computer algorithms.
Perform Offline QC Checks
Fill-six program or QC Spreadsheet
Use Backup WL data, compatible nearby station
data, predictions, or curve fit for small breaks
• Perform Offline QC Checks
• Check and correct erroneous data using the
QC Spreadsheet, nearby station checks
1.
Two-hour rule: Adjacent high and low waters must be different by 2 hours or more in
2.
One-tenth of a foot rule (same as 0.03 m rule): Adjacent high and low waters must be
time in order to be counted as a tide.
different in elevation be one tenth of a foot (or 0.03 m) or more in order to be counted as a
tide for tabulation.
Fill Breaks
Difference in
elevation
Fill with backup (B1) or nearby station
Backup Fill
Curve fit
Difference in time
Fill with predicted (PR)
data
Monthly Means
2. Tabulation (Cont’d)
• Compute Monthly Means
• Mark data Complete
• Make output reports
• Final Time Series Check
– 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
Hourly Heights
Hi-Low Picks
Tide Check Report
2. Tabulation
• Tabulate High and Low waters
Hi-Low Water
4.Verification
• Check by a senior analyst
5.Compute Datums
Verified
Monthly
Means
RAW SIX-MINUTE
WATER LEVEL
Verified HI / LO
ACCEPTED Datums
Verified
SIX-MINUTE
WATER LEVEL
Verified WATER
LEVEL HOURLY
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Final Water Level Products
•
•
•
•
6 minute data values
Hourly Heights
Highs and Lows
Monthly means
Tide Analysis & Prediction
Harmonic Constituents
- 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
Principal components that make up tide signal, & are used to make tide predictions
More than 1 component from
sun & moon
• due to their orbits being
elliptical
• and at angles to the plane
S2 - Principal solar
• both changing over time
N2 - Larger lunar elliptic
Analysis & Prediction
• Observed tides are
analyzed for their
constituents
Portland, ME
M2 - Principal lunar
• Constituents are then used
to create predicted tides
K1 - Luni-solar diurnal
O1 - Principal lunar diurnal
P1 - Principal solar diurnal
Need observations over a
suitable period of time
• 1 – 10yrs depending on
constituent to analyze
COMPARISON OF TIDAL VS. NON
NON--TIDAL EFFECTS
REDUCTION OF VARIANCE STATISTICS
(FROM ONEONE-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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US Tide Types by Region
two daily highs & lows
~ similar height
Most common
Ocean City, MD
East Coast
Primarily Semidiurnal
San Francisco, CA
two daily highs & lows
~ not similar height
West Coast & Alaska
Primarily Mixed
Panama City, FL
one daily high & low
Gulf Coast
Primarily Diurnal
Tide Type Varies by Region due to Local Hydrodynamics
Examples for East Coast
Eastport, ME
Established in 1929
Mean Range = 5.59m
Mean High Water = 5.729m (MLLW)
Mean Low Water = 0.136m (MLLW)
(K1 + O1) / (M2 + S2) = 0.09
(Semidiurnal = 0.0 - 0.24)
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Effects 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 period
Examples for Gulf Coast
Primarily Diurnal
Galveston Pleasure Pier, TX
Established in 1957
Mean Range = 1.46ft
Mean High Water = 1.85ft (MLLW)
Mean Low Water = 0.39ft (MLLW)
(K1 + O1) / (M2 + S2) = 1.92
(Mixed – Diurnal = 1.5-2.99)
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Primarily Diurnal
Primarily Diurnal
Primarily Diurnal
Primarily Diurnal
Primarily Diurnal
Primarily Diurnal
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Examples for West Coast & Alaska
Primarily Mixed
Primarily Mixed
Primarily Mixed
Primarily Mixed
Primarily Mixed
Primarily Mixed
North Spit, CA
Established in 1977
Mean Range = 4.89ft
Mean High Water = 6.15ft
Mean Low Water = 1.26ft
(K1 + O1) / (M2 + S2) = 0.74
(Mixed – Semidiurnal = 0.25-1.49)
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Primarily Mixed
Primarily Mixed
feet
Alaska
feet
feet
feet
Bering Sea Tidal Characteristics
Examples for Great Lakes
Examples for Great Lakes
Lake Superior
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 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 long term 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 affects 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)
• 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 and
apparent environmental trends in sea level that affect the accuracy of tidal datums
1983-2001 EPOCH
Mean Sea Level Trends
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COMPUTING TIDAL DATUMS IN AREAS OF ANOMALOUS SEA LEVEL TRENDS
There are areas of Louisiana, Texas, SE Alaska and SW Alaska where
there are anomalous sea level trends compared to most other
geographic regions of the United States.
“New Procedures” have been developed to address these regions so
that published tidal and geodetic relationships are representative of
current conditions
Base reference elevation from which local water levels are measured
Tidal Datums
Vertical Datum: Base elevation used as a reference from which to reckon heights
or depths
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
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 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 Water
The average height of the higher high water of each tidal day observed over the NTDE
MHW: Mean High Water
The average of all the high water heights observed over the NTDE
DTL: Diurnal Tide Level
The arithmetic mean of mean higher high water and mean lower low water
MTL: Mean Tide Level
The arithmetic mean of mean high water and mean low water
MSL: Mean Sea Level or LMSL: Local Mean Sea Level
The arithmetic mean of hourly heights observed over the NTDE
MLW: Mean Low Water
The average of all the low water heights observed over the NTDE
MLLW: Mean Lower Low Water
The average of the lower low water height of each tidal day observed over the NTDE
Definitions of some commonly used Datums (cont’d)
GT: Great Diurnal Range
The difference in height between mean higher high water and mean lower low water
MN: Mean Range of Tide
The difference in height between mean high water and mean low water
DHQ: Mean Diurnal High Water Inequality
The difference in height of the two high waters of each tidal day for a mixed or semidiurnal tide
DLQ: Mean Diurnal Low Water Inequality
The 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 and
the 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 and
the following low water at a location
TcHHWI: Tropic higher high water interval
The lunitidal interval pertaining to the higher high waters
TcLLWI: Tropic lower low water interval
The lunitidal interval pertaining to the lower low waters
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Principal tidal datums related to a beach profile
The intersection of tidal datums with land define marine boundaries
Chart Datum
The chart datum is the level of water that charted depths displayed on nautical
charts are measured from. The chart datum is generally a tidal datum; that is, a
datum derived from some phase of the tide. Common chart datums are lowest
astronomical tide and mean lower low water.
Tidal Datums from time series data
Higher High
Higher High
MHHW
Mean Lower Low Water
The United States' National Oceanic and Atmospheric Administration uses mean
lower low water (MLLW), which is the average of the lowest tide recorded at a tide
station each day during the recording period. MLLW is generally located above LAT
and therefore some tidal states may have negative heights. The advantage of using
Mean Lower Low Water is avoiding the costs and confusion that moving to LAT
would involve.
Lowest Astronomical Tide
Many national charting agencies, including the United Kingdom Hydrographic Office
and other hydrographic services, such as those of Canada and Australia, that
originated with the British Admiralty use the Lowest astronomical tide (LAT), the
height of the water at the lowest possible theoretical tide, as chart datum. The
advantage 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 the
LAT only allows for gravitational effects so lower tides may occur in practice due to
other factors (e.g. meteorological effects such as high pressure systems).
Special Datums
(Non
(Non--Tidal Regions)
MHW
High
Observed
Water Level
Low
Lower Low
MLW
Low
Lower Low
Day 1
MLLW
Day 2
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)
Special Datums
(Non-Tidal Regions)
(NonNon-Tidal = GT < 0.3’
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Special Datums
(Non
(Non--Tidal Regions)
Special Datums
(Non-Tidal Regions)
(Non-
West Bank 1, Bayou Gauche, LA
Columbia River, OR & WA
8762482
Great Lakes and IGLD
Datum Computation
1. Make observations (NWLON Stations)
2. Tabulate the tides (Data Processing)
Datum Computation
Verified
Monthly
Means
ACCEPTED Datums
A. Control Stations – Primary determination using First Reduction
3. Compute tidal datums
A. Control 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. Subordinate Stations - Stations with less than 19 years data
Secondary determination (NTDE Equivalent Tidal Datums)
Method: Simultaneous comparison - Subordinate Station with Control Station
3 Methods for Simultaneous Comparison: (Depending on tide type)

Standard Method

Modified-Range Ratio Method

Direct Method
• Average of observations over a 19-year National
Tidal Datum Epoch (NTDE)
• Mean of all tidal heights for a particular phase (ie
HW or LW) over the epoch time period
• Accepted NTDE datum values for that station
• Available online at CO-OPS Tides & Currents
Website
• Used as a reference for converting elevations taken
in that area to a common datum
(i.e. hydro survey depths to MLLW for charting)
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Datum Computation
Methods for Subordinate Stations
Simultaneous Comparison – compare monthly means between control & subordinate station
B. Subordinate Stations - Secondary determination using Simultaneous Comparison
1. Choose an appropriate control station to compare with
2. Choose an appropriate computation method for the tide type
3. Compare values to the control stations to correct to NTDE equivalent
Method of Comparison of Simultaneous Observations is a twotwo-step process:
1. Compute the differences and/or ratios in the tidal parameters and differences in
mean values between short-term and control stations over the period of
simultaneous comparison.
2. Apply the differences and ratios computed above to the NTDE Accepted Values at
the control station. This provides equivalent NTDE values for the short-term station.
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 available
Datums determined by direct comparison with appropriate control station
ESTIMATING ACCURACIES OF TIDAL DATUMS
FROM SHORT TERM OBSERVATIONS
The Bodnar Report
Bodnar (1981), drawing upon Swanson (1974) applied regression
equations estimating the accuracy of computed datums
Bodnar developed formulas for
Mean 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
ADLWI : average difference between low water intervals
SRGDIST: square root of the distance between stations
MNR: mean range of the tide signal
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East Coast Example 1 – Comparison of Monthly Means
Fort Pulaski, GA – Subordinate Station
1. Make Observations
WL Data collected at 6-minute intervals, downloaded to
DMS, CORMS & Auto QC
Check station parameters, initialize data into working
table, fill gaps, QC
3. Tabulation
Tabulate Highs & Lows, QC & edit Hourly Heights & Hi/Lo
picks, Compute Monthly Means
4. Compute Datums - Subordinate Station with <19ys of data
Make secondary determinations using simultaneous comparison of Monthly Means
• Choose appropriate control station
Need corrected MTL, DTL, Mn, & GT from comparison to appropriate control
station
MLW = MTL - (0.5*Mn)
MHHW = MLLW + GT
MHW = MLW + Mn
DHQ = MHHW - MHW
MLLW = DTL - (0.5*GT)
DLQ = MLW - MLLW
Charleston, SC
• Choose appropriate method
(east coast=Semidiurnal)
Modified
Modified--Range Ratio Method
•
Calculate mean monthly difference between control and subordinate values
for each MTL, DTL, Mn, & GT over the length of the data set
•
Then correct MTL, DTL, Mn, & GT for the subordinate station using the mean
difference & accepted 19yr datum from the control station
I.e. Corrected MTL = MTL Accepted + MTL Computed
mean
monthly
difference
19yr datum
from control
station
MTL mean monthly difference
(Sub. - control station)
= 1.622
+ 0.497
= 2.119
Accepted 19yr Tidal Datums - control station (Charleston)
Worksheet
Computed
MTL mean
monthly
difference
Accepted MTL 19yr datum
from control station
West Coast Example 1 – Comparison of Monthly Means
Alameda, CA – Subordinate Station
B. Apply corrected MTL, DTL, Mn, & GT to formulas for Modified-Range Ratio
Method to calculate remaining NTDE equivalent datums for the subordinate
Ft. Pulaski NTDE Equivalent datums
MLW = 2.119 - (0.5*2.146) = 1.046
MHW = 1.046 + 2.146
= 3.192
MLLW = 2.137 - (0.5*2.325) = 0.974
3. Tabulation
MHHW = 0.974 + 2.325 = 3.299
DHQ = 3.299 - 3.192 = 0.107
DLQ = 1.046 - 0.974 = 0.072
4. Compute Datums - Subordinate Station with <19ys of data
Make secondary determinations using simultaneous comparison of Monthly Means
San Francisco, CA
(west coast=Mixed)
Standard Method
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•
Calculate mean monthly difference between control and subordinate values
for each MTL, Mn, DHQ, & DLQ over the length of the data set
•
Then correct MTL, Mn, DHQ, & DLQ for the subordinate station using the
mean difference & accepted 19yr datum from the control station
I.e. Corrected MTL = MTL Accepted + MTL Computed
MTL mean monthly difference
(Sub. - control station)
19yr datum
from control
station
= 2.728
mean
monthly
difference
+ -0.685
= 2.043
Accepted 19yr Tidal Datums - control station (San Francisco)
Computed
MTL mean
monthly
difference
Worksheet
Accepted MTL 19yr datum
from control station
East Coast Example 2 – Tide by Tide Comparison
B. Apply corrected MTL, Mn, DHQ, & DLQ to formulas for Standard Method to
calculate 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 + DHQ
MHW = MLW + Mn
DTL = 0.5*(MHHW + MLLW)
MLLW = MLW - DLQ
GT = MHHW - MLLW
Alameda NTDE Equivalent datums
MLW = 2.043 - (0.5*1.479) = 1.304
MHW = 1.304 + 1.479 = 2.783
MLLW = 1.304 – 0.339 = 0.965
MHHW = 2.783 + 0.188 = 2.971
DTL = 0.5*(2.971 + 0.965) = 1.968
GT = 2.971 - 0.965 = 2.006
3. Tabulation
*** This example - Data series too short to compute monthly means, or data starts & ends in middle
of months
4. Compute Datums - Subordinate Station with <1 month of data
Make secondary determinations using simultaneous comparison of High & Low waters
Charleston, SC
(east coast=Semidiurnal)
Modified
Modified--Range Ratio Method
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 LL
to L so that the pair remains matched in designation)
3.
Using the above values calculated in step 2, and the accepted means from the
control station, calculate the corrected MTL, DTL, Mn, & GT for the subordinate
to use in Modified-Range Ratio calculations
Corrected MTL = MTL Accepted + ∆MTL = 1.622 + 0.484 = 2.106
19yr datum
from control
station
Corrected DTL = DTL Accepted + ∆DTL = 1.643 + 0.482 = 2.125
Corrected Mn = Mn
Accepted
* Mn ratio = 1.606 * 1.369 = 2.198
Corrected GT = Gt Accepted * Gt ratio = 1.768 * 1.339 = 2.367
Accepted 19yr Tidal Datums - control station (Charleston)
18
12/20/2011
Example 3 (West Coast) – Direct Method
Hamilton AFB, CA – Subordinate 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
Richmond, CA
(west coast=Mixed – full range of tidal values not available)
Direct Method
Types of Heights
Orthometric (H) - i.e. Leveling
• The distance between the geoid and a
point on the Earths surface measured
along the plumb line
Ellipsoid (h) - i.e. GPS
• The distance along a perpendicular from
the ellipsoid to a point on the Earth’s
surface
GPS Connections Between Benchmarks
GPS-Derived Orthometric Heights
H = Orthometric Height (NAVD 88)
h = Ellipsoidal Height (NAD 83)
H =h-N
N = Geoid Height (Geoid03)
H
TOPOGRAPHIC
SURFACE
h
• 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
N
Geoid
GEOID 03
(Hi Res Model)
Ellipsoid
Ellipsoid
GPS
Receiver
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
http://www.tidesandcurrents.noaa.gov
GPS Receivers collecting simultaneous
data over existing bench marks allow for
datum transformation.
Pier
1.150 m
(example)
2.736 m
MHW
Geodetic Benchmark
2.000 m
(and its WGS84 value)
Relative to Tidal Datum
MLLW
Tidal Bench mark
4811 G 2004
1.220 m
NAVD88
Bench mark
with geodetic control
(NAVD88, WGS84,etc.)
Orifice
Station Datum
Web Access to Benchmark Data
3.150 m
NOAA
Tide
Gauge
Tidal Bench mark
4811 G 2004
0.7428 m
Data Available through OPenDAP and
Web Services
19
12/20/2011
Getting IDB datasheets from NGS website
Start at: www.ngs.noaa.gov which is the NGS home page.
Getting OPUS datasheets from NGS website
Start at: www.ngs.noaa.gov which is the NGS home page.
 CO-OPS Published benchmark
Online GPS Processing
Lower accuracy than traditional leveling ~ cm
Rapid Return on Ellipsoidal Solution
Currently ~ 1000 records in OPUS Database
Geodetic comps sheet
sheet
 Elevations of individual
BM relative to tidal
datums.
 Can identify the relative
elevation differences
between individual BM
 Note the elevations are
based on a series (2 or
more) of levels.
 BM identified as unstable
based on elevations
relationships determined
by leveling will not be
included.
 Individual CO-OPS tidal
benchmarks with NGS IDB
PID will be hyperlinked to
the data sheets.
 CO-OPS Accepted Datums
page
 Published NAVD88 are
based on a minimum of
2 published NGS IDB
values.
 Values are within in 9mm
relative to one another
when set to local station
datum.
 Value are static
 Future alterations
 Currently working on
expanding to include
OPUS-DB values
 Publishing a single
NAVD88 value.
 Including Ellipsoidal
values.
20
12/20/2011
Datum
Information on
the BM Sheet
Epoch, Series &
Control Station
Tidal Datums
Relative to
MLLW
Benchmarks
Relative to
MLLW and
MHW
The 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.
Seattle, WA
Seattle, WA
Get Orthometric heights
from NGS data sheets
(Links on CO-OPS
Benchmark Sheet)
Unknown ?
Calculate NAVD
using heights from
NGS data sheets
and MLLW datum
from CO-OPS
Datums Page
NAVD 88 From
NGS Data Sheets
5.869m = 0.713m
4.896m = 0.714m
5.695m = 0.713m
6.519m = 0.712m
= 0.713m
Connection Between Tide Datums & Geodetic Datums
San Francisco, CA
Unknown ?
Calculate NAVD
using heights from
NGS data sheets
and MLLW datum
from CO-OPS
Datums Page
NAVD88 From
NGS Data Sheets
3.996m = -0.024m
5.029m = -0.016m
= -0.020m
21
12/20/2011
The Georgia Anomaly???
???
Tidal Datums Relative to Geodetic Datum NAVD88
CA
AK
22
12/20/2011
WA
OR
FL
LMSL Relative to NAVD88 2006.81 (m)
0.3500
0.109
0.1000
0.0500
0.071
0.034
0.0000
NAVD88 2006.81
-0.009
-0.013
-0.009
-0.0500
-0.1000
-0.1500
-0.090
-0.108
-0.102
-0.157
-0.134
-0.135
-0.2000
-0.240
-0.2500
-0.278
-0.3000
NOAA Water Level Stations (East to West)
LMSL Relative to NAVD88 2006.81 (m)
MLLW Relative to NAVD88 2006.81 (m)
0.1500
0.320
0.3000
0.2500
0.220
0.2000
0.161
0.1500
0.137
0.107
0.1000
0.070
0.0500
0.035
0.055
0.066
0.041
0.128
0.106
0.092
0.059
NAVD88 2006.81
0.0000
NOAA Water Level Stations (East to West)
23
12/20/2011
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
UNKNOWN
Sitka Dock (9432879) MTL – X = AVE. MTL – NAVD88
NAVD88 = 1.270 (MTL) – 1.097 (MTL – NAVD88)
Therefore NAVD88 @ Sitka Dock ~ 0.173 m
Available Data / Differing Datums
Sitka Dock ~ 0.173 m using interpolation, compare to published…..
All elevation data is referenced to a vertical datum.
BUT there are a many different vertical datums in
use around the nation
Ellipsoid Datums
18 3-D
Datums
WGS 84,
NAD 83
(NSRS), 17
others
Orthometric Datums
Geodetic
Datums
NAVD 88,
NGVD 29
Tidal Datums
For elevation data sets to be blended
together they must be referenced to same
vertical datum.
7 Tidal
Datums
MHHW, MHW,
MTL, DTL,
LMSL,
MLW, MLLW
24
12/20/2011
What is the Geoid?
GEODETIC DATUMS
Equipotential
Surface
of Gravity
Geoid---the shape the ocean surface would have
if it were not in motion and only influenced by
gravity.
● 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)
GRACE Gravity Model 01
- Released July 2003
Ellipsoidal Height (NAD 83)
Why do we need an ellipsoid?
 This image depicts the earth’s
shape without water and clouds.
 Calculation of geographic
position on this irregular surface
is very complex. A simpler
model is needed.
An ellipsoidal height (h) is the distance from a point on the Earth’s surface measured along a
line perpendicular to a mathematically-defined reference ellipsoid.
(Reference) ellipsoidal surface: a mathematical (geometric) model which approximates the
irregular shape of geoid.
Orthometric Height (NAVD 88)
An orthometric height (H) is the distance from a point on the Earth’s surface measured along a
line perpendicular to a geoid.
GPS - Derived Ellipsoid Heights
P
Earth’s
Surface
H =h-N
N = Geoid Height (GEOID 03)
 This simplified mathematical
Zero
Meridian
Reference Ellipsoid
h
TOPOGRAPHIC SURFACE
Y Axis
A
Ellipsoid
(NAD 83)
Geoid
(NAVD 88)
H
N

B
Geoid Height
(GEOID03)

X Axis
Tri office responsibilities
(X,Y,Z) = P (,,h)
h
H = Orthometric Height (NAVD 88)
h = Ellipsoidal Height (NAD 83)
surface is the ellipsoid.
Z Axis
Ellipsoid, Geoid, and Orthometric Heights
Mean Equatorial Plane
CO-OPS
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 or
greater
• Datum relationships: Identify
orthometric (NAVD88) or ellipsoidal
(NAD83) dynamic regions
• Marine analysis:
• Bathy depths
• Identify bottom types.
• Identify dredged areas.
• Identify commercial transit routes.
Results:
• New geodetic survey on
benchmark that is connected to
existing stations with 83-01 epoch
data to establish tidal geodetic
connection.
• Installations of a new CO-OPS
water level station.
• Reoccupation of historical COOPS water level station.
• Hydrodynamic model:
• Infer tidal dynamics and current
dynamics.
25
12/20/2011
Report:
National VDatum
Documentation of existing 83-01
datums.
Definition of stations requiring
surveys or installations.
Vertical Datum Transformation Tool
• software tool to allow a seamless transform of elevations between approximately 27
vertical 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
Survey work lists
Geoid
Model
Graphic:
Tidal
Model
Ellipsoid
Model
Bathy/
Bathy/Topo
Topo
Digital Elevation Model
USGS
Topography
Present data
Recommendations
Datum errors
NOAA
Bathymetry
Datum relationships
NWLON gaps
National VDatum
( Vertical Datum Transform Tool )
VDatum and Creation of Digital Elevation Models
Vertical Datum Transformation “Roadmap”
Bathy/Topo
Digital Elevation Model
VDatum
Topography
Orthometric
Datums
3D Datums
WGS 84 (G1150)
WGS 84 (G873)
Calibrated Helmert
Transformations
NGVD 29
WGS 84 (G730)
Bathymetry
Tidal Datums
Tide Models
MHHW
WGS 84 (orig.)
ITRF2000
VERTCON
MHW
ITRF97
Applications for Seamless Bathy/Topo Datasets:
ITRF96
• Inundation modeling from storm surge,
tsunamis, and sea level rise.
• Navigation Products and
Services
• Erosion, accretion, renourishment
• Habitat restoration
• Analyzing storm impacts
• Shoreline Change Analysis
• Determining setback lines
• Analyzing environmental and
natural resources
• Determining local, state, and national
boundaries
ITRF94
NAVD 88
LMSL
MTL
DTL
ITRF93
ITRF92
MLW
ITRF91
ITRF90
ITRF89
ITRF88
SIO/MIT 92
NEOS 90
• Permitting
NAD83 (NSRS)
GEOID99,
GEOID03
TSS
(Topography of
the Sea Surface)
MLLW
PNEOS 90
Choose input and
output vertical
datums:
Uncertainty has been calculated for transformations
across the full process…
Choose a geoid model
Choose a horizontal datum
Run as single point, batch, or insert into programming
Ellipsoid
Orthometric
Tidal
26
12/20/2011
VDatum.noaa.gov
Current VDatum Availability
Questions?
162
27
12/20/2011
Michael Michalski, NOAA/National Ocean Service
Center for Operational Oceanographic Products and Services
Monday, January 9 2012
28

available here

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