Determination of Station Depths Relative to NGVD29

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Determination of Station Depths Relative to NGVD29

• Methods and results

Jan 24, 2003 Charles Seaton
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Some useful terms
NGVD29 Fixed reference vertical datum (used in
CORIE model) MLLW (Mean Lower Low Water) The
mean of the daily lower low water over a 19 year
Tidal Epoch. MHHW (Mean Higher High water) The
mean of the daily higher high water over the
tidal epoch MLW (Mean Low Water) The mean of
both daily low waters over the tidal epoch MHW
(Mean High Water) The mean of both daily high
waters over the tidal epoch MTL (Mean Tide
Level) The average of the MLW and the MHW Tidal
Epoch 19 year period (currently 1960 to 1978)
over which the tides are averaged to determine
the tidal datums
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Derive properties of tidal record

1. Determine high waters (HW) and low waters (LW)
   from data.
2. For each pair of LW, the lower one is the lower
   low water (LLW)
3. For each pair of HW, the higher one is the higher
   high water (HHW)
4. Low pass filtered data is determined by running
   the data through a filter with a cutoff frequency
   of 0.5 cycles/day

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• Objective Derive station depths relative to
  NGVD29 from pressure record
• Procedure
• Convert pressure to depth
• Derive properties of tidal record
• LLW, LW, HHW, HW, low pass filtered data
• Adjust derived properties to account for
  incomplete tidal record
• Convert tidal datum to fixed vertical datum
  (NGVD29)

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Conversion of Pressure to Depth

• Adjust pressure to remove variation in
  atmospheric pressure
• Convert pressure to depth
• a) pressure is affected by salinity and velocity
  of water column)
• b) h(P/rhog) - ((v2)/2g) rho 999
  kg/m2 0.808 S
• c) try 4 possible values for S 35 ppt, actual
  S, actual S 0.5, and 0
• d) velocity set at 0 m/s (over-estimates
  depth)
• v of 2 m/s introduces error of 20 cm
• v of 1 m/s introduces error of 5 cm

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Adjust derived properties

• To determine the local tidal datums (e.g. MLLW)
  directly from the data, 19 years of tidal data is
  required.
• Lacking 19 years of data, it is necessary to
  adjust the tidal properties (e.g. LLW) by the
  variation in that tidal property at an
  appropriate tidal station with a known tidal
  datum.
• This adjustment corrects for the bias that would
  be introduced by using an atypical time period.
• The mean of the adjusted tidal property will give
  the local tidal datum
• MLLWlocal mean( LLWlocal LLWknown)

CO-OPS, Tidal datums and their applications,
NOAA Special Publications NOS CO-OPS 1, p 41, 2000
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Relationship of Station Depth and Reference
Station Tides
Variation in LLW
Conversion from reference MLLW to NGVD29
Reference Station
depth below MHHW
depth below MLLW
depth below NGVD29
depth at LLW
Offset btwn LLW and MLLW
Instrument
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Procedure for adjusting tidal properties

1. Derive tidal properties (LLW, LW, etc.) at Tongue
   Point from hourly tide data
2. Derive tidal properties (LLW, LW, etc.) at
   station from depth data
3. Find matching points in Tongue Point property for
   points in station property (accounts for tidal
   phase shift over estuary)
4. Subtract Tongue Point values (referenced to MLLW)
   from station values
5. For properties other than LLW, it is necessary to
   correct for the variation in the difference
   between MLLW and the relevant tidal datum (e.g.
   MHHW) over the estuary
6. Mean of remainder gives depth of station relative
   to MLLW

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Variation in adjusted LLW
At eliot, shows seasonal variation, std dev
0.19 m At tansy, shows jump, std dev 0.16 m At
yacht, shows jump, std dev 0.15 m At dsdma,
shows large jump, std dev 0.31 m dsdma clearly
needs to split up into 2 depths At sveni, no
jumps or seasonal, std dev 0.08 m Excluding
dsdma, range of std dev is 0.07-0.19 m Concern
is not with variability from match Concern is
with bias, which cannot be determined from std
dev Inaccuracy of tidal variation adjustment
method estimated to be 0.02 - 0.04 depending on
the length of the record (1-12 months)
Swanson, RL, Variability of tidal datums and
accuracy in determining datums from short series
of observations, NOAA Tech Rep. NOS 64,pp 41,
1974 cited in CO-OPS 1
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Conversion from local MLLW to NGVD29 in Columbia
Estuary

• MLLW varies from location to location
• In Columbia Estuary, dominant variation in is
  upwards slope towards upriver direction
• While continuous tidal data is only available for
  Tongue Point, MLLW datums referenced against
  NGVD29 are available for several benchmark
  stations in lower estuary
• In the region covered by CORIE field stations
  (Mouth to Skamokawa), the slope of the MLLW
  against NGVD29 can be approximated by a linear
  regression of the conversion against the
  longitude (since the up river direction is
  primarily eastward).
• Cross estuary slope is negligible.

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MLLW to NGVD29 within lower Estuary
Inclusion of Skamokawa lowers std dev of error ,
but raises maximum error Maximum error
(including Skamokawa) is 0.1 (near
eliot) Maximum error (excluding Skamokawa) is
0.06 (near red26)
ngvd7.3158-1.7861e-5xmllw X is in ORSPCS-N
NAD27 meters
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Restatement of variants tested

• For each station, depth relative to NGVD29 was
  computed using 4 methods of handling salinity,
  and 6 methods for determining MLLW
• The 4 methods for handling salinity were assume
  35 psu salinity, assume column of salinity at
  instrument, assume column w/ average salinity of
  half instrument salinity,assume 0 psu salinity
• The 6 methods for determining MLLW water
  weremean adjusted LLW (MLLW)mean adjusted LW
  (MLW) converted to MLLWmean adjusted HW (MHW)
  converted to MLLWmean adjusted HHW (MHHW)
  converted to MLLWmean tide level (MTL) converted
  to MLLWmean adjusted low pass filter converted
  to MLLW

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Comparison of results of variants salinity
Effect of salinity is much less than expected,
particularly for MLLW, and introduces lt0.05 m
error

• Results from 35 sal variant excluded (ranged from
  0.05-0.45)
• Results vary with both depth and salinity
• MLLW is the least affected (consistently lt0.05 m
  uncertainty in depth)
• Odd behavior at woody, cbnc3, and lght6 is caused
  by lack of valid salinity for extensive portion
  of data

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Comparison of results of variants tidal property
Use of different tidal properties produces a
maximum error of lt0.2 m due to variation over
estuary of shape of tides

• Although reference tide data was in MLLW datum,
  there is no inherent reason to prefer MLLW over
  any other datum
• Standard deviation of results for all tidal
  properties (for 0 sal) is 0.064
• Low pass should be excluded due to the lack of an
  established low pass datum
• Excluding low pass reduces standard deviation to
  0.59

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Other Sources of Error

1. Atmospheric correction atmospheric pressure not
   identical over estuary (effect unquatified, but
   expected to be ltlt0.2 m)
2. Velocity effect on pressure (unquantified, but
   expected to be ltlt0.05 m)
3. Inaccuracy of tidal variation adjustment
   (estimated to be 0.02 - 0.04 depending on the
   length of the record (1-12 months))
4. Inaccuracy of linear estimate of MLLW-gt NGVD29
   (3std err 0.48 m)
5. Error in calculation of depth is ltlt0.2 m
6. Error in determination of MLLW is

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Using HHW referenced to MLLW as a correction for
HHW

1. Since the reference datum is MLLW, then the local
   datum will also be MLLW
2. Need to take into account the variation in the
   conversion between MLLW and MHHW over the estuary
3. Variation can be approximated as linear with x
   coordinate over lower estuary
4. Essentially, converting reference datum from MLLW
   to MHHW at reference station, adjusting local HHW
   (which gives depth relative to MHHW), and then
   converting local MHHW to local MLLW, so all that
   is needed is the difference between MLLW-gt MHHW
   at the local station versus the reference station
   (see plot)
5. Equivalent methods were used for MLW, MHW, and
   MTL
6. No equivalent method was possible for low pass
   filtered data (no reference datum available