Transcript Determination of Station Depths Relative to NGVD29

Determination of Station Depths
Relative to NGVD29
Methods and results
Jan 24, 2003
Charles Seaton
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
Derive properties of tidal record
HHW
LHW
HLW
LLW
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
Objective: Derive station depths relative to
NGVD29 from pressure record
Procedure:
1)
2)
3)
4)
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)
Conversion of Pressure to Depth
1)
2)
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/rho*g) - ((v^2)/2*g) rho ~ 999 kg/m^2 + 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
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
Relationship of Station Depth
and Reference Station Tides
MHHW(unknown)
Variation
in LLW
MHHW (known)
Offset btwn LLW and MLLW
depth below MLLW
Reference Station
depth at LLW
MLLW (known)
depth below MHHW
MLLW (unknown)
depth below NGVD29
Conversion from
reference MLLW to
NGVD29
NGVD29
Instrument
Procedure for adjusting tidal properties
1)
2)
3)
4)
5)
6)
Derive tidal properties (LLW, LW, etc.) at Tongue Point from hourly
tide data
Derive tidal properties (LLW, LW, etc.) at station from depth data
Find matching points in Tongue Point property for points in station
property (accounts for tidal phase shift over estuary)
Subtract Tongue Point values (referenced to MLLW) from station
values
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
Mean of remainder gives depth of station relative to MLLW
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
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.
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)
ngvd=7.3158-1.7861e-5*x+mllw
X is in ORSPCS-N NAD27 meters
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 were:
mean adjusted LLW (MLLW)
mean adjusted LW (MLW) converted to MLLW
mean adjusted HW (MHW) converted to MLLW
mean adjusted HHW (MHHW) converted to MLLW
mean tide level (MTL) converted to MLLW
mean adjusted low pass filter converted to MLLW
Comparison of results of variants: salinity
Effect of salinity is much less than expected, particularly
for MLLW, and introduces <0.05 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 <0.05 m
uncertainty in depth)
Odd behavior at woody,
cbnc3, and lght6 is caused
by lack of valid salinity for
extensive portion of data
Comparison of results of variants: tidal property
Use of different tidal properties produces a maximum error
of <0.2 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
Other Sources of Error
1)
2)
3)
4)
5)
6)
Atmospheric correction: atmospheric pressure not identical over estuary
(effect unquatified, but expected to be <<0.2 m)
Velocity effect on pressure (unquantified, but expected to be <<0.05 m)
Inaccuracy of tidal variation adjustment (estimated to be 0.02 - 0.04
depending on the length of the record (1-12 months)*)
Inaccuracy of linear estimate of MLLW-> NGVD29 (3*std err = 0.48 m)
Error in calculation of depth is <<0.2 m
Error in determination of MLLW is
Using HHW referenced to MLLW as a
correction for HHW
1)
2)
3)
4)
5)
6)
Since the reference datum is MLLW, then the local datum will also
be MLLW
Need to take into account the variation in the conversion between
MLLW and MHHW over the estuary
Variation can be approximated as linear with x coordinate over
lower estuary
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-> MHHW at the
local station versus the reference station (see plot)
Equivalent methods were used for MLW, MHW, and MTL
No equivalent method was possible for low pass filtered data (no
reference datum available