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Appendix D
Long-Term Tide Gage Stability From Leveling Data
James Foster, University of Hawai'i at Manoa
Note: The committee commissioned the following discus- all tide gages except Los Angeles: some are clearly due
sion paper. Dr. Foster's views, as expressed below, may not to changes in equipment, others are less clearly attribut-
always reflect the views of the Committee on Sea Level able to mechanical issues at the sites and may indicate
Rise in California, Oregon, and Washington, or vice versa. corresponding steps remain uncorrected in the sea-level
time series data.
Abstract
INTRODUCTION
Leveling observations from tide gage benchmark
networks can be used to assess the long-term stability The observations recorded by tide gages are relative
of the tide gage with respect to the benchmarks, to pro- sea-level values, and are a linear combination of real
vide estimates on the degree to which short-term (e.g., changes in local sea level as well as any local vertical
decadal timescale) estimates of vertical motion can be motions, due to either regional tectonics, local subsid-
inferred to represent longer term rates, and to provide ence/uplift of the ground, and possibly offsets due to
a means for detecting and estimating possible steps motions of the tide gage itself with respect to its mount.
in the sea-level record due to changes in tide gage in- Routine leveling at tide gages has been performed for
strumentation, monument instabilities or local ground many decades, and provides a resource with which to
motion. Leveling data from six California tide gages explore the issues of local vertical land motions (Shinkle
confirm that long-term vertical motions of the tide and Dokka, 2004) and tide gage stability over longer
gages are small, typically less than 0.25 mm yr-1 with timescales than is possible with more modern geodetic
respect to the stable local coastline, and represent only techniques such as Global Navigation Satellite Systems
a very minor portion of the relative sea-level change (GNSS, such as GPS) measurements or satellite-based
budget. Decadal timescale estimates of benchmark ver- Interferometric Synthetic Aperture Radar (InSAR).
tical motions mostly range between ± 0.5 mm yr-1 from With this data set it is possible to assess two key issues
their long-term values, indicating that decadal scale of importance to understanding long-term relative sea-
estimates of geodetic motion are generally a reasonable level rise: (1) What proportion of the observed sea-level
approximation to longer-term rates. The formal errors change is due to local vertical motions of the tide gage
on the rate estimates however, based on an assumption itself, or its immediate vicinity? (2) How representative
of white noise, are over optimistically tight and should are the vertical land motions estimated from GNSS/
be scaled up by a factor of 2.33 to provide more realistic InSAR data over the last 515 years of multidecadal
bounds. This analysis also suggests that the tide gage to century scale rates? Leveling data from 6 California
at Point Reyes may be experiencing recent subsidence, tide gage networks (Figure D.1) were used to address
despite the long-term estimates indicating relative these questions.
stability. Jumps were evident in the leveling data from
179
OCR for page 180
180 APPENDIX D
term that is applied to the raw ranges it observes to the
sea-surface in order to map them to the vertical datum
defined by the primary benchmark. Every time the gage
is either changed, upgraded, or experiences some pos-
sible vertical offset--due, for example, to being hit by a
harbor vehicle--a new correction term is calculated by
performing leveling between the primary benchmark
and the reference point on the new (or newly offset)
tide gage. This term is applied to the data stream so that
is it transparent to the end-user of the data, maintaining
what is, in theory, a continuous record of sea level with
respect to the primary benchmark, rather than the gage
itself. Although these constants are recorded as they are
recalculated and programmed into the tide gage data
logger, they are not all archived digitally, and were not
available for this study.
Current recommended operating procedures re-
quire a network of at least 10 benchmarks be estab-
lished and monitored in support of tide gage sea-level
observations (Woodworth, 2002). Historically, how-
ever, significantly fewer marks have been regularly
observed--some of which may no longer exist due to
FIGURE D.1 Location of tide gages examined with inset show- construction (or other reasons) around the typically
ing schematic of a tide gage and benchmark leveling network extremely changeable industrial environment of the
illustrating fundamental ambiguity that may exist between motion harbors, where most tide gages are installed. Leveling
of the tide gage instrument and local land motion.
of the west coast network is currently performed using
2nd Order Levels standards approximately annually,
though historically it was often done much less fre-
Tide gages measure the height of the sea surface quently and to a lower standard. The leveling data are
with respect to their own internal reference level. As the used to determine the general stability of each bench-
gages require relatively deep water to operate in, away mark as well as the tide gage, and identify any tide gage
from shore wave breaks and currents, they are often offsets (any jump greater than 6 mm) necessitating a
installed on manmade structures such as piers, built out site correction factor adjustment. The long-term rela-
from the coast. Although tide gage locations are chosen tive vertical velocity of the tide gage with respect to
carefully in an effort to ensure long-term stability and the primary benchmark is not applied as a correction
a minimum of vertical motion, it is impossible to guar- to the sea-level time series.
antee these qualities in a site. In order to maintain an
accessible external reference mark from which the local DATA AND METHODS
sea-level datums can be assigned, to allow for tide gage
equipment changes, and to confirm the stability of the The leveling data, corrected for atmospheric
gage, each tide gage is supported by a network of level refraction, from all occupations of the tide gage
ing benchmarks, with one of these designated as the benchmark networks for San Diego, Los Angeles, Port
primary benchmark. This is normally chosen to be both San Luis, San Francisco, Point Reyes, and Crescent
as close to the tide gage as possible, and installed in as City, were provided by the National Oceanographic
stable a location as can be found (Hicks et al., 1987). and Atmospheric Administration's (NOAA's) Center
As the local sea-level datums are defined with respect to for Operational Oceanographic Products and Services
this primary benchmark, each tide gage has a correction (CO-OPS). Each benchmark network data set con-
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APPENDIX D 181
sisted of a spreadsheet listing the date of each leveling given a stability rating of C or D by the NGS, indicating
project and the height determined for each benchmark unknown or doubtful long-term stability. However, in
occupied during that project. The recorded heights some cases even benchmarks with the highest A rating
themselves have little value for the purposes of this were found to have velocities and/or variances at odds
study, as they are determined with respect to some arbi- with the neighboring marks.
trary starting height (typically a predefined value for the Both the formal NGS/CO-OPS datum definition
height of the primary benchmark) for each leveling run. and, at this stage in the processing, this analysis, define
The observations required for this study are changes the primary benchmark as a fixed reference. There is
in the height differences between benchmarks, so the clearly a danger, however, that the primary benchmark
first step was to determine the differential heights mea- itself might experience vertical motions, due either to
sured during each project with respect to the primary local benchmark instability or real land motions. In
benchmark. A network solution was then performed order to assess and account for this, a subset of the
to estimate and remove the mean differential height benchmarks in the network that show no sign of either
for each benchmark from the observations, generating monument instability or anomalous rates of motion
a time series of observed changes in relative height was used to define a combined vertical reference datum
for each benchmark in the network. Bad data points, for the network, which should provide a more robust
due to incorrect readings or transcriptions of values, datum. The choice of benchmarks is somewhat subjec-
contaminate this initial analysis, and were identified tive, and is unable to correct for vertical deformation
and removed from the data set. These points are typi- occurring on spatial scales greater than the width of the
cally obvious as single observation outliers, displaced network. It turns out, however, that the specific choice
by several centimeters from the trend defined by the of reference benchmarks has only a small impact on the
remainder of that benchmark's data. final estimates of rates of vertical motion for the tide
To interpret observed vertical motions and assess gage and primary benchmark.
whether they are likely due to benchmark instability The rates of vertical motion were estimated using
(Karcz et al., 1976) or rather to local land motions, the a robust linear fit that uses an iterative reweighting
approximate spatial locations of the benchmarks are re- scheme to reduce the impact of outlier observations
quired. These locations were determined either by digi- on the final estimation of slope. To assess the degree to
tizing the survey benchmark sketches or, if available, which estimates of vertical motions based on decadal
extracted from the National Geodetic Survey (NGS) scale windows of data can be trusted as reasonable
benchmark data sheet database. Some of the older, dis- approximations to the longer-term trends, a moving
continued benchmarks have no recorded location and window was applied to the data set, and vertical rates
could not contribute to this aspect of the analysis. In for each window were estimated. A minimum of 5
most cases, the digitized locations of the benchmarks observations and at least a 10-year time span were
are estimated to be accurate to 40 m or better, while required for each window location in order to generate
those determined by the NGS using GPS or other an estimate for any given period in order to prevent the
methods are considerably more accurate. This accuracy results being merely a reflection of the measurement
is sufficient to allow us to examine and interpret spatial errors and/or sparse data.
patterns of vertical motions. Benchmarks interpreted
as being unstable are identified from their time series, RESULTS
either objectively by virtue of very high variance about
their mean trend (typically greater than 10 mm2, in
San Diego
contrast to most benchmarks which have variances
typically less than 2 mm2), or more subjectively due Three benchmarks--9, N 57, and RIVET--
to having high apparent relative vertical v elocities, showed anomalous vertical motions and were excluded
uncorrelated with their neighboring marks, by com-
from the spatial analysis. Benchmarks RIVET and
parison with the rest of the network. In most cases, N 75 were given a D stability code by the National
those benchmarks identified as unstable have been Geodetic Survey, indicating they might be expected
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182 APPENDIX D
to be unstable. Benchmark 9, on the other hand, has 10
an A rating, indicating highest level of confidence in
Adjusted Height Di . (mm)
5
the benchmark stability. It is, however, located in the 0
middle of downtown San Diego, and it is possible that -5
this location has over the decades experienced signifi- -10
cant vertical motion due to construction and settling, -15
unrelated to broader underlying tectonic trends. For -20
the remaining network (Figure D.2), vertical motions
1
suggest a gentle northwest to southeast trend, with the
Vertical Velocity (mm/yr)
majority of benchmarks nearest to the tide gage loca- 0.5
tion in close agreement. Defining a network vertical
reference using these sites implies a vertical motion 0
for the primary benchmark of -0.03 mm yr-1, and for
-0.5
the tide gage reference marks of +0.07 mm yr-1. Esti
mating the apparent decadal scale vertical velocities -1
1930 1940 1950 1960 1970 1980 1990 2000 2010
by calculating rates for each 10 consecutive measure-
ments shows that these rates range from -0.4 mm yr-1
to nearly 1 mm yr-1, though mostly clustered between
± 0.2 mm yr-1. The exceptional rates in the 1980s are
possibly due to a small, unmodeled residual step in
the tide gage leveling time series, either at the tide
gage itself, or possibly at the primary benchmark, as
the other benchmark time series also show excursions
at this time. With less consistent and rigorous field
operational procedures, data prior to 1970 are noisier, 1
and this is reflected in the increased range and errors
0.5
for the velocity estimates for this period.
0
Los Angeles -0.5
Los Angeles is recognized as having complex -1
temporal and spatial variations in vertical deformation
(Brooks et al., 2007), and this complexity is evident
in the range of vertical motions calculated for the FIGURE D.2(Top) Time series of vertical displacements for San
tide gage leveling network and their spatial pattern Diego (9410170) tide gage leveling network. All benchmarks
(Figure D.3; for which the limited and inconsistent are shown in gray except tide gage marks RM OF ETG (yellow)
4 measurements for a STAFF STOP tide gage mark and AQUATRAK (cyan). (Middle) Time series of apparent verti-
cal velocities based on at least 5 consecutive observations cover-
were ignored). Although it appears that a large por- ing at least 10 years (approximately decadal). All benchmarks
tion of the pier on which the tide gage is installed is are shown in gray except tide gage marks RM OF ETG (yellow)
experiencing significant subsidence relative to the coast, and AQUATRAK (cyan). (Bottom) Contours of best-fit linear verti-
cal deformation rates for San Diego benchmarks with respect to
the end nearest the tide gage and primary benchmark
network vertical reference frame. Contours every 0.1 mm yr-1.
sees less of this. The choice of benchmarks for the net-
work vertical reference is particularly difficult for this
location, as there is no obvious subset of benchmarks
demonstrating broadly similar motion that might be
interpreted as "stable." However, excluding benchmarks
with the most extreme motions results in a reference
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APPENDIX D 183
frame in which the primary benchmark is experiencing
10
0.14 ± 0.14 mm yr-1 uplift, and the tide gage subsid-
Adjusted Height Di . (mm)
5 ing at 0.17 ± 0.12 mm yr-1. The large errors probably
0 reflect the strong quasi-seasonal signals recognized in
-5 Los Angeles (Bawden et al., 2001) that will be strongly
-10 aliased into the roughly annual leveling campaigns. The
-15 vertical velocity time series suggests relatively large
variations in apparent velocities on the decadal scale,
1
with a strong perturbation in the 1990s due largely to
Vertical Velocity (mm/yr)
0.5 a leveling run that recorded unusual, but not obviously
0 incorrect, values.
-0.5
Port San Luis
-1
-1.5 The benchmark network at Port San Luis appears
1950 1960 1970 1980 1990 2000 2010
particularly stable, with the exception of two bench-
1 marks (B and H 828), which were removed from the
analysis. The network vertical reference implies a small
0.5 uplift of 0.08 ± 0.05 mm yr-1 for the primary bench-
mark, and slight subsidence of 0.05 ± 0.05 mm yr-1
0
for the tide gage, which for this location is located at
-0.5 the end of a long pier (Figure D.4). Notably, there is
a distinct downward step in the leveling time series
-1
for both tide gage marks in 1996 with a mean value
of -5.25 ± 0.59 mm. It is not clear whether this step
is a result of equipment change or some other source;
however, it should be noted that when corrected, the
sign of the tide gage motion changes, with slight uplift
indicated (0.29 ± 0.05 mm yr-1). All plots in Figure D.4
show the data after these steps have been estimated and
removed from the time series. If left in, this step domi-
nates the analysis of the decadal-scale velocity estimate
stability. If removed, however, the short-term velocities
FIGURE D.3(Top) Time series of vertical displacements for Los
indicate that all (stable) benchmarks are well described
Angeles (9410660) tide gage leveling network. All benchmarks over their lifetime by a consistent vertical velocity.
shown in gray except tide gage mark AQUATRAK (green). (Mid-
dle) Time series of apparent decadal-scale vertical velocities. All
benchmarks shown in gray except tide gage mark AQUATRAK San Francisco
(green). (Bottom) Contours of best-fit linear vertical deformation
rates for Los Angeles benchmarks with respect to network vertical San Francisco has a very long record of benchmark
reference frame. Contours every 0.1 mm yr-1. leveling, with the earliest measurements dating from
the mid 1920s. Several of the benchmarks show signifi-
cant excursions over that time period (Figure D.5), yet
the long-term pattern is of relative consistency. Steps
were estimates and removed from benchmarks 173
(in 1943) and 175 (in 1980). Benchmarks M and 175
were considered outlier time series and not included
in the spatial analysis. The network vertical reference
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184 APPENDIX D
20
20
Adjusted Height Di . (mm)
Adjusted Height Di . (mm)
10
10
0 0
-10
-10
-20
-20
1.5
3
1
Vertical Velocity (mm/yr)
Vertical Velocity (mm/yr)
0.5
2
0
1 -0.5
-1
0
-1.5
-1 -2
1950 1960 1970 1980 1990 2000 2010 1930 1940 1950 1960 1970 1980 1990 2000 2010
1
0.5 1
0 0.5
-0.5 0
-1 -0.5
-1
FIGURE D.4(Top) Time series of vertical displacements for Port FIGURE D.5 (Top) Time series of vertical displacements for San
San Luis (9412110) tide gage leveling network. All benchmarks Francisco (9414290) tide gage leveling network. All benchmarks
shown in gray except tide gage marks AQUAREF (yellow) and shown in gray except tide gage marks AQUATRAK REF (red),
AQUATRAK (red). Steps in the tide gage time series have been AQUATRAK (cyan), RM OF ETG (green) and STAFF STOP (or-
removed. Unstable benchmark BM B clearly visible as outlier time ange). (Middle) Time series of apparent decadal-scale vertical
series. (Middle) Time series of apparent decadal-scale vertical velocities. All benchmarks shown in gray except tide gage marks
velocities. All benchmarks shown in gray except tide gage marks AQUATRAK (cyan) and RM OF ETG (green) (AQUATRAK REF
AQUAREF (yellow) and AQUATRAK (red). (Bottom) Contours and STAFF STOP did not have long enough time series to gen-
of best-fit linear vertical deformation rates for Port San Luis erate decadal velocity estimates). (Bottom) Contours of best-fit
benchmarks with respect to network vertical reference frame. linear vertical deformation rates for San Francisco benchmarks
Contours every 0.1 mm yr-1. with respect to network vertical reference frame. Contours every
0.1 mm yr-1.
OCR for page 185
APPENDIX D 185
analysis suggests that in late 1989--around the time of 10
the Loma Prieta earthquake--the primary benchmark
Adjusted Height Di . (mm)
5
moved with respect to the rest of the network. Correct-
0
ing the data for this motion does not entirely remove
-5
the apparent upward motions of several benchmarks
at this time, or shortly afterward, suggesting that the -10
monuments or the local ground around them moved -15
either during the shaking of the earthquake itself or
0.5
during a period of post-seismic adjustment. Despite
Vertical Velocity (mm/yr)
this, the rate of motion calculated for the primary
0
benchmark is small (0.05 ± 0.07 mm yr-1) and the mean
tide gage motion is negligible (0.01 ± 0.07 mm yr-1). As
there is little spatial coherence in the vertical velocities, -0.5
with adjacent benchmarks often exhibiting opposite
senses of motion, the contour map results in only small -1
1975 1980 1985 1990 1995 2000 2005 2010
amplitude variability in vertical motion rates. The
decadal-scale vertical velocities are strongly affected 1
by the 1989 events, but nonetheless generally indicate
that estimates of long-term vertical motions based on 0.5
any 10-year period would be accurate to better than 0
0.5 mm yr-1.
-0.5
Point Reyes -1
Although the time series from Point Reyes is rela-
tively short, with the first regular observations starting
in 1973 (an initial leveling run in 1930 was too removed
from the rest of the data set to contribute usefully to
the analysis), it shows relatively complex behavior
(Figure D.6). The AQUAREF mark, observed between
1990 and 1999, shows strong linear downward motion,
at odds with the other tide gage mark, AQUATRAK,
and were ignored during the spatial analysis, as were
outlier records from benchmarks 1 FMK and 11. FIGURE D.6 ( Top ) Time series of vertical displacements
The benchmark leveling observations, which were for Point Reyes (9415020) tide gage leveling network. All
otherwise largely stable prior to ~2001, show strong benchmarks shown in gray except tide gage marks AQUAREF
heterogeneous motions after this point, with many sites (orange), AQUATRAK (magenta) and RM OF ETG (blue).
(M iddle ) Time series of apparent decadal-scale vertical
uplifted for several years before subsiding back to their velocities. All benchmarks shown in gray except tide gage marks
long-term baselines. The recent AQUATRAK record, AQUAREF ( orange), AQUATRAK (magenta) and RM OF ETG
however, shows continued subsidence. The contour plot (blue). (Bottom) Contours of best-fit linear vertical deformation
rates for Point Reyes benchmarks with respect to network verti-
highlights an area experiencing significant uplift to the
cal reference frame. Contours every 0.1 mm yr-1. White line
southeast of the tide gage, with all other benchmarks indicates mapped fault trace.
appearing relatively stable over the full time window of
the observations. This uplift may be related to motion
on a mapped fault segment (Clark and Brabb, 1997)
near the eastern edge of the network. Although there
is no evidence to suggest this fault is affecting the
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186 APPENDIX D
tide gage itself, it emphasizes the tectonic complex- 20
ity of many locations along the California coast. The
Adjusted Height Di . (mm)
10
velocity stability analysis highlights the AQUAREF
outlier velocities, suggesting that these observations 0
are most likely indicating monument instability. The
-10
other benchmarks have decadal velocity estimates
consistent to ± 0.5 mm yr-1, until the impact of the -20
events of 20012011, which indicate some possibly
0.5
transient deformation event affecting a subset of the
Vertical Velocity (mm/yr)
benchmark network. Interestingly, the vertical velocity 0
rate estimates for the AQUATRAK suggest continued,
or even accelerating subsidence, with the most recent -0.5
decadal rate approaching -1 mm yr-1.
-1
Crescent City -1.5
1940 1950 1960 1970 1980 1990 2000 2010
Long-term relative height residuals are generally 1
small, though several benchmarks show unusually
large motions compared to the rest of the network, 0.5
presumably due to benchmark instability (Figure D.7).
0
The pattern of the contours suggest that the bench-
marks nearest the main downtown area are being -0.5
uplifted slightly relative to the benchmarks around
-1
the port. It is perhaps more likely that the port area
is subsiding; however, the relative rates are small. The
velocity analysis highlights one of the more unstable
benchmarks (NO 24), which was excluded from the
contouring solution, along with outliers PASS and 18.
It also, however, highlights a change in behavior of the
RM OF ETG tide gage mark in the late 1980s. Follow
ing a relatively small possible step in the time series
sometime between September 1986 and September
1987, there is a strong change in decadal vertical veloc-
ity. A large step in November 1988 indicates a change FIGURE D.7 ( Top ) Time series of vertical displacements
in equipment. However, the apparent motion continues for Crescent City (9419750) tide gage leveling network. All
past this date, perhaps indicating a problem with the benchmarks shown in gray except tide gage marks AQUAREF
tide gage monument, as the AQUATRAK mark, ob- (magenta), AQUATRAK (red) and RM OF ETG (yellow). (Middle)
Time series of apparent decadal-scale vertical velocities. All
served from 1989, does not show the same motion. For benchmarks shown in gray except tide gage marks AQUAREF
the other marks, decadal velocity estimates are generally (magenta), AQUATRAK (red) and RM OF ETG (yellow). (Bottom)
within ± 0.4 mm yr-1, indicating long-term rates can be Contours of best-fit linear vertical deformation rates for Crescent
City benchmarks with respect to network vertical reference
reasonably reliably inferred from relatively short-term
frame. Contours every 0.1 mm yr-1.
observation records.
DISCUSSION
The locations of tide gages are chosen to be stable,
and so it is unsurprising--though reassuring--that in
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APPENDIX D 187
general they show only small vertical motions with re- Prieta earthquake, while Point Reyes appears to have
spect to their benchmark leveling networks (Table D.1). experienced a longer period event, whose impact might
Some of the motions approach 0.25 mm yr-1, however, still be influencing the tide gage.
which is large enough that they should be accounted for Another issue of concern is the impact of tide gage
when assessing the long-term rates of relative sea-level monument instability on estimates of relative sea-level
rise. The data indicate that, although the long-term change. Standard procedures for tide gage operations
vertical motion rates are small, there are significant and maintenance of the local vertical reference datum
spatial and temporal variations in these rates within include programming the tide gage data logger with a
several of the networks. Although several instances of correction constant that takes into account changes in
apparent monument instability are evident, in most the instrument height during equipment changes or
cases these motions appear to reflect real local ground other events. In particular, any change of more than
motions. Some of these spatial patterns appear to be 6 mm is assumed to reflect instrument monument
consistent over the time window of leveling observa- instability and should be accounted for by a change in
tions, but others show changes in behavior over time. the correction constant. Unfortunately, although the
In particular, the San Francisco tide gage network ap- values of these constants and when they were changed
pears to have been significantly affected by the Loma have been recorded and archived, they are mostly in
TABLE D.1 Long-Term Vertical Motion Estimates for Primary Benchmarks and Tide Gage Reference Marks, with
Respect to a Network Defined Vertical Reference
Tide Gage Location Benchmark Vertical Velocity (mm yr-1) Velocity Error (mm yr-1)a Data Range
San Diego (9410170) 12 (primary benchmark) -0.03 0.02/0.05 19172011
AQUATRAK +0.06 0.05/0.12 19902011
RM of ETG +0.08 0.05/0.12 19661994
Mean +0.07 0.02/0.05
Los Angeles (9410660) 814 FT ABOVE MLLW (primary benchmark) +0.14 0.14/0.33 19202011
AQUATRAK -0.17 0.14/0.33 19902011
STAFF STOP +126 144/335 19801984
Mean -0.17 0.14/0.33
Port San Luisb (9412110) 6 (primary benchmark) +0.08 0.05/0.12 19332011
AQUAREF (-0.10) +0.24 (0.11) 0.09/0.21 19892011
AQUATRAK (-0.03) +0.32 (0.08) 0.07/0.16 19892011
Mean (-0.05) +0.29 (0.05) 0.05/0.12
San Francisco (9414290) 180 (primary benchmark) -0.05 0.07/0.16 19252011
AQUATRAK REF -0.06 0.12/0.28 19902000
AQUATRAK -0.06 0.12/0.28 19892003
RM of ETG -0.01 0.10/0.23 19781999
STAFF STOP +0.16 0.17/0.40 19911999
Mean -0.01 0.07/0.16
Point Reyes (9415020) B243 (primary benchmark) +0.03 0.02/0.05 19302011
AQUAREF -1.78 0.11/0.26 19901999
AQUATRAK -0.28 0.05/0.12 19902011
RM of ETG -0.22 0.07/0.16 19821994
Mean -0.22 0.07/0.16
Crescent City (9419750) TIDAL 20 1959 RESET (primary benchmark) +0.05 0.03/0.07 19332011
AQUAREF -0.24 0.04/0.09 19892011
AQUATRAK -0.11 0.05/0.12 19892011
RM of ETG -0.23 0.09/0.21 19821996
Mean -0.20 0.06/0.14
a Two error estimates are listed: the formal error and the formal error multiplied by the empirically determined 2.33 scale factor.
b Values for Port San Luis in parentheses are calculated before a ~6.5 mm step in 1996 is removed from the time series.
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188 APPENDIX D
analog form and were not available to this study. With- 15
out them it becomes impossible to say with complete 16
12
confidence whether any particular step detected in
12
the leveling data for a tide gage has been accurately
Count (%)
Count (%)
9
removed a priori from the sea-level time series by ad- 8
6
justment of the on-site correction value. Each of San
4
Diego, Point Reyes and Crescent City tide gages have 3
significant steps in the leveling (Table D.2) that appear 0 0
-1 -0.5 0 0.5 1 -8 -4 0 4 8
to match detectable steps in the sea-level record (Larry Rate Difference (mm/yr) Rate Difference factor
Breaker, personal communication). The smaller of
these (e.g., 11.2 mm at San Diego) would have only a FIGURE D.8 Histograms of differences between decadal-scale
minor impact on long-term sea-level change estimates; estimates of vertical motion rates and the long-term rate deter-
mined from the full time series. (Left) Rate differences observed
however the larger ones, if entirely uncorrected, could in mm yr-1. (Right) Rate differences expressed as multiples of the
contribute significantly to apparent rates of change. It formal error determined for the decadal velocity fit.
is unclear whether it is possible to retroactively deter-
mine whether these steps have been entirely, partly, or
not corrected. This problem increases the ambiguity of rate estimates are significantly too optimistic, with the
whether a leveling step indicates a recognized change 2s value being 4.66. Interestingly this 2.33 multiple of
or step in the tide gage instrumentation, a problem with the formal error is close to the 2.5 empirical scale fac-
the mounting of the tide gage instrument, or motion of tor often adopted in GPS geodesy to take account of
the entire pier, due to either settling or, possibly, local red noise in the time series produced by quasi-seasonal
ground motion. and other long-term signals. Detailed analyses of the
The analysis of the stability of decadal-scale ve- noise character of GPS coordinate time series (Mao et
locity estimates suggests that, for most tide gages and al., 1999; Williams et al., 2004) find that the errors are
benchmark networks, although there is significant vari- typically well described by a power-law function. The
ation over the full time window, the limi ted range sug- results presented here suggest that the same power-law
gests it is largely reasonable to extrapolate vertical rates functions describing noise in decadal-scale GPS verti-
based on a limited time window of observations. Figure cal time series may also be applicable to multi-decadal
D.8 shows the rate differences between the decadal- leveling measurements.
scale rate estimates and the final "correct" long-term
estimate. These results confirm that the decadal-scale
REFERENCES
rate estimates are tightly clustered around their long-
term values with 2s = 0.48 mm yr-1. The same data can Bawden, G.W., W.R. Thatcher, R.S. Stein, K.W. Hudnut, and
be mapped into differences expressed as multiples of G. Peltzer, 2001, Tectonic contraction across Los Angeles after
removal of groundwater pumping effects, Nature, 412, 812-815.
the formal errors determined for the decadal-scale rate
estimates (Figure D.8 right). Presented this way, the
2s limits indicate that the formal errors for the decadal
TABLE D.2 Steps Detected in Tide Gage Leveling Marks
Location Step Size (mm) Step Date
San Diego +11.2 Early 1974
Port San Luis -6.5 Between late 1995 and late 1996
San Francisco +15.0 May 9, 1979
San Francisco -5.0 Between November 17, 1983, and May 31, 1984
Point Reyes +42.3 1994
Crescent City +84.5 Between November 2 and 9, 1988
Crescent City +3.0 Between September 1986 and September 1987
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APPENDIX D 189
Brooks, B.A., M.A. Merrifield, J. Foster, C.L. Werner, F. Go- ACKNOWLEDGMENTS
mez, M. Bevis, and S. Gill, 2007, Space geodetic deter-
mination of spatial variability in relative sea level change, Thanks to Todd Ehret of NOAA CO-OPS for
Los Angeles Basin, Geophysical Research Letters, 34, L01611,
doi:10.1029/2006GL028171. providing the leveling data and Clyde Kakazu, Marti
Clark, J.C., and E.E. Brabb, 1997, Geology of Point Reyes National Ikehara, and Stephen Gill for valuable discussion about
Seashore and Vicinity, California: A Digital Database, U.S. Geo- the NGS/CO-OPS leveling procedures and data han-
logical Survey Open File Report 97-456, available at
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