Appendix D

Long-Term Tide Gage Stability From Leveling Data

James Foster, University of Hawai’i at Manoa

Note: The committee commissioned the following discussion paper. Dr. Foster’s views, as expressed below, may not always reflect the views of the Committee on Sea Level Rise in California, Oregon, and Washington, or vice versa.

Abstract

Leveling observations from tide gage benchmark networks can be used to assess the long-term stability of the tide gage with respect to the benchmarks, to provide estimates on the degree to which short-term (e.g., decadal timescale) estimates of vertical motion can be inferred to represent longer term rates, and to provide a means for detecting and estimating possible steps in the sea-level record due to changes in tide gage instrumentation, monument instabilities or local ground motion. Leveling data from six California tide gages confirm that long-term vertical motions of the tide gages are small, typically less than 0.25 mm yr-1 with respect to the stable local coastline, and represent only a very minor portion of the relative sea-level change budget. Decadal timescale estimates of benchmark vertical motions mostly range between ± 0.5 mm yr-1 from their long-term values, indicating that decadal scale estimates of geodetic motion are generally a reasonable approximation to longer-term rates. The formal errors on the rate estimates however, based on an assumption of white noise, are over optimistically tight and should be scaled up by a factor of 2.33 to provide more realistic bounds. This analysis also suggests that the tide gage at Point Reyes may be experiencing recent subsidence, despite the long-term estimates indicating relative stability. Jumps were evident in the leveling data from all tide gages except Los Angeles: some are clearly due to changes in equipment, others are less clearly attributable to mechanical issues at the sites and may indicate corresponding steps remain uncorrected in the sea-level time series data.

INTRODUCTION

The observations recorded by tide gages are relative sea-level values, and are a linear combination of real changes in local sea level as well as any local vertical motions, due to either regional tectonics, local subsidence/uplift of the ground, and possibly offsets due to motions of the tide gage itself with respect to its mount. Routine leveling at tide gages has been performed for many decades, and provides a resource with which to explore the issues of local vertical land motions (Shinkle and Dokka, 2004) and tide gage stability over longer timescales than is possible with more modern geodetic techniques such as Global Navigation Satellite Systems (GNSS, such as GPS) measurements or satellite-based Interferometric Synthetic Aperture Radar (InSAR). With this data set it is possible to assess two key issues of importance to understanding long-term relative sea-level rise: (1) What proportion of the observed sea-level change is due to local vertical motions of the tide gage itself, or its immediate vicinity? (2) How representative are the vertical land motions estimated from GNSS/InSAR data over the last 5–15 years of multidecadal to century scale rates? Leveling data from 6 California tide gage networks (Figure D.1) were used to address these questions.



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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

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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.

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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 . Hicks, S.D., P.C. Morris, H.A. Lippincott, and M.C. O'Hargan, 1987, User's Guide for the Installation of Bench Marks and Leveling GLOSSARY Requirements for Water Level Stations, NOAA National Ocean Service, Rockville, MD, 73 pp. Karcz, I., J. Morreale, and F. Porebski, 1976, Assessment of bench- AQUAREF/ Physical point on tide gage used for mark credibility in the study of recent vertical crustal move- AQUATRAKleveling ments, Tectonophysics, 33, T1-T6. REF Mao, A., C.G.A. Harrison, and T.H. Dixon, 1999, Noise in GPS coordinate time series, Journal of Geophysical Research, 104, AQUATRAK Physical point on tide gage used for 2797-2816. leveling Shinkle, K.D., and R.K. Dokka, 2004, Rates of Vertical Displacement at Benchmarks in the Lower Mississippi Valley and the Northern Primary Bench Benchmark which defines the local Gulf Coast, NOAA Technical Report NOS/NGS 50, 135 pp. Mark (PBM) vertical datum Williams, S.D.P., Y. Bock, P. Fang, P. Jamason, R.M. Nikolaidis, L. Prawirodirdjo, M. Miller, and D.J. Johnson, 2004, Error analysis RM OF ETG Physical point on tide gage used for of continuous GPS position time series, Journal of Geophysical Research, 109, B03412, doi:10.1029/2003JB002741. leveling (reference mark of electric Woodworth, P.L., 2002, Manual on Sea Level Measurement and In- tape gage) terpretation, Volume III - Reappraisals and Recommendations as of the Year 2000, Intergovernmental Oceanographic Commission, STAFF STOP Physical point on tide gage used for Manuals and Guides, 14, 49 pp. leveling

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