The GPS vertical velocities were used to correct for the land motion affecting the tide gauge records to derive absolute (geocentric) changes in sea level (Figure 1). This exercise was carried out at coastal sites with tide gauge records fulfilling the Douglas  selection criteria in determining a global rate of sea level rise. That is, tide gauge records were required to contain more than 85% of valid data over a time span of at least 60 years. The final number of records complying with the selection criteria was identical to the number of records used by Douglas , as it was for the number of regions, respectively 27 and 10 (Figure 1), if the Fernandina record was discarded (see discussion). The tide gauge records and their analysis were presented by Wöppelmann et al. . The results are summarized in Table 1, and completed with the 3-year extended ULR solutions presented in section 3.2 (ULR2 and ULR3). The tide gauge and GPS error estimates were each of comparable size, supporting the exercise of applying the GPS vertical velocities for land motion corrections. The “CATS” error bars (section 2.2) are shown for the ‘best' vertical GPS velocity field (ULR3).
Figure 1. Time series of annual mean sea-level values from: (left) tide gauges; (middle) tide gauges corrected for GIA using Peltier  ICE5G (VM2) model predictions; and (right) GPS-corrected tide gauge records in the ITRF2005 reference frame; in (top) Northern Europe and (bottom) North West America. The time series are displayed with arbitrary offsets for presentation purposes (units are in mm).
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Table 1. Relative and Absolute Sea Level Trends From Tide Gauge Records Using Different Vertical Velocity Fields Computed at ULRa
|Groups of Stations||Span (yr)||Tide Gauges (TG) Trend (mm/yr)||GPS/TG Dist. (m)||Span (yr)||ULR1 Trend (mm/yr)||TG+ULR1 Trend (mm/yr)||Span (yr)||ULR2 Trend (mm/yr)||TG+ULR2 Trend (mm/yr)||ULR3 Trend (mm/yr)||TG+ULR3 Trend (mm/yr)|
|North Sea + English Channel|
|ABERDEEN I+II||103||0.58 ± 0.10||2||6.7||0.15||0.73||8.2||−0.10||0.48||0.67 ± 0.22||1.25|
|NEWLYN||87||1.69 ± 0.11||10||6.7||−1.04||0.65||8.1||−0.90||0.79||−0.21 ± 0.27||1.48|
|BREST||83||1.40 ± 0.05||350||6.7||−1.18||0.22||8.0||−1.18||0.22||−0.54 ± 0.77||0.86|
|CASCAIS||97||1.22 ± 0.10||84||6.7||−0.58||0.64||8.1||−0.37||0.85||0.12 ± 0.19||1.34|
|LAGOS||61||1.35 ± 0.18||138||5.3||−0.32||1.03||6.6||−0.59||0.76||−0.10 ± 0.29||1.25|
|MARSEILLE||105||1.27 ± 0.09||5||6.7||−0.32||0.95||8.3||0.34||1.61||0.82 ± 0.37||2.09|
|GENOVA||78||1.20 ± 0.07||1000||6.6||−0.26||0.94||8.3||−0.61||0.59||−0.16 ± 0.85||1.04|
|AUCKLAND II||85||1.30 ± 0.13||5||3.9||1.61||2.91||5.3||1.47||2.77||−0.87 ± 0.48||0.43|
|PORT LYTTELTON||101||2.08b ± 0.11||2||5.8||1.21||3.29||7.0||1.66||3.74||−0.59 ± 0.35||1.49|
|HONOLULU||99||1.46 ± 0.13||5||6.5||0.46||1.92||8.6||0.12||1.58||−0.15 ± 0.36||1.31|
|SW North America|
|LA JOLLA||72||2.11 ± 0.16||700||6.7||−1.36||0.75||9.8||−0.75||1.36||−0.38 ± 0.62||1.73|
|LOS ANGELES||78||0.86 ± 0.15||2200||6.7||−0.64||0.22||7.9||−0.67||0.19||−0.30 ± 0.48||0.56|
|SE North America|
|CHARLESTON I||82||3.23 ± 0.16||8200||4.8||−1.80||1.43||6.9||−1.76||1.47||−1.31 ± 0.44||1.92|
|FERNANDINA||83||2.00 ± 0.13||5500||6.7||−4.28||−2.28||9.4||−3.99||−1.99||−3.58 ± 0.30||−1.58|
|GALVESTON II||94||6.47 ± 0.17||4200||4.5||−6.85||−0.38||5.9||−6.30||0.17||−5.89 ± 0.61||0.58|
|MIAMI BEACH||45||2.29 ± 0.26||4800||5.2||0.92||3.21||6.7||0.08||2.37||0.46 ± 0.61||2.75|
|KEY WEST||90||2.23 ± 0.10||16000||6.7||−0.50||1.73||9.4||−0.97||1.26||−0.59 ± 0.38||1.64|
|NE North America|
|EASTPORT||63||2.07 ± 0.16||800||6.2||1.39||3.46||8.1||1.48||3.55||2.07 ± 0.87||4.14|
|NEWPORT||70||2.48 ± 0.14||500||6.1||−0.18||2.3||7.3||−0.18||2.3||0.42 ± 0.37||2.9|
|HALIFAX||77||3.29 ± 0.11||3100||2.8||−1.57||1.72||3.9||−1.5||1.79||−0.72 ± 0.31||2.57|
|ANNAPOLIS||70||3.46 ± 0.17||100||6.7||−0.12||3.34||8.9||0.19||3.65||0.69 ± 0.94||4.15|
|SOLOMON'S ISL.||62||3.36 ± 0.19||200||6.7||−3.36||0.00||9.8||−2.92||0.44||−2.43 ± 0.69||0.93|
|STAVANGER||63||0.27 ± 0.17||16000||4.7||0.23||0.50||6.0||1.81||2.08||2.68 ± 0.82||2.95|
|KOBENHAVN||101||0.32 ± 0.12||7300||2.6||−0.08||0.24||3.9||0.25||0.57||0.97 ± 0.35||1.29|
|NEDRE GAVLE||90||−6.05 ± 0.23||11000||6.4||6.22||0.17||7.7||6.46||0.41||7.12 ± 0.19||1.07|
|NW North America|
|VICTORIA||86||1.10 ± 0.15||12000||6.7||0.68||1.78||9.8||0.65||1.75||1.20 ± 0.23||2.30|
|NEAH BAY||65||−1.59 ± 0.22||7800||6.7||4.21||2.62||8.8||3.28||1.69||3.82 ± 0.69||2.23|
|SEATTLE||104||2.06 ± 0.11||5900||6.7||−0.57||1.49||8.8||−0.42||1.64||0.14 ± 0.31||2.20|
 Although the above mentioned error estimates take into account the noise properties of the GPS position time series, they remain an intra-technique estimate. From herein, intra and inter-regional agreement of the sea level trends will be regarded as a most robust estimate of uncertainty.
 In estimating absolute sea level trends, we assumed that land motion is essentially linear on the time span considered here (100 years). This assumption is supported by the very small scatter of the acceleration term in the tide gauge records longer than 50–60 years, suggesting that vertical land motion rates are nearly constant at most sites [Douglas, 2001, Figure 3.16, p. 61]. Observational evidence for acceleration was only detected in reconstructions of global sea level curves using large amounts of data [Church and White, 2006; Jevrejeva et al., 2008]. In addition, we assumed that the local vertical displacements of the relatively close observation points (tide gauges and GPS antennae) are under the sub-mm per year level. The validity of this second working hypothesis is raised, especially at Fernandina, where the land motion corrections failed to provide an agreement with the other stations in the South-East North America region. In absence of repeated high-precision levelling data between the GPS antenna and the tide gauge benchmarks, the hypothesis was necessitated in our exercise.
 Table 2 summarises the scatter of the individual-, and regional rates of sea level change as measured by the standard deviation statistic. It reveals a slight but steady progress in the land motion corrections performed by the successive ULR solutions. Wöppelmann et al.  already noted that GPS corrections provided figures that were more in agreement within a region than GIA corrections from Peltier  (e.g., Figure 1). However, the most striking improvement shown here is the significant reduction in the scatter of the regionally averaged sea level trends using ITRF2005 (ULR3 solution, Table 2). Progresses were definitely made in the reference frame realization when shifting to ITRF2005. In contrast, the 3-year data extension barely reduced this scatter using ITRF2000 (ULR1 to ULR2), suggesting that the limitation was more in the analysis strategy (models, reference frame) than in the data span. This remark is consistent with the predicted standard errors that were obtained for the GPS vertical velocities as a function of the time span of the GPS data (Figure S4). For comparison, the predicted standard errors were also plotted assuming a pure white noise, or using the best noise characteristics observed by Williams et al.  in previous global network solutions using similar data spans. GPS analyses have thus reached the maturity to provide useful information for separating land motion from sea level changes recorded by tide gauges, in particular the most underrated and difficult to model effects that are sediment compaction and land subsidence associated with coastal reclamation, development and withdrawal of underground water (Figure 1). Such effects are very site specific, but are sufficiently frequently associated with harbours and tide gauge sites to raise serious concerns on the validity of global averages obtained from uncorrected secular trends.
Table 2. Scatter of the Individual-, and Regional Rates of Sea-Level Change as Measured by the Standard Deviation Statistic Using Different Land Motion Correctionsa
|Land Motion Correction at the Tide Gauges||No Correction||GIA-Corrected ICE5G (VM2)||GPS-Corrected|
|ULR 1||ULR 2||ULR 3|
|Scatter of the individual rates of sea-level change||2.05 mm/yr||1.49 mm/yr||1.32 mm/yr (1.15)||1.23 mm/yr (1.06)||1.15 mm/yr (0.98)|
|Scatter of the regional rates of sea-level change||1.37 mm/yr||0.98 mm/yr||0.93 mm/yr (0.91)||0.87 mm/yr (0.83)||0.62 mm/yr (0.60)|
 There might be a limit in the reduction of the scatter of long term sea level trends, however. The issue is the subject of an extensive scientific debate. Sea level rise is expected to vary spatially as a result of the redistribution of melt-water within the Earth system [e.g., Mitrovica et al., 2001]. These variations are long wavelength (>1000 km), and could explain that using ITRF2005 or ITRF2000 did not change significantly the scatter of the geocentric sea-level trends within a region. However, the GPS-corrected trends were different in ITRF2005 or ITRF2000 due to the systematic differences between the frames (section 2.3); leading to different values of regionally averaged sea level trends, and scatter (Table 2).
 In contrast, Douglas  found no conclusive evidence of glacial melting fingerprints in any of the long tide gauge records that were used by most authors in their determinations of global sea level rise. The assumption that underlies the studies which aim at estimating a secular rate of global sea level rise is that the longer the period of sea level variation, the greater the spatial extent of that signal.
 Furthermore, Prandi et al.  did not find any significant difference between coastal and global mean sea level rise, comparing tide gauges and satellite altimetry data over 1993–2007. Using Douglas  approach and our best estimates of land motion from GPS (ULR3 corrections) yielded a global-average rate of geocentric sea-level rise for the past century which is in good agreement with the recent estimates (e.g., 1.7 mm/yr [Church and White, 2006; Holgate, 2007]). Including or discarding the anomalous Fernandina record resulted in an estimate of 1.55 ± 0.19 mm/yr or 1.61 ± 0.19 mm/yr, respectively. The approach is therefore robust (see also figures in parenthesis in Table 2), and gave further support to the Douglas  morphological grouping of tide gauges, which was based on their correlation at low frequencies with their neighbours. Despite the different time spans, our estimate of global sea level rise appeared to be in good agreement with the sum of steric sea level and land ice contributions estimated by Leuliette and Miller  over the recent period of 2003–2007 (1.5 mm/yr) using altimetry, Argo, and GRACE gravity observations.