15-km value is somewhat arbitrary, but it is similar to the distance threshold typically used in previous joint GPS and tide gage analyses (e.g., Mazzotti et al., 2007; Wöppelmann et al., 2007). The committee’s estimated rates of vertical land motions are given in Table A.1. Positive values of vertical land motion mean that the land is rising. Table A.1 also reports the standard deviation of vertical land motion within a 15-km radius of each tide gage station. This value was used in the uncertainty estimate described below.

To test the importance of the CGPS solution on the calculated rate of vertical land motion, the committee compared the SOPAC-derived rates with rates published in the literature. Although most published reports for coastal areas south of the Mendocino Triple Junction present only horizontal rates (e.g., Spinler et al., 2010), the SOPAC rates for Cascadia are similar to vertical rates for the same sites published in Mazzotti et al. (2008). Mazzotti et al. (2008) estimated rates using different GPS processing software (BERNESE) than that used by SOPAC. The correspondence in rates produced by two independent approaches suggests that the committee’s results are reasonable.

Uncertainty in Vertical Land Motion

The estimated error in the vertical land motion adjustment to the tide gage records can be expressed as eTG = ev + esv + eref, where ev is the error in the velocity estimation, is the error associated with spatial variability in vertical land motion between a CGPS station and the tide gage, and eref is the error associated with the definition of the GPS reference frame. Of these error sources, ev is well defined (Nikolaidis, 2002; Williams et al., 2004) and is taken to be the vertical land motion error associated with the nearest CGPS station to the tide gage (and fifth and sixth columns of Table A.1).

Error in the spatial variability of vertical land motion between a CGPS station and a tide gage, esv, is locally variable and cannot be determined without more detailed studies. For example, Brooks et al. (2007) reported a variation of ~ ± 3 mm yr-1 for esv in the Los Angeles Basin. To estimate esv, the committee used the standard deviation of vertical land motion within a 15-km radius of each tide gage (right two columns in Table A.1). Using this value, rather than the formal error estimate associated with any given GPS station’s velocity, seemed justifed, given the potential for significant variability in vertical land motion at the km scale. For instance, the Santa Monica tide gage has seven CGPS stations within a 15-km radius, with vertical land motion estimates ranging from -1.5 mm yr-1 to 1.8 mm yr-1. The nearest CGPS station, WRHS, has the minimum vertical land motion estimate (-1.5 mm yr-1) and may be the most appropriate value for the correction. However, confidence in this value is diminished by the local spatial variability, which is reflected in the 15-km standard deviation value (Table A.1).

The reference frame error (eref) is a classical geodetic problem (Strang and Borre, 1997). The SOPAC

TABLE A.1 Parameters for Vertical Land Motion Correction

Vertical Land Motion,
Nearest Station
Vertical Land Motion,
15-km Radiusa
Tide Gage Nearest CGPS Station Start Date Distance (km) Rate (mm yr-1) Error (1σ) Rate (mm yr-1) Error (1σ)
Friday Harbor SC02 2001.860 0.70 0.90 0.70
Neah Bay NEAH 1996.000 7.71 3.00 0.40
Seattle SEAT 1996.000 6.25 0.20 0.50 -1.10 0.94
Astoria TPW2 2000.247 1.08 0.60 0.00 1.20 0.40
Crescent City PTSG 1999.820 5.85 2.60 0.40
San Francisco TIBB 1994.460 10.23 -1.40 0.50 -1.44 1.97
Alameda P224 2005.174 12.90 -0.20 0.60 -1.58 1.20
Port San Luis P524 2007.048 14.50 1.70 0.30
Santa Monica WRHS 1999.770 9.36 -1.50 0.60 -0.01 1.34
Los Angeles VTIS 1998.938 2.54 -0.50 0.50 -0.27 2.34
La Jolla SIO3 1993.522 0.26 2.10 0.50 0.73 1.11
San Diego P475 2007.601 9.17 -3.00 0.20 -4.50 0.81

a Rates and errors are not reported for 15-km areas with only 1 CGPS station.

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