BOX 2.1
Inferring Sea Level from Proxy Measurements

Sea-level “proxies” are natural archives that record rates of sea-level rise prior to the mid-19th century, when tide gage measurements became relatively common. Proxy indicators are generally calibrated against data from modern instruments and then used to reconstruct past sea levels. Three types of proxy archives can be measured with sufficient precision to be compared with the instrumental record: salt-marsh sediments, micro-atolls, and archaeological observations. Stratigraphic sequences from salt marshes record changes in the frequency and duration of tidal inundation, and thus past sea levels. The recent discovery of correlations between microfossils, such as foraminifera, and tidal elevation has significantly improved the precision of many sea-level reconstructions based on salt marshes (Horton and Edwards, 2006). Coral microatolls grow in a narrow range of sea levels. Growth at the upper surface of the coral potentially records fluctuations in relative sea level (e.g., Smithers and Woodroffe, 2001). Finally, some archaeological observations are relatable to sea level, including coastal water wells and Roman fish ponds (e.g., Lambeck et al., 2004).

Detailed proxy studies have not been done along the west coast of the United States. An example of the use of salt-marsh sediments from North Carolina to estimate rates of sea-level rise is shown in the figure below. Analysis of sediment cores suggest that the rate of sea-level rise changed three times: increasing between 853 and 1076, decreasing between 1274 and 1476, then substantially increasing between 1865 and 1892 (Kemp et al., 2011).

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FIGURE Two thousand years of sea-level rise estimates from two North Carolina salt marshes (Sand Point and Tump Point). Errors in the data are represented by parallelograms; the correction for glacial isostatic adjustment is larger at the old end of the error box. The red line is the best fit to the sea-level data. Green shapes indicate when significant changes occurred in the rate of sea-level rise. SOURCE: Kemp et al. (2011).

than 2,000 tide gages worldwide, most of which were established since 1950 (Jevrejeva et al., 2006).

By averaging the water levels measured at the gage over a long period of time (daily, monthly), the effect of daily tides is removed, leaving only the relative sea level. This water level reflects not only the sea level, but also the effects of the weather, such as persistent wind systems and changes in atmospheric pressure; interannual to decadal climate variability; changes in oceanic currents; and vertical motions of the land on which the gage sits. These effects must be removed from the tide gage measurement to obtain the change in sea level caused by changes in ocean water volume or mass (see Appendix A).

The global mean sea level is determined by spatially averaging all of the qualified tide gage records from around the world. Spatial averaging provides a means to avoid bias due to regional climate variations. Sampling bias due to the small number of tide gages, particularly before 1950, and their concentration in the Northern Hemisphere and along coasts and islands is a major source of uncertainty in sea-level change estimates (Peltier and Tushingham, 1989; Church, 2001; Holgate and Woodworth, 2004). Long tide gage records (e.g., at least 50–60 years) are commonly used to average out decadal variability of the oceans’ surface (Douglas, 1992).

The rate of sea-level change is estimated by fitting a curve through the historical tide gage readings. The curve could be a straight line or a higher order polynomial over the whole length of the record or shorter sections. More sophisticated data-dependent decompositions of the tide gage record also have been used (e.g., Peltier and Tushingham, 1989; Moore et al.,



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