Rates of global sea-level rise over the past several millennia are inferred from geological and archeological (proxy) evidence. Modern rates are estimated using tide gage measurements, which in some places date back to the 17th century, and satellite altimetry measurements of sea-surface heights, which have been available for the past two decades. Gravity Recovery and Climate Experiment (GRACE) satellite measurements, beginning in 2002, offer a possible additional estimate of global sea level.
Following a few thousand years of relative stability, global sea level began rising shortly after the beginning of the industrial era. The Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report estimated that more modern rates of sea-level rise began sometime between the mid-19th and mid-20th centuries, based on geological and archeological observations and some of the longest tide gage records (Bindoff et al., 2007). Tide gage measurements indicate that global mean sea level rose 1.7 ± 0.5 mm yr-1 over the 20th century and 1.8 ± 0.5 mm yr-1 from 1961 to 2003. Rates from satellite altimetry and tide gages were higher from 1993 to 2003—3.1 ± 0.7 mm yr-1—but the IPCC was unable to determine whether the higher rate was due to decadal variability of the oceans or to an acceleration in sea-level rise. This chapter describes how sea level is measured and summarizes rates of sea-level rise estimated since the IPCC Fourth Assessment Report was published.
Salt-marsh sediments, micro-atolls, and archaeological indicators are capable of capturing sub-meter-scale sea-level changes during the past 2000 years (Box 2.1). The most robust signal in these proxy records is an acceleration from relatively low rates of sea-level change during the past two millennia (order 0.1 mm yr-1) to higher modern rates of sea-level rise (2–3 mm yr-1; e.g., Lambeck et al., 2004; Gehrels, 2010; Kemp et al., 2011). Both the magnitude and timing of the acceleration vary among reconstructions, likely because of different assumptions about the underlying geophysical processes and uncertainties in determining height and time from proxy records. Recent reconstructions place the onset of acceleration in sea-level rise between 1840 and 1920 (Donnelly et al., 2004; Gehrels et al., 2006, 2008; Kemp et al., 2009, 2011). This late 19th or early 20th century acceleration in sea-level rise is also visible in the longest tide gage records of Brest (Wöppelmann et al., 2008), Amsterdam (Jevrejeva et al., 2008), Liverpool (Woodworth, 1999), Stockholm (Ekman, 1988), and San Francisco (Breaker and Ruzmaikin, 2010).
Tide gages measure the water level at the location of the gage (Box 2.2). Originally designed for navigational purposes, the first gages began operating in the ports of Stockholm, Sweden, and Amsterdam, The Netherlands, in the 17th century. There are now more
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).
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.,
Tide Gage Measurements
Tide gages measure the height of the water relative to a monitored geodetic benchmark on land (Figure). Tide gages originally used a float to track the water level inside a vertical tube. The bottom of the tube was closed except for a hole that permitted a small amount of water to enter the tube with time, thus serving as a temporal filter. Slow changes in the sea surface caused by tides or storm surges have sufficient time to fill the tube, while passing waves do not. Today, electronic sensors or bubbler gages have replaced tide gage floats.
Two organizations collect and preserve tide gage records from around the world: the Global Sea Level Observing System, which has established a network of 290 tide gages worldwide; and the Permanent Service for Mean Sea Level, which stores and disseminates the tidal records from more than 2,000 stations around the world.
FIGURE Examples of tide gage stations. (a) A float and stilling-well gage at Holyhead, UK. SOURCE: UK National Oceanography Centre. (b) A float gage at Vernadsky, Antarctica. SOURCE: British Antarctic Survey. (c) A radar tide gage at Alexandria, Egypt. SOURCE: Courtesy of T. Aarup, Intergovernmental Oceanographic Commission. (d) An acoustic gage at Vaca Key, Florida. Acoustic gages now form the majority of the U.S. sea-level network. SOURCE: National Oceanic and Atmospheric Administration.
2005; Jevrejeva et al., 2006). Because sea level exhibits considerable interannual and decadal variability, the calculated rate of change depends on the length and start date of the record used. For example, Church and White (2006) found that the global rate of sea-level rise was 1.7 ± 0.3 mm yr-1 for the 20th century, 0.71 ± 0.4 mm yr-1 for 1870–1935, and 1.84 ± 0.19 mm yr-1 for 1936–2001. Their results are shown in Figure 2.1, compared to other independent estimates of global sea-level rise from tide gages.
The time dependency of global sea level can be seen in the analysis of Church and White (2011), who calculated the sea-level rise using 16-year moving windows of data, as shown in Figure 2.2 (see also Box A.1 in Appendix A). In this example, the linear trend in global sea-level rise was 1.7 mm yr-1 from 1900 to 2009, with some 16-year intervals yielding rates of 2–3 mm yr-1 in the 1940s, 1970s, and 1990s. This variability has been attributed to natural climate variability (e.g., El Niño-Southern Oscillation [ENSO]), which causes short-term variations in global mean temperature, and to large volcanic eruptions, which briefly cool the Earth’s surface and troposphere (e.g., Hegerl et al., 2007).
FIGURE 2.1 Global sea-level time series from Church and White (2006; red) compared with independent global sea-level time series from (a) Trupin and Wahr (1992), (b) Holgate (2007), (c) Gornitz and Lebedeff (1987), and (d) Jevrejeva et al. (2006) in black. Time series are arbitrarily shifted vertically for clarity. SOURCE: Woodworth et al. (2009).
FIGURE 2.2 Sixteen-year running averages of global sea-level rise trends showing variability in rates over short timescales. SOURCE: Church and White (2011).
Recent estimates of rates of global sea-level rise are presented in Table 2.1. In general, the new estimates over the entire 20th century are similar to those reported in the IPCC Fourth Assessment Report. Rates for the last decade of the 20th century are higher and similar to IPCC (2007) rates estimated from satellite altimetry and confirmed by tide gages (see results of Jevrejeva et al., 2008; Merrifield et al., 2009; and Church and White, 2011). Because of natural temporal (e.g., Figure 2.2) and spatial variability in the sea-level signal, the meaning of the higher rates of global sea-level rise since the early 1990s is subject to interpretation. For example, Merrifield et al. (2009) attributed most of the recent rise to higher rates of sea-level rise in the Southern Hemisphere and tropical regions, which had been seen by Cabanes et al. (2001) in satellite altimetry data.
It is also possible that the recent higher rate of sea-level rise represents an acceleration in the long-term trend. The record of sea-level rise is punctuated by periods of acceleration and deceleration. Jevrejeva et al. (2008) used a Monte-Carlo-Singular Spectrum Analysis to remove the 2- to 30-year variability from more than 1,000 tide gage records from around the world. They found an acceleration of 0.01 mm yr-2 over the entire 300-year period, with 60- to 65-year periodicity in acceleration and deceleration for the preindustrial 18th and 19th centuries. The fastest rises in sea level occurred between 1920 and 1950 (up to 2.5 mm yr-1) and between 1992 and 2002 (3.4 mm yr-1; Jevrejeva et al., 2008). Many, but not all long tide gage records around the world show an acceleration in global sea-level rise around 1920–1930 and a deceleration around 1960 (Woodworth et al., 2009; see also Figure 2.1). Although Houston and Dean (2011) found a slight deceleration since 1930, Rahmstorf and Vermeer (2011) argued that this result reflects the choice of start date (1930) and the regional character of the gages used in their analysis.
Even if the higher rates since the 1990s represent a persistent acceleration in sea-level rise, significant additional acceleration would be required to reach commonly projected sea levels (e.g., Hansen, 2007; Rahmstorf, 2007; Vermeer and Rahmstorf, 2009). For example, taking a rate of 3.1 mm yr-1 from satellite altimetry, sea level would rise only 0.28 m over the next 89 years. To reach 1 m by 2100 would require a positive acceleration of 0.182 mm yr-2 for the entire time period, based on the following quadratic equation:
H = H0 + (b × t) + (c/2) t2,
where H0 is the current sea level, b is the linear rate of sea-level rise, and c is the acceleration in units of mm yr-2. In this example, acceleration would account for more than 72 percent of the future sea-level rise. Such rapid acceleration is not seen in the 20th century tide gage record, except for short periods of time, such as the 1930s and the 1990s (Figure 2.2).
TABLE 2.1 Rates of Global Sea-Level Rise Estimated from Tide Gages
|Source||Period||Sampling||Rate of Sea-Level Rise (mm yr-1)|
|IPCC(2007)||1900–2000||Not specified||1.7 ± 0.5|
|1961–2003||1.8 ± 0.5|
|Church and White (2006)||1870–1935||400 gages, global coverage||0.71 ± 0.4|
|1956–2001||1.84 ± 0.19|
|Holgate (2007)||1904–1953||9 gages, mostly Northern Hemisphere||2.03 ± 0.35|
|1904–2003||1.45 ± 0.34|
|1904–2003||1.74 ± 0.16|
|Shum and Kuo (2011)||1900–2006||500 gages, global coverage||1.65 ± 0.4|
|Domingues et al. (2008)||1961–2003||Not specified||1.6 ± 0.2|
|Church and White (2011)||1900–2009||400 gages, global coverage||1.7 ± 0.2|
|1993–2009||2.8 ± 0.8|
|Jevrejeva et al. (2008)||1992–2002||1,023 gages, global coverage||3.4|
|Merrifield et al. (2009)||1993–2007||134 gages, global coverage||3.2 ± 0.4|
Satellite altimeters measure the sea-surface height with respect to the Earth’s center of mass (Box 2.3). The satellite measurement also includes large-scale deformation of the ocean basins caused by glacial isostatic adjustment (GIA), which must be removed from the signal to obtain the ocean volume change. The global mean sea level is calculated by averaging measurements of sea-surface height made by the various altimeters, three of which are currently operating, which revisit a given spot on the Earth every 10 to 35 days.
Recent altimetry estimates of sea-level rise are similar to those reported in the IPCC Fourth Assessment Report, ranging from 3.2 to 3.3 mm yr-1 from 1992 to 2010 (Table 2.2), and 2.9 ± 0.4 mm yr-1 from 1985 to 2010. The latter estimate includes data from higher latitudes and has a gap in data from 1988 to 1991 (Figure 2.3). A recent analysis of the total error budget due to instrument, orbit, media propagation errors, and geophysical corrections and their drifts suggests an uncertainty of ~0.4–0.5 mm yr-1 (Ablain et al., 2009), in agreement with external calibration using data from island tide gages (Mitchum et al., 2010).
The regional variability in sea level seen in many tide gage analyses has been confirmed by satellite altimetry records. Figure 2.4 shows the regional variation in sea-level trends in the global oceans based on 25 years (1985–2010 with a 3-year data gap) of satellite altimetry data. The largest variations are in the western Pacific and eastern Indian oceans, where sea level has been rising much faster than the global mean (warm colors in Figure 2.4). Sea level has been dropping in other areas, including the eastern Pacific Ocean (cool colors in Figure 2.4). The IPCC concluded that these spatial patterns reflect interannual to interdecadal variability resulting from the El Niño-Southern Oscillation, the North Atlantic Oscillation, the Pacific Decadal Oscillation, and other climate patterns (Bindoff et al., 2007).
Satellite altimetry and tide gage estimates of sea-level change over the same timespan are in good agreement (e.g., Nerem et al., 2010). However, there are significant differences between long-term trends in tide gage records and the shorter satellite altimetry records. For example, Shum and Kuo (2011) estimated a tide-gage trend of 1.50 mm yr-1 for 1880–2008 and a satellite altimetry trend of 2.59 mm yr-1 for 1985–1987 and 1991–2010 (Figure 2.5). Differences in trends for the two types of measurements for other data periods have also been reported (e.g., Church and White, 2011). These differences are likely due to contamination of the altimetry trend by interannual or longer variations in the ocean (e.g., Willis et al., 2010; Shum and Kuo, 2011) and, to a smaller extent, to sampling biases. Satellite altimetry records are shorter than tide gage records but cover more of the global ocean (81.5°N–81.5°S in Figure 2.5). In addition, the sea-level signal from altimetry is dominated by the open ocean whereas the signal from tide gages is more strongly affected by the coastal ocean (e.g., Holgate and Woodworth, 2004).
The GRACE mission makes detailed measurements of the Earth’s gravity field and its variability over time. Among the gravity variations detected by GRACE are mass changes in the ocean and land reservoirs (e.g., land ice, groundwater) that contribute to sea-level change (Box 2.4). The land ice and water components are discussed in Chapter 3. For the ocean component, GRACE measures the ocean bottom pressure—the sum of the mass of the ocean and atmosphere above—at spatial resolutions of ~500 km. Ocean bottom pressure changes when winds move water across the ocean surface or when water is added to the oceans (e.g., through ice melt, stream runoff), increasing the ocean mass. The ocean mass change is determined by computing gravity field changes from the GRACE signal (Chambers et al., 2004; Tapley et al., 2004), then correcting for the effect of glacial isostatic adjustment and high frequency ocean responses to wind and surface pressure forcing. When combined with other observations—such as altimetry data that have been corrected for temperature and salinity effects—GRACE data offer a potential means of distinguishing how much global sea-level change is due to changes in mass and how much is due to changes in temperature and salinity.
Currently, however, there are difficulties associated with using GRACE data to infer ocean mass changes. Changes in gravity over the ocean, and thus the ocean bottom pressure signal, are small relative to
Satellite Radar Altimetry Measurements
The first altimeter mission observing the global ocean was launched in 1978 (Seasat), but routine measurements of sea level from satellites began with the launch of TOPEX/Poseidon (1992–2006) and ERS-1 (1991–2000), and continued with ERS-2 (1996–2011), Geosat Follow-on (1998–2001), Jason-1 (2001–present), Envisat (2002–present), Jason-2 (2008–present), and Cryosat-2 (2010–present). Although these satellites are sometimes maneuvered in geodetic phases or interleave orbits, they have occupied essentially the same ground tracks as 10-day, 17-day, or 35-day repeat orbits, providing a long data set of compatible observations. These satellites were equipped with radar altimeters to determine the distance between the satellite and the sea surface (see Figure). The location of the satellite, which has to be accurately known at all times, is determined using tracking data from the Satellite Laser Ranging network, the Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) land-based beacons, and the Global Navigation Satellite System (GNSS). Using the range or range-rate information from these tracking systems, the position and velocity of the satellite are determined and the radial orbit is then calculated. The sea surface is estimated by averaging measurements taken over a 10-, 17-, or 35-day satellite track repeat cycle. The accuracy of the sea surface height measurements for TOPEX-class altimetry systems, considered to be the most accurate among the radar altimetry missions due to their optimal orbital sampling and high instrument precision, is a few cm (1 σ), after correcting for instrument and media errors and geophysical phenomena.
The TOPEX and Jason satellites measure(d) the global ocean to latitudes of 66° north and south. Satellite altimeters that extend observations into the polar ocean include Geosat (1984–1987) and Geosat Follow-on, which covered latitudes of 71° north and south; ERS-1 and -2 and Envisat, which cover latitudes of 81.5° north and south; and Cryosat-2, which covers latitudes of 88° north and south. Their repeat orbits are longer than the TOPEX and Jason satellites: 17 days for Geosat and Geosat Follow-on, 35 days for ERS-1 and -2 and Envisat, and 365 days with 30-day subcycles for Cryosat-2.
FIGURE The Jason-2 satellite uses a radar altimetry instrument to accurately measure sea-surface heights. SOURCE: COMET® Website at <http://meted.ucar.edu/> of the University Corporation for Atmospheric Research, sponsored in part through cooperative agreement(s) with the National Oceanic and Atmospheric Administration, U.S. Department of Commerce. ©1997-2011 University Corporation for Atmospheric Research. All rights reserved.
TABLE 2.2 Rates of Global Sea-Level Rise Estimated from Satellite Altimetry
|Source||Period||Latitude||Instruments||Rate of Sea-Level Rise (mm yr-1)a|
|D. Chambers (personal communication)||1992–2010||± 66°||TOPEX and Jason-1, -2||3.3 ± 0.5|
|Nerem et al. (2010)||1992–2010||± 66°||TOPEX and Jason-1, -2||3.3 ± 0.5|
|Leuliette and Miller (2009)||1992–2010||± 66°||TOPEX and Jason-1, -2||3.2 ± 0.3|
|Cazenave et al. (2009)||1992–2010||± 66°||TOPEX and Jason-1, -2||3.3 ± 0.2|
|Church and White (2011)||1993–2009||± 66°||TOPEX and Jason-1, -2||3.2 ± 0.4|
|Shum and Kuo (2011)||1985–2010||± 81.5°||Geosat, Geosat Follow-on, ERS, TOPEX, Envisat, and Jason-1, -2||2.9 ± 0.5|
a All rates were corrected for glacial isostatic adjustment using the ICE-5G (VM2) model (Peltier, 2004) and atmospheric pressure effects (see Appendix B).
FIGURE 2.3 Global sea-level rise trends from different satellite altimeters for 1985–2010. The measured trend is 2.6 ± 0.4 mm yr-1, and the trend corrected for glacial isostatic adjustment and atmospheric effects is 2.9 ± 0.4 mm yr-1. Seasonal variations in the time series were not removed, but the trend was estimated simultaneously with periodicities associated with seasonal variations. SOURCE: Updated from Shum and Kuo (2011).
the GRACE accuracy limit and to the land gravity signal. Moreover, uncertainties in GIA models strongly affect the ocean mass calculated from GRACE (e.g., Cazenave et al., 2009). Finally, GRACE data must be adjusted to reduce high-frequency barotropic signals over the ocean and over land (Flechtner, 2007) and to account for motion of the geocenter (e.g., using laser ranging or Global Positioning System [GPS] data; Swenson et al., 2008). Once a consensus is reached on how to handle the processing and corrections, GRACE data may provide a valuable constraint on the ocean mass component of sea level and on the total sea-level budget.
Recent estimates of global sea-level rise are in close agreement with estimates in the IPCC Fourth Assess-
FIGURE 2.4 Regional variations in global sea-level rise based on observations from satellite altimetry from 1985 to 2010. The data were corrected for glacial isostatic adjustment, atmospheric barotropic pressure response, and various instrument, media, and geophysical effects. SOURCE: Updated from Shum and Kuo (2011).
FIGURE 2.5 Comparison of sea-level time series from tide gages (1880–2008; blue lines) and from satellite altimetry (1985–1987 and 1991–2010; red lines) after corrections for atmospheric barotropic pressure effects and glacial isostatic adjustment (using the ICE-5G [VM2] model, Peltier, 2004). The thin blue line represents average monthly sea level from global tide gage data. The thick blue line represents yearly sea-level changes from a moving average of tide gage observations, and the shaded area represents the sea-level uncertainty, which reflects the number of gage sites used in the global averages, the number of data points, and the standard deviations of the fit of seasonal signals and the trend of the original gage time series. The thick red line is the yearly averaged altimetry sea-level data. SOURCE: Updated from Shum and Kuo (2011).
The Gravity Recovery and Climate Experiment measures changes of the mass distribution on Earth. The twin satellites travel in the same polar orbit 500 km above the Earth, with one satellite leading the other by approximately 220 km (Figure). When the lead satellite passes over a region of relatively high mass, it will accelerate because of increased gravitational attraction and will increase the distance between the satellites. On the other side of the region of high mass, it will slow again. The same effect applies to the trailing satellite. By monitoring the changing distances between the satellites, and knowing their positions in space accurately via GPS and star cameras, the distribution of mass below the satellites can be determined. Mass redistributions of the Earth are manifested in temporal gravity signals with a monthly sampling and spatial resolution longer than 300–400 km (half-wavelength; Tapley et al., 2004). GRACE data can be used to measure changes in mass of the ocean and its land reservoirs (e.g., land ice and groundwater; see Chapter 3). Launched in 2002, the mission is expected to end in 2015.
FIGURE An artist’s concept of GRACE satellites with ranging link between the two craft. SOURCE: National Aeronautics and Space Administration.
ment Report, with long-term (50–100 years) rates of about 1.8 mm yr-1 estimated from tide gages, and recent (post-1990) rates of about 3.2 mm yr-1 estimated from satellite altimetry and tide gages. The higher rates of recent sea-level rise may reflect interannual and longer variations due to ENSO and other climate patterns. Increases of 3–4 times the current rate would be required to realize scenarios of 1 m sea-level rise by 2100. Such an acceleration has not yet been detected.