Modern melting of land ice affects sea level along the west coast of the United States in two ways. First, the large mass of glaciers and ice sheets generates an additional gravitational pull that draws ocean water closer, raising relative sea level near the ice masses. As the ice melts, the amount of ice mass on land declines, decreasing its gravitational pull on the ocean water. The loss of mass also results in uplift of the land mass under the ice. The combination of these effects causes relative sea level to fall in the vicinity of the ice mass. The fall extends, at decreasing rates, in the region within a few thousand km of the melting ice. Second, ice melt enters the ocean, raising global mean sea level. Because of gravitational and deformational effects, however, the distribution of new ice melt is nonuniform over the globe. Relative sea level falls near the shrinking ice mass and rises everywhere else. This effect is shown schematically in Figure 4.8. The combined effect of new water mass entering the ocean and altered gravitational attraction results in a spatial pattern of sea-level rise that is unique for each ice sheet or glacier (Mitrovica et al., 2001; Tamisiea et al., 2003). As a consequence, these sea-surface geometries have come to be known as sea-level fingerprints.

Only a few studies have attempted to map the sea-level fingerprints of melting land ice along the west coast of the United States (e.g., Tamisiea et al., 2003, 2005). Figure 4.9A shows the sea-level fingerprints of the three largest sources of land ice that are most likely to have significant effects on west coast sea level: Alaska, Greenland, and Antarctica. The figure shows that melting of Alaska glaciers creates a strong north-south gradient in relative sea-level change along the west coast. The gradient from uniform melting of the Greenland Ice Sheet is much smaller (Figure 4.9B). Uniform melting of either the Antarctic Ice Sheet or the West Antarctic Ice Sheet leads to a uniform change in relative sea level along the entire west coast (Figure 4.9C).

To estimate the effect of fingerprinting from these three ice masses on relative sea level, it is necessary only to multiply the global sea-level equivalent of the mass loss from each source by the appropriate scale factor (colored contours) indicated in the figure and then add the contributions from all three sources. Scale factors greater than 0 indicate that the sea-level fingerprint increases relative sea-level rise at that location, and scale factors greater than 1 indicate that the rise is higher than the global sea-level equivalent value. Scale factors less than 0 mean that the effect of mass loss from a source causes the relative sea level to fall. Scale factors for other ice sources (e.g., European Alps, northeastern Canadian Arctic, Patagonia) are not available at the resolution shown in Figure 4.9, but these sources are likely too small and/or too distant to affect the gradient in sea-level change along the U.S. west coast.

The scale factors and ice loss rates used to calculate the adjusted rates of relative sea-level rise are given in Table 4.1. Modeling or estimating individual regional land ice losses is beyond the scope of this study, so


FIGURE 4.8 Schematic view of the changing sea level caused by a shrinking land ice mass. Relative sea level at time t1 exceeds the mean sea level near the ice mass and is less than the mean at some distance beyond the mass. As the land ice mass decreases (time t2), the local gravitational attraction decreases and the land in the vicinity of the ice rises, causing the relative sea level to fall, even though the mean sea level increases. SOURCE: Adapted from Tamisiea et al. (2003).

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