21. See supporting material on Science Online

melt fraction will be more gradual, reflecting the gradual increase of water solubility in olivine and orthopyroxene. Our results therefore support the concept that the low-velocity zone may be related to partial melting (1, 2, 6). However, even in the absence of melting, the partitioning of water between olivine and orthopyroxene would strongly depend on depth. The high water solubilities in aluminous orthopyroxene at low pressure and temperature will effectively "dry out" olivine, and this may also contribute to a stiffening of the lithosphere. In any case, however, our results imply that the existence of an asthenosphere-and therefore of plate tectonics as we know it-is possible only in a planet with a water-bearing mantle. Stefan Rahmstorf A semi-empirical relation is presented that connects global sea-level rise to global mean surface temperature. It is proposed that, for time scales relevant to anthropogenic warming, the rate of sea-level rise is roughly proportional to the magnitude of warming above the temperatures of the pre-Industrial Age. This holds to good approximation for temperature and sea-level changes during the 20th century, with a proportionality constant of 3.4 millimeters/year per°C. When applied to future warming scenarios of the Intergovernmental Panel on Climate Change, this relationship results in a projected sea-level rise in 2100 of 0.5 to 1.4 meters above the 1990 level. U nderstanding global sea-level changes is a difficult physical problem, because complex mechanisms with different time scales play a role (1), including thermal expansion of water due to the uptake and penetration of heat into the oceans, input of water into the ocean from glaciers and ice sheets, and changed water storage on land. Ice sheets have the largest potential effect, because their complete melting would result in a global sea-level rise of about 70 m. Yet their dynamics are poorly understood, and the key processes that control the response of ice flow to a warming climate are not included in current ice sheet models [for example, meltwater lubrication of the ice sheet bed (2) or increased ice stream flow after the removal of buttressing ice shelves (3)]. Large uncertainties exist even in the projection of thermal expansion, and estimates of the total volume of ice in mountain glaciers and ice caps that are remote from the continental ice sheets are uncertain by a factor of two (4). Finally, there are as yet no published physically based projections of ice loss from glaciers and ice caps fringing Greenland and Antarctica. For this reason, our capability for calculating future sea-level changes in response to a given surface warming scenario with present physicsbased models is very limited, and models are not able to fully reproduce the sea-level rise of recent decades. Rates of sea-level rise calculated with climate and ice sheet models are generally lower than observed rates. Since 1990, observed sea level has followed the uppermost uncertainty limit of the Intergovernmental Panel on Climate Change (IPCC) Third Assessment Report (TAR), which was constructed by assuming the highest emission scenario combined with the highest climate sensitivity and adding an ad hoc amount of sea-level rise for "ice sheet uncertainty" (1). While process-based physical models of sealevel rise are not yet mature, semi-empirical models can provide a pragmatic alternative to estimate the sea-level response. This is also the approach taken for predicting tides along coasts (for example, the well-known tide tables), where the driver (tidal forces) is known, but the calculation of the sea-level response from first principles is so complex that semi-empirical relationships perform better. Likewise, with current and future sea-level rise, the driver is known [global warming (1)], but the computation of the link between the driver and the response from first principles remains elusive. Here, we will explore a semiempirical method for estimating sea-level rise. As a driver, we will use the global average near-surface air temperature, which is the standard diagnostic used to describe global warming