River runoff is a key index of renewable water resources which affect almost all human and natural systems. Any substantial change in runoff will therefore have serious social, environmental, and ecological consequences. We estimate the runoff response to global mean temperature change implied by the climate change experiments generated for the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4). In contrast to previous studies, we estimate the runoff sensitivity using global mean temperature change as an index of anthropogenic climate changes in temperature and precipitation, with the rationale that this removes the dependence on emissions scenarios. Our results show that the runoff sensitivity implied by the IPCC experiments is relatively stable across emissions scenarios and global mean temperature increments, but varies substantially across models with the exception of the high-latitudes and currently arid or semi-arid areas. The runoff sensitivities are slightly higher at 0.5°C warming than for larger amounts of warming. The estimated ratio of runoff change to (local) precipitation change (runoff elasticity) ranges from about one to three, and the runoff temperature sensitivity (change in runoff per degree C of local temperature increase) ranges from decreases of about 2 to 6% over most basins in North America and the middle and high latitudes of Eurasia.
 Water is a vital resource for human well-being [Oki and Kanae, 2006] and the functioning of ecosystems [Zhao and Running, 2010]. Decreasing freshwater discharge to the oceans and increasing global aridity have been reported since the 1970s, in association with (although we emphasize, not necessarily caused by) increases in global mean temperature [Dai et al., 2009; Cayan et al., 2010]. Understanding predictions for future changes in runoff for large global river basins is central to assessing the impact of climate change on water resources [Vörösmarty et al., 2000a]. However, there is considerable uncertainty in predictions of future changes in runoff from general circulation models (GCMs) [Allen and Ingram, 2002].
 Future changes in the major climatic drivers of runoff (especially precipitation and temperature) are closely related to cumulative global greenhouse gas emissions, and in turn to global mean temperature change [Murphy et al., 2004; Watterson and Whetton, 2011]. We therefore take an approach that differs somewhat from past studies of water resources susceptibility to climate change for specific future times [Arnell, 2003; Milly et al., 2005; Nohara et al., 2006], and instead use an approach similar to a recent National Research Council Report [National Research Council (NRC), 2010] and compute relative runoff change per degree C of increase in global mean temperature [Chiew et al., 2009]. By so doing, the dependence on emissions scenarios is mostly decoupled, as the global mean temperature change is a good index of cumulative emissions and does not depend on the emission pathway [Matthews et al., 2009]. It should be noted that the global mean temperature (denoted as GMT hereafter) is an index which links global climate change in temperature, precipitation (both amount and intensity), and other climatic variables and changes in land surface hydrology, but is not necessarily indicative of the causes of the changes [Held and Soden, 2006]. The climate change experiments generated for the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC) are used in this analysis, and our inferred runoff sensitivity estimates are therefore reflective of the state of the art of the AR4 GCMs.
 We analyzed model outputs from the IPCC SRES B1, A1B, and A2 emissions scenarios for the 23 GCMs which performed most of the experiments for these scenarios. The relative runoff change was computed from the difference between the basin-averaged runoff for 1971–2000 and the 30-year average for the future periods for GMT increments that we prescribed (seeauxiliary material). We calculated the multimodel-ensemble medians (MMs) of relative runoff change per degree of GMT increase (i.e. runoff sensitivity) from different subsets of the GCMs, emissions scenarios, and GMT increments to show the effects of emissions scenarios and GMT increment on the sensitivities. We did not attempt to select models from the pool of AR4 models according to their performance, both because the superiority of the multimodel ensemble method to any individual model has been demonstrated in both global and regional studies [Reichler and Kim, 2008; Pierce et al., 2009], and because attempts to rank or weight AR4 models based on their performance have generally found that the results are highly dependent on the evaluation criteria [Mote et al., 2011]. The superiority of the MMs is largely caused by the cancellation of offsetting errors in the individual global models [Pierce et al., 2009]. The number of global basins with decreasing runoff at the GMT increment, and associated global land area, world population, and GDP, were also estimated. In addition, we fit linear models [Anderson and Legendre, 1999] for each river basin using the 30-year average data to analyze the runoff sensitivities to basin mean annual precipitation change (β) and basin average temperature change (α) (see auxiliary material).
 Consistent with the rationale that the effects of cumulative emissions, rather than emissions pathways, are associated with the GMT rise [Allen et al., 2009], we found little difference in the runoff sensitivities for different emissions scenarios. Figure 1ashows the runoff sensitivity for each river basin estimated using the multimodel-ensemble median (MM) across all GMT increments for each emissions scenario (red, yellow, and blue lines) and MM across all emissions scenarios and GMT increments (black line). Estimates for different emissions scenarios are generally similar to the ensemble medians over the emissions scenarios.Figure 1b shows the runoff sensitivity for each river basin estimated as MM across all of the three emissions scenarios for each GMT increment (colored lines) and the ensemble median value across all emissions scenarios and GMT increments (black line). The estimates are quite similar, with little difference aside from the values estimated from 0.5°C GMT increase, which show slightly higher sensitivities than for larger increases. The runoff sensitivities for large GMT increases (over 1.0°C) are generally within the interquartile range of the ensemble values across all emissions scenarios and GMT increments.
 Most model runs agree as to the direction of changes in runoff in the regions where the ensemble mean changes are greatest. Figure 2 shows the runoff sensitivity estimated as MM across all emissions scenarios and GMT increments (same values as black lines in Figure 1), along with the fraction of positive minus negative (FPN) estimates as in work by Milly et al.  and NRC . FPN is calculated as the number of the ensemble members showing a positive change minus the number showing a negative change, divided by the total number of the ensemble members. Areas of prominent agreement are the high-latitudes and currently arid or semi-arid areas. Runoff decreases are projected in many temperate river basins outside Eurasia, with the greatest decreases in areas that are currently arid or semi-arid. Results show that projected drying of the southwestern United States extends east to the Gulf of Mexico and south to the Caribbean Sea region. On the other hand, the results show no obvious direction of runoff change in the Amazon region, supporting neither a positive change [Nohara et al., 2006] nor a negative change [Milly et al., 2005] as suggested in previous studies (Figure 2a and Table S1). In general, the number of river basins with decreasing runoff, and subsequently effected global population and GDP, is expected to grow as GMT increases (Figure S1). The portion of GDP increases much faster than either the land area or population because expanding dry areas are mostly in areas with high GDP such as the U.S. Southwest and southern Europe.
 The runoff response along the trajectory of global mean warming is approximately linear over most of the global land area. Figure S2 (see auxiliary material) compares the relative runoff change per degree of warming estimated at 0.5 °C increase in GMT with that estimated over all 5 GMT increments. Nonlinearities are most apparent in West Africa, Central Australia, the U.S. South, and the southeastern part of continental Eurasia, with deviations from linearity most apparent for small increments in GMT. The nonlinearities, where most apparent, tend to stabilize for larger increments in GMT (Figure S3). The apparent nonlinear responses of runoff to warming suggests that current decadal trends (when GMT increase is less than about 0.5 °C) may not be representative of the long term response.
Figure 3 shows the runoff sensitivities to local mean precipitation change and local temperature change among the 194 global river basins. The inferred elasticities of runoff with respect to mean annual precipitation (fractional change in runoff per fractional change in local precipitation) generally range from 1.0 to 3.0 (Figure 3a and Table S1), i.e., a 10% change in mean annual precipitation results in a 10 to 30% change in mean annual runoff. This range is generally consistent with regional studies of precipitation elasticity from observations [Sankarasubramanian et al., 2001; Chiew, 2006]. The lower runoff elasticities (<1.8) are in mid latitudes of the Northern Hemisphere including North Africa and basins with cold climates. The higher runoff elasticities (>2.2) are in mid latitudes of the Southern Hemisphere, Australia, equatorial Africa, eastern North America, and eastern Asia.
 The estimated runoff sensitivity to local temperature change (i.e., per degree C of local warming) is negative for most river basins (Figure 3b and Table S1), and typically ranges from −2 to −6 percent per degree of local warming, with the largest sensitivities in absolute value in eastern North America, southern Europe, and eastern Asia. The estimated runoff sensitivity to local temperature change is positive in a few river basins in Australia, northwest Africa, and southern Asia. It should be noted that local air temperature increases have several potentially competing implications for runoff. First, higher temperatures are usually associated with increased evaporation which implies decreased runoff. Second, higher temperatures in most models lead to increased frequency of extreme precipitation. Increased precipitation intensities generally imply increased runoff [Wainwright and Parsons, 2002]. The relative magnitudes of these effects, however, vary among basins. Figure 3 suggests that evaporation responses are the dominant effect in most river basins. The positive runoff sensitivities in Australia, northwest Africa, and southern Asia suggest that increased extreme precipitation frequency may offset the evaporation response in those water limited areas.
4. Summary and Conclusions
 Our results show that projected runoff sensitivities to anthropogenic climate change are relatively stable across emissions scenarios and GMT increments up to 2.5°C. The runoff response, which includes runoff change in response to changes in temperature, precipitation, and other climatic variables, generally appears to be approximately linear with respect to GMT change over most of the global land area. However, the changes are relatively nonlinear in West Africa, central Australia, the U.S. South, and the southeastern part of Eurasia when the GMT increment is small. In the areas showing large nonlinearity, the sensitivity in runoff per degree of GMT increase tends to be highest for small GMT increments and to stabilize to smaller values when the GMT increment is 1.0 °C or larger.
 The estimated runoff sensitivity to mean annual precipitation change generally ranges from one to three. The estimated runoff sensitivity to local temperature change is negative over most river basins, with the exception of North Africa, much of Australia, and other mostly arid areas. Over most basins in North America, and the middle and high latitudes of Eurasia, runoff sensitivities to local temperature change range from −2 to −6% per degree of local temperature increase.
 The fact that runoff sensitivities are mostly approximately linear with respect to GMT rise (independent of the emissions scenario) provides a compelling argument to view inter-model differences in the context of increments of GMT rise, rather than time slices, as has been done more commonly in the past. Furthermore, the fact that nonlinearities, where apparent, tend to be highest for small GMT increments suggests that the effects of anthropogenic climate change should not be extrapolated from recent hydrologic trends. Nonetheless, it is important to emphasize that temperature changes (global or local) must be viewed as an index to, rather than a causative factor of, runoff change. What this work does show is that runoff changes in the IPCC AR4 experiments track the predicted GMT changes in a somewhat coherent manner, which is, aside from slight differences at the lowest GMT changes, linear, and which does not depend on the emissions pathway.
 The genesis of some of the ideas reported in this paper, notably exploring the relationship of runoff change per unit of GMT change, came about when D. P. Lettenmaier served as a member of the NRC Committee on Stabilization Targets for Atmospheric Greenhouse Gas Concentrations [NRC, 2010], and the authors acknowledge the role that those discussions had in development of the paper, especially conversations with I. M. Held. The authors also appreciate the comments of P. C. D. Milly on an earlier version of the paper. We thank J. Vano for her comments and two anonymous reviewers for thoughtful comments and recommendations. Financial support for this study came from the National Natural Science Foundation of China (grant 41171031), National Basic Research Program of China (grants 2012CB955403 and 2010CB950100), Strategic Priority Research Program (grants XDA05080101) and Hundred Talents Program of the Chinese Academy of Sciences, and U.S. Department of Energy grant DE-FG02-08ER64589 to the University of Washington.
 The Editor would like to thank two anonymous reviewers for their assistance with this paper.