Text S1
Description of the methods.
We extracted model outputs from 23 GCMs from the Coupled Model Intercomparison
Project phase 3 (CMIP3) data base archived by the Program for Climate Model
Diagnosis and Intercomparison (PCMDI). Access to IPCC AR4 model output was via
the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the
World Climate Research Program (WCRP) Working Group on Coupled Modeling for
the CMIP3 multi-model dataset. Support of this dataset is provided by the Office of
Science, U.S. Department of Energy. Output from the Intergovernmental Panel on
Climate Change (IPCC) SRES B1, A1B, and A2 emissions scenarios were combined
with the output from 20C3M experiments (twentieth century, with historical
emissions) for each of the models. Model output at the archived spatial resolution was
interpolated over a common 0.5 by 0.5 degree grid mask. The global mean
temperature (GMT) for each year was calculated for each model and emissions
scenario, and sequences of 30-year moving averages of the GMT were computed for
each model and emissions scenario. The years GMT moving average first became
larger than the same model’s average from its 20C3M run for the period 1971-2000
(denoted as 1985, the center year of the period) by 0.5, 1.0, 1.5, 2.0, and 2.5 °C were
determined. The resulting list of years (the center year of the 30-year moving average)
for different GMT increments is given in Table S2 (auxiliary material). The relative
runoff change of each model and emissions scenario was computed from the
difference between the basin-averaged runoff for 1971-2000 (denoted as 1985) and
the 30-year average for the future periods covered by the respective moving averages.
The relative runoff change per degree of warming (i.e. runoff sensitivity) was then
computed as the relative runoff change divided by the given increment (0.5, 1.0, 1.5,
2.0, or 2.5 °C) in GMT.
For each of the above sensitivities, we computed multimodel-ensemble medians
(MMs) from different subsets of the 23 models, 3 emissions scenarios, and 5 GMT
increments to show the effects of emissions scenarios and GMT increment on the
sensitivities. Most model runs were 100 years in length, so for some models, for
instance CSIRO MK3.0, there was no 30-year period for which the GMT rise reached
2.5 °C (or in a few cases, 2.0 °C). From the runoff sensitivity results for the individual
models and emissions scenarios, we formed the multimodel-ensembles across the five
GMT increments for each emissions scenario for each river basin, and computed the
MMs for each emissions scenario and across all emissions scenarios, thus highlighting
the differences in runoff sensitivities between emissions scenarios. We then computed
the MM across the three emissions scenarios for each GMT increment, as well as the
ensemble median value of the sensitivities across all emissions scenarios and GMT
increments. This allowed us to highlight the differences in the runoff sensitivities with
GMT increments. For the multimodel-ensemble across all emissions scenarios and
GMT increments, there are only 263 rather than 23×5×3 values because not all
models have three emissions scenarios and not all models predict the largest GMT
increases.
We fit linear models for each river basin to analyze the 30-year average runoff
elasticities with respect to basin mean precipitation (β) and sensitivities to basin
average temperature change (α). We used the Gauss-Jordan regression method
[Anderson and Legendre, 1999] to obtain equations of the form dR/R = β dP/P + α dT
for each GCM. Here dR/R, dP/P, and dT are the relative runoff change, relative mean
precipitation change, and mean basin temperature change computed for each
emissions scenario and GMT increment. The MM values of β and α from the 23
GCMs were calculated for each river basin.