SUPPLEMENTAL MATERIAL:
Near-term increase in frequency of seasonal temperature extremes prior to
the 2 C global warming target
BRUCE T. ANDERSON
Electronic Supplemental Materials:
Method Section:
To determine future increases in global and regional temperatures, we first calculate the
linear trend of the global-mean temperatures from each CMIP3 model for the full time period
(2000-2100). Based upon these trends we can determine when a given model’s global-mean
temperature exceeds a particular threshold (relative to the initial value). Next, we calculate the
linear trends of the grid-point temperatures from each CMIP3 model for the full time-period. We
then find the value of the grid-point trends at the time the respective model’s global-mean
temperature trend exceeds a given threshold. Finally, we average the grid-point temperature
increases across all models to determine the multi-model mean temperature increase at each gridpoint for the given global-mean temperature increase. As such, differences in the grid-point
temperature increases from one model to another are not systematic of the models’ differing
global climate sensitivities (as they would be if we were to calculate the grid-point trends as a
function of time). Since the magnitudes of the grid-point linear trends vary by time of year, we
perform the analysis separately for the 3-month mean temperatures centered on each month (i.e.
we calculate the linear trends separately for Jan.-Mar., Feb.-Apr. and so forth). This method is
functionally equivalent to the pattern scaling method discussed and evaluated in Mitchell (2003),
here calculated using trends as opposed to a sequence of fixed time-periods; as in Mitchell
(2003), Anderson (2011) found that using temperature changes associated with the long-term
trends reduces the errors that can be introduced when spatial anomaly patterns from a particular
time period (or “time slice”) are used to infer the response pattern itself.
Next we determine the overall grid-point base temperature for each 3-month season (for a
given increase in global-mean temperature) by calculating the observed seasonal-mean grid-point
temperature value in year 2000 using a linear interpolation of the CPC (CRU) data from 19502009 (1944-2005) for the given season. We then add to that the corresponding 3-month mean
grid-point temperature change (representative of a given global-mean temperature increase) as
determined from the models. The 3-month mean grid-point temperature change that we add can
be the multi-model mean temperature increase at each grid-point, as derived above.
Alternatively we can add the grid-point temperature increases derived from each model
separately, which results in 22 separate grid-point base temperature values.
Next, it is necessary to calculate the range of seasonal-mean temperature variability at each
grid-point, which is done here using the observed seasonal-mean temperature anomalies for each
3-month season as determined from the CPC (CRU) data for the period 1950-2009 (1944-2005).
The seasonal-mean temperature anomalies are computed by first removing the seasonal-mean
climatology (calculated from the average of the 60 yearly values for each 3-month season), then
removing a linear trend (again, calculated from the 60 yearly values for each 3-month season).
Next, we generate 1000 randomized time-series of 60-year temperature anomalies following the
method of Ebisuzaki (1997). For this method, the power spectra for each 3-month mean grid-
point temperature anomaly time-series spanning 1950-2009 (1944-2005) is calculated based
upon the CPC (CRU) data. The randomized grid-point anomaly time-series is produced by
randomizing the phase of the associated power spectra, and then reconstructing the time-series
using the amplitudes.
In this way, the grid-point auto-correlation structure and standard
deviation of the observed seasonal-mean temperature anomalies are preserved.
From each randomized 60-year time-series, we select the first decade worth of values, which
as before represent anomalies, and add it to the seasonally-varying 3-month mean grid-point base
temperatures (again, the base temperatures can be derived from the multi-model mean
temperature increase at each grid-point or alternatively from the individual model grid-point
temperature increases). In this way we construct 1000 stochastic, 10-year temperature records in
which interannual-to-decadal variability matches that found in the observed record—thereby
avoiding biases introduced by the underestimation (or overestimation) of natural variability
within numerical climate models (e.g. Wang et al., 2009; Bauser et al., 2009; Diffenbaugh and
Scherer, 2011)—but in which the overall base temperatures change in accordance with the
projections of future temperature increases found in the models. Support for using this type of
anomaly method comes from the fact that for future global-mean temperature increases of 1.2 °C
(or less) seasonal-mean temperature variability does not change appreciably (less than 10% over
most of the globe, with a few locations in northern North America and Europe experiencing
increases of 10-20% - not shown) and even when it does its magnitude (<0.2 °C everywhere),
and hence its relative contribution to extreme event frequency, is small compared with the
change in base temperatures themselves (Ballester et al., 2010).
References
Anderson BT (2011) Intensification of seasonal extremes given a 2C global warming target.
Climatic Change (in review)
Ballester J, Rodo X, Giorgi F (2010) Future changes in Central Europe heat waves expected to
mostly follow summer mean warming Clim Dyn 35: 1191-1205
Bauser CM et al (2009) Bayesian multi-model projection of climate: Bias assumptions and
interannual variability. Clim Dyn 33: 849-868
Diffenbaugh NS, Scherer M (2011) Observational and model evidence of global emergence of
permanent, unprecedented heat in the 20th and 21st centuries, Climatic Change:
doi:10.1007/s10584-011-0112-y
Ebisuzaki W (1997) A method to estimate the statistical significance of a correlation when the
data are serially correlated. J. Climate 9: 2147-2153.
Mitchell TD (2003) Pattern Scaling: An examination of the accuracy of the technique for
describing future climates, Climatic Change 60: 217-242
Wang H et al (2009) Attribution of the seasonality and regionality in climate trends over the
United States during 1950-2000. J Climate 22: 2571-2590