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Supplemental Material© Copyright 2017 American Meteorological Society
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Supplementary Material toToward a New Estimate of “Time of Emergence” of Anthropogenic Warming:
Insights from Dynamical Adjustment and a Large Initial-Condition ModelEnsemble
Flavio Lehner1, Clara Deser1, Laurent Terray2
1

Climate and Global Dynamics Laboratory, National Center for Atmospheric Research, Boulder,USA
2

Sciences de L’Univers au CERFACS, URA-1875, CERFACS/CNRS, Toulouse, France

Published in Journal of Climate 2017
(Manuscript received 8 November 2016, in final form 9 June 2017)

Content•Choice of data pool to choose circulation analogues from (Figure S1)•Choice of running mean length (Figure S2)•

Choice of observational dataset (Figure S3)•Alternative ToE calculation (Figure S4)2

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Choice of data pool to choose circulation analogues fromThe dynamical adjustment with atmospheric circulation analogues as carried out in this study
makes an assumption of stationarity regarding the relationship between an SLP pattern and theassociated SAT anomalies. It does so in that it chooses circulation analogues from a preindustrialcontrol simulation, which by design includes no forced climate change. To test whether thisassumption has a significant influence on the outcome of our analysis, we repeat the dynamicaladjustment (and subsequent ToE calculation) for the first 10 CESM LE members, but this time
we choose circulation analogues from the historical (1920-2009) part of the CESM LE itself
rather than from the preindustrial control simulation. Specifically, we detrend SAT from CESM
LE members 11 to 30 by subtracting the CESM LE ensemble mean at each grid point andconcatenate them to form a “pseudo control simulation” of 1800-year length (equal to thepreindustrial control simulation). We also adjust the long term mean of this pseudo control
simulation at each grid point to match the one of the preindustrial control simulation. Similarly,
we concatenate SLP from the same 20 ensemble members (without detrending) to form a pseudo
control simulation, also adjusting the mean. We then repeat the dynamical adjustment using
these pseudo control simulations of SLP and SAT to find circulation analogues. Large
differences between the two dynamical adjustment calculation would point to a change in therelationship between SLP and SAT throughout the period 1920-2009 and possibly beyond. Fig.
S1 shows the ToE calculated for the first 10 CESM LE members with the two approaches. There
are differences between the two approaches, such as later ToE over northern North America andearlier ToE over Scandinavia, that might be related to a forced response in SLP, such as astrengthening of the Azores High. However, the differences in ToE are typically small, certainlyin comparison to other sources of uncertainty discussed in this study.

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Figure S 1: Same as (b) and (d) in Figure 3 of the main text, but only for 10 CESM LE members
and using (top) dynamically adjusted SAT from the preindustrial control and (bottom) from theconcatenated historical part of the CESM LE (“pseudo control simulation”).

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Choice of running mean length
Fig. S2 shows an error metric for different running means applied to the data before conducting
the time of emergence (ToE) analysis. The error indicates how accurate the estimate of ToE is,given that the observational record of surface air temperature (SAT) currently stops in 2015. Thisis tested within the CESM LE model world, where we know the evolution of SAT until 2100 andhence can calculate the actual ToE and then contrast it with the ToE using the model simulations
until 2015 only. Fig. S2 illustrates that the error is reduced from 5- to 20-year running means
with little additional error reduction afterwards. Fig. S2 also shows that in DJF for the 10-year
running mean the error reduction achieved by the dynamical adjustment is as large as the error
reduction from using a 20- instead of 10-year running mean.

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Figure S 2: Error in time of emergence calculated using the CESM LE simulations until 2015
and time of emergence calculated using the full CESM LE simulations until 2100, with 5-, 10-,20-, 30-, and 50-year running mean applied, calculated separately for the raw and dynamicallyadjusted data. The error is calculated as follows. First, the difference in time of emergence using
the full simulations until 2100 and the simulations until 2015 is calculated for each grid point(∆ToE). For a fair comparison, ∆ToE is calculated only where emergence has occurred
according to the 10-year running mean time series ending in 2015. Then, ∆ToE at each grid
point is summed across all CESM LE members, divided by the number of CESM LE membersthat showed emergence at that grid point, and then summed across North American and Europe.
This yields a cumulative error in units of years. Finally, the error for both seasons is normalized
by dividing by the error based on the raw data DJF. Note that for this analysis, the time ofemergence threshold (2 standard deviations during the reference period 1920-1949) is derived
from the concatenated reference periods of all CESM LE members. That is, for each runningmean time series, the threshold used is the same for all CESM LE members.

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Choice of observational dataset
Fig. S3 shows ToE calculated for different SAT datasets. Overall patterns are similar acrossdatasets, although the exact ToE can differ, illustrating observational uncertainty in ToE
estimates. Some differences might be related to how SAT variability is captured due to thedifferent horizontal resolutions of the datasets.

Figure S 3: Same as Figure 1 of the main text, but for two additional SAT datasets MLOST andUniversity of Delaware. Panels for BEST are identical to Figure 1.
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Alternative ToE calculation

Figure S 4: Time of emergence of observed surface air temperature (BEST dataset) calculated asin Mahlstein et al. (2011) for DJF based on (a) raw and (b) dynamically-adjusted data. (c-d)
Same as (a-b), but for JJA. Grey shading indicates where emergence has not yet occurred.

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References
Mahlstein, I., R. Knutti, S. Solomon, and R. W. Portmann, 2011: Early onset of significant local
warming in low latitude countries. Environ. Res. Lett., 6, 34009, doi:10.1088/17489326/6/3/034009.

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