http://dx.doi.org/10.1175/JCLI-D-16-0905.s1

McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

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Supplementary materials for ‘An ‘Observational Large Ensemble’ to compare2

observed and modeled temperature trend uncertainty due to internal variabil-

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ity’

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Karen A. McKinnon, Andrew Poppick, Etienne Dunn-Sigouin, and Clara Deser1http://dx.doi.org/10.1175/JCLI-D-16-0905.s1

McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

Figure S1: As in Fig. 1, but using the NASA GISTEMP dataset.

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McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

Figure S2: As in Fig. 5, but using the NASA GISTEMP dataset.

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McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

Figure S3: As in Fig. 1, but using the HadCRUT4 dataset.

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McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

Figure S4: As in Fig. 5, but using the HadCRUT4 dataset.

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McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. DeserFigure S5: As in Fig. 1, but using the Dai et al. (2015) methodology to calculate the forcedtrend. Specifically, the forced trend at a given gridbox is calculated as the regression onto
the global-mean ensemble-mean trend across the NCAR CESM1 Large Ensemble. Internalvariability is estimated as the residual from this forced trend.

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McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

Figure S6: As in Fig. 5, but using the Dai et al. (2015) methodology to calculate theforced trend. For ease of comparison to Fig. 5, the trends shown remain linear in time, buthere the forced trend at a given gridbox is calculated as the regression onto the global-mean
ensemble-mean trend across the NCAR CESM1 Large Ensemble, and internal variability isestimated as the residual from this forced trend estimate. The synthetic ensemble is thencreated by resampling the residual and adding it back to the forced trend estimate.
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http://dx.doi.org/10.1175/JCLI-D-16-0905.s1

McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

Figure S7: As in Fig. 2, but using SLP from the 20CRv2c reanalysis. Because the reanalysis
ends in 2014, the variability is calculated using data from the 49-year period spanning 1966–2014.

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http://dx.doi.org/10.1175/JCLI-D-16-0905.s1

McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

Figure S8: Empirical lag-one year autocorrelation coefficients for detrended DJF temperaturein each member of the NCAR CESM1 Large Ensemble. The numbers in the lower right-handcorner of each subplot indicate the ensemble number; the last five begin at 101 because they
were created on a different supercomputer from the first 35.

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McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. DeserFigure S9: Empirical lag-one year autcorrelation, φ̂, of detrended DJF temperatures in (a)the BEST dataset and (b) the NCAR CESM1 Large Ensemble (LENS). In (b), the autocorrelation is calculated treating all ensemble members from LENS as identically distributed. (c)The difference between the lag-one autocorrelations in the observations and LENS, i.e. (b)(a). Stippling indicates gridboxes that are not significant (see main text). Unlike in Fig. 1,
nearly all gridboxes are found to be insignificant due to the variability of the estimator for
autocorrelation coefficients from short time series (see Fig. S5).
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http://dx.doi.org/10.1175/JCLI-D-16-0905.s1McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

Figure S10: As in Fig. 5, but using the standard deviation inferred from the observations
based on the methods of Thompson et al. (2015). Stippling indicates regions where thedifference between the NCAR CESM1 Large Ensemble and the observations is identified as
insignificant (see main text).

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McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

Figure S11: The bias in estimating the true uncertainty in a trend depending on the covariance structure of the noise and the method used to estimate the uncertainty. Bias ismeasured as the difference between the inferred and true standard deviation of the trend.
The purple bars are for white noise (WN), whereas the green bars are for noise produced
from an AR(1) model with a lag-one year autocorrelation coefficient of 0.5. For white noise,
the use of a bootstrap (BS) with a block size of one leads to less biased and less variable
estimates of the standard error of the trend than when the standard error is inferred fromfitting an AR(1) model. For highly-autocorrelated data (green bars), however, the use of
a bootstrap with an appropriate block size of five leads to a very biased estimate of thestandard error in the trend. As such, the bootstrap is a better choice for data with smallautocorrelation, but should not be used when data is highly-autocorrelated.

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McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. DeserFigure S12: As in Fig. 6, but based upon the actual output from the NCAR CESM1 Large
Ensemble. The numbers in the lower right-hand corner of each subplot indicate the ensemble
number; the last five begin at 101 because they were created on a different supercomputerfrom the first 35.
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McKinnon, K. A., A. Poppick, E. Dunn-Sigouin, and C. Deser

5References

6Dai, A., J. C. Fyfe, S.-P. Xie, and X. Dai, 2015: Decadal modulation of global surface

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temperature by internal climate variability. Nature Climate Change, 5 (6), 555–559.

8Thompson, D. W., E. A. Barnes, C. Deser, W. E. Foust, and A. S. Phillips, 2015: Quantifying

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the role of internal climate variability in future climate trends. Journal of Climate, 28 (16),106443–6456.

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