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1 Geophysical Research Letters Supporting Information for Predictability of the Recent Slowdown and Subsequent Recovery of Large-Scale Surface Warming using Statistical Methods Michael E. Mann 1, Byron A. Steinman 2 *, Sonya K. Miller 1, Leela M. Frankcombe 3, Matthew H. England 3, Anson H. Cheung 4 1 Department of Meteorology and Earth and Environmental Systems Institute, Pennsylvania State University, University Park, PA, USA. 2 Department of Earth and Environmental Sciences and Large Lakes Observatory, University of Minnesota Duluth, Duluth, MN, USA. 3 ARC Centre of Excellence for Climate System Science, University of New South Wales, New South Wales 2052, Australia 4 Department of Geosciences, The University of Arizona, Tucson, AZ, USA *Correspondence author: bsteinma@d.umn.edu Contents of this file Text S1 Figures S1 to S3 Table S1 Introduction This supplemental information section includes text, figures, and tables that support the methods discussed in the main text. Text S1. Observation and Model Temperature Series We defined the North Atlantic (NA) and North Pacific (NP) SST series by target regions spanning the equator to 60 degrees north over the Atlantic ( E) and Pacific ( E) oceans (i.e. the areal mean over all SST gridboxes in each basin), respectively. We used GISTEMP [Hansen et al., 2010] to define the observational Northern Hemisphere (NH) mean (land+ocean) series. The observational SST estimates were defined as the mean of the HadISST [Cowtan and Way, 2014], NOAA ERSST [Rayner, 2003; Smith et al., 2008], and Kaplan [Kaplan et al., 1998] products. The CMIP5 historical multimodel ensemble (see Table S1) runs were used to calculate corresponding ensemble mean NA, NP and NH series (shown in Fig. S1). The multimodel mean 1

2 series were obtained by 1) calculating a mean series for each model realization for the respective target regions, 2) mean centering the series for each realization, 3) averaging the realizations for each model to produce a model mean, then 4) averaging the model means. This ensured that each model was equally represented in the ensemble mean and that models with a large number of realizations (e.g. GISSE2-R/H) did not have a relatively larger influence on the CMIP5-All temperature series. All CMIP5 model simulation data were re-gridded at 5 spatial resolution prior to analysis. For the NH mean, to allow direct comparison with instrumental NH mean series, which are based on Surface Air Temperature (SAT) over land and Sea Surface Temperature (SST) over ocean regions, we calculated the mean (latitude weighted) SAT over land by masking ocean grid cells, calculated the mean (latitude weighted) SST over the ocean, and combined the two series using a weighted average based on a land coverage value of 39% and an ocean coverage value of 61% for the northern hemisphere. The CMIP5 series we used [Steinman et al., 2015] terminate in 2005 and were extended through 2014 prior to analysis based on each of two different alternative methods (see Forecasts of Forced Component sub-section below). Target Region Regression Method To calculate the AMO, PMO, and NMO we used the method described by [Steinman et al., 2015]: We first (1) regressed the observed mean temperature series onto the model derived estimate of the forced component to allow for differences in amplitude of forced responses between the observations and multimodel mean. Using the preferred (see Forecasts of Forced Component sub-section below) second of the two extension approaches, we obtain for the NH series, a scaling coefficient and one sigma uncertainty range of b = / , while for the NA series we obtain b = / Thus, the CMIP5 multimodel mean response to forcings is consistent with the observations in both cases. By contrast, we obtain for the NP series b = / , suggesting that the amplitude of the CMIP5 multimodel mean response is slightly too great for the North Pacific, as commented upon previously by [Steinman et al., 2015]. We next (2) subtracted the forced component estimated in step (1) from the observational series, to isolate the internal variability component. While [Steinman et al., 2015] used a fixed 40 year smoothing timescale to define the NMO/PMO/AMO series, in our case we employ a smoothing timescale/frequency that is specific to the particular hindcast experiment results. As discussed in the main article, we select as the optimal smoothing frequency that yields minimum accumulated RMSE in the hindcast experiments. This timescale, in practice, varies from 20 years to 50 years in our experiments and depends on the results of the particular hindcast. For simplicity, therefore, we use a common, fixed (f= cycle/year, i.e. 20 year period) smoothing timescale for the purpose of depicting the NMO/PMO/AMO time series shown in Figure 1 of the main article. The uncertainties in b are used to estimate corresponding uncertainties in the estimated forced series (and associated hindcasts and forecasts). Forecasts of Forced Component We used two different schemes for forecasting the forced signal. In the first scheme, we calculate the linear trend in the forced component over the most recent climatological (20 year) interval, and simply projected that trend forward in time. 2

3 In the second scheme, we use a more elaborate and better performing procedure. Recognizing the tendency of the first procedure to yield a systematic (downward) bias in the forced component when the initial year of the hindcast lies within the (artificially cool) recovery period that follows an explosive volcanic eruption (see Fig. 2ab in main article), we use a procedure that is insensitive to volcanic impacts. This procedure involves using the CMIP5 anthropogenic-only forcing experiments (Table S1) to define an anthropogenic-only multimodel mean temperature series. The same scaling coefficient calculated using the all-forcing series from the target regression approach (see Target Region Regression Method sub-section above) is applied to the anthropogenic-only series. However, the series is re-centered to have the same mean as the allforcing series over the volcanic-free interval of to yield an estimate of the temperature trajectory that would be expected in the absence of volcanic forcing events. As is evident from Fig. 2 of the main article (and Fig. S1 below, which compares the all-forcing, anthropogenic-only and natural-only forced series), this scheme yields an unbiased estimate of the long-term forced component. As a result, predictions based on the simple forward projection of this series (see Fig. 2 of main article) yield a much more skillful forecast of the actual future forced temperature response. Note that for consistency, the same scheme used to forecast the forced component in a particular set of hindcast experiments was also used to extend the (scaled) CMIP5 multimodel mean series (which end in 2005) through the 2014 boundary. [Steinman et al., 2015] used scheme #1 to extend the CMIP5 temperature series through Our present analysis finds scheme #2 to be preferable. This difference in choice (along with the inclusion of the two additional years 2013 and 2014) explains the differences near the ends of the NMO/PMO/AMO time series in this article (see Figure 1) and in Steinman et al. [2015]. Forecasts of Oscillatory Signal Forecasts of the oscillatory signal (the NMO/PMO/AMO series) were made by fitting a simple 2 nd order autoregressive (AR2) time series model to the historical NMO/PMO/AMO series, and using the resulting model coefficients to generate a forward prediction, using information about the phase and amplitude of the oscillatory signal. Such a model is favored by parsimony considerations. It is the lowest order AR model that can (through the combination of a positive lag-one coefficient and a negative lag-two coefficient), describe an oscillatory signal and it is less prone to statistical over-fitting than a more elaborate (i.e. higher-order ARMA) model. Skill Assessment We compared the RMSE of our forecasts (Fig. 2c-f and Fig. 5ab of main article and Figs. S2-S3 below) to that obtained for several different alternative null forecasts, including standard climatological and simple persistence forecasts. For the former, we used a climatology defined by the mean of the most recent 20 years leading up to the time of the forecast. For the latter, we simply assume a constant mean value equal to the most recent annual value at the time of the forecast. In addition, we calculated a damped persistence forecast, wherein the forecast decays exponentially from its current value to the climatological mean value (defined as described above by the most recent 20 year period) with an e-folding timescale defined by the lag-one autocorrelation coefficient of the series being forecast. Finally, we considered an extended persistence forecast, wherein the forecast predicts the mean over the past k values, where k is the length of the forecast being made. In the limiting case k=1, this forecast becomes equal to our simple persistence forecast, while for the case k=20 it would become equal to our climatological 3

4 forecast. If our optimal forecasting scheme exceeds all null forecasts at a given lead time, it is deemed skillful for that lead time. Energy Balance Model Simulations We employed a simple zero-dimensional Energy Balance Model ( EBM ) of the form C dt/dt = S(1-α)/4 + F GHG -A-B T + w(t) to model the response of the Northern Hemisphere mean temperature to historical natural and anthropogenic radiative forcing as in other recent studies [Mann, 2014; Mann et al, 2014]. Here T is the global-average temperature of Earth s surface (approximated as the surface of a 70 m deep mixed layer ocean covering 70% of Earth s surface area), C=2.08 x 10 8 J K -1 m -2 is an effective heat capacity that accounts for the thermal inertia of the mixed layer ocean, but does not allow for heat exchange with the deep ocean, S 1370 Wm -2 is the solar constant, and α is the effective surface albedo. F GHG is the radiative forcing by greenhouse gases. w(t) represents random weather effects, and was set to zero to analyze the pure radiatively forced response. The linear gray body approximation LW=A+B T was used to model outgoing longwave radiation in a way that accounts for the greenhouse effect. The choice A=221.3 WK -1 m -2 and B=1.25 Wm -2 yields a realistic pre-industrial global mean temperature T=14.8 o C and an equilibrium climate sensitivity (ECS) of ΔT 2xCO2 =3.0 o C, consistent with mid-range IPCC [2007] estimates. The model was driven with estimated annual natural (solar and volcanic) and anthropogenic (greenhouse gas and sulphate aerosol) forcing for the Northern Hemisphere over AD as in Mann [2014]. Runs were performed both with and without the volcanic forcing of the 1991 Mt. Pinatubo eruption. Additional References Cowtan, K., and R. G. Way (2014), Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends, Q. J. R. Meteorol. Soc., 140(683), , doi:1002/qj Hansen, J., R. Ruedy, M. Sato, and K. Lo (2010), Global surface temperature change, Rev. Geophys., 48, doi:1029/2010rg IPCC (2007) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M.Tignor and H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. Kaplan, A., M. A. Cane, A. C. Clement, M. B. Blumenthal, B. Rajagopalan, and C. Bottoraley (1998), Analyses of global sea surface temperature , J. Geophys. Res., 103, 18,567 18,589, doi:1029/97jc Mann, M.E., Steinman, B.A., Miller, S.K. (2014), On Forced Temperature Changes, Internal Variability and the AMO, Geophys. Res. Lett. ( Frontier article), 41, , doi:1002/2014gl Mann, M.E. (2014) False Hope: The rate of global temperature rise may have hit a plateau, but a climate crisis still looms in the near future, Scientific American, p , April Rayner, N. A. (2003), Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century, J. Geophys. Res., 108(D14), 4407, doi:1029/2002jd

5 Smith, T. M., R. W. Reynolds, T. C. Peterson, and J. Lawrimore (2008), Improvements to NOAA s Historical Merged Land Ocean Surface Temperature Analysis ( ), J. Clim., 21, , doi:1175/2007jcli210. Steinman, B. A., M. E. Mann, and S. K. Miller (2015), Atlantic and Pacific multidecadal oscillations and Northern Hemisphere temperatures., Science, 347(6225), , doi:1126/science

6 a Temperature Anomaly ( o C) Year b Temperature Anomaly ( o C) Year c Temperature Anomaly ( o C) Year Figure S1. Observed vs. modeled temperature series for (a) NH, (b) NA, and (c) NP. Observations (black) are shown along with scaled CMIP5 modeled series (red) using both approaches for extending the model series through 2014 (solid=approach #2, dashed=approach #1). Anthropogenic (green) and natural (magenta) forced responses (defined as the difference between the full-forced and anthropogenic-only forced series) are both shown. Series are centered relative to their long-term mean. Note that the scaling of the two CMIP5 series is slightly different in the two approaches since scaling in the target region regression method is determined based on the full (i.e. in this case ) time interval, and the two series differ over the sub-interval. 6

7 4 2 a. Prediction Forced model Lower error bound Climatology Damped persistence Persistence Extended persistence 4 2 b Lead (years) c Lead (years) d Lead (years) Lead (years) e. f Frequency (cycles/yr) g. h Frequency (cycles/yr) Frequency (cycles/yr) Frequency (cycles/yr) Figure S2. Forecast skill for regional temperature predictions. Panels a-d indicate RMSE for optimal total forecast vs. lead relative to null forecasts (i.e. similar to Fig. 2cd of main article), using the two different schemes for predicting forced component: projection of climatological total forced trend (left) and projection of estimated anthropogenic-only trend (right). Results are shown for both NP (a-b) and NA (c-d) regions. Panels e-h indicate RMSE for total forecast relative to null forecasts (i.e. similar to Fig 2ef of main article) as a function of the frequency of smoothing of the residual series for 14 year lead predictions. Conventions are as in Fig. 2 of the main article. 7

8 5 a. b. 5 prediction persistence extended persistence climatology damped persistence 5 forced model model diff Hindcast Year Hindcast Year Figure. S3. RMSE of optimal NMO forecast vs. other forecasts as a function of hindcast year using the two different schemes for predicting forced component: projection of climatological total forced trend (left) and projection of estimated anthropogenic-only trend (right). 8

9 Model Number of Realizations Length of run Start year AD End Year AD 1 st and 2 nd aerosol indirect effects All Forcing Simulations GISS-E2-R N GISS-E2-H N CNRM-CM N CSIRO-Mk Y GFDL-CM N HadCM N CCSM N IPSL-CM5A-LR N CanESM N GFDL-CM3* Y HadGEM2-ES Y MIROC Y MRI-CGCM Y ACCESS Y bcc-csm N bcc-csm1-1m N CESM1-CAM Y CESM1-FASTCHEM N FIO-ESM N IPSL-CM5A-MR N MPI-ESM-MR** N MIROC-ESM Y MPI-ESM-LR* N NorESM1-M Y MPI-ESM-P** N CESM1-WACCM N HadGEM2-CC Y HadGEM2-AO** Y ACCESS Y BNU-ESM N CESM1-BGC N CMCC-CESM N CMCC-CM N CMCC-CMS N CNRM-CM N GFDL-ESM2G N GFDL-ESM2M N GISS-E2-H-CC N GISS-E2-R-CC N INM-CM N IPSL-CM5B-LR N MRI-ESM Y FGOALS-g2** Y NorESM1-ME Y Anthropogenic Simulations CNRM-CM N GISS-E2-H N GISS-E2-R N CCSM N CESM1-CAM Y GFDL-CM Y IPSL-CM5A-LR N GFDL-ESM2M N *One realization from this model was not included in the SAT/SST model means. **This model was not included in the SAT/SST model means. Table S1. CMIP5 Climate Model Simulations 9