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1 Supplementary Material to: Weakening of Tropical Pacific Atmospheric Circulation due to Anthropogenic Forcing Gabriel A. Vecchi*, Brian J. Soden§, Andrew T. Wittenberg◊, Isaac M. Held◊, Ants Leetmaa◊, Matthew J. Harrison◊ *University Corporation for Atmospheric Research Visiting Scientist Program at NOAA/GFDL, Princeton, NJ, USA. § Rosenstiel School for Marine and Atmospheric Sciences, University of Miami, Miami, FL, USA. ◊ NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, NJ, USA Tests for Statistical Significance: In both the individual model ensemble members and in the observational record, there is substantial decadal variability of SLP (the difference in sea level pressure anomalies averaged in the region (80°E-160°E,5°S-5°N) with those averaged in the region (160°W-80°W,5°S-5°N), which serves as a useful proxy for zonal winds across the equatorial Pacific) arising from processes internal to the coupled system (i.e. not forced by radiative changes, natural or anthropogenic); this variability is often larger than that coming from the long-term trend (see Supp. Fig. 1). The statistical significance of long-term trends should be computed against trends that may arise in the absence of long-term forcing. A 2,000-year integration with invariant radiative conditions from the 1860s serves as a Control to the historical experiments, and can be used compute statistical 2 significance estimates. For individual ensemble members, two-sided statistical significance from a zero trend for linear least squared trends computed from N-years of data is estimated from the statistical distribution of the (2000-N+1) “N”-year trends from the 2,000-year Control integration. The p=0.05 range is computed as that for which only 5% of the trends from the Control integration have an amplitude larger than the extremes of the range, after removing the long-term trend of the Control integration (long term trend in Control is an order of magnitude smaller than forced trend in historical runs). The apparent trends in SLP that arise from internal variability in an individual realization can be substantial, especially for short records (Supp. Fig. 2). The strong decadal variations make estimating the long-term trend in SLP from a record shorter than about 100 years problematic. For model records as long as 100-years there is at least a 5% chance that individual ensemble members could show nominally positive trends, even though the long-term forced trend is negative. However, for the record lengths available, the modelled and observed long-term trends in SLP are significantly different from zero, at p=0.05; and all show a weakening of SLP. A Bootstrap method (with 100,000 Bootstrap samples) is applied to the Control integration to estimate the significance of the ensemble-means of 3- and 5-members. Three (and five) member ensembles are created by sampling from the entire population of “N”-year trends in the Control simulation, with replacement, 100,000 times. Estimates of statistical significance of ensemble-mean trends are computed from the statistical distribution of these artificial ensemble-means. Inter-model Comparison: 3 Many institutions around the World have generated model runs similar to the ones described here for the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC-AR4), and some of the output from these models is available to us (provided by U.S. Department of Energy Program for Climate Model Diagnosis and Intercomparison; data available at https://esg.llnl.gov:8443/home/publicHomePage.do ). With this data we can test the inter-model robustness of our results. SLP trends from 19 models submitted to the IPCC-AR4 are explored here, which provide a total 67 ensemble members of historical simulations (19th through 20th Century). We have excluded from analysis two models that have a large-scale time-averaged zonal SLP gradient of the opposite sign as that observed. As described above, the Control simulations using pre-industrial (mid-19th Century) radiative and land use forcing, allow the estimation of the statistical significance of observed SLP trends (removing the linear trend over the entire record for each control run, since some models exhibited substantial drift). Shown in Suppl. Fig. 3 are the two-sided p=0.05 range on zero trend of different lengths from the 19 Control simulations (only the GFDL-CM2.1 GCM is identified). The GFDL-CM2.1 estimates on statistical significance on SLP trends are among the more conservative. Further, each of the observed long-term SLP trends is significantly different from zero at p=0.05, for all of the IPCC-AR4 GCMs. Based on all of the models submitted to the IPCC-AR4, the observed reduction in SLP since the mid-19th Century is statistically significant at p=0.05. It should be noted that the length of the Control simulation for each of the models differs (the range is between 250 and 940 years for the models explored here). The utility of having a 2,000 year Control simulation with GFDLCM2.1 to estimate significance of fairly long trends (>100 years) is highlighted by the second model from the right in Suppl. Fig. 3, for which the range for 152-year trends is larger than that for 140-year trends – this counterintuitive finding is likely spurious and 4 due to the short record (351 years) relative to the trends being estimated (140 and 152 years). In agreement with the observed trend, a reduction in SLP since the 19th Century is the consensus of the 67 historical simulations in the IPCC-AR4 database (Suppl. Fig. 4). The duration of the simulations of historical climate also vary (the range is between the period 1890-2000 – 110 years - and the period 1849-2000 - 152 years), and aspects of the radiative forcing differ between the various models; here, trends are computed for either the period 1861-2000 or the entire available record from each model (whichever is shorter). Significance estimates are computed for trends of corresponding length for each model; the model that shows very large error-bars (third from the right) is a set of experiments that are each only 110 years long. The long-term trend of each Control simulation is removed. There is substantial spread in the linear trends across the various ensemble members, however there is only one ensemble member that exhibits a significantly positive trend, contrasted with 12 ensemble members showing a significantly (at p=0.05) negative trend. Further, 66% of the ensemble members exhibit a nominally negative trend, and 8 of 19 models have at least one ensemble member with significant weakening of SLP. Though GFDL-CM2.1 exhibits the strongest and one of the most consistent responses in this particular index of the Walker Circulation, the reduction of SLP since the mid-19th Century is the consensus of the IPCC-AR4 simulations. Acknowledgements GAV supported by the Visiting Scientist Program at the NOAA/GFDL administered by UCAR. We are extremely grateful to the model development teams at GFDL. Thanks to A.E. Johansson, M.P. Vecchi, T. Knutson, T. Delworth, J. Russell and three anonymous reviewers for comments and suggestions. 5 Correspondence and requests for materials should be addressed to G.A.V. (e-mail: [email protected]). Supplementary Figure 1: Evolution of SLP from GFDL-CM2.1 historical integrations. Five-year running-mean SLP for: five-member ensemble mean in upper left panel, five individual ensemble members in other panels. In each panel, the linear-trend in SLP corresponding to each time-series is shown. Note the substantial decadal variability in each ensemble member, and the impact of the decadal variability on the computed trend. Supplementary Figure 2: Statistical significance limits of single-member SLP trends of different lengths, estimated from the 2,000-year control GFDL-CM2.1 integration. Shading indicates the two-sided p-value of a trend of a particular value (vertical axes) computed from a SLP record of a particular length (horizontal axes). Thick black line shows the 5-member ensemble-mean trend from the all-forcing GCM experiment (the model trend to be detected), a vertical dash indicates the length of the trends from the GCM. Symbols show the observed trends from: Kaplan29 (star symbol), Hadley28 (circle symbol), Kaplan29/Hadley28/NCEP27 blend (square symbol). Supplementary Figure 3: Two-sided confidence intervals on zero SLP trend from pre-Industrial IPCC-AR4 GCM control experiments. Bars show the negative side of the two-sided p=0.05 range on single member SLP trends of lengths corresponding to those of the three observational records. Dashed lines show the linear trends computed from the three observational datasets: Kaplan29 (1854-1992), Hadley Centre28 (1871-1998), and a blend of Hadley28 and Kaplan29, extended into 2005 using the NCEP gridded27 ship data (18542005). Units are Pa.year-1. Number of Control years available indicated inside each column. 6 Supplementary Figure 4: Linear-trends of SLP from IPCC-AR4 models. Linear trends of SLP for the 19th-through-20th Century simulations of 67 historical runs of 19 models in the IPCC-AR4 database. Dots show trend value for each ensemble member, over either the period 1861-2000 or (if the available record was shorter) the entire model record. Bars indicate the p=0.05 limits on singleensemble member trends from a record of length corresponding to that of each model. Only the model used in this study is identified. Units are Pa.year-1. Years over which model trends were computed are indicated over each column. Supplementary Figure 5: Modelled changes in equatorial Pacific oceanic currents. GFDL-CM2.1 modelled linear trends over 1861-2000 in nearequatorial (a) zonal current (10-2 m s-1 year-1), and (b) vertical currents (10-2 m day-1 year-1), from the five-member ensemble-mean all forcing experiment. Positive zonal currents are west-to-east, positive vertical currents are upward (upwelling). Note the reduction of in surface zonal currents, the upward shift of subsurface zonal currents, and the upward shift and reduction of upward (positive) vertical velocities. Supplementary Figure 6: Evolution of equatorial Pacific thermocline depth and slope. Model and observed anomalies in mean east-west slope of equatorial Pacific thermocline (blue line) and equatorial Pacific zonal-mean thermocline depth (black line). Left panel is from the ensemble-mean all-forcing GCM experiment, five-year running mean. Right panel is from an observational estimate30, thick lines are five-year running means and thin lines are annualmeans. Thermocline slope defined as the thermocline depth averaged (140°E180°E, 2°S-2°N) minus that averaged (130°W-90°W, 2°S-2°N). Thermocline defined as the location of the maximum vertical temperature gradient.