APPENDIX I. The TALDICE-1 age scale For the TALDICE ice core, we use the TALDICE-1 age scale built by Buiron et al., (2011). Between 20 and 50 ky BP, it relies on the synchronization of the TALDICE methane profile (Buiron et al., 2011), with the Greenland composite one of Blunier et al. (2007) itself on the absolute GICC05 age scale (Svensson et al., 2008). 18 age markers have been defined by wiggle-matching, chosen at the CH4 mid-slope or maximum or minimum depending on the signal shape, with an associated age uncertainty of ± 200 yr for sharp transitions of major DO events. A new inverse dating method has been used (Buiron et al., 2011; Lemieux-Dudon et al., 2009) to calculate the best compromise between the CH4 age markers and a background dating scenario provided by an 1D ice flow model (Parrenin et al., 2007). The model optimises three glaciological entities: the accumulation rate scenario, the thinning function, and the evolution of the Close-Off-Depth expressed in Ice-Equivalent (CODIE), the latter corresponding to the depth where air bubbles are definitively trapped in the surrounding ice. Different a posteriori evaluations of the resulting chronology have been performed. The inverse model provides a confidence interval on the chronology through probabilistic combinations of uncertainties from the model and observations. The largest ice age uncertainty (± 1500 yr) corresponds to the time interval ranging between 20 and 25 ky BP where CH4 variations are too small to allow firm definition of tie points (Figure S1). It then improves and typically lies between 450 and 650 yr during MIS 3. In other words the chronological uncertainty remains smaller than the duration of AIM events, thus enabling to properly study the timing and duration of each single event. II. Calculation of AIM 8 and 12 warming duration 1. Method used for TALDICE, EDML and EDC ice cores For these three ice cores we calculate the first derivative of the isotopic profile after it has been smoothed and resampled at 200 yr (for AIM12 at EDC, resampling is done at 300 yr). The onset and end of each warming phase is determined where the sign of the first derivative changes (Figure S2). The associated age uncertainty is estimated to be ± 300 yr. Results are summarized in Table S1. 2. Quantification of the warming phase in the four other ice cores For the Dome F, Vostok, Siple Dome and Byrd remaining ice cores, our estimate is only indicative because their chronologies are less accurate and in particular not common with the one of EDC, EDML, and TALDICE. The duration of each warming phase has thus been visually defined between the minimum and maximum isotopic data (Figure S3). III. Further climatic simulations To further analyze the atmospheric teleconnections between the tropics and the southern Pacific in our experiments, we have run LGM atmosphere-only GCM simulations in which we have imposed different surface ocean conditions. Figure S4c presents the result of simulations where we use the reference surface ocean conditions for the LGM (LGM-ref) everywhere but in the tropical Atlantic. In this region, the SST of LGM conditions with freshwater were imposed (LGM-fw). Figure S4d shows the result of the symmetric experiment, in which the SST of LGM conditions with freshwater (LGM-fw) were applied everywhere but in the tropical Atlantic. In this region, the reference surface ocean conditions for the LGM (LGM-ref) were imposed. The aim of these 2 experiments is to disentangle the part of the atmospheric response related to surface changes in the tropical Atlantic and the part related to surface changes outside this region. Comparison of figures S4c and S4d shows that the two northernmost centers of action located over the southeast Pacific are a constant feature in both simulations, but with a strongest expression when freshwater SST conditions are not applied on the tropical Atlantic. This suggests that the tropical Atlantic ITCZ and SST changes are able to generate a stationary wave reaching the southeast Pacific, which can be amplified by local interactions with the surface ocean. Bibliography Blunier, T., Spahni, R., Barnola, J.M., Chappellaz, J., Loulergue, L., Schwander, J., 2007. Synchronization of ice core records via atmospheric gases. Climate of the Past 3, 325-330. Buiron, D., Chappellaz, J., Stenni, B., Frezzotti, M., Baumgartner, M., Capron, E., Landais, A., Lemieux-Dudon, B., Masson-Delmotte, V., Montagnat, M., Parrenin, F., Schilt, A., 2011. TALDICE-1 age scale of the Talos Dome deep ice core, East Antarctica. Climate of the Past 7, 1-16. Lemieux-Dudon, B., Parrenin, F. and Blayo, E., 2009. A probabilistic method to construct a common and optimal chronology for an ice core, Hondoh, Hokkaido University Collection of Scholarly and Academic Papers (Ed.). Parrenin, F., Dreyfus, G., Durand, G., Fujita, S., Gagliardini, O., Gillet, F., Jouzel, J., Kawamura, K., Lhomme, N., Masson-Delmotte, V., 2007. 1-D-ice flow modelling at EPICA Dome C and Dome Fuji, East Antarctica, Climate of the Past 3, 243–59. Svensson, A., Andersen, K. K., Bigler, M., Clausen, H. B., Dahl-Jensen, D., Davies, S. M., Johnsen, S. J., Muscheler, R., Parrenin, F., Rasmussen, S.O., 2008. A 60 000 year Greenland stratigraphic ice core chronology. Climate of the Past 4, 47–57. Figure S1: TALDICE-1 age scale between 20 and 50ky BP. Upper two curves: methane profiles of the Greenland Composite (black line) and TALDICE (blue line), on the GICC05 age scale. Black diamonds indicate the tie points. Middle curve: TALDICE-1 ice age uncertainty estimated with the inverse model of Lemieux-Dudon et al. (2009). Lower two curves: age/depth relationship for the ice (purple line) and for the gas (blue line), including the CH4 markers (black diamonds). Figure S2: From top to bottom and from left to right: TALDICE, EDML and EDC AIM 8 and 12. In each graph, the upper record corresponds to the isotopic signal (black line), with running average (blue line) followed by regular resampling (pink line). The black line below is the first derivative of the resampled isotopic data. Purple shading highlights the warming periods. The warming phase duration is written. Orange and blue shadings correspond to warming and cooling phases respectively. Note that the smoothing process looses part of the real amplitude. Figure S3: Determination of the warming phase duration for both AIM 8 and 12 according to the isotopic signal of each Antarctic ice cores for. The records are represented on relative age scales based on official chronologies of each ice core, where the origin corresponds to the isotopic maximum (dashed line). Black arrows point the beginning of the southern warming observed in each signal. Figure S4: Teleconnection from the tropical Atlantic to the South East Pacific and Antarctica. Results from the Atmosphere-only GCM, using different surface ocean forcing. All fields are shown for JuneJuly-August. 4a: reference run LGM-refatm, using surface ocean conditions from LGM-ref: SAT (°C, shading) and 200 hPa stream function (106 m2/s, contours). Other panels: anomalies in SAT (°C, shading) and stream function (106 m2/s, contours, dashed for zero line, dotted for negative values) for the FWglobal SST experiment (4b), the FW-TA-SST experiment (4c) and the FW-out-TA-SSTexperiment (4d). Table S1: Ages of onset and end of both AIM 8 and 12 warming in TALDICE, EDC, and EDML ice cores. Table S1: Ages of onset and end of both AIM 8 and 12 warming in TALDICE, EDC, and EDML ice cores. AIM 8 Warming onset (yr BP) Warming end (yr BP) Total duration (yr) TALDICE 39 850 38 200 1 650 EDC 39 750 38 150 1 600 EDML 39 900 39 050 850 AIM 12 Warming onset (yr BP) Warming end (yr BP) Total duration (yr) TALDICE 48 650 46 850 1 800 EDC 48 250 46 670 1 600 EDML 48 470 47 500 970