Supplementary Figure 1. Comparison of the cumulative

Supplementary Figure 1. Comparison of the cumulative Photosynthetically Active
Radiation (PAR, Einsteins m-2 day-1 ) received in the 2 months prior to bleaching in
2005-2006 between regions with no (0% of corals bleached), low (1-10%), medium (>1030%) and high (>30%) bleaching (H=0.387, df=3, P=0.943).
Supplementary Figure 2. The M-SSA eigenvalue spectra with window widths (M) of
65, 90 and 120.
Supplementary Figure 3. Cross wavelet (Top) and wavelet coherence (Bottom)
analyses between principal components (PCs) 2 and 3, indicating times and frequencies
over which the two PCs display high common power and coherence, and the phase
relationship between them. Arrows straight up or down indicate the two are out-of-phase
by 90°.
Supplementary Figure 4: The low-frequency (dotted) and high-frequency (solid)
reconstructed components from M-SSA of the nine detrended δ18O and Sr/Ca records.