Auxiliary Material for
Assessing millennial-scale variability during the Holocene: A perspective from the western tropical Pacific
Khider, D. (1,2), Jackson C.S. (1), Stott, L.D. (2)
(1) Institute for Geophysics, University of Texas at Austin
(2) Department of Earth Science, University of Southern California
Paleoceanography

Introduction
The supplementary section of this manuscript contains 1 PDF file detailing the Bayesian calibration of the Mg/Ca and d18O thermometer, 4 additional figures and a supplementary excel file containing age model information for core MD98-2181.

Supplementary Text S1: Details of the Bayesian calculation

Figure S1: Timescales of tropical Pacific Variability. Left. 900-1200 year band-pass record of SST (red) and δ^18O_sw (green). The shaded area corresponds to the 50%, 68%, and 90% confidence level on the band-passed records obtained from the 10,000 Monte Carlo simulations. The vertical lines correspond to times of higher SSTs. Middle. Same as  left for the 1200-2000 years band-pass filter. Right. Same as left for the 2000-3000 years band-pass filter. Note that the y-axis amplitude is the same for all filters to highlight the different amplitude of variability among the different timescales. The uncertainty on the band-pass filters was estimated for the common length of the age model as extrapolation would bias the uncertainty estimates. 

Figure S2: Alternate age model for core MD98-2181 assuming a similar response to solar forcing. The black circles represent the original tie points based on 14C measurements. The solid black line represents the original age model while the dashed lines represent the 95% confidence limit for the age model. The blue (red) circles represent the an alternate age model in which cold (warm) tropical Pacific SST coincides with high insolation. 

Figure S3: Lomb-Scargle periodogram for the records of Oppo et al. [2003], Thornalley et al. [2009] and Hoogaker et al. [2011]. The red lines represent the 50%, 80%, and 95% ensemble of the red noise (AR1) model. The AR1 models were generated using a characteristic timescales inferred from the software TAUEST [Mudelsee, 2002].

Figure S4: Lomb-Scargle periodogram for a red noise model with our best guess for the values of gamma (0.3) and inferred frequency/amplitude of volcanic forcing, capable of reproducing a 0.5°C millennial-scale variability. Prior to spectral analysis, the red noise model was low-pass filtered at 125 years to mimic the effect of bioturbation (we assumed a bioturbation layer of 10cm and a sedimentation rate of 80cm/kyr) and put on the unevenly-spaced MD81 timescale.  

Figure S5: Red Noise Model. Left Panels: No Volcanic Forcing. Right Panels: Volcanic Forcing. Simulated tropical millennial-scale SST variability for various values of the lag-1 auto-correlation coefficients (gamma). For high values of gamma, the simulated response on on par with the variability observed in the MD81 planktonic record.

TableS1: Age model information for core MD98-2181.