Fig. S1. Plots of jack-knife inferred summer SSSs (psu) using MAT (four analogues) against observed summer SSSs (psu) (A) and of the differences between jack-knife inferred and observed summer SSSs against observed summer SSSs (psu) (B). The inferred summer SSSs are always over-estimated when observed summer SSSs are lower than 32.5 (psu) and under-estimated when observed summer SSSs are higher than 33.8 (psu).

Table S1. Locations of the surface sediment diatom samples. The data from deep seas were mainly from World Ocean database 1998 (the NOAA National Oceanographic Data Centre) and data from the Chinese coasts and in the shallow water areas are mainly from Guo et al. (2004), who compiled the data during 1982–2002.

Table S2. Test of seven numerical reconstruction methods. Seven numerical reconstruction methods were tested, including weighted averaging (WA), weighted averaging with tolerance down-weighting (WA(tol)), partial least squares (PLS), weighted averaging partial least squares (WA-PLS), and modern analogue technique (MAT). Both inverse and classical deshrinking regression were used in the WA and WA(tol) reconstruction procedures (Juggins 2007). The results are presented as root-mean squared error of prediction based on the leave-one out jack-knifing (RMSEP(Jack)) test, maximum bias (Max_Bias(Jack)), and coefficient of determination between observed and predicted values r2(Jack).

Table S3. Calibrated ages of data points used for the age model of core 17940. Linear interpolation has been used between data points.

Table S4. Diatom-based summer SSS data from core 17940.

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