Methods are as per "Southward Shift of the Pacific ITCZ During the Holocene" in Paleoceanography and Paleoclimatology, volume 33, pages 1383-1395 (Sachs et al. 2018).

Sediment core PTLN‐PC1 was collected September 2013 in sequential 1m sections using a 5cm‐diameter Colinvaux‐Vohnout Livingstone‐type rod‐operated piston corer (Geocore, Columbus, Ohio). Each section was sealed in the field and refrigerated at 4 °C until core splitting and subsampling.

Sample ages were linearly interpolated from calibrated 14C dates (see dataset "T Lake PC1 Chronology") using the Clam 2.2 (Blaauw, 2010) software package.

Sediment subsamples were transferred to combusted glass vials, frozen, then freeze dried. Lipids were extracted with 10% methanol in dichloromethane on an accelerated solvent extractor (ASE 200; Dionex) at 100°C and 1500 psi with three 5‐min static cycles. Lipid extracts were saponified using 2:1 1N KOH in methanol:water at 70°C overnight. Saponified extracts were acidified to pH ~1 with HCl, neutral lipids extracted from the water/methanol phase with hexane, and the hexane extracts washed with water. Lipid extracts were acetylated at 70°C for 30 min in a mixture of 20 μl acetic anhydride of known isotopic composition and 20 μl pyridine. Sterol acetates were then isolated via preparative high‐performance liquid chromatography as per the methods in Nelson and Sachs (2013, 2014). Extracts were taken up in 25 μl of 2:1 dichloromethane:methanol and the complete volume injected onto an Agilent 1100 high‐performance liquid chromatography system equipped with a Zorbax Eclipse XDB C18 column; after an initial elution of polar compounds in 5:95 methanol:acetonitrile, sterol acetates were eluted with an isocratic mobile phase of 5:10:85 methanol:ethyl acetate:acetonitrile. Aliquots (5%) of each sample were injected on an Agilent 6890N GC with flame ionization detector and PTV inlet, equipped with an Agilent VF‐17 ms column (60 m × 0.32 mm × 0.25 μm), in splitless mode at 300°C using helium carrier gas at 1.5 ml/min. The initial oven temperature was 110°C, followed by a ramp to 320°C at 5°C/min, and was then held for 20 min. Detector response was determined via an α‐cholestane internal standard. Dinosterol fluxes were calculated from the product of dinosterol concentration per gram dry weight of sediment, the linear sediment accumulation rate, and the dry bulk density of sediment. Uncertainty in dinosterol fluxes is conservatively assumed to be 25%.

Hydrogen isotopes of dinosterol were measured via a modification of the procedures outlined in Nelson and Sachs (2013). Gas chromatography was conducted using a Thermo Trace GC Ultra equipped with a GC‐TC interface. Samples were injected into the 330°C inlet in splitless mode, with a 1.1 ml/min helium carrier flow through a VF‐17 ms column (60 m × 0.25 mm × 0.25 μm). The oven temperature was held at 120°C for the 2‐min splitless time, increased to 260 °C at 20 °C/min, increased to 325°C at 1°C/min, and held for 10 min. The pyrolysis interface was operated at 1400°C, and the sample hydrogen admitted to a Thermo Delta V Plus isotope ratio mass spectrometer via open split.

Isotope measurements are given as δ²>H values relative to Vienna Standard Mean Ocean Water and calibrated via external isotope standards (Arndt Schimmelmann, Indiana University). Secondary corrections were determined based on time‐in‐sequence, retention time, and peak area, as necessary, on a sequence‐by‐sequence basis. Each sample analyzed at least three times. δ²H values were corrected for added acetate hydrogen (−124.4‰ ± 8.1) via mass balance. Uncertainty is given as the standard deviation of these replicate analyses and uncertainty in the value of the known acetate, propagated through the mass balance calculation.