“…Differential equations Ocean-atmosphere C dA/dt = Fd -Fw + Fox -Fmorg -Ftorg + FLIP mol C yr-1 Ocean P balance dP/dt = FPw -FOrgP -FFeP -FCaP mol P yr-1 Ocean U balance dU/dt = Friv -Fanoxic -Fother mol U yr-1 C isotope balance dδA/dt = (Fin × (δin -δA) + FLIP × (δLIP -δA) -Forg × (-Δ))/A ‰ yr-1 U isotope balance dδU/dt = (Friv × (δriv -δU) -Fanoxic × Δanoxic -Fother × Δother)/U Clarkson et al, (2018Clarkson et al, ( , 2019 Stirling et al, (2007,2015) Dahl et al, (2014, 2017) Tissot et al, (2015) Lau et al, (2016, 2017 coral, speleothem, chimney 0.6 M or 1 M sodium acetate, pH > 5 10 % CH 3 COOH rock surface contaminats were leached by 10 % acetic acid surface contaminants were removed by ultrasonic agitation with distilled ethanol diluted HNO 3 Chen et al, (2018a, b) 1M HNO 3 Zhang et al, (2018aZhang et al, ( , b, c, 2019aZhang et al, ( , b, 2020a rock surface washed by MQ-water White et al, (2018) Table A four-columns uranium purification method for carbonate U isotope analysis (Dahl et al, 2014(Dahl et al, , 2017(Dahl et al, , 2019. This purification protocol is intended for extremely low U samples such as brachiopod shells.…”