Tree-ring δ13C of Pinus koraiensis is a better tracer of gross primary productivity than tree-ring width index in an old-growth temperate forest

•The correlation between tree-ring δ13C and ecosystem GPP was assessed in a forest.•Early-wood and late-wood δ13C were analyzed separately.•Tree-ring δ13C positively correlated with forest GPP of the current-year.•Early- and late-wood δ13C traced GPP seasonally and annually.