Fig. 6: Interannual variance of the normalized Metabolic Index (ϕ) is mainly contributed by its oxygen-related components in the Pacific.

a–e Decomposition of interannual variance of the normalized Metabolic Index (\(\phi\); a) into contributions from the dissolved oxygen (\({\phi }_{{{{{{{\rm{O}}}}}}}_{2}}\); b), temperature (\({\phi }_{{{{{{\rm{T}}}}}}}\); c), and their covariance (between \({\phi }_{{{{{{{\rm{O}}}}}}}_{2}}\) and \({\phi }_{{{{{{\rm{T}}}}}}}\); d) components, as well as a residual term (e) at the upper-200 m depth habitat, based on Eq. (7). f–h The variance of the \({\phi }_{{{{{{{\rm{O}}}}}}}_{2}}\) is further decomposed into three components: the oxygen solubility (\({\phi }_{{{{{{{\rm{O}}}}}}}_{2}^{{{{{{\rm{sol}}}}}}}}\); f), apparent oxygen utilization (\({\phi }_{{{{{{\rm{AOU}}}}}}}\); g), and their covariance between \({\phi }_{{{{{{{\rm{O}}}}}}}_{2}^{{{{{{\rm{sol}}}}}}}}\) and \({\phi }_{{{{{{\rm{AOU}}}}}}}\) (h), based on Eq. (8). i, j The covariance term between \({\phi }_{{{{{{{\rm{O}}}}}}}_{2}}\) and \({\phi }_{{{{{{\rm{T}}}}}}}\) is also decomposed into two covariance terms between \({\phi }_{{{{{{{\rm{O}}}}}}}_{2}^{{{{{{\rm{sol}}}}}}}}\) and \({\phi }_{{{{{{\rm{T}}}}}}}\) (i), and between \({\phi }_{{{{{{\rm{AOU}}}}}}}\) and \({\phi }_{{{{{{\rm{T}}}}}}}\) (j), based on Eq. (9). Data to reproduce the figures are shared on Figshare53.