Extended Data Fig. 6: Number of years in each category distribution.

Distribution of the number of years attributed to each category based on random sampling of annual balances of the SMB-D* in the presence of SMB uncertainties (N=5000). The four categories shown are a, ACN + | SVA + and b, ACN – | SVA – (synchronous), as well as c, ACN + | SVA – and d, ACN – | SVA + (asynchronous). The analysis is limited to the periods with maximum correlation (1963–1977; purple bars) and anti-correlation (2004–2018; brown bars) between the mass balances in ACN and SVA. The mean and standard deviation of the number of years belonging to each time period and category is specified with matching colours in the diagram, together with the amount of overlap (%; darker shading of bars) between the early and late period. Without noise in the SMB estimates, each period would be associated with a distinct number of years in each category. With noise dominating the SMB data, the same number of years would belong to each category, impeding a meaningful categorization.