Fig. 4: Domain-wide potential predictability of surface pH anomalies.

a Anomaly correlation coefficients (ACCs) for 10 lead years for (blue) the Community Earth System Decadal Prediction Large Ensemble (CESM-DPLE), (black) a persistence forecast from the reconstruction, and (gray) the uninitialized CESM Large Ensemble (CESM-LE) ensemble mean. Filled circles denote statistically significant positive correlations at the 95% level using a t test. An effective sample size is used in the t test to account for autocorrelation in the two time series being correlated. The critical value required for a statistically significant correlation ranges from 0.26 to 0.32 across leads, as computed by inverting the t statistic formula. Black and gray asterisks indicate significant predictability over persistence and the uninitialized forecast at the 95% level using a z test, respectively. b As in a, but for normalized mean absolute error (NMAE) and without significance testing. Values below (above) one indicate that the forecast falls within (outside of) the interannual variability of surface pH in the reconstruction. c Scaled predictability in common pH units (see Linear Decomposition in Methods) of (black) sea surface salinity (SSS), (teal) sea surface temperature (SST), (gold) salinity-normalized alkalinity (sALK), and (red) salinity-normalized dissolved inorganic carbon (sDIC).