Fig. 4: Causality testing.

Cross-map skill vs library size (red lines) showcasing statistically significant convergence levels for the cross-maps from TX to Z500 (a), SD (c), SM (e), and TN (g). Corresponding CCM maps (maximum cross-map skill vs lon/lat coordinates) are shown in (b, d, e, f, h). Statistical significance is assessed with two surrogate models: Ebisuzaki (light gray areas in (a, c, e, g) and bootstrap (dark gray areas in (a, c, e, h) at the 95th significance levels. Marked grid points in the CCM maps represent statistically significant cross maps at that grid point under the Ebisuzaki model. For all CCMs (graph and map), an embedding dimension of E = 5 is used and lags between –4 and 0, consistent with an in-phase causal signal nearly concurrent at monthly resolution.