Fig. 4: Bayesian Networks (BN) of direct and mediated drivers of surface runoff efficiency (REt).

PC1 BN depicting hypothesized and learned dependencies influencing REt in the Upper Colorado River Basin with results applied to (a) DAG for the full period (1906–‍2020); (b) DAG for the NDVI – SWE period (1983–‍2020). The DAGs show the full postulated BNs. Non-significant arcs (α > 0.05) are shown using dashed lines, significant arcs (0.01 <α ≤ 0.05) are shown using thin solid lines, and highly significant arcs (α ≤ 0.01) are shown using thick solid lines. Arrow direction indicates pre-specified directions of causality of all the variables based on physically plausible hypotheses. Bayesian Information Criterion (BIC) scores and p-values indicating model fit and arc significance are provided in Supplementary Tables S8 and S9. Supplementary Fig. S10 presents the DAG analogous to Fig. 4b, except with TMAMJt directing an arc to SWEMAXt. The SWEMAXt to TMAMJt arc shown here is more significant (p = 3.73e-06) than the TMAMJt to SWEMAXt arc (p = 3.62e-02) shown in Supplementary Fig. S10.