Clarify why CCM and PCMCI fail to detect top-down causality in turbulent boundary layer data

Determine the underlying reason for the failure of Convergent Cross-Mapping (CCM) and Peter and Clark momentary conditional independence (PCMCI) to support top-down interactions between inner-layer and outer-layer streamwise velocity signals in the high-Reynolds-number turbulent boundary layer dataset (Re_tau = 14,750), and ascertain whether the large causality leak quantified by the Synergistic-Unique-Redundant Decomposition (SURD) explains this discrepancy.

Background

The paper analyzes causality between inner-layer and outer-layer streamwise velocity motions in a high-Reynolds-number turbulent boundary layer using SURD and compares results with CCM, PCMCI, CGC, and CTE. SURD indicates dominant top-down unique causality from outer-layer motions to inner-layer motions and quantifies a very large causality leak for both signals.

In the same section, the authors report that CCM and PCMCI do not support the top-down interaction hypothesis in this dataset and explicitly note that the reason for this failure is unclear, speculating it might be related to the high causality leak. Identifying the cause of this discrepancy is important for understanding the limitations of CCM and PCMCI in turbulent flow applications and for interpreting causality under high leak conditions.