Pankaj Dey,
Hydrologist

Complexity sits between the two extremes of perfect order and pure randomness, and across the MOPEX catchments it is far from arbitrary. It declines systematically as catchments become more arid, and it rises hand-in-hand with the Hurst exponent — the classical marker of long-term persistence, or memory. Wetter, snow-influenced basins (fₛ > 0.15) produce more symmetric flow distributions and richer, more persistent dynamics, while arid basins yield sharply skewed, intermittent flows with weaker structure. Read together, aridity, memory, and the shape of the flow distribution describe each catchment as a complex system whose signature is written into its streamflow.

Because streamflow carries memory, standard causal-detection tools can be misled by it. Using synthetic coupled systems where the true direction is known (X → Y), three methods — Granger Causality (GC), Transfer Entropy (TE), and a complexity-based detector (CD) — are stress-tested across varying coupling strength and source-variable persistence (anti-persistent, random, positively persistent). The left block tracks how often each method recovers the true direction; the right block tracks how often it invents the false one (Y → X). The persistence of the source variable systematically reshapes both rates: GC and CD are especially sensitive, reporting a substantial share of spurious causal directions as memory increases. The message for hydrology is direct — the memory embedded in streamflow can manufacture false causality unless it is explicitly accounted for.

The wavelet transforms decompose each daily streamflow record across timescales, revealing which periodicities are significant through time. After the Tehri dam begins operating in 2005, the annual (~365-day) frequency disappears at the Tehri station (c), and this loss propagates downstream to Devprayag (d). At the upstream stations — Uttarkashi (a) and Rudraprayag (b) — the annual band remains intact, confirming the effect is dam-driven rather than climatic.

The year 1995 is taken as the change point because flood frequencies in the basin rose significantly thereafter. Importantly, the wavelet analysis captures the catchment's hydrological response — the periodic structure of streamflow — rather than the flood frequencies themselves.