Falsification Programme

F-1 · Regime occupancy test Highest priority

Objective

Compute annually fitted \((r_y, \delta_y)\) from long gauge series at Óbidos and Manaus. Classify each year via DC-A / DC-B root-count discriminants.

Output

\(P(\text{two-maxima})\) — the fraction of years in the "bimodal" regime — and its trend over the record length.

Data requirements

Long daily or monthly discharge series at Óbidos (1928–present if available) and Manaus (stage → discharge conversion required). Source: ANA (Brazilian National Water Agency) / HYBAM / UNH/GRDC composite.

Method

For each year y: fit \(Q_y(t) = c_0 + B_{1,y}\cos(\omega t - \psi_{1,y}) + B_{2,y}\cos(2\omega t - \psi_{2,y})\) via least-squares to monthly means (or low-passed daily series). Extract \(r_y = B_{2,y}/B_{1,y}\) and \(\delta_y = \psi_{2,y} - 2\psi_{1,y}\). Apply DC-B root-count test. Alternatively, apply DC-A directly to the smoothed hydrograph without assuming harmonic form.

Dependencies resolved

UC-1 (annual \(r_y, \delta_y\) series) · CL-3 upgrade gate

Staleness policy

Re-evaluate after 6 months or upon availability of new gauge data, whichever comes first.

F-2 · ENSO-conditioned shift

Objective

Condition \((r_y, \delta_y)\) and peak-shape metrics on ENSO/Atlantic indices (per the HESS framework [2]) to test whether climate modes push the system across the DC-B discriminant boundary.

Output

Conditional distributions \(P(r_y, \delta_y \,|\, \text{ENSO type})\) and statistical test of whether any ENSO category produces a significantly different regime occupancy.

Method

Use F-1 output. Partition years by ENSO classification (El Niño / La Niña / Neutral, or finer typology per [2]: Eastern Pacific vs Central Pacific events). Compare \(r_y\) distributions across categories using non-parametric tests (Kruskal-Wallis or permutation test). Also condition on tropical Atlantic SST anomaly indices.

Dependencies

Requires F-1 completion. Addresses DS-3 (ENSO modulation of secondary peaks).

F-3 · Kernel drift / hysteresis check

Objective

Test whether the effective routing delay differs between rising and falling limbs of the hydrograph (hysteresis signature). Quantify asymmetry if nonlinear extension is invoked.

Output

Effective delay \(\tau_\uparrow\) (rising limb) vs \(\tau_\downarrow\) (falling limb), and any secular trend in \(\tau\) over the record length that could indicate kernel drift from land-use change.

Method

Cross-correlate upstream forcing (e.g., sub-basin rainfall or upstream gauge) with Óbidos discharge, computed separately for rising and falling limbs. Alternatively, use a state-dependent transfer function model with discharge-dependent lag parameter. Assess trend in lag residuals across decades.

Dependencies resolved

UC-3 (kernel drift proxies) · DS-4 (routing kernel parameterisation). Partially addresses UC-4 (rating curves) if stage data are used.