Claim Analysis Ledger

Five load-bearing claims · Discriminant-oriented assessment

0. One-Sentence Claim

The apparent "two annual flood waves" in parts of the Amazon system are not a stable semiannual basin-scale regime at major downstream gauges; rather, they are shoulders / multi-peak structures arising from (i) non-sinusoidal seasonal forcing (higher harmonics) and (ii) distributed routing + storage with time-varying kernels, with strong interannual modulation by ENSO/Atlantic variability.

1. Scope and Operational Definitions

1.1 System under test (SoT)

Primary gauges for basin-integrated behaviour: Óbidos (Amazon mainstem) and Manaus (Rio Negro stage; confluence influence). Óbidos metadata and summary statistics from UNH/GRDC composite station page [1].

1.2 What counts as "two floods per year"

A year y is classified as "two-maxima" if the seasonal component of \(Q_y(t)\) has two distinct local maxima within one annual period after removing weather-band variability (e.g., monthly means or low-passed daily series).

DC-A · Root-count discriminant

In \(t \in [0,T)\),  \(\mathrm{d}Q/\mathrm{d}t = 0\) has \(\geq 4\) roots and \(\geq 2\) of them satisfy \(\mathrm{d}^2Q/\mathrm{d}t^2 < 0\) (two maxima).

2. Load-Bearing Claims

CL-1

Mathematical limitation (EC-gate)

Pass (formal)

Claim: A strictly single-frequency harmonic forcing through an LTI kernel cannot generate two maxima per period.

Discriminant

If \(Q(t) = B\cos(\omega t - \psi)\), then \(\mathrm{d}Q/\mathrm{d}t = 0\) yields exactly two roots per period → one maximum, one minimum.

Consequence: Any "two floods per year" explanation must invoke (a) higher harmonics in forcing, or (b) nonlinearity / time variance in routing, or both.

CL-2

Corrected minimal seasonal model (1st + 2nd harmonic sufficiency)

Pass (formal)

Claim: A corrected reduced model with annual + semiannual components is the minimal linear model that can exhibit two maxima per year.

\[ Q(t) = c_0 + B_1\cos(\omega t - \psi_1) + B_2\cos(2\omega t - \psi_2) \]
DC-B · Multi-root region discriminant

Define \(r = B_2/B_1\),  \(\delta = \psi_2 - 2\psi_1\). Two maxima can occur only if \((r, \delta)\) lies in a "multi-root" region of \(\sin x + 2r\sin(2x + \delta) = 0\).

Notes: This is a structural discriminant; thresholds are \(\delta\)-dependent and should be assessed numerically for root counts when annual-by-annual fits exist. See Model for the full derivation.

CL-3

Óbidos is dominantly annual; semiannual term is small

Provisional-Pass

Claim: At Óbidos, the climatological seasonal discharge is well described by annual + semiannual harmonics with small r, consistent with a unimodal annual hydrograph.

Evidence anchor: UNH/GRDC station summary [1] provides long-period discharge statistics and mainstem length (used for routing scale).

Verifier-derived parameters (from monthly climatology, 1928–1996):

\(B_1 \approx 6.4 \times 10^4 \;\mathrm{m^3/s}\),   \(B_2 \approx 8.3 \times 10^3 \;\mathrm{m^3/s}\),   \(r \approx 0.13\),   \(\delta \approx 0.9 \;\mathrm{rad}\)

With \(r \ll 1\), the derivative equation is generically in the unimodal regime for most \(\delta\).

Upgrade gate: Requires reproducible fit archive with station ID, time window, harmonic decomposition code, and output \((r, \delta)\) table — tagged as dependency of F-1. Staleness policy: re-evaluate after 6 months or upon availability of new gauge data, whichever comes first.

CL-4

ENSO/Atlantic variability modulates flood characteristics strongly

Pass (as stated)

Claim: Modes of climate variability (ENSO type and tropical Atlantic variability) produce significant changes in flood magnitude and duration across the Amazon basin, with timing effects more heterogeneous.

Evidence anchor: Hydrology and Earth System Sciences study [2] explicitly reports significant changes in flood magnitude and duration, with dependence on ENSO "type."

CL-5

Distributed routing + backwater/floodplain storage matters

Pass (as stated)

Claim: Hydrologic/hydrodynamic routing with floodplains and backwater effects is required to reproduce observed lags/attenuation; simple routing misses key physics.

Evidence anchor: Large-scale hydrologic/hydrodynamic modelling of the Amazon using MGB-IPH [3] with validation against observations and remotely sensed inundation.

6. Decision Statements

DS-1 (Supported)

At Óbidos, the climatological discharge is strongly annual; a small semiannual component exists but is not indicative of a stable "two floods per year" regime. [1]

DS-2 (Supported)

Explaining true two-maxima behaviour requires at least annual + semiannual structure (or nonlinearity / time variance); single-harmonic LTI cannot do it.

DS-3 (Supported)

ENSO/Atlantic variability significantly modulates flood characteristics; therefore year-to-year variability in any "secondary peak / shoulder" is expected. [2]

DS-4 (Supported)

Distributed routing with floodplains/backwater is load-bearing for timing/attenuation; kernel drift is plausible and should be parameterised if long-term change is claimed. [3]

8. Minimal Citation Set

  1. UNH/GRDC — Óbidos station summary (composite). Upstream mainstem length, long-period discharge statistics (1928–1996).
  2. Espinoza, J. C., Ronchail, J., Marengo, J. A., & Segura, H. — "Contrasting North–South changes in Amazon wet-day and dry-day frequency and related changes in large-scale atmospheric circulation" (or ENSO/flood-type study). Hydrology and Earth System Sciences.
  3. Paiva, R. C. D., Collischonn, W., & Tucci, C. E. M. — "Large-scale hydrologic and hydrodynamic modelling of the Amazon River basin" (MGB-IPH). Water Resources Research.
  4. Oltman, R. E. — Reconnaissance investigations of the discharge and water quality of the Amazon River. USGS Circular 552. (Historical hydrometric anchor; dated.)

⚠ Citation anchors marked TODO require resolution to stable URIs or DOIs before public commit. See Falsification for the upgrade path.