Overview
V4.2 extends V3.6 hydrology by treating basin geometry as a tuning system. We quantify how fan symmetry, divide curvature, and karst porosity shape the harmonic field H; then we test whether watershed “organs” increase node stability, discharge control, or signal clarity during deglacial pulses (handoff from V4.1).
Key Findings
- Tri-river fan resonance: Major threefold confluences and deltas exhibit coherent phase behavior (reduced timing jitter) and elevated G near Codex nodes.
- Radial headwaters: Mountain “sunburst” divides (5–12 spokes) correlate with predictable corridor activation and terrace pacing during sea-level and precipitation shifts.
- Karst chambers: Basin-scale karst networks act as low-pass filters, dampening high-frequency floods while preserving long-cycle aquifer signals (boosts HTCI components Ag, ΨσK).
- Architectural coupling: Pyramidal/mound complexes at fan termini (e.g., platform towns, causewayed enclosures) sit on maxima of modeled resonance clarity.
Data Inputs
| Layer | Source Types | Use in Model |
|---|---|---|
| DEM/DTM | 1–30 m relief; divide maps | Radial spokes, curvature, flow routing |
| Hydrography | Rivers, confluences, deltas | Tri-fan detection; resonance loci |
| Karst & Subsurface | Doline/cave inventories; transmissivity | Porosity fields; low-pass filter parameterization |
| Sediment Systems | Fan thickness; terrace rasters; grain size | Attenuation/delay estimation |
| Mineralogy (V3.5) | Quartz/feldspar indices; fabric | Resonant media weighting in H |
| Chronologies | Varves; OSL/IRSL; tephra | Timing calibration; ±σ propagation |
Methods
- Fan & Radial Extraction: Detect tri-fan confluences (≥3 primary channels within θ tolerance) and headwater radials via divide curvature + spoke count.
- Resonance Field H: Compose H from (a) basin geometry (curvature, bifurcation ratios), (b) karst porosity/connectedness, (c) mineral resonance score (V4.10).
- Signal Metrics: Estimate phase stability (φ), attenuation (α), and delay (τ) using synthetic hydrographs and paleoflow constraints.
- ChiR Coupling: Compute G = V × H² for corridors and nodes; compare ΔG across deglacial pulse windows (handoff from V4.1).
- Temporal Anchoring: Tie terrace/fan growth and karst speleothem phases to event stacks; propagate joint uncertainty.
Algorithm Hooks (ChiR Library)
| Function | Description | I/O |
|---|---|---|
chir.watershed.find_tri_fans(hydro, dem, theta=35) |
Identify tri-river confluences/fans and geometry | Lines+raster → features {apex, arms, area, slope} |
chir.watershed.radial_headwaters(divides, k=5..12) |
Detect radial spoke systems at headwaters | Divide raster → spokes, symmetry score |
chir.karst.porosity_field(dolines, caves, T) |
Build karst porosity/connectedness grid | Points+lines+transmissivity → porosity H-term |
chir.harmonics.compose_H(geom, karst, mineral) |
Combine geometry/karst/mineral into H | Grids → H grid [0,1] |
chir.harmonics.phi_alpha_tau(fan, hydrograph) |
Phase stability, attenuation, delay estimators | Fan feature + Q(t) → {φ, α, τ} |
chir.harmonics.compute_G(V,H) |
Return resonance scalar/array | V,H → G |
Phase metrics (φ, α, τ) are reported per-feature and aggregated to corridors for cross-basin comparison.
Model Outputs
- Resonance Atlas: tri-fan and radial headwater maps with symmetry and phase metrics.
- H-Grids: basin-scale harmonic fields incorporating karst and mineral weighting.
- Node Coupling: ΔG stacks per pulse window; ranked stability/clarity indices for Codex nodes.
Validation & Reproducibility
- Hydrograph fit: compare modeled α, τ against gauged floods (where available) and terrace/varve chronologies.
- Null topology: randomize confluence angles and spoke counts; verify observed symmetry scores exceed null.
- Cross-module checks: ensure H-agreement with V3.6 HTCI components and V4.1 ΔG timing.
Bridges
- From V4.1: uses pulse windows and ΔV fields.
- To V4.3: exports karst-weighted H for subterranean memory encoding.
- To V4.7: flags lowland sacred drainage candidates at fan termini for cultural coupling tests.