Mathematical Warning Model · v1 Technical Documentation
Version: v1 (first release) Algorithm name: Wind baseline + sliding baseline warning model Date: 2026-08-14
1. Overview
The v1 model consists of 5 independent warning paths, computed every second. The final level is the maximum of all paths:
Final level = max(Debris flow D, Flash flood F, Wind, Flow spike, Surge)Levels: 0 = Normal / 1 = Level-3 warning / 2 = Level-2 warning / 3 = Level-1 warning (most severe)
2. Warning Paths
2.1 Debris Flow (four-factor weighted)
D = 0.30 × S̄ + 0.35 × Q̄ + 0.20 × dQ̄ + 0.15 × ΔS̄| Factor | Meaning | Normalization |
|---|---|---|
| S̄ | Soil moisture level | Sliding baseline [P10,P95] percentile; fallback: reading/100 |
| Q̄ | Flow level | Sliding baseline; fallback: flow/30 L/min |
| dQ̄ | Flow change rate | min(rate/5 L/min/s, 1) |
| ΔS̄ | Soil 10-min rise | min(rise/15%, 1) |
Gate: soil moisture < 60% (unsaturated) → debris flow path skipped (debris flow cannot start in dry soil).
Thresholds: D ≥ 0.45 → L3 / ≥ 0.55 → L2 / ≥ 0.75 → L1
Special rules (priority):
- Soil above local P90 + rising flow + 5-min continuous rise → L1 directly
- Soil above local P90 + flow ≥ 70% of channel capacity → L2 directly
- Soil 10-min rise ≥ 20% → at least L3
v1 weight adjustment note: soil moisture 0.40 → 0.30 (soil saturates easily and dominated the score); flow raised to the highest weight 0.35 (flash-flood signal is more critical); ΔS̄ 0.10 → 0.15.
2.2 Flash Flood (independent index, new in this version)
F = 0.60 × Q̄ + 0.40 × dQ̄- Not gated by soil moisture — triggers on flow surge alone, simulating upstream rainstorm floods (water arrives before soil saturates)
- Same thresholds: F ≥ 0.45 → L3 / ≥ 0.55 → L2 / ≥ 0.75 → L1
- Acts as a flow-based approximation of the Manning equation (ultrasonic water-level sensor not yet available, so flow level + change rate substitute for the 70% Manning component)
2.3 Wind
| Wind speed | Level |
|---|---|
| ≥ 25 km/h | L3 |
| ≥ 40 km/h | L2 |
| ≥ 60 km/h | L1 |
- Wind risk index:
wind_risk = min(wind/40, 1)(for display) - Strong wind treated as a precursor of severe convection (flash-flood trigger)
2.4 Flow Spike
- Per-second flow change rate compared against the local 24h historical distribution; above P95 = high risk
- spike_risk ≥ 0.8 → L3; ≥ 1.0 (above P95) → L2
- Fallback when baseline insufficient: rate ≥ 2 L/min/s = full scale
2.5 Surge (second-level response)
| Surge | Trigger |
|---|---|
| Soil rises ≥ 20% within 5 s | L3 immediately (saturation/seepage signal) |
| Wind rises ≥ 12 km/h within 60 s | L3 immediately (sudden gale) |
3. Sliding Baseline (core mechanism)
- Window: 24 h, sampled once per minute
- Normalization: map current value to the [P10, P95] range of local history → 0~1 relative position
- Purpose: self-adapts to local climate — 20% moisture can be "high" in arid regions, 60% only "high" in humid regions; no manual threshold calibration
- Cold start: baseline inactive until 2 h of data; falls back to absolute thresholds (soil/100, flow/30)
4. Strengths
- Adaptive: sliding baseline makes one algorithm work across climates without recalibration
- Independent paths: debris flow / flash flood / wind / spike / surge do not interfere; a failed path does not block others; soil gate cannot block the flood path
- Second-level surge response: sudden events (soil saturation, gale, flow surge) do not wait for 5–10 min windows
- Simple & explainable: no neural networks or complex statistics — weighted sums + thresholds, easy to deploy, debug, and explain to field staff
- Cold-start capable: falls back to absolute thresholds when baseline data is insufficient
5. Limitations
- Missing 70% Manning component: no ultrasonic water-level sensor, so the main Manning equation (R = 0.7M + 0.3S) cannot run; flow approximation reduces accuracy
- Fixed wind thresholds: 25/40/60 km/h are empirical; not adapted to local wind climate (coastal vs inland "strong wind" differ)
- Soil <60% hard gate may miss events: upstream rainstorm floods can occur while local soil is still dry — mitigated by the flood F path, but F depends on the flow sensor; a failed flow sensor means missed alerts
- Cold-start window: first 2 h uses absolute fallbacks, which may misjudge extreme climates (very arid/humid)
- Narrow flow-sensor range: YF-S401 measures 0.3–3 L/min only; very low/high flows are inaccurate, degrading Q̄ and dQ̄
- 10-min soil-rise lag: ΔS̄ needs a 10-min window; sudden wetting relies on the surge path (5 s +20%), leaving a gap in between
- Hard thresholds: 0.45/0.55/0.75 step jumps with no probability/confidence output; boundary values (0.44 vs 0.45) jump semantically
6. Characteristics
- Real-time: recomputed every second; web page refreshes every 0.5 s
- Visualized: warning card shows 8 metrics — debris D, flood F, soil S̄, flow Q̄, dQ̄, ΔS̄, spike risk, wind risk
- Multi-sensor fusion: soil moisture + water flow + wind + temperature/humidity (DHT11)
- Explainable: every level can be traced to a specific path and factor, suitable for review/demo presentations
- Modular: 5 independent paths; any path can be replaced separately in future versions (e.g., add the Manning 70% component) without affecting the others
7. Version Plan (iteration direction)
- v2 (planned): add ultrasonic water-level sensor → complete the Manning 70% component (R = 0.7M + 0.3S)
- v2 (planned): sliding-baseline adaptation for wind thresholds (replace fixed 25/40/60)
- v2 (planned): confidence/persistence check (trigger only after N seconds above threshold to reduce single-point false alarms)