Each buoy measures the true hazard intensity s(t) plus independent sensor noise: xᵢ = s(t) + N(0, σ²). Averaging n buoys gives the network estimate:
x̄ = (1/n) Σ xᵢ
Var(x̄) = σ² / n → noise shrinks as 1/√n
Alert fires when: x̄ ≥ θ (detection threshold)
This is classic signal detection theory: raising θ cuts false alarms during quiet periods but delays real detections, while a bigger sensor network (larger n) narrows the noise band around the true signal so a lower, faster-triggering θ stays safe — the core trade-off behind every real buoy/gauge early-warning array.
The Sendai Framework for Disaster Risk Reduction names four pillars a warning chain must complete before impact: (1) risk knowledge, (2) monitoring & detection — the buoy network above, (3) dissemination & communication, and (4) response capability. This sim models pillars 3–4 as one latency τ:
Lead time delivered = max(0, T_landfall − T_alert − τ)
Evacuated fraction = 1 / (1 + e^-((L − L50) / k)) (logistic response curve)
Even a perfect detector delivers zero useful lead time if τ (dissemination + evacuation mobilization) eats the whole warning window — which is exactly why real EWS programs invest as much in the "last mile" (sirens, cell alerts, evacuation drills) as in the sensors themselves.
Reading the panels: the main view is a bird's-eye map — ocean at top, shoreline in the middle, town inland at the bottom. Drag to pan it, scroll/pinch to zoom. The bottom-left strip chart plots the live network mean x̄ against your threshold over time (green dots on the strip mark false alarms during quiet periods). The bottom-right panel plots the fixed logistic evacuation-response curve with a marker at the current lead time and evacuated fraction — the horizontal axis auto-scales to your storm approach window.
- Detection threshold — how strong the averaged signal must be before an alert is issued.
- Buoy network size — more independent sensors reduce noise, making detection faster and false alarms rarer at the same threshold.
- Dissemination & response latency — minutes lost between alert and public action; subtracted straight from lead time.
- Storm approach window — total minutes available from storm formation to landfall, the whole budget the warning chain has to work with.