A Flood Witness Network for the Settlements That Flood First: Design and a Computed Lead-Time Law for Low-Cost River and Rain Gauge Nodes at US$94 per River Node

SIMULATED, NOT MEASURED. A design and computation study of a low-cost flood witness network: pressure-transducer river nodes at US$94.00 in parts, rain nodes at US$88.00, LoRa telemetry, and solar-plus-battery power. The lead-time law T_lead = D/c - 20 minutes, with kinematic-wave celerity from Manning friction, gives 75 minutes for a 200 km2 catchment at slope 0.003, 21 minutes for 50 km2, 229 minutes for 1,000 km2, and no usable lead for 10 km2. Where lead collapses to minutes the design serves evacuation of people, not property. A reference network protecting 500 households costs US$1.35 per household per year over five years. AI use disclosed: prepared with the assistance of Dave, an AI system, under the author's direction.