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Forecasts come from the National Weather Service's own computer models, and current conditions from the nearest reporting weather station. Both are served through the weather API. A forecast is guidance, not a warning, and anything the Weather Service has actually issued is on the live map.
Madison sits at 38.0642°N, 81.7949°W in Boone County, West Virginia. The forecast above is drawn for that point from the National Weather Service's own computer models: a seven-day outlook, and a finer-grained one covering the next eighteen hours where it reaches, and the radar and alert panels show what the Weather Service has out over the area right now.
Place data from the US Census Bureau. Coordinates are the Census internal point for Madison, and the forecast is for that location, not for every address inside the city limits, and a large city can have real weather differences from one side to the other.
The nearest Doppler radar is KRLX (Charleston, WV), 18 miles to the NNE. A WSR-88D's lowest routine scan sits half a degree above horizontal, and the earth curves away beneath it, so by the time that beam reaches Madison its centre is about 960 ft above ground. That is about as close as radar coverage gets in the United States: the lowest scan is still near the ground when it reaches Madison, so low-level rotation and the leading edge of a gust front show up on it. Madison is closer to its radar than 88% of US cities.
The closest instrument actually measuring the air is K6L4 · Logan Cnty on the ASOS/AWOS network, 16 miles away. Far enough that "current conditions" for Madison is an educated reading of somewhere else, worth knowing before you plan around a single temperature.
Beam height is the standard 4/3-earth approximation for the 0.5° scan and assumes normal refraction; it is where the centre of the beam is, not its edges, and unusual temperature profiles bend it. Radar siting from the NWS WSR-88D network, station positions from the West Virginia observing network as of this build.
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