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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 41.8527°N, 84.0731°W in Lenawee County, Michigan. 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 KDTX (Detroit, MI), 66 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 5,200 ft above ground. That is far enough out that the beam has climbed above the lowest few thousand feet. Storm structure aloft is visible; a shallow circulation near the ground may not be, and a warning here can arrive before anything looks dramatic on the radar picture.
The closest instrument actually measuring the air is KADG · Adrian/Lenawee Cnty on the ASOS/AWOS network, 1.1 miles away. Close enough that its readings are, for practical purposes, the conditions in town.
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 Michigan observing network as of this build.
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