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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.
Urban Honolulu sits at 21.3243°N, 157.8476°W in Honolulu County, Hawaii. 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 Urban Honolulu, 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 PHMO (Molokai, HI), 45 miles to the ESE. 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 Urban Honolulu its centre is about 3,100 ft above ground. That is comfortably inside the useful range. The lowest scan passes low enough over Urban Honolulu to show rotation in the part of a storm where tornadoes actually form.
The closest instrument actually measuring the air is PHNL · Honolulu Intl on the ASOS/AWOS network, 5.0 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 Hawaii observing network as of this build.