Picking up bits here and there over the years, I believe the weather products we get from NOAA & AWS are derived from
• radiosonde data gathered at various locations across the country each day. See
wiki on radiosondes. They have a radiosonde that is released at Atlantic Aero here in Greensboro daily, it is a small balloon with a radio unit attached to the rope. They try and recover the radios, but I guess they lose quite a few.
• METARs and weather stations at airports across the world.
• ACARS data from airliners. See
wiki on ACARS weather data.
This probably leaves out other pieces of the puzzle. But the basic idea is a huge supercomputer constantly running weather modeling equations with scads of variables indexed to real weather sensors. This is called "indexing to boundary conditions" -see
wiki on boundary conditions. It works fairly well, weather modeling is pretty accurate these days, although they still have trouble nailing it because the earth's atmosphere is so complex.