Garmin GPSmap 76S
Plot of the GPS Altitude Calibrating the Barometer Altitude

In this plot, the barometer altitude was incorrectly calibrated about 100 feet too high.  (The correct altitude is 1,025 feet).  After allowing at about one hour for the GPS to calibrate the barometer, the barometer readout was within 0.02" (about 20 feet) of the weather bureau measurement. It will take this long for the barometer altitude to indicate the best accuracy.  Why the GPS altitude oscillates up and down over a period of about 15 minutes, is unknown.