FAI controller described a departure event when aircraft was permitted to depart VFR with weather below basic VFR conditions; citing ASOS clock error as one causal factor.

Narrative

Local Control called Tower visibility of 5 or maybe 7 miles and updated the ASOS prior to the hourly weather observation. I must have heard the ASOS beep as I thought the change had been accepted and the timing was correct for our typical hourly report (53-54 minutes after the hour). A carrier jet called for clearance and a PA31 called for a VFR TRSA departure and taxi. I issued the TRSA and taxi; and then issued the IFR clearance. After receiving a rolling call; the TRACON rang the Tower phone to inquire about whether the field was VFR; at which point I noticed that the ASOS was still showing an IFR visibility and the pending hourly observation with a VFR visibility. This observation should have already been steadied as it was about 55 or 45 minutes after the hour. The TRSA departure was midfield airborne and the Local Controller was already taking action to fix the situation. I believe he offered an IFR clearance and the Pilot requested and received an SVFR clearance. The clock on the ASOS was several minutes off from the Tower's GPS clocks. The facility initially investigated this event as a possible operational error/operational deviation; but found it to be a non-event. Management is pursuing a correction to the ASOS clock.