SFO Controller described when landing traffic was not issued a mandatory go-around instruction following a false AMASS alert indicating any action on their part simply would not have been in time.

Narrative

I was working Local Control with Radar Coordinator combined to me. Aircraft X was cleared to land on Runway 28L. Runway 28R was closed and AMASS was set appropriately showing Runway 28R closed. I saw Aircraft X lined up for Runway 28L on short final over the lights and I then scanned some strips. AMASS alerted; 'WARNING! GO AROUND! RUNWAY TWO EIGHT RIGHT!' I immediately looked at the ASDE and saw the alert for Runaway 28R as well as a target on Runway 28L. I realized that the alert was probably a false alert. I immediately looked at Runway 28L and saw Aircraft X touching down on the runway near November. I scanned the runway and it appeared clear. There was nothing I could do anyway. The false alert really surprised me and it took quite awhile for me to recover. I was quite fatigued at the time. It was XC:13 in the morning and I had been up since XA:00. I was tired and had not had adequate rest for the entire workweek. I had worked XL:00-XT:00 on Tuesday; XK:20-XS:20 on Wednesday and XC:30-XK:30 on the previous day Thursday. It is difficult to get adequate rest when working the rotating shifts that we work. In addition I was working two positions (Local Control and Radar Control) combined during a very complex operation. There was a lot of coordination with Departure Control as well as with Ground Control; clearances needed to be changed; strips needed to be marked; the City was conducting the runway inspections; and training was going on at Ground Control. With all that was going on I had less time to be aware of or anticipate the possibility of the false alert. As a result I was taken by surprise when the false alert happened.