Tower Controller in Charge reported they told the Local Controller to issue a go around to an aircraft on short final after the Local Controller cleared another aircraft for takeoff from the same runway.

Narrative

I was working GC/CD (Clearance Delivery)/CIC (Controller in Charge) combined which was normal for this time of day. We had 4 controllers and no supervisors/management for the morning shift. 2 controllers on break with 1 in the Tower coming back from break to relieve Local. Local Controller 1 was being relieved by Local Controller 2. They completed the relief briefing and Controller 1 completed 2 minute overlap of the position. When Controller 2 took the LC (Local Control) position there were two arriving aircraft that had been cleared to land Runway 30L by the previous Controller. Traffic was all briefed/received appropriately. Within a few minutes of assuming the position I overhear some back and forth clarification between LC and Aircraft Y on what exactly he wanted to do as he was departing VFR and wanting to remain in the Class C airspace for a maintenance flight. I then subsequently overhear LC clear for take off Aircraft Y from 30L @ D with Aircraft X short final landing Runway 30L. I was performing my duty of monitoring the Tower cab as a CIC; while also working GC/FD (Flight Data) positions; and heard Locals instructions and immediately saw the conflict between the departure and arrival. Without hesitation; I instruct the LC Controller to send Aircraft X around right now. LC was very receptive to my instructions and complied without hesitation. Aircraft X overflew Aircraft Y; whom had crossed the white Runway edge line and was beginning take off roll; by approximately 300 feet. The LC stated he had not seen the arriving Aircraft X due to the bar/bevel between the window panes. This window at the Local Control position has fog/condensation issues between the double glass panes as well. It is a known safety hazard and needs to be replaced. LC was also scanning the Runway in the opposite direction and issued Runway crossing instructions to a previous arrival at the time I was instructing him to send Aircraft X around. This was a tense moment in the Tower and we all worked very well as a Tower team. I overhear LC issuing traffic to Aircraft X for the previous departure Aircraft Z who was approximately 2 miles in the upwind. Tower applied visual was being utilized and they had nearly 030 vertical separation when LC issued the 'fly Runway heading climb and maintain 030'. LC was coordinating effectively with NorCal Tracon when Aircraft Y continued on his take off clearance heading 200. I was simultaneously working GC/CD while overseeing the situation at hand with LC; and I believe I appropriately and effectively performed my duties as a CIC in a potentially significant event. This was a save from a potential collision due to my quick actions as well as LC for being receptive to CIC instructions. It is my recommendation that we have a staffed supervisor or a 5th Controller for each shift to help with the recommended 'stand alone CIC' position. A 4 person rotation with 'stand alone CIC' can become cumbersome with increasing our time on position which can negatively affect controller morale and concentration. However; in this instance I believe the way I handled the situation was as good if not better than if we had a 'stand alone CIC'. We are already on forced 6 day work weeks working overtime every week. This Leads to Controller fatigue very quickly. We need more staffing.