Clarice is a name which Fox Mulder once, while undergoing imprisonment in 2002, jokingly called Dana Scully. He sinisterly said, "I smelled you coming, Clarice." This momentarily shocked Scully, until she realized he was joking. (TXF: "The Truth")
The reference to "Clarice" was clearly intended to be to Clarice Starling, a character from The Silence of the Lambs. Jodie Foster's realistic portrayal of Starling in that film made the creators of The X-Files realize Scully likewise had to seem believable. (The Truth Is Out There: The Official Guide to The X-Files, p. 15) Stated Glen Morgan, "Scully, especially in the beginning, was very much like the Jodie Foster character [from The Silence of the Lambs]." (X-Files Confidential, p. 88) Similarly, voicing an indirect reference to Starling, series creator Chris Carter noted, "Scully is obviously a Jodi Foster-like character." (The Complete X-Files: Behind the Series, the Myths and the Movies, p. 28) In fact, Clarice Starling was one of Carter's main inspirations when he initially created the Scully character. Starling's respect for her superiors yet bold attitude when need be are an integral part of Scully's personality. One scene depicting Starling dictating her observations on tape during an autopsy led to the trademark Scully autopsy scenes. (citation(s) required)
Physical likeness to Clarice Starling is present in the pilot episode of The X-Files, where Scully's hair and clothes are reminiscent of Starling's. Scully plays a similar kind of role in "Beyond the Sea" to the one Starling fulfils in The Silence of the Lambs, consulting a convicted murderer about an active killer. Also, the death of Starling's father in childhood is an event that still haunts the recruit and Scully experiences her own father's death in "Beyond the Sea", which likewise torments her.