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The depth of a Resolving Tree is the number of levels of links, not including the top. The depth of the link is the minimal depth for any Resolving Tree of that link. The only links of length 0 are the trivial links. A Knot of length 1 is always a trivial Knot and links of depth one are always Hopf Links, possibly with a few additional trivial components (Bleiler and Scharlemann). The Links of depth two have also been classified (Thompson and Scharlemann).
References
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York:
W. H. Freeman, p. 169, 1994.