  In this paper, we focus on a numerical technique, the weighted Birkhoff
average (WBA) to distinguish between four categories of dynamics for
quasiperiodically-forced circle maps. Regular dynamics can be classified by
rotation vectors, and these can be rapidly computed to machine precision using
the WBA. Regular orbits can be resonant or incommensurate and we distinguish
between these by computing their "resonance order." When the dynamics is
chaotic the WBA converges slowly. Such orbits can be strongly chaotic, when
they have a positive Lyapunov exponent or weakly chaotic, when the maximal
Lyapunov exponent is zero. The latter correspond to the strange nonchaotic
attractors (SNA) that have been observed in quasiperiodically-forced circle
maps beginning with the models introduced by Ding, Grebogi, and Ott. The WBA
provides a new technique to find SNAs, and allows us to accurately compute the
proportions of each of the four orbit types as a function of map parameters.
