  The impact of weak disorder and its spatial correlation on the topology of a
Floquet system is not well understood so far. In this study, we investigate a
model closely related to a two-dimensional Floquet system that has been
realized in experiments. In the absence of disorder, we determine the phase
diagram and identify a new phase characterized by edge states with alternating
chirality in adjacent gaps. When weak disorder is introduced, we examine the
disorder-averaged Bott index and analyze why the anomalous Floquet topological
insulator is favored by both uncorrelated and correlated disorder, with the
latter having a stronger effect. For a system with a ring-shaped gap, the Born
approximation fails to explain the topological phase transition, unlike for a
system with a point-like gap.
