In order to overcome these challenges, we borrow methods from theoretical ecology and data mining that allow us to reconstruct the full state space of the tropical Pacific system from a single index. We perform this reconstruction using the NINO3 index from a 100,000-year unforced run of the Zebiak-Cane model. This reconstruction of the state space allows us to identify regime-like behavior of the tropical Pacific system in this model on decadal timescales that corresponds to the PDV. We find that the transitions into negative PDV states occur in a localized region of the state space, allowing for high-skill prediction. We then examine the characteristics of this region of the state space in terms of physical variables such as sea surface temperatures, thermocline depth, and wind stress in the tropical Pacific, and draw a comparison of this state of the system in the model with the state of the system at the beginning of known transitions in the observations with the ultimate aim of developing a method to detect PDV phase shifts in the real world as they occur.