Using unstable periodic orbits to understand blocking behavior in a low order land-atmosphere model

Unstable Periodic Orbits (UPOs) were used to identify regimes, and transitions between regimes, in a reduced-order coupled atmosphere-land spectral model. In this paper, we describe how the chaotic attractor of this model was clustered using the numerically derived set of UPOs. Using continuation software, the origin of these clusters was also investigated. The flow of model trajectories can be approximated using UPOs, a concept known as shadowing. Here, we extend that idea to look at the number of times a UPO shadows a model trajectory over a fixed time period, which we call cumulative shadowing. This concept was used to identify sets of UPOs that describe different life cycles of each cluster. The different regions of the attractor that were identified in the current work, and the transitions between these regions, are linked to specific atmospheric features known as atmospheric blocks.