Hitting times, recurrence, and local dimension under nonstationary forcing with applications to climate data

Recurrence and hitting time statistics provide a dynamical system perspective on rare events by linking the temporal occurrence and recurrence of states to the geometric structure of the attractor. In autonomous chaotic systems, theoretical results relate the scaling of hitting or return times to shrinking neighborhoods to the local dimension of the invariant measure. Here, we investigate numerically how robust this relation remains under time dependent forcing. We first analyze a non-autonomous Hénon map as a controlled benchmark and compare recurrence and hitting time exponents with independent estimates of local dimension. We then apply the same framework to high dimensional climate simulations of sea level pressure and near surface temperature from the IPSL-CM6A-LR model under historical and future forcing scenarios. In both systems, recurrence statistics exhibit approximate scaling across spatial scales and remain broadly consistent with EVT based dimension estimates at the ensemble level, although with substantial pointwise variability. In climate simulations, future forcing scenarios show systematically shorter recurrence times for comparable spatial scales, indicating more frequent revisits of similar atmospheric configurations.