Sensitivity of dynamical systems instantaneous dimension and its insights on sea surface temperature anomaly field over the tropical Pacific

Abstract. Sea surface temperature anomaly (SSTA) fields over the tropical Pacific exhibit complex spatiotemporal variability that traditional regional average indices may fail to capture. In this study, we take the evolution of daily SSTA fields as a dynamical system (DS) and compute the DS instantaneous dimension (DSID) to characterize local dynamical properties. Our results reveal a significant shift in the mean value (SMV) of DSID around the year 2007 over the western tropical Pacific (notably the Niño 4 and Niño 3.4 regions), a phenomenon that is absent in the eastern Pacific.To explain this region-dependent SMV of DSID in SSTA fields, we examine the sensitivity of DSID to the changes of the system states using idealized system models, such low-dimensional (Lorenz-63) and high-dimensional (Lorenz-96) systems. Results demonstrate that the estimation of DSID is sensitive to variations in both high-frequency variability and system states,for both low-dimensional and high-dimensional systems. These findings from idealized systems provide a theoretical basis for interpreting the observed SMV in SSTA fields. Further analysis reveals that the SMV in DSID can be largely attributed to changes in high-frequency variability across different time spans. Collectively, these results advance our understanding of the physical interpretation of DSID and offer valuable insights for the study of complex real-world systems.