RESUMEN
Phase space reconstruction (PSR) methods allow for the analysis of low-dimensional data with methods from dynamical systems theory, but their application to prediction models, such as those from machine learning (ML), is limited. Therefore, we here present a model adaptive phase space reconstruction (MAPSR) method that unifies the process of PSR with the modeling of the dynamical system. MAPSR is a differentiable PSR based on time-delay embedding and enables ML methods for modeling. The quality of the reconstruction is evaluated by the prediction loss. The discrete-time signal is converted into a continuous-time signal to achieve a loss function, which is differentiable with respect to the embedding delays. The delay vector, which stores all potential embedding delays, is updated along with the trainable parameters of the model to minimize prediction loss. Thus, MAPSR does not rely on any threshold or statistical criterion for determining the dimension and the set of delay values for the embedding process. We apply the MAPSR method to uni- and multivariate time series stemming from chaotic dynamical systems and a turbulent combustor. We find that for the Lorenz system, the model trained with the MAPSR method is able to predict chaotic time series for nearly seven to eight Lyapunov time scales, which is found to be much better compared to other PSR methods [AMI-FNN (average mutual information-false nearest neighbor) and PECUZAL (Pecora-Uzal) methods]. For the univariate time series from the turbulent combustor, the long-term cumulative prediction error of the MAPSR method for the regime of chaos stays between other methods, and for the regime of intermittency, MAPSR outperforms other PSR methods.
RESUMEN
The dominant mode of intraseasonal precipitation variability during the South American monsoon is the so-called precipitation dipole between the South Atlantic convergence zone (SACZ) and southeastern South America (SESA). It affects highly populated areas that are of substantial importance for the regional food supplies. Previous studies using principal components analysis or complex networks were able to describe and characterize this variability pattern, but crucial questions regarding the responsible physical mechanism remain open. Here, we use phase synchronization techniques to study the relation between precipitation in the SACZ and SESA on the one hand and southern hemisphere Rossby wave trains on the other hand. In combination with a conceptual model, this approach demonstrates that the dipolar precipitation pattern is caused by the southern hemisphere Rossby waves. Our results thus show that Rossby waves are the main driver of the monsoon season variability in South America, a finding that has important implications for synoptic-scale weather forecasts.
RESUMEN
Climate networks have proven to be a valuable method to investigate spatial connectivity patterns of the climate system. However, so far such networks have mostly been applied to scalar observables. In this study, we propose a new method for constructing networks from atmospheric wind fields on two-dimensional isobaric surfaces. By connecting nodes along a spatial environment based on the local wind flow, we derive a network representation of the low-level circulation that captures its most important characteristics. In our approach, network links are placed according to a suitable statistical null model that takes into account the direction and magnitude of the flow. We compare a simulation-based (numerically costly) and a semi-analytical (numerically cheaper) approach to determine the statistical significance of possible connections, and find that both methods yield qualitatively similar results. As an application, we choose the regional climate system of South America and focus on the monsoon season in austral summer. Monsoon systems are generally characterized by substantial changes in the large-scale wind directions, and therefore provide ideal applications for the proposed wind networks. Based on these networks, we are able to reveal the key features of the low-level circulation of the South American Monsoon System, including the South American Low-Level Jet. Networks of the dry and the wet season are compared with each other and their differences are consistent with the literature on South American climate.