Séminaire

In studies of ensembles of systems with nontrivial temporal evolution, it is fruitful to detect and quantify their couplings since the latter often determine basic features of the collective behavior. For a deeper understanding it is particularly important to reveal “directional” (causal) couplings, i.e. to answer the question “who drives whom”. For example, many studies look for couplings between large-scale modes of climate variability and global climatic processes from observed data. To reveal couplings from a time series of certain observed variables, one often uses the celebrated concept of Granger causality (originally suggested in the field of econometrics and mathematical statistics) whose generalized, actively used, and highly trusted version is an information-theoretic measure called “transfer entropy” (TE). Such approaches are getting more frequently used in climate research as well. However, they turn out to face serious difficulties under quite realistic conditions so that special efforts are required to avoid spurious detections of couplings and to reach meaningful interpretations of the coupling estimates obtained. Here, I discuss such difficulties arising under the typical conditions of low temporal resolution of the data, significant observational noise, and hidden state variables. It is demonstrated that in an analysis of couplings between two systems the TE values may well be nonzero in both directions even in case of a unidirectional coupling between the systems under study. It leads to spurious coupling detection under a naive interpretation of the TE estimates. Special tests for bidirectional coupling accounting for the above factors are suggested. It is further shown that Granger causality idea does not suffice to characterize diverse effects of directional couplings (e.g. long-term changes in the dynamics of one system under a certain change in the properties of another system or in the coupling parameters) and it should often be fruitful to complement it with a study of an auxiliary empirical model behavior to assess "longer-term causal effects". Both the test for bidirectional coupling and the long-term causality assessment are applied to studying interactions between large-scale climatic processes such as El-Nino-Southern Oscillation, North Atlantic SST variations, and Indian monsoon. The latter is done in collaboration with Prof. Juergen Kurths (PIK, Potsdam, Germany) and Prof. Igor Mokhov (A.M. Obukhov Institute of Atmospheric Physics of the Russian Academy of Sciences, Moscow, Russia)."