Fig. 3
From: Inferring causation from time series in Earth system sciences
Key generic problems in Earth system sciences. a Causal hypothesis testing in climate research. The question of how the position of the jet stream depends on Arctic and tropical drivers is challenging due to different temporal scales and the spatial definition of variables (hatched regions). b Climate network analysis attempts to describe dynamics of the Earth system using complex network theory. Basing this theory on causal network measures allows one to better interpret network properties. Here major tropical atmospheric uplifts were identified as causal gateways with strong average causal effect and average causal susceptibility in the network (more details in ref. 66). Nodes correspond to climatic subprocesses in different regions and the lower right graph illustrates the causal network metrics for a variable X: the average causal effect is the average change in any other component (node) induced by a one-standard-deviation increase (perturbation) in X. Conversely, the average causal susceptibility is the average change in X induced by perturbations in any other component. Here, the Out-Degree refers to the fraction of components significantly (at 5% level) affected by a component and correspondingly for the In-Degree. c Identifying drivers of extreme impacts is challenging due to the typically large amount of correlated drivers compared to much fewer causally relevant drivers, that, furthermore, may only in combination have a large effect (synergy). For example, a flood might require both storm surges and precipitation to be in an extreme state. Such types of dependencies are difficult to represent with a pairwise network. d Basing model evaluation on causal statistics allows to better identify models with similar causal interaction structure as observational data, rather than comparing averages and climatologies. Shown is gross primary production (GPP) from observations and four illustrative models where the challenge lies in the extraction of variables (X1, X2, …), here shown by some red encircled regions, as well as defining suitable network comparison metrics (panel b) based on causal link weights (edge colors) and aggregate node measures (node colors)
