Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Here we propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.

We propose a new measure based on drought period length to assess the temporal difference between the recent two severe droughts of 2005 and 2010 in the Amazonia. The sensitivity of the measure is demonstrated by disclosing the distinct spatial responding mechanisms of the Northeastern and Southwestern Amazon (NA, SA) to the surrounding sea surface temperature (SST) variabilities. The Pacific and Atlantic oceans have different roles on the precipitation patterns in Amazonia. More specifically, the very dry periods in the NA are influenced by El Niño events, while the very dry periods in the SA are affected by the anomalously warming of the SST in the North Atlantic. We show convincingly that the drought 2005 hit SA, which is caused by the North Atlantic only. There are two phases in the drought 2010: (i) it was started in the NA in August 2009 affected by the El Niño event, and (ii) later shifted the center of action to SA resulted from anomalously high SST in North Atlantic, which further intensifies the impacts on the spatial coverage.

Transfer Entropy has been applied to experimental datasets to unveil causality between variables. In particular, its application to non-stationary systems has posed a great challenge due to restrictions on the sample size. Here, we have investigated the minimum sample size that produces a reliable causal inference. The methodology has been applied to two prototypical models: the linear model autoregressive-moving average and the non-linear logistic map. The relationship between the Transfer Entropy value and the sample size has been systematically examined. Additionally, we have shown the dependence of the reliable sample size and the strength of coupling between the variables. Our methodology offers a realistic lower bound for the sample size to produce a reliable outcome.

The present work uses a new approach to causal inference between complex systems called the Recurrence Measure of Conditional Dependence () based on the recurrence plots theory, in order to study the role of the Amazon River basin (AM) as a land-atmosphere bridge between the Niño 3.0 region in the Pacific Ocean and the Tropical North Atlantic. Two anomalous droughts in the Amazon River basin were selected, one mainly attributed to the warming of the Tropical North Atlantic (2005) and the other to a warm phase of El Niño-Southern Oscillation (2010). The results of the RMCD analysis evidence the distinctive behavior in the causal information transferred between the two oceanic regions during the two extreme droughts, suggesting that the land-atmosphere bridge operating over the AM is an active hydroclimate mechanism at interannual timescales, and that the analysis may be an ancillary resort to complement early warning systems.