Identifying causal relationships from observational time series data is a key problem in disciplines such as climate science or neuroscience, where experiments are often not possible. Data-driven causal inference is challenging since datasets are often high-dimensional and nonlinear with limited sample sizes. Here we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm that allows to reconstruct causal networks from large-scale time series datasets. We validate the method on a well-established climatic teleconnection connecting the tropical Pacific with extra-tropical temperatures and using large-scale synthetic datasets mimicking the typical properties of real data. The experiments demonstrate that our method outperforms alternative techniques in detection power from small to large-scale datasets and opens up entirely new possibilities to discover causal networks from time series across a range of research fields. X 1 X 2 X 3 X 4 linear nonlinear X 1 X 2 X 3 spurious associations causal links X 4 1 2 1 B Causal discovery A Large-scale time series dataset C FULLCI E time lags Figure 1. Causal discovery problem. Consider a large-scale time series dataset (panel A) from a complex system such as the Earth system of which we try to reconstruct the underlying causal dependencies (panel B), accounting for linear and nonlinear dependencies and including their time lags (link labels). Pairwise correlations yield spurious associations due to common drivers (e.g., X 1 ← X 2 → X 3 ) or transitive indirect paths (e.g., X 2 → X 3 → X 4 ). Causal discovery aims to unveil such spurious associations leading to reconstructed causal networks that are, therefore, much sparser than correlation networks.leads to a dilemma that has limited applications of Granger causality mostly to bivariate analyses that cannot, however, account for indirect links and common drivers. There are methods that can cope with high-dimensionality such as regularized regression techniques 11, 12 , but mainly in the context of prediction and not causal discovery where assessing the significance of causal links is more important. An exception is Lasso regression 11 which also allows to discover active variables. Another approach with some recent applications in climate research 13-15 are algorithms aimed specifically at causal discovery [16][17][18] , which remove redundant or irrelevant variables utilizing iterative independence and conditional independence testing. However, both regularized regression and recent implementations of causal discovery algorithms do not deal well with the strong interdependencies due to the spatiotemporal nature of the variables as we show here. In particular, controlling false positives at a desired level is difficult for such methods 19-21 , and becomes even more challenging for nonlinear estimators. In summary, these problems lead to brittle causal network reconstructions and a more reliable methodology is required.We present a causal discovery m...

State-of-the-art climate models now include more climate processes which are simulated at higher spatial resolution than ever1. Nevertheless, some processes, such as atmospheric chemical feedbacks, are still computationally expensive and are often ignored in climate simulations1,2. Here we present evidence that how stratospheric ozone is represented in climate models can have a first order impact on estimates of effective climate sensitivity. Using a comprehensive atmosphere-ocean chemistry-climate model, we find an increase in global mean surface warming of around 1°C (~20%) after 75 years when ozone is prescribed at pre-industrial levels compared with when it is allowed to evolve self-consistently in response to an abrupt 4×CO2 forcing. The difference is primarily attributed to changes in longwave radiative feedbacks associated with circulation-driven decreases in tropical lower stratospheric ozone and related stratospheric water vapour and cirrus cloud changes. This has important implications for global model intercomparison studies1,2 in which participating models often use simplified treatments of atmospheric composition changes that are neither consistent with the specified greenhouse gas forcing scenario nor with the associated atmospheric circulation feedbacks3-5.

Charge transport in conjugated polymer semiconductors has traditionally been thought to be limited to a low-mobility regime by pronounced energetic disorder. Much progress has recently been made in advancing carrier mobilities in field-effect transistors through developing low-disorder conjugated polymers. However, in diodes these polymers have to date not shown much improved mobilities, presumably reflecting the fact that in diodes lower carrier concentrations are available to fill up residual tail states in the density of states. Here, we show that the bulk charge transport in low-disorder polymers is limited by water-induced trap states and that their concentration can be dramatically reduced through incorporating small molecular additives into the polymer film. Upon incorporation of the additives we achieve space-charge limited current characteristics that resemble molecular single crystals such as rubrene with high, trap-free SCLC mobilities up to 0.2 cm 2 /Vs and a width of the residual tail state distribution comparable to k B T .

Global climate models are central tools for understanding past and future climate change. The assessment of model skill, in turn, can benefit from modern data science approaches. Here we apply causal discovery algorithms to sea level pressure data from a large set of climate model simulations and, as a proxy for observations, meteorological reanalyses. We demonstrate how the resulting causal networks (fingerprints) offer an objective pathway for process-oriented model evaluation. Models with fingerprints closer to observations better reproduce important precipitation patterns over highly populated areas such as the Indian subcontinent, Africa, East Asia, Europe and North America. We further identify expected model interdependencies due to shared development backgrounds. Finally, our network metrics provide stronger relationships for constraining precipitation projections under climate change as compared to traditional evaluation metrics for storm tracks or precipitation itself. Such emergent relationships highlight the potential of causal networks to constrain longstanding uncertainties in climate change projections.