Quantitative Comparison of Causal Inference Methods for Climate Tipping Points [Software]

Updated Version v2: We added several sensitivity experiments to the method comparison, and robustness tests to the applied experiment on interactions between Arctic summer sea ice and the AMOC. This project contains the implementation for evaluations of three causal inference methods, the PCMCI method by Runge et al. [1], the Liang-Kleeman Information Flow (LKIF) by Liang [2] and the Granger Causality for State Space Models (GCSS) [3]. For applied experiments, we provide a pipeline script for causal inference of multivariate time series. The user can configure data sources, preprocessing options and the causal methods used for causal analysis. We provide a custom aggregation of neXtSIM sea ice reanalysis data by the E.U. Copernicus Marine Service Information [4] and we're grateful for (and also provide here) several AMOC data series as aggregated by Högner et al. [5]. Setup It's recommended to start by installing GNU Octave, which is used to run the GCSS algorithm, and adding it to the PATH (see https://pypi.org/project/oct2py/). After that, install the full-env.yaml (into a conda virtual environment), and install the tigramite package manually, following https://github.com/jakobrunge/tigramite/. Usage The script Evaluation.py was used to evaluate the methods on synthetic data, one can entirely reproduce the corresponding results from the main method. The Pipeline.py file contains the main pipeline for applying the causal inference methods to custom data (in .csv format), which can be run from the command line with several arguments, run Pipeline.py -h for a list and description of arguments. The data used in the paper is provided in the file DataSheet.csv. References [1] The PCMCI algorithm and the tigramite package are by Runge: https://github.com/jakobrunge/tigramite/ Runge, J., Nowack, P., Kretschmer, M., Flaxman, S., and Sejdinovic, D.: Detecting and Quantifying Causal Associations in Large Nonlinear Time Series Datasets, Science Advances, 5, eaau4996, https://doi.org/10.1126/sciadv.aau4996, 2019b. [2] The package used for LKIF was developed by Rong based on work by Liang: https://github.com/YinengRong/LKIF/tree/main Liang, X. S.: Normalized Multivariate Time Series Causality Analysis and Causal Graph Reconstruction, Entropy, 23, 679, https://doi.org/10.3390/e23060679, 2021. [3] The GCSS algorithm and its implementation are by Barnett & Seth: https://github.com/lcbarnett/ssgc/tree/master Barnett, L. and Seth, A. K.: Granger Causality for State-Space Models, Physical Review E, 91, 040 101, https://doi.org/10.1103/PhysRevE.91.040101, 2015. [4] Sea ice reanalysis data was aggregated over a slice [90°W - 90°E], within which the 33 percentiles of highest variance of sea ice concentration are chosen. E.U. Copernicus Marine Service Information; https://doi.org/10.48670/mds-00336 [5] AMOC data was provided by Annika Högner, as used in Högner et al. 2025. Högner, A., Di Capua, G., Donges, J. F., Donner, R. V., Feulner, G., and Wunderling, N.: Causal Pathway from AMOC to Southern Amazon Rainforest Indicates Stabilising Interaction between Two Climate Tipping Elements, Environmental Research Letters, 20, 074 026, https://doi.org/10.1088/1748-9326/addb62, 2025.