Early warning signals of tipping points: A deep learning approach to direction and timing

Chris A Boulton , Muhammed Fadera

The crossing of climate tipping points poses serious risk to life on Earth due to the impacts they cause, and their irreversibility. These systems generally exhibit critical slowing down on their approach to tipping point, or bifurcation, which can be detected by looking for changes in statistical properties of a time series from the system, such as an increasing lag-1 autocorrelation or variance. Recently, there has been interest in the use of deep learning in tipping point detection. However, there has been a strong focus on predicting the movement towards tipping only.

Here, we present results from a CNN-GRU architecture, trained on 3 normal forms of bifurcation, linearly forced either towards or away from the bifurcation point, or remaining a constant distance away. Predicting these 3 categories yields an overall accuracy of 67%, increasing to 78% for the longest time series, outperforming traditional early warning signals in a number of ROC tests. A complementary time-to-tip model predicts the distance to tipping should the linear forcing be extrapolated towards the tipping point, with a mean absolute error of 241 time steps which decreases as the time series lengthens. Using AMOC collapse output from a GCM, the categorical model is able to correctly identify which run is forced towards tipping, and which is the control, unforced run, with the time-to-tip model able to predict a decrease in the time to tip for the forced run, and a relatively stable distance in the control run. Although it overestimates tipping distance, we attribute this to struggles the model has with the saddle-node bifurcation type of which the collapse is likely to be. Attention weight analysis of the DL model shows clear, interpretable behaviour; the categorical model searches for signals at the beginning and end of the series to determine direction, whereas the time-to-tip model uses the beginning to ascertain distance from tipping. Testing with red noise data suggests there is a ceiling to improvements due to some reliance on critical slowing down indicators.

Our work presents a novel framework that adds considerations of time series moving away from tipping as part of the null category. Although this makes our model more general than those in the literature in dealing with false positives, it also highlights the limitation of classification-based DL models – a rich set of nulls are needed to help them capture more features of tipping trajectories that distinguish it from non-tipping trajectories. Together with our complementary time to tip model, these new additions have policy relevancy regarding monitoring such as intervention or planning strategies. We hope this framework can be built upon, by exploring training sets that could reduce false positives, and use output from more complex climate models to aid in the prediction of real world climate systems.